Finite Group Databasebeta

← #11884125

Subgroups — #11884125

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#915C211yesmaximal, characteristic, complemented
2C2×C3×D3×SD16C211yesmaximal, characteristic, complemented
3Q8×#625C211yesmaximal, characteristic, complemented
4#10595244C211yesmaximal, characteristic
5#10592863C211yesmaximal, characteristic, complemented
6#10591612C211yesmaximal, characteristic, complemented
7#10591594C211yesmaximal, characteristic, complemented
8#10591583C211yesmaximal, characteristic, complemented
9#10591497C211yesmaximal, characteristic, complemented
10#10591461C211yesmaximal, characteristic, complemented
11#10591458C211yesmaximal, characteristic, complemented
12#10590870C211yesmaximal, characteristic, complemented
13#10590851C211yesmaximal, characteristic, complemented
14#10590833C211yesmaximal, characteristic, complemented
15#10590722C211yesmaximal, characteristic, complemented
16#83987—31nomaximal
17#83866—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×C3×#237C2211yescharacteristic
21C2×C3×D3×D4C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic, complemented
24D4×C3⋊Dic3C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic, complemented
26C2×C3×#215C2211yescharacteristic
27C2×C3×#214C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C3×#915—24no—
30C3×D3×SD16—24no—
31C2×C3×Dic12C2211yescharacteristic, complemented
32C2×C3×#204C2211yescharacteristic
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
34C2×C3×D3×C8C2211yescharacteristic
35#63980—21no—
36#63976—21no—
37#63961—21no—
38C2×(C2×D3)⋊Dic3—21no—
39#63908C2211yescharacteristic
40C4×#625—21no—
41C4×#625C2211yescharacteristic
42#63873—21no—
43#63873C2211yescharacteristic, complemented
44#63863C2211yescharacteristic
45#63856—21no—
46#63856—21no—
47#63856C2211yescharacteristic
48#63856C2211yescharacteristic
49#63856C2211yescharacteristic, complemented
50C2×#3718C2211yescharacteristic, complemented
51C2×#3715C2211yescharacteristic
52#63662C2211yescharacteristic, complemented
53#63659C2211yescharacteristic
54#63645C2211yescharacteristic, complemented
55#63642C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64C22×C3×SD16—31no—
65#5829—31no—
66Q8×#67—31no—
67Q8×#67—31no—
68#5806—31no—
69C2×#915D311yescharacteristic, complemented
70C2×D3×SD16D311yescharacteristic, complemented
71#5239—31no—
72#5228—31no—
73#5227—31no—
74#5218—31no—
75#5190—31no—
76#5188—31no—
77#5186—31no—
78#5185—31no—
79#5174—31no—
80#5173—31no—
81#5170—31no—
82#5169—31no—
83#5167—31no—
84#5166—31no—
85#5164—31no—
86#5164—31no—
87#5164—61no—
88#5162—31no—
89#5162—31no—
90#5134—31no—
91#5127—31no—
92#5116—31no—
93#5111—31no—
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C22×C3⋊Dic3—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×D3×Q8—22no—
102C3×D3×Q8—22no—
103C3×D3×Q8—41no—
104C3×D3×Q8—41no—
105C3×#237—22no—
106C3×#237—41no—
107C3×D3×D4—22no—
108C3×D3×D4—41no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×Dic6—21no—
115C2×C3×Dic6—21no—
116C2×C3×Dic6C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C2×#625—21no—
120C2×#625D411yescharacteristic
121C32×SD16D414yescomplemented
122C2×C32×C8C2311yescharacteristic
123#3757—21no—
124C4⋊(C3⋊Dic3)—21no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127C4×C3⋊Dic3—21no—
128C4×C3⋊Dic3C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#216—22no—
131C3×#215—22no—
132C3×#214—22no—
133C3×#214—22no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C3×Dic12—22no—
