Finite Group Databasebeta

← #11884403

Subgroups — #11884403

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 925 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595410C211yesmaximal, characteristic, complemented
2C2×#63950C211yesmaximal, characteristic, complemented
3C2×#63939C211yesmaximal, characteristic, complemented
4#10594629C211yesmaximal, characteristic, complemented
5#10592509C211yesmaximal, characteristic, complemented
6C3×#4817C211yesmaximal, characteristic, complemented
7C3×#4808C211yesmaximal, characteristic, complemented
8#10591607C211yesmaximal, characteristic, complemented
9#10590964C211yesmaximal, characteristic, complemented
10#10590947C211yesmaximal, characteristic, complemented
11#10590881C211yesmaximal, characteristic, complemented
12#10590739C211yesmaximal, characteristic, complemented
13#10590585C211yesmaximal, characteristic, complemented
14#10590547C211yesmaximal, characteristic, complemented
15#10590509C211yesmaximal, characteristic, complemented
16#80266—31nomaximal
17#79796—31nomaximal
18C2×#3832C2211yescharacteristic, complemented
19C2×C3×#239C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×#3796C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C2×#3745C2211yescharacteristic
24#64104C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic, complemented
26C2×C3×#216C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic
30C3×#893C2211yescharacteristic
31#63950—24no—
32#63939—24no—
33#63923—21no—
34D3×(C2×D3)⋊C4—21no—
35#63916—21no—
36#63916C2211yescharacteristic, complemented
37#63911—21no—
38#63911C2211yescharacteristic, complemented
39#63909—21no—
40#63909—21no—
41#63909C2211yescharacteristic
42C4×#626—21no—
43C4×#626C2211yescharacteristic
44#63890—21no—
45#63864C2211yescharacteristic
46C2×#3717C2211yescharacteristic, complemented
47C2×#3714C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51C2×#3710C2211yescharacteristic, complemented
52C32×#103C2211yescharacteristic, complemented
53#63647C2211yescharacteristic, complemented
54#63636C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×#815C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59C3×#807C2211yescharacteristic, complemented
60Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic
63#5834—31no—
64C2×#949—31no—
65C2×#919—31no—
66C2×#916—31no—
67C2×#914—31no—
68#5630—31no—
69#5577—31no—
70#5554—31no—
71C3×#452—31no—
72C3×#440—31no—
73#5185—31no—
74#5176—31no—
75#5172—31no—
76#5049—31no—
77#5028—31no—
78#5015—31no—
79#4886—31no—
80#4883—31no—
81#4817D311yescharacteristic, complemented
82#4810—31no—
83#4810—31no—
84#4810—61no—
85#4808D311yescharacteristic, complemented
86#4786—31no—
87#4781—31no—
88#4775—31no—
89#4773—31no—
90#4732—31no—
91#4728—31no—
92#4712—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96#3832—22no—
97#3832—41no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C3×#239—22no—
105C3×#239—41no—
106C2×C3×D12—21no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#626D411yescharacteristic
120C2×D3×Dic3—21no—
121D3×D12—22no—
122D3×D12—41no—
123#3796—22no—
124#3796—41no—
125C2×C32×C8C2311yescharacteristic
126C32×C4⋊C4C2311yescharacteristic
127#3755—22no—
128#3752—21no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3745—41no—
131C3×#216—22no—
132C3×#215D414yescomplemented
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3—21no—
137C3×C4⋊Dic3C2311yescharacteristic
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×#204—41no—
