Finite Group Databasebeta

← #11884124

Subgroups — #11884124

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#915C211yesmaximal, characteristic, complemented
3Q8×#626C211yesmaximal, characteristic, complemented
4#10595254C211yesmaximal, characteristic
5C3×#5164C211yesmaximal, characteristic, complemented
6#10591607C211yesmaximal, characteristic, complemented
7#10591603C211yesmaximal, characteristic, complemented
8#10591584C211yesmaximal, characteristic, complemented
9#10591489C211yesmaximal, characteristic, complemented
10#10591467C211yesmaximal, characteristic, complemented
11#10591463C211yesmaximal, characteristic, complemented
12#10590899C211yesmaximal, characteristic, complemented
13#10590857C211yesmaximal, characteristic, complemented
14#10590838C211yesmaximal, characteristic, complemented
15#10590736C211yesmaximal, characteristic, complemented
16#83987—31nomaximal
17#79795—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic, complemented
21C2×C3×#237C2211yescharacteristic
22C2×C32×SD16C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24C2×#3754C2211yescharacteristic
25SD16×C3⋊D3—24no—
26C2×#3744C2211yescharacteristic
27C2×C8×C3⋊D3C2211yescharacteristic
28C3×Q8×Dic3C2211yescharacteristic, complemented
29C2×C3×#216C2211yescharacteristic, complemented
30C3×D4×Dic3C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C3×#915—24no—
33C2×C3×Dic12C2211yescharacteristic, complemented
34C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
35#63981—21no—
36#63978—21no—
37#63966—21no—
38C2×#3722—21no—
39#63909C2211yescharacteristic
40C4×#626—21no—
41C4×#626C2211yescharacteristic
42#63871—21no—
43#63871C2211yescharacteristic
44#63871C2211yescharacteristic
45#63866—21no—
46#63866C2211yescharacteristic, complemented
47#63864C2211yescharacteristic
48#63857—21no—
49#63857C2211yescharacteristic, complemented
50C2×#3719C2211yescharacteristic, complemented
51C2×#3717C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic
54C3×#818C2211yescharacteristic, complemented
55C3×#815C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63564C2211yescharacteristic
61#63557C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×#137—31no—
64#5829—31no—
65Q8×#67—31no—
66C2×#915D311yescharacteristic, complemented
67C2×D3×SD16—31no—
68C2×D3×SD16—31no—
69C2×D3×SD16—61no—
70Q8×D12—31no—
71#5554—31no—
72C3×#440—31no—
73#5239—31no—
74#5227—31no—
75#5190—31no—
76#5188—31no—
77#5186—31no—
78#5185—31no—
79#5169—31no—
80#5164D311yescharacteristic, complemented
81#5162—31no—
82#5134—31no—
83#5127—31no—
84#5028—31no—
85#5019—31no—
86#4887—31no—
87#4886—31no—
88#4809—31no—
89#4806—31no—
90#4783—31no—
91#4776—31no—
92#4715—31no—
93#4706—31no—
94C23×C3⋊D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98Q8×C3⋊D3—22no—
99Q8×C3⋊D3—41no—
100D4×C3⋊D3—22no—
101D4×C3⋊D3—41no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3—21no—
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×#634—21no—
106C2×#634C2311yescharacteristic
107C2×C3×#67—21no—
108C22×C3×Dic3—21no—
109C22×C3×Dic3—21no—