137C3×#204—22no—
138C3×ΓL(1,𝔽25)—22no—
139C3×D3×C8—22no—
140#3724—21no—
141#3724—21no—
142#3724—21no—
143#3724—21no—
144#3724—21no—
145#3724D411yescharacteristic
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3D411yescharacteristic
153(C2×D3)⋊Dic3D411yescharacteristic
154#3718—41no—
155#3715—41no—
156#3266—91noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C22×C3×Q8—31no—
160C22×C3×D4—31no—
161C2×D3×Q8C2×D311yescharacteristic
162C2×D3×Q8C2×D311yescharacteristic, complemented
163C2×#237C2×D311yescharacteristic
164C2×D3×D4C2×D311yescharacteristic
165C3×#137—64no—
166C2×C3×Q16—31no—
167C2×C3×Q16—31no—
168C2×C3×SD16—21no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×SD16—64no—
174C2×C3×SD16C2×D311yescharacteristic
175C2×C3×SD16C2×D311yescharacteristic
176C2×C3×M16—31no—
177C22×C3×C8—31no—
178#953—61no—
179C2×#217—61no—
180#947—31no—
181#946—31no—
182#946—31no—
183#946—31no—
184#946—61no—
185#946—61no—
186Q8×Dic3—31no—
187Q8×Dic3—31no—
188Q8×Dic3—61no—
189#944—31no—
190#944—31no—
191#944—61no—
192#944—61no—
193C2×#216—31no—
194C2×#216—31no—
195C2×#216C2×D311yescharacteristic, complemented
196C2×#215—31no—
197C2×#215C2×D311yescharacteristic
198#939—61no—
199#939—61no—
200#938—31no—
201#937—61no—
202#936—31no—
203#935—61no—
204D4×Dic3—31no—
205D4×Dic3—31no—
206D4×Dic3—61no—
207C2×#214—31no—
208C2×#214C2×D311yescharacteristic
209C2×#214C2×D311yescharacteristic
210#930—31no—
211#929—61no—
212C4×#67—31no—
213C4×#67—31no—
214C4×#67—61no—
215C4×#67—61no—
216C2×(C2×D3)⋊C4—61no—
217#924—31no—
218#924—31no—
219#924—31no—
220#924—61no—
221#924—61no—
222#915—24no—
223D3×SD16—24no—
224C2×Dic12C2×D311yescharacteristic, complemented
225C2×#204C2×D311yescharacteristic
226C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
227C2×D3×C8C2×D311yescharacteristic
228#835—31no—
229#835—31no—
230#835—31no—
231#835—31no—
232#835—31no—
233#835—61no—
234#832—31no—
235#832—31no—
236#832—31no—
237#832—61no—
238#830—31no—
239#830—31no—
240#821—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—31no—
243#818—31no—
244#818—31no—
245#818—61no—
246#816—31no—
247#816—31no—
248#816—31no—
249#815—31no—
250#815—31no—
251#815—61no—
252Dic3⋊C8—31no—
253Dic3⋊C8—31no—
254C23×C32—21no—
255C22×C3×D3—21no—
256C22×C3×D3—42no—
257C22×C3×D3—42no—
258C22×C3×D3—81no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C32×Q8—21no—
262C32×Q8C2×D412yes—
263C32×D4—21no—
264C32×D4C2×D412yes—
265C2×C32×C4—21no—
266C2×C32×C4C2411yescharacteristic
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—81no—
270C2×C3⋊Dic3C2×D411yescharacteristic
271C2×C3⋊Dic3C2×D411yescharacteristic
272C3×#67—42no—
273C3×#67—42no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—42no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—42no—
287C3×C4×D3—42no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—42no—
295C3×Dic6—42no—
296#625—22no—
297#625—81no—
298C32×C8C2×D412yes—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×#137—31no—
303C22×SD16—31no—
304D4×Q8—91no—
305#546—91no—
306#497—91no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—91no—
311#452—91no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—91no—
317C24×C3—61no—
318C23×D3—21no—
319C3×#41—62no—
320C3×#41—121no—
321C2×C3×Q8—21no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×Q8—31no—
325C2×C3×Q8—61no—
326C2×C3×Q8—61no—
327C2×C3×Q8—62no—
328C2×C3×Q8—62no—
329C2×C3×Q8—121no—
330C2×C3×Q8—121no—
331C2×C3×Q8C22×D311yescharacteristic
