Finite Group Databasebeta

← #11869690

Subgroups — #11869690

Order 1152.

919 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#117C211yesmaximal, characteristic, complemented
2#10595023C211yesmaximal, characteristic
3#10592701C211yesmaximal, characteristic, complemented
4C3×#4998C211yesmaximal, characteristic, complemented
5#10591138C211yesmaximal, characteristic, complemented
6#10591105C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590429C211yesmaximal, characteristic, complemented
9#10590428C211yesmaximal, characteristic, complemented
10#10590427C211yesmaximal, characteristic, complemented
11#10590426C211yesmaximal, characteristic, complemented
12#10590425C211yesmaximal, characteristic, complemented
13#10590424C211yesmaximal, characteristic, complemented
14#10590423C211yesmaximal, characteristic, complemented
15#10590422C211yesmaximal, characteristic, complemented
16#82215—31nomaximal
17#79185—31nomaximal
18C2×#3828C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C32×#117C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#926C2211yescharacteristic
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#63977—21no—
34#63966—21no—
35#63909C2211yescharacteristic
36#63909C2211yescharacteristic
37C4×#626—21no—
38C4×#626—21no—
39#63857C2211yescharacteristic
40#63857C2211yescharacteristic
41#63637C2211yescharacteristic, complemented
42#63637C2211yescharacteristic, complemented
43#63636C2211yescharacteristic, complemented
44#63636C2211yescharacteristic, complemented
45C3×#808C2211yescharacteristic, complemented
46C3×#808C2211yescharacteristic, complemented
47C3×#807C2211yescharacteristic, complemented
48C3×#807C2211yescharacteristic, complemented
49#63576C2211yescharacteristic, complemented
50#63576C2211yescharacteristic, complemented
51#63574C2211yescharacteristic, complemented
52#63574C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63567C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, 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#5791—31no—
63#5524—31no—
64D3×#117D311yescharacteristic, complemented
65C3×#427—31no—
66C2×#830—31no—
67#5113—31no—
68C2×(C2×D3)⋊C8—31no—
69#5003—31no—
70#5003—31no—
71#5002—31no—
72#5002—31no—
73#5002—31no—
74#5002—61no—
75#4998—31no—
76#4998—31no—
77#4998D311yescharacteristic, complemented
78#4996—31no—
79#4996—31no—
80#4971—31no—
81#4970—31no—
82#4968—31no—
83#4967—31no—
84#4888—31no—
85#4885—31no—
86#4884—31no—
87#4882—31no—
88#4868—31no—
89#4866—31no—
90#4863—31no—
91#4862—31no—
92C23×C3×D3D411yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95#3828—22no—
96#3828—22no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634C2311yescharacteristic
100C22×C3×Dic3D411yescharacteristic
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×#626—21no—
110C2×#626—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C42—21no—
115C2×C3⋊(C3⋊C8)—22no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—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
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141#3091—91noSylow
142C23×C3×C4—31no—
143C2×#235—31no—
144C2×#235—31no—
145C2×#235—61no—
146C22×C4×D3C2×D311yescharacteristic
147C22×C3×C8—31no—
148C3×#117—21no—
149C3×#117—31no—
150C3×#117—31no—
151C3×#117—31no—
152C3×#117—31no—
153C3×#117—61no—
154C3×#117—61no—
155C3×#117C2×D311yescharacteristic
156C3×#117C2×D311yescharacteristic
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—31no—
159C2×C3×C22⋊C4—61no—
160C2×C3×C42—61no—
161#953—61no—
162#930—31no—
163#930—31no—
164#929—61no—
165C4×#67—61no—
166C4×#67—61no—
167#926C2×D311yescharacteristic
168#926C2×D311yescharacteristic
169#924—31no—
170#924—31no—
171C22×C3⋊C8—31no—
172C22×C3⋊C8—31no—
173C22×C3⋊C8—61no—
174C22×C3⋊C8C2×D311yescharacteristic
175#897—31no—
176#897—31no—
177#895—31no—
178#895—31no—
179#892C2×D311yescharacteristic
180#892C2×D311yescharacteristic
181D3×C4⋊C4C2×D311yescharacteristic
182D3×C4⋊C4C2×D311yescharacteristic
183#886—61no—
184#882—61no—
185D3×C22⋊C4—21no—
186#877—21no—
187C4×D12—61no—
188C4×D12—61no—
189#872—21no—
190C42×D3—21no—
191C3×#107—31no—
192C3×#107—31no—
193C3×#106—31no—
194C3×#106—31no—
195#830—31no—
196#830—31no—
197#830—31no—
198#830—31no—
199#821—31no—
200#821—31no—
201(C2×D3)⋊C8—31no—
202(C2×D3)⋊C8—31no—
203(C2×D3)⋊C8—31no—
204(C2×D3)⋊C8—31no—
205#816—31no—
206#816—31no—
207#810—31no—
208#810—31no—
209#810—31no—
210#810—31no—
211#810—31no—
212#810—31no—
213#810—61no—
214#810—61no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—61no—
222#809—61no—
