Finite Group Databasebeta

← #11869692

Subgroups — #11869692

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 779 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#117C211yesmaximal, characteristic, complemented
2#10595022C211yesmaximal, characteristic
3#10592697C211yesmaximal, characteristic, complemented
4C3×#5002C211yesmaximal, characteristic, complemented
5#10591122C211yesmaximal, characteristic, complemented
6#10591083C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590521C211yesmaximal, characteristic, complemented
9#10590519C211yesmaximal, characteristic, complemented
10#10590517C211yesmaximal, characteristic, complemented
11#10590516C211yesmaximal, characteristic, complemented
12#10590505C211yesmaximal, characteristic, complemented
13#10590502C211yesmaximal, characteristic, complemented
14#10590500C211yesmaximal, characteristic, complemented
15#10590498C211yesmaximal, characteristic, complemented
16#82215—31nomaximal
17#78842—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C32×#117C2211yescharacteristic
21#64135C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C3×#892C2211yescharacteristic
26C3×#892C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic
29C3×D3×C22⋊C4—21no—
30C3×#877—21no—
31C3×#872—21no—
32C3×C42×D3—21no—
33#63976—21no—
34#63961—21no—
35#63908C2211yescharacteristic
36#63908C2211yescharacteristic
37C4×#625—21no—
38C4×#625—21no—
39#63856C2211yescharacteristic
40#63856C2211yescharacteristic
41#63635C2211yescharacteristic, complemented
42#63635C2211yescharacteristic, complemented
43#63634C2211yescharacteristic, complemented
44#63634C2211yescharacteristic, complemented
45C3×#810C2211yescharacteristic, complemented
46C3×#810C2211yescharacteristic, complemented
47C3×#809C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic, complemented
49#63575C2211yescharacteristic, complemented
50#63575C2211yescharacteristic, complemented
51#63573C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63565C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63562C2211yescharacteristic, complemented
56#63562C2211yescharacteristic, complemented
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C2×C3×#117—31no—
62#5828—31no—
63#5791—31no—
64D3×#117D311yescharacteristic, complemented
65C3×#416—31no—
66#5233—31no—
67C2×#830—31no—
68C2×(C2×D3)⋊C8—31no—
69#5106—31no—
70#5003—31no—
71#5003—31no—
72#5002—31no—
73#5002D311yescharacteristic, complemented
74#4998—31no—
75#4998—31no—
76#4998—31no—
77#4998—61no—
78#4996—31no—
79#4996—31no—
80#4971—31no—
81#4970—31no—
82#4968—31no—
83#4967—31no—
84#4815—31no—
85#4814—31no—
86#4811—31no—
87#4805—31no—
88#4784—31no—
89#4779—31no—
90#4777—31no—
91#4774—31no—
92C23×C3×D3D411yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×C3×#67—21no—
95C22×C3×Dic3D411yescharacteristic
96C3×#235—22no—
97C3×#235—22no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—22no—
100C2×C3×C4×D3—22no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#625—21no—
110C2×#625—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C42—21no—
115#3757—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4×C3⋊Dic3—21no—
119C2×C3⋊(C3⋊C8)—22no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C2×C3×C3⋊C8—22no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136#3724—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141#3091—91noSylow
142C2×C3×#41—31no—
143C23×C3×C4—31no—
144C2×#235C2×D311yescharacteristic
145C22×C4×D3C2×D311yescharacteristic
146C22×C3×C8—31no—
147C3×#117—21no—
148C3×#117—31no—
149C3×#117—31no—
150C3×#117—31no—
151C3×#117—61no—
