Finite Group Databasebeta

← #11872768

Subgroups — #11872768

Order 1152.

889 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic, complemented
2#10594985C211yesmaximal, characteristic, complemented
3#10592702C211yesmaximal, characteristic, complemented
4C3×#5003C211yesmaximal, characteristic, complemented
5#10591162C211yesmaximal, characteristic, complemented
6#10591160C211yesmaximal, characteristic, complemented
7#10591056C211yesmaximal, characteristic, complemented
8#10590589C211yesmaximal, characteristic, complemented
9#10590547C211yesmaximal, characteristic, complemented
10#10590547C211yesmaximal, characteristic, complemented
11#10590545C211yesmaximal, characteristic, complemented
12#10590542C211yesmaximal, characteristic, complemented
13#10590456C211yesmaximal, characteristic, complemented
14#10590455C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#82542—31nomaximal
17#81354—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C32×#117C2211yescharacteristic
20#64139C2211yescharacteristic
21C3×#930C2211yescharacteristic
22C3×#926C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×#893C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×D3×C22⋊C4—21no—
28C3×D3×C22⋊C4—21no—
29C3×C4×D12—21no—
30C3×C4×D12—21no—
31#63971—21no—
32#63958—21no—
33#63911C2211yescharacteristic, complemented
34#63894C2211yescharacteristic, complemented
35Dic3×D12C2211yescharacteristic, complemented
36#63890—21no—
37#63869C2211yescharacteristic, complemented
38#63854—21no—
39C2×#3714C2211yescharacteristic
40C2×#3714C2211yescharacteristic
41C2×#3713C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63657C2211yescharacteristic
44#63636C2211yescharacteristic, complemented
45#63636C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic
49C3×#809C2211yescharacteristic, complemented
50C3×#809C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#518—31no—
62#5619—31no—
63#5535—31no—
64#5521D311yescharacteristic, complemented
65C3×#482—31no—
66#5217—31no—
67#5217—31no—
68#5036—31no—
69#5015—31no—
70#5015—31no—
71#5014—31no—
72#5014—31no—
73C4×#213—31no—
74C4×#213—31no—
75#5009—31no—
76#5009—31no—
77#5003—31no—
78#5003—31no—
79#5003—61no—
80#5003D311yescharacteristic, complemented
81#5000—31no—
82#4891—31no—
83#4872—31no—
84#4871—31no—
85#4869—31no—
86#4786—31no—
87#4786—31no—
88#4785—31no—
89#4756—31no—
90#4732—31no—
91#4720—31no—
92C23×C3×D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×D12—21no—
98C2×C3×D12—22no—
99C2×C3×D12—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C42—21no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217D411yescharacteristic
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3D411yescharacteristic
127C3×C4⋊Dic3D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137#3714—22no—
138#3714—22no—
139#3713—22no—
140#3713—22no—
141#3122—91noSylow
142C22×C3×D4—31no—
143C22×D12C2×D311yescharacteristic
144C3×#121—31no—
145C3×C4×D4—31no—
146C3×C4×D4—31no—
147C3×C4×D4—31no—
148C3×C4×D4—31no—
149C3×C4×D4—61no—
150C3×C4×D4—61no—
151C3×#117—21no—
152C3×#117—31no—
153C3×#117C2×D311yescharacteristic
154C3×#117C2×D311yescharacteristic
155C2×C3×C22⋊C4—61no—
156C2×C3×C22⋊C4—61no—
157#940—31no—
158#939—61no—
159#938—61no—
160D4×Dic3—31no—
161C2×#213—31no—
162C2×#213—31no—
163C2×#213—31no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—31no—
167#930—31no—
168#930—31no—
169#930—61no—
170#930C2×D311yescharacteristic
171#926C2×D311yescharacteristic
172C2×D24—31no—
173C2×D24—31no—
174#894—61no—
175#894—61no—
176#893—31no—
177#893C2×D311yescharacteristic
178#893C2×D311yescharacteristic
179#893C2×D311yescharacteristic
180#893C2×D311yescharacteristic
181#890—31no—
182#886—61no—
183#884—61no—
184#884—61no—
185#883—61no—
186D3×C22⋊C4—21no—
187D3×C22⋊C4—21no—
188#874—31no—
189C4×D12—21no—
190C4×D12—21no—
191C4×D12—31no—
192C4×D12—31no—
193#870—31no—
194C3×#107—31no—
195C3×#106—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×C22⋊C8—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#830—31no—
204#830—31no—
205#830—61no—
206#830C2×D311yescharacteristic
207#821—31no—
208#821—31no—
209#815—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212C8×Dic3—31no—
213#809—31no—
214#809—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—61no—
220#809—61no—
221#809C2×D311yescharacteristic, complemented
222#809C2×D311yescharacteristic, complemented
223#808—31no—
224#808—31no—
225#808—61no—
226#808C2×D311yescharacteristic, complemented
227#807—31no—
228#807—31no—
229#807—61no—
230#807C2×D311yescharacteristic, complemented
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—24no—
240C22×C3×D3—21no—
