Finite Group Databasebeta

← #11884500

Subgroups — #11884500

Order 1152.

1119 conjugacy classes of subgroups.

The subgroup lattice has 931 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595018C211yesmaximal, characteristic, complemented
2#10595007C211yesmaximal, characteristic, complemented
3C2×#63825C211yesmaximal, characteristic, complemented
4C2×#63808C211yesmaximal, characteristic, complemented
5#10592431C211yesmaximal, characteristic, complemented
6C3×#4733C211yesmaximal, characteristic, complemented
7C3×#4728C211yesmaximal, characteristic, complemented
8#10591178C211yesmaximal, characteristic, complemented
9#10590967C211yesmaximal, characteristic, complemented
10#10590881C211yesmaximal, characteristic, complemented
11#10590826C211yesmaximal, characteristic, complemented
12#10590823C211yesmaximal, characteristic, complemented
13#10590801C211yesmaximal, characteristic, complemented
14#10590795C211yesmaximal, characteristic, complemented
15#10590765C211yesmaximal, characteristic, complemented
16#80266—31nomaximal
17#79497—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×#3799C2211yescharacteristic, complemented
22#64139C2211yescharacteristic
23C2×#3745C2211yescharacteristic
24C2×#3745C2211yescharacteristic
25C3×C4×#67C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C2×C3×Dic12C2211yescharacteristic, complemented
29C2×C3×#204C2211yescharacteristic, complemented
30C2×C3×D3×C8C2211yescharacteristic, complemented
31#63981—21no—
32#63979—21no—
33#63974—21no—
34#63958—21no—
35#63911C2211yescharacteristic, complemented
36#63910—21no—
37#63909C2211yescharacteristic
38#63908C2211yescharacteristic, complemented
39#63906—21no—
40#63904—21no—
41#63897—21no—
42#63894C2211yescharacteristic
43#63864C2211yescharacteristic
44Dic3×Dic6C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic, complemented
48#63825—24no—
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51#63808—24no—
52C32×C22⋊C8C2211yescharacteristic
53#63648C2211yescharacteristic
54#63648C2211yescharacteristic
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58C3×#815C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#5834—31no—
64C2×#949—31no—
65C2×#919—31no—
66C2×#908—31no—
67C2×#904—31no—
68#5630—31no—
69#5553—31no—
70#5550—31no—
71C3×#452—31no—
72C3×#435—31no—
73#5185—31no—
74#5176—31no—
75#5172—31no—
76#5134—31no—
77#5115—31no—
78#5049—31no—
79#4845—31no—
80#4843—31no—
81#4817—31no—
82#4810—31no—
83#4786—31no—
84#4775—31no—
85#4734—31no—
86#4734—31no—
87#4733D311yescharacteristic, complemented
88#4732—31no—
89#4732—31no—
90#4732—61no—
91#4728D311yescharacteristic, complemented
92#4712—31no—
93#4710—31no—
94C23×C3⋊D3—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)—21no—
99C2×C4⋊(C3⋊D3)—41no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67D411yescharacteristic
105C3×#235—22no—
106C3×#235—41no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#625—21no—
118C2×#624—21no—
119C2×#624—21no—
120C2×#624—21no—
121#3799—22no—
122#3799—22no—
123#3799—41no—
124#3799—41no—
125C2×C32×C8C2311yescharacteristic
126C2×C32×C8C2311yescharacteristic
127#3752—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3745—22no—
130#3745—41no—
131C3×#217—21no—
132C3×#217D411yescharacteristic
133C3×(C2×D3)⋊C4D411yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4D411yescharacteristic
