Finite Group Databasebeta

← #11884278

Subgroups — #11884278

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64120C211yesmaximal, characteristic, complemented
2C2×C3×#912C211yesmaximal, characteristic, complemented
3#10595254C211yesmaximal, characteristic, complemented
4#10595248C211yesmaximal, characteristic, complemented
5C3×#5152C211yesmaximal, characteristic, complemented
6#10591489C211yesmaximal, characteristic, complemented
7#10591471C211yesmaximal, characteristic, complemented
8#10591467C211yesmaximal, characteristic, complemented
9#10591466C211yesmaximal, characteristic, complemented
10#10591463C211yesmaximal, characteristic, complemented
11#10591452C211yesmaximal, characteristic, complemented
12#10590899C211yesmaximal, characteristic, complemented
13#10590858C211yesmaximal, characteristic, complemented
14#10590830C211yesmaximal, characteristic, complemented
15#10590726C211yesmaximal, characteristic, complemented
16#83921—31nomaximal
17#79879—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic
21C2×C3×#237C2211yescharacteristic, complemented
22C2×C32×D8C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24C2×#3753C2211yescharacteristic
25#64120—24no—
26C2×#3744C2211yescharacteristic
27C2×#3743C2211yescharacteristic
28C3×D4×Dic3C2211yescharacteristic
29C3×D4×Dic3C2211yescharacteristic, complemented
30C2×C3×#214C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic, complemented
32C3×#912—24no—
33C2×C3×Dic12C2211yescharacteristic, complemented
34C2×C3×D3×C8C2211yescharacteristic, complemented
35#63981—21no—
36#63978—21no—
37#63978—21no—
38#63966—21no—
39#63966—21no—
40C2×Dic3⋊Dic3—21no—
41C2×#3722—21no—
42#63962—21no—
43#63909C2211yescharacteristic
44C4×#626C2211yescharacteristic
45#63871C2211yescharacteristic
46#63871C2211yescharacteristic
47#63866C2211yescharacteristic, complemented
48#63864C2211yescharacteristic
49#63857C2211yescharacteristic, complemented
50C2×#3719C2211yescharacteristic, complemented
51C2×#3717C2211yescharacteristic
52C3×#832C2211yescharacteristic
53C3×#832C2211yescharacteristic, complemented
54C3×#817C2211yescharacteristic, 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×#135—31no—
64#5829—31no—
65#5824—31no—
66C2×#912D311yescharacteristic, complemented
67C2×#911—31no—
68C2×#911—31no—
69C2×#911—61no—
70#5555—31no—
71#5554—31no—
72C3×#442—31no—
73#5239—31no—
74#5238—31no—
75#5190—31no—
76#5189—31no—
77#5173—31no—
78#5169—31no—
79#5165—31no—
80#5162—31no—
81#5152D311yescharacteristic, complemented
82#5114—31no—
83#5111—31no—
84#5019—31no—
85#5016—31no—
86#4867—31no—
87#4864—31no—
88#4783—31no—
89#4783—31no—
90#4781—31no—
91#4776—31no—
92#4715—31no—
93#4706—31no—
94C23×C3⋊D3—21no—
95C2×C32×D4C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—21no—
98C2×#638—21no—
99C22×C3⋊Dic3—21no—
100#3830—22no—
101#3830—41no—
102D4×C3⋊D3—22no—
103D4×C3⋊D3—41no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×#634C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C22×C3×Dic3—21no—
