Finite Group Databasebeta

← #11872724

Subgroups — #11872724

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×#5619C211yesmaximal, characteristic, complemented
2#10594982C211yesmaximal, characteristic, complemented
3#10592734C211yesmaximal, characteristic, complemented
4C3×#5036C211yesmaximal, characteristic, complemented
5#10591430C211yesmaximal, characteristic, complemented
6#10591428C211yesmaximal, characteristic, complemented
7#10591428C211yesmaximal, characteristic, complemented
8Dic3×#213C211yesmaximal, characteristic, complemented
9#10591160C211yesmaximal, characteristic, complemented
10#10591093C211yesmaximal, characteristic, complemented
11#10591056C211yesmaximal, characteristic, complemented
12#10590469C211yesmaximal, characteristic, complemented
13#10590467C211yesmaximal, characteristic, complemented
14#10590455C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic, complemented
16#83435—31nomaximal
17#79993—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C32×#121C2211yescharacteristic
20#64135C2211yescharacteristic
21C3×#940C2211yescharacteristic, complemented
22C3×#939—21no—
23C3×#938—21no—
24C3×D4×Dic3C2211yescharacteristic, complemented
25C2×C3×#213C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×#930C2211yescharacteristic
28C3×#926C2211yescharacteristic
29C3×#893C2211yescharacteristic, complemented
30C3×#890C2211yescharacteristic, complemented
31C3×#886—21no—
32C3×#883—21no—
33D3×#217—21no—
34D3×#217—21no—
35#63898—21no—
36#63898—21no—
37Dic3×D12C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40Dic3×D12C2211yescharacteristic
41C2×#3713C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63659C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45#63657C2211yescharacteristic
46#63635C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63563C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#540—31no—
62#5798—31no—
63#5619D311yescharacteristic, complemented
64#5521—31no—
65C3×#447—31no—
66#5217—31no—
67#5152—31no—
68#5150—31no—
69#5150—31no—
70Dic3×D8—31no—
71#5072—31no—
72#5072—31no—
73#5066—31no—
74#5066—31no—
75#5036—31no—
76#5036D311yescharacteristic, complemented
77#5035—31no—
78#5035—31no—
79#5035—31no—
80#5035—61no—
81#5014—31no—
82#5014—31no—
83C4×#213—31no—
84C4×#213—31no—
85#5000—31no—
86#4785—31no—
87#4766—31no—
88#4763—31no—
89#4756—31no—
90#4737—31no—
91#4720—31no—
92C23×C3×D3—21no—
93C2×C32×D4—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C2×C3×D12—21no—
101C2×C3×D12—22no—
102C2×C3×D12—22no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113#3757—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×#217D411yescharacteristic
122C3×#213—22no—
123C3×#213—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3D411yescharacteristic
128C3×C4⋊Dic3D411yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3C2311yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3713—22no—
140#3713—22no—
141#3122—91noSylow
142C22×C3×D4—31no—
143C22×D12C2×D311yescharacteristic
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C3×#127—31no—
147C3×#125—31no—
148C3×#123—61no—
149C3×#123—61no—
150C3×#121—21no—
151C3×#121—31no—
152C3×#121—61no—
153C3×#121—61no—
154C3×#121C2×D311yescharacteristic
155C3×#121C2×D311yescharacteristic
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×#117—31no—
159C2×#217—61no—
160C2×#217—61no—
161#940C2×D311yescharacteristic, complemented
162#939—21no—
163#938—21no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—31no—
168D4×Dic3—61no—
169D4×Dic3—61no—
170D4×Dic3C2×D311yescharacteristic, complemented
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—31no—
174C2×#213—31no—
175C2×#213C2×D311yescharacteristic
176C2×#213C2×D311yescharacteristic
177#930C2×D311yescharacteristic
178#926—31no—
179#926—31no—
180#926—61no—
181#926C2×D311yescharacteristic
182#893—61no—
183#893—61no—
184#893C2×D311yescharacteristic, complemented
185#890C2×D311yescharacteristic, complemented
186#886—21no—
187#883—21no—
188D3×C22⋊C4—61no—
189D3×C22⋊C4—61no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—31no—
194C3×#102—31no—
195C3×#102—31no—
196C3×C22⋊C8—31no—
197#832—31no—
198#832—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—61no—
206#832—61no—
207#830—31no—
208#830—31no—
209#830—61no—
210#830C2×D311yescharacteristic
211#821—31no—
212#821—31no—
213#818—31no—
214#817—31no—