137C3×C4×Dic3C2311yescharacteristic
138C3×#208—22no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×Dic12—22no—
142C3×#204—41no—
143C3×D3×C8—22no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146#3722—21no—
147#3722—21no—
148#3722—21no—
149(C2×D3)⋊Dic3—21no—
150Dic32—21no—
151#3717—22no—
152#3717—22no—
153#3717D414yescomplemented
154#3714—22no—
155#3714—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×#239—31no—
159C2×#239—31no—
160C2×#235—31no—
161C2×#235—31no—
162C2×#235C2×D311yescharacteristic
163C22×D12—31no—
164C22×D12—31no—
165C22×D12—61no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×M16—31no—
169C22×C3×C8—31no—
170C3×C22⋊Q8—31no—
171C3×C4×D4—31no—
172#949—64no—
173#947—31no—
174Q8×Dic3—31no—
175C2×#215—31no—
176C2×#215—31no—
177C2×#215—31no—
178#940—31no—
179#940—61no—
180#940—61no—
181#938—31no—
182#938—61no—
183#937—61no—
184C2×#213—31no—
185C2×#213—31no—
186#930—31no—
187#930—31no—
188#930—31no—
189#930—31no—
190#930—61no—
191#930—61no—
192C4×#67—61no—
193C4×#67C2×D311yescharacteristic
194#924C2×D311yescharacteristic
195C2×#208C2×D311yescharacteristic
196#919—64no—
197#908—64no—
198C2×Dic12C2×D311yescharacteristic, complemented
199#904—64no—
200C2×D24—31no—
201C2×D24—31no—
202C2×D24—31no—
203C2×D24—31no—
204C2×D24—31no—
205C2×D24—31no—
206C2×D24—61no—
207C2×D24—61no—
208C2×#204—31no—
209C2×#204—31no—
210C2×#204—31no—
211C2×#204C2×D311yescharacteristic, complemented
212C2×D3×C8C2×D311yescharacteristic, complemented
213#895—31no—
214#895—61no—
215#894—61no—
216#894—61no—
217#893—31no—
218#893—61no—
219#884—61no—
220#884—61no—
221#884—61no—
222#882—61no—
223D3×C22⋊C4—61no—
224D3×C22⋊C4—61no—
225#875—31no—
226#874—31no—
227C4×D12—31no—
228C4×Dic6—31no—
229C3×C4⋊C8—31no—
230C3×#103—31no—
231C3×#102—31no—
232C3×C22⋊C8—21no—
233C3×C22⋊C8—31no—
234C3×C22⋊C8C2×D311yescharacteristic
235C3×C22⋊C8C2×D311yescharacteristic
236C3×#97—31no—
237#835—31no—
238#821—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—31no—
243#821—61no—
244#821—61no—
245#821C2×D311yescharacteristic, complemented
246(C2×D3)⋊C8C2×D311yescharacteristic, complemented
247#818—31no—
248#816—31no—
249#816C2×D311yescharacteristic, complemented
250#815C2×D311yescharacteristic, complemented
251Dic3⋊C8C2×D311yescharacteristic, complemented
252#809—31no—
253#807—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3—42no—
260C22×C3⋊D3—81no—
261C22×C3×D3—21no—
262C22×C3×D3C2×D411yescharacteristic
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267#638—81no—
268C2×C3⋊Dic3—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—42no—
275C4⋊(C3⋊D3)C2×D412yes—
276C3×#67—41no—
277C3×#67—42no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—42no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6C2×D412yes—
293#626—42no—
294#626—42no—
295#626—42no—
296#626—81no—
297#626—81no—
298#625—81no—
299#624—42no—
300#624—42no—
301#624—81no—
302C32×C8—21no—
303C32×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—91no—
320#435—31no—
321C23×D3—61no—
322C23×D3—61no—
323C23×D3—121no—
324C3×#41—62no—
325C3×#41—121no—
326C2×C3×Q8—31no—
327C2×C3×Q8—31no—
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—61no—
331C22×C3×C4—21no—
332C22×C3×C4—31no—
333C22×C3×C4—61no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C2×#67—21no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—121no—