110C3×D3×Q8—22no—
111C3×D3×Q8—41no—
112C3×#237—22no—
113C3×#237—41no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6—21no—
117C2×C3×Dic6C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C2×#626—21no—
120C2×#626D411yescharacteristic
121C32×SD16D414yescomplemented
122C2×C32×C8C2311yescharacteristic
123#3755—22no—
124#3754—22no—
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3744—22no—
127C8×C3⋊D3—22no—
128C3×#217—21no—
129C3×#216—22no—
130C3×#214—22no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×Dic12—22no—
139C3×ΓL(1,𝔽25)—22no—
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3D411yescharacteristic
146#3722—21no—
147#3722—21no—
148#3722—21no—
149#3722—21no—
150#3722—21no—
151#3722D411yescharacteristic
152(C2×D3)⋊Dic3—21no—
153(C2×D3)⋊Dic3D411yescharacteristic
154#3719—41no—
155#3717—41no—
156#3266—91noSylow
157C2×C3×#41—31no—
158C22×C3×Q8—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×D3×Q8—61no—
162C2×D3×Q8C2×D311yescharacteristic, complemented
163C2×#237C2×D311yescharacteristic
164C2×D3×D4—31no—
165C2×D3×D4—31no—
166C2×D3×D4—61no—
167C3×#137—64no—
168C2×C3×Q16—31no—
169C2×C3×Q16—31no—
170C2×C3×SD16—21no—
171C2×C3×SD16—31no—
172C2×C3×SD16C2×D311yescharacteristic
173C2×C3×SD16C2×D311yescharacteristic
174C2×C3×M16—31no—
175C3×C4×Q8—31no—
176C3×C4×D4—31no—
177#947—31no—
178#946—31no—
179#946—31no—
180#946—61no—
181Q8×Dic3C2×D311yescharacteristic, complemented
182#944—31no—
183#944—61no—
184C2×#216—31no—
185C2×#216C2×D311yescharacteristic, complemented
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—61no—
190#939—61no—
191#937—61no—
192D4×Dic3C2×D311yescharacteristic
193C2×#214—31no—
194C2×#214—31no—
195C2×#214—61no—
196C2×#214C2×D311yescharacteristic
197#930—31no—
198#930—61no—
199#929—61no—
200C4×#67—31no—
201C4×#67—61no—
202C2×(C2×D3)⋊C4—61no—
203C2×(C2×D3)⋊C4—61no—
204#924—31no—
205#924—61no—
206#915—24no—
207D3×SD16—68no—
208D3×SD16—64no—
209D3×SD16—64no—
210C2×Dic12—31no—
211C2×Dic12C2×D311yescharacteristic, complemented
212C2×#204—31no—
213C2×#204—31no—
214C2×#204—31no—
215C2×#204—61no—
216C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
217C2×D3×C8—31no—
218C2×D3×C8—31no—
219C2×D3×C8—61no—
220#897—31no—
221#897—31no—
222#897—31no—
223#897—61no—
224#897—61no—
225#895—31no—
226#886—61no—
227#882—61no—
228#875—31no—
229C4×D12—31no—
230C4×D12—61no—
231#869—31no—
232#869—61no—
233C3×#107—31no—
234C3×#103—31no—
235C3×#102—31no—
236C3×#97—31no—
237#835—31no—
238#835—31no—
239#835C2×D311yescharacteristic, complemented
240#832C2×D311yescharacteristic
241#830—31no—
242#821—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246#818C2×D311yescharacteristic, complemented
247#816—31no—
248#815C2×D311yescharacteristic, complemented
249Dic3⋊C8—31no—
250#810—31no—
251#810—31no—
252#810—31no—
253#809—31no—
254C4⋊(C3⋊C8)—31no—
255C23×C32—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—42no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3—81no—
260C22×C3⋊D3C2×D411yescharacteristic
261C22×C3×D3C2×D411yescharacteristic