241C22×C3×D3—81no—
242C22×C3×D3—81no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249#638—81no—
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C3×#67—81no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—24no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12#4112yes—
265C3×D12#4112yes—
266C3×C4×D3—81no—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269C3×C4×D3—81no—
270#626—81no—
271#626—81no—
272#624—81no—
273D3×Dic3—81no—
274C3⋊(C3⋊C8)—21no—
275C3⋊(C3⋊C8)—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#540—91no—
279#518—31no—
280#482—31no—
281#482—91no—
282#478—91no—
283#478—91no—
284#459—91no—
285#459—91no—
286#447—91no—
287#447—91no—
288#442—91no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—91no—
293C24×C3—61no—
294C23×D3—21no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—62no—
299C2×C3×D4—62no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C22×C3×C4—21no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—21no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—121no—
315C22×Dic3—61no—
316C2×D12—21no—
317C2×D12—22no—
318C2×D12—22no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12C22×D311yescharacteristic
325C2×D12C22×D311yescharacteristic
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C22⋊C4—21no—
346C3×C22⋊C4—21no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—41no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—21no—
356C3×C42—21no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42—41no—
360#217—61no—
361#217#6711yescharacteristic
362#217#6711yescharacteristic
363#213—62no—
364#213—62no—
365#213—62no—
366#213—62no—
367#213—62no—
368#213—62no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—21no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—121no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3#6711yescharacteristic
385C4⋊Dic3#6711yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390C4×Dic3C22×D311yescharacteristic
391C4×Dic3C22×D311yescharacteristic
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8C22×D311yescharacteristic
399C2×C3⋊C8C22×D311yescharacteristic
400D24—62no—
401D24—62no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32C22×D411yescharacteristic
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3×D3—22no—
410C2×C3×D3—22no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3—84no—
419C32×C4—21no—
420C32×C4—41no—
421C32×C4—41no—
422C32×C4C2×#4111yescharacteristic
423C32×C4C2×#4111yescharacteristic
424C3⋊Dic3—41no—
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C22×D4—31no—
431C2×D8—91no—
432C2×D8—91no—
433C2×D8—91no—
434C2×D8—91no—
435#127—91no—
436#125—91no—
437#123—181no—
438#123—181no—
439#121—31no—
440#121—91no—
441#121—181no—
442#121—181no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—31no—
446C4×D4—31no—
447C4×D4—61no—
448C4×D4—61no—
449C4×D4—91no—
450C4×D4—91no—
451#117—31no—
452#117D3211yescharacteristic
453C2×C22⋊C4—61no—
454C2×C22⋊C4—61no—
455#107—31no—
456#107—91no—
457#106—31no—
458#106—91no—
459C4⋊C8—91no—
460C4⋊C8—91no—
461#102—31no—
462#102—31no—
463#102—91no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468#102—91no—
469C22⋊C8—31no—
470C22⋊C8—91no—
471#97—91no—
472C4×C8—91no—
473C23×C3—21no—
474C23×C3—64no—
475C23×C3—61no—
476C23×C3—61no—
477C23×C3—61no—
478C23×C3—241no—
479C23×C3—241no—
480C23×C3D3×D411yescharacteristic
481C23×C3C2×#6711yescharacteristic
482C22×D3—21no—
483C22×D3—21no—
484C22×D3—24no—
485C22×D3—21no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—81no—
489C22×D3—81no—
490C22×D3—121no—
491C3×D4—32no—
492C3×D4—32no—
493C3×D4—64no—
494C3×D4—61no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—241no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
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—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—61no—
518C2×C3×C4—241no—
519C2×C3×C4—241no—
520C2×C3×C4—241no—
521C2×C3×C4—241no—
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4C2×#6711yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526#67—81no—
527#67—241no—
528#67—241no—
529#67—241no—
530#67—241no—
531#67—242no—
532C2×Dic3—21no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—121no—
536C2×Dic3—241no—
537C2×Dic3C2×#6711yescharacteristic
538C2×Dic3C2×#6711yescharacteristic
539C2×Dic3C2×#6711yescharacteristic
540C2×Dic3C2×#6711yescharacteristic
541D12—24no—
542D12—21no—
543D12—21no—
544D12—21no—
545D12—21no—
546D12—61no—
547D12—61no—
548D12—61no—
549D12—61no—
550D12—121no—
551D12—121no—
552D12—241no—
553D12—241no—
554D12#23512yes—
555D12#23512yes—
556C4×D3—81no—
557C4×D3—81no—
