Finite Group Databasebeta

← #11884185

Subgroups — #11884185

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595427C211yesmaximal, characteristic
2C2×#63943C211yesmaximal, characteristic, complemented
3C2×D3×#204C211yesmaximal, characteristic, complemented
4#10594526C211yesmaximal, characteristic, complemented
5#10592497C211yesmaximal, characteristic, complemented
6C3×#4813C211yesmaximal, characteristic, complemented
7C3×#4808C211yesmaximal, characteristic, complemented
8#10591653C211yesmaximal, characteristic, complemented
9#10591629C211yesmaximal, characteristic, complemented
10#10590951C211yesmaximal, characteristic, complemented
11#10590748C211yesmaximal, characteristic, complemented
12#10590723C211yesmaximal, characteristic, complemented
13#10590596C211yesmaximal, characteristic, complemented
14#10590585C211yesmaximal, characteristic, complemented
15#10590461C211yesmaximal, characteristic, complemented
16#80771—31nomaximal
17#80241—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic, complemented
22#64156C2211yescharacteristic
23C2×#3756C2211yescharacteristic, complemented
24C2×#3744C2211yescharacteristic
25#64096C2211yescharacteristic, complemented
26C3×#946C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#216C2211yescharacteristic, complemented
29C2×C3×#204C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic
31C3×#897C2211yescharacteristic
32C3×#897C2211yescharacteristic, complemented
33#63943—24no—
34#63922—21no—
35D3×(C2×D3)⋊C4—21no—
36#63919—21no—
37#63909C2211yescharacteristic
38#63902—21no—
39C4×#625C2211yescharacteristic
40#63899—21no—
41#63899—21no—
42#63898C2211yescharacteristic
43#63886—21no—
44#63873C2211yescharacteristic, complemented
45#63850—21no—
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3711C2211yescharacteristic, complemented
51D3×#204—24no—
52C32×#103C2211yescharacteristic, complemented
53#63641C2211yescharacteristic, complemented
54#63636C2211yescharacteristic
55C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#807C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63555C2211yescharacteristic, complemented
63#5829—31no—
64C2×#951—31no—
65C2×#918—31no—
66C2×D3×SD16—31no—
67C22×#204—31no—
68#5632—31no—
69#5632—31no—
70#5630—31no—
71C3×#467—31no—
72C3×#452—31no—
73#5190—31no—
74#5190—31no—
75#5186—31no—
76#5162—31no—
77#5111—31no—
78#5050—31no—
79#5049—31no—
80#5046—31no—
81#4889—31no—
82#4886—31no—
83#4818—31no—
84#4813D311yescharacteristic, complemented
85#4808D311yescharacteristic, complemented
86#4806—31no—
87#4798—31no—
88#4798—31no—
89#4798—61no—
90#4776—31no—
91#4757—31no—
92#4738—31no—
93#4728—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C3×#239—22no—
99C3×#239—41no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#627—21no—
108C2×#627—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#625D411yescharacteristic
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114C2×D3×Dic3—21no—
115D3×D12—22no—
116D3×D12—41no—
117D3×Dic6—22no—
118D3×Dic6—22no—
119D3×Dic6—41no—
120D3×Dic6—41no—
121C2×C32×C8C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3756—22no—
124#3752—21no—
125#3752—21no—
126#3750—21no—
127C4×C3⋊Dic3—21no—
128C4×C3⋊Dic3C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3744—22no—
131C3×#216—22no—
132C3×#216—41no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×Dic3⋊C4—21no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×#204—22no—
143C3×D3×C8—22no—
144#3724—21no—
145#3724—21no—