143Dic3⋊Dic3D411yescharacteristic
144#3722—21no—
145#3722—21no—
146#3722—21no—
147#3722D411yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3D411yescharacteristic
150#3717—22no—
151#3714—22no—
152#3714—22no—
153#3713—22no—
154#3711—22no—
155#3710—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#239—31no—
161C2×#239—61no—
162C2×#239C2×D311yescharacteristic
163C2×#237—31no—
164C2×D3×D4—31no—
165C22×D12—31no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C3×C22⋊Q8—31no—
170C3×C4×Q8—31no—
171C3×C4×D4—31no—
172#949—64no—
173#947—31no—
174Q8×Dic3C2×D311yescharacteristic, complemented
175C2×#216C2×D311yescharacteristic, complemented
176C2×#215—31no—
177C2×#215—31no—
178C2×#215—31no—
179C2×#215—61no—
180C2×#215C2×D311yescharacteristic
181#940—31no—
182#940—61no—
183#938—31no—
184#938—61no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—31no—
189#930—31no—
190#930—61no—
191#930—61no—
192C4×#67—31no—
193C4×#67—61no—
194C2×(C2×D3)⋊C4—61no—
195C2×#208—31no—
196#919—64no—
197#916—64no—
198#914—64no—
199C2×D24—31no—
200C2×D24—31no—
201C2×D24—31no—
202C2×D24—31no—
203C2×D24—61no—
204C2×#204—31no—
205C2×#204C2×D311yescharacteristic, complemented
206C2×ΓL(1,𝔽25)—31no—
207C2×D3×C8—31no—
208C2×D3×C8—31no—
209#897C2×D311yescharacteristic
210#895—31no—
211#895—31no—
212#895—31no—
213#895—31no—
214#895—61no—
215#895—61no—
216#895—61no—
217#895—61no—
218#894—61no—
219#893C2×D311yescharacteristic
220#886—61no—
221#882—61no—
222#882—61no—
223D3×C22⋊C4—61no—
224#875—31no—
225#874—31no—
226#874—61no—
227C4×D12—31no—
228C4×D12—61no—
229C3×#107—31no—
230C3×#103—21no—
231C3×#103C2×D311yescharacteristic, complemented
232C3×#103C2×D311yescharacteristic, complemented
233C3×#102—31no—
234C3×#102—31no—
235C3×C22⋊C8—31no—
236C3×#97—31no—
237#835—31no—
238#821—31no—
239#821C2×D311yescharacteristic
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—61no—
243(C2×D3)⋊C8C2×D311yescharacteristic
244#815C2×D311yescharacteristic, complemented
245Dic3⋊C8—31no—
246#810—31no—
247#809—31no—
248#809—31no—
249#809—31no—
250#809—61no—
251#809C2×D311yescharacteristic, complemented
252#807C2×D311yescharacteristic, complemented
253C4⋊(C3⋊C8)—31no—
254C22×C3⋊D3—21no—
255C22×C3⋊D3—21no—
256C22×C3⋊D3C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C32×Q8—21no—
264C32×Q8C2×D412yes—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2411yescharacteristic
268C2×C3⋊Dic3C2×D411yescharacteristic
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—42no—
274C4⋊(C3⋊D3)—81no—
275C4×C3⋊D3—21no—
276C4×C3⋊D3—21no—
277C4×C3⋊D3—42no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—42no—
287C3×D12C2×D412yes—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—42no—
291C3×C4×D3—81no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294#626—41no—
295#626—42no—
296#626—42no—
297#626—42no—
298#626—81no—
299#626—81no—
300#626—81no—
301D3×Dic3—42no—
302C32×C8—21no—
303C3⋊(C3⋊C8)—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—91no—
314#459—91no—
315#452—31no—
316#449—91no—
317#449—91no—
318#447—91no—
319#440—31no—
320#435—91no—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—121no—
325C2×C3×Q8—21no—
326C2×C3×Q8—31no—
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—61no—
332C22×C3×C4—31no—
333C22×C3×C4—61no—
334C22×C3×C4—61no—
335C2×#67—31no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C22×Dic3—61no—
343#239—22no—
344#239—41no—
345#239—62no—
346#239—62no—
347#239—62no—
348#239—122no—
349#239—121no—
