Finite Group Databasebeta

← #11889717

Subgroups — #11889717

Order 1152.

877 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5635C211yesmaximal, characteristic, complemented
2#10594886C211yesmaximal, characteristic
3#10592750C211yesmaximal, characteristic, complemented
4C3×#5046C211yesmaximal, characteristic, complemented
5#10591655C211yesmaximal, characteristic, complemented
6#10591604C211yesmaximal, characteristic, complemented
7#10591587C211yesmaximal, characteristic, complemented
8#10591566C211yesmaximal, characteristic, complemented
9#10591158C211yesmaximal, characteristic, complemented
10#10591135C211yesmaximal, characteristic, complemented
11C2×#63562C211yesmaximal, characteristic, complemented
12#10590607C211yesmaximal, characteristic, complemented
13#10590531C211yesmaximal, characteristic, complemented
14#10590498C211yesmaximal, characteristic, complemented
15#10590463C211yesmaximal, characteristic, complemented
16#83635—31nomaximal
17#80163—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic, complemented
22#64133C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×#946C2211yescharacteristic, complemented
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic
28C3×C4×#67C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C3×#897—21no—
31C3×D3×C4⋊C4C2211yescharacteristic, complemented
32C3×#889—21no—
33C3×#888C2211yescharacteristic, complemented
34C3×#67⋊C4—21no—
35C3×#878—21no—
36#63976—21no—
37D3×#217—21no—
38#63908C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40#63885—21no—
41#63884—21no—
42#63860C2211yescharacteristic
43C2×#3711C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63637C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic
50#63575C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63567C2211yescharacteristic, complemented
54#63567C2211yescharacteristic, complemented
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×#554—31no—
62#5806—31no—
63#5635D311yescharacteristic, complemented
64#5550—31no—
65C3×#450—31no—
66C2×#832—31no—
67#5174—31no—
68#5173—31no—
69#5166—31no—
70#5164—31no—
71#5089—31no—
72#5087—31no—
73#5051—31no—
74#5051—31no—
75#5051—61no—
76#5049—31no—
77#5047—31no—
78#5046D311yescharacteristic, complemented
79#5028—31no—
80#5026—31no—
81#5011—31no—
82#4970—31no—
83#4967—31no—
84#4966—31no—
85C2×#809—31no—
86#4774—31no—
87#4771—31no—
88#4765—31no—
89#4759—31no—
90#4730—31no—
91#4722—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67D411yescharacteristic
97C22×C3×Dic3—21no—
98C2×C3×D12—22no—
99C2×C3×D12—21no—
100C2×C3×D12—41no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×#625—21no—
107C2×#625—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795—41no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115#3757—21no—
116#3756—41no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C2×C3⋊(C3⋊C8)—41no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217D411yescharacteristic
123C3×#215—22no—
124C3×#215—41no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3711—41no—
144#3314—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#235—31no—
148C22×D12C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C3×C4⋊Q8—31no—
152C3×#125—61no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—61no—
156C3×C22⋊Q8—61no—
157C3×C22⋊Q8C2×D311yescharacteristic
158C3×C22⋊Q8C2×D311yescharacteristic
159C3×C4×Q8—31no—
160C3×C4×D4—31no—
161C3×C4×D4—61no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164#953—61no—
165C2×#217—61no—
166#946C2×D311yescharacteristic, complemented
167Q8×Dic3C2×D311yescharacteristic, complemented
168C2×#216—31no—
169C2×#216—31no—
170C2×#216—61no—
171C2×#215C2×D311yescharacteristic
172C2×#215C2×D311yescharacteristic
173#939—61no—
174#938—31no—
175#937—61no—
176#936—31no—
177#935—61no—
178D4×Dic3—31no—
179#930—31no—
180C4×#67C2×D311yescharacteristic
181C2×C4⋊Dic3C2×D311yescharacteristic
182#924—31no—
183#924—31no—
184#924—61no—
185C2×#208—31no—
186C22×C3⋊C8—31no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8—61no—
189C2×ΓL(1,𝔽25)—31no—
190#897—21no—
191#894—61no—
192D3×C4⋊C4C2×D311yescharacteristic, complemented
193#889—21no—
194#888C2×D311yescharacteristic, complemented
195#884—61no—
196#67⋊C4—21no—
197D3×C22⋊C4—61no—
198#878—21no—
199#875—31no—
200C4×D12—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×C22⋊C8—31no—
204#835—31no—
205#835—31no—
206#835—61no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#830—31no—
212#830C2×D311yescharacteristic
213(C2×D3)⋊C8—31no—
214#818—31no—
215#818—31no—
216#816—31no—
217#816—31no—
218#815—31no—
219Dic3⋊C8—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—61no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809C2×D311yescharacteristic
