Finite Group Databasebeta

← #11872295

Subgroups — #11872295

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5827C211yesmaximal, characteristic, complemented
2#10594985C211yesmaximal, characteristic, complemented
3#10592937C211yesmaximal, characteristic, complemented
4C3×#5238C211yesmaximal, characteristic, complemented
5#10591617C211yesmaximal, characteristic, complemented
6#10591566C211yesmaximal, characteristic, complemented
7#10591547C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10591481C211yesmaximal, characteristic, complemented
10Dic3×#213C211yesmaximal, characteristic, complemented
11#10591411C211yesmaximal, characteristic, complemented
12#10591404C211yesmaximal, characteristic, complemented
13#10591133C211yesmaximal, characteristic, complemented
14#10591091C211yesmaximal, characteristic, complemented
15#10591056C211yesmaximal, characteristic, complemented
16#82568—31nomaximal
17#80072—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×#3755C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21#64139C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×D4×Dic3—21no—
26C3×D4×Dic3—21no—
27C3×D4×Dic3C2211yescharacteristic
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#213C2211yescharacteristic
30C3×#930C2211yescharacteristic
31C3×#926—21no—
32C3×#926C2211yescharacteristic
33C2×C3×C4⋊Dic3—21no—
34C2×C3×C4⋊Dic3C2211yescharacteristic
35#63971—21no—
36#63958—21no—
37#63911C2211yescharacteristic
38#63894C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40#63890—21no—
41#63869C2211yescharacteristic
42#63854—21no—
43#63662C2211yescharacteristic
44#63659C2211yescharacteristic
45#63657C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#830C2211yescharacteristic
49#63575C2211yescharacteristic
50#63575C2211yescharacteristic
51#63574C2211yescharacteristic
52#63574C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#520—31no—
62#5827D311yescharacteristic, complemented
63#5619—31no—
64#5535—31no—
65C3×#449—31no—
66#5238—31no—
67#5238—31no—
68#5238—61no—
69#5238D311yescharacteristic, complemented
70#5164—31no—
71#5163—31no—
72#5150—31no—
73Dic3×D8—31no—
74#5034—31no—
75#5027—31no—
76#5026—31no—
77C4×#215—31no—
78#5022—31no—
79#5015—31no—
80#5014—31no—
81C4×#213—31no—
82#5009—31no—
83#5000—31no—
84#4968—31no—
85#4967—31no—
86#4796—31no—
87#4788—31no—
88#4785—31no—
89#4766—31no—
90#4736—31no—
91#4720—31no—
92C32×#41—22no—
93C32×#41—22no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C22×C3×Dic3—21no—
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C2×C3×D12C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110#3755—22no—
111#3753—22no—
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×#217D411yescharacteristic
120C3×#215—22no—
121C3×#213—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3D411yescharacteristic
127C3×C4⋊Dic3D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141#3119—91noSylow
142C2×C3×#41—21no—
143C2×C3×#41C2×D311yescharacteristic
144C2×C3×#41C2×D311yescharacteristic
145C2×C3×SD16—31no—
146C2×C3×D8—31no—
147C3×#121—31no—
148C3×C4×Q8—31no—
149C3×C4×Q8—31no—
150C3×C4×D4—31no—
151C3×C4×D4—31no—
152C3×C4×D4—61no—
153C3×C4×D4—61no—
154C3×#117—31no—
155C3×#117—61no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4—61no—
158Q8×Dic3C2×D311yescharacteristic
159Q8×Dic3C2×D311yescharacteristic
160C2×#215—31no—
161C2×#215—31no—
162C2×#215—61no—
163C2×#215C2×D311yescharacteristic
164#940—31no—
165#939—61no—
166#938—61no—
167D4×Dic3—21no—
168D4×Dic3—21no—
169D4×Dic3—31no—
170D4×Dic3C2×D311yescharacteristic
171D4×Dic3C2×D311yescharacteristic
172C2×#213—31no—
173C2×#213—31no—
174C2×#213—61no—
175C2×#213C2×D311yescharacteristic
176#930—31no—
177#930—31no—
178#930—61no—
179#930C2×D311yescharacteristic
180#926—21no—
181#926C2×D311yescharacteristic
182C2×C4⋊Dic3—21no—
183C2×C4⋊Dic3C2×D311yescharacteristic
184#894—61no—
185#894—61no—
186#893—31no—
187#890—31no—
188#886—61no—
189#884—61no—
190#884—61no—
191#883—61no—
192#874—31no—
193C4×D12—31no—
194C4×D12—31no—
195#870—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×C22⋊C8—31no—
199#835—31no—
200#835—31no—
201#835—61no—
202#835C2×D311yescharacteristic
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—61no—
208#832C2×D311yescharacteristic
209#830—31no—
210#830—31no—
211#830—61no—
212#830C2×D311yescharacteristic
213#821—31no—
214#821—31no—
215#818—31no—
216#818—31no—
217#815—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220C8×Dic3—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#808—31no—
