Finite Group Databasebeta

← C2×#10594003 #11902467

Subgroups — C2×#10594003 #11902467

Order 1152.

3965 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D12C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64084C211yesmaximal, characteristic, complemented
4C2×C3×C4×D12C211yesmaximal, characteristic, complemented
5C2×C3×C4×D12C211yesmaximal, characteristic, complemented
6C2×#63922C212yesmaximal, complemented
7C2×D3×(C2×D3)⋊C4C212yesmaximal, complemented
8C2×#63909C211yesmaximal, characteristic, complemented
9C2×#63906C212yesmaximal, complemented
10C2×#63890C212yesmaximal, complemented
11C2×#63857C211yesmaximal, characteristic, complemented
12#10594003C2116yesmaximal, direct product factor
13C2×#5550—31nomaximal
14C2×#5554—31nomaximal
15C23×D32C2212yes—
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C22×#634C2211yescharacteristic, complemented
18C22×C3×D12C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic, complemented
22C22×C3×C4×D3C2212yescomplemented
23C22×#626C2212yes—
24C22×#626C2212yescomplemented
25C22×#625C2212yescomplemented
26C22×D3×Dic3C2212yescomplemented
27C2×D3×D12—28no—
28C2×D3×D12C2218yescomplemented
29C2×#3795—28no—
30C2×#3795C2218yescomplemented
31C2×C32×C42C2211yescharacteristic, complemented
32C2×#3752C2212yescomplemented
33C2×#3752C2212yescomplemented
34#64084C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2212yescomplemented
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
39C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
40C3×C4×D12C2218yescomplemented
41C3×C4×D12C2218yescomplemented
42C2×Dic3⋊Dic3C2212yescomplemented
43C2×#3722C2212yescomplemented
44C2×(C2×D3)⋊Dic3C2212yes—
45#63922C22116yescomplemented
46D3×(C2×D3)⋊C4C22116yescomplemented
47#63909C2218yescomplemented
48#63906C22116yescomplemented
49#63890C22116yescomplemented
50#63857C2218yescomplemented
51C22×#237—31no—
52C22×D3×D4—31no—
53C22×#235—31no—
54C23×D12—31no—
55C2×C3×C4×D4—31no—
56C2×C3×C4×D4—31no—
57C2×#937—32no—
58C2×#930—32no—
59C2×#930—31no—
60C22×(C2×D3)⋊C4—32no—
61C2×#924—31no—
62#5554—316no—
63#5550—316no—
64C2×#897—31no—
65C2×#895—31no—
66C2×#894—32no—
67C2×#886—32no—
68C2×#884—32no—
69C2×#882—32no—
70C2×D3×C22⋊C4—32no—
71C2×#875—31no—
72C2×#875—31no—
73C2×#875—61no—
74C2×C4×D12D311yescharacteristic, complemented
75C2×C4×D12D311yescharacteristic, complemented
76C23×C3⋊D3C2312yes—
77C23×C3×D3C2311yescharacteristic
78C23×C3×D3C2312yes—
79C23×C3×D3C2311yescharacteristic
80C22×D32—28no—
81C22×D32—28no—
82C22×D32—44no—
83C22×D32C2318yes—
84C22×C32×C4C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C3⋊Dic3C2312yes—
88C2×C4⋊(C3⋊D3)—24no—
89C2×C4⋊(C3⋊D3)C2314yes—
90C2×#634—24no—