215#815—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218C8×Dic3—31no—
219#809—31no—
220#809—31no—
221#809C2×D311yescharacteristic
222#809C2×D311yescharacteristic
223#808—31no—
224#808—31no—
225#808—31no—
226#808—61no—
227#807—31no—
228#807—31no—
229#807—31no—
230#807—61no—
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—21no—
241C22×C3×D3—81no—
242C22×C3×D3—81no—
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
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C3×#67—81no—
254C3×#67—81no—
255C3×#67—81no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—81no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—24no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12#4112yes—
268C3×D12#4112yes—
269C3×C4×D3—81no—
270D3×Dic3—81no—
271D3×Dic3—81no—
272D3×Dic3—81no—
273D3×Dic3—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—91no—
281#482—91no—
282#478—91no—
283#478—91no—
284#459—91no—
285#459—91no—
286#447—31no—
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—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—31no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—41no—
302C2×C3×D4—62no—
303C2×C3×D4—62no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4C22×D311yescharacteristic
309C2×C3×D4C22×D311yescharacteristic
310C22×C3×C4—21no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C2×#67—21no—
316C2×#67—21no—
317C2×#67—21no—
318C22×Dic3—21no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C2×D12—21no—
324C2×D12—22no—
325C2×D12—22no—
326C2×D12C22×D311yescharacteristic
327C2×D12C22×D311yescharacteristic
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C3×D8—62no—
335C3×D8—62no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—21no—
347C3×C22⋊C4—21no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—41no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—31no—
355C3×C42—31no—
356#217—21no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—121no—
364#217#6711yescharacteristic
365#217#6711yescharacteristic
366#213—22no—
367#213—22no—
368#213—62no—
369#213—62no—
370#213—62no—
371#213—62no—
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—
378C4⋊Dic3—21no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3#6711yescharacteristic
386C4⋊Dic3#6711yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—121no—
392C4×Dic3C22×D311yescharacteristic
393C4×Dic3C22×D311yescharacteristic
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32C22×D411yescharacteristic
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×C4C2×#4111yescharacteristic
422C32×C4C2×#4111yescharacteristic
423C3⋊Dic3—41no—
424C3⋊Dic3—41no—
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C22×D4—31no—
431C2×D8—31no—
432C2×D8—31no—
433C2×D8—91no—
434C2×D8—91no—
435#127—31no—
436#125—31no—
437#123—61no—
438#123—61no—
439#121—31no—
440#121—61no—
441#121—61no—
442#121D3211yescharacteristic
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—91no—
446C4×D4—91no—
447C4×D4—91no—
448C4×D4—91no—
449C4×D4—181no—
450C4×D4—181no—
451#117—31no—
452#117—91no—
453C2×C22⋊C4—181no—
454C2×C22⋊C4—181no—
455#107—91no—
456#107—91no—
457#106—91no—
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—21no—
475C23×C3—21no—
476C23×C3—41no—
477C23×C3—64no—
478C23×C3—61no—
479C23×C3—61no—
480C23×C3—61no—
481C23×C3—241no—
482C23×C3—241no—
483C23×C3D3×D411yescharacteristic
484C23×C3C2×#6711yescharacteristic
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—24no—
488C22×D3—21no—
489C22×D3—81no—
490C22×D3—81no—
491C3×D4—21no—
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—32no—
496C3×D4—32no—
497C3×D4—41no—
498C3×D4—41no—
499C3×D4—64no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—81no—
505C3×D4—81no—
506C3×D4—82no—
507C3×D4—241no—
508C3×D4—241no—
509C3×D4—241no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—61no—
526C2×C3×C4—241no—
527C2×C3×C4—241no—
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4C2×#6711yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532#67—81no—
533#67—81no—
534#67—81no—
535C2×Dic3—21no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—81no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—241no—
544C2×Dic3—241no—
545C2×Dic3—241no—
546C2×Dic3—241no—
547C2×Dic3C2×#6711yescharacteristic
548C2×Dic3C2×#6711yescharacteristic
549C2×Dic3C2×#6711yescharacteristic
550C2×Dic3C2×#6711yescharacteristic
