Finite Group Databasebeta

← #11887223

Subgroups — #11887223

Order 1152.

878 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5639C211yesmaximal, characteristic, complemented
2#10595067C211yesmaximal, characteristic
3#10592747C211yesmaximal, characteristic, complemented
4C3×#5047C211yesmaximal, characteristic, complemented
5#10591651C211yesmaximal, characteristic, complemented
6#10591635C211yesmaximal, characteristic, complemented
7#10591607C211yesmaximal, characteristic, complemented
8Dic3×#215C211yesmaximal, characteristic, complemented
9#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#10591136C211yesmaximal, characteristic, complemented
11#10591083C211yesmaximal, characteristic, complemented
12D3×#809C211yesmaximal, characteristic, complemented
13#10590537C211yesmaximal, characteristic, complemented
14#10590516C211yesmaximal, characteristic, complemented
15#10590469C211yesmaximal, characteristic, complemented
16#83598—31nomaximal
17#80246—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic, complemented
21C2×#3755C2211yescharacteristic
22#64139C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C3×C4×#67C2211yescharacteristic
29C3×#926C2211yescharacteristic, complemented
30C3×#892—21no—
31C3×D3×C4⋊C4C2211yescharacteristic
32C3×#890C2211yescharacteristic, complemented
33C3×#889—21no—
34C3×#883—21no—
35C3×#879—21no—
36#63983—21no—
37#63971—21no—
38D3×(C2×D3)⋊C4—21no—
39Dic3×D12C2211yescharacteristic
40#63864C2211yescharacteristic
41#63856C2211yescharacteristic
42#63850—21no—
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic, complemented
45#63636C2211yescharacteristic
46#63635C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic, complemented
48C3×#810C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50#63575C2211yescharacteristic, complemented
51#63573C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63565C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#552—31no—
62#5829—31no—
63#5639D311yescharacteristic, complemented
64#5550—31no—
65C3×#452—31no—
66#5233—31no—
67#5188—31no—
68#5185—31no—
69#5169—31no—
70Dic3×SD16—31no—
71#5068—31no—
72#5066—31no—
73#5051—31no—
74#5048—31no—
75#5048—31no—
76#5048—61no—
77#5047D311yescharacteristic, complemented
78#5046—31no—
79#5028—31no—
80C4×#215—31no—
81D4×C3⋊C8—31no—
82#5003—31no—
83#5002—31no—
84#4971—31no—
85C2×#809—31no—
86#4805—31no—
87#4800—31no—
88D3×#102—31no—
89#4766—31no—
90#4737—31no—
91#67⋊C8—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67D411yescharacteristic
99C3×#235—22no—
100C3×#235—41no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×D3×Dic3—21no—
108D3×D12—22no—
109D3×D12—41no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113#3755—41no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)—41no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×#216—41no—
122C3×#215—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3724—21no—
139#3722—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×C3×#41—31no—
146C2×D3×D4—31no—
147C2×#235C2×D311yescharacteristic
148C22×D12—31no—
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C3×#126—61no—
152C3×#125—31no—
153C3×#125—61no—
154C3×#123—61no—
155C3×C22⋊Q8—21no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8C2×D311yescharacteristic, complemented
158C3×C22⋊Q8C2×D311yescharacteristic, complemented
159C3×C4×Q8—31no—
160C3×C4×D4—31no—
161C3×#117—31no—
162C3×#117—61no—
163C2×C3×C4⋊C4—31no—
164#947—31no—
165#946—31no—
166#946C2×D311yescharacteristic
167Q8×Dic3C2×D311yescharacteristic, complemented
168C2×#216C2×D311yescharacteristic, complemented
169C2×#215—31no—
170C2×#215—31no—
171C2×#215—61no—
172C2×#215C2×D311yescharacteristic
173#939—61no—
174#937—61no—
175#937—61no—
176D4×Dic3—31no—
177#930—31no—
178#930—31no—
179#930—61no—
180#929—61no—
181C4×#67C2×D311yescharacteristic
182C2×(C2×D3)⋊C4—61no—
183#926C2×D311yescharacteristic, complemented
184#924—31no—
185C22×C3⋊C8—31no—
186C22×C3⋊C8—31no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8—61no—
189C2×D3×C8—31no—
190#894—61no—
191#892—21no—
192D3×C4⋊C4C2×D311yescharacteristic
193#890C2×D311yescharacteristic, complemented
194#889—21no—
195#884—61no—
196#883—21no—
197D3×C22⋊C4—61no—
198#879—21no—
199#875—31no—
200C4×D12—31no—
201C3×#103—31no—
202C3×#102—31no—
203C3×C22⋊C8—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—61no—
209#832—31no—
210#832—31no—
211#830—31no—
212#830C2×D311yescharacteristic, complemented
213#821—31no—
214#821—31no—
215(C2×D3)⋊C8—31no—
216#818—31no—
217#817—31no—
218Dic3⋊C8—31no—
219C8×Dic3—31no—