91C2×#634C2314yescomplemented
92C22×C3×Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2312yes—
95C2×C3×D12—24no—
96C2×C3×D12D418yescomplemented
97C2×C3×D12C2314yes—
98C2×C3×D12C2314yes—
99C2×C3×C4×D3—24no—
100C2×C3×C4×D3—24no—
101C2×C3×C4×D3—44no—
102C2×C3×C4×D3C2314yes—
103C2×C3×C4×D3C2314yescomplemented
104C2×C3×C4×D3C2318yescomplemented
105C2×#626—28no—
106C2×#626—44no—
107C2×#626C2318yes—
108C2×#626C2318yescomplemented
109C2×#625—28no—
110C2×#625C2318yescomplemented
111C2×D3×Dic3—28no—
112C2×D3×Dic3C2318yescomplemented
113D3×D12—232no—
114#3795—232no—
115C32×C42C2314yescomplemented
116#3752C2318yescomplemented
117#3752C2318yescomplemented
118C3×(C2×D3)⋊C4C2314yes—
119C3×(C2×D3)⋊C4C2318yescomplemented
120C3×(C2×D3)⋊C4C2314yescomplemented
121C3×C4⋊Dic3C2314yescomplemented
122C3×C4⋊Dic3C2314yescomplemented
123Dic3⋊Dic3C2318yescomplemented
124#3722C2318yescomplemented
125(C2×D3)⋊Dic3C2318yes—
126C2×#546—91noSylow
127C24×D3—32no—
128C24×D3—32no—
129C22×C3×D4—31no—
130C22×C3×D4—31no—
131C23×C3×C4—31no—
132C23×C3×C4—31no—
133C23×C3×C4—32no—
134C22×#67—32no—
135C22×#67—32no—
136C22×#67—32no—
137C22×#67—32no—
138C23×Dic3—32no—
139C2×#237—38no—
140C2×#237—68no—
141C2×D3×D4—38no—
142C2×D3×D4—68no—
143C2×#235—38no—
144C2×#235—68no—
145C22×D12—32no—
146C22×D12—31no—
147C22×D12—31no—
148C22×D12—32no—
149C22×D12—38no—
150C22×D12—61no—
151C22×D12—68no—
152C22×D12C2×D311yescharacteristic
153C22×D12C2×D311yescharacteristic
154C22×C4×D3—32no—
155C22×C4×D3C2×D311yescharacteristic
156C22×C4×D3C2×D311yescharacteristic, complemented
157C22×C4×D3C2×D312yescomplemented
158C22×Dic6—31no—
159C22×Dic6—31no—
160C22×Dic6—61no—
161C3×C4×D4—38no—
162C3×C4×D4—38no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—32no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C42—21no—
169C2×C3×C42C2×D311yescharacteristic, complemented
170C2×C3×C42C2×D311yescharacteristic, complemented
171C2×#217—32no—
172#937—316no—
173#930—316no—
174#930—38no—
175C2×(C2×D3)⋊C4—32no—
176C2×(C2×D3)⋊C4—32no—
177C2×(C2×D3)⋊C4—32no—
178C2×(C2×D3)⋊C4—32no—
179C2×(C2×D3)⋊C4—32no—
180C2×(C2×D3)⋊C4—32no—
181C2×(C2×D3)⋊C4—32no—
182C2×(C2×D3)⋊C4—316no—
183C2×(C2×D3)⋊C4—62no—
184C2×(C2×D3)⋊C4—62no—
185C2×(C2×D3)⋊C4C2×D311yescharacteristic
186C2×(C2×D3)⋊C4C2×D312yescomplemented
187C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
188C2×C4⋊Dic3—32no—
189C2×C4⋊Dic3C2×D311yescharacteristic, complemented
190C2×C4⋊Dic3C2×D311yescharacteristic, complemented
191#924—38no—
192C2×Dic3⋊C4—32no—
193#897—38no—
194#895—38no—
195#894—316no—
196#886—316no—
197#884—316no—
198#882—316no—
199D3×C22⋊C4—316no—
200#875—38no—
201#875—38no—
202#875—68no—
