Finite Group Databasebeta

← #11887169

Subgroups — #11887169

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594621C211yesmaximal, characteristic
2#10594536C211yesmaximal, characteristic, complemented
3#10592562C211yesmaximal, characteristic, complemented
4C3×#4863C211yesmaximal, characteristic, complemented
5C3×#4852C211yesmaximal, characteristic, complemented
6#10590943C211yesmaximal, characteristic, complemented
7#10590942C211yesmaximal, characteristic, complemented
8#10590878C211yesmaximal, characteristic, complemented
9#10590721C211yesmaximal, characteristic, complemented
10#10590593C211yesmaximal, characteristic, complemented
11D3×#809C211yesmaximal, characteristic, complemented
12#10590558C211yesmaximal, characteristic, complemented
13#10590549C211yesmaximal, characteristic, complemented
14#10590523C211yesmaximal, characteristic, complemented
15#10590514C211yesmaximal, characteristic, complemented
16#81342—31nomaximal
17#79676—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×D3×D12—21no—
20C2×D3×D12C2211yescharacteristic
21#64104C2211yescharacteristic
22C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C3×#204C2211yescharacteristic
24C3×#895C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic, complemented
27C3×#887C2211yescharacteristic, complemented
28#63923—21no—
29#63922—21no—
30#63918C2211yescharacteristic, complemented
31#63911C2211yescharacteristic
32#63906—21no—
33C4×#626—21no—
34C4×#626C2211yescharacteristic
35#63871C2211yescharacteristic, complemented
36#63867—21no—
37#63865—21no—
38#63856C2211yescharacteristic, complemented
39#63851—21no—
40C2×#3717C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic, complemented
42C2×#3710C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#106C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63647C2211yescharacteristic, complemented
47#63636C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×C8×Dic3C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#809C2211yescharacteristic, complemented
55C3×#808C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61#5609—31no—
62#5579—31no—
63D4×D12—31no—
64#5511—31no—
65C3×#481—31no—
66C3×C4×SD16—31no—
67#5169—31no—
68#5169—31no—
69#5041—31no—
70#5027—31no—
71#5008—31no—
72C2×#809—31no—
73#4870—31no—
74#4864—31no—
75#4863—31no—
76#4863—31no—
77#4863—61no—
78#4863D311yescharacteristic, complemented
79#4852D311yescharacteristic, complemented
80#4807—31no—
81#4807—31no—
82#4776—31no—
83D3×#102—31no—
84D3×#102—31no—
85D3×#102—31no—
86#4762—31no—
87#4760—31no—
88#4731—31no—
89#67⋊C8—31no—
90#4694—31no—
91C8×D12—31no—
92C22×D32—21no—
93C22×D32—21no—
94C2×C4⋊(C3⋊D3)—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#626D411yescharacteristic
110C2×#625—21no—
111#3802—22no—
112#3802—41no—
113D3×D12—22no—
114D3×D12—41no—
115D3×D12—44no—
116C2×C32×C8C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119#3752—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×#204—22no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722—21no—
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141#3717—41no—
142#3715—41no—
143#3710—41no—
144D3×C3⋊C8—41no—
145#3295—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12—61no—
152C2×C3×SD16—31no—
153C3×#121—31no—
154C3×C4×Q8—31no—
155C3×C4×D4—31no—
156C2×C3×C4⋊C4—31no—
157#946—31no—
158#946—31no—
159C2×#215—31no—
160C2×#215—31no—
161#940—31no—
162#937—61no—
163C2×#214—31no—
164#930—61no—
165C4×#67—31no—
166C4×#67—61no—
167#924—31no—
168#924—61no—
169C22×C3⋊C8—31no—
170C2×#204—31no—
171C2×#204C2×D311yescharacteristic
172C2×D3×C8—31no—
173C2×D3×C8—31no—
174C2×D3×C8—31no—
175#897—31no—
176#896—61no—
177#896—61no—
178#896—61no—
179#895—31no—
180#895—31no—
181#895—61no—
182#895C2×D311yescharacteristic
183#893C2×D311yescharacteristic
184D3×C4⋊C4—31no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—61no—
187D3×C4⋊C4C2×D311yescharacteristic, complemented
188#889—61no—
189#888—31no—
190#887C2×D311yescharacteristic, complemented
191#884—61no—
192#882—61no—
193#882—61no—
194#882—61no—
195#874—31no—
196C4×D12—31no—