220#810—31no—
221#810—31no—
222#810C2×D311yescharacteristic, complemented
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—61no—
230#809C2×D311yescharacteristic
231#808—31no—
232#808—31no—
233#808—31no—
234#808—61no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253#638—81no—
254C2×C3⋊Dic3—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C3×#67—22no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—42no—
270C3×C4×D3—42no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273#626—42no—
274D3×Dic3—81no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—31no—
280#546—91no—
281#488—91no—
282#483—91no—
283#482—91no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—31no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8—31no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—61no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
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—121no—
316C2×#67#6711yescharacteristic
317C22×Dic3—61no—
318D3×D4—62no—
319D3×D4—121no—
320#235—22no—
321#235—41no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—61no—
325C2×D12—62no—
326C2×D12—61no—
327C2×D12—121no—
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6C22×D311yescharacteristic
334C3×Q16—121no—
335C3×SD16—62no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—41no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
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×C42—31no—
360C3×C42—61no—
361C3×C42—61no—
362#217—21no—
363#217—61no—
364#217—61no—
365#217#6711yescharacteristic
366#216—41no—
367#215—22no—
368#215—121no—
369#215—121no—
370#215—122no—
371(C2×D3)⋊C4—21no—
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—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—121no—
381(C2×D3)⋊C4#6711yescharacteristic
382C4⋊Dic3—21no—
383C4⋊Dic3—21no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4#6711yescharacteristic
395C4×Dic3—21no—
396C4×Dic3—21no—
397C4×Dic3C22×D311yescharacteristic
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8—122no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410D3×C8—121no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3#13512yes—
424D32—84no—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—31no—
438C22×D4—91no—
439C2×Q16—31no—
440C2×SD16—31no—
441C2×SD16—91no—
442C22×C8—91no—
443C22×C8—91no—
444#126—61no—
445#125—31no—
446#125—61no—
447#124—91no—
448#123—61no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452C22⋊Q8D3211yescharacteristic, complemented
453#121—91no—
454#121—181no—
455#120—181no—
456C4×Q8—31no—
457C4×D4—31no—
458C4×D4—91no—
459#117—31no—
460#117—61no—
461C2×C4⋊C4—31no—
462C2×C22⋊C4—181no—
463#107—91no—
464#106—91no—
465#106—91no—
466C4⋊C8—91no—
467#103—31no—
468#103—91no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—31no—
478C22⋊C8—91no—
479C4×C8—91no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—61no—
483C23×C3D3×D411yescharacteristic
484C23×C3C2×#6711yescharacteristic
485C22×D3—21no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—121no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—241no—
494C22×D3—241no—
495C22×D3C2×#6711yescharacteristic
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—41no—
501C3×Q8—41no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×D4—32no—
505C3×D4—62no—
506C3×D4—61no—
507C3×D4—122no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
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—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—122no—
531C2×C3×C4—122no—
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4C2×#6711yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536#67—22no—
537#67—42no—
538#67—122no—
539#67—241no—
540#67—241no—
541#67—242no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3—241no—
549C2×Dic3C2×#6711yescharacteristic
550C2×Dic3C2×#6711yescharacteristic
551C2×Dic3C2×#6711yescharacteristic
552D12—21no—
553D12—61no—
554D12—61no—
555D12—61no—
556D12—61no—
557D12—121no—
558D12—121no—
559D12—122no—
560D12#23712yes—
561C4×D3—21no—
562C4×D3—21no—
563C4×D3—42no—
564C4×D3—42no—
565C4×D3—241no—
566Dic6—21no—
567Dic6—21no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—62no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C3⋊C8—121no—
578C2×C32—41no—
579C2×C32#54611yescharacteristic
580C2×C32C2×#13511yescharacteristic
581C2×C32#57711yescharacteristic
582C3⋊D3—81no—
583C3×D3—22no—
584C3×D3—42no—
585C24—181no—
586#41—62no—
587#41—121no—
588C2×Q8—31no—
589C2×Q8C2×D3211yescharacteristic
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—61no—
