Finite Group Databasebeta

← C2×D3×#1790 #72247694

Subgroups — C2×D3×#1790 #72247694

Order 1536.

40316 conjugacy classes of subgroups.

The subgroup lattice has 1534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×H(5,𝔽2)C211yesmaximal, characteristic
2C22×D3×#99C213yesmaximal, complemented
3C2×D3×#386C213yesmaximal, complemented
4C2×#72142C211yesmaximal, characteristic, complemented
5C2×#69598C213yesmaximal, complemented
6C2×#70033C213yesmaximal, complemented
7D3×#1790C2116yesmaximal, direct product factor
8C2×C3×#1790C211yesmaximal, characteristic, complemented
9C22×#1790—31nomaximal, Sylow
10C22×C3×H(5,𝔽2)C2211yescharacteristic
11C2×D3×H(5,𝔽2)—224no—
12C2×D3×H(5,𝔽2)—212no—
13C2×D3×H(5,𝔽2)C4116yescomplemented
14C2×D3×H(5,𝔽2)C2218yes—
15C22×#1009—23no—
16C22×D3×#41—23no—
17C22×#1004—23no—
18C22×#1004C2213yes—
19C23×D3×D4—23no—
20C23×D3×D4C2213yes—
21C24×C4×D3C2211yescharacteristic, complemented
22C22×D3×C22⋊C4—23no—
23C22×D3×C22⋊C4C2213yescomplemented
24C22×C3×#99C2213yescomplemented
25C2×C3×#386C2213yescomplemented
26C2×#5220C2213yescomplemented
27C22×#834C2213yescomplemented
28C2×#5213C2213yescomplemented
29C2×#4956—23no—
30C22×#806C2216yescomplemented
31C2×#4958C2213yescomplemented
32C2×D3×#99—224no—
33C2×D3×#99C22124yescomplemented
34D3×#386—212no—
35D3×#386C22124yescomplemented
36C2×#4665—23no—
37C2×D3×#95—23no—
38C3×#1790C2218yescomplemented
39#72142C2218yescomplemented
40#70033C22124yescomplemented
41#69598C22124yescomplemented
42C23×H(5,𝔽2)—31no—
43C23×#99—33no—
44C22×#386—33no—
45C2×#1790—316no—
46C2×#1790—33no—
47C2×#1790—33no—
48C2×#1790—31no—
49C2×#1790D311yescharacteristic, direct product factor
50C25×D3—21no—
51C25×D3D413yes—
52C25×D3C2311yescharacteristic
53C2×C3×H(5,𝔽2)—212no—
54C2×C3×H(5,𝔽2)—26no—
55C2×C3×H(5,𝔽2)C2×C418yescomplemented
56C2×C3×H(5,𝔽2)C2314yes—
57C22×C3×#41—23no—
58C23×C3×D4—23no—
59C23×C3×D4C2313yes—
60C24×C3×C4C2311yescharacteristic, complemented
61C23×#67—23no—
62C23×#67—23no—
63C23×#67D413yes—
64C23×#67C2313yes—
65C24×Dic3C2311yescharacteristic, complemented
66D3×H(5,𝔽2)—2192no—
67D3×H(5,𝔽2)—2192no—
68D3×H(5,𝔽2)—296no—
69D3×H(5,𝔽2)C2×C4164yescomplemented
70C2×#1009—224no—
71C2×#1009—248no—
72C2×#1009—248no—
73C2×#1009—224no—
74C2×D3×#41—224no—
75C2×D3×#41—248no—
76C2×D3×#41—248no—
77C2×D3×#41—224no—
78C22×#239—23no—
79C22×D3×Q8—21no—
80C2×#1004—224no—
81C2×#1004—248no—
82C2×#1004—212no—
83C2×#1004—26no—
84C2×#1004—248no—
85C2×#1004—224no—
86C2×#1004—224no—
87C2×#1004—212no—
88C2×#1004C2×C4124yescomplemented
89C2×#1004C23112yes—
90C22×#237—23no—
91C22×#237—26no—
92C22×D3×D4—23no—
93C22×D3×D4—26no—
94C22×D3×D4—224no—
95C22×D3×D4—248no—
96C22×D3×D4—248no—
97C22×D3×D4—26no—
98C22×D3×D4—26no—
99C22×D3×D4—224no—
100C22×D3×D4—26no—
101C22×D3×D4—224no—
102C22×D3×D4—212no—
103C22×D3×D4C2×C4124yes—
104C22×D3×D4D4124yes—
105C22×D3×D4D4112yes—
106C22×D3×D4C23112yes—
107C22×#235—26no—
108C22×#235—23no—
109C23×D12—23no—
110C23×D12D413yes—
111C23×C4×D3—23no—
112C23×C4×D3—23no—
113C23×C4×D3—26no—
114C23×C4×D3—23no—
115C23×C4×D3—23no—
116C23×C4×D3—48no—
117C23×C4×D3D413yes—
118C23×C4×D3C2314yescomplemented
119C22×C3×C22⋊C4—23no—
120C22×C3×C22⋊C4C2313yescomplemented
121C22×#217—23no—
122C22×#217C2313yescomplemented
123C22×(C2×D3)⋊C4—23no—
124C22×(C2×D3)⋊C4—23no—
125C22×(C2×D3)⋊C4—23no—
126C2×D3×C22⋊C4—224no—
127C2×D3×C22⋊C4—26no—
128C2×D3×C22⋊C4—224no—
129C2×D3×C22⋊C4—424no—
130C2×D3×C22⋊C4C23112yescomplemented
131C2×C3×#99—212no—
132C2×C3×#99C23112yescomplemented
133C3×#386—26no—
134C3×#386C23112yescomplemented
135C2×C3×#95—23no—
136#5220—26no—
137#5220C23112yescomplemented
138C2×#834—212no—
139C2×#834C23112yescomplemented
140#5213—26no—
141#5213C23112yescomplemented
142C2×C3⋊#95—23no—
143C2×C3⋊#95—23no—
144C2×C3⋊#95—23no—
145#4958—26no—
146#4958C23112yescomplemented
147#4956—224no—
148C2×#806—224no—
149C2×#806C23124yescomplemented
150D3×#99—296no—
151#4665—224no—
152D3×#95—224no—
153C22×H(5,𝔽2)—316no—
154C22×H(5,𝔽2)—38no—
155C22×H(5,𝔽2)—33no—
156C22×H(5,𝔽2)—63no—
157C22×H(5,𝔽2)—63no—
158C22×H(5,𝔽2)—624no—
159C22×H(5,𝔽2)—612no—