110C22×C3×Dic3—21no—
111C22×C3×Dic3—21no—
112C22×C3×Dic3—21no—
113C3×#237—22no—
114C3×#237—22no—
115C3×#237—41no—
116C3×#237—41no—
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×#626—21no—
121C2×#626D411yescharacteristic
122C32×D8D414yescomplemented
123C2×C32×C8C2311yescharacteristic
124#3754—22no—
125#3753—22no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3744—22no—
128#3743—22no—
129C3×#217—21no—
130C3×#217—21no—
131C3×#214—22no—
132C3×#214—22no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×Dic12—22no—
139C3×D3×C8—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#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#237—31no—
160C2×#237—31no—
161C2×#237—61no—
162C2×#237C2×D311yescharacteristic
163C2×#237C2×D311yescharacteristic, complemented
164C2×D3×D4—31no—
165C2×D3×D4—31no—
166C2×D3×D4—61no—
167C3×#135—64no—
168C2×C3×Q16—31no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×D8—21no—
172C2×C3×D8C2×D311yescharacteristic
173C2×C3×D8C2×D311yescharacteristic
174C22×C3×C8—31no—
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177#947—31no—
178#946—31no—
179#946—31no—
180#944—31no—
181C2×#216—31no—
182C2×#215—31no—
183#939—61no—
184#939—61no—
185#937—61no—
186#935—61no—
187D4×Dic3C2×D311yescharacteristic
188D4×Dic3C2×D311yescharacteristic, complemented
189C2×#214—31no—
190C2×#214—31no—
191C2×#214—61no—
192C2×#214C2×D311yescharacteristic
193C2×#214C2×D311yescharacteristic, complemented
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—61no—
197#930—31no—
198#930—61no—
199#930—61no—
200#929—61no—
201#929—61no—
202C4×#67—31no—
203C2×(C2×D3)⋊C4—61no—
204C2×(C2×D3)⋊C4—61no—
205C2×C4⋊Dic3—61no—
206#924—31no—
207C2×Dic3⋊C4—61no—
208#912—24no—
209#911—68no—
210#911—64no—
211#911—64no—
212C2×Dic12—31no—
213C2×Dic12C2×D311yescharacteristic, complemented
214C2×#204—31no—
215C2×#204—31no—
216C2×#204—31no—
217C2×#204—61no—
218C2×ΓL(1,𝔽25)—31no—
219C2×ΓL(1,𝔽25)—31no—
220C2×ΓL(1,𝔽25)—61no—
221C2×D3×C8C2×D311yescharacteristic, complemented
222#897—31no—
223#897—31no—
224#897—31no—
225#895—31no—
226#886—61no—
227#886—61no—
228#886—61no—
229#882—61no—
230#875—31no—
231C4×D12—31no—
232#869—31no—
233C3×#106—31no—
234C3×#102—31no—
235C3×#102—31no—
236C3×#97—31no—
237#835—31no—
238#835—31no—
239#832C2×D311yescharacteristic
240#832C2×D311yescharacteristic, complemented
241#830—31no—
242#821—31no—
243(C2×D3)⋊C8—31no—
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246#817C2×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—
256C23×C32—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3—42no—
260C22×C3⋊D3—81no—
261C22×C3⋊D3C2×D411yescharacteristic
262C22×C3×D3C2×D411yescharacteristic
263C32×D4—21no—
264C32×D4—21no—
265C32×D4C2×D412yes—
266C32×D4C2×D412yes—
267C2×C32×C4C2411yescharacteristic
268#638—42no—
269#638—42no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—42no—
272C2×C3⋊Dic3C2×D411yescharacteristic
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C4×C3⋊D3—21no—
276C4×C3⋊D3—21no—