347C2×#67D1211yescharacteristic
348#239—62no—
349#239—62no—
350#239—121no—
351#239—121no—
352#235—22no—
353#235—41no—
354#235—62no—
355#235—62no—
356#235—121no—
357#235—121no—
358C2×D12—31no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—31no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—61no—
367C2×D12—62no—
368C2×D12—62no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—122no—
377C2×D12—121no—
378C2×D12—121no—
379C2×D12—121no—
380C2×D12—122no—
381C2×D12C22×D311yescharacteristic
382C2×C4×D3—21no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3C22×D311yescharacteristic
390C2×Dic6C22×D311yescharacteristic
391C2×Dic6C22×D311yescharacteristic
392C3×Q16—62no—
393C3×SD16—121no—
394C3×M16—62no—
395C2×C3×C8—21no—
396C2×C3×C8—21no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8—62no—
400C2×C3×C8C22×D311yescharacteristic
401C2×C3×C8C22×D311yescharacteristic
402C2×C3×C8C22×D311yescharacteristic
403C2×C3×C8C22×D311yescharacteristic
404C3×C4⋊C4—31no—
405C3×C4⋊C4—31no—
406C3×C4⋊C4—61no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—61no—
410C3×C42—31no—
411#217—21no—
412#217—61no—
413#217D1211yescharacteristic
414#215—34no—
415#215—62no—
416#215—62no—
417#213—62no—
418#213—62no—
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—
430(C2×D3)⋊C4—121no—
431(C2×D3)⋊C4D1211yescharacteristic
432C4⋊Dic3—31no—
433C4⋊Dic3—31no—
434C4⋊Dic3—61no—
435C4⋊Dic3—61no—
436C4⋊Dic3C22×D311yescharacteristic
437Dic3⋊C4—21no—
438Dic3⋊C4—61no—
439Dic3⋊C4D1211yescharacteristic
440C4×Dic3—61no—
441C4×Dic3—61no—
442C4×Dic3C22×D311yescharacteristic
443#208—22no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446Dic12—22no—
447D24—62no—
448D24—62no—
449D24—62no—
450D24—62no—
451D24—122no—
452D24—121no—
453D24—121no—
454D24—122no—
455#204—34no—
456#204—41no—
457#204—62no—
458#204—62no—
459D3×C8—22no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—22no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—41no—
473C2×C3⋊D3—84no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C32×C4—21no—
481C32×C4C22×D411yescharacteristic
482C32×C4H(5,𝔽2)11yescharacteristic
483C3⋊Dic3—41no—
484C3×Dic3—21no—
485C3×Dic3—22no—
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—91no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×D8—91no—
504C2×D8—91no—
505C2×M16—31no—
506C22×C8—31no—
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—91no—
520C4×D4—31no—
521C4×D4—91no—
522C4×D4—181no—
523C2×C22⋊C4—181no—
524#107—91no—
525C4⋊C8—31no—
526#103—31no—
527#103—91no—
528#102—31no—
529#102—91no—
530#102—91no—
531#102—91no—
532C22⋊C8—31no—
533C22⋊C8D3211yescharacteristic
534#97—31no—
535C23×C3—21no—
536C23×C3—31no—
537C23×C3—61no—
538C23×C3C2×D1211yescharacteristic
539C23×C3D3×D411yescharacteristic
540C22×D3—21no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—121no—
548C22×D3—121no—
549C22×D3—121no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—124no—
555C22×D3—242no—
556C22×D3—241no—
557C22×D3—241no—
558C22×D3—242no—
559C22×D3C2×D1211yescharacteristic
560C3×Q8—32no—
561C3×Q8—61no—
562C3×Q8—61no—
563C3×Q8—61no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—121no—
567C3×D4—122no—
568C2×C3×C4—21no—
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—61no—
584C2×C3×C4—122no—
585C2×C3×C4C2×D1211yescharacteristic
586C2×C3×C4D3×D411yescharacteristic