197C4×D12—61no—
198#870—61no—
199#869—31no—
200C3×#106—21no—
201C3×#106—31no—
202C3×#106C2×D311yescharacteristic, complemented
203C3×#106C2×D311yescharacteristic, complemented
204C3×#103—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×C22⋊C8—31no—
209C3×C4×C8—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—61no—
219#821C2×D311yescharacteristic, complemented
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—61no—
223(C2×D3)⋊C8C2×D311yescharacteristic, complemented
224Dic3⋊C8—31no—
225C8×Dic3C2×D311yescharacteristic, complemented
226#810C2×D311yescharacteristic, complemented
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—61no—
232#809C2×D311yescharacteristic
233#809C2×D311yescharacteristic, complemented
234#808—31no—
235#808—31no—
236#808—61no—
237#808C2×D311yescharacteristic, complemented
238C4⋊(C3⋊C8)—31no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3C2×D411yescharacteristic
244C2×D32—42no—
245C2×D32—42no—
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—81no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2411yescharacteristic
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—42no—
258C4×C3⋊D3—21no—
259C4×C3⋊D3—21no—
260C4×C3⋊D3—81no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—42no—
270C3×D12#4112yes—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273C3×C4×D3—42no—
274C3×C4×D3—81no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277#627—81no—
278#626—42no—
279#626—42no—
280#626—81no—
281#626SD1614yescomplemented
282#625—42no—
283C32×C8—21no—
284C3⋊(C3⋊C8)—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287#554—91no—
288D42—91no—
289#486—91no—
290#481—31no—
291#481—91no—
292#476—91no—
293#465—91no—
294#465—91no—
295#460—91no—
296#450—91no—
297#450—91no—
298C4×SD16—31no—
299C8×D4—91no—
300C2×#102—91no—
301C2×#102—91no—
302C23×D3—61no—
303C23×D3—61no—
304C23×D3—61no—
305C23×D3—61no—
306C2×C3×Q8—31no—
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—61no—
310C22×C3×C4—31no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C2×#67—31no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319D3×D4—62no—
320D3×D4—62no—
321D3×D4—62no—
322D3×D4—121no—
323D3×D4—124no—
324D3×D4—121no—
325D3×D4—121no—
326C2×D12—21no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—61no—
331C2×D12—62no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—121no—
338C2×D12—121no—
339C2×D12—124no—
340C2×D12C22×D311yescharacteristic
341C2×D12C22×D311yescharacteristic
342C2×C4×D3—21no—
343C2×C4×D3—21no—
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—121no—
350C2×C4×D3C22×D311yescharacteristic
351C2×Dic6—61no—
352C2×Dic6—61no—
353C2×Dic6C22×D311yescharacteristic
354C3×SD16—62no—
355C2×C3×C8—21no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C22×D311yescharacteristic
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C4⋊C4C22×D311yescharacteristic
366C3×C4⋊C4C22×D311yescharacteristic
367C3×C4⋊C4C22×D311yescharacteristic
368C3×C4⋊C4C22×D311yescharacteristic
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—31no—
372C3×C42—61no—
373#217—31no—
374#217—61no—
375#215—121no—
376#215—121no—
377#214—121no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—121no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—31no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—121no—
406C4×Dic3—21no—
407C4×Dic3C22×D311yescharacteristic
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—61no—
411C2×C3⋊C8—121no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414#204—22no—
415#204—121no—
416D3×C8—121no—
417D3×C8—121no—
418D3×C8—121no—
419C22×C32C22×D411yescharacteristic
420C2×C3⋊D3—21no—
421C2×C3⋊D3—21no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3C2×SD1612yes—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—22no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3C2×SD1612yes—
435D32—84no—
436D32—84no—
437C32×C4—41no—
438C32×C4—41no—
439C32×C4C2×#4111yescharacteristic
440C32×C4H(5,𝔽2)11yescharacteristic
441C3⋊Dic3—21no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3C2×SD1612yes—
448C22×D4—91no—
449C22×D4—91no—