277#634—21no—
278#634—21no—
279C3×#67—42no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—42no—
286C2×C3×Dic3—42no—
287C2×C3×Dic3—42no—
288C2×C3×Dic3—81no—
289C2×C3×Dic3C2×D411yescharacteristic
290C2×C3×Dic3C2×D411yescharacteristic
291C2×C3×Dic3C2×D411yescharacteristic
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298#626—41no—
299#626—81no—
300C32×C8C2×D412yes—
301C3⋊(C3⋊C8)—21no—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C2×AGL(1,ℤ/8)—91no—
305C2×#135—31no—
306#547—91no—
307#546—91no—
308#497—91no—
309#470—91no—
310#465—91no—
311#463—91no—
312#461—91no—
313#452—91no—
314#452—91no—
315#450—91no—
316#449—91no—
317#442—31no—
318#435—91no—
319C23×D3—61no—
320C23×D3—61no—
321C23×D3—121no—
322C3×#41—62no—
323C3×#41—62no—
324C3×#41—121no—
325C3×#41—121no—
326C2×C3×Q8—31no—
327C2×C3×Q8—31no—
328C2×C3×D4—21no—
329C2×C3×D4—21no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C22×C3×C4—31no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—31no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—121no—
350C2×#67—121no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—121no—
358#237—22no—
359#237—22no—
360#237—41no—
361#237—41no—
362#237—64no—
363#237—62no—
364#237—62no—
365#237—121no—
366#237—121no—
367#237—122no—
368D3×D4—64no—
369D3×D4—62no—
370D3×D4—62no—
371D3×D4—121no—
372D3×D4—121no—
373D3×D4—122no—
374C2×D12—31no—
375C2×D12—31no—
376C2×D12—31no—
377C2×D12—61no—
378C2×D12—61no—
379C2×C4×D3—31no—
380C2×C4×D3—31no—
381C2×C4×D3—61no—
382C2×C4×D3C22×D311yescharacteristic
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—61no—
386C2×Dic6C22×D311yescharacteristic
387C2×Dic6C22×D311yescharacteristic
388C3×Q16—62no—
389C3×SD16—62no—
390C3×SD16—62no—
391C3×D8—24no—
392C3×D8D1214yescomplemented
393C3×D8#6714yescomplemented
394C2×C3×C8—21no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C2×C3×C8—62no—
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C3×C4⋊C4—31no—
401C3×C4⋊C4—31no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C42—31no—
405#217—21no—
406#217—21no—
407#217—31no—
408#217—61no—
409#216—121no—
410#215—121no—
411#214—22no—
412#214—22no—
413#214—64no—
414#214—62no—
415#214—62no—
416#213—64no—
417#213—62no—
418#213—62no—
419(C2×D3)⋊C4—31no—
420(C2×D3)⋊C4—31no—
421(C2×D3)⋊C4—31no—
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—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433C4⋊Dic3—31no—
434C4⋊Dic3—61no—
435C4⋊Dic3—61no—
436C4⋊Dic3—61no—
437C4⋊Dic3—61no—
438C4⋊Dic3—61no—
439C4⋊Dic3C22×D311yescharacteristic
440C4⋊Dic3C22×D311yescharacteristic
441Dic3⋊C4—31no—
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444Dic3⋊C4—61no—
445Dic3⋊C4—61no—
446Dic3⋊C4—61no—
447C4×Dic3C22×D311yescharacteristic
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—61no—
451C2×C3⋊C8C22×D311yescharacteristic
452C2×C3⋊C8C22×D311yescharacteristic
453Dic12—22no—
454Dic12—121no—
455#204—64no—
456#204—62no—
457#204—62no—
458#204—121no—
459ΓL(1,𝔽25)—64no—
460ΓL(1,𝔽25)—62no—