203C4×D12C2×D318yescomplemented
204C4×D12C2×D318yescomplemented
205C23×C32C2411yescharacteristic
206C22×C3⋊D3—24no—
207C22×C3⋊D3—24no—
208C22×C3⋊D3—24no—
209C22×C3⋊D3C2414yes—
210C22×C3×D3—22no—
211C22×C3×D3—24no—
212C22×C3×D3—22no—
213C22×C3×D3—24no—
214C22×C3×D3—22no—
215C22×C3×D3—22no—
216C22×C3×D3—22no—
217C22×C3×D3C2×D418yes—
218C22×C3×D3#4114yescomplemented
219C22×C3×D3C2412yes—
220C22×C3×D3C2414yes—
221C22×C3×D3C2412yes—
222C2×D32—216no—
223C2×D32—216no—
224C2×D32—48no—
225C2×D32—432no—
226C2×C32×C4—22no—
227C2×C32×C4—22no—
228C2×C32×C4C2×D414yes—
229C2×C32×C4C2412yes—
230C2×C32×C4C2412yes—
231C2×C32×C4C2412yes—
232C2×C3⋊Dic3—24no—
233C2×C3⋊Dic3C2414yes—
234C4⋊(C3⋊D3)—28no—
235#634—28no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—22no—
238C2×C3×Dic3—24no—
239C2×C3×Dic3C2414yes—
240C2×C3×Dic3C2412yes—
241C2×C3×Dic3C2412yes—
242C3×D12—28no—
243C3×D12C2×D4116yescomplemented
244C3×C4×D3—28no—
245C3×C4×D3—28no—
246C3×C4×D3—48no—
247#626—216no—
248#626—48no—
249#625—216no—
250D3×Dic3—216no—
251C22×#41—91no—
252C23×D4—91no—
253#546—916no—
254C2×#124—91no—
255C2×#123—92no—
256C2×C22⋊Q8—91no—
257C2×#121—92no—
258C2×#121—91no—
259C2×#120—92no—
260C2×C4×D4—31no—
261C2×C4×D4—31no—
262C22×C22⋊C4—92no—
263C24×C3—31no—
264C24×C3—32no—
265C24×C3—31no—
266C23×D3—32no—
267C23×D3—32no—
268C23×D3—38no—
269C23×D3—38no—
270C23×D3—62no—
271C23×D3—68no—
272C23×D3—68no—
273C23×D3—68no—
274C23×D3—68no—
275C23×D3—124no—
276C23×D3—124no—
277C23×D3C22×D311yescharacteristic
278C23×D3C22×D312yes—
279C23×D3C22×D311yescharacteristic
280C2×C3×D4—38no—
281C2×C3×D4—34no—
282C2×C3×D4—34no—
283C2×C3×D4—64no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—31no—
288C22×C3×C4—32no—
289C22×C3×C4—31no—
290C22×C3×C4—34no—
291C22×C3×C4—34no—
292C22×C3×C4—38no—
293C22×C3×C4—64no—
294C22×C3×C4—64no—
295C22×C3×C4—124no—
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C2×#67—38no—
303C2×#67—38no—
304C2×#67—38no—
305C2×#67—38no—
306C2×#67—68no—
307C2×#67—68no—
308C2×#67—68no—
309C2×#67—124no—
310C22×Dic3—32no—
311C22×Dic3—32no—
312C22×Dic3—38no—
313C22×Dic3—62no—
314C22×Dic3—68no—
315C22×Dic3C22×D312yes—
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318#237—632no—
319D3×D4—632no—
320#235—632no—
321C2×D12—24no—
322C2×D12—38no—
323C2×D12—34no—
324C2×D12—34no—
325C2×D12—38no—
326C2×D12—64no—
327C2×D12—68no—
328C2×D12—64no—
329C2×D12—64no—
330C2×D12—632no—
331C2×D12—124no—
332C2×D12—124no—
333C2×D12D1218yescomplemented
334C2×D12C22×D314yes—
335C2×D12C22×D314yes—
336C2×C4×D3—24no—
337C2×C4×D3—24no—
338C2×C4×D3—38no—
339C2×C4×D3—44no—
340C2×C4×D3—68no—
341C2×C4×D3C22×D314yes—
342C2×C4×D3C22×D314yescomplemented
343C2×C4×D3C22×D318yescomplemented