450C22×D4—181no—
451C2×SD16—31no—
452C2×SD16—91no—
453C2×SD16—91no—
454C22×C8—91no—
455C22×C8—91no—
456C4⋊Q8—91no—
457#127—91no—
458#125—181no—
459C22⋊Q8—91no—
460C22⋊Q8—91no—
461C22⋊Q8—181no—
462C22⋊Q8—181no—
463#121—31no—
464#121—91no—
465#121—181no—
466#120—181no—
467#120—181no—
468C4×Q8—31no—
469C4×D4—31no—
470C4×D4—91no—
471C4×D4—181no—
472C2×C4⋊C4—31no—
473C2×C4⋊C4—91no—
474#106—31no—
475#106—91no—
476#106D3211yescharacteristic, complemented
477C4⋊C8—91no—
478#103—31no—
479#102—31no—
480#102—31no—
481#102—31no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488C22⋊C8—31no—
489C22⋊C8—91no—
490C4×C8—31no—
491C23×C3—31no—
492C23×C3—61no—
493C23×C3—61no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—31no—
497C22×D3—31no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—61no—
501C22×D3—121no—
502C22×D3—122no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—241no—
511C22×D3—241no—
512C22×D3—241no—
513C22×D3—241no—
514C22×D3D3×D411yescharacteristic
515C3×Q8—61no—
516C3×Q8—61no—
517C3×D4—32no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—61no—
521C3×D4—122no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—31no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—122no—
537C2×C3×C4—241no—
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—34no—
541#67—122no—
542#67—122no—
543#67—122no—
544#67—122no—
545#67—241no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—31no—
549C2×Dic3—31no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—121no—
554C2×Dic3D3×D411yescharacteristic
555C2×Dic3D3×D411yescharacteristic
556C2×Dic3D3×D411yescharacteristic
557D12—21no—
558D12—21no—
559D12—21no—
560D12—34no—
561D12—42no—
562D12—61no—
563D12—61no—
564D12—61no—
565D12—61no—
566D12—121no—
567D12—121no—
568D12—122no—
569D12—122no—
570D12—122no—
571D12—122no—
572D12—242no—
573D12—241no—
574D12#23512yes—
575C4×D3—21no—
576C4×D3—21no—
577C4×D3—42no—
578C4×D3—61no—
579C4×D3—61no—
580C4×D3—61no—
581C4×D3—61no—
582C4×D3—81no—
583C4×D3—121no—
584C4×D3—121no—
585C4×D3—241no—
586C4×D3—241no—
587C4×D3—242no—
588Dic6—21no—
589Dic6—21no—
590Dic6—241no—
591Dic6—241no—
592C3×C8—21no—
593C3×C8—21no—
594C3×C8—41no—
595C3×C8—61no—
596C3×C8—61no—
597C3⋊C8—21no—
598C3⋊C8—21no—
599C3⋊C8—61no—
600C3⋊C8—61no—
601C3⋊C8—121no—
602C2×C32#54611yescharacteristic
603C2×C32C22×SD1611yescharacteristic
604C2×C32#57611yescharacteristic
605C3⋊D3—22no—
606C3⋊D3—81no—
607C3×D3—22no—
608C3×D3—42no—
609C3×D3—81no—
610C24—181no—
611C24—181no—
612C2×Q8—31no—
613C2×Q8—181no—
614C2×D4—31no—
615C2×D4—31no—
616C2×D4—61no—
617C2×D4—91no—
618C2×D4—91no—
619C2×D4—181no—
620C2×D4—181no—
621C2×D4—181no—
622C2×D4—181no—
623C2×D4—182no—
624C2×D4—181no—
625C2×D4—182no—
626C2×D4—361no—
627C2×D4—364no—
628C2×D4—361no—
629C22×C4—31no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—91no—
633C22×C4—181no—
634SD16—62no—
635SD16—361no—
636SD16—361no—
637C2×C8—31no—
638C2×C8—31no—
639C2×C8—91no—
640C2×C8—361no—
641C2×C8—361no—
642C2×C8C2×D3211yescharacteristic
643C4⋊C4—31no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—91no—
647C4⋊C4—91no—
648C4⋊C4—181no—
649C4⋊C4—181no—
650C4⋊C4—181no—
651C4⋊C4—181no—
652C4⋊C4C2×D3211yescharacteristic
653C4⋊C4C2×D3211yescharacteristic
654C22⋊C4—61no—
655C22⋊C4—61no—
656C22⋊C4—91no—
657C22⋊C4—91no—
658C22⋊C4—181no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C42—31no—
662C42—61no—
663C22×C3—21no—
664C22×C3—32no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—62no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3C2×D3×D411yescharacteristic
674C22×C3C2×D3×D411yescharacteristic
675C2×D3—21no—
676C2×D3—21no—
677C2×D3—22no—
678C2×D3—32no—
679C2×D3—32no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—62no—
686C2×D3—61no—
687C2×D3—61no—
688C2×D3—61no—
689C2×D3—61no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—241no—
699C2×D3—241no—
700C2×D3—241no—
701C2×D3—244no—
702C2×D3—244no—
703C2×D3—244no—
704C2×D3—244no—
705C2×D3D3×SD1612yes—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—32no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4—61no—