160C22×H(5,𝔽2)C2×D311yescharacteristic
161C23×#41—63no—
162C24×D4—33no—
163C24×D4—63no—
164C25×C4—31no—
165C23×C22⋊C4—33no—
166C23×C22⋊C4—63no—
167C22×#99—324no—
168C22×#99—33no—
169C22×#99—36no—
170C22×#99—624no—
171C22×#99C2×D313yescomplemented
172C2×#386—324no—
173C2×#386—33no—
174C2×#386—33no—
175C2×#386—33no—
176C2×#386—63no—
177C2×#386—63no—
178C2×#386—612no—
179C2×#386C2×D313yescomplemented
180C22×#95—63no—
181#1790—324no—
182#1790—324no—
183#1790—38no—
184#1790C2×D318yesdirect product factor
185C25×C3—21no—
186C25×C3C2×D413yes—
187C25×C3C2411yescharacteristic
188C24×D3—23no—
189C24×D3—28no—
190C24×D3—216no—
191C24×D3—23no—
192C24×D3—23no—
193C24×D3—26no—
194C24×D3—212no—
195C24×D3—44no—
196C24×D3—44no—
197C24×D3—412no—
198C24×D3—412no—
199C24×D3—84no—
200C24×D3—84no—
201C24×D3C22⋊C4124yescomplemented
202C24×D3C22×C414yes—
203C24×D3C2×D413yes—
204C24×D3C2×D413yes—
205C24×D3C2×D4112yes—
206C24×D3C2×D413yes—
207C24×D3C2×D416yes—
208C24×D3C2×D4112yes—
209C24×D3C2412yes—
210C3×H(5,𝔽2)—248no—
211C3×H(5,𝔽2)—248no—
212C3×H(5,𝔽2)—224no—
213C3×H(5,𝔽2)C22×C4116yescomplemented
214C2×C3×#41—212no—
215C2×C3×#41—224no—
216C2×C3×#41—224no—
217C2×C3×#41—212no—
218C22×C3×Q8—21no—
219C22×C3×D4—23no—
220C22×C3×D4—212no—
221C22×C3×D4—224no—
222C22×C3×D4—224no—
223C22×C3×D4—26no—
224C22×C3×D4—212no—
225C22×C3×D4—212no—
226C22×C3×D4—26no—
227C22×C3×D4C22×C4112yes—
228C22×C3×D4C2×D4112yes—
229C22×C3×D4C2×D416yes—
230C22×C3×D4C2416yes—
231C23×C3×C4—23no—
232C23×C3×C4—23no—
233C23×C3×C4—23no—
234C23×C3×C4—23no—
235C23×C3×C4—44no—
236C23×C3×C4C2×D413yes—
237C23×C3×C4C2412yescomplemented
238C22×#67—26no—
239C22×#67—212no—
240C22×#67—224no—
241C22×#67—224no—
242C22×#67—248no—
243C22×#67—224no—
244C22×#67—26no—
245C22×#67—212no—
246C22×#67—26no—
247C22×#67—212no—
248C22×#67—26no—
249C22×#67—26no—
250C22×#67—212no—
251C22×#67C22⋊C4124yescomplemented
252C22×#67C22×C4112yes—
253C22×#67C2×D4112yes—
254C22×#67C2×D416yes—
255C22×#67C2×D4112yes—
256C22×#67C2416yes—
257C23×Dic3—23no—
258C23×Dic3—23no—
259C23×Dic3—23no—
260C23×Dic3—23no—
261C23×Dic3—44no—
262C23×Dic3C2×D413yes—
263C23×Dic3C2412yescomplemented
264#1009—2192no—
265#1009—2384no—
266#1009—2192no—
267D3×#41—2192no—
268D3×#41—2384no—
269D3×#41—2192no—
270C2×#239—224no—
271C2×#239—248no—
272C2×D3×Q8—28no—
273C2×D3×Q8—216no—
274#1004—248no—
275#1004—296no—
276#1004—2192no—
277#1004—2384no—
278#1004—248no—
279#1004—224no—
280#1004—2192no—
281#1004—296no—
282#1004—248no—
283#1004C22×C4148yescomplemented
284C2×#237—224no—
285C2×#237—248no—
286C2×#237—224no—
287C2×#237—248no—
288C2×#237—248no—
289C2×#237—224no—
290C2×D3×D4—224no—
291C2×D3×D4—248no—
292C2×D3×D4—224no—
293C2×D3×D4—248no—
294C2×D3×D4—248no—
295C2×D3×D4—296no—
296C2×D3×D4—2192no—
297C2×D3×D4—2384no—
298C2×D3×D4—248no—
299C2×D3×D4—248no—
300C2×D3×D4—296no—
301C2×D3×D4—248no—
302C2×D3×D4—2192no—
303C2×D3×D4—224no—
304C2×D3×D4—248no—
305C2×D3×D4—224no—
306C2×D3×D4—248no—
307C2×D3×D4—248no—
308C2×D3×D4—296no—
309C2×D3×D4—224no—
310C2×D3×D4—224no—
311C2×D3×D4—224no—
312C2×D3×D4—248no—
313C2×D3×D4C22⋊C4196yescomplemented
314C2×D3×D4C22×C4148yes—
315C2×D3×D4C2×D4148yes—
316C2×#235—212no—
317C2×#235—224no—
318C2×#235—248no—
319C2×#235—296no—
320C2×#235—224no—
321C2×#235—212no—
322C22×D12—23no—
323C22×D12—224no—
324C22×D12—248no—
325C22×D12—26no—
326C22×D12—26no—
327C22×D12—212no—
328C22×D12C22⋊C4124yescomplemented
329C22×D12C2×D4112yes—
330C22×C4×D3—26no—
331C22×C4×D3—224no—
332C22×C4×D3—248no—
333C22×C4×D3—23no—
334C22×C4×D3—23no—
335C22×C4×D3—26no—
336C22×C4×D3—212no—
337C22×C4×D3—224no—
338C22×C4×D3—212no—
339C22×C4×D3—212no—
340C22×C4×D3—212no—
341C22×C4×D3—416no—
342C22×C4×D3—448no—
343C22×C4×D3—412no—
344C22×C4×D3—412no—
345C22×C4×D3—412no—
346C22×C4×D3—43no—
347C22×C4×D3—46no—
348C22×C4×D3—46no—
349C22×C4×D3—41no—
350C22×C4×D3—412no—
351C22×C4×D3—412no—
352C22×C4×D3—412no—
353C22×C4×D3C22⋊C4124yescomplemented
354C22×C4×D3C2×D4112yes—
355C22×Dic6—23no—
356C2×C3×C22⋊C4—212no—
357C2×C3×C22⋊C4—212no—
358C2×C3×C22⋊C4—23no—
359C2×C3×C22⋊C4—412no—
