Finite Group Databasebeta

← #11872722

Subgroups — #11872722

Order 1152.

935 conjugacy classes of subgroups.

The subgroup lattice has 823 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5619C211yesmaximal, characteristic, complemented
2#10594996C211yesmaximal, characteristic, complemented
3#10592735C211yesmaximal, characteristic, complemented
4C3×#5035C211yesmaximal, characteristic, complemented
5#10591429C211yesmaximal, characteristic, complemented
6#10591429C211yesmaximal, characteristic, complemented
7#10591404C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10591168C211yesmaximal, characteristic, complemented
10#10591090C211yesmaximal, characteristic, complemented
11#10591056C211yesmaximal, characteristic, complemented
12#10590589C211yesmaximal, characteristic, complemented
13#10590470C211yesmaximal, characteristic, complemented
14#10590468C211yesmaximal, characteristic, complemented
15#10590456C211yesmaximal, characteristic, complemented
16#83435—31nomaximal
17#81354—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C32×#121C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C3×#940C2211yescharacteristic, complemented
23C3×#939—21no—
24C3×#938—21no—
25C3×D4×Dic3C2211yescharacteristic, complemented
26C3×#930C2211yescharacteristic
27C3×#926C2211yescharacteristic
28C3×#926C2211yescharacteristic
29C3×#893C2211yescharacteristic, complemented
30C3×#890C2211yescharacteristic, complemented
31C3×#886—21no—
32C3×#883—21no—
33#63974—21no—
34#63974—21no—
35#63894—21no—
36#63894—21no—
37#63894C2211yescharacteristic
38#63894C2211yescharacteristic
39#63894C2211yescharacteristic
40#63894C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43#63657C2211yescharacteristic
44#63636C2211yescharacteristic
45#63636C2211yescharacteristic
46C3×#832C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic
49C3×#808C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63574C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#540—31no—
62#5619D311yescharacteristic, complemented
63#5521—31no—
64#5521—31no—
65C3×#482—31no—
66#5072—31no—
67#5072—31no—
68#5066—31no—
69#5066—31no—
70#5036—31no—
71#5036—31no—
72#5036—31no—
73#5036—61no—
74#5035—31no—
75#5035D311yescharacteristic, complemented
76#5014—31no—
77#5014—31no—
78C4×#213—31no—
79C4×#213—31no—
80#5003—31no—
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—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)—22no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C22×C3×Dic3—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×#624—21no—
108C2×#624—21no—
109C2×#624—21no—
110C2×#624—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113#3753—22no—
114#3753—22no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3D411yescharacteristic
125C3×C4⋊Dic3D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139#3714—22no—
140#3714—22no—
141#3122—91noSylow
142C22×D12—31no—
143C22×D12—31no—
144C22×D12—61no—
145C3×#127—31no—
146C3×#125—31no—
147C3×#123—61no—
148C3×#123—61no—
149C3×#121—21no—
150C3×#121—31no—
151C3×#121—61no—
152C3×#121—61no—
153C3×#121C2×D311yescharacteristic
154C3×#121C2×D311yescharacteristic
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157C3×#117—31no—
158C3×#117—31no—
159#940C2×D311yescharacteristic, complemented
160#939—21no—
161#938—21no—
162D4×Dic3C2×D311yescharacteristic, complemented
163C2×#213—31no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—31no—
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—61no—
170C2×#213—61no—
171#930C2×D311yescharacteristic
172#926C2×D311yescharacteristic
173#926C2×D311yescharacteristic
174C2×D24—31no—
175C2×D24—31no—
176#893—31no—
177#893—31no—
178#893—31no—
179#893—31no—
180#893—61no—
181#893—61no—
182#893C2×D311yescharacteristic, complemented
183#890C2×D311yescharacteristic, complemented
184#886—21no—
185#883—21no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188D3×C22⋊C4—61no—
189D3×C22⋊C4—61no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—31no—
194C4×D12—61no—
195C4×D12—61no—
196C3×#107—31no—
197C3×#106—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×C22⋊C8—31no—
201#832—31no—
202#832—31no—
203#832C2×D311yescharacteristic, complemented
204#832C2×D311yescharacteristic, complemented
205#830—31no—
206#830—31no—
207#830—61no—
208#830C2×D311yescharacteristic
209#821—31no—
210#821—31no—
211#815—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214C8×Dic3—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—61no—
224#809—61no—
225#808—31no—
226#808—31no—
227#808C2×D311yescharacteristic, complemented
228#807—31no—
229#807—31no—
230#807C2×D311yescharacteristic, complemented