344C2×Dic6—34no—
345C2×Dic6—34no—
346C2×Dic6—64no—
347C2×Dic6—64no—
348C2×Dic6—64no—
349C2×Dic6—124no—
350C3×C4⋊C4—34no—
351C3×C4⋊C4—34no—
352C3×C22⋊C4—34no—
353C3×C22⋊C4—38no—
354C3×C22⋊C4—34no—
355C3×C42—24no—
356C3×C42C22×D314yescomplemented
357C3×C42C22×D314yescomplemented
358#217—38no—
359(C2×D3)⋊C4—38no—
360(C2×D3)⋊C4—38no—
361(C2×D3)⋊C4—38no—
362(C2×D3)⋊C4—38no—
363(C2×D3)⋊C4—38no—
364(C2×D3)⋊C4—38no—
365(C2×D3)⋊C4—38no—
366(C2×D3)⋊C4—68no—
367(C2×D3)⋊C4—68no—
368(C2×D3)⋊C4C22×D314yes—
369(C2×D3)⋊C4C22×D318yescomplemented
370(C2×D3)⋊C4C22×D314yescomplemented
371C4⋊Dic3—38no—
372C4⋊Dic3C22×D314yescomplemented
373C4⋊Dic3C22×D314yescomplemented
374Dic3⋊C4—38no—
375C22×C32C22×D412yes—
376C22×C32C2×#4112yes—
377C22×C32H(5,𝔽2)12yes—
378C22×C32C2511yescharacteristic
379C2×C3⋊D3—24no—
380C2×C3⋊D3—24no—
381C2×C3⋊D3—24no—
382C2×C3⋊D3—48no—
383C2×C3×D3—28no—
384C2×C3×D3—216no—
385C2×C3×D3—22no—
386C2×C3×D3—24no—
387C2×C3×D3—24no—
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—22no—
392C2×C3×D3—44no—
393C2×C3×D3C22×D418yes—
394C2×C3×D3C2×#4114yescomplemented
395D32—432no—
396C32×C4—22no—
397C32×C4—22no—
398C32×C4C22×D414yes—
399C3⋊Dic3—24no—
400C3×Dic3—22no—
401C3×Dic3—22no—
402C3×Dic3—24no—
403C25—92no—
404C2×#41—98no—
405C2×#41—188no—
406C22×Q8—91no—
407C22×D4—31no—
408C22×D4—31no—
409C22×D4—98no—
410C22×D4—92no—
411C22×D4—92no—
412C22×D4—92no—
413C22×D4—91no—
414C22×D4—188no—
415C23×C4—31no—
416C23×C4—31no—
417C23×C4—32no—
418C23×C4—92no—
419#124—98no—
420#123—916no—
421C22⋊Q8—98no—
422#121—916no—
423#121—98no—
424#120—916no—
425C4×D4—38no—
426C4×D4—38no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—92no—
430C2×C22⋊C4—31no—
431C2×C22⋊C4—32no—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—916no—
434C2×C22⋊C4—92no—
435C2×C22⋊C4—92no—
436C2×C22⋊C4—92no—
437C2×C22⋊C4—92no—
438C2×C42D3211yescharacteristic, complemented
439C23×C3—21no—
440C23×C3—38no—
441C23×C3—34no—
442C23×C3—32no—
443C23×C3—34no—
444C23×C3—32no—
445C23×C3—62no—
446C23×C3—64no—
447C23×C3—62no—
448C23×C3—64no—
449C23×C3—62no—
450C23×C3—62no—
451C23×C3—62no—
452C23×C3C23×D311yescharacteristic
453C23×C3C23×D311yescharacteristic
454C22×D3—22no—
455C22×D3—24no—
456C22×D3—24no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—34no—
462C22×D3—34no—
463C22×D3—64no—
464C22×D3—616no—
465C22×D3—616no—
466C22×D3—64no—
467C22×D3—64no—
468C22×D3—64no—
469C22×D3—64no—
470C22×D3—64no—
471C22×D3—64no—
472C22×D3—616no—
473C22×D3—616no—
474C22×D3—124no—
475C22×D3—124no—
476C22×D3—124no—
477C22×D3—128no—
478C22×D3—128no—
479C22×D3—1232no—
480C22×D3—1232no—
481C22×D3C2×D1218yes—
482C22×D3#23514yescomplemented
483C22×D3C23×D312yes—