360C2×C3×C22⋊C4C2416yescomplemented
361C2×#217—212no—
362C2×#217—212no—
363C2×#217—23no—
364C2×#217—412no—
365C2×#217C2416yescomplemented
366C2×(C2×D3)⋊C4—212no—
367C2×(C2×D3)⋊C4—212no—
368C2×(C2×D3)⋊C4—212no—
369C2×(C2×D3)⋊C4—412no—
370C2×(C2×D3)⋊C4—412no—
371C2×(C2×D3)⋊C4—412no—
372D3×C22⋊C4—248no—
373D3×C22⋊C4—496no—
374D3×C22⋊C4—424no—
375C3×#99—224no—
376C3×#95—212no—
377#834—224no—
378C3⋊#95—212no—
379C3⋊#95—212no—
380C3⋊#95—212no—
381#806—248no—
382C26—31no—
383C26—33no—
384C26—61no—
385C2×H(5,𝔽2)—212no—
386C2×H(5,𝔽2)—26no—
387C2×H(5,𝔽2)—364no—
388C2×H(5,𝔽2)—324no—
389C2×H(5,𝔽2)—312no—
390C2×H(5,𝔽2)—648no—
391C2×H(5,𝔽2)—624no—
392C2×H(5,𝔽2)—612no—
393C2×H(5,𝔽2)—624no—
394C2×H(5,𝔽2)—648no—
395C2×H(5,𝔽2)—624no—
396C2×H(5,𝔽2)—648no—
397C2×H(5,𝔽2)—624no—
398C2×H(5,𝔽2)—6192no—
399C2×H(5,𝔽2)—696no—
400C2×H(5,𝔽2)—648no—
401C2×H(5,𝔽2)—624no—
402C2×H(5,𝔽2)—6192no—
403C2×H(5,𝔽2)—612no—
404C2×H(5,𝔽2)—66no—
405C2×H(5,𝔽2)C4×D318yescomplemented
406C2×H(5,𝔽2)C22×D314yes—
407C22×#41—23no—
408C22×#41—66no—
409C22×#41—66no—
410C22×#41—648no—
411C22×#41—624no—
412C22×#41—63no—
413C22×#41—63no—
414C22×#41—648no—
415C22×#41—624no—
416C22×#41—63no—
417C23×Q8—61no—
418C23×D4—23no—
419C23×D4—33no—
420C23×D4—33no—
421C23×D4—324no—
422C23×D4—324no—
423C23×D4—312no—
424C23×D4—312no—
425C23×D4—33no—
426C23×D4—63no—
427C23×D4—66no—
428C23×D4—66no—
429C23×D4—624no—
430C23×D4—612no—
431C23×D4—648no—
432C23×D4—66no—
433C23×D4—624no—
434C23×D4—63no—
435C23×D4—66no—
436C23×D4—648no—
437C23×D4—624no—
438C23×D4—63no—
439C23×D4—63no—
440C23×D4C22×D313yes—
441C24×C4—33no—
442C24×C4—31no—
443C24×C4—34no—
444C24×C4—63no—
445C24×C4—63no—
446C24×C4—63no—
447C24×C4—66no—
448C24×C4—63no—
449C24×C4—128no—
450C24×C4C22×D311yescharacteristic, complemented
451C22×C22⋊C4—23no—
452C22×C22⋊C4—33no—
453C22×C22⋊C4—312no—
454C22×C22⋊C4—624no—
455C22×C22⋊C4—66no—
456C22×C22⋊C4—624no—
457C22×C22⋊C4—63no—
458C22×C22⋊C4—63no—
459C22×C22⋊C4—63no—
460C22×C22⋊C4—63no—
461C22×C22⋊C4—1224no—
462C22×C22⋊C4C22×D313yescomplemented
463C2×#99—212no—
464C2×#99—312no—
465C2×#99—324no—
466C2×#99—696no—
467C2×#99—624no—
468C2×#99—612no—
469C2×#99C22×D3112yescomplemented
470#386—26no—
471#386—312no—
472#386—312no—
473#386—312no—
474#386—624no—
475#386—624no—
476#386—66no—
477#386—66no—
478#386—66no—
479#386C22×D3112yescomplemented
480C2×#95—23no—
481C2×#95—624no—
482C2×#95—63no—
483C2×#95—63no—
484C2×#95—63no—
485C24×C3—24no—
486C24×C3—28no—
487C24×C3—23no—
488C24×C3—23no—
489C24×C3—26no—
490C24×C3—42no—
491C24×C3—42no—
492C24×C3—46no—
493C24×C3—46no—
494C24×C3—82no—
495C24×C3—82no—
496C24×C3C2×C22⋊C4112yescomplemented
497C24×C3C23×C412yes—
498C24×C3C22×D413yes—
499C24×C3C22×D416yes—
500C24×C3C22×D416yes—
501C24×C3C22×D413yes—
502C24×C3C2511yescharacteristic
503C23×D3—212no—
504C23×D3—212no—
505C23×D3—23no—
506C23×D3—212no—
507C23×D3—224no—
508C23×D3—264no—
509C23×D3—23no—
510C23×D3—26no—
511C23×D3—212no—
512C23×D3—224no—
513C23×D3—212no—
514C23×D3—224no—
515C23×D3—224no—
516C23×D3—248no—
517C23×D3—412no—
518C23×D3—44no—
519C23×D3—416no—
520C23×D3—412no—
521C23×D3—448no—
522C23×D3—44no—
523C23×D3—46no—
524C23×D3—46no—
525C23×D3—424no—
526C23×D3—496no—
527C23×D3—424no—
528C23×D3—412no—
529C23×D3—412no—
530C23×D3—46no—
531C23×D3—46no—
532C23×D3—812no—
533C23×D3—812no—
534C23×D3—848no—
535C23×D3—86no—
536C23×D3—86no—
537C23×D3—816no—
538C23×D3—816no—
539C23×D3—864no—
540C23×D3—86no—
541C23×D3—86no—
542C23×D3C2×C22⋊C4112yes—
543C23×D3C2×C22⋊C4112yes—
544C23×D3C2×C22⋊C4124yes—
545C23×D3C2×C22⋊C4148yescomplemented
546C23×D3C2×C22⋊C4112yescomplemented
547C23×D3#12013yes—
548C23×D3#12016yes—
549C23×D3#120112yes—
550C23×D3#120124yes—
551C23×D3#120112yes—
552C23×D3#12016yes—
553C23×D3#12011yescharacteristic
554C23×D3C23×C414yes—
555C23×D3C22×D416yes—
556C23×D3C22×D416yes—
557C23×D3C22×D4112yes—
558C23×D3C22×D416yes—
559C3×#41—248no—
560C3×#41—296no—
561C3×#41—248no—
562C2×C3×Q8—24no—
563C2×C3×Q8—28no—
564C2×C3×D4—212no—
565C2×C3×D4—224no—
566C2×C3×D4—248no—
567C2×C3×D4—296no—
568C2×C3×D4—224no—
569C2×C3×D4—224no—
570C2×C3×D4—248no—