223#808—31no—
224#808—31no—
225#808—31no—
226#808—31no—
227#808C2×D311yescharacteristic, complemented
228#808C2×D311yescharacteristic, complemented
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807C2×D311yescharacteristic, complemented
234#807C2×D311yescharacteristic, complemented
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3—21no—
237C22×C3×D3—22no—
238C22×C3×D3—22no—
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
248#638—42no—
249C2×C3⋊Dic3—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4×C3⋊D3—42no—
253#634—21no—
254#634—21no—
255C2×C3×Dic3—22no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×C4×D3—22no—
263C3×C4×D3—22no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—42no—
269C3×C4×D3—42no—
270#626—42no—
271#626—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—31no—
287#427—91no—
288#416—91no—
289#416—91no—
290C2×C22⋊C8—91no—
291C24×C3—31no—
292C23×D3#6711yescharacteristic
293C22×C3×C4—21no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C22×C3×C4—62no—
302C22×C3×C4—62no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—121no—
310C22×Dic3#6711yescharacteristic
311#235—64no—
312#235—62no—
313#235—62no—
314#235—62no—
315#235—62no—
316#235—122no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×C4×D3—22no—
323C2×C4×D3—22no—
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—121no—
329C2×C4×D3#6711yescharacteristic
330C2×C4×D3#6711yescharacteristic
331C2×C4×D3C22×D311yescharacteristic
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8—62no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—41no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—21no—
359C3×C42—21no—
360C3×C42—41no—
361C3×C42—61no—
362C3×C42—61no—
363C3×C42—61no—
364C3×C42—61no—
365#217—21no—
366#217—21no—
367#217—61no—
368#217—61no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C2×C3⋊C8—22no—
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⋊C8—62no—
399C2×C3⋊C8—62no—
400C2×C3⋊C8—122no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403C22×C32—21no—
404C22×C32—21no—
405C22×C32#12312yes—
406C22×C32C22×D411yescharacteristic
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—44no—
416C2×C3×D3#13512yes—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4#12312yes—
420C32×C4C2×#4111yescharacteristic
421C32×C4C2×#4111yescharacteristic
422C3⋊Dic3—41no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C2×#41—91no—
430C23×C4—31no—
431C22×C8—31no—
432C22×C8—91no—
433#123—181no—
434C22⋊Q8—91no—
435C22⋊Q8—91no—
436#121—91no—
437#121—91no—
438#120—181no—
439C4×D4—181no—
440C4×D4—181no—
441#117—31no—
442#117—31no—
443#117—31no—
444#117—31no—
445#117—61no—
446#117—61no—
447#117D3211yescharacteristic
448C2×C4⋊C4—31no—
449C2×C4⋊C4—31no—
450C2×C22⋊C4—61no—
451C2×C42—61no—
452#107—31no—
453#107—31no—
454#107—91no—
455#107—91no—
456#106—31no—
457#106—31no—
458#106—91no—
459#106—91no—
460#103—91no—
461#103—91no—
462#103—91no—
463#103—91no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468C22⋊C8—91no—
469C22⋊C8—91no—
470C22⋊C8—91no—
471C22⋊C8—91no—
472C23×C3—21no—
473C23×C3—31no—
474C23×C3—31no—
475C23×C3—62no—
476C23×C3—62no—
477C23×C3—121no—
478C23×C3D3×D411yescharacteristic
479C23×C3C2×#6711yescharacteristic
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—41no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—121no—
486C22×D3C2×#6711yescharacteristic
487C22×D3C2×#6711yescharacteristic
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—21no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—62no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
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—122no—
512C2×C3×C4—122no—
513C2×C3×C4#23512yes—
514C2×C3×C4#23512yes—
515C2×C3×C4#23512yes—
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4#23912yes—
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—122no—
522#67—122no—
523#67—124no—
524#67—122no—
525#67—122no—
526C2×Dic3—22no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—121no—
534C2×Dic3C2×#6711yescharacteristic
535C2×Dic3C2×#6711yescharacteristic
536D12—62no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12—61no—
541D12—121no—
542D12—122no—
543D12—122no—
544C4×D3—22no—
545C4×D3—22no—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—42no—
551C4×D3—42no—
552C4×D3—124no—
553C4×D3—122no—
554C4×D3—122no—
555Dic6—62no—
556Dic6—61no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—121no—
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—22no—
572C2×C32C2×#12311yescharacteristic