262C32×Q8—21no—
263C32×Q8C2×D412yes—
264C32×D4—21no—
265C32×D4C2×D412yes—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268#638—42no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3C2×D411yescharacteristic
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4×C3⋊D3—21no—
274C4×C3⋊D3—21no—
275C4×C3⋊D3—42no—
276#634—21no—
277#634—21no—
278#634—42no—
279C3×#67—42no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—42no—
285C2×C3×Dic3—81no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—42no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—42no—
297#626—22no—
298#626—81no—
299C32×C8C2×D412yes—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×#137—31no—
304C22×SD16—91no—
305D4×Q8—91no—
306#546—91no—
307#497—91no—
308#468—91no—
309#467—91no—
310#464—91no—
311#461—91no—
312#452—91no—
313#451—91no—
314#450—91no—
315#448—91no—
316#440—31no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C23×D3—121no—
321C3×#41—62no—
322C3×#41—121no—
323C2×C3×Q8—21no—
324C2×C3×Q8—31no—
325C2×C3×Q8—31no—
326C2×C3×Q8—61no—
327C2×C3×Q8—62no—
328C2×C3×Q8—121no—
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×Q8C22×D311yescharacteristic
331C2×C3×D4—21no—
332C2×C3×D4—61no—
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C22×D311yescharacteristic
335C22×C3×C4—31no—
336C22×C3×C4—61no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C2×#67—21no—
340C2×#67—31no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—121no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347D3×Q8—22no—
348D3×Q8—41no—
349D3×Q8—64no—
350D3×Q8—62no—
351D3×Q8—62no—
352D3×Q8—121no—
353D3×Q8—121no—
354D3×Q8—122no—
355#237—22no—
356#237—41no—
357D3×D4—64no—
358D3×D4—62no—
359D3×D4—62no—
360D3×D4—121no—
361D3×D4—121no—
362D3×D4—122no—
363C2×D12—31no—
364C2×D12—31no—
365C2×D12—31no—
366C2×D12—61no—
367C2×D12—61no—
368C2×C4×D3—21no—
369C2×C4×D3—31no—
370C2×C4×D3—31no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—121no—
375C2×C4×D3C22×D311yescharacteristic
376C2×Dic6—21no—
377C2×Dic6—31no—
378C2×Dic6—31no—
379C2×Dic6—61no—
380C2×Dic6—61no—
381C2×Dic6—61no—
382C2×Dic6—121no—
383C2×Dic6C22×D311yescharacteristic
384C2×Dic6C22×D311yescharacteristic
385C3×Q16—62no—
386C3×Q16—62no—
387C3×SD16—24no—
388C3×SD16—62no—
389C3×SD16D1214yescomplemented
390C3×SD16#6714yescomplemented
391C3×M16—62no—
392C2×C3×C8—21no—
393C2×C3×C8—31no—
394C2×C3×C8—31no—
395C2×C3×C8C22×D311yescharacteristic
396C2×C3×C8C22×D311yescharacteristic
397C3×C4⋊C4—31no—
398C3×C4⋊C4—31no—
399C3×C4⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C42—31no—
402C3×C42—61no—
403#217—21no—
404#217—31no—
405#217—61no—
406#216—22no—
407#216—121no—
408#215—64no—
409#215—62no—
410#215—62no—
411#215—121no—
412#214—22no—
413#214—64no—
414#214—62no—
415#214—62no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—31no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430C4⋊Dic3—21no—
431C4⋊Dic3—31no—
432C4⋊Dic3—61no—
433C4⋊Dic3—61no—
434C4⋊Dic3—61no—
435C4⋊Dic3—61no—
436C4⋊Dic3—61no—
437C4⋊Dic3C22×D311yescharacteristic