571C2×C3×D4—212no—
572C2×C3×D4—224no—
573C2×C3×D4—212no—
574C2×C3×D4—224no—
575C2×C3×D4—212no—
576C2×C3×D4—212no—
577C2×C3×D4C2×C22⋊C4124yescomplemented
578C2×C3×D4C23×C4112yes—
579C2×C3×D4C22×D4112yes—
580C22×C3×C4—212no—
581C22×C3×C4—224no—
582C22×C3×C4—23no—
583C22×C3×C4—23no—
584C22×C3×C4—26no—
585C22×C3×C4—212no—
586C22×C3×C4—26no—
587C22×C3×C4—26no—
588C22×C3×C4—44no—
589C22×C3×C4—412no—
590C22×C3×C4—46no—
591C22×C3×C4—43no—
592C22×C3×C4—41no—
593C22×C3×C4—46no—
594C22×C3×C4—46no—
595C22×C3×C4—46no—
596C22×C3×C4C2×C22⋊C4112yescomplemented
597C22×C3×C4C22×D416yes—
598C2×#67—224no—
599C2×#67—248no—
600C2×#67—248no—
601C2×#67—296no—
602C2×#67—2192no—
603C2×#67—224no—
604C2×#67—224no—
605C2×#67—248no—
606C2×#67—212no—
607C2×#67—224no—
608C2×#67—212no—
609C2×#67—224no—
610C2×#67—212no—
611C2×#67—212no—
612C2×#67—224no—
613C2×#67—224no—
614C2×#67—248no—
615C2×#67—248no—
616C2×#67C2×C22⋊C4148yescomplemented
617C2×#67C2×C22⋊C4124yescomplemented
618C2×#67C23×C4112yes—
619C2×#67C22×D4112yes—
620C22×Dic3—212no—
621C22×Dic3—224no—
622C22×Dic3—23no—
623C22×Dic3—23no—
624C22×Dic3—26no—
625C22×Dic3—212no—
626C22×Dic3—26no—
627C22×Dic3—26no—
628C22×Dic3—44no—
629C22×Dic3—412no—
630C22×Dic3—46no—
631C22×Dic3—43no—
632C22×Dic3—41no—
633C22×Dic3—46no—
634C22×Dic3—46no—
635C22×Dic3—46no—
636C22×Dic3C2×C22⋊C4112yescomplemented
637C22×Dic3C22×D416yes—
638#239—2192no—
639D3×Q8—264no—
640#237—296no—
641#237—2192no—
642#237—2192no—
643#237—296no—
644D3×D4—2192no—
645D3×D4—296no—
646D3×D4—2192no—
647D3×D4—2384no—
648D3×D4—296no—
649D3×D4—296no—
650D3×D4—296no—
651D3×D4—296no—
652D3×D4—296no—
653D3×D4—2192no—
654D3×D4—2192no—
655#235—248no—
656#235—296no—
657#235—2384no—
658#235—248no—
659C2×D12—212no—
660C2×D12—224no—
661C2×D12—2192no—
662C2×D12—224no—
663C2×D12—224no—
664C2×D12—248no—
665C2×D12—248no—
666C2×D12C2×C22⋊C4148yescomplemented
667C2×C4×D3—224no—
668C2×C4×D3—248no—
669C2×C4×D3—2192no—
670C2×C4×D3—212no—
671C2×C4×D3—212no—
672C2×C4×D3—224no—
673C2×C4×D3—224no—
674C2×C4×D3—224no—
675C2×C4×D3—248no—
676C2×C4×D3—248no—
677C2×C4×D3—424no—
678C2×C4×D3—424no—
679C2×C4×D3—424no—
680C2×C4×D3—424no—
681C2×C4×D3—448no—
682C2×C4×D3—448no—
683C2×C4×D3—412no—
684C2×C4×D3—44no—
685C2×C4×D3—48no—
686C2×C4×D3—424no—
687C2×C4×D3—424no—
688C2×C4×D3—424no—
689C2×C4×D3—848no—
690C2×C4×D3C2×C22⋊C4148yescomplemented
691C2×Dic6—212no—
692C2×Dic6—224no—
693C3×C22⋊C4—212no—
694C3×C22⋊C4—424no—
695C3×C22⋊C4—46no—
696#217—212no—
697#217—424no—
698#217—46no—
699(C2×D3)⋊C4—424no—
700(C2×D3)⋊C4—424no—
701(C2×D3)⋊C4—424no—
702C25—21no—
703C25—33no—
704C25—34no—
705C25—312no—
706C25—36no—
707C25—33no—
708C25—32no—
709C25—324no—
710C25—312no—
711C25—33no—
712C25—63no—
713C25—63no—
714C25—612no—
715C25—66no—
716C25—616no—
717C25—68no—
718C25—63no—
719C25—124no—
720C25—124no—
721C25—1212no—
722C25—1212no—
723C25—244no—
724C25—244no—
725C25D3×D413yes—
726C25C23×D311yescharacteristic
727H(5,𝔽2)—248no—
728H(5,𝔽2)—248no—
729H(5,𝔽2)—224no—
730H(5,𝔽2)—348no—
731H(5,𝔽2)—648no—
732H(5,𝔽2)—696no—
733H(5,𝔽2)—6192no—
734H(5,𝔽2)—6384no—
735H(5,𝔽2)—6192no—
736H(5,𝔽2)—696no—
737H(5,𝔽2)—648no—
738H(5,𝔽2)—6192no—
739H(5,𝔽2)—6384no—
740H(5,𝔽2)—6192no—
741H(5,𝔽2)—648no—
742H(5,𝔽2)—624no—
743H(5,𝔽2)C2×C4×D3116yescomplemented
744C2×#41—224no—
745C2×#41—212no—
746C2×#41—224no—
747C2×#41—212no—
748C2×#41—696no—
749C2×#41—648no—
750C2×#41—624no—
751C2×#41—612no—
752C2×#41—624no—
753C2×#41—648no—
754C2×#41—6192no—
755C2×#41—648no—
756C2×#41—624no—
757C2×#41—648no—
758C2×#41—624no—
759C2×#41—648no—
760C2×#41—624no—
761C2×#41—6384no—
762C2×#41—6192no—
763C2×#41—624no—
764C2×#41—612no—
765C22×Q8—21no—
766C22×Q8—63no—
767C22×Q8—616no—
768C22×Q8—68no—
769C22×D4—23no—
770C22×D4—224no—
771C22×D4—212no—
772C22×D4—224no—
773C22×D4—26no—
774C22×D4—212no—
775C22×D4—26no—
776C22×D4—212no—
777C22×D4—324no—
778C22×D4—312no—
779C22×D4—36no—
780C22×D4—312no—
781C22×D4—312no—
782C22×D4—36no—
783C22×D4—396no—
784C22×D4—348no—
785C22×D4—348no—
786C22×D4—324no—
787C22×D4—312no—
788C22×D4—66no—
789C22×D4—612no—
790C22×D4—66no—