146#3724D411yescharacteristic
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150(C2×D3)⋊Dic3D411yescharacteristic
151#3717—22no—
152#3717—41no—
153#3716D414yescomplemented
154#3715—22no—
155#3711—22no—
156#3266—91noSylow
157C2×C3×#41—31no—
158C2×#239C2×D311yescharacteristic
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×D3×D4—31no—
162C22×D12—31no—
163C22×Dic6—31no—
164C22×Dic6—31no—
165C2×C3×Q16—31no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C22×C3×C8—31no—
169C3×C22⋊Q8—31no—
170C3×C22⋊Q8—31no—
171C3×C22⋊Q8—31no—
172#951—64no—
173#947—31no—
174#947—31no—
175#947—61no—
176#946C2×D311yescharacteristic
177#944—31no—
178#944—31no—
179C2×#216—31no—
180C2×#216—31no—
181C2×#216—61no—
182C2×#216C2×D311yescharacteristic, complemented
183C2×#216C2×D311yescharacteristic, complemented
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187#939—61no—
188#937—61no—
189D4×Dic3—31no—
190C2×#214—31no—
191C2×#214—31no—
192#930—31no—
193#929—61no—
194C4×#67—31no—
195C4×#67—31no—
196C2×(C2×D3)⋊C4—61no—
197C2×#208—31no—
198#918—64no—
199D3×SD16—64no—
200C2×#204—31no—
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—31no—
205C2×#204—61no—
206C2×#204—64no—
207C2×#204C2×D311yescharacteristic
208C2×ΓL(1,𝔽25)—31no—
209C2×D3×C8C2×D311yescharacteristic
210#897C2×D311yescharacteristic
211#897C2×D311yescharacteristic, complemented
212#896—61no—
213#896—61no—
214#895—31no—
215#895—61no—
216#894—61no—
217#893—31no—
218#888—61no—
219#888—61no—
220#887—31no—
221#887—31no—
222#887—61no—
223#882—61no—
224#67⋊C4—61no—
225#67⋊C4—61no—
226D3×C22⋊C4—61no—
227#878—61no—
228#878—61no—
229C3×#107—31no—
230C3×#103—21no—
231C3×#103—31no—
232C3×#103C2×D311yescharacteristic, complemented
233C3×#103C2×D311yescharacteristic, complemented
234C3×#102—31no—
235C3×C22⋊C8—31no—
236#835—31no—
237#830—31no—
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8C2×D311yescharacteristic, complemented
240#816—31no—
241#816C2×D311yescharacteristic, complemented
242#815—31no—
243#815—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—61no—
247#810—31no—
248#810—31no—
249#809—31no—
250#809—31no—
251#809—61no—
252#809C2×D311yescharacteristic
253#807C2×D311yescharacteristic, complemented
254C22×C3⋊D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C22×C3×D3C2×D411yescharacteristic
258C2×D32—42no—
259C2×D32—42no—
260C2×D32—81no—
261C32×Q8—21no—
262C32×Q8—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3C2×D411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271#634—21no—
272#634C2×D412yes—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C3×D12—21no—
279C3×D12—42no—
280C3×D12C2×D412yes—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283C3×C4×D3—21no—
284C3×C4×D3—21no—
285C3×C4×D3—42no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290#627—42no—
291#627—42no—
292#626—42no—
293#626—81no—
294#625—22no—
295D3×Dic3—42no—
296D3×Dic3—42no—
297D3×Dic3—81no—
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—91no—
305#546—91no—
306#497—91no—
307#468—91no—
308#467—31no—
309#464—91no—
310#461—91no—
311#452—31no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—91no—
317C23×D3—61no—
318C23×D3—61no—
319C3×#41—62no—
320C3×#41—121no—
321C2×C3×Q8—21no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×Q8C22×D311yescharacteristic
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—61no—
331C2×#67—31no—
332C2×#67—31no—
333C2×#67—61no—
334C2×#67—61no—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338#239—22no—
