Finite Group Databasebeta

← C2×#86715 #11703655

Subgroups — C2×#86715 #11703655

Order 768.

11534 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#1009C211yesmaximal, characteristic, complemented
2C22×#1007C211yesmaximal, characteristic, complemented
3C2×C3×#548C211yesmaximal, characteristic, complemented
4C2×#5831C211yesmaximal, characteristic, complemented
5C2×#5817C211yesmaximal, characteristic, complemented
6#86715C2132yesmaximal, direct product factor
7C2×#5676C213yesmaximal, complemented
8C2×D3×#124C213yesmaximal, complemented
9C2×#5630C213yesmaximal, complemented
10C2×#5628C213yesmaximal, complemented
11C2×#5612C213yesmaximal, complemented
12C2×#5607C213yesmaximal, complemented
13C2×#5576C211yesmaximal, characteristic, complemented
14C2×C4×#239C211yesmaximal, characteristic, complemented
15C2×#5550C213yesmaximal, complemented
16C2×#5548C213yesmaximal, complemented
17C2×#3500—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic, complemented
20C2×#1009—216no—
21C2×#1009C22116yescomplemented
22C2×#1007—216no—
23C2×#1007C22116yescomplemented
24C22×#239C2211yescharacteristic
25C22×#239C2211yescharacteristic
26C22×#239C2213yescomplemented
27C22×D3×Q8C2211yescharacteristic, complemented
28C22×D3×Q8C2213yescomplemented
29C22×D3×D4C2213yes—
30C22×D3×D4C2213yes—
31C22×#235C2213yes—
32C22×#235C2213yescomplemented
33C22×#235C2213yescomplemented
34C23×D12C2213yes—
35C3×#548C22116yescomplemented
36C2×C3×#124C2213yescomplemented
37C2×C3×C22⋊Q8C2213yescomplemented
38C2×C3×#121C2213yescomplemented
39C2×C3×C4×Q8C2211yescharacteristic, complemented
40C2×C3×C4×D4C2213yescomplemented
41#5831C22116yescomplemented
42#5817C22116yescomplemented
43C2×#947C2213yescomplemented
44C2×#946C2213yescomplemented
45C2×Q8×Dic3C2211yescharacteristic, complemented
46C2×#940C2213yescomplemented
47C2×#938C2213yescomplemented
48C2×#938C2213yescomplemented
49C2×#937C2216yescomplemented
50C2×#936C2213yescomplemented
51C2×#930C2213yescomplemented
52C2×C4×#67C2213yescomplemented
53C2×C4×#67C2213yescomplemented
54C2×#924C2213yescomplemented
55#5676C22148yescomplemented
56D3×#124C22148yescomplemented
57#5630C22148yescomplemented
58#5628C22148yescomplemented
59#5612C22148yescomplemented
60#5607C22148yescomplemented
61#5576C22116yescomplemented
62C4×#239C22116yescomplemented
63#5550C22148yescomplemented
64#5548C22148yescomplemented
65C2×#897C2213yescomplemented
66C2×#895C2213yescomplemented
67C2×#895C2213yescomplemented
68C2×#894C2216yescomplemented
69C2×#893C2213yescomplemented
70C2×#892C2213yescomplemented
71C2×#888C2213yescomplemented
72C2×#885C2211yescharacteristic, complemented
73C2×#885C2213yescomplemented
74C2×#885C2216yescomplemented