461ΓL(1,𝔽25)—62no—
462D3×C8—22no—
463C22×C32—22no—
464C22×C32—22no—
465C22×C32—41no—
466C22×C32—41no—
467C22×C32—41no—
468C22×C32—41no—
469C22×C32C22×D411yescharacteristic
470C2×C3⋊D3—21no—
471C2×C3⋊D3—21no—
472C2×C3⋊D3—21no—
473C2×C3⋊D3—41no—
474C2×C3⋊D3—41no—
475C2×C3⋊D3—41no—
476C2×C3⋊D3—84no—
477C2×C3×D3—21no—
478C2×C3×D3—21no—
479C2×C3×D3—21no—
480C32×C4C22×D411yescharacteristic
481C32×C4H(5,𝔽2)11yescharacteristic
482C3⋊Dic3—21no—
483C3⋊Dic3—41no—
484C3×Dic3—21no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—41no—
488C3×Dic3—41no—
489C3×Dic3—41no—
490C3×Dic3—41no—
491C2×#41—31no—
492C2×#41—31no—
493C2×#41—91no—
494C22×D4—91no—
495AGL(1,ℤ/8)—184no—
496#135—64no—
497C2×Q16—31no—
498C2×Q16—91no—
499C2×SD16—31no—
500C2×SD16—31no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×D8—91no—
505C2×D8D3211yescharacteristic
506C2×M16—91no—
507C22×C8—31no—
508C4⋊Q8—91no—
509#124—91no—
510#123—181no—
511#123—181no—
512#123—181no—
513C22⋊Q8—91no—
514C22⋊Q8—91no—
515C22⋊Q8—91no—
516#121—91no—
517#121—181no—
518#121—181no—
519#120—181no—
520C4×D4—31no—
521C4×D4—31no—
522C4×D4—91no—
523C2×C4⋊C4—181no—
524C2×C22⋊C4—181no—
525#106—31no—
526C4⋊C8—91no—
527#103—91no—
528#103—91no—
529#103—91no—
530#102—31no—
531#102—31no—
532#102—91no—
533C22⋊C8—91no—
534C22⋊C8—91no—
535#97—31no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—31no—
541C23×C3—41no—
542C23×C3—41no—
543C22×D3—31no—
544C22×D3—31no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—121no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—124no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—242no—
555C22×D3—241no—
556C22×D3—241no—
557C22×D3—242no—
558C22×D3D3×D411yescharacteristic
559C3×Q8—61no—
560C3×Q8—61no—
561C3×Q8—61no—
562C3×Q8—61no—
563C3×D4—21no—
564C3×D4—21no—
565C3×D4—21no—
566C3×D4—21no—
567C3×D4—22no—
568C3×D4—22no—
569C3×D4—41no—
570C3×D4—41no—
571C3×D4—122no—
572C3×D4—122no—
573C3×D4C2×D1212yes—
574C3×D4C2×D1212yes—
575C3×D4C2×#6712yes—
576C3×D4C2×#6712yes—
577C2×C3×C4—21no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—31no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—61no—
584C2×C3×C4—61no—
585C2×C3×C4—61no—
586C2×C3×C4—61no—
587C2×C3×C4—122no—
588C2×C3×C4—122no—
589C2×C3×C4—122no—
590C2×C3×C4—241no—
591C2×C3×C4C23×D311yescharacteristic
592C2×C3×C4C23×D311yescharacteristic
593#67—42no—
594#67—42no—
595#67—121no—
596#67—122no—
597#67—122no—
598#67—124no—
599#67—122no—
600#67—122no—
601#67—124no—
602#67—241no—
603C2×Dic3—21no—
604C2×Dic3—21no—
605C2×Dic3—21no—
606C2×Dic3—21no—
607C2×Dic3—31no—
608C2×Dic3—31no—
609C2×Dic3—42no—
610C2×Dic3—42no—
611C2×Dic3—42no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—81no—
616C2×Dic3—121no—
617C2×Dic3—122no—
618C2×Dic3—122no—
619C2×Dic3—124no—
620C2×Dic3D3×D411yescharacteristic
621C2×Dic3D3×D411yescharacteristic
622C2×Dic3D3×D411yescharacteristic
623D12—62no—
624D12—61no—
625D12—61no—
626D12—61no—
627D12—61no—
628D12—121no—
629D12—121no—
630D12—241no—
631C4×D3—21no—
632C4×D3—21no—