350#239—121no—
351#239—121no—
352#239—122no—
353#237—62no—
354#237—121no—
355D3×D4—62no—
356D3×D4—121no—
357C2×D12—21no—
358C2×D12—31no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—62no—
366C2×D12—61no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—121no—
377C2×D12—121no—
378C2×D12—121no—
379C2×D12C22×D311yescharacteristic
380C2×D12C22×D311yescharacteristic
381C2×C4×D3—21no—
382C2×C4×D3—21no—
383C2×C4×D3—31no—
384C2×C4×D3—31no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—121no—
390C2×C4×D3C22×D311yescharacteristic
391C2×Dic6C22×D311yescharacteristic
392C3×Q16—62no—
393C3×SD16—34no—
394C3×SD16—121no—
395C2×C3×C8—21no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C3×C4⋊C4—21no—
401C3×C4⋊C4—31no—
402C3×C4⋊C4—61no—
403C3×C4⋊C4—61no—
404C3×C4⋊C4C22×D311yescharacteristic
405C3×C4⋊C4C22×D311yescharacteristic
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C42—31no—
409C3×C42—61no—
410#217—31no—
411#217—61no—
412#216—22no—
413#215—62no—
414#215—62no—
415#215—62no—
416#215—122no—
417#215D1214yescomplemented
418#213—62no—
419#213—62no—
420#213—62no—
421#213—62no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—31no—
425(C2×D3)⋊C4—31no—
426(C2×D3)⋊C4—31no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—121no—
437C4⋊Dic3—21no—
438C4⋊Dic3—21no—
439C4⋊Dic3—31no—
440C4⋊Dic3C22×D311yescharacteristic
441Dic3⋊C4—31no—
442C4×Dic3—21no—
443C4×Dic3C22×D311yescharacteristic
444#208—62no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450D24—62no—
451D24—62no—
452D24—121no—
453D24—121no—
454D24—122no—
455#204—41no—
456#204—62no—
457ΓL(1,𝔽25)—62no—
458D3×C8—62no—
459D3×C8—62no—
460C22×C32C22×D411yescharacteristic
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—22no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—21no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479D32—84no—
480C32×C4—22no—
481C32×C4—41no—
482C32×C4C22×D411yescharacteristic
483C32×C4H(5,𝔽2)11yescharacteristic
484C3⋊Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C2×#41—31no—
491C2×#41—91no—
492C2×#41—91no—
493C22×D4—91no—
494AGL(1,ℤ/8)—184no—
495#135—184no—
496C2×Q16—31no—
497C2×SD16—31no—
498C2×SD16—31no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×D8—91no—
504C2×D8—91no—
505C2×M16—91no—
506C22×C8—91no—
507#127—91no—
508#127—181no—
509#124—91no—
510#123—181no—
511C22⋊Q8—31no—
512#121—91no—
513#121—91no—
514#121—91no—
515#121—181no—
516#121—181no—
517#121—181no—
518#120—181no—
519C4×Q8—31no—
520C4×D4—31no—
521C4×D4—91no—
522C4×D4—181no—
523C2×C22⋊C4—181no—
524#107—31no—
525C4⋊C8—91no—
526#103—91no—
527#103D3211yescharacteristic, complemented
528#102—31no—
529#102—31no—
530#102—91no—
531#102—91no—
532C22⋊C8—31no—
533C22⋊C8—91no—
534#97—31no—
535C23×C3—31no—
536C23×C3—61no—
537C23×C3—61no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—31no—
541C22×D3—31no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—121no—
548C22×D3—121no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—241no—
554C22×D3—241no—
555C22×D3D3×D411yescharacteristic
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—22no—
559C3×Q8—41no—
560C3×Q8—61no—
561C3×Q8—61no—
562C3×Q8C2×D1212yes—
563C3×Q8D3×D412yes—
564C3×D4—32no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—122no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
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—41no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—122no—
584C2×C3×C4—241no—
585C2×C3×C4C23×D311yescharacteristic