75C2×#884C2213yescomplemented
76C2×#884C2213yescomplemented
77C2×#883C2216yescomplemented
78C2×#882C2216yescomplemented
79C2×D3×C22⋊C4C2216yescomplemented
80C2×D3×C22⋊C4C2216yescomplemented
81C2×#875C2213yescomplemented
82C2×C4×D12C2213yescomplemented
83C2×C4×D12C2213yescomplemented
84C2×C42×D3C2213yescomplemented
85C22×2−1+4—31no—
86C22×H(5,𝔽2)—31no—
87#3500—332no—
88C2×#548—31no—
89C2×#548—31no—
90C2×#548—31no—
91C2×#548D311yescharacteristic, complemented
92C2×#546—33no—
93C2×#546—33no—
94C2×#546—33no—
95C2×#546—33no—
96C2×#536—33no—
97C2×#535—33no—
98C2×#532—33no—
99C22×#124—33no—
100C2×C4×#41—31no—
101C24×D3C2316yes—
102C2×C3×#41—28no—
103C2×C3×#41C2318yes—
104C22×C3×Q8—28no—
105C22×C3×Q8C2313yes—
106C22×C3×Q8C2311yescharacteristic
107C22×C3×Q8C2318yescomplemented
108C22×C3×D4C2313yes—
109C22×C3×D4C2313yes—
110C23×C3×C4C2313yes—
111C23×C3×C4C2313yes—
112C22×#67C2313yes—
113C22×#67C2313yes—
114C22×#67C2313yes—
115C22×#67C2311yescharacteristic
116C22×#67C2313yes—
117C22×#67C2313yes—
118#1009—2128no—
119#1007—2128no—
120C2×#239—28no—
121C2×#239—224no—
122C2×#239D4116yescomplemented
123C2×#239C2318yes—
124C2×#239C2318yes—
125C2×#239C23124yescomplemented
126C2×D3×Q8—28no—
127C2×D3×Q8—224no—
128C2×D3×Q8C23124yescomplemented
129C2×D3×Q8C2318yescomplemented
130C2×D3×D4—224no—
131C2×D3×D4—224no—
132C2×D3×D4C23124yes—
133C2×D3×D4C23124yes—
134C2×#235—224no—
135C2×#235—224no—
136C2×#235—224no—
137C2×#235C23124yes—
138C2×#235C23124yescomplemented
139C2×#235C23124yescomplemented
140C22×D12—224no—
141C22×D12C2313yes—
142C22×D12C2313yes—
143C22×D12C23124yes—
144C22×D12C2313yes—
145C22×D12C2313yes—
146C22×D12C2313yes—
147C22×C4×D3C2313yes—
148C22×C4×D3C2313yes—
149C22×C4×D3C2316yes—
150C22×C4×D3C2313yes—
151C22×C4×D3C2313yes—
152C22×C4×D3C2313yes—
153C22×Dic6C2311yescharacteristic
154C22×Dic6C2313yes—
155C22×Dic6C2313yes—
156C3×#124C23124yescomplemented
157C3×C22⋊Q8C23124yescomplemented
158C3×#121C23124yescomplemented
159C3×C4×Q8C2318yescomplemented
160C3×C4×D4C23124yescomplemented
161C2×C3×C4⋊C4C2313yes—
162C2×C3×C4⋊C4C2313yes—
163C2×C3×C22⋊C4C2313yes—
164C2×C3×C22⋊C4C2316yes—
165C2×C3×C22⋊C4C2311yescharacteristic
166C2×C3×C42C2313yes—
167C2×#217C2313yes—
168C2×#217C2316yes—
169C2×#217C2311yescharacteristic
170#947C23124yescomplemented
171#946C23124yescomplemented
172Q8×Dic3C2318yescomplemented
173#940C23124yescomplemented
174#938C23124yescomplemented
175#938C23124yescomplemented
176#937C23148yescomplemented
177#936C23124yescomplemented
178#930C23124yescomplemented
179C4×#67C23124yescomplemented
180C4×#67C23124yescomplemented
181C2×(C2×D3)⋊C4C2311yescharacteristic
182C2×(C2×D3)⋊C4C2313yes—
183C2×(C2×D3)⋊C4C2316yes—
184C2×(C2×D3)⋊C4C2316yes—