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—
239C22×C3⋊D3—24no—
240C22×C3⋊D3—81no—
241C22×C3⋊D3—81no—
242C22×C3×D3—21no—
243C32×D4—21no—
244C32×D4—21no—
245C32×D4—81no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251C4⋊(C3⋊D3)—24no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)#4112yes—
255C4⋊(C3⋊D3)#4112yes—
256C3×#67—81no—
257C3×#67—81no—
258C3×#67—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—81no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×C4×D3—81no—
270#624—81no—
271#624—81no—
272#624—81no—
273#624—81no—
274C3⋊(C3⋊C8)—21no—
275C3⋊(C3⋊C8)—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#540—31no—
279#518—91no—
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—
293C23×D3—61no—
294C23×D3—61no—
295C23×D3—121no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—31no—
300C2×C3×D4—41no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—21no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C2×#67—21no—
312C2×#67—21no—
313C2×#67—21no—
314C22×Dic3—21no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—62no—
322C2×D12—62no—
323C2×D12—62no—
324C2×D12—62no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12—122no—
328C2×D12—122no—
329C2×D12—121no—
330C2×D12C22×D311yescharacteristic
331C2×C4×D3—21no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C22⋊C4—21no—
353C3×C22⋊C4—21no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—41no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C42—31no—
362C3×C42—31no—
363C3×C42—61no—
364#217—21no—
365#217—21no—
366#217#6711yescharacteristic
367#217#6711yescharacteristic
368#213—62no—
369#213—62no—
370#213—62no—
371#213—62no—
372#213—62no—
373#213—62no—
374#213—122no—
375#213—122no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386C4⋊Dic3—21no—
387C4⋊Dic3#6711yescharacteristic
388C4⋊Dic3#6711yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393C4×Dic3—21no—
394C4×Dic3C22×D311yescharacteristic
395C4×Dic3C22×D311yescharacteristic
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404D24—62no—
405D24—62no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—22no—
414C2×C3⋊D3—22no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—84no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C32×C4—21no—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4C2×#4111yescharacteristic
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C22×D4—91no—
435C2×D8—91no—
436C2×D8—91no—
437C2×D8—91no—
438C2×D8—91no—
439#127—31no—
440#125—31no—
441#123—61no—
442#123—61no—
443#121—31no—
444#121—61no—
445#121—61no—
446#121D3211yescharacteristic
447C4×D4—31no—
448C4×D4—31no—
449C4×D4—91no—
450C4×D4—91no—
451C4×D4—91no—
452C4×D4—91no—
453C4×D4—181no—
454C4×D4—181no—
455#117—31no—
456#117—31no—
457C2×C22⋊C4—181no—
458C2×C22⋊C4—181no—
459#107—31no—
460#107—91no—
461#106—31no—
462#106—91no—
463C4⋊C8—91no—
464C4⋊C8—91no—
465#102—31no—
466#102—31no—
467#102—91no—
468#102—91no—
469#102—91no—
470#102—91no—
471#102—91no—
472#102—91no—
473C22⋊C8—31no—
474C22⋊C8—91no—
475#97—91no—
476C4×C8—91no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—41no—
481C23×C3—61no—
482C23×C3D3×D411yescharacteristic
483C23×C3C2×#6711yescharacteristic
484C22×D3—21no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—64no—
490C22×D3—64no—
491C22×D3—121no—
492C22×D3—121no—
493C22×D3—124no—
494C22×D3—241no—
495C22×D3—241no—
496C22×D3—241no—
497C22×D3—241no—
498C22×D3—242no—
499C22×D3—242no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—41no—
505C3×D4—41no—
506C3×D4—61no—
507C3×D4—61no—
508C3×D4—81no—
509C3×D4—81no—
510C3×D4—82no—
511C3×D4—241no—
512C3×D4—241no—
513C3×D4—241no—
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—31no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—241no—
533C2×C3×C4—241no—
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4C2×#6711yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538#67—81no—
539#67—81no—
540#67—81no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—81no—
545C2×Dic3C2×#6711yescharacteristic
546C2×Dic3C2×#6711yescharacteristic
547C2×Dic3C2×#6711yescharacteristic
548C2×Dic3C2×#6711yescharacteristic
549D12—21no—
550D12—21no—
551D12—32no—
552D12—32no—
553D12—32no—
554D12—32no—
555D12—62no—
556D12—62no—
557D12—64no—
558D12—64no—
559D12—61no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—121no—
564D12—121no—
565D12—124no—
566C4×D3—81no—
567C4×D3—241no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—241no—
575C3×C8—61no—
576C3×C8—61no—
577C3⋊C8—21no—
578C3⋊C8—21no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—121no—
584C3⋊C8—121no—
