Finite Group Databasebeta

← #11889711

Subgroups — #11889711

Order 1152.

882 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5550C211yesmaximal, characteristic
2C3×#5543C211yesmaximal, characteristic, complemented
3#10592710C211yesmaximal, characteristic, complemented
4#10591188C211yesmaximal, characteristic, complemented
5#10591180C211yesmaximal, characteristic, complemented
6#10591170C211yesmaximal, characteristic, complemented
7#10591169C211yesmaximal, characteristic, complemented
8#10591132C211yesmaximal, characteristic, complemented
9#10591089C211yesmaximal, characteristic, complemented
10#10591087C211yesmaximal, characteristic, complemented
11C2×#63562C211yesmaximal, characteristic, complemented
12#10590358C211yesmaximal, characteristic, complemented
13#10590280C211yesmaximal, characteristic, complemented
14#10590269C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#83635—31nomaximal
17#83498—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C2×#3748C2211yescharacteristic, complemented
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#937—21no—
24C3×D4×Dic3—21no—
25C3×#930C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
28C3×#924C2211yescharacteristic
29C3×#924C2211yescharacteristic
30C3×#924C2211yescharacteristic, complemented
31C3×#894—21no—
32C3×#890—21no—
33C3×#884—21no—
34C3×D3×C22⋊C4—21no—
35C3×#878—21no—
36C3×#878—21no—
37C3×#875C2211yescharacteristic
38C3×C4×D12C2211yescharacteristic
39C3×#869C2211yescharacteristic, complemented
40C3×C4×Dic6C2211yescharacteristic, complemented
41C2×#3718C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44#63657C2211yescharacteristic
45#63657C2211yescharacteristic, complemented
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
47#63630C2211yescharacteristic, complemented
48#63576C2211yescharacteristic, complemented
49#63576C2211yescharacteristic, complemented
50#63576C2211yescharacteristic, complemented
51#63565C2211yescharacteristic, complemented
52#63565C2211yescharacteristic, complemented
53#63565C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61C3×#554—31no—
62C3×#546—31no—
63#5550D311yescharacteristic
64#5543D311yescharacteristic, complemented
65#5239—31no—
66#5232—31no—
67#5218—31no—
68C2×#832—31no—
69#5089—31no—
70#5087—31no—
71#5055—31no—
72#5054—31no—
73#5051—31no—
74#5051—31no—
75#5049—31no—
76#5047—31no—
77#5046—31no—
78#5044—31no—
79#5042—31no—
80#5033—31no—
81#5028—31no—
82#5026—31no—
83#5018—31no—
84#5011—31no—
85#5011—31no—
86#5011—61no—
87#5007—31no—
88#4970—31no—
89#4967—31no—
90#4966—31no—
91C2×#809—31no—
92C23×C3×D3—21no—
93C2×C32×D4D411yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C3×#235—22no—
101C3×#235—41no—
102C2×C3×D12—22no—
103C2×C3×D12—21no—
104C2×C3×D12—41no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×Dic6—21no—
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C32×C4⋊C4D411yescharacteristic
113C32×C22⋊C4D411yescharacteristic
114C32×C22⋊C4D411yescharacteristic
115C32×C42C2311yescharacteristic
116#3748—41no—
117C2×C3⋊(C3⋊C8)—41no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—21no—
123C3×#217—21no—
124C3×#217—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×C4×Dic3—21no—
141#3718—41no—
142#3715—22no—
143#3715—41no—
144#3314—91noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#235C2×D311yescharacteristic
148C22×D12C2×D311yescharacteristic
149C3×C4⋊Q8—31no—
150C3×#125—61no—
151C3×#124—31no—
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—61no—
157C3×C22⋊Q8—61no—
158C3×#121—31no—
159C3×#121—61no—
160C3×#120—61no—