185C2×(C2×D3)⋊C4C2313yes—
186C2×(C2×D3)⋊C4C2316yes—
187C2×(C2×D3)⋊C4C2311yescharacteristic
188C2×C4⋊Dic3C2313yes—
189C2×C4⋊Dic3C2313yes—
190#924C23124yescomplemented
191C2×Dic3⋊C4C2313yes—
192C2×Dic3⋊C4C2313yes—
193C2×C4×Dic3C2311yescharacteristic
194C2×C4×Dic3C2313yes—
195C2×C4×Dic3C2313yes—
196#897C23124yescomplemented
197#895C23124yescomplemented
198#895C23124yescomplemented
199#894C23148yescomplemented
200#893C23124yescomplemented
201#892C23124yescomplemented
202#888C23124yescomplemented
203#885C23124yescomplemented
204#885C23148yescomplemented
205#885C2318yescomplemented
206#884C23124yescomplemented
207#884C23124yescomplemented
208#883C23148yescomplemented
209#882C23148yescomplemented
210D3×C22⋊C4C23148yescomplemented
211D3×C22⋊C4C23148yescomplemented
212#875C23124yescomplemented
213C4×D12C23124yescomplemented
214C4×D12C23124yescomplemented
215C42×D3C23124yescomplemented
216C2×2−1+4—316no—
217C2×2−1+4—616no—
218C2×H(5,𝔽2)—316no—
219C2×H(5,𝔽2)—616no—
220C22×#41—31no—
221C22×#41—31no—
222C22×#41—33no—
223C22×#41—33no—
224C22×#41—33no—
225C22×#41—33no—
226C22×#41C2×D311yescharacteristic
227C23×Q8—33no—
228C23×Q8—31no—
229C23×Q8C2×D311yescharacteristic, complemented
230C23×D4—33no—
231C23×D4—33no—
232C23×D4—33no—
233#548—316no—
234#548—316no—
235#548—316no—
236#548C2×D3116yescomplemented
237#546—348no—
238#546—348no—
239#546—348no—
240#546—348no—
241#536—348no—
242#535—348no—
243#532—348no—
244C2×C4⋊Q8—33no—
245C2×#127—33no—
246C2×#124—33no—
247C2×#124—33no—
248C2×#124—348no—
249C2×#124—33no—
250C2×#124—36no—
251C2×#124—31no—
252C2×#124—33no—
253C2×#124C2×D313yescomplemented
254C2×#123—36no—
255C2×#123—36no—
256C2×C22⋊Q8—33no—
257C2×C22⋊Q8—33no—
258C2×C22⋊Q8—33no—
259C2×C22⋊Q8C2×D313yescomplemented
260C2×#121—33no—
261C2×#121—33no—
262C2×#121—33no—
263C2×#121—33no—
264C2×#121—33no—
265C2×#121—33no—
266C2×#121—33no—
267C2×#121C2×D313yescomplemented
268C2×#120—36no—
269C2×#120—36no—
270C4×#41—316no—
271C2×C4×Q8—31no—
272C2×C4×Q8C2×D311yescharacteristic, complemented
273C2×C4×D4—33no—
274C2×C4×D4—33no—
275C2×C4×D4—33no—
276C2×C4×D4—33no—
277C2×C4×D4—33no—
278C2×C4×D4C2×D313yescomplemented
279C2×#117—33no—
280C22×C22⋊C4—36no—
281C22×C22⋊C4—36no—
282C22×C42—33no—
283C24×C3C2413yes—
284C24×C3C2411yescharacteristic
285C23×D3—224no—
286C23×D3—412no—
287C23×D3—412no—
288C23×D3C2413yes—
289C23×D3C2411yescharacteristic
290C23×D3C2413yes—
291C23×D3C24124yes—
292C3×#41—232no—
293C2×C3×Q8—232no—
294C2×C3×Q8—212no—
295C2×C3×Q8C2×D418yes—
296C2×C3×Q8C24112yes—
297C2×C3×Q8C2414yes—
298C2×C3×D4—212no—
299C2×C3×D4—46no—
300C2×C3×D4C24112yes—
301C2×C3×D4C24112yes—
302C22×C3×C4—212no—
303C22×C3×C4—212no—
304C22×C3×C4C2413yes—
305C22×C3×C4C2411yescharacteristic