339#239—41no—
340D3×Q8—62no—
341D3×Q8—62no—
342D3×Q8—121no—
343D3×Q8—121no—
344D3×D4—62no—
345D3×D4—121no—
346C2×D12—21no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—61no—
350C2×D12—62no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12—121no—
354C2×D12C22×D311yescharacteristic
355C2×C4×D3—21no—
356C2×C4×D3—61no—
357C2×C4×D3—61no—
358C2×C4×D3—61no—
359C2×C4×D3C22×D311yescharacteristic
360C2×C4×D3C22×D311yescharacteristic
361C2×Dic6—31no—
362C2×Dic6—31no—
363C2×Dic6—61no—
364C2×Dic6—62no—
365C2×Dic6—62no—
366C2×Dic6—61no—
367C2×Dic6—61no—
368C2×Dic6—61no—
369C2×Dic6—61no—
370C2×Dic6—121no—
371C2×Dic6—121no—
372C2×Dic6C22×D311yescharacteristic
373C2×Dic6C22×D311yescharacteristic
374C3×Q16—62no—
375C3×Q16—121no—
376C3×SD16—62no—
377C2×C3×C8—21no—
378C2×C3×C8—31no—
379C2×C3×C8—31no—
380C2×C3×C8—62no—
381C2×C3×C8C22×D311yescharacteristic
382C2×C3×C8C22×D311yescharacteristic
383C3×C4⋊C4—21no—
384C3×C4⋊C4—31no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4—61no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C4⋊C4C22×D311yescharacteristic
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4—61no—
393#217—31no—
394#217—31no—
395#217—61no—
396#216—22no—
397#216—41no—
398#216—62no—
399#216—62no—
400#216—122no—
401#215—62no—
402#215—62no—
403#215—121no—
404#214—34no—
405#214—62no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—21no—
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—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—121no—
419(C2×D3)⋊C4—121no—
420C4⋊Dic3—21no—
421C4⋊Dic3—21no—
422C4⋊Dic3C22×D311yescharacteristic
423Dic3⋊C4—21no—
424Dic3⋊C4—31no—
425Dic3⋊C4—31no—
426Dic3⋊C4—61no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—121no—
433C4×Dic3—31no—
434C4×Dic3—31no—
435C4×Dic3—61no—
436C4×Dic3—61no—
437C4×Dic3—61no—
438C4×Dic3—121no—
439#208—62no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—61no—
443C2×C3⋊C8C22×D311yescharacteristic
444C2×C3⋊C8C22×D311yescharacteristic
445#204—22no—
446#204—34no—
447#204—62no—
448#204—62no—
449#204—62no—
450#204—122no—
451#204—121no—
452ΓL(1,𝔽25)—62no—
453D3×C8—22no—
454C22×C32C22×D411yescharacteristic
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—22no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3#13712yescomplemented
467D32—84no—
468C32×C4—41no—
469C32×C4—41no—
470C32×C4C22×D411yescharacteristic
471C32×C4H(5,𝔽2)11yescharacteristic
472C3⋊Dic3—22no—
473C3⋊Dic3—21no—
474C3⋊Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—21no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C2×#41—31no—
481C22×Q8—91no—
482C22×Q8—91no—
483C22×D4—91no—
484#137—184no—
485C2×Q16—31no—
486C2×Q16—31no—
487C2×Q16—91no—
488C2×SD16—31no—
489C2×SD16—91no—
490C2×SD16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—184no—
495C2×M16—91no—
496C22×C8—31no—
497C4⋊Q8—91no—
498C4⋊Q8—181no—
499#124—91no—
500#123—181no—
501C22⋊Q8—31no—
502C22⋊Q8—31no—
503C22⋊Q8—31no—
504C22⋊Q8—181no—
505C22⋊Q8—181no—
506#121—91no—
507#121—181no—
508#120—181no—
509C4×Q8—91no—
510C4×D4—91no—
511C4×D4—91no—
512C4×D4—181no—
513C2×C22⋊C4—181no—
514#107—31no—
515C4⋊C8—91no—
516#103—31no—
517#103—91no—
518#103—91no—
519#103D3211yescharacteristic, complemented
520#102—31no—
521#102—91no—
522C22⋊C8—31no—
523C22⋊C8—91no—
524#97—91no—
525C23×C3—31no—
526C23×C3—31no—
527C23×C3—61no—
528C22×D3—21no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—121no—
532C22×D3—122no—
533C22×D3—122no—
