Finite Group Databasebeta

← #11884188

Subgroups — #11884188

Order 1152.

1067 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595361C211yesmaximal, characteristic, complemented
2C2×#63951C211yesmaximal, characteristic, complemented
3C2×D3×#204C211yesmaximal, characteristic, complemented
4#10594629C211yesmaximal, characteristic
5#10592505C211yesmaximal, characteristic, complemented
6C3×#4818C211yesmaximal, characteristic, complemented
7C3×#4813C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591608C211yesmaximal, characteristic, complemented
10#10590961C211yesmaximal, characteristic, complemented
11#10590813C211yesmaximal, characteristic, complemented
12#10590727C211yesmaximal, characteristic, complemented
13#10590604C211yesmaximal, characteristic, complemented
14#10590590C211yesmaximal, characteristic, complemented
15#10590522C211yesmaximal, characteristic, complemented
16#80771—31nomaximal
17#80444—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C2×D3×D12C2211yescharacteristic
20C2×#3796C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C2×#3744C2211yescharacteristic
24#64104C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×#944C2211yescharacteristic, complemented
27C2×C3×#216C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic
31C3×#897C2211yescharacteristic
32C3×#893C2211yescharacteristic
33#63951—24no—
34#63923—21no—
35D3×(C2×D3)⋊C4—21no—
36#63909—21no—
37C4×#626C2211yescharacteristic
38#63896—21no—
39#63890—21no—
40#63881—21no—
41#63871C2211yescharacteristic, complemented
42#63865—21no—
43#63864C2211yescharacteristic
44#63844C2211yescharacteristic, complemented
45#63840—21no—
46C2×#3719C2211yescharacteristic, complemented
47C2×#3718C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic
49C2×#3716C2211yescharacteristic
50C2×#3712C2211yescharacteristic, complemented
51D3×#204—24no—
52C32×#103C2211yescharacteristic, complemented
53#63647C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#807C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C2×#918—31no—
64C2×#915—31no—
65C2×D3×SD16—31no—
66C22×#204—31no—
67#5727—31no—
68#5632—31no—
69#5630—31no—
70#5554—31no—
71C3×#467—31no—
72C3×#461—31no—
73#5190—31no—
74#5173—31no—
75#5169—31no—
76#5111—31no—
77#5086—31no—
78#5050—31no—
79#5046—31no—
80#5018—31no—
81#4889—31no—
82#4886—31no—
83#4845—31no—
84#4836—31no—
85#4818D311yescharacteristic, complemented
86#4813D311yescharacteristic, complemented
87#4812—31no—
88#4809—31no—
89#4808—31no—
90#4806—31no—
91#4806—31no—
92#4806—61no—
93#4798—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96Q8×C3⋊D3—22no—
97Q8×C3⋊D3—41no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×#634—21no—
103C2×#634C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#626D411yescharacteristic
113C2×D3×Dic3—21no—
114C2×D3×Dic3—21no—
115D3×D12—22no—
116D3×D12—41no—
117#3796—22no—
118#3796—41no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121C2×C32×C8C2311yescharacteristic
122C32×C4⋊C4C2311yescharacteristic
123#3755—41no—
124#3752—21no—
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3744—22no—
127C3×#216—22no—
128C3×#215—22no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×#204—22no—
141C3×D3×C8—22no—
142#3724—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3D411yescharacteristic
145#3722—21no—
146#3722—21no—
147#3722—21no—
148#3722D411yescharacteristic
149(C2×D3)⋊Dic3D411yescharacteristic
150Dic32—21no—
151#3719—22no—
