Finite Group Databasebeta

← #11878507

Subgroups — #11878507

Order 1152.

880 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5833C211yesmaximal, characteristic, complemented
2#10595004C211yesmaximal, characteristic, complemented
3#10592938C211yesmaximal, characteristic, complemented
4C3×#5238C211yesmaximal, characteristic, complemented
5#10591655C211yesmaximal, characteristic, complemented
6#10591596C211yesmaximal, characteristic, complemented
7#10591587C211yesmaximal, characteristic, complemented
8#10591551C211yesmaximal, characteristic, complemented
9#10591519C211yesmaximal, characteristic, complemented
10#10591498C211yesmaximal, characteristic, complemented
11#10591462C211yesmaximal, characteristic, complemented
12#10591413C211yesmaximal, characteristic, complemented
13#10591145C211yesmaximal, characteristic, complemented
14#10591135C211yesmaximal, characteristic, complemented
15#10591089C211yesmaximal, characteristic, complemented
16#83426—31nomaximal
17#80095—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23#64133C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27C3×#939—21no—
28C3×#939—21no—
29C3×#938C2211yescharacteristic
30C3×#938C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×#930—21no—
33C3×#930C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C3×#924—21no—
36#63970—21no—
37#63970—21no—
38#63908C2211yescharacteristic
39D3×C4⋊Dic3C2211yescharacteristic
40#63887—21no—
41#63885—21no—
42#63857C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63662C2211yescharacteristic
46#63659C2211yescharacteristic
47#63657C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63576C2211yescharacteristic
52#63576C2211yescharacteristic
53#63575C2211yescharacteristic
54#63575C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#537—31no—
62#5833—31no—
63#5833D311yescharacteristic, complemented
64#5608—31no—
65C3×#449—31no—
66#5239—31no—
67#5239—31no—
68#5239—61no—
69#5238D311yescharacteristic, complemented
70#5234—31no—
71#5174—31no—
72#5173—31no—
73#5158—31no—
74#5157—31no—
75#5051—31no—
76#5049—31no—
77#5047—31no—
78#5044—31no—
79#5042—31no—
80#5038—31no—
81#5037—31no—
82#5033—31no—
83#5033—31no—
84#4970—31no—
85#4967—31no—
86#4813—31no—
87#4811—31no—
88#4780—31no—
89#4774—31no—
90#4727—31no—
91#4722—31no—
92C32×#41—41no—
93C32×#41—41no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67D411yescharacteristic
104C2×C3×#67D411yescharacteristic
105C22×C3×Dic3—21no—
106C3×#235—41no—
107C3×#235—41no—
108C2×C3×D12D411yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6D411yescharacteristic
113C2×#625—21no—
114C2×#625—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117#3795—41no—
118#3795—41no—
119#3757—21no—
120#3756—41no—
121#3754—41no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123#3750—21no—
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#217—21no—
127C3×#217—21no—
128C3×#215—41no—
129C3×#213—41no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145#3711—41no—
146D3×C3⋊C8—41no—
147#3203—91noSylow
148C2×C3×#41—21no—
149C2×C3×#41—31no—
150C2×C3×#41C2×D311yescharacteristic
151C2×C3×#41C2×D311yescharacteristic
152C2×#237—31no—
153C2×#235—31no—
154C2×#235C2×D311yescharacteristic
155C2×C3×SD16—31no—
156C2×C3×D8—31no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—31no—
159C3×C22⋊Q8—61no—
160C3×#121—31no—
161C3×#121—31no—
162C3×#121—31no—
163C3×#121—61no—
164C3×#121—61no—
165C3×#121—61no—
166C2×C3×C4⋊C4—31no—
167#946—61no—
168#946C2×D311yescharacteristic
169#946C2×D311yescharacteristic
170C2×#216—31no—
171C2×#216—31no—
172C2×#216—61no—
173C2×#215C2×D311yescharacteristic
174#939—21no—
175#939—21no—
176#939—61no—
177#939—61no—
178#939—61no—
179#938—31no—
180#938—61no—
181#938—61no—
182#938C2×D311yescharacteristic
183#938C2×D311yescharacteristic
184C2×#214—31no—