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589#67—41no—
590#67—42no—
591#67—122no—
592#67—122no—
593#67—122no—
594#67—241no—
595#67—241no—
596#67—241no—
597#67—241no—
598#67—241no—
599#67—241no—
600#67—242no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—21no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—121no—
607C2×Dic3C2×D1211yescharacteristic
608C2×Dic3C2×D1211yescharacteristic
609C2×Dic3C2×D1211yescharacteristic
610D12—21no—
611D12—21no—
612D12—32no—
613D12—32no—
614D12—62no—
615D12—62no—
616D12—61no—
617D12—61no—
618D12—61no—
619D12—61no—
620D12—61no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—61no—
625D12—61no—
626D12—121no—
627D12—121no—
628D12—121no—
629D12—121no—
630D12—122no—
631D12—122no—
632D12—124no—
633D12—122no—
634D12—122no—
635D12—122no—
636D12—241no—
637D12—241no—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—42no—
641C4×D3—122no—
642C4×D3—122no—
643C4×D3—122no—
644C4×D3—122no—
645C4×D3—241no—
646C4×D3—241no—
647Dic6—21no—
648Dic6—21no—
649Dic6—21no—
650Dic6D3×D412yes—
651C3×C8—21no—
652C3×C8—21no—
653C3×C8—21no—
654C3×C8—21no—
655C3×C8—32no—
656C3×C8—41no—
657C3×C8—41no—
658C3×C8—61no—
659C3⋊C8—21no—
660C3⋊C8D3×D412yes—
661C2×C32—41no—
662C2×C32D4211yescharacteristic
663C2×C32#57511yescharacteristic
664C2×C32#57611yescharacteristic
665C3⋊D3—42no—
666C3⋊D3—81no—
667C3⋊D3—81no—
668C3×D3—41no—
669C3×D3—81no—
670C24—181no—
671#41—62no—
672#41—121no—
673#41—182no—
674#41—182no—
675#41—361no—
676#41—361no—
677C2×Q8—31no—
678C2×Q8—31no—
679C2×D4—31no—
680C2×D4—31no—
681C2×D4—61no—
682C2×D4—91no—
683C2×D4—91no—
684C2×D4—91no—
685C2×D4—182no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—361no—
695C22×C4—31no—
696C22×C4—61no—
697C22×C4—181no—
698C22×C4—181no—
699C22×C4—181no—
700C22×C4C2×D3211yescharacteristic
701Q16—62no—
702SD16—94no—
703SD16—121no—
704SD16—182no—
705SD16—182no—
706D8—182no—
707D8—182no—
708D8—182no—
709D8—361no—
710M16—62no—
711C2×C8—31no—
712C2×C8—31no—
713C2×C8—62no—
714C2×C8C2×D3211yescharacteristic
715C2×C8C2×D3211yescharacteristic
716C4⋊C4—31no—
717C4⋊C4—31no—
718C4⋊C4—61no—
719C4⋊C4—91no—
720C4⋊C4—181no—
721C22⋊C4—31no—
722C22⋊C4—31no—
723C22⋊C4—61no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C42—31no—
731C42—181no—
732C22×C3—22no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3C22×D1211yescharacteristic
749C22×C3C2×D3×D411yescharacteristic
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—122no—
759C2×D3—121no—
760C2×D3—121no—
761C2×D3—121no—
762C2×D3—121no—
763C2×D3—122no—
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—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—241no—
777C2×D3—241no—
778C2×D3—241no—
779C2×D3—241no—
780C2×D3—241no—
781C2×D3—241no—
782C2×D3—241no—
783C2×D3—244no—
784C2×D3—244no—
785C2×D3—248no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—41no—
791C3×C4—61no—
792C3×C4—61no—
793C3×C4—62no—
794C3×C4—61no—
795C3×C4—121no—
796C3×C4—121no—
797C3×C4C2×D3×D411yescharacteristic
798C3×C4C2×D3×D411yescharacteristic
799C3×C4#100411yescharacteristic
800C3×C4#100911yescharacteristic
801Dic3—21no—
802Dic3—21no—
803Dic3—21no—
804Dic3—22no—
805Dic3—41no—
806Dic3—41no—
807Dic3—121no—
808Dic3—121no—
809Dic3—241no—
810C32#326811yescharacteristic, complemented, Sylow
811C23—31no—
812C23—61no—
813C23—181no—
814C23—181no—
815C23—181no—
816C23—362no—
817C23—362no—