152#3718—41no—
153#3717—22no—
154#3716D414yescomplemented
155#3712—22no—
156#3266—91noSylow
157C2×#239—31no—
158C2×D3×Q8—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×D3×Q8—61no—
162C2×#237—31no—
163C2×D3×D4—31no—
164C22×D12—31no—
165C22×Dic6—31no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C22×C3×C8—31no—
170C3×C4⋊Q8—31no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×C4×D4—31no—
174#947—31no—
175#946—31no—
176#946C2×D311yescharacteristic
177#944C2×D311yescharacteristic, complemented
178C2×#216—31no—
179C2×#216—31no—
180C2×#216—31no—
181C2×#216C2×D311yescharacteristic, complemented
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—61no—
186C2×#215C2×D311yescharacteristic
187C2×#214—31no—
188#930—61no—
189C4×#67—31no—
190C2×(C2×D3)⋊C4—61no—
191#918—64no—
192#915—64no—
193D3×SD16—64no—
194C2×Dic12—31no—
195C2×#204—31no—
196C2×#204—31no—
197C2×#204—31no—
198C2×#204—31no—
199C2×#204—61no—
200C2×#204—64no—
201C2×#204C2×D311yescharacteristic
202C2×ΓL(1,𝔽25)—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×D3×C8C2×D311yescharacteristic
205#897—31no—
206#897C2×D311yescharacteristic
207#896—61no—
208#896—61no—
209#896—61no—
210#895—31no—
211#895—31no—
212#895—61no—
213#895—61no—
214#894—61no—
215#893—61no—
216#893C2×D311yescharacteristic
217#888—61no—
218#888—61no—
219#887—31no—
220#886—61no—
221#882—61no—
222#882—61no—
223#67⋊C4—61no—
224D3×C22⋊C4—61no—
225#878—61no—
226#875—31no—
227C4×D12—31no—
228C4×Dic6—31no—
229C3×#107—31no—
230C3×C4⋊C8—31no—
231C3×#103—21no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#103C2×D311yescharacteristic, complemented
235C3×#103C2×D311yescharacteristic, complemented
236#832—31no—
237#830—31no—
238#821—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—61no—
243#816C2×D311yescharacteristic, complemented
244#815—31no—
245Dic3⋊C8C2×D311yescharacteristic, complemented
246#810—31no—
247#810—31no—
248#810—61no—
249#810C2×D311yescharacteristic, complemented
250#809—31no—
251#809—31no—
252#807C2×D311yescharacteristic, complemented
253#803—31no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3C2×D411yescharacteristic
256C22×C3×D3—21no—
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
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—81no—
271C4×C3⋊D3—21no—
272C4×C3⋊D3—21no—
273C4×C3⋊D3—42no—
274#634—21no—
275#634—42no—
276#634C2×D412yes—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12C2×D412yes—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—81no—
288C3×Dic6—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292#627—42no—
293#626—22no—
294#626—42no—
295#626—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
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—31no—
311#452—91no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—91no—
317C23×D3—61no—
318C23×D3—61no—
319C2×C3×Q8—21no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×D4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—61no—
327C2×#67—31no—
328C2×#67—61no—
329C2×#67—61no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332#239—62no—
333#239—121no—
334D3×Q8—62no—
335D3×Q8—62no—
336D3×Q8—62no—
337D3×Q8—122no—
338D3×Q8—121no—
339D3×Q8—121no—
340D3×Q8—121no—
341D3×Q8—122no—
342#237—62no—
343#237—121no—
344D3×D4—62no—
345D3×D4—121no—
346C2×D12—31no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—61no—
350C2×D12—62no—
351C2×D12—61no—
352C2×D12—61no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—121no—