230#809C2×D311yescharacteristic
231#807—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235#807—61no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
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
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255#634—21no—
256#634—21no—
257C3×#67—22no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—42no—
268C3×D12#4112yes—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—81no—
272C3×Dic6—81no—
273#625—42no—
274#625—81no—
275D3×Dic3—42no—
276D3×Dic3—81no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281#554—31no—
282#546—91no—
283#489—91no—
284#484—91no—
285#480—91no—
286#474—91no—
287#468—91no—
288#467—91no—
289#464—91no—
290#452—91no—
291#450—31no—
292#440—91no—
293#435—91no—
294#417—91no—
295C2×#102—91no—
296C24×C3—61no—
297C23×D3—21no—
298C2×C3×Q8—21no—
299C2×C3×Q8—61no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—62no—
306C2×C3×D4—61no—
307C2×C3×D4—121no—
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67#6711yescharacteristic
319C22×Dic3—21no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322#237—62no—
323#237—121no—
324#235—62no—
325#235—121no—
326C2×D12—22no—
327C2×D12—21no—
328C2×D12—41no—
329C2×D12C22×D311yescharacteristic
330C2×D12C22×D311yescharacteristic
331C2×C4×D3—21no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3C22×D311yescharacteristic
335C2×Dic6—21no—
336C2×Dic6—31no—
337C2×Dic6—31no—
338C2×Dic6—61no—
339C3×SD16—62no—
340C3×SD16—121no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—41no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—41no—
362C3×C22⋊C4—61no—
363C3×C42—31no—
364C3×C42—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—121no—
372#217#6711yescharacteristic
373#216—121no—
374#216—121no—
375#216—122no—
376#215—22no—
377#215—41no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4#6711yescharacteristic
384C4⋊Dic3—21no—
385C4⋊Dic3—21no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—61no—
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—121no—
397Dic3⋊C4#6711yescharacteristic
398C4×Dic3—21no—
399C4×Dic3C22×D311yescharacteristic
400#208—121no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8—122no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412ΓL(1,𝔽25)—121no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32#13712yes—
416C22×C32C22×D411yescharacteristic
417C2×C3×D3—22no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—84no—
427C32×C4—21no—
428C32×C4—41no—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—31no—
441C2×Q16—91no—
442C2×SD16—31no—
443C2×SD16—31no—
444C2×M16—91no—
445C22×C8—91no—
446C4⋊Q8—31no—
447#125—61no—
448#124—91no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—61no—
452C22⋊Q8—61no—
453C22⋊Q8—91no—
454C22⋊Q8D3211yescharacteristic
455#121—91no—
456#121—181no—
457#120—181no—
458C4×Q8—31no—
459C4×D4—31no—
460C4×D4—61no—
461C4×D4—91no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—31no—
464C2×C22⋊C4—181no—
465#107—91no—
466#107—91no—
467#107—91no—
468C4⋊C8—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8—91no—
481#97—91no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3—122no—
487C23×C3—122no—
488C23×C3—241no—
489C23×C3D3×D411yescharacteristic
490C23×C3C2×#6711yescharacteristic
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—42no—
494C22×D3—42no—
495C22×D3—81no—
496C22×D3C2×#6711yescharacteristic
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—41no—
502C3×Q8—41no—
503C3×Q8—241no—
504C3×D4—32no—
505C3×D4—62no—
506C3×D4—61no—
507C3×D4—61no—
508C3×D4—61no—
509C3×D4—122no—
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—21no—
519C2×C3×C4—21no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—241no—
532C2×C3×C4—241no—
533C2×C3×C4D3×D411yescharacteristic
534C2×C3×C4C2×#6711yescharacteristic
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—22no—
538#67—122no—
539#67—122no—
540#67—241no—
541#67—241no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—81no—
549C2×Dic3—121no—
550C2×Dic3—121no—
551C2×Dic3—122no—
552C2×Dic3—241no—
553C2×Dic3C2×#6711yescharacteristic
554C2×Dic3C2×#6711yescharacteristic
555C2×Dic3C2×#6711yescharacteristic
556D12—21no—
557D12—21no—
558D12—21no—
559D12—42no—
560D12#23712yes—
561C4×D3—21no—
562C4×D3—21no—
563C4×D3—81no—
564C4×D3—122no—
565C4×D3—241no—
566Dic6—61no—
567Dic6—61no—
568Dic6—61no—
569Dic6—61no—
570Dic6—81no—
571Dic6—121no—
572Dic6—121no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C3⋊C8—62no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C2×C32—22no—
584C2×C32#54611yescharacteristic
585C2×C32C2×#13711yescharacteristic