551D12—24no—
552D12—21no—
553D12—21no—
554D12—21no—
555D12—21no—
556D12#23712yes—
557D12#23712yes—
558C4×D3—81no—
559C4×D3—241no—
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—81no—
575C2×C32#52511yescharacteristic
576C2×C32#57611yescharacteristic
577C2×C32#57611yescharacteristic
578C3×D3—42no—
579C3×D3—42no—
580C3×D3—81no—
581C24—61no—
582C2×D4—21no—
583C2×D4—31no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—62no—
587C2×D4—62no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4C2×D3211yescharacteristic
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4C2×D3211yescharacteristic
600D8—62no—
601D8—62no—
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—61no—
612C4⋊C4—61no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4C2×D3211yescharacteristic
616C22⋊C4—21no—
617C22⋊C4—31no—
618C22⋊C4—31no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C42—31no—
628C42—31no—
629C42—181no—
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—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—62no—
647C22×C3—62no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—244no—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C22×#6711yescharacteristic
661C2×D3—22no—
662C2×D3—22no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—84no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—81no—
683C3×C4—121no—
684C3×C4C2×#23711yescharacteristic
685C3×C4C2×#23711yescharacteristic
686C3×C4D3×#4111yescharacteristic
687C3×C4D3×#4111yescharacteristic
688Dic3—21no—
689Dic3—21no—
690Dic3—21no—
691Dic3—21no—
692Dic3—41no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—241no—
698Dic3—241no—
699C32#312211yescharacteristic, complemented, Sylow
700C23—21no—
701C23—64no—
702C23—61no—
703C23—61no—
704C23—61no—
705C23—241no—
706C23—241no—
707C23D3×#6711yescharacteristic
708D4—21no—
709D4—21no—
710D4—32no—
711D4—32no—
712D4—64no—
713D4—61no—
714D4—61no—
715D4—61no—
716D4—61no—
717D4—81no—
718D4—241no—
719D4—241no—
720D4—241no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—61no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—241no—
732C2×C4—241no—
733C2×C4—721no—
734C2×C4—721no—
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—81no—
750C2×C3—81no—
751C2×C3—122no—
752C2×C3—122no—
753C2×C3—161no—
754C2×C3—241no—
755C2×C3#558611yescharacteristic
756C2×C3#575711yescharacteristic
757C2×C3#577411yescharacteristic
758C2×C3#582811yescharacteristic
759C2×C3#583511yescharacteristic
760C2×C3#583511yescharacteristic
761D3—42no—
762D3—42no—
763D3—81no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—62no—
771C22—62no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22—244no—
780C22C2×D3×#6711yescharacteristic
781C4—21no—
782C4—41no—
783C4—61no—
784C4—61no—
785C4—61no—
786C4—61no—
787C4—121no—
788C4—361no—
789C4—361no—
790C4D3×#23711yescharacteristic
791C4D3×#23711yescharacteristic
792C3—21no—
793C3#7999311yescharacteristic, complemented
794C3#8343511yescharacteristic, complemented
795C2—41no—
796C2—81no—
797C2—122no—
798C2—122no—
799C2—241no—
800C2#1059509611yescharacteristic
801C2#1059515411yescharacteristic
802C2#1059545411yescharacteristic
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. #10594982C2semidirect
3. #10592734C2semidirect
4. C3×#5036C2semidirect
5. #10591430C2semidirect
6. #10591428C2semidirect
7. #10591428C2semidirect
8. Dic3×#213C2semidirect
9. #10591160C2semidirect
10. #10591093C2semidirect
11. #10591056C2semidirect
12. #10590469C2semidirect
13. #10590467C2semidirect
14. #10590455C2semidirect
15. #10590452C2semidirect
21. C3×#940C22semidirect
24. C3×D4×Dic3C22semidirect
29. C3×#893C22semidirect
30. C3×#890C22semidirect
43. #63659C22semidirect
44. #63659C22semidirect
46. #63635C22semidirect
47. #63634C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63563C22semidirect
56. #63563C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
63. #5619D3semidirect
76. #5036D3semidirect
161. #940C2×D3semidirect
170. D4×Dic3C2×D3semidirect
184. #893C2×D3semidirect
185. #890C2×D3semidirect
699. C32#3122semidirect
793. C3#79993semidirect
794. C3#83435semidirect

Maximal subgroups

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

subgroupindex
C3×#56192
#105949822
#105927342
C3×#50362
#105914302
#105914282
Dic3×#2132
#105911602
#105910932
#105910562
#105904692
#105904672
#105904552
#105904522
#834353
#799933