306C22×C3×C4C2411yescharacteristic
307C22×C3×C4C2413yes—
308C22×C3×C4C24112yes—
309C22×C3×C4C24112yes—
310C22×C3×C4C2413yes—
311C2×#67—212no—
312C2×#67—212no—
313C2×#67—24no—
314C2×#67—212no—
315C2×#67—46no—
316C2×#67—46no—
317C2×#67C24112yes—
318C2×#67C24112yes—
319C2×#67C24112yes—
320C2×#67C2414yes—
321C2×#67C24112yes—
322C2×#67C24112yes—
323C22×Dic3C2411yescharacteristic
324C22×Dic3C2413yes—
325C22×Dic3C2411yescharacteristic
326C22×Dic3C2413yes—
327C22×Dic3C2411yescharacteristic
328#239—232no—
329#239—296no—
330#239C2×D4164yescomplemented
331D3×Q8—232no—
332D3×Q8—296no—
333D3×D4—296no—
334D3×D4—296no—
335#235—296no—
336#235—296no—
337#235—296no—
338C2×D12—212no—
339C2×D12—212no—
340C2×D12—212no—
341C2×D12—296no—
342C2×D12—46no—
343C2×D12C2×D4124yes—
344C2×D12C24112yes—
345C2×D12C24112yes—
346C2×D12C24112yes—
347C2×D12C24112yes—
348C2×D12C24112yes—
349C2×C4×D3—224no—
350C2×C4×D3—212no—
351C2×C4×D3—212no—
352C2×C4×D3—46no—
353C2×C4×D3—46no—
354C2×C4×D3C2×D4124yes—
355C2×C4×D3C24112yes—
356C2×C4×D3C24112yes—
357C2×C4×D3C24124yes—
358C2×C4×D3C24112yes—
359C2×C4×D3C24112yes—
360C2×C4×D3C24112yes—
361C2×Dic6—212no—
362C2×Dic6—24no—
363C2×Dic6—212no—
364C2×Dic6C24112yes—
365C2×Dic6C24112yes—
366C2×Dic6C2414yes—
367C3×C4⋊C4C24112yes—
368C3×C4⋊C4C24112yes—
369C3×C22⋊C4C24112yes—
370C3×C22⋊C4C24124yes—
371C3×C22⋊C4C2414yes—
372C3×C42C24112yes—
373#217C24112yes—
374#217C24124yes—
375#217C2414yes—
376(C2×D3)⋊C4C2414yes—
377(C2×D3)⋊C4C24112yes—
378(C2×D3)⋊C4C24124yes—
379(C2×D3)⋊C4C24124yes—
380(C2×D3)⋊C4C24112yes—
381(C2×D3)⋊C4C24124yes—
382(C2×D3)⋊C4C2414yes—
383C4⋊Dic3C24112yes—
384C4⋊Dic3C24112yes—
385Dic3⋊C4C24112yes—
386Dic3⋊C4C24112yes—
387C4×Dic3C2414yes—
388C4×Dic3C24112yes—
389C4×Dic3C24112yes—
390C25—36no—
3912−1+4—6128no—
392H(5,𝔽2)—6128no—
393C2×#41—28no—
394C2×#41—316no—
395C2×#41—38no—
396C2×#41—324no—
397C2×#41—38no—
398C2×#41—324no—
399C2×#41—324no—
400C2×#41—324no—
401C2×#41—624no—
402C2×#41—624no—
403C2×#41—624no—
404C2×#41—624no—
405C2×#41—68no—
406C2×#41C22×D318yes—
407C22×Q8—28no—
408C22×Q8—324no—
409C22×Q8—38no—
410C22×Q8—33no—
411C22×Q8—33no—
412C22×Q8—31no—
413C22×Q8—624no—
414C22×Q8—68no—
415C22×Q8C22×D313yes—
416C22×Q8C22×D311yescharacteristic
417C22×Q8C22×D318yescomplemented
418C22×D4—33no—
419C22×D4—33no—
420C22×D4—33no—
421C22×D4—31no—
422C22×D4—33no—
423C22×D4—33no—
424C22×D4—324no—
425C22×D4—324no—
426C22×D4—33no—
427C22×D4—33no—
428C22×D4—33no—
429C22×D4—33no—
430C22×D4—324no—
431C22×D4—33no—
432C22×D4—624no—
433C22×D4—624no—
434C22×D4—624no—
435C22×D4C22×D313yes—
436C22×D4C22×D313yes—
437C23×C4—33no—
438C23×C4—36no—
439C23×C4—33no—
440C23×C4—33no—
441C23×C4—33no—
442C23×C4—33no—
443C23×C4C22×D313yes—