791C22×D4—63no—
792C22×D4—648no—
793C22×D4—624no—
794C22×D4—624no—
795C22×D4—648no—
796C22×D4—648no—
797C22×D4—624no—
798C22×D4—624no—
799C22×D4—648no—
800C22×D4—648no—
801C22×D4—696no—
802C22×D4—648no—
803C22×D4—624no—
804C22×D4—696no—
805C22×D4—648no—
806C22×D4—624no—
807C22×D4—648no—
808C22×D4—6192no—
809C22×D4—648no—
810C22×D4—624no—
811C22×D4—696no—
812C22×D4—648no—
813C22×D4—6384no—
814C22×D4—6192no—
815C22×D4—648no—
816C22×D4—624no—
817C22×D4—66no—
818C22×D4—612no—
819C22×D4—66no—
820C22×D4—66no—
821C22×D4—648no—
822C22×D4—624no—
823C22×D4—624no—
824C22×D4—612no—
825C22×D4—624no—
826C22×D4—66no—
827C22×D4—66no—
828C22×D4—612no—
829C22×D4—612no—
830C22×D4C2×C4×D3112yes—
831C22×D4D3×D4112yes—
832C22×D4D3×D416yes—
833C22×D4C23×D316yes—
834C23×C4—23no—
835C23×C4—23no—
836C23×C4—23no—
837C23×C4—23no—
838C23×C4—33no—
839C23×C4—324no—
840C23×C4—312no—
841C23×C4—32no—
842C23×C4—44no—
843C23×C4—63no—
844C23×C4—612no—
845C23×C4—66no—
846C23×C4—63no—
847C23×C4—648no—
848C23×C4—624no—
849C23×C4—66no—
850C23×C4—612no—
851C23×C4—624no—
852C23×C4—612no—
853C23×C4—612no—
854C23×C4—63no—
855C23×C4—63no—
856C23×C4—63no—
857C23×C4—63no—
858C23×C4—1212no—
859C23×C4—1216no—
860C23×C4—1248no—
861C23×C4—1212no—
862C23×C4—126no—
863C23×C4—126no—
864C23×C4—121no—
865C23×C4—123no—
866C23×C4—1212no—
867C23×C4—1212no—
868C23×C4—1212no—
869C23×C4—1212no—
870C23×C4—124no—
871C23×C4D3×D413yes—
872C23×C4C23×D312yescomplemented
873C2×C22⋊C4—212no—
874C2×C22⋊C4—212no—
875C2×C22⋊C4—23no—
876C2×C22⋊C4—36no—
877C2×C22⋊C4—412no—
878C2×C22⋊C4—648no—
879C2×C22⋊C4—612no—
880C2×C22⋊C4—612no—
881C2×C22⋊C4—612no—
882C2×C22⋊C4—612no—
883C2×C22⋊C4—63no—
884C2×C22⋊C4—612no—
885C2×C22⋊C4—1296no—
886C2×C22⋊C4—1224no—
887C2×C22⋊C4—1212no—
888C2×C22⋊C4—1212no—
889C2×C22⋊C4—1212no—
890C2×C22⋊C4—1212no—
891C2×C22⋊C4C23×D316yescomplemented
892#99—224no—
893#99—648no—
894#99—624no—
895#95—212no—
896#95—612no—
897#95—612no—
898#95—612no—
899C23×C3—26no—
900C23×C3—26no—
901C23×C3—216no—
902C23×C3—26no—
903C23×C3—212no—
904C23×C3—26no—
905C23×C3—212no—
906C23×C3—43no—
907C23×C3—41no—
908C23×C3—44no—
909C23×C3—412no—
910C23×C3—43no—
911C23×C3—41no—
912C23×C3—46no—
913C23×C3—424no—
914C23×C3—46no—
915C23×C3—46no—
916C23×C3—46no—
917C23×C3—812no—
918C23×C3—83no—
919C23×C3—83no—
920C23×C3—816no—
921C23×C3—84no—
922C23×C3—84no—
923C23×C3C22×C22⋊C416yes—
924C23×C3C22×C22⋊C416yes—
925C23×C3C22×C22⋊C4112yescomplemented
926C23×C3C2×#12016yes—
927C23×C3C2×#12013yes—
928C23×C3C2×#12016yes—
929C23×C3C2×#12011yescharacteristic
930C23×C3C24×C411yescharacteristic
931C23×C3C23×D413yes—
932C23×C3C23×D413yes—
933C22×D3—26no—
934C22×D3—26no—
935C22×D3—212no—
936C22×D3—212no—
937C22×D3—212no—
938C22×D3—212no—
939C22×D3—248no—
940C22×D3—248no—
941C22×D3—26no—
942C22×D3—212no—
943C22×D3—248no—
944C22×D3—26no—
945C22×D3—212no—
946C22×D3—248no—
947C22×D3—248no—
948C22×D3—448no—
949C22×D3—448no—
950C22×D3—48no—
951C22×D3—424no—
952C22×D3—46no—
953C22×D3—46no—
954C22×D3—424no—
955C22×D3—424no—
956C22×D3—46no—
957C22×D3—46no—
958C22×D3—496no—
959C22×D3—46no—
960C22×D3—46no—
961C22×D3—424no—
962C22×D3—424no—
963C22×D3—496no—
964C22×D3—46no—
965C22×D3—424no—
966C22×D3—46no—
967C22×D3—848no—
968C22×D3—896no—
969C22×D3—848no—
970C22×D3—812no—
971C22×D3—812no—
972C22×D3—8128no—
973C22×D3—812no—
974C22×D3—83no—
975C22×D3—83no—
976C22×D3—848no—
977C22×D3—812no—
978C22×D3—812no—
979C22×D3#379112yes—
980C22×D3#379124yes—
981C22×D3#379124yes—
982C22×D3#37914yes—
983C22×D3B(4,𝔽2)14yes—
984C22×D3#45814yes—
985C22×D3C22×C22⋊C4112yes—
986C22×D3C22×C22⋊C4112yes—
987C22×D3C22×C22⋊C4112yescomplemented
988C22×D3C2×#12016yes—
989C22×D3C2×#120112yes—
990C22×D3C2×#120112yes—
991C22×D3C2×#12012yes—
992C3×Q8—216no—
993C3×D4—248no—
994C3×D4—224no—
995C3×D4—224no—
996C3×D4—248no—
997C2×C3×C4—248no—
998C2×C3×C4—26no—
999C2×C3×C4—26no—
1000C2×C3×C4—212no—
1001C2×C3×C4—212no—
1002C2×C3×C4—212no—
1003C2×C3×C4—46no—
1004C2×C3×C4—412no—
1005C2×C3×C4—42no—
1006C2×C3×C4—44no—
1007C2×C3×C4—46no—
1008C2×C3×C4—46no—
1009C2×C3×C4—46no—
1010C2×C3×C4—812no—
