Finite Group Databasebeta

← #11887577

Subgroups — #11887577

Order 1152.

902 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594517C211yesmaximal, characteristic
2#10594383C211yesmaximal, characteristic, complemented
3#10592563C211yesmaximal, characteristic, complemented
4C3×#4862C211yesmaximal, characteristic, complemented
5C3×#4854C211yesmaximal, characteristic, complemented
6#10590951C211yesmaximal, characteristic, complemented
7#10590906C211yesmaximal, characteristic, complemented
8#10590760C211yesmaximal, characteristic, complemented
9#10590672C211yesmaximal, characteristic, complemented
10#10590606C211yesmaximal, characteristic, complemented
11D3×#810C211yesmaximal, characteristic, complemented
12#10590577C211yesmaximal, characteristic, complemented
13#10590560C211yesmaximal, characteristic, complemented
14#10590458C211yesmaximal, characteristic, complemented
15#10590443C211yesmaximal, characteristic, complemented
16#81450—31nomaximal
17#81022—31nomaximal
18C2×#3799—21no—
19C2×#3797C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22C2×C8×C3⋊D3C2211yescharacteristic
23#64106C2211yescharacteristic
24#64104C2211yescharacteristic
25C3×#897C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#888C2211yescharacteristic
28C3×#887C2211yescharacteristic
29#63918—21no—
30#63909C2211yescharacteristic
31C4×#626C2211yescharacteristic
32#63900C2211yescharacteristic
33#63897—21no—
34#63895—21no—
35#63894C2211yescharacteristic
36#63893—21no—
37#63888—21no—
38#63880—21no—
39#63866C2211yescharacteristic
40#63850—21no—
41C2×#3717C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#106C2211yescharacteristic
45#63637C2211yescharacteristic
46#63636C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#808C2211yescharacteristic
54C3×#808C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63557C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5726—31no—
62#5632—31no—
63Q8×D12—31no—
64#5507—31no—
65C3×#483—31no—
66C3×#475—31no—
67#5093—31no—
68#5048—31no—
69C4×#215—31no—
70C2×#810—31no—
71#4864—31no—
72#4864—31no—
73#4864—31no—
74#4864—61no—
75#4862—31no—
76#4862—31no—
77#4862D311yescharacteristic, complemented
78#4854D311yescharacteristic, complemented
79#4852—31no—
80#4841—31no—
81#4834—31no—
82#4818—31no—
83#4806—31no—
84#4806—31no—
85#4806—31no—
86D3×#103—31no—
87D3×#103—31no—
88D3×#103—31no—
89#4792—31no—
90#4738—31no—
91#67⋊C8—31no—
92C2×C4⋊(C3⋊D3)—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6—21no—
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#627—21no—
102C2×#627—21no—
103C2×#626—21no—
104C2×#626D411yescharacteristic
105C2×#624—21no—
106C2×#624—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109#3799—44no—
110#3797—22no—
111#3797—41no—
112D3×Dic6—22no—
113D3×Dic6—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117#3752—21no—
118#3752—21no—
119C4⋊(C3⋊Dic3)—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121#3744—41no—
122C8×C3⋊D3—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3D411yescharacteristic
138#3722—21no—
139#3722—21no—
140#3722D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142#3717—22no—
143#3717—41no—
144D3×C3⋊C8—41no—
145#3298—91noSylow
146C2×#239—61no—
147C2×D3×Q8—31no—
148C2×D3×Q8—31no—
149C2×D3×Q8—31no—
150C2×#235—61no—
151C22×Dic6—31no—
152C3×C4⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C4×Q8—31no—
155C2×C3×C4⋊C4—31no—
156#946—61no—
157#944—31no—
158C2×#215—31no—
159C2×#215—31no—
160#930—31no—
161#929—61no—
162C4×#67—31no—
163C22×C3⋊C8—31no—
164C2×#204—31no—
165C2×#204—31no—
166C2×#204—31no—
167C2×#204—31no—
168C2×#204—61no—
169C2×D3×C8—31no—
170C2×D3×C8—31no—
171C2×D3×C8—31no—
172C2×D3×C8—61no—
173#897—31no—
174#897—31no—
175#897—61no—
176#897—61no—
177#897—61no—
178#897C2×D311yescharacteristic
179#896—61no—
180#896—61no—
181#895—31no—
182#895—31no—
183#895—31no—
184#895—61no—
185#894—61no—
186#894—61no—
187#894—61no—
188#893—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—31no—
191D3×C4⋊C4C2×D311yescharacteristic
192#888—61no—
193#888C2×D311yescharacteristic
194#887C2×D311yescharacteristic
195#67⋊C4—61no—
196#878—61no—
197C4×D12—31no—
198C4×D12—31no—
199C4×D12—61no—
200#869—31no—
201#869—61no—
202C3×#106—21no—
203C3×#106—31no—
204C3×#106—31no—
205C3×#106C2×D311yescharacteristic
206C3×#106C2×D311yescharacteristic
207C3×C4⋊C8—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×C22⋊C8—31no—
213#835—31no—
214#835—31no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8C2×D311yescharacteristic
218#816—31no—
219#816—31no—
220#816C2×D311yescharacteristic
221#816C2×D311yescharacteristic