444C23×C4C22×D313yes—
445C4⋊Q8—324no—
446#127—324no—
447#124—324no—
448#124—324no—
449#124—324no—
450#124—348no—
451#124—38no—
452#124—324no—
453#124C22×D3124yescomplemented
454#123—348no—
455#123—348no—
456C22⋊Q8—324no—
457C22⋊Q8—324no—
458C22⋊Q8—324no—
459C22⋊Q8C22×D3124yescomplemented
460#121—324no—
461#121—324no—
462#121—324no—
463#121—324no—
464#121—324no—
465#121—324no—
466#121—324no—
467#121C22×D3124yescomplemented
468#120—348no—
469#120—348no—
470C4×Q8—38no—
471C4×Q8C22×D318yescomplemented
472C4×D4—324no—
473C4×D4—324no—
474C4×D4—324no—
475C4×D4—324no—
476C4×D4—324no—
477C4×D4C22×D3124yescomplemented
478#117—324no—
479C2×C4⋊C4—33no—
480C2×C4⋊C4—33no—
481C2×C4⋊C4—33no—
482C2×C4⋊C4—33no—
483C2×C4⋊C4C22×D313yes—
484C2×C4⋊C4C22×D313yes—
485C2×C22⋊C4—33no—
486C2×C22⋊C4—36no—
487C2×C22⋊C4—31no—
488C2×C22⋊C4—33no—
489C2×C22⋊C4—33no—
490C2×C22⋊C4—36no—
491C2×C22⋊C4—36no—
492C2×C22⋊C4—36no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—31no—
495C2×C22⋊C4—348no—
496C2×C22⋊C4—348no—
497C2×C22⋊C4C22×D313yes—
498C2×C22⋊C4C22×D316yes—
499C2×C22⋊C4C22×D311yescharacteristic
500C2×C42—33no—
501C2×C42—33no—
502C2×C42—31no—
503C2×C42—324no—
504C2×C42C22×D313yes—
505C23×C3—22no—
506C23×C3—26no—
507C23×C3—22no—
508C23×C3—26no—
509C23×C3—22no—
510C23×C3—26no—
511C23×C3C2516yes—
512C23×C3C2512yes—
513C23×C3C2511yescharacteristic
514C22×D3—26no—
515C22×D3—26no—
516C22×D3—22no—
517C22×D3—26no—
518C22×D3—22no—
519C22×D3—26no—
520C22×D3—22no—
521C22×D3—26no—
522C22×D3—248no—
523C22×D3—424no—
524C22×D3—424no—
525C22×D3—848no—
526C22×D3C22×D4112yes—
527C22×D3C2516yes—
528C22×D3C2512yes—
529C22×D3C2516yes—
530C3×Q8—224no—
531C3×Q8C22×D4116yes—
532C3×D4—224no—
533C3×D4—412no—
534C2×C3×C4—26no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—26no—
538C2×C3×C4—224no—
539C2×C3×C4—224no—
540C2×C3×C4C22×D4112yes—
541C2×C3×C4C2516yes—
542C2×C3×C4C2512yes—
543C2×C3×C4C2512yes—
544C2×C3×C4C2516yes—
545C2×C3×C4C2516yes—
546#67—224no—
547#67—224no—
548#67—28no—
549#67—224no—
550#67—412no—
551#67—412no—
552C2×Dic3—26no—
553C2×Dic3—22no—
554C2×Dic3—22no—
555C2×Dic3—26no—
556C2×Dic3C22×D414yes—
557C2×Dic3C2512yes—
558C2×Dic3C2516yes—
559C2×Dic3C2512yes—
560C2×Dic3C2516yes—
561C2×Dic3C2512yes—
562D12—224no—
563D12—224no—
564D12—224no—
565D12—412no—
566D12C22×D4148yes—
567C4×D3—248no—
568C4×D3—224no—
569C4×D3—224no—
570C4×D3—412no—
571C4×D3—412no—
572C4×D3C22×D4148yes—
573Dic6—224no—
574Dic6—28no—
575Dic6—224no—
576C24—33no—
577C24—33no—
578C24—31no—
579C24—324no—
580C24—624no—
581C24—1212no—
582C24—1212no—
583C24C23×D313yes—
584C24C23×D311yescharacteristic
585#41—232no—
586#41—364no—
587#41—696no—
588#41—696no—
589#41—696no—
590#41—696no—
591#41—632no—