534C22×D3—122no—
535C22×D3—122no—
536C22×D3—241no—
537C22×D3—241no—
538C22×D3D3×D411yescharacteristic
539C22×D3D3×D411yescharacteristic
540C3×Q8—21no—
541C3×Q8—21no—
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—41no—
545C3×Q8—41no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×D4—32no—
551C3×D4—61no—
552C3×D4—122no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—122no—
570C2×C3×C4C23×D311yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572#67—62no—
573#67—62no—
574#67—122no—
575#67—241no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—31no—
580C2×Dic3—31no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—121no—
588C2×Dic3—122no—
589C2×Dic3—122no—
590C2×Dic3—241no—
591C2×Dic3D3×D411yescharacteristic
592C2×Dic3D3×D411yescharacteristic
593D12—21no—
594D12—42no—
595D12—61no—
596D12—61no—
597D12—61no—
598D12—61no—
599D12—121no—
600D12—121no—
601D12—122no—
602D12—241no—
603D12D3×D412yes—
604C4×D3—21no—
605C4×D3—21no—
606C4×D3—21no—
607C4×D3—21no—
608C4×D3—42no—
609C4×D3—122no—
610C4×D3—122no—
611C4×D3—241no—
612Dic6—21no—
613Dic6—21no—
614Dic6—21no—
615Dic6—21no—
616Dic6—32no—
617Dic6—32no—
618Dic6—62no—
619Dic6—61no—
620Dic6—61no—
621Dic6—121no—
622Dic6—122no—
623Dic6—122no—
624Dic6—122no—
625Dic6—122no—
626C3×C8—21no—
627C3×C8—21no—
628C3×C8—32no—
629C3×C8—41no—
630C3×C8—61no—
631C3⋊C8—21no—
632C3⋊C8—61no—
633C3⋊C8—61no—
634C3⋊C8—121no—
635C3⋊C8D3×D412yes—
636C2×C32D4211yescharacteristic
637C2×C32C2×#13711yescharacteristic
638C2×C32#57711yescharacteristic
639C3⋊D3—81no—
640C3×D3—22no—
641C3×D3—42no—
642C3×D3—41no—
643C24—181no—
644#41—62no—
645#41—121no—
646C2×Q8—31no—
647C2×Q8—31no—
648C2×Q8—91no—
649C2×Q8—181no—
650C2×Q8—181no—
651C2×Q8—182no—
652C2×Q8—182no—
653C2×Q8—361no—
654C2×Q8—361no—
655C2×Q8C2×D3211yescharacteristic
656C2×D4—31no—
657C2×D4—61no—
658C2×D4—91no—
659C2×D4—91no—
660C2×D4—181no—
661C2×D4—182no—
662C2×D4—181no—
663C2×D4—361no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—61no—
667C22×C4—181no—
668C22×C4—181no—
669C22×C4—181no—
670Q16—62no—
671Q16—121no—
672Q16—182no—
673SD16—62no—
674SD16—94no—
675SD16—182no—
676SD16—182no—
677SD16—182no—
678SD16—361no—
679M16—182no—
680C2×C8—31no—
681C2×C8—31no—
682C2×C8—62no—
683C2×C8—91no—
684C2×C8C2×D3211yescharacteristic
685C4⋊C4—31no—
686C4⋊C4—61no—
687C4⋊C4—61no—
688C4⋊C4—61no—
689C4⋊C4—91no—
690C4⋊C4—181no—
691C4⋊C4—181no—
692C4⋊C4—181no—
693C4⋊C4C2×D3211yescharacteristic
694C22⋊C4—61no—
695C22⋊C4—61no—
696C22⋊C4—61no—
697C22⋊C4—91no—
698C22⋊C4—91no—
699C22⋊C4—181no—
700C22⋊C4—181no—
701C22⋊C4—181no—
702C22⋊C4—181no—
703C42—91no—
704C42—181no—
705C22×C3—21no—
706C22×C3—32no—
707C22×C3—61no—
708C22×C3—61no—
709C22×C3—61no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3—62no—
713C22×C3—121no—
714C22×C3—121no—
715C22×C3C2×D3×D411yescharacteristic
716C22×C3C2×D3×D411yescharacteristic
717C2×D3—21no—
718C2×D3—21no—
719C2×D3—21no—
720C2×D3—21no—
721C2×D3—21no—
722C2×D3—22no—
723C2×D3—41no—
724C2×D3—41no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—241no—
732C2×D3—241no—
733C2×D3—241no—
734C2×D3—244no—
735C2×D3—244no—
736C2×D3#91812yescomplemented
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—41no—
743C3×C4—61no—
744C3×C4—61no—
745C3×C4—81no—
746C3×C4—81no—
747C3×C4—121no—
748C3×C4—121no—
749C3×C4—121no—
750C3×C4C2×D3×D411yescharacteristic
751C3×C4C2×D3×D411yescharacteristic
752C3×C4#100411yescharacteristic
753C3×C4#100911yescharacteristic
754Dic3—21no—
755Dic3—21no—