1011C2×C3×C4C22×C22⋊C4112yescomplemented
1012#67—296no—
1013#67—224no—
1014#67—224no—
1015#67—248no—
1016#67—296no—
1017C2×Dic3—248no—
1018C2×Dic3—26no—
1019C2×Dic3—26no—
1020C2×Dic3—212no—
1021C2×Dic3—212no—
1022C2×Dic3—212no—
1023C2×Dic3—46no—
1024C2×Dic3—412no—
1025C2×Dic3—42no—
1026C2×Dic3—44no—
1027C2×Dic3—46no—
1028C2×Dic3—46no—
1029C2×Dic3—46no—
1030C2×Dic3—812no—
1031C2×Dic3C22×C22⋊C4112yescomplemented
1032D12—248no—
1033D12—296no—
1034C4×D3—296no—
1035C4×D3—248no—
1036C4×D3—248no—
1037C4×D3—448no—
1038C4×D3—416no—
1039C4×D3—848no—
1040Dic6—248no—
1041C24—28no—
1042C24—24no—
1043C24—23no—
1044C24—26no—
1045C24—23no—
1046C24—31no—
1047C24—36no—
1048C24—312no—
1049C24—312no—
1050C24—36no—
1051C24—33no—
1052C24—34no—
1053C24—312no—
1054C24—36no—
1055C24—324no—
1056C24—312no—
1057C24—324no—
1058C24—312no—
1059C24—36no—
1060C24—36no—
1061C24—312no—
1062C24—348no—
1063C24—42no—
1064C24—42no—
1065C24—46no—
1066C24—46no—
1067C24—612no—
1068C24—612no—
1069C24—624no—
1070C24—612no—
1071C24—624no—
1072C24—612no—
1073C24—648no—
1074C24—624no—
1075C24—664no—
1076C24—624no—
1077C24—612no—
1078C24—63no—
1079C24—66no—
1080C24—63no—
1081C24—82no—
1082C24—82no—
1083C24—126no—
1084C24—126no—
1085C24—126no—
1086C24—126no—
1087C24—1212no—
1088C24—1212no—
1089C24—1212no—
1090C24—124no—
1091C24—1216no—
1092C24—1212no—
1093C24—1248no—
1094C24—124no—
1095C24—1224no—
1096C24—1296no—
1097C24—1224no—
1098C24—246no—
1099C24—246no—
1100C24—246no—
1101C24—246no—
1102C24—2412no—
1103C24—2448no—
1104C24—2412no—
1105C24—2416no—
1106C24—2416no—
1107C24—2464no—
1108C24D3×C22⋊C4112yescomplemented
1109C24C22×C4×D312yes—
1110C24C2×D3×D413yes—
1111C24C2×D3×D416yes—
1112C24C2×D3×D416yes—
1113C24C2×D3×D413yes—
1114C24C24×D311yescharacteristic
1115#41—296no—
1116#41—248no—
1117#41—248no—
1118#41—6384no—
1119#41—696no—
1120#41—648no—
1121#41—696no—
1122#41—6192no—
1123#41—6192no—
1124#41—696no—
1125#41—6192no—
1126#41—648no—
1127C2×Q8—28no—
1128C2×Q8—24no—
1129C2×Q8—624no—
1130C2×Q8—612no—
1131C2×Q8—664no—
1132C2×D4—224no—
1133C2×D4—212no—
1134C2×D4—296no—
1135C2×D4—248no—
1136C2×D4—212no—
1137C2×D4—212no—
1138C2×D4—224no—
1139C2×D4—224no—
1140C2×D4—248no—
1141C2×D4—224no—
1142C2×D4—212no—
1143C2×D4—224no—
1144C2×D4—212no—
1145C2×D4—312no—
1146C2×D4—312no—
1147C2×D4—324no—
1148C2×D4—348no—
1149C2×D4—348no—
1150C2×D4—648no—
1151C2×D4—624no—
1152C2×D4—648no—
1153C2×D4—624no—
1154C2×D4—624no—
1155C2×D4—612no—
1156C2×D4—6192no—
1157C2×D4—6192no—
1158C2×D4—696no—
1159C2×D4—696no—
1160C2×D4—6192no—
1161C2×D4—696no—
1162C2×D4—696no—
1163C2×D4—696no—
1164C2×D4—6192no—
1165C2×D4—6384no—
1166C2×D4—6192no—
1167C2×D4—696no—
1168C2×D4—648no—
1169C2×D4—624no—
1170C2×D4—648no—
1171C2×D4—624no—
1172C2×D4—648no—
1173C2×D4—624no—
1174C2×D4—6192no—
1175C2×D4—696no—
1176C2×D4—648no—
1177C2×D4—612no—
1178C2×D4—612no—
1179C2×D4—624no—
1180C2×D4—624no—
1181C2×D4—648no—
1182C2×D4—624no—
1183C2×D4—612no—
1184C2×D4—624no—
1185C2×D4—612no—
1186C2×D4D3×C22⋊C4124yescomplemented
1187C2×D4C22×C4×D3112yes—
1188C2×D4C2×D3×D4112yes—
1189C22×C4—224no—
1190C22×C4—212no—
1191C22×C4—26no—
1192C22×C4—23no—
1193C22×C4—23no—
1194C22×C4—212no—
1195C22×C4—26no—
1196C22×C4—26no—
1197C22×C4—36no—
1198C22×C4—312no—
1199C22×C4—348no—
1200C22×C4—44no—
1201C22×C4—412no—
1202C22×C4—46no—
1203C22×C4—43no—
1204C22×C4—41no—
1205C22×C4—46no—
1206C22×C4—46no—
1207C22×C4—46no—
1208C22×C4—624no—
1209C22×C4—612no—
1210C22×C4—624no—
1211C22×C4—648no—
1212C22×C4—612no—
1213C22×C4—624no—
1214C22×C4—6192no—
1215C22×C4—648no—
1216C22×C4—624no—
1217C22×C4—648no—
1218C22×C4—624no—
1219C22×C4—612no—
1220C22×C4—66no—
1221C22×C4—63no—
1222C22×C4—63no—
1223C22×C4—612no—
1224C22×C4—66no—
1225C22×C4—66no—
1226C22×C4—1224no—
1227C22×C4—1224no—
1228C22×C4—124no—
1229C22×C4—1212no—
1230C22×C4—128no—
1231C22×C4—1224no—
1232C22×C4—1248no—
1233C22×C4—1224no—
1234C22×C4—1248no—
1235C22×C4—1224no—
1236C22×C4—1224no—
1237C22×C4—1224no—
1238C22×C4—124no—
1239C22×C4—1212no—
1240C22×C4—126no—
1241C22×C4—123no—
1242C22×C4—121no—
1243C22×C4—126no—
1244C22×C4—126no—