592C2×Q8—232no—
593C2×Q8—212no—
594C2×Q8—312no—
595C2×Q8—312no—
596C2×Q8—34no—
597C2×Q8—612no—
598C2×Q8—64no—
599C2×Q8—696no—
600C2×Q8—632no—
601C2×Q8—612no—
602C2×Q8D3×D418yes—
603C2×Q8C23×D3112yes—
604C2×Q8C23×D314yes—
605C2×D4—212no—
606C2×D4—312no—
607C2×D4—312no—
608C2×D4—312no—
609C2×D4—34no—
610C2×D4—312no—
611C2×D4—312no—
612C2×D4—324no—
613C2×D4—312no—
614C2×D4—312no—
615C2×D4—312no—
616C2×D4—312no—
617C2×D4—312no—
618C2×D4—46no—
619C2×D4—696no—
620C2×D4—612no—
621C2×D4—612no—
622C2×D4—696no—
623C2×D4—612no—
624C2×D4—64no—
625C2×D4—696no—
626C2×D4—612no—
627C2×D4—612no—
628C2×D4—612no—
629C2×D4—126no—
630C2×D4—126no—
631C2×D4—126no—
632C2×D4C23×D3112yes—
633C2×D4C23×D3112yes—
634C22×C4—212no—
635C22×C4—212no—
636C22×C4—31no—
637C22×C4—324no—
638C22×C4—312no—
639C22×C4—31no—
640C22×C4—33no—
641C22×C4—33no—
642C22×C4—31no—
643C22×C4—324no—
644C22×C4—312no—
645C22×C4—312no—
646C22×C4—312no—
647C22×C4—312no—
648C22×C4—624no—
649C22×C4—612no—
650C22×C4—612no—
651C22×C4—126no—
652C22×C4—126no—
653C22×C4C23×D3112yes—
654C22×C4C23×D3112yes—
655C22×C4C23×D311yescharacteristic
656C22×C4C23×D313yes—
657C22×C4C23×D313yes—
658C22×C4C23×D311yescharacteristic
659C22×C4C23×D313yes—
660C4⋊C4—312no—
661C4⋊C4—312no—
662C4⋊C4—312no—
663C4⋊C4—312no—
664C4⋊C4C23×D3112yes—
665C4⋊C4C23×D3112yes—
666C22⋊C4—312no—
667C22⋊C4—324no—
668C22⋊C4—34no—
669C22⋊C4—312no—
670C22⋊C4—312no—
671C22⋊C4—324no—
672C22⋊C4—324no—
673C22⋊C4—324no—
674C22⋊C4—34no—
675C22⋊C4—34no—
676C22⋊C4C23×D3112yes—
677C22⋊C4C23×D3124yes—
678C22⋊C4C23×D314yes—
679C42—34no—
680C42—312no—
681C42—312no—
682C42C23×D3112yes—
683C22×C3—22no—
684C22×C3—26no—
685C22×C3—22no—
686C22×C3—26no—
687C22×C3—22no—
688C22×C3—26no—
689C22×C3—412no—
690C22×C3—44no—
691C22×C3C23×D412yes—
692C22×C3#58512yes—
693C22×C3#58512yes—
694C22×C3C2611yescharacteristic
695C2×D3—26no—
696C2×D3—26no—
697C2×D3—224no—
698C2×D3—22no—
699C2×D3—26no—
700C2×D3—22no—
701C2×D3—26no—
702C2×D3—22no—
703C2×D3—26no—
704C2×D3—44no—
705C2×D3—412no—
706C2×D3—848no—
707C2×D3C23×D4112yes—
708C3×C4—26no—
709C3×C4—22no—
710C3×C4—22no—
711C3×C4—26no—
712C3×C4C23×D4112yes—
713Dic3—26no—
714Dic3—22no—
715Dic3—22no—
716Dic3—26no—
717Dic3C23×D414yes—
718C23—22no—
719C23—26no—
720C23—22no—
721C23—26no—
722C23—22no—
723C23—26no—
724C23—312no—
725C23—36no—
726C23—36no—
727C23—32no—
728C23—648no—
729C23—66no—
730C23—66no—
731C23—62no—
732C23—66no—
733C23—62no—
734C23—66no—
735C23—62no—
736C23—66no—
737C23—1224no—
738C23—1224no—
739C23—2448no—
740C23C24×D316yes—
741C23C24×D312yes—
742C23C24×D311yescharacteristic
743Q8—224no—
744Q8—624no—
745Q8—68no—
746Q8—624no—
747Q8C2×D3×D4116yes—
748D4—224no—
749D4—348no—
750D4—412no—
751D4—624no—