633C4×D3—62no—
634C4×D3—62no—
635C4×D3—61no—
636C4×D3—61no—
637C4×D3—61no—
638C4×D3—61no—
639Dic6—21no—
640Dic6—21no—
641Dic6—21no—
642Dic6—21no—
643Dic6—62no—
644Dic6—61no—
645Dic6—61no—
646Dic6—61no—
647Dic6—61no—
648Dic6—121no—
649C3×C8—22no—
650C3×C8—61no—
651C3×C8—61no—
652C3×C8C2×D1212yes—
653C3×C8C2×#6712yes—
654C3⋊C8—21no—
655C3⋊C8—21no—
656C3⋊C8—62no—
657C3⋊C8—61no—
658C3⋊C8—61no—
659C2×C32—42no—
660C2×C32—42no—
661C2×C32D4211yescharacteristic
662C2×C32#57511yescharacteristic
663C2×C32#57711yescharacteristic
664C3⋊D3—41no—
665C3⋊D3—81no—
666C3×D3—41no—
667C24—181no—
668#41—62no—
669#41—62no—
670#41—121no—
671#41—121no—
672#41—182no—
673#41—361no—
674C2×Q8—31no—
675C2×Q8—31no—
676C2×Q8—91no—
677C2×D4—61no—
678C2×D4—61no—
679C2×D4—91no—
680C2×D4—91no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4—182no—
684C2×D4—181no—
685C2×D4—361no—
686C2×D4C2×D3211yescharacteristic
687C2×D4C2×D3211yescharacteristic
688C22×C4—31no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—91no—
694C22×C4—181no—
695Q16—62no—
696Q16—361no—
697SD16—62no—
698SD16—62no—
699SD16—182no—
700SD16—182no—
701SD16—361no—
702D8—182no—
703D8#62614yescomplemented
704M16—182no—
705C2×C8—31no—
706C2×C8—31no—
707C2×C8—62no—
708C2×C8—91no—
709C2×C8C2×D3211yescharacteristic
710C4⋊C4—31no—
711C4⋊C4—31no—
712C4⋊C4—91no—
713C4⋊C4—181no—
714C4⋊C4—181no—
715C4⋊C4—181no—
716C4⋊C4—181no—
717C4⋊C4—181no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—91no—
721C22⋊C4—91no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C42—31no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—21no—
734C22×C3—42no—
735C22×C3—42no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3—81no—
748C22×C3—81no—
749C22×C3—81no—
750C22×C3—81no—
751C22×C3C2×D3×D411yescharacteristic
752C22×C3C2×D3×D411yescharacteristic
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—62no—
757C2×D3—61no—
758C2×D3—61no—
759C2×D3—61no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—122no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—241no—
773C2×D3—241no—
774C2×D3—244no—
775C2×D3—244no—
776C2×D3—248no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—61no—
780C3×C4—61no—
781C3×C4—61no—
782C3×C4—121no—
783C3×C4—121no—
784C3×C4—121no—
785C3×C4—121no—
786C3×C4C22×D1211yescharacteristic
787C3×C4#100411yescharacteristic
788C3×C4#100911yescharacteristic
789C3×C4C22×#6711yescharacteristic
790Dic3—21no—
791Dic3—21no—
792Dic3—21no—
793Dic3—41no—
794Dic3—41no—
795Dic3—41no—
796Dic3—41no—
797Dic3—62no—
798Dic3—61no—
799Dic3—61no—
800Dic3—122no—
801Dic3—121no—
802Dic3—121no—
803C32#326711yescharacteristic, complemented, Sylow
804C23—21no—
805C23—21no—
806C23—31no—
807C23—91no—
808C23—181no—
809C23—362no—
810C23—362no—
811C23—721no—
812Q8—61no—
813Q8—61no—
814Q8—61no—
815Q8—61no—
816Q8—181no—
817Q8—181no—
818D4—21no—
819D4—21no—
820D4—122no—
821D4—122no—
822D4—181no—
823D4—181no—
824D4—361no—
825D4—362no—
826D4—362no—
827D4—721no—
828D4C2×#62612yes—
829D4C2×#62612yes—
830C2×C4—31no—
831C2×C4—31no—