161C3×C4×Q8—31no—
162C3×C4×D4—21no—
163C3×C4×D4—31no—
164C3×C4×D4—61no—
165C3×C4×D4C2×D311yescharacteristic
166C3×C4×D4C2×D311yescharacteristic
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C22⋊C4—61no—
170C2×#216—31no—
171C2×#216—31no—
172C2×#215—31no—
173C2×#215—31no—
174#937—21no—
175D4×Dic3—21no—
176C2×#214—31no—
177C2×#214—31no—
178#930C2×D311yescharacteristic
179C2×C4⋊Dic3C2×D311yescharacteristic
180C2×C4⋊Dic3C2×D311yescharacteristic, complemented
181#924C2×D311yescharacteristic
182#924C2×D311yescharacteristic
183#924C2×D311yescharacteristic, complemented
184C2×#208—31no—
185C2×#208—31no—
186C2×#208—61no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8—31no—
189C22×C3⋊C8—61no—
190#894—21no—
191#890—21no—
192#884—21no—
193D3×C22⋊C4—21no—
194#878—21no—
195#878—21no—
196#875C2×D311yescharacteristic
197C4×D12C2×D311yescharacteristic
198#869C2×D311yescharacteristic, complemented
199C4×Dic6C2×D311yescharacteristic, complemented
200#835—31no—
201#835—31no—
202#835—31no—
203#835—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#830—31no—
211#830—31no—
212#830—31no—
213#830—31no—
214#830—61no—
215#830—61no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#807—31no—
227#807—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232C4⋊(C3⋊C8)—31no—
233C4⋊(C3⋊C8)—31no—
234C4⋊(C3⋊C8)—61no—
235#803—31no—
236#803—31no—
237#803—61no—
238C23×C32C2×D411yescharacteristic
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C32×D4—22no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C3×#67—42no—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3—81no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—42no—
269C3×D12#4112yes—
270C3×C4×D3—42no—
271C3×C4×D3—81no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276C3×Dic6—81no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3⋊(C3⋊C8)—21no—
281#554—31no—
282#546—31no—
283#489—91no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—91no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C24×C3—61no—
297C23×D3—21no—
298C3×#41—62no—
299C3×#41—121no—
300C2×C3×Q8—31no—
301C2×C3×Q8—31no—
302C2×C3×Q8—61no—
303C2×C3×D4—21no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—62no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—121no—
311C2×C3×D4#6711yescharacteristic
312C2×C3×D4#6711yescharacteristic
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C2×#67—21no—
324C2×#67—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327#235—22no—
328#235—41no—
329C2×D12—22no—
330C2×D12—21no—
331C2×D12—41no—
332C2×D12C22×D311yescharacteristic
333C2×D12C22×D311yescharacteristic
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×Dic6—21no—
337C2×Dic6C22×D311yescharacteristic
338C2×Dic6C22×D311yescharacteristic
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4#6711yescharacteristic
352C3×C4⋊C4#6711yescharacteristic
353C3×C22⋊C4—21no—
354C3×C22⋊C4—21no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4#6711yescharacteristic
363C3×C22⋊C4#6711yescharacteristic
364C3×C22⋊C4#6711yescharacteristic
365C3×C22⋊C4#6711yescharacteristic
366C3×C42—21no—
367C3×C42—61no—
368C3×C42C22×D311yescharacteristic
369C3×C42C22×D311yescharacteristic
370#217—21no—
371#217—21no—
372#217—21no—
373#216—121no—
374#216—121no—
375#215—62no—
376#215—121no—
377#214—62no—
378#214—121no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383C4⋊Dic3—21no—
384C4⋊Dic3—21no—
385C4⋊Dic3—21no—
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394C4×Dic3—21no—
395#208—121no—
396#208—121no—
397#208—122no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8—121no—