438C4⋊Dic3C22×D311yescharacteristic
439Dic3⋊C4—31no—
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444Dic3⋊C4—61no—
445C4×Dic3—21no—
446C4×Dic3C22×D311yescharacteristic
447C2×C3⋊C8—31no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8C22×D311yescharacteristic
451C2×C3⋊C8C22×D311yescharacteristic
452Dic12—22no—
453Dic12—121no—
454#204—64no—
455#204—62no—
456#204—62no—
457#204—121no—
458ΓL(1,𝔽25)—22no—
459D3×C8—64no—
460D3×C8—62no—
461D3×C8—62no—
462C22×C32—22no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32C22×D411yescharacteristic
466C2×C3⋊D3—21no—
467C2×C3⋊D3—21no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—84no—
472C2×C3⋊D3#13712yescomplemented
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C32×C4—22no—
477C32×C4C22×D411yescharacteristic
478C32×C4H(5,𝔽2)11yescharacteristic
479C3⋊Dic3—21no—
480C3⋊Dic3—41no—
481C3×Dic3—21no—
482C3×Dic3—21no—
483C3×Dic3—21no—
484C3×Dic3—41no—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—31no—
489C22×Q8—31no—
490C22×Q8—91no—
491C22×D4—91no—
492#137—64no—
493C2×Q16—31no—
494C2×Q16—31no—
495C2×Q16—91no—
496C2×SD16—31no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×SD16—184no—
502C2×SD16D3211yescharacteristic
503C2×M16—31no—
504C22×C8—91no—
505C4⋊Q8—91no—
506C4⋊Q8—181no—
507#124—91no—
508#123—181no—
509C22⋊Q8—91no—
510C22⋊Q8—91no—
511C22⋊Q8—91no—
512C22⋊Q8—181no—
513C22⋊Q8—181no—
514#121—91no—
515#121—181no—
516#120—181no—
517C4×Q8—31no—
518C4×D4—31no—
519C4×D4—91no—
520C4×D4—181no—
521C2×C22⋊C4—181no—
522#107—31no—
523C4⋊C8—91no—
524#103—31no—
525#103—91no—
526#103—91no—
527#103—91no—
528#102—31no—
529#102—91no—
530C22⋊C8—91no—
531C22⋊C8—91no—
532#97—31no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—31no—
536C23×C3—41no—
537C22×D3—31no—
538C22×D3—31no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—61no—
542C22×D3—121no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3—124no—
548C22×D3—242no—
549C22×D3—241no—
550C22×D3—241no—
551C22×D3—242no—
552C22×D3D3×D411yescharacteristic
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—22no—
556C3×Q8—41no—
557C3×Q8—61no—
558C3×Q8—61no—
559C3×Q8—61no—
560C3×Q8—61no—
561C3×Q8—122no—
562C3×Q8C2×D1212yes—
563C3×Q8C2×#6712yes—
564C3×D4—21no—
565C3×D4—21no—
566C3×D4—22no—
567C3×D4—41no—
568C3×D4—122no—
569C3×D4C2×D1212yes—
570C3×D4C2×#6712yes—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—41no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—122no—
585C2×C3×C4—122no—
586C2×C3×C4—241no—
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589#67—42no—
590#67—62no—
591#67—122no—
592#67—122no—
593#67—124no—
594#67—241no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—31no—
600C2×Dic3—31no—
601C2×Dic3—42no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—81no—
606C2×Dic3—121no—
607C2×Dic3D3×D411yescharacteristic
608C2×Dic3D3×D411yescharacteristic
609C2×Dic3D3×D411yescharacteristic
610D12—62no—
611D12—62no—
612D12—61no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—121no—
617D12—241no—
618C4×D3—21no—