185C2×#214—31no—
186C2×#214—61no—
187C2×#213C2×D311yescharacteristic
188#930—21no—
189#930—31no—
190#930C2×D311yescharacteristic
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3C2×D311yescharacteristic
193#924—21no—
194#924—31no—
195#924—31no—
196#924—31no—
197#924—61no—
198C2×#208—31no—
199C22×C3⋊C8—31no—
200C2×ΓL(1,𝔽25)—31no—
201C2×D3×C8—31no—
202#897—31no—
203D3×C4⋊C4—31no—
204#884—61no—
205#878—61no—
206C3×#103—31no—
207C3×#102—31no—
208C3×C22⋊C8—31no—
209#835—31no—
210#835—31no—
211#835—61no—
212#835C2×D311yescharacteristic
213#832—31no—
214#832—31no—
215#832—31no—
216#832—31no—
217#832—61no—
218#832C2×D311yescharacteristic
219#830—31no—
220#830—31no—
221#830—31no—
222#830—31no—
223#830—61no—
224#830C2×D311yescharacteristic
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—31no—
227#818—31no—
228#818—31no—
229#816—31no—
230#816—31no—
231#810—31no—
232#810—31no—
233#809—31no—
234#809—31no—
235#807—31no—
236#807—31no—
237#807—31no—
238#807—31no—
239#807—31no—
240#807—31no—
241C23×C32—21no—
242C23×C32C2×D411yescharacteristic
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C22×C3×D3C2×D411yescharacteristic
246C32×Q8—21no—
247C32×Q8—21no—
248C32×D4—21no—
249C32×D4—21no—
250C32×D4—42no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—42no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259#634—21no—
260#634—21no—
261C3×#67—41no—
262C3×#67—41no—
263C3×#67—81no—
264C3×#67—81no—
265C3×#67—81no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—81no—
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12—21no—
274C3×D12—41no—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×Dic6—41no—
280#625—42no—
281#625—81no—
282D3×Dic3—42no—
283D3×Dic3—81no—
284C3⋊(C3⋊C8)—21no—
285C3⋊(C3⋊C8)—21no—
286C3×C3⋊C8—21no—
287C3×C3⋊C8—21no—
288#537—31no—
289#537—91no—
290#484—91no—
291#484—91no—
292#480—91no—
293#480—91no—
294#468—91no—
295#468—91no—
296#467—91no—
297#466—91no—
298#452—91no—
299#452—91no—
300#449—31no—
301#449—91no—
302#408—91no—
303C3×#41—41no—
304C3×#41—41no—
305C3×#41—41no—
306C3×#41—41no—
307C3×#41—42no—
308C3×#41—42no—
309C3×#41—121no—
310C3×#41—121no—
311C2×C3×Q8—21no—
312C2×C3×Q8—31no—
313C2×C3×Q8C22×D311yescharacteristic
314C2×C3×Q8C22×D311yescharacteristic
315C2×C3×D4—21no—
316C2×C3×D4—21no—
317C2×C3×D4—21no—
318C2×C3×D4—31no—
319C2×C3×D4—31no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—41no—
323C2×C3×D4—61no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C2×C3×D4C22×D311yescharacteristic
327C2×C3×D4C22×D311yescharacteristic
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—41no—
334C22×C3×C4—61no—
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C2×#67—21no—
338C2×#67—21no—
339C2×#67—21no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67#6711yescharacteristic
345C2×#67#6711yescharacteristic
346C22×Dic3—21no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349#237—121no—
350#237—121no—
351#235—41no—
352#235—41no—
353#235—121no—
354#235—121no—
355C2×D12#6711yescharacteristic
356C2×D12C22×D311yescharacteristic
357C2×C4×D3—61no—
358C2×C4×D3—61no—
359C2×C4×D3C22×D311yescharacteristic
360C2×C4×D3C22×D311yescharacteristic
361C2×Dic6—31no—
362C2×Dic6—31no—
363C2×Dic6—61no—
364C2×Dic6#6711yescharacteristic
365C3×SD16—121no—
366C3×D8—121no—
367C2×C3×C8—31no—
368C2×C3×C8—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4—61no—
375C3×C22⋊C4—61no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380#217—21no—
381#217—21no—
382#217—61no—
383#217—61no—
384#217—61no—
385#217—61no—
386#217—121no—
387#216—121no—
388#216—121no—
389#216—122no—
390#215—41no—
391#214—121no—
392#214—121no—
393#214—122no—
394#213—41no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400C4⋊Dic3—21no—
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3C22×D311yescharacteristic