332C2×C3×Q8C22×D311yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—31no—
335C2×C3×D4—61no—
336C2×C3×D4—62no—
337C2×C3×D4—61no—
338C2×C3×D4—121no—
339C2×C3×D4C22×D311yescharacteristic
340C2×C3×D4C22×D311yescharacteristic
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—61no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C2×#67—21no—
347C2×#67—21no—
348C2×#67—31no—
349C2×#67—31no—
350C2×#67—61no—
351C2×#67—61no—
352C22×Dic3—21no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3—121no—
356D3×Q8—22no—
357D3×Q8—22no—
358D3×Q8—41no—
359D3×Q8—41no—
360#237—22no—
361#237—41no—
362D3×D4—22no—
363D3×D4—41no—
364C2×D12C22×D311yescharacteristic
365C2×C4×D3—21no—
366C2×C4×D3—21no—
367C2×C4×D3C22×D311yescharacteristic
368C2×C4×D3C22×D311yescharacteristic
369C2×Dic6—21no—
370C2×Dic6—21no—
371C2×Dic6C22×D311yescharacteristic
372C2×Dic6C22×D311yescharacteristic
373C2×Dic6C22×D311yescharacteristic
374C3×Q16—62no—
375C3×Q16—62no—
376C3×SD16—24no—
377C3×SD16—62no—
378C3×SD16—62no—
379C3×SD16—62no—
380C3×SD16—62no—
381C3×SD16#6714yescomplemented
382C3×SD16#6714yescomplemented
383C3×M16—62no—
384C2×C3×C8—21no—
385C2×C3×C8—31no—
386C2×C3×C8—31no—
387C2×C3×C8—62no—
388C2×C3×C8C22×D311yescharacteristic
389C2×C3×C8C22×D311yescharacteristic
390#217—31no—
391#217—31no—
392#217—61no—
393#217—61no—
394#217—61no—
395#217—61no—
396#217—61no—
397#217—61no—
398#217—61no—
399#217—61no—
400#217—121no—
401#216—22no—
402#216—121no—
403#216—121no—
404#215—22no—
405#215—121no—
406#214—22no—
407#214—22no—
408#214—121no—
409(C2×D3)⋊C4—31no—
410(C2×D3)⋊C4—31no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417C4⋊Dic3—31no—
418C4⋊Dic3—31no—
419C4⋊Dic3—31no—
420C4⋊Dic3—31no—
421C4⋊Dic3—61no—
422C4⋊Dic3—61no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3—121no—
426Dic3⋊C4—31no—
427Dic3⋊C4—31no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438C4×Dic3—31no—
439C4×Dic3—31no—
440C4×Dic3—61no—
441C4×Dic3—61no—
442C4×Dic3—61no—
443C4×Dic3—121no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449Dic12—22no—
450#204—22no—
451ΓL(1,𝔽25)—22no—
452D3×C8—22no—
453C22×C32—22no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32C22×D411yescharacteristic
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—84no—
466C2×C3×D3#13712yescomplemented
467C32×C4—22no—
468C32×C4C22×D411yescharacteristic
469C32×C4H(5,𝔽2)11yescharacteristic
470C3⋊Dic3—21no—
471C3⋊Dic3—21no—
472C3⋊Dic3—41no—
473C3⋊Dic3—41no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C2×#41—31no—
480C22×Q8—31no—
481C22×Q8—31no—
482C22×D4—31no—
483#137—64no—
484C2×Q16—31no—
485C2×Q16—31no—
486C2×Q16—91no—
487C2×SD16—31no—
488C2×SD16—31no—
489C2×SD16—31no—
490C2×SD16—31no—
491C2×SD16—64no—
492C2×SD16—91no—
493C2×SD16D3211yescharacteristic
494C2×M16—31no—
495C22×C8—31no—
496C4⋊Q8—91no—
497C4⋊Q8—181no—
498#124—91no—
499#123—181no—
500C22⋊Q8—91no—
501C22⋊Q8—91no—
502C22⋊Q8—91no—
503C22⋊Q8—181no—
504C22⋊Q8—181no—
505#121—91no—
506#121—181no—
507#120—181no—
508C4×Q8—91no—
509C4×D4—91no—
510C4×D4—91no—
511C4×D4—181no—
512C2×C22⋊C4—181no—
513#107—91no—
514C4⋊C8—91no—
515#103—91no—
516#103—91no—
517#103—91no—
518#103—91no—
519#102—91no—
520#102—91no—
521C22⋊C8—91no—
522C22⋊C8—91no—
523#97—91no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—31no—
528C23×C3—41no—
529C23×C3—61no—
530C23×C3—122no—
531C23×C3—122no—
532C23×C3—241no—
533C22×D3—21no—
534C22×D3—42no—
535C22×D3—42no—
536C22×D3—81no—
537C22×D3D3×D411yescharacteristic