356C2×D12—121no—
357C2×D12C22×D311yescharacteristic
358C2×C4×D3—21no—
359C2×C4×D3—31no—
360C2×C4×D3—31no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3—121no—
367C2×C4×D3C22×D311yescharacteristic
368C2×Dic6—31no—
369C2×Dic6—31no—
370C2×Dic6—61no—
371C2×Dic6—62no—
372C2×Dic6—61no—
373C2×Dic6—61no—
374C2×Dic6—61no—
375C2×Dic6—61no—
376C2×Dic6—121no—
377C2×Dic6—121no—
378C2×Dic6C22×D311yescharacteristic
379C2×Dic6C22×D311yescharacteristic
380C3×Q16—62no—
381C3×SD16—62no—
382C3×SD16—62no—
383C2×C3×C8—21no—
384C2×C3×C8—31no—
385C2×C3×C8—31no—
386C2×C3×C8—62no—
387C2×C3×C8C22×D311yescharacteristic
388C2×C3×C8C22×D311yescharacteristic
389C3×C4⋊C4—21no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4—61no—
395C3×C4⋊C4C22×D311yescharacteristic
396C3×C4⋊C4C22×D311yescharacteristic
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400C3×C42—31no—
401#217—31no—
402#216—22no—
403#216—62no—
404#216—121no—
405#216—121no—
406#215—22no—
407#215—62no—
408#215—121no—
409#215—121no—
410#215—122no—
411#214—34no—
412(C2×D3)⋊C4—21no—
413(C2×D3)⋊C4—21no—
414(C2×D3)⋊C4—21no—
415(C2×D3)⋊C4—31no—
416(C2×D3)⋊C4—31no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—61no—
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—121no—
427C4⋊Dic3—21no—
428C4⋊Dic3—31no—
429C4⋊Dic3—61no—
430C4⋊Dic3C22×D311yescharacteristic
431Dic3⋊C4—21no—
432Dic3⋊C4—21no—
433Dic3⋊C4—21no—
434Dic3⋊C4—31no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438C4×Dic3—61no—
439C4×Dic3—61no—
440C4×Dic3C22×D311yescharacteristic
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—61no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446Dic12—62no—
447#204—22no—
448#204—34no—
449#204—62no—
450#204—62no—
451#204—62no—
452#204—122no—
453ΓL(1,𝔽25)—62no—
454ΓL(1,𝔽25)—62no—
455D3×C8—22no—
456C22×C32C22×D411yescharacteristic
457C2×C3⋊D3—21no—
458C2×C3⋊D3—21no—
459C2×C3⋊D3—21no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—22no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3#13712yescomplemented
469D32—84no—
470C32×C4—41no—
471C32×C4—41no—
472C32×C4C22×D411yescharacteristic
473C32×C4H(5,𝔽2)11yescharacteristic
474C3⋊Dic3—21no—
475C3⋊Dic3—22no—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—91no—
483C22×Q8—91no—
484C22×Q8—91no—
485C22×D4—91no—
486#137—184no—
487C2×Q16—31no—
488C2×Q16—91no—
489C2×Q16—91no—
490C2×SD16—31no—
491C2×SD16—31no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—184no—
497C2×M16—91no—
498C22×C8—31no—
499C4⋊Q8—31no—
500C4⋊Q8—181no—
501#124—91no—
502#123—181no—
503C22⋊Q8—31no—
504C22⋊Q8—31no—
505C22⋊Q8—91no—
506C22⋊Q8—181no—
507C22⋊Q8—181no—
508#121—91no—
509#121—181no—
510#120—181no—
511C4×Q8—91no—
512C4×D4—31no—
513C4×D4—91no—
514C4×D4—181no—
515C2×C22⋊C4—181no—
516#107—31no—
517C4⋊C8—31no—
518#103—31no—
519#103—31no—
520#103—91no—
521#103D3211yescharacteristic, complemented
522#102—91no—
523#102—91no—
524C22⋊C8—91no—
525C22⋊C8—91no—
526#97—91no—
527C23×C3—31no—
528C23×C3—61no—
529C22×D3—21no—
530C22×D3—31no—
531C22×D3—31no—
532C22×D3—61no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—121no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—241no—
541C22×D3—241no—
542C22×D3D3×D411yescharacteristic
543C3×Q8—22no—
544C3×Q8—21no—
545C3×Q8—21no—
546C3×Q8—21no—
547C3×Q8—21no—
548C3×Q8—41no—
549C3×Q8—61no—
550C3×Q8—61no—
551C3×Q8—61no—
552C3×Q8—61no—
553C3×D4—32no—
554C3×D4—61no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—31no—