1245C22×C4—126no—
1246C22×C4—2448no—
1247C22×C4D3×C22⋊C4112yescomplemented
1248C22×C4C2×D3×D416yes—
1249C22⋊C4—212no—
1250C22⋊C4—424no—
1251C22⋊C4—46no—
1252C22⋊C4—612no—
1253C22⋊C4—1224no—
1254C22⋊C4—1224no—
1255C22⋊C4—1224no—
1256C22⋊C4—1224no—
1257C22⋊C4—126no—
1258C22×C3—212no—
1259C22×C3—212no—
1260C22×C3—23no—
1261C22×C3—23no—
1262C22×C3—23no—
1263C22×C3—23no—
1264C22×C3—212no—
1265C22×C3—46no—
1266C22×C3—46no—
1267C22×C3—41no—
1268C22×C3—43no—
1269C22×C3—412no—
1270C22×C3—424no—
1271C22×C3—46no—
1272C22×C3—46no—
1273C22×C3—86no—
1274C22×C3—812no—
1275C22×C3—816no—
1276C22×C3C2×#37916yes—
1277C22×C3C2×#37912yes—
1278C22×C3C2×B(4,𝔽2)12yes—
1279C22×C3C2×#45812yes—
1280C22×C3C23×C22⋊C413yes—
1281C22×C3C22×#12013yes—
1282C22×C3C22×#12011yescharacteristic
1283C2×D3—224no—
1284C2×D3—26no—
1285C2×D3—26no—
1286C2×D3—224no—
1287C2×D3—224no—
1288C2×D3—248no—
1289C2×D3—212no—
1290C2×D3—412no—
1291C2×D3—412no—
1292C2×D3—424no—
1293C2×D3—424no—
1294C2×D3—46no—
1295C2×D3—46no—
1296C2×D3—496no—
1297C2×D3—412no—
1298C2×D3—848no—
1299C2×D3—86no—
1300C2×D3—812no—
1301C2×D3—848no—
1302C2×D3#1790116yesdirect product factor
1303C2×D3C2×#379112yes—
1304C2×D3C2×#37914yes—
1305C2×D3C2×B(4,𝔽2)14yes—
1306C2×D3C2×#45814yes—
1307C3×C4—212no—
1308C3×C4—44no—
1309C3×C4—86no—
1310Dic3—212no—
1311Dic3—44no—
1312Dic3—86no—
1313C23—26no—
1314C23—26no—
1315C23—216no—
1316C23—212no—
1317C23—26no—
1318C23—212no—
1319C23—26no—
1320C23—34no—
1321C23—32no—
1322C23—34no—
1323C23—34no—
1324C23—324no—
1325C23—312no—
1326C23—312no—
1327C23—36no—
1328C23—312no—
1329C23—324no—
1330C23—312no—
1331C23—312no—
1332C23—312no—
1333C23—43no—
1334C23—41no—
1335C23—44no—
1336C23—43no—
1337C23—412no—
1338C23—41no—
1339C23—46no—
1340C23—424no—
1341C23—46no—
1342C23—46no—
1343C23—46no—
1344C23—612no—
1345C23—612no—
1346C23—612no—
1347C23—648no—
1348C23—648no—
1349C23—612no—
1350C23—648no—
1351C23—648no—
1352C23—648no—
1353C23—66no—
1354C23—66no—
1355C23—612no—
1356C23—66no—
1357C23—612no—
1358C23—66no—
1359C23—83no—
1360C23—83no—
1361C23—812no—
1362C23—84no—
1363C23—84no—
1364C23—816no—
1365C23—126no—
1366C23—126no—
1367C23—126no—
1368C23—126no—
1369C23—1224no—
1370C23—1224no—
1371C23—126no—
1372C23—126no—
1373C23—1224no—
1374C23—1224no—
1375C23—1224no—
1376C23—1296no—
1377C23—128no—
1378C23—1224no—
1379C23—1248no—
1380C23—1248no—
1381C23—1296no—
1382C23—126no—
1383C23—126no—
1384C23—243no—
1385C23—243no—
1386C23—2412no—
1387C23—2412no—
1388C23—2412no—
1389C23—2448no—
1390C23—2412no—
1391C23—2412no—
1392C23—2448no—
1393C23—2448no—
1394C23—2496no—
1395C23—24128no—
1396C23C2×D3×C22⋊C416yes—
1397C23C2×D3×C22⋊C416yes—
1398C23C2×D3×C22⋊C4112yescomplemented
1399C23D3×#12013yes—
1400C23D3×#12016yes—
1401C23D3×#12016yes—
1402C23D3×#12011yescharacteristic
1403C23C23×C4×D311yescharacteristic
1404C23C22×D3×D413yes—
1405C23C22×D3×D413yes—
1406Q8—216no—
1407Q8—648no—
1408D4—248no—
1409D4—248no—
1410D4—224no—
1411D4—224no—
1412D4—696no—
1413D4—648no—
1414D4—696no—
1415D4—696no—
1416D4—648no—
1417D4—624no—
1418D4—624no—
1419C2×C4—248no—
1420C2×C4—212no—
1421C2×C4—212no—
1422C2×C4—26no—
1423C2×C4—26no—
1424C2×C4—212no—
1425C2×C4—312no—
1426C2×C4—46no—
1427C2×C4—412no—
1428C2×C4—42no—
1429C2×C4—44no—
1430C2×C4—46no—
1431C2×C4—46no—
1432C2×C4—46no—
1433C2×C4—648no—
1434C2×C4—648no—
1435C2×C4—696no—
1436C2×C4—648no—
1437C2×C4—612no—
1438C2×C4—612no—
1439C2×C4—66no—
1440C2×C4—66no—
1441C2×C4—612no—
1442C2×C4—812no—
1443C2×C4—1216no—
1444C2×C4—1248no—
1445C2×C4—126no—
1446C2×C4—1212no—
1447C2×C4—122no—
1448C2×C4—124no—
1449C2×C4—126no—
1450C2×C4—126no—
1451C2×C4—126no—
1452C2×C4—2448no—
1453C2×C4—2412no—
1454C2×C4C2×D3×C22⋊C4112yescomplemented
1455C2×C3—23no—
1456C2×C3—23no—
1457C2×C3—26no—
1458C2×C3—412no—
1459C2×C3C2×#179014yescomplemented
1460C2×C3C22×#37911yescharacteristic
1461C2×C3C22×B(4,𝔽2)11yescharacteristic
1462C2×C3C22×#45811yescharacteristic
1463D3—212no—
1464D3—412no—
1465D3C2×#179018yesdirect product factor
1466C22—23no—
1467C22—23no—
1468C22—23no—
1469C22—23no—
1470C22—212no—
1471C22—212no—
1472C22—212no—