411C2×C3⋊C8—121no—
412C2×C3⋊C8—122no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32#13712yes—
419C22×C32C22×D411yescharacteristic
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—84no—
427C32×C4—21no—
428C32×C4—21no—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4C2×#4111yescharacteristic
432C32×C4H(5,𝔽2)11yescharacteristic
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—31no—
440C22×D4—31no—
441C2×Q16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C2×M16—91no—
445C22×C8—91no—
446C4⋊Q8—31no—
447#125—61no—
448#124—31no—
449#123—61no—
450C22⋊Q8—31no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453C22⋊Q8—61no—
454C22⋊Q8—61no—
455#121—31no—
456#121—61no—
457#120—61no—
458C4×Q8—31no—
459C4×D4—31no—
460C4×D4—61no—
461C4×D4D3211yescharacteristic
462C2×C4⋊C4—31no—
463C2×C4⋊C4—31no—
464C2×C22⋊C4—61no—
465#107—91no—
466#107—91no—
467#107—91no—
468C4⋊C8—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—91no—
480C22⋊C8—91no—
481#97—91no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3—122no—
487C23×C3—122no—
488C23×C3—241no—
489C23×C3C2×#6711yescharacteristic
490C23×C3C2×#6711yescharacteristic
491C23×C3C2×#6711yescharacteristic
492C23×C3C2×#6711yescharacteristic
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—42no—
496C22×D3—42no—
497C22×D3—81no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×Q8—61no—
502C3×Q8—241no—
503C3×D4—22no—
504C3×D4—22no—
505C3×D4—32no—
506C3×D4—42no—
507C3×D4—61no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—122no—
511C3×D4—122no—
512C3×D4—241no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—122no—
537C2×C3×C4—241no—
538C2×C3×C4—241no—
539C2×C3×C4—241no—
540C2×C3×C4C2×#6711yescharacteristic
541C2×C3×C4C2×#6711yescharacteristic
542C2×C3×C4C2×#6711yescharacteristic
543C2×C3×C4C2×#6711yescharacteristic
544C2×C3×C4C2×#6711yescharacteristic
545C2×C3×C4C2×#6711yescharacteristic
546C2×C3×C4C2×#6711yescharacteristic
547C2×C3×C4C2×#6711yescharacteristic
548C2×C3×C4C23×D311yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550#67—42no—
551#67—81no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—81no—
559C2×Dic3—81no—
560D12—21no—
561D12—21no—
562D12—21no—
563D12—42no—
564D12#23712yes—
565C4×D3—42no—
566C4×D3—81no—
567Dic6—21no—
568Dic6—21no—
569Dic6—21no—
570Dic6—21no—
571Dic6—81no—
572C3⋊C8—62no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—121no—
582C3⋊C8—121no—
583C3⋊C8—121no—
584C2×C32—22no—
585C2×C32—41no—
586C2×C32#54611yescharacteristic
587C2×C32C2×#13711yescharacteristic
588C2×C32#57611yescharacteristic
589C3×D3—42no—
590C3×D3—81no—
591C24—61no—
592#41—62no—
593#41—121no—
594C2×Q8—31no—
595C2×Q8—31no—
596C2×Q8—61no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—62no—
600C2×D4—61no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—121no—
604C2×D4#62511yescharacteristic
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4C2×D3211yescharacteristic
610C22×C4C2×D3211yescharacteristic
611Q16—361no—
612SD16—182no—
613SD16—361no—
614M16—361no—
615C2×C8—91no—
616C2×C8—91no—
617C2×C8—91no—
618C2×C8—91no—
619C2×C8—361no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4#62511yescharacteristic
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4#62511yescharacteristic
640C22⋊C4#62511yescharacteristic
641C42—61no—
642C42C2×D3211yescharacteristic
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—22no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—62no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—244no—
667C22×C3#94212yes—
668C22×C3#95112yes—