561C2×C3×C4—31no—
562C2×C3×C4—31no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—241no—
571C2×C3×C4C23×D311yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573#67—62no—
574#67—122no—
575#67—122no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—31no—
580C2×Dic3—31no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—121no—
585C2×Dic3—122no—
586C2×Dic3—122no—
587C2×Dic3D3×D411yescharacteristic
588C2×Dic3D3×D411yescharacteristic
589C2×Dic3D3×D411yescharacteristic
590D12—21no—
591D12—62no—
592D12—61no—
593D12—61no—
594D12—61no—
595D12—61no—
596D12—121no—
597D12—121no—
598D12—122no—
599D12—122no—
600D12—241no—
601D12—241no—
602D12—242no—
603D12D3×D412yes—
604C4×D3—21no—
605C4×D3—21no—
606C4×D3—61no—
607C4×D3—61no—
608C4×D3—61no—
609C4×D3—61no—
610C4×D3—81no—
611C4×D3—121no—
612C4×D3—121no—
613C4×D3—122no—
614C4×D3—122no—
615C4×D3—122no—
616C4×D3—122no—
617C4×D3—124no—
618Dic6—21no—
619Dic6—21no—
620Dic6—21no—
621Dic6—21no—
622Dic6—32no—
623Dic6—32no—
624Dic6—62no—
625Dic6—61no—
626Dic6—61no—
627Dic6—121no—
628Dic6—122no—
629Dic6—122no—
630Dic6—122no—
631Dic6—122no—
632Dic6—124no—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—32no—
636C3×C8—41no—
637C3×C8—61no—
638C3⋊C8—21no—
639C3⋊C8—61no—
640C3⋊C8—61no—
641C3⋊C8—121no—
642C3⋊C8D3×D412yes—
643C2×C32D4211yescharacteristic
644C2×C32C2×#13711yescharacteristic
645C2×C32#57711yescharacteristic
646C3⋊D3—41no—
647C3⋊D3—81no—
648C3×D3—22no—
649C3×D3—42no—
650C24—181no—
651#41—182no—
652#41—361no—
653C2×Q8—31no—
654C2×Q8—31no—
655C2×Q8—91no—
656C2×Q8—181no—
657C2×Q8—181no—
658C2×Q8—182no—
659C2×Q8—182no—
660C2×Q8—361no—
661C2×Q8—361no—
662C2×Q8C2×D3211yescharacteristic
663C2×D4—31no—
664C2×D4—91no—
665C2×D4—91no—
666C2×D4—181no—
667C2×D4—181no—
668C2×D4—182no—
669C2×D4—181no—
670C2×D4—361no—
671C22×C4—31no—
672C22×C4—61no—
673C22×C4—91no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677Q16—62no—
678Q16—182no—
679Q16—361no—
680SD16—62no—
681SD16—62no—
682SD16—94no—
683SD16—182no—
684SD16—182no—
685SD16—361no—
686M16—182no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—62no—
690C2×C8—91no—
691C2×C8C2×D3211yescharacteristic
692C4⋊C4—31no—
693C4⋊C4—61no—
694C4⋊C4—61no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—91no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4C2×D3211yescharacteristic
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—91no—
705C22⋊C4—91no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C42—31no—
711C42—181no—
712C22×C3—21no—
713C22×C3—32no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—62no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3C2×D3×D411yescharacteristic
720C22×C3C2×D3×D411yescharacteristic
721C2×D3—21no—
722C2×D3—21no—
723C2×D3—22no—
724C2×D3—41no—
725C2×D3—41no—
726C2×D3—62no—
727C2×D3—61no—
728C2×D3—61no—
729C2×D3—61no—
730C2×D3—61no—
731C2×D3—61no—
732C2×D3—61no—
733C2×D3—121no—
734C2×D3—121no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—241no—
742C2×D3—241no—
743C2×D3—241no—
744C2×D3—244no—
745C2×D3—244no—
746C2×D3#91812yescomplemented
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—42no—
750C3×C4—41no—
751C3×C4—41no—
752C3×C4—41no—
753C3×C4—41no—
754C3×C4—61no—
755C3×C4—61no—
756C3×C4—61no—
757C3×C4—81no—
758C3×C4—121no—
759C3×C4—121no—
760C3×C4—121no—
761C3×C4C2×D3×D411yescharacteristic
762C3×C4C2×D3×D411yescharacteristic
763C3×C4#100911yescharacteristic
764C3×C4#100911yescharacteristic
765Dic3—21no—
766Dic3—21no—