484C22×D3C23×D314yes—
485C22×D3C23×D312yes—
486C3×D4—316no—
487C3×D4—68no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—24no—
496C2×C3×C4—32no—
497C2×C3×C4—34no—
498C2×C3×C4—32no—
499C2×C3×C4—42no—
500C2×C3×C4—42no—
501C2×C3×C4—62no—
502C2×C3×C4—62no—
503C2×C3×C4—64no—
504C2×C3×C4—68no—
505C2×C3×C4—68no—
506C2×C3×C4—128no—
507C2×C3×C4C2×D1214yes—
508C2×C3×C4D3×D414yes—
509C2×C3×C4C23×D312yes—
510C2×C3×C4C23×D312yes—
511C2×C3×C4C23×D312yes—
512C2×C3×C4C23×D312yes—
513C2×C3×C4C23×D312yes—
514C2×C3×C4C23×D312yes—
515#67—616no—
516#67—616no—
517#67—616no—
518#67—128no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—24no—
522C2×Dic3—34no—
523C2×Dic3—34no—
524C2×Dic3—64no—
525C2×Dic3—616no—
526C2×Dic3—64no—
527C2×Dic3—64no—
528C2×Dic3—124no—
529C2×Dic3C23×D314yes—
530C2×Dic3C23×D312yes—
531C2×Dic3C23×D312yes—
532D12—28no—
533D12—616no—
534D12—68no—
535D12—68no—
536D12—128no—
537D12—128no—
538D12C2×D12116yescomplemented
539C4×D3—28no—
540C4×D3—28no—
541C4×D3—48no—
542C4×D3—616no—
543Dic6—68no—
544Dic6—68no—
545Dic6—128no—
546C2×C32#54614yescomplemented
547C2×C32C23×D411yescharacteristic
548C2×C32C22×#4111yescharacteristic
549C2×C32C2×H(5,𝔽2)11yescharacteristic
550C3⋊D3—44no—
551C3×D3—24no—
552C3×D3—28no—
553C3×D3—42no—
554C24—31no—
555C24—32no—
556C24—31no—
557C24—98no—
558C24—92no—
559C24—188no—
560C24—188no—
561C24—364no—
562#41—1832no—
563C2×Q8—94no—
564C2×Q8—184no—
565C2×D4—34no—
566C2×D4—34no—
567C2×D4—38no—
568C2×D4—64no—
569C2×D4—98no—
570C2×D4—98no—
571C2×D4—98no—
572C2×D4—94no—
573C2×D4—1832no—
574C2×D4—188no—
575C2×D4—188no—
576C2×D4—184no—
577C2×D4—364no—
578C22×C4—32no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—34no—
582C22×C4—34no—
583C22×C4—38no—
584C22×C4—64no—
585C22×C4—64no—
586C22×C4—98no—
587C22×C4—92no—
588C22×C4—124no—
589C22×C4—188no—
590C22×C4C2×D3211yescharacteristic
591C22×C4C2×D3211yescharacteristic
592C22×C4C2×D3211yescharacteristic
593C4⋊C4—34no—
594C4⋊C4—34no—
595C4⋊C4—98no—
596C22⋊C4—34no—
597C22⋊C4—38no—
598C22⋊C4—34no—
599C22⋊C4—98no—
600C22⋊C4—98no—
601C22⋊C4—98no—
602C22⋊C4—98no—
603C42C2×D3214yescomplemented
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—21no—
608C22×C3—38no—
609C22×C3—34no—
610C22×C3—62no—
611C22×C3—64no—
612C22×C3—62no—
613C22×C3—64no—
614C22×C3—616no—
615C22×C3—68no—
616C22×C3—62no—
617C22×C3—62no—
618C22×C3—62no—
619C22×C3—124no—
620C22×C3C22×D1212yes—
621C22×C3C2×#23512yes—
622C22×C3C2×D3×D412yes—
623C22×C3#100412yes—
624C22×C3D3×#4112yes—
625C22×C3#100912yes—
626C22×C3C24×D311yescharacteristic
627C22×C3C24×D311yescharacteristic
628C2×D3—22no—
629C2×D3—24no—
630C2×D3—24no—
631C2×D3—22no—
632C2×D3—28no—
633C2×D3—216no—