558C4×D3—81no—
559C4×D3—81no—
560C4×D3—241no—
561C4×D3—241no—
562C4×D3—241no—
563C3×C8—61no—
564C3×C8—61no—
565C3⋊C8—21no—
566C3⋊C8—21no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—121no—
572C3⋊C8—121no—
573C2×C32—41no—
574C2×C32#52511yescharacteristic
575C2×C32#57611yescharacteristic
576C2×C32#57611yescharacteristic
577C3⋊D3—81no—
578C3×D3—42no—
579C3×D3—42no—
580C3×D3—81no—
581C24—61no—
582C2×D4—31no—
583C2×D4—31no—
584C2×D4—31no—
585C2×D4—62no—
586C2×D4—62no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—91no—
590C2×D4—181no—
591C2×D4—181no—
592C2×D4—181no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4C2×D3211yescharacteristic
600D8—182no—
601D8—182no—
602D8—182no—
603D8—182no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—91no—
607C2×C8—91no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4C2×D3211yescharacteristic
615C4⋊C4C2×D3211yescharacteristic
616C22⋊C4—21no—
617C22⋊C4—31no—
618C22⋊C4—31no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C42—21no—
628C42—31no—
629C42—31no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—62no—
641C22×C3—62no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—244no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C22×#6711yescharacteristic
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—84no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—241no—
669C2×D3—241no—
670C2×D3—241no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—81no—
685C3×C4—81no—
686C3×C4—121no—
687C3×C4C2×#23511yescharacteristic
688C3×C4C2×#23511yescharacteristic
689C3×C4D3×#4111yescharacteristic
690C3×C4D3×#4111yescharacteristic
691Dic3—21no—
692Dic3—21no—
693Dic3—21no—
694Dic3—21no—
695Dic3—41no—
696Dic3—121no—
697Dic3—121no—
698Dic3—241no—
699C32#312211yescharacteristic, complemented, Sylow
700C23—64no—
701C23—61no—
702C23—61no—
703C23—61no—
704C23—181no—
705C23—241no—
706C23—241no—
707C23D3×#6711yescharacteristic
708D4—32no—
709D4—32no—
710D4—64no—
711D4—61no—
712D4—61no—
713D4—61no—
714D4—61no—
715D4—181no—
716D4—181no—
717D4—241no—
718D4—721no—
719D4—721no—
720D4—721no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—61no—
730C2×C4—181no—
731C2×C4—241no—
732C2×C4—241no—
733C2×C4—241no—
734C2×C4—241no—
735C2×C4—721no—
736C2×C4—721no—
737C2×C4D3×#6711yescharacteristic
738C2×C4C22×D3211yescharacteristic
739C8—61no—
740C8—61no—
741C8—181no—
742C8—181no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—41no—
747C2×C3—41no—
748C2×C3—81no—
749C2×C3—122no—
750C2×C3—122no—
751C2×C3—241no—
752C2×C3#565611yescharacteristic
753C2×C3#576911yescharacteristic
754C2×C3#577411yescharacteristic
755C2×C3#579111yescharacteristic
756C2×C3#583511yescharacteristic
757C2×C3#583511yescharacteristic
758D3—42no—
759D3—42no—
760D3—81no—
761D3—241no—
762D3—241no—
763D3—481no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—62no—
768C22—62no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—244no—
777C22—361no—
778C22—361no—
779C22—361no—
780C22C2×D3×#6711yescharacteristic
781C4—21no—
782C4—41no—
783C4—41no—
784C4—61no—
785C4—61no—
786C4—61no—
787C4—61no—
788C4—121no—
789C4—361no—
790C4D3×#23511yescharacteristic
791C4D3×#23511yescharacteristic
792C3—21no—
793C3#8135411yescharacteristic, complemented
794C3#8254211yescharacteristic, complemented
795C2—41no—
796C2—122no—
797C2—122no—
798C2—241no—
799C2—721no—
800C2#1059489611yescharacteristic
801C2#1059545411yescharacteristic
802C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
hypercenter#117D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5521C2semidirect
2. #10594985C2semidirect
3. #10592702C2semidirect
4. C3×#5003C2semidirect
5. #10591162C2semidirect
6. #10591160C2semidirect
7. #10591056C2semidirect
8. #10590589C2semidirect
9. #10590547C2semidirect
10. #10590547C2semidirect
11. #10590545C2semidirect
12. #10590542C2semidirect
13. #10590456C2semidirect
14. #10590455C2semidirect
15. #10590452C2semidirect
33. #63911C22semidirect
34. #63894C22semidirect
35. Dic3×D12C22semidirect
37. #63869C22semidirect
44. #63636C22semidirect
45. #63636C22semidirect
46. #63635C22semidirect
47. #63634C22semidirect
49. C3×#809C22semidirect
50. C3×#809C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
64. #5521D3semidirect
80. #5003D3semidirect
221. #809C2×D3semidirect
222. #809C2×D3semidirect
226. #808C2×D3semidirect
230. #807C2×D3semidirect
699. C32#3122semidirect
793. C3#81354semidirect
794. C3#82542semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
#105949852
#105927022
C3×#50032
#105911622
#105911602
#105910562
#105905892
#105905472
#105905452
#105905422
#105904562
#105904552
#105904522
#825423
#813543