407C4⋊Dic3C22×D311yescharacteristic
408C4⋊Dic3C22×D311yescharacteristic
409Dic3⋊C4—21no—
410Dic3⋊C4—21no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4—121no—
416#208—121no—
417C2×C3⋊C8—31no—
418C2×C3⋊C8—31no—
419C2×C3⋊C8—31no—
420C2×C3⋊C8—31no—
421C2×C3⋊C8—61no—
422C2×C3⋊C8—61no—
423C2×C3⋊C8—121no—
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426ΓL(1,𝔽25)—121no—
427D3×C8—121no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32C22×D411yescharacteristic
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C32×C4—21no—
445C32×C4—41no—
446C32×C4H(5,𝔽2)11yescharacteristic
447C32×C4H(5,𝔽2)11yescharacteristic
448C3⋊Dic3—41no—
449C3⋊Dic3—41no—
450C3×Dic3—21no—
451C3×Dic3—21no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C2×#41—31no—
456C2×#41—91no—
457C2×#41D3211yescharacteristic
458C2×Q16—91no—
459C2×SD16—31no—
460C2×SD16—91no—
461C2×D8—31no—
462C2×M16—91no—
463C22×C8—91no—
464C22⋊Q8—31no—
465C22⋊Q8—31no—
466C22⋊Q8—61no—
467C22⋊Q8—91no—
468C22⋊Q8—91no—
469C22⋊Q8—181no—
470#121—31no—
471#121—31no—
472#121—31no—
473#121—61no—
474#121—61no—
475#121—61no—
476#121—91no—
477#121—181no—
478#121—181no—
479#121—181no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—91no—
482#107—91no—
483#107—91no—
484#107—91no—
485#107—91no—
486#103—31no—
487#103—91no—
488#103—91no—
489#103—91no—
490#102—31no—
491#102—91no—
492#102—91no—
493#102—91no—
494C22⋊C8—31no—
495C22⋊C8—91no—
496C22⋊C8—91no—
497C22⋊C8—91no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—31no—
502C23×C3—31no—
503C23×C3—41no—
504C23×C3—61no—
505C23×C3D3×D411yescharacteristic
506C23×C3C2×#6711yescharacteristic
507C22×D3—21no—
508C22×D3C2×#6711yescharacteristic
509C22×D3C2×#6711yescharacteristic
510C3×Q8—22no—
511C3×Q8—21no—
512C3×Q8—21no—
513C3×Q8—21no—
514C3×Q8—21no—
515C3×Q8—41no—
516C3×Q8—121no—
517C3×D4—22no—
518C3×D4—21no—
519C3×D4—21no—
520C3×D4—21no—
521C3×D4—21no—
522C3×D4—41no—
523C3×D4—42no—
524C3×D4—42no—
525C3×D4—44no—
526C3×D4—61no—
527C3×D4—61no—
528C3×D4—121no—
529C3×D4—121no—
530C3×D4—121no—
531C3×D4—241no—
532C3×D4—241no—
533C3×D4—241no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—41no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—42no—
548C2×C3×C4—42no—
549C2×C3×C4—44no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—241no—
558C2×C3×C4D3×D411yescharacteristic
559C2×C3×C4C2×#6711yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562#67—41no—
563#67—41no—
564#67—81no—
565#67—81no—
566#67—81no—
567#67—122no—
568#67—122no—
569#67—241no—
570#67—241no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—81no—
579C2×Dic3—121no—
580C2×Dic3—121no—
581C2×Dic3—122no—
582C2×Dic3—241no—
583C2×Dic3C2×#6711yescharacteristic
584C2×Dic3C2×#6711yescharacteristic
585D12—21no—
586D12—21no—
587D12—41no—
588C4×D3—21no—
589C4×D3—21no—
590C4×D3—21no—
591C4×D3—21no—
592C4×D3—122no—
593C4×D3—241no—
594Dic6—41no—
595Dic6—61no—
596Dic6—61no—
597Dic6—61no—
598Dic6—61no—
599Dic6—121no—
600Dic6—121no—
601C3×C8—61no—
602C3×C8—61no—
603C3⋊C8—21no—
604C3⋊C8—21no—
605C3⋊C8—61no—
606C3⋊C8—61no—
607C3⋊C8—61no—
608C3⋊C8—61no—
609C3⋊C8—121no—
610C3⋊C8—121no—
611C2×C32—41no—
612C2×C32—81no—
613C2×C32#53411yescharacteristic
614C2×C32#57611yescharacteristic
615C2×C32#57811yescharacteristic
616C3×D3—41no—
617C3×D3—41no—
618C3×D3—81no—
619#41—41no—
620#41—41no—
621#41—121no—
622#41—121no—
623#41—361no—
624#41—361no—
625C2×Q8—31no—
626C2×Q8—91no—
627C2×Q8C2×D3211yescharacteristic
628C2×D4—21no—
629C2×D4—31no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—31no—
633C2×D4—61no—
634C2×D4—61no—
635C2×D4—61no—
636C2×D4—181no—
637C2×D4—181no—
638C2×D4C2×D3211yescharacteristic
639C22×C4—21no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—61no—
643C22×C4—181no—
644C22×C4—181no—
645C22×C4C2×D3211yescharacteristic