152C3×#117—61no—
153C3×#117C2×D311yescharacteristic
154C3×#117C2×D311yescharacteristic
155C2×C3×C4⋊C4—31no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C22⋊C4—61no—
158C2×C3×C42—61no—
159#953—61no—
160#946—31no—
161#946—31no—
162#938—31no—
163#938—31no—
164#937—61no—
165#935—61no—
166#930—31no—
167#930—31no—
168#929—61no—
169C4×#67—61no—
170C4×#67—61no—
171C4×#67—61no—
172C4×#67—61no—
173#926—31no—
174#926—31no—
175#926—61no—
176#926C2×D311yescharacteristic
177#924—31no—
178#924—31no—
179C22×C3⋊C8—31no—
180C22×C3⋊C8—31no—
181C22×C3⋊C8—61no—
182C22×C3⋊C8C2×D311yescharacteristic
183#892C2×D311yescharacteristic
184#892C2×D311yescharacteristic
185D3×C4⋊C4C2×D311yescharacteristic
186D3×C4⋊C4C2×D311yescharacteristic
187D3×C22⋊C4—21no—
188#877—21no—
189#872—21no—
190C42×D3—21no—
191C3×#103—31no—
192C3×#103—31no—
193C3×#102—31no—
194C3×#102—31no—
195#835—31no—
196#835—31no—
197#832—31no—
198#832—31no—
199#830—31no—
200#830—31no—
201#830—31no—
202#830—31no—
203(C2×D3)⋊C8—31no—
204(C2×D3)⋊C8—31no—
205(C2×D3)⋊C8—31no—
206(C2×D3)⋊C8—31no—
207#818—31no—
208#818—31no—
209#817—31no—
210#817—31no—
211#810—31no—
212#810—31no—
213#810C2×D311yescharacteristic, complemented
214#810C2×D311yescharacteristic, complemented
215#809—31no—
216#809—31no—
217#809C2×D311yescharacteristic, complemented
218#809C2×D311yescharacteristic, complemented
219#808—31no—
220#808—31no—
221#808—31no—
222#808—31no—
223#808—31no—
224#808—31no—
225#808—61no—
226#808—61no—
227#807—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807—61no—
234#807—61no—
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—22no—
237C22×C3×D3—22no—
238C22×C3×D3—21no—
239C22×C3×D3—41no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4#4112yes—
246C2×C32×C4#4112yes—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C3×#67—42no—
251C2×C3×Dic3—22no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—21no—
258C3×D12—21no—
259C3×C4×D3—22no—
260C3×C4×D3—22no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—42no—
266C3×C4×D3—42no—
267C3×C4×D3—42no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#625—42no—
271#625—42no—
272C3⋊(C3⋊C8)—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#525—91no—
277C2×#117—31no—
278#485—91no—
279#485—91no—
280#484—91no—
281#483—91no—
282#482—91no—
283#482—91no—
284#481—91no—
285#480—91no—
286#427—91no—
287#427—91no—
288#416—31no—
289#416—91no—
290C2×C22⋊C8—91no—
291C24×C3—31no—
292C23×D3#6711yescharacteristic
293C3×#41—62no—
294C3×#41—62no—
295C2×C3×Q8—31no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—62no—
307C22×C3×C4—62no—
308C22×C3×C4—61no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C2×#67—21no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C22×Dic3#6711yescharacteristic
317#235—22no—
318#235—22no—
319C2×D12C22×D311yescharacteristic
320C2×C4×D3—22no—
321C2×C4×D3—22no—
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3#6711yescharacteristic
326C2×C4×D3#6711yescharacteristic
327C2×C4×D3C22×D311yescharacteristic
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C2×C3×C8—62no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C22⋊C4—21no—
344C3×C22⋊C4—21no—
345C3×C22⋊C4—41no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—41no—
352C3×C42—61no—
353C3×C42—61no—
354C3×C42—61no—
355#217—21no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—121no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383C4×Dic3—21no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—121no—
389C2×C3⋊C8—22no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—64no—
397C2×C3⋊C8—62no—