818C23—721no—
819C23D3×D1211yescharacteristic
820Q8—32no—
821Q8—61no—
822Q8—61no—
823Q8—61no—
824D4—61no—
825D4—61no—
826D4—92no—
827D4—121no—
828D4—122no—
829D4—181no—
830D4—181no—
831D4—181no—
832D4—181no—
833D4—181no—
834D4—362no—
835D4—362no—
836D4—362no—
837D4—362no—
838D4—721no—
839D4—721no—
840D4—721no—
841D4—721no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—31no—
845C2×C4—31no—
846C2×C4—31no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—122no—
853C2×C4—181no—
854C2×C4—362no—
855C2×C4—362no—
856C2×C4—721no—
857C2×C4D3×D1211yescharacteristic
858C2×C4C22×D3211yescharacteristic
859C8—21no—
860C8—21no—
861C8—32no—
862C8—61no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—42no—
867C2×C3—41no—
868C2×C3—41no—
869C2×C3—121no—
870C2×C3—241no—
871C2×C3D4×D1211yescharacteristic
872C2×C3#559011yescharacteristic
873C2×C3#574811yescharacteristic
874C2×C3#575211yescharacteristic
875C2×C3#576911yescharacteristic
876C2×C3#577711yescharacteristic
877D3—41no—
878D3—81no—
879D3—122no—
880D3—122no—
881D3—242no—
882D3—242no—
883D3—241no—
884D3—241no—
885D3—241no—
886D3—241no—
887D3—481no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—61no—
892C22—61no—
893C22—61no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—182no—
898C22—361no—
899C22—361no—
900C22—361no—
901C22—361no—
902C22—361no—
903C22—361no—
904C22—361no—
905C22—361no—
906C22—724no—
907C22C2×D3×D1211yescharacteristic
908C4—21no—
909C4—61no—
910C4—61no—
911C4—61no—
912C4—62no—
913C4—121no—
914C4—121no—
915C4—361no—
916C4D32×D411yescharacteristic
917C4#6431411yescharacteristic
918C3—21no—
919C3#7949711yescharacteristic, complemented
920C3#8026611yescharacteristic, complemented
921C2—41no—
922C2—121no—
923C2—241no—
924C2—362no—
925C2—721no—
926C2—721no—
927C2#1059427711yescharacteristic
928C2#1059468011yescharacteristic
929C2#1059471111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10595018C2semidirect
2. #10595007C2semidirect
3. C2×#63825C2semidirect
4. C2×#63808C2semidirect
5. #10592431C2semidirect
6. C3×#4733C2semidirect
7. C3×#4728C2semidirect
8. #10591178C2semidirect
9. #10590967C2semidirect
10. #10590881C2semidirect
11. #10590826C2semidirect
12. #10590823C2semidirect
13. #10590801C2semidirect
14. #10590795C2semidirect
15. #10590765C2semidirect
21. C2×#3799C22semidirect
28. C2×C3×Dic12C22semidirect
29. C2×C3×#204C22semidirect
30. C2×C3×D3×C8C22semidirect
35. #63911C22semidirect
38. #63908C22semidirect
44. Dic3×Dic6C22semidirect
47. C2×#3717C22semidirect
55. C3×#821C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#816C22semidirect
58. C3×#815C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. #63575C22semidirect
61. #63566C22semidirect
62. #63564C22semidirect
87. #4733D3semidirect
91. #4728D3semidirect
153. #3717D4semidirect
198. C2×Dic12C2×D3semidirect
211. C2×#204C2×D3semidirect
212. C2×D3×C8C2×D3semidirect
245. #821C2×D3semidirect
246. (C2×D3)⋊C8C2×D3semidirect
249. #816C2×D3semidirect
250. #815C2×D3semidirect
251. Dic3⋊C8C2×D3semidirect
810. C32#3268semidirect
919. C3#79497semidirect
920. C3#80266semidirect

Maximal subgroups

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

subgroupindex
#105950182
#105950072
C2×#638252
C2×#638082
#105924312
C3×#47332
C3×#47282
#105911782
#105909672
#105908812
#105908262
#105908232
#105908012
#105907952
#105907652
#802663
#794973