646Q16—361no—
647SD16—121no—
648SD16—361no—
649D8—121no—
650M16—361no—
651C2×C8—31no—
652C2×C8—31no—
653C2×C8—91no—
654C2×C8—91no—
655C2×C8—361no—
656C4⋊C4—31no—
657C4⋊C4—31no—
658C4⋊C4—31no—
659C4⋊C4—61no—
660C4⋊C4—61no—
661C4⋊C4—61no—
662C4⋊C4—91no—
663C4⋊C4—181no—
664C4⋊C4—181no—
665C4⋊C4—181no—
666C22⋊C4—61no—
667C22⋊C4—61no—
668C22⋊C4—61no—
669C22⋊C4—61no—
670C22⋊C4—61no—
671C22⋊C4—181no—
672C22⋊C4—181no—
673C22⋊C4—181no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—42no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3C2×D3×D411yescharacteristic
703C22×C3C22×#6711yescharacteristic
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—21no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—41no—
718C3×C4—42no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—61no—
722C3×C4—61no—
723C3×C4—121no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4#100411yescharacteristic
727C3×C4#100411yescharacteristic
728C3×C4#100411yescharacteristic
729C3×C4#100411yescharacteristic
730Dic3—21no—
731Dic3—21no—
732Dic3—41no—
733Dic3—41no—
734Dic3—41no—
735Dic3—121no—
736Dic3—121no—
737Dic3—121no—
738Dic3—121no—
739Dic3—241no—
740Dic3—241no—
741C32#320311yescharacteristic, complemented, Sylow
742C23—21no—
743C23—31no—
744C23—31no—
745C23—61no—
746C23D3×#6711yescharacteristic
747Q8—21no—
748Q8—21no—
749Q8—121no—
750Q8—181no—
751Q8—181no—
752D4—21no—
753D4—21no—
754D4—42no—
755D4—61no—
756D4—61no—
757D4—121no—
758D4—121no—
759D4—121no—
760D4—241no—
761D4—241no—
762D4—241no—
763D4—362no—
764D4—721no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—31no—
769C2×C4—31no—
770C2×C4—42no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—181no—
779C2×C4—181no—
780C2×C4—241no—
781C2×C4—362no—
782C2×C4—721no—
783C2×C4D3×#6711yescharacteristic
784C2×C4C22×D3211yescharacteristic
785C8—61no—
786C8—61no—
787C8—181no—
788C8—181no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—41no—
793C2×C3—41no—
794C2×C3—81no—
795C2×C3—82no—
796C2×C3—81no—
797C2×C3—81no—
798C2×C3—121no—
799C2×C3—121no—
800C2×C3—241no—
801C2×C3#558911yescharacteristic
802C2×C3#577111yescharacteristic
803C2×C3#577411yescharacteristic
804C2×C3#580411yescharacteristic
805C2×C3#583511yescharacteristic
806C2×C3#583811yescharacteristic
807D3—41no—
808D3—41no—
809D3—81no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—61no—
817C22—61no—
818C22—61no—
819C22—61no—
820C22—61no—
821C22—61no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22C2×D3×#6711yescharacteristic
826C4—21no—
827C4—41no—
828C4—61no—
829C4—61no—
830C4—121no—
831C4—121no—
832C4—121no—
833C4—361no—
834C4—361no—
835C4#6433011yescharacteristic
836C4#6433011yescharacteristic
837C3—21no—
838C3#8009511yescharacteristic, complemented
839C3#8342611yescharacteristic, complemented
840C2—41no—
841C2—81no—
842C2—121no—
843C2—121no—
844C2—241no—
845C2#1059545411yescharacteristic
846C2#1059546711yescharacteristic
847C2#1059552411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3203
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5833C2semidirect
2. #10595004C2semidirect
3. #10592938C2semidirect
4. C3×#5238C2semidirect
5. #10591655C2semidirect
6. #10591596C2semidirect
7. #10591587C2semidirect
8. #10591551C2semidirect
9. #10591519C2semidirect
10. #10591498C2semidirect
11. #10591462C2semidirect
12. #10591413C2semidirect
13. #10591145C2semidirect
14. #10591135C2semidirect
15. #10591089C2semidirect
63. #5833D3semidirect
69. #5238D3semidirect
741. C32#3203semidirect
838. C3#80095semidirect
839. C3#83426semidirect

Maximal subgroups

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

subgroupindex
C3×#58332
#105950042
#105929382
C3×#52382
#105916552
#105915962
#105915872
#105915512
#105915192
#105914982
#105914622
#105914132
#105911452
#105911352
#105910892
#834263
#800953