538C22×D3D3×D411yescharacteristic
539C3×Q8—21no—
540C3×Q8—21no—
541C3×Q8—22no—
542C3×Q8—41no—
543C3×Q8—61no—
544C3×Q8—61no—
545C3×Q8—61no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—122no—
550C3×Q8—122no—
551C3×Q8C2×#6712yes—
552C3×Q8C2×#6712yes—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—22no—
556C3×D4—41no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—122no—
560C3×D4—122no—
561C3×D4C2×#6712yes—
562C3×D4C2×#6712yes—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
568C2×C3×C4—41no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—122no—
577C2×C3×C4—122no—
578C2×C3×C4—122no—
579C2×C3×C4C23×D311yescharacteristic
580C2×C3×C4C23×D311yescharacteristic
581#67—42no—
582#67—42no—
583#67—62no—
584#67—62no—
585#67—241no—
586#67—241no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—31no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—42no—
595C2×Dic3—61no—
596C2×Dic3—61no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—121no—
602C2×Dic3—121no—
603C2×Dic3—241no—
604C2×Dic3—241no—
605C2×Dic3—242no—
606C2×Dic3D3×D411yescharacteristic
607C2×Dic3D3×D411yescharacteristic
608D12—21no—
609D12—21no—
610C4×D3—21no—
611C4×D3—21no—
612C4×D3—21no—
613C4×D3—21no—
614C4×D3—42no—
615C4×D3—42no—
616Dic6—21no—
617Dic6—21no—
618Dic6—21no—
619Dic6—21no—
620Dic6—21no—
621Dic6—21no—
622Dic6—42no—
623Dic6—42no—
624C3×C8—22no—
625C3×C8—61no—
626C3×C8—61no—
627C3×C8C2×#6712yes—
628C3×C8C2×#6712yes—
629C3⋊C8—21no—
630C3⋊C8—21no—
631C3⋊C8—61no—
632C3⋊C8—61no—
633C3⋊C8—121no—
634C2×C32—42no—
635C2×C32D4211yescharacteristic
636C2×C32C2×#13711yescharacteristic
637C2×C32#57711yescharacteristic
638C3×D3—22no—
639C3×D3—41no—
640C3×D3—81no—
641C24—61no—
642#41—62no—
643#41—121no—
644C2×Q8—31no—
645C2×Q8—31no—
646C2×Q8—31no—
647C2×Q8—61no—
648C2×Q8—61no—
649C2×Q8—62no—
650C2×Q8—62no—
651C2×Q8—121no—
652C2×Q8—121no—
653C2×Q8C2×D3211yescharacteristic
654C2×D4—31no—
655C2×D4—61no—
656C2×D4—62no—
657C2×D4—61no—
658C2×D4—91no—
659C2×D4—121no—
660C2×D4—181no—
661C2×D4C2×D3211yescharacteristic
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—61no—
665C22×C4—61no—
666C22×C4—61no—
667C22×C4—181no—
668Q16—62no—
669Q16—62no—
670Q16—361no—
671SD16—62no—
672SD16—62no—
673SD16—62no—
674SD16—62no—
675SD16—361no—
676SD16#62514yescomplemented
677M16—62no—
678C2×C8—31no—
679C2×C8—31no—
680C2×C8—62no—
681C2×C8—91no—
682C2×C8C2×D3211yescharacteristic
683C4⋊C4—91no—
684C4⋊C4—91no—
685C4⋊C4—91no—
686C4⋊C4—181no—
687C4⋊C4—181no—
688C4⋊C4—181no—
689C4⋊C4—181no—
690C4⋊C4—181no—
691C4⋊C4—181no—
692C22⋊C4—91no—
693C22⋊C4—91no—
694C22⋊C4—181no—
695C22⋊C4—181no—
696C22⋊C4—181no—
697C22⋊C4—181no—
698C22⋊C4—181no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C42—91no—
702C42—181no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—21no—
706C22×C3—32no—
707C22×C3—42no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—81no—
718C22×C3—81no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3—244no—
723C22×C3C2×D3×D411yescharacteristic
724C22×C3C2×D3×D411yescharacteristic
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—41no—
733C2×D3—84no—
734C2×D3#91512yescomplemented
735C3×C4—22no—
736C3×C4—22no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—42no—
740C3×C4—61no—
741C3×C4—61no—
742C3×C4—121no—
743C3×C4—121no—
744C3×C4—121no—
745C3×C4#100411yescharacteristic
746C3×C4#100411yescharacteristic
747C3×C4C22×#6711yescharacteristic
748C3×C4C22×#6711yescharacteristic
749Dic3—21no—
750Dic3—21no—