222Dic3⋊C8C2×D311yescharacteristic
223C8×Dic3—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—61no—
231#810C2×D311yescharacteristic
232#810C2×D311yescharacteristic
233#809—31no—
234#809—31no—
235#809—61no—
236#808C2×D311yescharacteristic
237#808C2×D311yescharacteristic
238C4×C3⋊C8—31no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3C2×D411yescharacteristic
247C4⋊(C3⋊D3)—21no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—42no—
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252#634—21no—
253#634—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—42no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—42no—
268C3×Dic6#4112yescomplemented
269#627—42no—
270#627—42no—
271#626—42no—
272#626SD1614yescomplemented
273#624—42no—
274#624—42no—
275#624—42no—
276D3×Dic3—42no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281D4×Q8—91no—
282#547—91no—
283#487—91no—
284#483—31no—
285#483—91no—
286#475—31no—
287#465—91no—
288#465—91no—
289#461—91no—
290#448—91no—
291#448—91no—
292C4×SD16—91no—
293C8×D4—91no—
294C2×#103—91no—
295C2×#103—91no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C2×#67—31no—
302C2×#67—61no—
303C22×Dic3—61no—
304#239—124no—
305D3×Q8—62no—
306D3×Q8—62no—
307D3×Q8—62no—
308D3×Q8—121no—
309D3×Q8—121no—
310D3×Q8—121no—
311#235—124no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—121no—
320C2×C4×D3—21no—
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3C22×D311yescharacteristic
332C2×Dic6—21no—
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×Dic6—62no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C2×Dic6—61no—
340C2×Dic6—61no—
341C2×Dic6—121no—
342C2×Dic6C22×D311yescharacteristic
343C2×Dic6C22×D311yescharacteristic
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C22⋊C4—61no—
362C3×C42—31no—
363C3×C42—61no—
364#217—31no—
365#215—62no—
366#215—121no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
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—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—121no—
380(C2×D3)⋊C4—121no—
381C4⋊Dic3—21no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—121no—
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—31no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398C4×Dic3—21no—
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—121no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406#204—62no—
407#204—121no—
408#204—121no—
409#204—122no—
410#204—121no—
411D3×C8—121no—
412D3×C8—121no—
413D3×C8—121no—
414D3×C8—122no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3C2×SD1612yes—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3C2×SD1612yes—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3×Dic3—22no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3C2×SD1612yes—
438C2×#41—181no—
439C22×Q8—91no—
440C22×Q8—91no—
441C2×SD16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C22×C8—91no—
445C22×C8—91no—
446C4⋊Q8—31no—
447C4⋊Q8—91no—
448C4⋊Q8—181no—
449#123—181no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455C22⋊Q8—181no—
456#121—91no—
457#121—91no—
458C4×Q8—31no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—91no—
464#106—31no—
465#106—31no—
466#106D3211yescharacteristic
467C4⋊C8—31no—
468#103—31no—
469#103—31no—
470#103—31no—
471#103—31no—
472#103—91no—
473#103—91no—
474#103—91no—
475#103—91no—
476#103—91no—
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8—91no—
480C4×C8—91no—
481C23×C3—31no—
482C22×D3—31no—
483C22×D3—31no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—121no—
488C22×D3D3×D411yescharacteristic
489C3×Q8—32no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—122no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
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—122no—
511C2×C3×C4C23×D311yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513#67—34no—
514#67—122no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—121no—
525C2×Dic3—122no—
526C2×Dic3D3×D411yescharacteristic
527C2×Dic3D3×D411yescharacteristic
528C2×Dic3D3×D411yescharacteristic
529D12—34no—
530D12—61no—
531D12—61no—
532D12—61no—
533D12—61no—
534D12—121no—
535D12—121no—
536D12—122no—
537D12—122no—
538D12—122no—
539D12—242no—
540C4×D3—21no—
541C4×D3—21no—
542C4×D3—42no—
543C4×D3—61no—
544C4×D3—61no—
545C4×D3—61no—
546C4×D3—61no—
547C4×D3—121no—
548C4×D3—121no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3—122no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—122no—
555C4×D3—122no—
556Dic6—21no—
557Dic6—21no—
558Dic6—21no—
559Dic6—42no—
560Dic6—61no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—121no—