586C2×C3×C4C23×D311yescharacteristic
587#67—121no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—241no—
592#67—241no—
593#67—241no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—31no—
597C2×Dic3—31no—
598C2×Dic3—61no—
599C2×Dic3—122no—
600C2×Dic3D3×D411yescharacteristic
601C2×Dic3D3×D411yescharacteristic
602C2×Dic3D3×D411yescharacteristic
603D12—21no—
604D12—21no—
605D12—21no—
606D12—42no—
607D12—62no—
608D12—61no—
609D12—61no—
610D12—61no—
611D12—61no—
612D12—61no—
613D12—61no—
614D12—61no—
615D12—61no—
616D12—121no—
617D12—121no—
618D12—121no—
619D12—122no—
620D12—122no—
621D12—124no—
622D12—121no—
623D12—122no—
624D12—122no—
625D12—122no—
626D12—241no—
627D12—241no—
628D12—241no—
629D12—242no—
630D12—241no—
631D12—241no—
632D12C2×D1212yes—
633C4×D3—21no—
634C4×D3—21no—
635C4×D3—42no—
636C4×D3—61no—
637C4×D3—61no—
638C4×D3—61no—
639C4×D3—61no—
640C4×D3—81no—
641C4×D3—121no—
642C4×D3—121no—
643C4×D3—122no—
644C4×D3—122no—
645C4×D3—122no—
646C4×D3—124no—
647Dic6—21no—
648Dic6—21no—
649C3×C8—21no—
650C3×C8—21no—
651C3×C8—32no—
652C3×C8—41no—
653C3×C8—61no—
654C3⋊C8—21no—
655C3⋊C8—61no—
656C3⋊C8—61no—
657C3⋊C8—121no—
658C3⋊C8C2×D1212yes—
659C2×C32D4211yescharacteristic
660C2×C32#57511yescharacteristic
661C2×C32#57611yescharacteristic
662C3⋊D3—41no—
663C3⋊D3—81no—
664C3⋊D3—81no—
665C3×D3—41no—
666C3×D3—42no—
667C3×D3—81no—
668C24—181no—
669#41—62no—
670#41—121no—
671#41—182no—
672#41—182no—
673#41—361no—
674#41—361no—
675C2×Q8—31no—
676C2×Q8C2×D3211yescharacteristic
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—61no—
680C2×D4—91no—
681C2×D4—91no—
682C2×D4—91no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—182no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—361no—
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—91no—
697C22×C4—181no—
698C22×C4—181no—
699Q16—62no—
700SD16—34no—
701SD16—121no—
702SD16—182no—
703SD16—182no—
704D8—182no—
705D8—182no—
706D8—182no—
707D8—361no—
708M16—182no—
709C2×C8—31no—
710C2×C8—31no—
711C2×C8—91no—
712C2×C8—182no—
713C2×C8C2×D3211yescharacteristic
714C4⋊C4—31no—
715C4⋊C4—61no—
716C4⋊C4—61no—
717C4⋊C4—91no—
718C4⋊C4C2×D3211yescharacteristic
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—91no—
722C22⋊C4—91no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C42—31no—
729C42—61no—
730C22×C3—21no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—62no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3C2×D3×D411yescharacteristic
741C22×C3C2×D3×D411yescharacteristic
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—22no—
745C2×D3—21no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—61no—
752C2×D3—61no—
753C2×D3—61no—
754C2×D3—61no—
755C2×D3—61no—
756C2×D3—61no—
757C2×D3—121no—
758C2×D3—121no—
759C2×D3—121no—
760C2×D3—122no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—241no—
774C2×D3—241no—
775C2×D3—241no—
776C2×D3—241no—
777C2×D3—241no—
778C2×D3—244no—
779C2×D3—244no—
780C3×C4—22no—
781C3×C4—22no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—42no—
785C3×C4—41no—
786C3×C4—41no—
787C3×C4—61no—
788C3×C4—61no—
789C3×C4—61no—
790C3×C4—81no—
791C3×C4—121no—
792C3×C4—121no—
793C3×C4C22×D1211yescharacteristic
794C3×C4C2×D3×D411yescharacteristic
795C3×C4#100411yescharacteristic
796C3×C4#100911yescharacteristic
797Dic3—21no—
798Dic3—21no—
799Dic3—21no—
800Dic3—41no—
801Dic3—41no—
802Dic3—61no—
803Dic3—61no—
804Dic3—121no—
805C32#326811yescharacteristic, complemented, Sylow