832C2×C4—31no—
833C2×C4—61no—
834C2×C4—61no—
835C2×C4—61no—
836C2×C4—61no—
837C2×C4—61no—
838C2×C4—61no—
839C2×C4—91no—
840C2×C4—122no—
841C2×C4—122no—
842C2×C4—122no—
843C2×C4—181no—
844C2×C4—181no—
845C2×C4—181no—
846C2×C4—241no—
847C2×C4—362no—
848C2×C4C22×D3211yescharacteristic
849C8—61no—
850C8—61no—
851C8—181no—
852C8C2×#62612yes—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—42no—
857C2×C3—42no—
858C2×C3—42no—
859C2×C3—42no—
860C2×C3—82no—
861C2×C3—82no—
862C2×C3—121no—
863C2×C3D4×D1211yescharacteristic
864C2×C3#576811yescharacteristic
865C2×C3#577011yescharacteristic
866C2×C3#577311yescharacteristic
867C2×C3#577511yescharacteristic
868C2×C3D4×#6711yescharacteristic
869D3—41no—
870D3—122no—
871D3—121no—
872D3—121no—
873D3—242no—
874D3—241no—
875D3—241no—
876C22—22no—
877C22—22no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—61no—
883C22—61no—
884C22—61no—
885C22—181no—
886C22—181no—
887C22—181no—
888C22—361no—
889C22—361no—
890C22—361no—
891C22—724no—
892C22D32×D411yescharacteristic
893C4—61no—
894C4—61no—
895C4—61no—
896C4—121no—
897C4—121no—
898C4—121no—
899C4—121no—
900C4—181no—
901C4—361no—
902C4#6431411yescharacteristic
903C4C22×#62611yescharacteristic
904C3—21no—
905C3#7987911yescharacteristic, complemented
906C3#8392111yescharacteristic, complemented
907C2—42no—
908C2—42no—
909C2—121no—
910C2—361no—
911C2—721no—
912C2#1059472911yescharacteristic
913C2#1059473611yescharacteristic
914C2D4×#62611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#64120C2semidirect
2. C2×C3×#912C2semidirect
3. #10595254C2semidirect
4. #10595248C2semidirect
5. C3×#5152C2semidirect
6. #10591489C2semidirect
7. #10591471C2semidirect
8. #10591467C2semidirect
9. #10591466C2semidirect
10. #10591463C2semidirect
11. #10591452C2semidirect
12. #10590899C2semidirect
13. #10590858C2semidirect
14. #10590830C2semidirect
15. #10590726C2semidirect
21. C2×C3×#237C22semidirect
29. C3×D4×Dic3C22semidirect
31. C2×C3×#214C22semidirect
33. C2×C3×Dic12C22semidirect
34. C2×C3×D3×C8C22semidirect
47. #63866C22semidirect
49. #63857C22semidirect
50. C2×#3719C22semidirect
53. C3×#832C22semidirect
54. C3×#817C22semidirect
55. C3×#815C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
59. #63565C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
66. C2×#912D3semidirect
81. #5152D3semidirect
122. C32×D8D4semidirect
163. C2×#237C2×D3semidirect
188. D4×Dic3C2×D3semidirect
193. C2×#214C2×D3semidirect
213. C2×Dic12C2×D3semidirect
221. C2×D3×C8C2×D3semidirect
240. #832C2×D3semidirect
246. #817C2×D3semidirect
248. #815C2×D3semidirect
392. C3×D8D12semidirect
393. C3×D8#67semidirect
703. D8#626semidirect
803. C32#3267semidirect
905. C3#79879semidirect
906. C3#83921semidirect

Maximal subgroups

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

subgroupindex
C2×#641202
C2×C3×#9122
#105952542
#105952482
C3×#51522
#105914892
#105914712
#105914672
#105914662
#105914632
#105914522
#105908992
#105908582
#105908302
#105907262
#839213
#798793