751Dic3—41no—
752Dic3—41no—
753Dic3—41no—
754Dic3—61no—
755Dic3—61no—
756Dic3—61no—
757Dic3—61no—
758Dic3—121no—
759Dic3—121no—
760Dic3—121no—
761Dic3—121no—
762Dic3—121no—
763Dic3—121no—
764Dic3—241no—
765Dic3—241no—
766C32#326611yescharacteristic, complemented, Sylow
767C23—21no—
768C23—31no—
769C23—31no—
770C23—61no—
771C23—122no—
772C23—122no—
773C23—241no—
774Q8—21no—
775Q8—61no—
776Q8—61no—
777Q8—61no—
778Q8—61no—
779Q8—61no—
780Q8—61no—
781Q8—122no—
782Q8—122no—
783Q8C2×#62512yes—
784D4—21no—
785D4—61no—
786D4—61no—
787D4—122no—
788D4—122no—
789D4—182no—
790D4—721no—
791D4C2×#62512yes—
792C2×C4—21no—
793C2×C4—31no—
794C2×C4—31no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—91no—
803C2×C4—91no—
804C2×C4—122no—
805C2×C4—122no—
806C2×C4—122no—
807C2×C4—181no—
808C2×C4—181no—
809C2×C4—721no—
810C2×C4C22×D3211yescharacteristic
811C8—61no—
812C8—61no—
813C8—181no—
814C8C2×#62512yes—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—42no—
819C2×C3—42no—
820C2×C3—62no—
821C2×C3—82no—
822C2×C3—121no—
823C2×C3—241no—
824C2×C3C2×#91511yescharacteristic
825C2×C3#576211yescharacteristic
826C2×C3D3×#13711yescharacteristic
827C2×C3#577811yescharacteristic
828C2×C3D4×#6711yescharacteristic
829C2×C3D4×#6711yescharacteristic
830D3—22no—
831D3—41no—
832D3—81no—
833C22—22no—
834C22—32no—
835C22—41no—
836C22—41no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—61no—
841C22—61no—
842C22—121no—
843C22—121no—
844C22—121no—
845C22—244no—
846C22D32×D411yescharacteristic
847C4—22no—
848C4—61no—
849C4—61no—
850C4—121no—
851C4—121no—
852C4—121no—
853C4—181no—
854C4—181no—
855C4—361no—
856C4—361no—
857C4#6431311yescharacteristic
858C4C22×#62511yescharacteristic
859C3—21no—
860C3#8386611yescharacteristic, complemented
861C3#8398711yescharacteristic, complemented
862C2—42no—
863C2—62no—
864C2—121no—
865C2—241no—
866C2D3×#91511yescharacteristic
867C2#1059475111yescharacteristic
868C2D4×#62511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595244C2
hypercenterC2×SD16D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#915C2semidirect
2. C2×C3×D3×SD16C2semidirect
3. Q8×#625C2semidirect
5. #10592863C2semidirect
6. #10591612C2semidirect
7. #10591594C2semidirect
8. #10591583C2semidirect
9. #10591497C2semidirect
10. #10591461C2semidirect
11. #10591458C2semidirect
12. #10590870C2semidirect
13. #10590851C2semidirect
14. #10590833C2semidirect
15. #10590722C2semidirect
19. C2×C3×D3×Q8C22semidirect
23. Q8×C3⋊Dic3C22semidirect
25. C2×C3×#216C22semidirect
31. C2×C3×Dic12C22semidirect
33. C2×C3×ΓL(1,𝔽25)C22semidirect
43. #63873C22semidirect
49. #63856C22semidirect
50. C2×#3718C22semidirect
52. #63662C22semidirect
54. #63645C22semidirect
55. #63642C22semidirect
56. #63572C22semidirect
57. #63566C22semidirect
58. #63566C22semidirect
59. #63566C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
69. C2×#915D3semidirect
70. C2×D3×SD16D3semidirect
121. C32×SD16D4semidirect
162. C2×D3×Q8C2×D3semidirect
195. C2×#216C2×D3semidirect
224. C2×Dic12C2×D3semidirect
226. C2×ΓL(1,𝔽25)C2×D3semidirect
381. C3×SD16#67semidirect
382. C3×SD16#67semidirect
466. C2×C3×D3#137semidirect
676. SD16#625semidirect
734. C2×D3#915semidirect
766. C32#3266semidirect
860. C3#83866semidirect
861. C3#83987semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9152
C2×C3×D3×SD162
Q8×#6252
#105952442
#105928632
#105916122
#105915942
#105915832
#105914972
#105914612
#105914582
#105908702
#105908512
#105908332
#105907222
#839873
#838663