619C4×D3—21no—
620C4×D3—42no—
621C4×D3—62no—
622C4×D3—62no—
623C4×D3—61no—
624C4×D3—61no—
625C4×D3—61no—
626C4×D3—61no—
627C4×D3—122no—
628C4×D3—122no—
629C4×D3—124no—
630Dic6—21no—
631Dic6—21no—
632Dic6—21no—
633Dic6—21no—
634Dic6—42no—
635Dic6—62no—
636Dic6—61no—
637Dic6—61no—
638Dic6—61no—
639Dic6—61no—
640Dic6—121no—
641Dic6—122no—
642Dic6—122no—
643Dic6—124no—
644C3×C8—22no—
645C3×C8—61no—
646C3×C8—61no—
647C3×C8C2×D1212yes—
648C3×C8C2×#6712yes—
649C3⋊C8—21no—
650C3⋊C8—21no—
651C3⋊C8—62no—
652C3⋊C8—61no—
653C3⋊C8—61no—
654C2×C32—42no—
655C2×C32D4211yescharacteristic
656C2×C32C2×#13711yescharacteristic
657C2×C32#57711yescharacteristic
658C3⋊D3—22no—
659C3⋊D3—81no—
660C3×D3—41no—
661C24—181no—
662#41—62no—
663#41—121no—
664C2×Q8—31no—
665C2×Q8—31no—
666C2×Q8—61no—
667C2×Q8—62no—
668C2×Q8—91no—
669C2×Q8—121no—
670C2×Q8—181no—
671C2×Q8—182no—
672C2×Q8—361no—
673C2×Q8C2×D3211yescharacteristic
674C2×D4—61no—
675C2×D4—91no—
676C2×D4—91no—
677C2×D4—181no—
678C2×D4—181no—
679C2×D4—182no—
680C2×D4—361no—
681C2×D4C2×D3211yescharacteristic
682C22×C4—31no—
683C22×C4—61no—
684C22×C4—61no—
685C22×C4—61no—
686C22×C4—91no—
687C22×C4—181no—
688Q16—62no—
689Q16—62no—
690Q16—361no—
691SD16—62no—
692SD16—182no—
693SD16—182no—
694SD16—182no—
695SD16—361no—
696SD16#62614yescomplemented
697M16—62no—
698C2×C8—31no—
699C2×C8—31no—
700C2×C8—91no—
701C2×C8—182no—
702C2×C8C2×D3211yescharacteristic
703C4⋊C4—31no—
704C4⋊C4—31no—
705C4⋊C4—61no—
706C4⋊C4—91no—
707C4⋊C4—181no—
708C4⋊C4—181no—
709C4⋊C4—181no—
710C4⋊C4—181no—
711C4⋊C4—181no—
712C22⋊C4—61no—
713C22⋊C4—91no—
714C22⋊C4—91no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C42—31no—
722C42—61no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—21no—
726C22×C3—42no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—81no—
735C22×C3—81no—
736C22×C3C2×D3×D411yescharacteristic
737C22×C3C2×D3×D411yescharacteristic
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—32no—
742C2×D3—32no—
743C2×D3—62no—
744C2×D3—62no—
745C2×D3—62no—
746C2×D3—61no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—122no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—241no—
758C2×D3—241no—
759C2×D3—244no—
760C2×D3—244no—
761C2×D3—248no—
762C3×C4—22no—
763C3×C4—22no—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—42no—
767C3×C4—61no—
768C3×C4—61no—
769C3×C4—61no—
770C3×C4—121no—
771C3×C4—121no—
772C3×C4—121no—
773C3×C4—121no—
774C3×C4C22×D1211yescharacteristic
775C3×C4#100411yescharacteristic
776C3×C4#100911yescharacteristic
777C3×C4C22×#6711yescharacteristic
778Dic3—21no—
779Dic3—21no—
780Dic3—21no—
781Dic3—41no—
782Dic3—41no—
783Dic3—41no—
784Dic3—41no—
785Dic3—62no—
786Dic3—61no—
787Dic3—61no—
788Dic3—122no—
789Dic3—121no—
790Dic3—121no—
791C32#326611yescharacteristic, complemented, Sylow
792C23—21no—
793C23—31no—
794C23—91no—
795C23—181no—
796C23—362no—
797C23—362no—
798C23—721no—
799Q8—21no—
800Q8—61no—
801Q8—61no—
802Q8—61no—
803Q8—61no—
804Q8—122no—
805Q8—181no—
806Q8—181no—
807Q8—362no—
808Q8C2×#62612yes—
809D4—21no—
810D4—122no—