669C22×C3C22×#6711yescharacteristic
670C22×C3C22×#6711yescharacteristic
671C2×D3—22no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—84no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4—121no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4C2×#23711yescharacteristic
699C3×C4#100411yescharacteristic
700C3×C4D3×#4111yescharacteristic
701C3×C4#100911yescharacteristic
702Dic3—41no—
703Dic3—41no—
704Dic3—41no—
705Dic3—41no—
706Dic3—41no—
707Dic3—41no—
708C32#331411yescharacteristic, complemented, Sylow
709C23—61no—
710C23—61no—
711C23—122no—
712C23—122no—
713C23—241no—
714C23C2×#62511yescharacteristic
715C23C2×#62511yescharacteristic
716Q8—61no—
717Q8—61no—
718Q8—61no—
719Q8—61no—
720Q8—241no—
721D4—22no—
722D4—32no—
723D4—61no—
724D4—61no—
725D4—61no—
726D4—122no—
727D4—122no—
728D4—241no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—122no—
740C2×C4—241no—
741C2×C4—241no—
742C2×C4—241no—
743C2×C4C2×#62511yescharacteristic
744C2×C4C2×#62511yescharacteristic
745C2×C4C2×#62511yescharacteristic
746C2×C4C2×#62511yescharacteristic
747C2×C4C22×D3211yescharacteristic
748C8—181no—
749C8—181no—
750C8—181no—
751C8—181no—
752C2×C3—22no—
753C2×C3—22no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—42no—
758C2×C3—41no—
759C2×C3—41no—
760C2×C3—81no—
761C2×C3—122no—
762C2×C3—241no—
763C2×C3#580611yescharacteristic
764C2×C3C2×#94211yescharacteristic
765C2×C3C2×#95111yescharacteristic
766C2×C3#582911yescharacteristic
767C2×C3#583511yescharacteristic
768C2×C3#583511yescharacteristic
769D3—42no—
770D3—81no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—62no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—121no—
782C22—244no—
783C22#6382712yes—
784C22C22×#62511yescharacteristic
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—121no—
790C4—121no—
791C4—121no—
792C4—121no—
793C4—121no—
794C4—121no—
795C4D3×#23711yescharacteristic
796C4#6431411yescharacteristic
797C3—21no—
798C3#8349811yescharacteristic, complemented
799C3#8363511yescharacteristic, complemented
800C2—22no—
801C2—41no—
802C2—122no—
803C2—241no—
804C2C2×#6382711yescharacteristic
805C2#1059524411yescharacteristic
806C2#1059544411yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#5550C2
hypercenterC4×D4D32
hypocenterC32#3314
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5543C2semidirect
3. #10592710C2semidirect
4. #10591188C2semidirect
5. #10591180C2semidirect
6. #10591170C2semidirect
7. #10591169C2semidirect
8. #10591132C2semidirect
9. #10591089C2semidirect
10. #10591087C2semidirect
11. C2×#63562C2semidirect
12. #10590358C2semidirect
13. #10590280C2semidirect
14. #10590269C2semidirect
15. #10590267C2semidirect
21. C2×#3748C22semidirect
27. C2×C3×C4⋊Dic3C22semidirect
30. C3×#924C22semidirect
39. C3×#869C22semidirect
40. C3×C4×Dic6C22semidirect
41. C2×#3718C22semidirect
45. #63657C22semidirect
46. C4⋊(C3⋊(C3⋊C8))C22semidirect
47. #63630C22semidirect
48. #63576C22semidirect
49. #63576C22semidirect
50. #63576C22semidirect
51. #63565C22semidirect
52. #63565C22semidirect
53. #63565C22semidirect
54. #63565C22semidirect
64. #5543D3semidirect
180. C2×C4⋊Dic3C2×D3semidirect
183. #924C2×D3semidirect
198. #869C2×D3semidirect
199. C4×Dic6C2×D3semidirect
708. C32#3314semidirect
798. C3#83498semidirect
799. C3#83635semidirect

Maximal subgroups

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

subgroupindex
C3×#55502
C3×#55432
#105927102
#105911882
#105911802
#105911702
#105911692
#105911322
#105910892
#105910872
C2×#635622
#105903582
#105902802
#105902692
#105902672
#836353
#834983