806C23—31no—
807C23—61no—
808C23—61no—
809C23—91no—
810C23—181no—
811C23—181no—
812C23—362no—
813C23—362no—
814C23—721no—
815Q8—21no—
816Q8—61no—
817Q8—61no—
818Q8D3×D1212yes—
819D4—32no—
820D4—61no—
821D4—61no—
822D4—61no—
823D4—122no—
824D4—181no—
825D4—181no—
826D4—181no—
827D4—181no—
828D4—362no—
829D4—361no—
830D4—362no—
831D4—362no—
832D4—362no—
833D4—721no—
834D4—721no—
835D4—721no—
836D4—721no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—31no—
840C2×C4—31no—
841C2×C4—31no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—91no—
847C2×C4—122no—
848C2×C4—181no—
849C2×C4—181no—
850C2×C4—241no—
851C2×C4—362no—
852C2×C4—362no—
853C2×C4C22×D3211yescharacteristic
854C8—21no—
855C8—32no—
856C8—61no—
857C8—181no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—122no—
862C2×C3—121no—
863C2×C3—241no—
864C2×C3D4×D1211yescharacteristic
865C2×C3#559011yescharacteristic
866C2×C3#576911yescharacteristic
867C2×C3#577411yescharacteristic
868C2×C3#577711yescharacteristic
869C2×C3#577711yescharacteristic
870D3—41no—
871D3—42no—
872D3—81no—
873D3—121no—
874D3—121no—
875D3—241no—
876D3—242no—
877D3—241no—
878D3—241no—
879D3—241no—
880D3—241no—
881D3—481no—
882C22—61no—
883C22—61no—
884C22—61no—
885C22—62no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—181no—
892C22—181no—
893C22—181no—
894C22—361no—
895C22—361no—
896C22—361no—
897C22—361no—
898C22—361no—
899C22—361no—
900C22—724no—
901C22D32×D411yescharacteristic
902C4—22no—
903C4—41no—
904C4—61no—
905C4—61no—
906C4—61no—
907C4—121no—
908C4—121no—
909C4—181no—
910C4C2×D3×D1211yescharacteristic
911C4#6431411yescharacteristic
912C3—21no—
913C3#7979611yescharacteristic, complemented
914C3#8026611yescharacteristic, complemented
915C2—121no—
916C2—122no—
917C2—241no—
918C2—361no—
919C2—721no—
920C2—721no—
921C2#1059427711yescharacteristic
922C2#1059475511yescharacteristic
923C2#1059476211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3268
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. #10595410C2semidirect
2. C2×#63950C2semidirect
3. C2×#63939C2semidirect
4. #10594629C2semidirect
5. #10592509C2semidirect
6. C3×#4817C2semidirect
7. C3×#4808C2semidirect
8. #10591607C2semidirect
9. #10590964C2semidirect
10. #10590947C2semidirect
11. #10590881C2semidirect
12. #10590739C2semidirect
13. #10590585C2semidirect
14. #10590547C2semidirect
15. #10590509C2semidirect
18. C2×#3832C22semidirect
25. C3×Q8×Dic3C22semidirect
26. C2×C3×#216C22semidirect
28. C2×C3×#204C22semidirect
36. #63916C22semidirect
38. #63911C22semidirect
46. C2×#3717C22semidirect
51. C2×#3710C22semidirect
52. C32×#103C22semidirect
53. #63647C22semidirect
54. #63636C22semidirect
57. C3×#815C22semidirect
58. C3×#809C22semidirect
59. C3×#807C22semidirect
60. Dic3⋊(C3⋊C8)C22semidirect
61. #63565C22semidirect
81. #4817D3semidirect
85. #4808D3semidirect
132. C3×#215D4semidirect
174. Q8×Dic3C2×D3semidirect
175. C2×#216C2×D3semidirect
205. C2×#204C2×D3semidirect
231. C3×#103C2×D3semidirect
232. C3×#103C2×D3semidirect
244. #815C2×D3semidirect
251. #809C2×D3semidirect
252. #807C2×D3semidirect
417. #215D12semidirect
527. #103D32semidirect
805. C32#3268semidirect
913. C3#79796semidirect
914. C3#80266semidirect

Maximal subgroups

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

subgroupindex
#105954102
C2×#639502
C2×#639392
#105946292
#105925092
C3×#48172
C3×#48082
#105916072
#105909642
#105909472
#105908812
#105907392
#105905852
#105905472
#105905092
#802663
#797963