Finite Group Databasebeta

← #11884106

Subgroups — #11884106

Order 1152.

1137 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3755C211yesmaximal, characteristic, complemented
2C3×Q8×#67C211yesmaximal, characteristic, complemented
3C2×#63948C211yesmaximal, characteristic, complemented
4#10595018C211yesmaximal, characteristic
5C3×#5228C211yesmaximal, characteristic, complemented
6#10591657C211yesmaximal, characteristic, complemented
7#10591608C211yesmaximal, characteristic, complemented
8#10591607C211yesmaximal, characteristic, complemented
9#10591589C211yesmaximal, characteristic, complemented
10#10591584C211yesmaximal, characteristic, complemented
11#10591565C211yesmaximal, characteristic, complemented
12#10591540C211yesmaximal, characteristic, complemented
13#10591188C211yesmaximal, characteristic, complemented
14#10591183C211yesmaximal, characteristic, complemented
15#10591158C211yesmaximal, characteristic, complemented
16#83559—31nomaximal
17#80204—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic, complemented
21C2×#3799C2211yescharacteristic
22C2×#3755—24no—
23C2×#3755C2211yescharacteristic
24C2×#3755C2211yescharacteristic
25C2×#3755C2211yescharacteristic
26C2×#3755C2211yescharacteristic
27C22×C3⋊(C3⋊C8)C2211yescharacteristic
28C3×#946—21no—
29C3×#946C2211yescharacteristic, complemented
30C3×Q8×Dic3C2211yescharacteristic, complemented
31C3×#944—21no—
32C3×#944C2211yescharacteristic, complemented
33C2×C3×#216C2211yescharacteristic, complemented
34C2×C3×#216C2211yescharacteristic, complemented
35C3×C4×#67—21no—
36C3×C4×#67C2211yescharacteristic
37C3×#924—21no—
38C3×#924C2211yescharacteristic
39C3×#924C2211yescharacteristic
40#63981—21no—
41#63974—21no—
42#63948—24no—
43#63910—21no—
44#63909C2211yescharacteristic
45#63897—21no—
46#63894C2211yescharacteristic
47#63864C2211yescharacteristic
48C2×#3718C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic
50C2×#3717C2211yescharacteristic
51C2×#3711C2211yescharacteristic, complemented
52C3×#835C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×D4×Q8—31no—
64Q8×#67D311yescharacteristic, complemented
65C2×#942—31no—
66C22×#215—31no—
67C22×#215—31no—
68C22×#215—61no—
69C2×#918—31no—
70#5630—31no—
71#5550—31no—
72C3×#451—31no—
73#5228D311yescharacteristic, complemented
74#5227—31no—
75#5190—31no—
76#5187—31no—
77#5185—31no—
78#5086—31no—
79#5083—31no—
80#5051—31no—
81#5051—31no—
82#5049—31no—
83#5047—31no—
84#5046—31no—
85#5028—31no—
86#5026—31no—
87#5011—31no—
88#4818—31no—
89#4817—31no—
90#4812—31no—
91#4806—31no—
92#4731—31no—
93#4730—31no—
94C23×C3⋊D3—21no—
95C2×C32×Q8—21no—
96C2×C32×Q8—22no—
97C2×C32×Q8—41no—
98C2×C32×Q8C2311yescharacteristic
99C2×C32×Q8C2311yescharacteristic
100C22×C32×C4—21no—
101C22×C32×C4C2311yescharacteristic
102C2×C4⋊(C3⋊D3)—22no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)—41no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C3×#67D411yescharacteristic
108C3×D3×Q8—22no—
109C3×D3×Q8—41no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6—21no—
113C2×C3×Dic6C2311yescharacteristic
114C2×C3×Dic6C2311yescharacteristic
115C2×#626—21no—
116C2×#626—21no—
117C2×#624—21no—
118C2×#624—21no—
119#3799—22no—
120#3799—41no—
121#3755—22no—
122#3755—22no—
123#3755—22no—
124#3755D414yescomplemented
125C2×C3⋊(C3⋊C8)—22no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#217—21no—