752D4—624no—
753D4—624no—
754D4—68no—
755D4—624no—
756D4—624no—
757D4—624no—
758D4—1212no—
759D4—1212no—
760D4—1212no—
761C2×C4—22no—
762C2×C4—26no—
763C2×C4—26no—
764C2×C4—22no—
765C2×C4—224no—
766C2×C4—224no—
767C2×C4—34no—
768C2×C4—32no—
769C2×C4—348no—
770C2×C4—32no—
771C2×C4—36no—
772C2×C4—36no—
773C2×C4—32no—
774C2×C4—648no—
775C2×C4—62no—
776C2×C4—66no—
777C2×C4—62no—
778C2×C4—66no—
779C2×C4—624no—
780C2×C4—624no—
781C2×C4—1212no—
782C2×C4—1212no—
783C2×C4C2×D3×D4112yes—
784C2×C4C24×D312yes—
785C2×C4C24×D316yes—
786C2×C4C24×D316yes—
787C2×C4C24×D312yes—
788C2×C4C24×D316yes—
789C2×C3—46no—
790C2×C3—42no—
791C2×C3#350014yescomplemented
792C2×C3C24×D411yescharacteristic
793C2×C3C2×#58511yescharacteristic
794C2×C3C2×#58511yescharacteristic
795D3—212no—
796D3—42no—
797D3—46no—
798C22—22no—
799C22—26no—
800C22—22no—
801C22—26no—
802C22—22no—
803C22—26no—
804C22—312no—
805C22—412no—
806C22—44no—
807C22—66no—
808C22—66no—
809C22—624no—
810C22—62no—
811C22—66no—
812C22—62no—
813C22—66no—
814C22—62no—
815C22—66no—
816C22—1212no—
817C22—124no—
818C22—2448no—
819C22C22×D3×D412yes—
820C22#596412yes—
821C22#596812yes—
822C22C25×D311yescharacteristic
823C4—22no—
824C4—26no—
825C4—26no—
826C4—22no—
827C4—34no—
828C4—62no—
829C4—66no—
830C4—62no—
831C4—66no—
832C4C22×D3×D4112yes—
833C3C2×#350011yescharacteristic, complemented, Sylow
834C2—46no—
835C2—42no—
836C2—612no—
837C2—126no—
838C2—122no—
839C2#8671514yesdirect product factor
840C2C23×D3×D411yescharacteristic
841C2C2×#596411yescharacteristic
842C2C2×#596811yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#548C2
socleC23×C3C25
hypercenterC2×#548D3
hypocenterC3C2×#3500
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#1009C2semidirect
2. C22×#1007C2semidirect
3. C2×C3×#548C2semidirect
4. C2×#5831C2semidirect
5. C2×#5817C2semidirect
6. #86715C2direct (N × H)
7. C2×#5676C2semidirect
8. C2×D3×#124C2semidirect
9. C2×#5630C2semidirect
10. C2×#5628C2semidirect
11. C2×#5612C2semidirect
12. C2×#5607C2semidirect
13. C2×#5576C2semidirect
14. C2×C4×#239C2semidirect
15. C2×#5550C2semidirect
16. C2×#5548C2semidirect
19. C23×C3×Q8C22semidirect
21. C2×#1009C22semidirect
23. C2×#1007C22semidirect
26. C22×#239C22semidirect
27. C22×D3×Q8C22semidirect
28. C22×D3×Q8C22semidirect
32. C22×#235C22semidirect
33. C22×#235C22semidirect
35. C3×#548C22semidirect
36. C2×C3×#124C22semidirect
37. C2×C3×C22⋊Q8C22semidirect
38. C2×C3×#121C22semidirect
39. C2×C3×C4×Q8C22semidirect
40. C2×C3×C4×D4C22semidirect
41. #5831C22semidirect
42. #5817C22semidirect
43. C2×#947C22semidirect
44. C2×#946C22semidirect
45. C2×Q8×Dic3C22semidirect
46. C2×#940C22semidirect
47. C2×#938C22semidirect
48. C2×#938C22semidirect