229#807—31no—
230#807—31no—
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C23×C32C2×D411yescharacteristic
237C22×C3⋊D3—21no—
238C22×C3×D3—21no—
239C32×Q8—21no—
240C32×Q8#4112yes—
241C32×D4—24no—
242C32×D4—21no—
243C32×D4#4112yes—
244C2×C32×C4—24no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250#638—81no—
251C2×C3⋊Dic3—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C3×#67—81no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3—81no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267#626—81no—
268#626—81no—
269#624—81no—
270D3×Dic3—81no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#540—91no—
276#520—31no—
277#481—91no—
278#480—91no—
279#479—91no—
280#478—91no—
281#460—91no—
282#459—91no—
283#449—31no—
284#449—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C3×#41—22no—
291C3×#41—22no—
292C3×#41—22no—
293C3×#41—22no—
294C3×#41—42no—
295C3×#41—42no—
296C2×C3×Q8—21no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×D4—21no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4—41no—
304C2×C3×D4—61no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—41no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C2×#67—21no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—121no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—61no—
326C2×D12—31no—
327C2×D12—31no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12C22×D311yescharacteristic
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C3×SD16—62no—
336C3×D8—62no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C3×C4⋊C4—31no—
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×C22⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—31no—
353C3×C42—31no—
354C3×C42—61no—
355C3×C42—61no—
356#217—21no—
357#217—21no—
358#217—61no—
359#217#6711yescharacteristic
360#217#6711yescharacteristic
361#215—22no—
362#215—62no—
363#215—62no—
364#215—122no—
365#213—22no—
366#213—62no—
367#213—62no—
368#213—122no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—121no—
376C4⋊Dic3—21no—
377C4⋊Dic3—21no—
378C4⋊Dic3—21no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3#6711yescharacteristic
384C4⋊Dic3#6711yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3C22×D311yescharacteristic
394C4×Dic3C22×D311yescharacteristic
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403C22×C32—21no—
404C22×C32—22no—
405C22×C32—21no—
406C22×C32—21no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C32×C4—21no—
417C32×C4—22no—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
420C3⋊Dic3—41no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C2×#41D3211yescharacteristic
429C2×SD16—31no—
430C2×SD16—91no—
431C2×D8—31no—
432C2×D8—91no—
433#127—91no—
434#125—91no—
435#123—181no—
436#123—181no—
437#121—31no—
438#121—91no—
439#121—181no—
440#121—181no—
441C4×Q8—31no—
442C4×Q8—31no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—61no—
446C4×D4—61no—
447C4×D4—91no—
448C4×D4—91no—
449#117—31no—
450#117—61no—
451C2×C4⋊C4—31no—
452C2×C4⋊C4—61no—
453#107—91no—
454#107—91no—
455#106—91no—
456#106—91no—
457C4⋊C8—91no—
458C4⋊C8—91no—
459#103—31no—
460#103—91no—
461#102—31no—
462#102—91no—
463#102—91no—
464#102—91no—
465#102—91no—
466#102—91no—
467C22⋊C8—31no—
468C22⋊C8—91no—
469#97—91no—
470C4×C8—91no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—41no—
475C23×C3—61no—
476C23×C3D3×D411yescharacteristic
477C23×C3C2×#6711yescharacteristic
478C22×D3—21no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—121no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—22no—
485C3×Q8—41no—
486C3×Q8#23512yes—
487C3×Q8#23712yes—
488C3×D4—24no—
489C3×D4—24no—
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—22no—
493C3×D4—41no—
494C3×D4—44no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—241no—
498C3×D4#23512yes—
499C3×D4#23712yes—
500C2×C3×C4—24no—
501C2×C3×C4—24no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—44no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—241no—
522C2×C3×C4—241no—
523C2×C3×C4—241no—
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4C2×#6711yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—81no—
529#67—241no—
530#67—241no—
531#67—241no—
532#67—241no—
533#67—242no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—81no—
540C2×Dic3—81no—
541C2×Dic3—81no—
542C2×Dic3—121no—
543C2×Dic3—241no—
544C2×Dic3C2×#6711yescharacteristic
545C2×Dic3C2×#6711yescharacteristic
546C2×Dic3C2×#6711yescharacteristic
547C2×Dic3C2×#6711yescharacteristic
548D12—21no—
549D12—21no—