756Dic3—41no—
757Dic3—41no—
758Dic3—41no—
759Dic3—61no—
760Dic3—61no—
761Dic3—61no—
762Dic3—61no—
763Dic3—62no—
764Dic3—62no—
765Dic3—122no—
766Dic3—121no—
767Dic3—121no—
768C32#326611yescharacteristic, complemented, Sylow
769C23—31no—
770C23—31no—
771C23—61no—
772C23—181no—
773C23—362no—
774C23—362no—
775C23—721no—
776Q8—21no—
777Q8—21no—
778Q8—61no—
779Q8—61no—
780Q8—61no—
781Q8—61no—
782Q8—92no—
783Q8—181no—
784Q8—362no—
785Q8—362no—
786D4—32no—
787D4—61no—
788D4—122no—
789D4—182no—
790D4—181no—
791D4—181no—
792D4—362no—
793D4—721no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—31no—
797C2×C4—31no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—91no—
806C2×C4—91no—
807C2×C4—122no—
808C2×C4—181no—
809C2×C4—362no—
810C2×C4—362no—
811C2×C4—721no—
812C2×C4C22×D3211yescharacteristic
813C8—21no—
814C8—32no—
815C8—61no—
816C8—181no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—62no—
821C2×C3—122no—
822C2×C3—121no—
823C2×C3#559011yescharacteristic
824C2×C3#560911yescharacteristic
825C2×C3C2×#91811yescharacteristic
826C2×C3#577011yescharacteristic
827C2×C3#577011yescharacteristic
828C2×C3D3×#13711yescharacteristic
829D3—22no—
830D3—41no—
831D3—42no—
832D3—241no—
833D3—241no—
834D3—481no—
835C22—32no—
836C22—61no—
837C22—61no—
838C22—61no—
839C22—61no—
840C22—61no—
841C22—62no—
842C22—121no—
843C22—121no—
844C22—361no—
845C22—361no—
846C22—361no—
847C22—724no—
848C22D32×D411yescharacteristic
849C4—41no—
850C4—41no—
851C4—61no—
852C4—61no—
853C4—121no—
854C4—121no—
855C4—121no—
856C4—181no—
857C4—181no—
858C4—182no—
859C4#6430711yescharacteristic
860C4D32×D411yescharacteristic
861C3—21no—
862C3#8024111yescharacteristic, complemented
863C3#8077111yescharacteristic, complemented
864C2—62no—
865C2—121no—
866C2—122no—
867C2—721no—
868C2#1059427511yescharacteristic
869C2#1059475711yescharacteristic
870C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10595427C2
hypercenter#103D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. C2×#63943C2semidirect
3. C2×D3×#204C2semidirect
4. #10594526C2semidirect
5. #10592497C2semidirect
6. C3×#4813C2semidirect
7. C3×#4808C2semidirect
8. #10591653C2semidirect
9. #10591629C2semidirect
10. #10590951C2semidirect
11. #10590748C2semidirect
12. #10590723C2semidirect
13. #10590596C2semidirect
14. #10590585C2semidirect
15. #10590461C2semidirect
21. C2×D3×Dic6C22semidirect
23. C2×#3756C22semidirect
25. #64096C22semidirect
27. C2×C3×#216C22semidirect
28. C2×C3×#216C22semidirect
32. C3×#897C22semidirect
44. #63873C22semidirect
50. C2×#3711C22semidirect
52. C32×#103C22semidirect
53. #63641C22semidirect
55. C3×(C2×D3)⋊C8C22semidirect
56. C3×#816C22semidirect
58. C3×#807C22semidirect
59. #63567C22semidirect
60. #63565C22semidirect
62. #63555C22semidirect
84. #4813D3semidirect
85. #4808D3semidirect
153. #3716D4semidirect
182. C2×#216C2×D3semidirect
183. C2×#216C2×D3semidirect
211. #897C2×D3semidirect
232. C3×#103C2×D3semidirect
233. C3×#103C2×D3semidirect
239. (C2×D3)⋊C8C2×D3semidirect
241. #816C2×D3semidirect
253. #807C2×D3semidirect
466. C2×C3×D3#137semidirect
519. #103D32semidirect
736. C2×D3#918semidirect
768. C32#3266semidirect
862. C3#80241semidirect
863. C3#80771semidirect

Maximal subgroups

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

subgroupindex
#105954272
C2×#639432
C2×D3×#2042
#105945262
#105924972
C3×#48132
C3×#48082
#105916532
#105916292
#105909512
#105907482
#105907232
#105905962
#105905852
#105904612
#807713
#802413