49. C2×#937C22semidirect
50. C2×#936C22semidirect
51. C2×#930C22semidirect
52. C2×C4×#67C22semidirect
53. C2×C4×#67C22semidirect
54. C2×#924C22semidirect
55. #5676C22semidirect
56. D3×#124C22semidirect
57. #5630C22semidirect
58. #5628C22semidirect
59. #5612C22semidirect
60. #5607C22semidirect
61. #5576C22semidirect
62. C4×#239C22semidirect
63. #5550C22semidirect
64. #5548C22semidirect
65. C2×#897C22semidirect
66. C2×#895C22semidirect
67. C2×#895C22semidirect
68. C2×#894C22semidirect
69. C2×#893C22semidirect
70. C2×#892C22semidirect
71. C2×#888C22semidirect
72. C2×#885C22semidirect
73. C2×#885C22semidirect
74. C2×#885C22semidirect
75. C2×#884C22semidirect
76. C2×#884C22semidirect
77. C2×#883C22semidirect
78. C2×#882C22semidirect
79. C2×D3×C22⋊C4C22semidirect
80. C2×D3×C22⋊C4C22semidirect
81. C2×#875C22semidirect
82. C2×C4×D12C22semidirect
83. C2×C4×D12C22semidirect
84. C2×C42×D3C22semidirect
91. C2×#548D3semidirect
107. C22×C3×Q8C23semidirect
122. C2×#239D4semidirect
125. C2×#239C23semidirect
128. C2×D3×Q8C23semidirect
129. C2×D3×Q8C23semidirect
138. C2×#235C23semidirect
139. C2×#235C23semidirect
156. C3×#124C23semidirect
157. C3×C22⋊Q8C23semidirect
158. C3×#121C23semidirect
159. C3×C4×Q8C23semidirect
160. C3×C4×D4C23semidirect
170. #947C23semidirect
171. #946C23semidirect
172. Q8×Dic3C23semidirect
173. #940C23semidirect
174. #938C23semidirect
175. #938C23semidirect
176. #937C23semidirect
177. #936C23semidirect
178. #930C23semidirect
179. C4×#67C23semidirect
180. C4×#67C23semidirect
190. #924C23semidirect
196. #897C23semidirect
197. #895C23semidirect
198. #895C23semidirect
199. #894C23semidirect
200. #893C23semidirect
201. #892C23semidirect
202. #888C23semidirect
203. #885C23semidirect
204. #885C23semidirect
205. #885C23semidirect
206. #884C23semidirect
207. #884C23semidirect
208. #883C23semidirect
209. #882C23semidirect
210. D3×C22⋊C4C23semidirect
211. D3×C22⋊C4C23semidirect
212. #875C23semidirect
213. C4×D12C23semidirect
214. C4×D12C23semidirect
215. C42×D3C23semidirect
229. C23×Q8C2×D3semidirect
236. #548C2×D3semidirect
253. C2×#124C2×D3semidirect
259. C2×C22⋊Q8C2×D3semidirect
267. C2×#121C2×D3semidirect
272. C2×C4×Q8C2×D3semidirect
278. C2×C4×D4C2×D3semidirect
330. #239C2×D4semidirect
417. C22×Q8C22×D3semidirect
453. #124C22×D3semidirect
459. C22⋊Q8C22×D3semidirect
467. #121C22×D3semidirect
471. C4×Q8C22×D3semidirect
477. C4×D4C22×D3semidirect
791. C2×C3#3500semidirect
833. C3C2×#3500semidirect
839. C2#86715direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#10092
C22×#10072
C2×C3×#5482
C2×#58312
C2×#58172
#867152
C2×#56762
C2×D3×#1242
C2×#56302
C2×#56282
C2×#56122
C2×#56072
C2×#55762
C2×C4×#2392
C2×#55502
C2×#55482
C2×#35003