811D4—182no—
812D4—181no—
813D4—181no—
814D4—362no—
815D4—721no—
816D4C2×#62612yes—
817C2×C4—21no—
818C2×C4—31no—
819C2×C4—31no—
820C2×C4—31no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—91no—
828C2×C4—122no—
829C2×C4—122no—
830C2×C4—181no—
831C2×C4—181no—
832C2×C4—181no—
833C2×C4—241no—
834C2×C4—362no—
835C2×C4C22×D3211yescharacteristic
836C8—61no—
837C8—61no—
838C8—181no—
839C8C2×#62612yes—
840C2×C3—21no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—42no—
844C2×C3—42no—
845C2×C3—82no—
846C2×C3—121no—
847C2×C3D4×D1211yescharacteristic
848C2×C3#577511yescharacteristic
849C2×C3D3×#13711yescharacteristic
850C2×C3D3×#13711yescharacteristic
851C2×C3#577811yescharacteristic
852C2×C3D4×#6711yescharacteristic
853D3—41no—
854D3—64no—
855D3—62no—
856D3—62no—
857D3—242no—
858D3—241no—
859D3—241no—
860C22—22no—
861C22—41no—
862C22—41no—
863C22—61no—
864C22—61no—
865C22—61no—
866C22—92no—
867C22—181no—
868C22—181no—
869C22—361no—
870C22—361no—
871C22—361no—
872C22—724no—
873C22D32×D411yescharacteristic
874C4—22no—
875C4—61no—
876C4—61no—
877C4—61no—
878C4—121no—
879C4—121no—
880C4—121no—
881C4—121no—
882C4—181no—
883C4—361no—
884C4#6431411yescharacteristic
885C4C22×#62611yescharacteristic
886C3—21no—
887C3#7979511yescharacteristic, complemented
888C3#8398711yescharacteristic, complemented
889C2—42no—
890C2—121no—
891C2—182no—
892C2—721no—
893C2#1059474211yescharacteristic
894C2#1059475411yescharacteristic
895C2D4×#62611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radical#10595254C2
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×SD16×C3⋊D3C2semidirect
2. C2×C3×#915C2semidirect
3. Q8×#626C2semidirect
5. C3×#5164C2semidirect
6. #10591607C2semidirect
7. #10591603C2semidirect
8. #10591584C2semidirect
9. #10591489C2semidirect
10. #10591467C2semidirect
11. #10591463C2semidirect
12. #10590899C2semidirect
13. #10590857C2semidirect
14. #10590838C2semidirect
15. #10590736C2semidirect
20. C2×C3×D3×Q8C22semidirect
28. C3×Q8×Dic3C22semidirect
29. C2×C3×#216C22semidirect
33. C2×C3×Dic12C22semidirect
34. C2×C3×ΓL(1,𝔽25)C22semidirect
46. #63866C22semidirect
49. #63857C22semidirect
50. C2×#3719C22semidirect
52. C3×#835C22semidirect
54. C3×#818C22semidirect
55. C3×#815C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
59. #63565C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
66. C2×#915D3semidirect
80. #5164D3semidirect
121. C32×SD16D4semidirect
162. C2×D3×Q8C2×D3semidirect
181. Q8×Dic3C2×D3semidirect
185. C2×#216C2×D3semidirect
211. C2×Dic12C2×D3semidirect
216. C2×ΓL(1,𝔽25)C2×D3semidirect
239. #835C2×D3semidirect
246. #818C2×D3semidirect
248. #815C2×D3semidirect
389. C3×SD16D12semidirect
390. C3×SD16#67semidirect
472. C2×C3⋊D3#137semidirect
696. SD16#626semidirect
791. C32#3266semidirect
887. C3#79795semidirect
888. C3#83987semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×C3⋊D32
C2×C3×#9152
Q8×#6262
#105952542
C3×#51642
#105916072
#105916032
#105915842
#105914892
#105914672
#105914632
#105908992
#105908572
#105908382
#105907362
#839873
#797953