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—44no—
638C2×D3—64no—
639C2×D3—64no—
640C2×D3—64no—
641C2×D3—64no—
642C2×D3—64no—
643C2×D3—64no—
644C2×D3—124no—
645C2×D3—124no—
646C2×D3—124no—
647C2×D3—1232no—
648C2×D3—1232no—
649C2×D3—128no—
650C2×D3—128no—
651C2×D3—248no—
652C2×D3C22×D1218yes—
653C2×D3C2×#23514yescomplemented
654C3×C4—22no—
655C3×C4—22no—
656C3×C4—22no—
657C3×C4—22no—
658C3×C4—24no—
659C3×C4—42no—
660C3×C4—42no—
661C3×C4—62no—
662C3×C4—62no—
663C3×C4—64no—
664C3×C4C22×D1214yes—
665C3×C4C2×D3×D414yes—
666Dic3—22no—
667Dic3—22no—
668Dic3—24no—
669Dic3—64no—
670Dic3—64no—
671Dic3—124no—
672C32C2×#54611yescharacteristic, complemented, Sylow
673C23—38no—
674C23—34no—
675C23—32no—
676C23—34no—
677C23—32no—
678C23—62no—
679C23—64no—
680C23—64no—
681C23—62no—
682C23—62no—
683C23—62no—
684C23—62no—
685C23—94no—
686C23—1816no—
687C23—1816no—
688C23—184no—
689C23—184no—
690C23—184no—
691C23—368no—
692C23—3632no—
693C23C22×D3211yescharacteristic
694Q8—188no—
695D4—316no—
696D4—68no—
697D4—1816no—
698D4—1816no—
699D4—188no—
700D4—368no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—34no—
704C2×C4—32no—
705C2×C4—32no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—64no—
709C2×C4—68no—
710C2×C4—68no—
711C2×C4—94no—
712C2×C4—128no—
713C2×C4—1816no—
714C2×C4—184no—
715C2×C4D3×D1214yes—
716C2×C4C22×D3212yes—
717C2×C4C22×D3212yes—
718C2×C4C22×D3212yes—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—24no—
723C2×C3—64no—
724C2×C3—68no—
725C2×C3—122no—
726C2×C3#555014yescomplemented
727C2×C3#555414yescomplemented
728C2×C3C23×D1211yescharacteristic
729C2×C3C22×#23511yescharacteristic
730C2×C3C22×D3×D411yescharacteristic
731C2×C3C2×#100411yescharacteristic
732C2×C3C2×D3×#4111yescharacteristic
733C2×C3C2×#100911yescharacteristic
734D3—28no—
735D3—24no—
736D3—42no—
737D3—124no—
738D3—124no—
739D3—244no—
740C22—38no—
741C22—34no—
742C22—62no—
743C22—64no—
744C22—64no—
745C22—62no—
746C22—68no—
747C22—616no—
748C22—62no—
749C22—62no—
750C22—62no—
751C22—124no—
752C22—184no—
753C22—184no—
754C22—184no—
755C22—3632no—
756C22—368no—
757C22C2×D3×D1212yes—
758C22D3×#23512yes—
759C22#6430712yes—
760C22C23×D3211yescharacteristic
761C4—22no—
762C4—22no—
763C4—62no—
764C4—62no—
765C4—64no—
766C4—184no—
767C4C2×D3×D1214yes—
768C3—21no—
769C3C2×#555411yescharacteristic, complemented
770C3C2×#555011yescharacteristic, complemented
771C2—64no—
772C2—68no—
773C2—122no—
774C2—364no—
775C2#1059400314yesdirect product factor
776C2C22×D3×D1211yescharacteristic
777C2C2×D3×#23511yescharacteristic
778C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×D3×D12C2semidirect
2. C22×#3795C2semidirect
3. C2×#64084C2semidirect