398C2×C3⋊C8—62no—
399C2×C3⋊C8C22×D311yescharacteristic
400C2×C3⋊C8C22×D311yescharacteristic
401C22×C32—21no—
402C22×C32—21no—
403C22×C32#12312yes—
404C22×C32C22×D411yescharacteristic
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—44no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3#13512yes—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4#12312yes—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
420C3⋊Dic3—41no—
421C3⋊Dic3—41no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C2×#41—31no—
428C23×C4—31no—
429C22×C8—31no—
430C22×C8—91no—
431#123—181no—
432C22⋊Q8—91no—
433C22⋊Q8—91no—
434#121—91no—
435#121—91no—
436#120—181no—
437C4×D4—181no—
438C4×D4—181no—
439#117—31no—
440#117—31no—
441#117—31no—
442#117—61no—
443#117—61no—
444#117—91no—
445#117D3211yescharacteristic
446C2×C4⋊C4—31no—
447C2×C4⋊C4—31no—
448C2×C22⋊C4—61no—
449C2×C42—61no—
450#107—91no—
451#107—91no—
452#107—91no—
453#107—91no—
454#106—91no—
455#106—91no—
456#106—91no—
457#106—91no—
458#103—31no—
459#103—31no—
460#103—91no—
461#103—91no—
462#102—31no—
463#102—31no—
464#102—91no—
465#102—91no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468C22⋊C8—91no—
469C22⋊C8—91no—
470C23×C3—21no—
471C23×C3—31no—
472C23×C3—31no—
473C23×C3—62no—
474C23×C3—62no—
475C23×C3—61no—
476C23×C3—121no—
477C23×C3D3×D411yescharacteristic
478C23×C3C2×#6711yescharacteristic
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—21no—
482C22×D3—41no—
483C22×D3C2×#6711yescharacteristic
484C22×D3C2×#6711yescharacteristic
485C3×Q8—61no—
486C3×Q8—61no—
487C3×D4—61no—
488C3×D4—61no—
489C3×D4—122no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—21no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—62no—
503C2×C3×C4—62no—
504C2×C3×C4—62no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—122no—
513C2×C3×C4—122no—
514C2×C3×C4—122no—
515C2×C3×C4#23512yes—
516C2×C3×C4#23512yes—
517C2×C3×C4#23512yes—
518C2×C3×C4D3×D411yescharacteristic
519C2×C3×C4#23712yes—
520C2×C3×C4C2×#6711yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—42no—
524#67—122no—
525#67—122no—
526#67—122no—
527#67—122no—
528C2×Dic3—22no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—121no—
537C2×Dic3—121no—
538C2×Dic3C2×#6711yescharacteristic
539C2×Dic3C2×#6711yescharacteristic
540D12—21no—
541D12—21no—
542C4×D3—22no—
543C4×D3—22no—
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—42no—
549C4×D3—42no—
550C4×D3—42no—
551Dic6—21no—
552Dic6—21no—
553C3×C8—61no—
554C3×C8—61no—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C3⋊C8—62no—
558C3⋊C8—62no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C2×C32—22no—
564C2×C32C2×#12311yescharacteristic
565C2×C32C2×#13511yescharacteristic
566C2×C32#57511yescharacteristic
567C3×D3—22no—
568C3×D3—41no—
569C3×D3—81no—
570C24—31no—
571#41—62no—
572#41—62no—
573C2×Q8—31no—
574C2×D4—31no—
575C2×D4—61no—
576C2×D4—181no—
577C2×D4—181no—
578C22×C4—31no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—62no—
586C22×C4—62no—
587C22×C4—61no—
588C22×C4C2×D3211yescharacteristic
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—62no—
592C2×C8—91no—
593C2×C8—91no—
594C2×C8—182no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4C2×D3211yescharacteristic
604C4⋊C4C2×D3211yescharacteristic
605C22⋊C4—21no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C42—21no—
615C42—61no—
616C42—61no—
617C42—61no—
618C42—181no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—22no—
625C22×C3—32no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—124no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3#88312yes—