585C2×C32—41no—
586C2×C32—81no—
587C2×C32#52511yescharacteristic
588C2×C32#57611yescharacteristic
589C2×C32#57611yescharacteristic
590C3⋊D3—42no—
591C3⋊D3—42no—
592C3×D3—81no—
593C24—181no—
594C2×D4—21no—
595C2×D4—31no—
596C2×D4—61no—
597C2×D4—61no—
598C2×D4—61no—
599C2×D4—91no—
600C2×D4—91no—
601C2×D4—182no—
602C2×D4—182no—
603C2×D4—181no—
604C2×D4C2×D3211yescharacteristic
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4C2×D3211yescharacteristic
612D8—182no—
613D8—182no—
614D8—182no—
615D8—182no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—91no—
619C2×C8—91no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4C2×D3211yescharacteristic
628C22⋊C4—21no—
629C22⋊C4—31no—
630C22⋊C4—31no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C42—31no—
640C42—31no—
641C42—61no—
642C22×C3—22no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3C2×D3×D411yescharacteristic
665C22×C3C22×#6711yescharacteristic
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—62no—
672C2×D3—62no—
673C2×D3—122no—
674C2×D3—122no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—241no—
684C2×D3—241no—
685C2×D3—241no—
686C2×D3—241no—
687C2×D3—244no—
688C2×D3—244no—
689C2×D3—248no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—61no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—61no—
701C3×C4—81no—
702C3×C4—121no—
703C3×C4—121no—
704C3×C4—121no—
705C3×C4D3×#4111yescharacteristic
706C3×C4D3×#4111yescharacteristic
707C3×C4D3×#4111yescharacteristic
708C3×C4D3×#4111yescharacteristic
709Dic3—21no—
710Dic3—21no—
711Dic3—21no—
712Dic3—21no—
713Dic3—41no—
714Dic3—41no—
715Dic3—41no—
716C32#312211yescharacteristic, complemented, Sylow
717C23—21no—
718C23—61no—
719C23—184no—
720C23—181no—
721C23—181no—
722C23—721no—
723C23—721no—
724C23D3×#6711yescharacteristic
725D4—21no—
726D4—21no—
727D4—61no—
728D4—61no—
729D4—81no—
730D4—92no—
731D4—92no—
732D4—184no—
733D4—181no—
734D4—181no—
735D4—241no—
736D4—241no—
737D4—241no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—31no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—241no—
749C2×C4—241no—
750C2×C4—721no—
751C2×C4—721no—
752C2×C4—721no—
753C2×C4—721no—
754C2×C4D3×#6711yescharacteristic
755C2×C4C22×D3211yescharacteristic
756C8—61no—
757C8—61no—
758C8—181no—
759C8—181no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—42no—
764C2×C3—41no—
765C2×C3—41no—
766C2×C3—81no—
767C2×C3—81no—
768C2×C3—161no—
769C2×C3—241no—
770C2×C3#565611yescharacteristic
771C2×C3#576911yescharacteristic
772C2×C3#577411yescharacteristic
773C2×C3#582811yescharacteristic
774C2×C3#583511yescharacteristic
775C2×C3#583511yescharacteristic
776D3—81no—
777D3—122no—
778D3—122no—
779D3—122no—
780D3—122no—
781D3—242no—
782D3—242no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—182no—
793C22—182no—
794C22—361no—
795C22—361no—
796C22—361no—
797C22—361no—
798C22—724no—
799C22C2×D3×#6711yescharacteristic
800C4—21no—
801C4—41no—
802C4—61no—
803C4—61no—
804C4—61no—
805C4—61no—
806C4—121no—
807C4—121no—
808C4—121no—
809C4#6431211yescharacteristic
810C4#6431211yescharacteristic
811C3—21no—
812C3#8135411yescharacteristic, complemented
813C3#8343511yescharacteristic, complemented
814C2—41no—
815C2—81no—
816C2—241no—
817C2—362no—
818C2—362no—
819C2#1059509711yescharacteristic
820C2#1059515911yescharacteristic
821C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5619C2semidirect
2. #10594996C2semidirect
3. #10592735C2semidirect
4. C3×#5035C2semidirect
5. #10591429C2semidirect
6. #10591429C2semidirect
7. #10591404C2semidirect
8. #10591400C2semidirect
9. #10591168C2semidirect
10. #10591090C2semidirect
11. #10591056C2semidirect
12. #10590589C2semidirect
13. #10590470C2semidirect
14. #10590468C2semidirect
15. #10590456C2semidirect
22. C3×#940C22semidirect
25. C3×D4×Dic3C22semidirect
29. C3×#893C22semidirect
30. C3×#890C22semidirect
46. C3×#832C22semidirect
47. C3×#832C22semidirect
49. C3×#808C22semidirect
50. C3×#807C22semidirect
51. #63576C22semidirect
52. #63574C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5619D3semidirect
75. #5035D3semidirect
159. #940C2×D3semidirect
162. D4×Dic3C2×D3semidirect
182. #893C2×D3semidirect
183. #890C2×D3semidirect
203. #832C2×D3semidirect
204. #832C2×D3semidirect
227. #808C2×D3semidirect
230. #807C2×D3semidirect
716. C32#3122semidirect
812. C3#81354semidirect
813. C3#83435semidirect

Maximal subgroups

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

subgroupindex
C3×#56192
#105949962
#105927352
C3×#50352
#105914292
#105914042
#105914002
#105911682
#105910902
#105910562
#105905892
#105904702
#105904682
#105904562
#834353
#813543