593C2×D4—91no—
594C2×D4—181no—
595C2×D4—182no—
596C2×D4—181no—
597C2×D4—361no—
598C22×C4—31no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—181no—
602C22×C4C2×D3211yescharacteristic
603Q16—121no—
604SD16—62no—
605SD16—361no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8—91no—
610C2×C8—361no—
611C2×C8—361no—
612C4⋊C4—21no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—91no—
622C4⋊C4—181no—
623C4⋊C4C2×D3211yescharacteristic
624C22⋊C4—21no—
625C22⋊C4—31no—
626C22⋊C4—31no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—31no—
635C42—61no—
636C42—61no—
637C22×C3—22no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—32no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—62no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3C2×D3×D411yescharacteristic
654C22×C3C22×#6711yescharacteristic
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—22no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—241no—
667C2×D3—241no—
668C2×D3—241no—
669C2×D3—244no—
670C2×D3—244no—
671C2×D3#95012yes—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—61no—
684C3×C4—81no—
685C3×C4—81no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4C2×#23711yescharacteristic
690C3×C4#100411yescharacteristic
691C3×C4D3×#4111yescharacteristic
692C3×C4#100911yescharacteristic
693Dic3—21no—
694Dic3—21no—
695Dic3—21no—
696Dic3—41no—
697Dic3—41no—
698Dic3—41no—
699Dic3—121no—
700Dic3—121no—
701Dic3—241no—
702C32#329611yescharacteristic, complemented, Sylow
703C23—31no—
704C23—61no—
705C23—181no—
706C23—362no—
707C23—362no—
708C23—721no—
709C23D3×#6711yescharacteristic
710Q8—21no—
711Q8—21no—
712Q8—61no—
713Q8—61no—
714D4—32no—
715D4—62no—
716D4—61no—
717D4—122no—
718D4—181no—
719D4—181no—
720D4—362no—
721D4—721no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—122no—
735C2×C4—122no—
736C2×C4—181no—
737C2×C4—721no—
738C2×C4D3×#6711yescharacteristic
739C2×C4C22×D3211yescharacteristic
740C8—61no—
741C8—61no—
742C8—181no—
743C8—181no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—42no—
748C2×C3—41no—
749C2×C3—41no—
750C2×C3—62no—
751C2×C3—122no—
752C2×C3#559111yescharacteristic
753C2×C3D3×#13511yescharacteristic
754C2×C3#577811yescharacteristic
755C2×C3C2×#95011yescharacteristic
756C2×C3#582911yescharacteristic
757C2×C3#583711yescharacteristic
758D3—22no—
759D3—42no—
760D3—241no—
761D3—241no—
762D3—481no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—32no—
767C22—61no—
768C22—61no—
769C22—62no—
770C22—121no—
771C22—121no—
772C22—361no—
773C22—361no—
774C22—361no—
775C22—724no—
776C22C2×D3×#6711yescharacteristic
777C4—21no—
778C4—41no—
779C4—41no—
780C4—61no—
781C4—61no—
782C4—61no—
783C4—121no—
784C4—121no—
785C4—121no—
786C4—361no—
787C4D3×#23711yescharacteristic
788C4#6431411yescharacteristic
789C3—21no—
790C3#8024611yescharacteristic, complemented
791C3#8359811yescharacteristic, complemented
792C2—41no—
793C2—62no—
794C2—122no—
795C2—721no—
796C2#1059530411yescharacteristic
797C2#1059531911yescharacteristic
798C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10595067C2
hypercenterC22⋊Q8D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5639C2semidirect
3. #10592747C2semidirect
4. C3×#5047C2semidirect
5. #10591651C2semidirect
6. #10591635C2semidirect
7. #10591607C2semidirect
8. Dic3×#215C2semidirect
9. #67⋊(C3⋊C8)C2semidirect
10. #10591136C2semidirect
11. #10591083C2semidirect
12. D3×#809C2semidirect
13. #10590537C2semidirect
14. #10590516C2semidirect
15. #10590469C2semidirect
20. C32×C22⋊Q8C22semidirect
23. C22×C3⋊(C3⋊C8)C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C2×C3×#216C22semidirect
29. C3×#926C22semidirect
32. C3×#890C22semidirect
44. #63662C22semidirect
46. #63635C22semidirect
47. C3×#830C22semidirect
48. C3×#810C22semidirect
50. #63575C22semidirect
51. #63573C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63565C22semidirect
54. #63565C22semidirect
60. Dic3×C3⋊C8C22semidirect
63. #5639D3semidirect
77. #5047D3semidirect
157. C3×C22⋊Q8C2×D3semidirect
158. C3×C22⋊Q8C2×D3semidirect
167. Q8×Dic3C2×D3semidirect
168. C2×#216C2×D3semidirect
183. #926C2×D3semidirect
193. #890C2×D3semidirect
212. #830C2×D3semidirect
222. #810C2×D3semidirect
452. C22⋊Q8D32semidirect
702. C32#3296semidirect
790. C3#80246semidirect
791. C3#83598semidirect

Maximal subgroups

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

subgroupindex
C3×#56392
#105950672
#105927472
C3×#50472
#105916512
#105916352
#105916072
Dic3×#2152
#67⋊(C3⋊C8)2
#105911362
#105910832
D3×#8092
#105905372
#105905162
#105904692
#835983
#802463