4. C2×C3×C4×D12C2semidirect
5. C2×C3×C4×D12C2semidirect
6. C2×#63922C2semidirect
7. C2×D3×(C2×D3)⋊C4C2semidirect
8. C2×#63909C2semidirect
9. C2×#63906C2semidirect
10. C2×#63890C2semidirect
11. C2×#63857C2semidirect
12. #10594003C2direct (N × H)
17. C22×#634C22semidirect
21. C22×C3×C4×D3C22semidirect
22. C22×C3×C4×D3C22semidirect
24. C22×#626C22semidirect
25. C22×#625C22semidirect
26. C22×D3×Dic3C22semidirect
28. C2×D3×D12C22semidirect
30. C2×#3795C22semidirect
31. C2×C32×C42C22semidirect
32. C2×#3752C22semidirect
33. C2×#3752C22semidirect
34. #64084C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
37. C2×C3×(C2×D3)⋊C4C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
39. C2×C3×C4⋊Dic3C22semidirect
40. C3×C4×D12C22semidirect
41. C3×C4×D12C22semidirect
42. C2×Dic3⋊Dic3C22semidirect
43. C2×#3722C22semidirect
45. #63922C22semidirect
46. D3×(C2×D3)⋊C4C22semidirect
47. #63909C22semidirect
48. #63906C22semidirect
49. #63890C22semidirect
50. #63857C22semidirect
74. C2×C4×D12D3semidirect
75. C2×C4×D12D3semidirect
91. C2×#634C23semidirect
96. C2×C3×D12D4semidirect
103. C2×C3×C4×D3C23semidirect
104. C2×C3×C4×D3C23semidirect
108. C2×#626C23semidirect
110. C2×#625C23semidirect
112. C2×D3×Dic3C23semidirect
115. C32×C42C23semidirect
116. #3752C23semidirect
117. #3752C23semidirect
119. C3×(C2×D3)⋊C4C23semidirect
120. C3×(C2×D3)⋊C4C23semidirect
121. C3×C4⋊Dic3C23semidirect
122. C3×C4⋊Dic3C23semidirect
123. Dic3⋊Dic3C23semidirect
124. #3722C23semidirect
156. C22×C4×D3C2×D3semidirect
157. C22×C4×D3C2×D3semidirect
169. C2×C3×C42C2×D3semidirect
170. C2×C3×C42C2×D3semidirect
186. C2×(C2×D3)⋊C4C2×D3semidirect
187. C2×(C2×D3)⋊C4C2×D3semidirect
189. C2×C4⋊Dic3C2×D3semidirect
190. C2×C4⋊Dic3C2×D3semidirect
203. C4×D12C2×D3semidirect
204. C4×D12C2×D3semidirect
218. C22×C3×D3#41semidirect
243. C3×D12C2×D4semidirect
333. C2×D12D12semidirect
342. C2×C4×D3C22×D3semidirect
343. C2×C4×D3C22×D3semidirect
356. C3×C42C22×D3semidirect
357. C3×C42C22×D3semidirect
369. (C2×D3)⋊C4C22×D3semidirect
370. (C2×D3)⋊C4C22×D3semidirect
372. C4⋊Dic3C22×D3semidirect
373. C4⋊Dic3C22×D3semidirect
394. C2×C3×D3C2×#41semidirect
438. C2×C42D32semidirect
482. C22×D3#235semidirect
538. D12C2×D12semidirect
546. C2×C32#546semidirect
603. C42C2×D32semidirect
653. C2×D3C2×#235semidirect
672. C32C2×#546semidirect
726. C2×C3#5550semidirect
727. C2×C3#5554semidirect
769. C3C2×#5554semidirect
770. C3C2×#5550semidirect
775. C2#10594003direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D122
C22×#37952
C2×#640842
C2×C3×C4×D122
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639092
C2×#639062
C2×#638902
C2×#638572
#105940032
C2×#55503
C2×#55543