550D12—61no—
551D12—61no—
552D12—61no—
553D12—61no—
554D12—121no—
555D12—121no—
556D12—241no—
557D12—241no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—241no—
561C3×C8—61no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C3⋊C8—61no—
566C3⋊C8—61no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—121no—
570C3⋊C8—121no—
571C2×C32—41no—
572C2×C32—42no—
573C2×C32#52511yescharacteristic
574C2×C32#57611yescharacteristic
575C2×C32#57711yescharacteristic
576C3⋊D3—81no—
577C3×D3—81no—
578#41—22no—
579#41—22no—
580C2×Q8C2×D3211yescharacteristic
581C2×D4—21no—
582C2×D4—31no—
583C2×D4—61no—
584C2×D4—91no—
585C2×D4—181no—
586C2×D4—181no—
587C2×D4—181no—
588C2×D4C2×D3211yescharacteristic
589C22×C4—21no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4C2×D3211yescharacteristic
596SD16—62no—
597SD16—182no—
598D8—62no—
599D8—182no—
600C2×C8—31no—
601C2×C8—31no—
602C2×C8—91no—
603C2×C8—91no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—91no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C22⋊C4—31no—
616C22⋊C4—31no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C42—31no—
624C42—31no—
625C42—61no—
626C42—61no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—22no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—41no—
637C22×C3—42no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3C2×D3×D411yescharacteristic
650C22×C3C22×#6711yescharacteristic
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—241no—
661C2×D3—241no—
662C2×D3—241no—
663C3×C4—21no—
664C3×C4—22no—
665C3×C4—21no—
666C3×C4—22no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—41no—
670C3×C4—42no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4C2×#23511yescharacteristic
679C3×C4C2×#23511yescharacteristic
680C3×C4C2×#23711yescharacteristic
681C3×C4C2×#23711yescharacteristic
682Dic3—21no—
683Dic3—21no—
684Dic3—21no—
685Dic3—21no—
686Dic3—41no—
687Dic3—41no—
688Dic3—41no—
689Dic3—121no—
690Dic3—121no—
691Dic3—241no—
692C32#311911yescharacteristic, complemented, Sylow
693C23—21no—
694C23—61no—
695C23—181no—
696C23D3×#6711yescharacteristic
697Q8—21no—
698Q8#380412yes—
699D4—24no—
700D4—21no—
701D4—61no—
702D4—61no—
703D4—181no—
704D4—181no—
705D4—241no—
706D4—721no—
707D4—721no—
708D4—721no—
709D4#380412yes—
710C2×C4—24no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—31no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—181no—
722C2×C4—241no—
723C2×C4—241no—
724C2×C4—241no—
725C2×C4—721no—
726C2×C4—721no—
727C2×C4D3×#6711yescharacteristic
728C2×C4C22×D3211yescharacteristic
729C8—61no—
730C8—61no—
731C8—181no—
732C8—181no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—41no—
737C2×C3—42no—
738C2×C3—41no—
739C2×C3—42no—
740C2×C3—81no—
741C2×C3—82no—
742C2×C3—241no—
743C2×C3#558611yescharacteristic
744C2×C3#576911yescharacteristic
745C2×C3#577511yescharacteristic
746C2×C3#579111yescharacteristic
747C2×C3#583511yescharacteristic
748C2×C3#583711yescharacteristic
749D3—81no—
750D3—241no—
751D3—241no—
752D3—481no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—22no—
757C22—41no—
758C22—41no—
759C22—121no—
760C22—121no—
761C22—121no—
762C22—361no—
763C22—361no—
764C22—361no—
765C22C2×D3×#6711yescharacteristic
766C4—21no—
767C4—22no—
768C4—61no—
769C4—61no—
770C4—61no—
771C4—61no—
772C4—121no—
773C4—121no—
774C4—121no—
775C4—361no—
776C4C2×#380411yescharacteristic
777C4C2×#380411yescharacteristic
778C3—21no—
779C3#8007211yescharacteristic, complemented
780C3#8256811yescharacteristic, complemented
781C2—41no—
782C2—42no—
783C2—241no—
784C2—721no—
785C2#1059545511yescharacteristic
786C2#1059545611yescharacteristic
787C2#1059549811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3119
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×#5827C2semidirect
2. #10594985C2semidirect
3. #10592937C2semidirect
4. C3×#5238C2semidirect
5. #10591617C2semidirect
6. #10591566C2semidirect
7. #10591547C2semidirect
8. #10591536C2semidirect
9. #10591481C2semidirect
10. Dic3×#213C2semidirect
11. #10591411C2semidirect
12. #10591404C2semidirect
13. #10591133C2semidirect
14. #10591091C2semidirect
15. #10591056C2semidirect
62. #5827D3semidirect
69. #5238D3semidirect
692. C32#3119semidirect
779. C3#80072semidirect
780. C3#82568semidirect

Maximal subgroups

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

subgroupindex
C3×#58272
#105949852
#105929372
C3×#52382
#105916172
#105915662
#105915472
#105915362
#105914812
Dic3×#2132
#105914112
#105914042
#105911332
#105910912
#105910562
#825683
#800723