714C3×C4—61no—
715C3×C4—81no—
716C3×C4—81no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4C2×#23511yescharacteristic
720C3×C4D3×#4111yescharacteristic
721C3×C4#100911yescharacteristic
722C3×C4#100911yescharacteristic
723Dic3—21no—
724Dic3—21no—
725Dic3—41no—
726Dic3—41no—
727Dic3—61no—
728Dic3—61no—
729Dic3—121no—
730Dic3—121no—
731Dic3—121no—
732Dic3—241no—
733Dic3D3×SD1612yes—
734C32#329511yescharacteristic, complemented, Sylow
735C23—31no—
736C23—61no—
737C23—61no—
738C23—91no—
739C23—181no—
740C23—362no—
741C23—362no—
742C23—362no—
743C23—362no—
744C23—721no—
745C23—721no—
746Q8—61no—
747Q8—61no—
748Q8—721no—
749D4—32no—
750D4—61no—
751D4—61no—
752D4—61no—
753D4—94no—
754D4—122no—
755D4—181no—
756D4—181no—
757D4—362no—
758D4—362no—
759D4—362no—
760D4—362no—
761D4—721no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—31no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—91no—
772C2×C4—122no—
773C2×C4—181no—
774C2×C4—181no—
775C2×C4—181no—
776C2×C4—241no—
777C2×C4—721no—
778C2×C4C22×D3211yescharacteristic
779C8—21no—
780C8—61no—
781C8—61no—
782C8—181no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—62no—
787C2×C3—122no—
788C2×C3—241no—
789C2×C3#555011yescharacteristic
790C2×C3#565411yescharacteristic
791C2×C3C2×D3×SD1611yescharacteristic
792C2×C3C2×D3×SD1611yescharacteristic
793C2×C3#576911yescharacteristic
794C2×C3#577411yescharacteristic
795D3—22no—
796D3—42no—
797D3—62no—
798D3—62no—
799D3—81no—
800D3—122no—
801D3—241no—
802D3—241no—
803D3—481no—
804C22—32no—
805C22—61no—
806C22—61no—
807C22—62no—
808C22—92no—
809C22—121no—
810C22—121no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22—181no—
815C22—181no—
816C22—361no—
817C22—361no—
818C22—361no—
819C22—724no—
820C22—724no—
821C22D32×D411yescharacteristic
822C4—32no—
823C4—41no—
824C4—41no—
825C4—61no—
826C4—61no—
827C4—121no—
828C4—121no—
829C4—181no—
830C4—361no—
831C4D3×#23511yescharacteristic
832C4#6432011yescharacteristic
833C3—21no—
834C3#7967611yescharacteristic, complemented
835C3#8134211yescharacteristic, complemented
836C2—62no—
837C2—122no—
838C2—182no—
839C2—241no—
840C2—721no—
841C2#1059461911yescharacteristic
842C2D32×SD1611yescharacteristic
843C2#1059475511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radical#10594621C2
hypercenter#106D32
hypocenterC32#3295
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. #10594536C2semidirect
3. #10592562C2semidirect
4. C3×#4863C2semidirect
5. C3×#4852C2semidirect
6. #10590943C2semidirect
7. #10590942C2semidirect
8. #10590878C2semidirect
9. #10590721C2semidirect
10. #10590593C2semidirect
11. D3×#809C2semidirect
12. #10590558C2semidirect
13. #10590549C2semidirect
14. #10590523C2semidirect
15. #10590514C2semidirect
22. C4⋊C4×C3⋊D3C22semidirect
26. C3×D3×C4⋊C4C22semidirect
27. C3×#887C22semidirect
30. #63918C22semidirect
35. #63871C22semidirect
38. #63856C22semidirect
40. C2×#3717C22semidirect
41. C2×#3715C22semidirect
42. C2×#3710C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. C32×#106C22semidirect
45. #63648C22semidirect
46. #63647C22semidirect
47. #63636C22semidirect
48. #63635C22semidirect
49. C3×#821C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×C8×Dic3C22semidirect
52. C3×#810C22semidirect
54. C3×#809C22semidirect
55. C3×#808C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63564C22semidirect
59. #63563C22semidirect
78. #4863D3semidirect
79. #4852D3semidirect
187. D3×C4⋊C4C2×D3semidirect
190. #887C2×D3semidirect
202. C3×#106C2×D3semidirect
203. C3×#106C2×D3semidirect
219. #821C2×D3semidirect
223. (C2×D3)⋊C8C2×D3semidirect
225. C8×Dic3C2×D3semidirect
226. #810C2×D3semidirect
233. #809C2×D3semidirect
237. #808C2×D3semidirect
281. #626SD16semidirect
476. #106D32semidirect
734. C32#3295semidirect
834. C3#79676semidirect
835. C3#81342semidirect

Maximal subgroups

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

subgroupindex
#105946212
#105945362
#105925622
C3×#48632
C3×#48522
#105909432
#105909422
#105908782
#105907212
#105905932
D3×#8092
#105905582
#105905492
#105905232
#105905142
#813423
#796763