638C22×C3#92912yes—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C22×#6711yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—44no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3#95012yes—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—22no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—81no—
661C3×C4—81no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4#88312yes—
666C3×C4#92912yes—
667C3×C4C2×#23511yescharacteristic
668C3×C4C2×#23511yescharacteristic
669C3×C4C2×#23511yescharacteristic
670C3×C4C2×#23711yescharacteristic
671Dic3—21no—
672Dic3—21no—
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3—241no—
682C32#309111yescharacteristic, complemented, Sylow
683C23—31no—
684C23—31no—
685C23—62no—
686C23—62no—
687C23—61no—
688C23—121no—
689C23D3×#6711yescharacteristic
690Q8—61no—
691Q8—61no—
692D4—61no—
693D4—61no—
694D4—122no—
695D4—362no—
696D4—362no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—62no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4#379512yes—
717C2×C4#379812yes—
718C2×C4D3×#6711yescharacteristic
719C2×C4C22×D3211yescharacteristic
720C8—61no—
721C8—61no—
722C8—181no—
723C8—181no—
724C2×C3—22no—
725C2×C3—22no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—42no—
730C2×C3—62no—
731C2×C3—121no—
732C2×C3—241no—
733C2×C3C2×#88311yescharacteristic
734C2×C3D3×#13511yescharacteristic
735C2×C3#576811yescharacteristic
736C2×C3C2×#92911yescharacteristic
737C2×C3C2×#95011yescharacteristic
738C2×C3#582211yescharacteristic
739D3—22no—
740D3—41no—
741D3—81no—
742C22—21no—
743C22—21no—
744C22—32no—
745C22—61no—
746C22—61no—
747C22—61no—
748C22—61no—
749C22—61no—
750C22—124no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22#6390512yes—
755C22C2×D3×#6711yescharacteristic
756C4—41no—
757C4—41no—
758C4—61no—
759C4—61no—
760C4—121no—
761C4—121no—
762C4—121no—
763C4—361no—
764C4—361no—
765C4#6390512yes—
766C4C2×#379511yescharacteristic
767C4C2×#379811yescharacteristic
768C3—21no—
769C3#7884211yescharacteristic, complemented
770C3#8221511yescharacteristic, complemented
771C2—22no—
772C2—62no—
773C2—121no—
774C2—241no—
775C2C2×#6390511yescharacteristic
776C2D3×#95011yescharacteristic
777C2#1059545311yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10595022C2
hypercenter#117D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×D3×#117C2semidirect
3. #10592697C2semidirect
4. C3×#5002C2semidirect
5. #10591122C2semidirect
6. #10591083C2semidirect
7. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
8. #10590521C2semidirect
9. #10590519C2semidirect
10. #10590517C2semidirect
11. #10590516C2semidirect
12. #10590505C2semidirect
13. #10590502C2semidirect
14. #10590500C2semidirect
15. #10590498C2semidirect
41. #63635C22semidirect
42. #63635C22semidirect
43. #63634C22semidirect
44. #63634C22semidirect
45. C3×#810C22semidirect
46. C3×#810C22semidirect
47. C3×#809C22semidirect
48. C3×#809C22semidirect
49. #63575C22semidirect
50. #63575C22semidirect
51. #63573C22semidirect
52. #63573C22semidirect
53. #63565C22semidirect
54. #63565C22semidirect
55. #63562C22semidirect
56. #63562C22semidirect
64. D3×#117D3semidirect
73. #5002D3semidirect
213. #810C2×D3semidirect
214. #810C2×D3semidirect
217. #809C2×D3semidirect
218. #809C2×D3semidirect
682. C32#3091semidirect
769. C3#78842semidirect
770. C3#82215semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#1172
#105950222
#105926972
C3×#50022
#105911222
#105910832
C2×(C2×D3)⋊(C3⋊C8)2
#105905212
#105905192
#105905172
#105905162
#105905052
#105905022
#105905002
#105904982
#822153
#788423