1473C22—34no—
1474C22—34no—
1475C22—316no—
1476C22—34no—
1477C22—312no—
1478C22—41no—
1479C22—43no—
1480C22—46no—
1481C22—46no—
1482C22—412no—
1483C22—46no—
1484C22—46no—
1485C22—424no—
1486C22—624no—
1487C22—624no—
1488C22—648no—
1489C22—66no—
1490C22—66no—
1491C22—624no—
1492C22—612no—
1493C22—86no—
1494C22—812no—
1495C22—816no—
1496C22—1212no—
1497C22—1212no—
1498C22—1224no—
1499C22—1212no—
1500C22—1296no—
1501C22—126no—
1502C22—126no—
1503C22—1224no—
1504C22—246no—
1505C22—2412no—
1506C22—2448no—
1507C22—2448no—
1508C22D3×#37916yes—
1509C22D3×#37912yes—
1510C22D3×B(4,𝔽2)12yes—
1511C22D3×#45812yes—
1512C22C22×D3×C22⋊C413yes—
1513C22C2×D3×#12013yes—
1514C22C2×D3×#12011yescharacteristic
1515C4—212no—
1516C4—44no—
1517C4—612no—
1518C4—86no—
1519C4—124no—
1520C4—246no—
1521C3C22×#179011yescharacteristic, complemented, Sylow
1522C2—23no—
1523C2—23no—
1524C2—26no—
1525C2—38no—
1526C2—412no—
1527C2—612no—
1528C2—1212no—
1529C2D3×#179014yesdirect product factor
1530C2C2×D3×#37911yescharacteristic
1531C2C2×D3×B(4,𝔽2)11yescharacteristic
1532C2C2×D3×#45811yescharacteristic
subgroupG/H
centerC23D3×#120
commutatorC23×C3C24×C4
FrattiniC24C24×D3
FittingC2×C3×#1790C2
socleC23×C3C2×#120
prime radicalC22×D3×H(5,𝔽2)C2
cosocleC24×C3C25
hypercenterC2×#1790D3
hypocenterC3C22×#1790
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C25 ◁ C2×#1790

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×D3×#99C2semidirect
3. C2×D3×#386C2semidirect
4. C2×#72142C2semidirect
5. C2×#69598C2semidirect
6. C2×#70033C2semidirect
7. D3×#1790C2direct (N × H)
8. C2×C3×#1790C2semidirect
13. C2×D3×H(5,𝔽2)C4semidirect
21. C24×C4×D3C22semidirect
23. C22×D3×C22⋊C4C22semidirect
24. C22×C3×#99C22semidirect
25. C2×C3×#386C22semidirect
26. C2×#5220C22semidirect
27. C22×#834C22semidirect
28. C2×#5213C22semidirect
30. C22×#806C22semidirect
31. C2×#4958C22semidirect
33. C2×D3×#99C22semidirect
35. D3×#386C22semidirect
38. C3×#1790C22semidirect
39. #72142C22semidirect
40. #70033C22semidirect
41. #69598C22semidirect
49. C2×#1790D3direct (N × H)
55. C2×C3×H(5,𝔽2)C2×C4semidirect
60. C24×C3×C4C23semidirect
65. C24×Dic3C23semidirect
69. D3×H(5,𝔽2)C2×C4semidirect
88. C2×#1004C2×C4semidirect
118. C23×C4×D3C23semidirect
120. C22×C3×C22⋊C4C23semidirect
122. C22×#217C23semidirect
130. C2×D3×C22⋊C4C23semidirect
132. C2×C3×#99C23semidirect
134. C3×#386C23semidirect
137. #5220C23semidirect
139. C2×#834C23semidirect
141. #5213C23semidirect
146. #4958C23semidirect
149. C2×#806C23semidirect
171. C22×#99C2×D3semidirect
179. C2×#386C2×D3semidirect
184. #1790C2×D3direct (N × H)
201. C24×D3C22⋊C4semidirect
213. C3×H(5,𝔽2)C22×C4semidirect
237. C23×C3×C4C24semidirect
251. C22×#67C22⋊C4semidirect
263. C23×Dic3C24semidirect
283. #1004C22×C4semidirect
313. C2×D3×D4C22⋊C4semidirect
328. C22×D12C22⋊C4semidirect
353. C22×C4×D3C22⋊C4semidirect
360. C2×C3×C22⋊C4C24semidirect
365. C2×#217C24semidirect
405. C2×H(5,𝔽2)C4×D3semidirect
450. C24×C4C22×D3semidirect
462. C22×C22⋊C4C22×D3semidirect
469. C2×#99C22×D3semidirect
479. #386C22×D3semidirect
496. C24×C3C2×C22⋊C4semidirect
545. C23×D3C2×C22⋊C4semidirect
546. C23×D3C2×C22⋊C4semidirect
577. C2×C3×D4C2×C22⋊C4semidirect
596. C22×C3×C4C2×C22⋊C4semidirect
616. C2×#67C2×C22⋊C4semidirect
617. C2×#67C2×C22⋊C4semidirect
636. C22×Dic3C2×C22⋊C4semidirect
666. C2×D12C2×C22⋊C4semidirect
690. C2×C4×D3C2×C22⋊C4semidirect
743. H(5,𝔽2)C2×C4×D3semidirect
872. C23×C4C23×D3semidirect
891. C2×C22⋊C4C23×D3semidirect
925. C23×C3C22×C22⋊C4semidirect
987. C22×D3C22×C22⋊C4semidirect
1011. C2×C3×C4C22×C22⋊C4semidirect
1031. C2×Dic3C22×C22⋊C4semidirect
1108. C24D3×C22⋊C4semidirect
1186. C2×D4D3×C22⋊C4semidirect
1247. C22×C4D3×C22⋊C4semidirect
1302. C2×D3#1790direct (N × H)
1398. C23C2×D3×C22⋊C4semidirect
1454. C2×C4C2×D3×C22⋊C4semidirect
1459. C2×C3C2×#1790semidirect
1465. D3C2×#1790direct (N × H)
1521. C3C22×#1790semidirect
1529. C2D3×#1790direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×D3×H(5,𝔽2)2
C22×D3×#992
C2×D3×#3862
C2×#721422
C2×#695982
C2×#700332
D3×#17902
C2×C3×#17902
C22×#17903