565Dic6—121no—
566Dic6—122no—
567Dic6—122no—
568Dic6—122no—
569Dic6—122no—
570Dic6#23912yescomplemented
571C3×C8—22no—
572C3×C8—21no—
573C3×C8—21no—
574C3×C8—61no—
575C3×C8—61no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—121no—
581C2×C32#54611yescharacteristic
582C2×C32C22×SD1611yescharacteristic
583C2×C32#57811yescharacteristic
584C3⋊D3—22no—
585C3⋊D3—81no—
586C3×D3—22no—
587#41—364no—
588C2×Q8—31no—
589C2×Q8—31no—
590C2×Q8—61no—
591C2×Q8—91no—
592C2×Q8—181no—
593C2×Q8—181no—
594C2×Q8—182no—
595C2×Q8—182no—
596C2×Q8—361no—
597C2×Q8—361no—
598C2×D4—91no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—181no—
602C22×C4—31no—
603C22×C4—61no—
604C22×C4—91no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—181no—
609SD16—182no—
610SD16—361no—
611SD16—361no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—91no—
615C2×C8—361no—
616C2×C8—361no—
617C2×C8C2×D3211yescharacteristic
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—61no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4C2×D3211yescharacteristic
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—61no—
632C22⋊C4—91no—
633C22⋊C4—91no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—31no—
639C42—61no—
640C22×C3—21no—
641C22×C3—32no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3C2×D3×D411yescharacteristic
645C22×C3C2×D3×D411yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—32no—
649C2×D3—32no—
650C2×D3—62no—
651C2×D3—61no—
652C2×D3—61no—
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—241no—
664C2×D3—241no—
665C2×D3—241no—
666C2×D3D3×SD1612yes—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—32no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—62no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—81no—
678C3×C4—81no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4C2×#23911yescharacteristic
683C3×C4D3×#4111yescharacteristic
684C3×C4#100911yescharacteristic
685C3×C4#100911yescharacteristic
686Dic3—21no—
687Dic3—21no—
688Dic3—22no—
689Dic3—41no—
690Dic3—41no—
691Dic3—41no—
692Dic3—61no—
693Dic3—61no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—241no—
698Dic3D3×SD1612yes—
699C32#329811yescharacteristic, complemented, Sylow
700C23—31no—
701C23—91no—
702C23—181no—
703Q8—32no—
704Q8—61no—
705Q8—61no—
706Q8—61no—
707Q8—122no—
708Q8—181no—
709Q8—181no—
710Q8—362no—
711Q8—362no—
712D4—94no—
713D4—181no—
714D4—181no—
715D4—362no—
716D4—362no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—91no—
729C2×C4—122no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—362no—
734C2×C4—362no—
735C2×C4—362no—
736C2×C4—362no—
737C2×C4C22×D3211yescharacteristic
738C8—21no—
739C8—61no—
740C8—61no—
741C8—181no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—62no—
746C2×C3#563011yescharacteristic
747C2×C3#565411yescharacteristic
748C2×C3C2×D3×SD1611yescharacteristic
749C2×C3C2×D3×SD1611yescharacteristic
750C2×C3#577911yescharacteristic
751C2×C3#577911yescharacteristic
752D3—22no—
753D3—62no—
754D3—62no—
755D3—122no—
756D3—241no—
757D3—241no—
758D3—481no—
759C22—32no—
760C22—61no—
761C22—61no—
762C22—92no—
763C22—181no—
764C22—181no—
765C22—361no—
766C22—361no—
767C22—361no—
768C22D32×D411yescharacteristic
769C4—32no—
770C4—41no—
771C4—41no—
772C4—61no—
773C4—62no—
774C4—61no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4—181no—
779C4—361no—
780C4#6430811yescharacteristic
781C4D3×#23911yescharacteristic
782C3—21no—
783C3#8102211yescharacteristic, complemented
784C3#8145011yescharacteristic, complemented
785C2—62no—
786C2—182no—
787C2—721no—
788C2#1059462011yescharacteristic
789C2D32×SD1611yescharacteristic
790C2#1059475211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10594517C2
hypercenter#106D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #10594383C2semidirect
3. #10592563C2semidirect
4. C3×#4862C2semidirect
5. C3×#4854C2semidirect
6. #10590951C2semidirect
7. #10590906C2semidirect
8. #10590760C2semidirect
9. #10590672C2semidirect
10. #10590606C2semidirect
11. D3×#810C2semidirect
12. #10590577C2semidirect
13. #10590560C2semidirect
14. #10590458C2semidirect
15. #10590443C2semidirect
77. #4862D3semidirect
78. #4854D3semidirect
268. C3×Dic6#41semidirect
272. #626SD16semidirect
570. Dic6#239semidirect
699. C32#3298semidirect
783. C3#81022semidirect
784. C3#81450semidirect

Maximal subgroups

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

subgroupindex
#105945172
#105943832
#105925632
C3×#48622
C3×#48542
#105909512
#105909062
#105907602
#105906722
#105906062
D3×#8102
#105905772
#105905602
#105904582
#105904432
#814503
#810223