586C2×C32#57611yescharacteristic
587C3×D3—41no—
588C3×D3—42no—
589C3×D3—81no—
590C24—61no—
591#41—182no—
592#41—361no—
593C2×Q8—61no—
594C2×Q8—91no—
595C2×Q8C2×D3211yescharacteristic
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—62no—
600C2×D4—61no—
601C2×D4—121no—
602C2×D4—181no—
603C2×D4—181no—
604C22×C4—31no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4C2×D3211yescharacteristic
610Q16—361no—
611SD16—62no—
612SD16—121no—
613M16—361no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—91no—
617C2×C8—91no—
618C2×C8—361no—
619C4⋊C4—21no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—91no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—21no—
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—61no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—31no—
641C42—61no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—22no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—62no—
653C22×C3—61no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—244no—
660C22×C3#91512yes—
661C22×C3#94212yes—
662C22×C3C2×D3×D411yescharacteristic
663C22×C3C22×#6711yescharacteristic
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—22no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—84no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—61no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—81no—
687C3×C4—81no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4C2×#23711yescharacteristic
691C3×C4#100411yescharacteristic
692C3×C4D3×#4111yescharacteristic
693C3×C4#100911yescharacteristic
694Dic3—21no—
695Dic3—21no—
696Dic3—21no—
697Dic3—41no—
698Dic3—41no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—241no—
704Dic3—241no—
705C32#331411yescharacteristic, complemented, Sylow
706C23—31no—
707C23—61no—
708C23—61no—
709C23—122no—
710C23—122no—
711C23—241no—
712C23D3×#6711yescharacteristic
713Q8—21no—
714Q8—21no—
715Q8—181no—
716Q8—181no—
717Q8—241no—
718D4—32no—
719D4—62no—
720D4—61no—
721D4—61no—
722D4—61no—
723D4—122no—
724D4—362no—
725D4—721no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—241no—
740C2×C4—241no—
741C2×C4—362no—
742C2×C4—721no—
743C2×C4D3×#6711yescharacteristic
744C2×C4C22×D3211yescharacteristic
745C8—61no—
746C8—61no—
747C8—181no—
748C8—181no—
749C2×C3—22no—
750C2×C3—22no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—42no—
755C2×C3—121no—
756C2×C3—122no—
757C2×C3—241no—
758C2×C3#559111yescharacteristic
759C2×C3C2×#91511yescharacteristic
760C2×C3#577411yescharacteristic
761C2×C3C2×#94211yescharacteristic
762C2×C3#582911yescharacteristic
763C2×C3#583511yescharacteristic
764D3—42no—
765D3—41no—
766D3—81no—
767C22—21no—
768C22—21no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—62no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—244no—
779C22#6394612yes—
780C22C2×D3×#6711yescharacteristic
781C4—21no—
782C4—41no—
783C4—41no—
784C4—61no—
785C4—61no—
786C4—61no—
787C4—121no—
788C4—121no—
789C4—361no—
790C4—361no—
791C4D3×#23711yescharacteristic
792C4#6431411yescharacteristic
793C3—21no—
794C3#8016311yescharacteristic, complemented
795C3#8363511yescharacteristic, complemented
796C2—22no—
797C2—121no—
798C2—122no—
799C2—241no—
800C2#1059530411yescharacteristic
801C2C2×#6394611yescharacteristic
802C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10594886C2
hypercenterC22⋊Q8D32
hypocenterC32#3314
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×#5635C2semidirect
3. #10592750C2semidirect
4. C3×#5046C2semidirect
5. #10591655C2semidirect
6. #10591604C2semidirect
7. #10591587C2semidirect
8. #10591566C2semidirect
9. #10591158C2semidirect
10. #10591135C2semidirect
11. C2×#63562C2semidirect
12. #10590607C2semidirect
13. #10590531C2semidirect
14. #10590498C2semidirect
15. #10590463C2semidirect
21. C2×#3756C22semidirect
24. C3×#946C22semidirect
25. C3×Q8×Dic3C22semidirect
31. C3×D3×C4⋊C4C22semidirect
33. C3×#888C22semidirect
43. C2×#3711C22semidirect
44. #63662C22semidirect
45. #63637C22semidirect
46. #63634C22semidirect
50. #63575C22semidirect
51. #63575C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
53. #63567C22semidirect
54. #63567C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
63. #5635D3semidirect
78. #5046D3semidirect
166. #946C2×D3semidirect
167. Q8×Dic3C2×D3semidirect
192. D3×C4⋊C4C2×D3semidirect
194. #888C2×D3semidirect
705. C32#3314semidirect
794. C3#80163semidirect
795. C3#83635semidirect

Maximal subgroups

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

subgroupindex
C3×#56352
#105948862
#105927502
C3×#50462
#105916552
#105916042
#105915872
#105915662
#105911582
#105911352
C2×#635622
#105906072
#105905312
#105904982
#105904632
#836353
#801633