767Dic3—21no—
768Dic3—41no—
769Dic3—41no—
770Dic3—41no—
771Dic3—62no—
772Dic3—62no—
773Dic3—61no—
774Dic3—61no—
775Dic3—122no—
776Dic3—121no—
777C32#326611yescharacteristic, complemented, Sylow
778C23—31no—
779C23—61no—
780C23—91no—
781C23—181no—
782C23—362no—
783C23—362no—
784C23—721no—
785Q8—21no—
786Q8—21no—
787Q8—61no—
788Q8—61no—
789Q8—61no—
790Q8—61no—
791Q8—92no—
792Q8—181no—
793Q8—362no—
794Q8—362no—
795D4—32no—
796D4—61no—
797D4—182no—
798D4—181no—
799D4—181no—
800D4—362no—
801D4—362no—
802D4—721no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—31no—
806C2×C4—31no—
807C2×C4—31no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—91no—
814C2×C4—181no—
815C2×C4—181no—
816C2×C4—181no—
817C2×C4—241no—
818C2×C4—362no—
819C2×C4—362no—
820C2×C4—362no—
821C2×C4C22×D3211yescharacteristic
822C8—21no—
823C8—32no—
824C8—61no—
825C8—181no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—62no—
830C2×C3—122no—
831C2×C3#560911yescharacteristic
832C2×C3#560911yescharacteristic
833C2×C3#576211yescharacteristic
834C2×C3C2×#91811yescharacteristic
835C2×C3#577011yescharacteristic
836C2×C3D3×#13711yescharacteristic
837D3—22no—
838D3—42no—
839D3—122no—
840D3—121no—
841D3—121no—
842D3—241no—
843D3—241no—
844D3—481no—
845C22—32no—
846C22—61no—
847C22—61no—
848C22—62no—
849C22—121no—
850C22—121no—
851C22—181no—
852C22—181no—
853C22—181no—
854C22—361no—
855C22—361no—
856C22—361no—
857C22—724no—
858C22D32×D411yescharacteristic
859C4—41no—
860C4—41no—
861C4—61no—
862C4—61no—
863C4—61no—
864C4—121no—
865C4—121no—
866C4—121no—
867C4—181no—
868C4—182no—
869C4#6430811yescharacteristic
870C4D32×D411yescharacteristic
871C3—21no—
872C3#8044411yescharacteristic, complemented
873C3#8077111yescharacteristic, complemented
874C2—62no—
875C2—122no—
876C2—361no—
877C2—721no—
878C2#1059428411yescharacteristic
879C2#1059475311yescharacteristic
880C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594629C2
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
1. #10595361C2semidirect
2. C2×#63951C2semidirect
3. C2×D3×#204C2semidirect
5. #10592505C2semidirect
6. C3×#4818C2semidirect
7. C3×#4813C2semidirect
8. #10591651C2semidirect
9. #10591608C2semidirect
10. #10590961C2semidirect
11. #10590813C2semidirect
12. #10590727C2semidirect
13. #10590604C2semidirect
14. #10590590C2semidirect
15. #10590522C2semidirect
18. C2×Q8×C3⋊D3C22semidirect
26. C3×#944C22semidirect
27. C2×C3×#216C22semidirect
41. #63871C22semidirect
44. #63844C22semidirect
46. C2×#3719C22semidirect
47. C2×#3718C22semidirect
50. C2×#3712C22semidirect
52. C32×#103C22semidirect
53. #63647C22semidirect
54. #63637C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×#810C22semidirect
58. C3×#807C22semidirect
62. #63554C22semidirect
85. #4818D3semidirect
86. #4813D3semidirect
154. #3716D4semidirect
177. #944C2×D3semidirect
181. C2×#216C2×D3semidirect
234. C3×#103C2×D3semidirect
235. C3×#103C2×D3semidirect
243. #816C2×D3semidirect
245. Dic3⋊C8C2×D3semidirect
249. #810C2×D3semidirect
252. #807C2×D3semidirect
468. C2×C3×D3#137semidirect
521. #103D32semidirect
746. C2×D3#918semidirect
777. C32#3266semidirect
872. C3#80444semidirect
873. C3#80771semidirect

Maximal subgroups

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

subgroupindex
#105953612
C2×#639512
C2×D3×#2042
#105946292
#105925052
C3×#48182
C3×#48132
#105916512
#105916082
#105909612
#105908132
#105907272
#105906042
#105905902
#105905222
#807713
#804443