573C2×C32C2×#13511yescharacteristic
574C2×C32#57511yescharacteristic
575C3⋊D3—81no—
576C3×D3—22no—
577C3×D3—41no—
578C24—31no—
579#41—182no—
580#41—182no—
581C2×Q8—91no—
582C2×D4—91no—
583C2×D4—181no—
584C2×D4—181no—
585C2×D4—181no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—62no—
594C22×C4—62no—
595C22×C4—181no—
596C22×C4C2×D3211yescharacteristic
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—62no—
600C2×C8—91no—
601C2×C8—91no—
602C2×C8—182no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4C2×D3211yescharacteristic
612C4⋊C4C2×D3211yescharacteristic
613C22⋊C4—21no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C42—21no—
623C42—61no—
624C42—61no—
625C42—61no—
626C42—61no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—22no—
633C22×C3—32no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—124no—
642C22×C3#89412yes—
643C22×C3#92912yes—
644C22×C3C2×D3×D411yescharacteristic
645C22×C3C22×#6711yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—44no—
652C2×D3—122no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—241no—
660C2×D3—241no—
661C2×D3#95012yes—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—22no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—81no—
672C3×C4—81no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4#89412yes—
678C3×C4#92912yes—
679C3×C4C2×#23511yescharacteristic
680C3×C4C2×#23511yescharacteristic
681C3×C4C2×#23511yescharacteristic
682C3×C4C2×#23911yescharacteristic
683Dic3—21no—
684Dic3—21no—
685Dic3—41no—
686Dic3—41no—
687Dic3—41no—
688Dic3—41no—
689Dic3—122no—
690Dic3—121no—
691Dic3—121no—
692C32#309111yescharacteristic, complemented, Sylow
693C23—31no—
694C23—31no—
695C23—62no—
696C23—62no—
697C23—121no—
698C23—181no—
699C23D3×#6711yescharacteristic
700Q8—181no—
701Q8—181no—
702D4—181no—
703D4—181no—
704D4—362no—
705D4—362no—
706D4—362no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—31no—
710C2×C4—31no—
711C2×C4—62no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—181no—
725C2×C4—362no—
726C2×C4#379812yes—
727C2×C4#379912yes—
728C2×C4D3×#6711yescharacteristic
729C2×C4C22×D3211yescharacteristic
730C8—61no—
731C8—61no—
732C8—181no—
733C8—181no—
734C2×C3—22no—
735C2×C3—22no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—42no—
740C2×C3—62no—
741C2×C3—121no—
742C2×C3C2×#89411yescharacteristic
743C2×C3D3×#13511yescharacteristic
744C2×C3#576811yescharacteristic
745C2×C3C2×#92911yescharacteristic
746C2×C3C2×#95011yescharacteristic
747C2×C3#582211yescharacteristic
748D3—22no—
749D3—41no—
750D3—242no—
751D3—241no—
752D3—241no—
753C22—21no—
754C22—21no—
755C22—32no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—124no—
762C22—361no—
763C22—361no—
764C22—361no—
765C22#6385012yes—
766C22C2×D3×#6711yescharacteristic
767C4—41no—
768C4—41no—
769C4—61no—
770C4—61no—
771C4—121no—
772C4—121no—
773C4—121no—
774C4—121no—
775C4—361no—
776C4#6385012yes—
777C4C2×#379811yescharacteristic
778C4C2×#379911yescharacteristic
779C3—21no—
780C3#7918511yescharacteristic, complemented
781C3#8221511yescharacteristic, complemented
782C2—22no—
783C2—62no—
784C2—121no—
785C2—721no—
786C2C2×#6385011yescharacteristic
787C2D3×#95011yescharacteristic
788C2#1059545311yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10595023C2
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. #10592701C2semidirect
4. C3×#4998C2semidirect
5. #10591138C2semidirect
6. #10591105C2semidirect
7. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
8. #10590429C2semidirect
9. #10590428C2semidirect
10. #10590427C2semidirect
11. #10590426C2semidirect
12. #10590425C2semidirect
13. #10590424C2semidirect
14. #10590423C2semidirect
15. #10590422C2semidirect
41. #63637C22semidirect
42. #63637C22semidirect
43. #63636C22semidirect
44. #63636C22semidirect
45. C3×#808C22semidirect
46. C3×#808C22semidirect
47. C3×#807C22semidirect
48. C3×#807C22semidirect
49. #63576C22semidirect
50. #63576C22semidirect
51. #63574C22semidirect
52. #63574C22semidirect
53. #63567C22semidirect
54. #63567C22semidirect
55. #63564C22semidirect
56. #63564C22semidirect
64. D3×#117D3semidirect
77. #4998D3semidirect
227. #808C2×D3semidirect
228. #808C2×D3semidirect
233. #807C2×D3semidirect
234. #807C2×D3semidirect
692. C32#3091semidirect
780. C3#79185semidirect
781. 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
#105950232
#105927012
C3×#49982
#105911382
#105911052
C2×(C2×D3)⋊(C3⋊C8)2
#105904292
#105904282
#105904272
#105904262
#105904252
#105904242
#105904232
#105904222
#822153
#791853