130C3×#217D411yescharacteristic
131C3×#216—22no—
132C3×#216—41no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4D411yescharacteristic
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×C4⋊Dic3C2311yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×Dic3⋊C4—21no—
141C3×Dic3⋊C4—21no—
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4D411yescharacteristic
144C3×C4×Dic3—21no—
145C3×C4×Dic3C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148#3722—21no—
149#3722—21no—
150#3722—21no—
151#3722—21no—
152#3718—22no—
153#3717—22no—
154#3717—41no—
155#3711—22no—
156#3266—91noSylow
157C22×C3×Q8—21no—
158C22×C3×Q8—31no—
159C22×C3×Q8C2×D311yescharacteristic
160C22×C3×Q8C2×D311yescharacteristic
161C2×#239—31no—
162C2×D3×Q8C2×D311yescharacteristic, complemented
163C2×#235—31no—
164C22×D12—31no—
165C22×D12—31no—
166C22×D12—61no—
167C2×C3×Q16—31no—
168C2×C3×Q16—31no—
169C3×C4⋊Q8—31no—
170C3×C4⋊Q8—61no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8—31no—
174C3×C22⋊Q8—61no—
175C3×C22⋊Q8—61no—
176C3×C4×Q8—31no—
177C3×C4×D4—31no—
178C3×C4×D4—61no—
179#947—31no—
180#946—21no—
181#946C2×D311yescharacteristic, complemented
182Q8×Dic3C2×D311yescharacteristic, complemented
183#944—21no—
184#944C2×D311yescharacteristic, complemented
185C2×#216—31no—
186C2×#216—31no—
187C2×#216C2×D311yescharacteristic, complemented
188C2×#216C2×D311yescharacteristic, complemented
189#942—64no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—31no—
194C2×#215—31no—
195C2×#215—31no—
196C2×#215—31no—
197C2×#215—31no—
198C2×#215—31no—
199C2×#215—31no—
200C2×#215—61no—
201C2×#215—61no—
202C2×#215—61no—
203C2×#215—61no—
204C2×#215—64no—
205C2×#215—64no—
206C2×#215—68no—
207#937—61no—
208#930—31no—
209C4×#67—21no—
210C4×#67C2×D311yescharacteristic
211#924—21no—
212#924C2×D311yescharacteristic
213#924C2×D311yescharacteristic
214C2×#208—31no—
215C22×C3⋊C8—31no—
216C22×C3⋊C8—31no—
217C22×C3⋊C8—61no—
218#918—64no—
219C2×#204—31no—
220C2×#204—31no—
221C2×ΓL(1,𝔽25)—31no—
222#895—31no—
223#895—61no—
224#894—61no—
225#894—61no—
226#893—31no—
227#884—61no—
228#882—61no—
229D3×C22⋊C4—61no—
230D3×C22⋊C4—61no—
231#875—31no—
232C4×D12—31no—
233C3×#103—31no—
234C3×#103—31no—
235C3×C22⋊C8—31no—
236#835—31no—
237#835—31no—
238#835C2×D311yescharacteristic, complemented
239#835C2×D311yescharacteristic, complemented
240#830—31no—
241#830C2×D311yescharacteristic
242#821—31no—
243#821—31no—
244(C2×D3)⋊C8—31no—
245#815—31no—
246Dic3⋊C8—31no—
247#810—31no—
248#810—31no—
249#809—31no—
250#809—31no—
251#807—31no—
252#807—31no—
253C4⋊(C3⋊C8)—31no—
254#803—31no—
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3—42no—
259C22×C3⋊D3—42no—
260C22×C3⋊D3—81no—
261C22×C3×D3C2×D411yescharacteristic
262C32×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×Q8—42no—
266C32×Q8C2×D412yes—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—42no—
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274C4⋊(C3⋊D3)—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)—42no—
278C4⋊(C3⋊D3)C2×D412yes—
279C3×#67—22no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—42no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—42no—
295#626—42no—
296#626—81no—
297#624—42no—
298#624—81no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)C2×D412yes—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×#137—91no—
304C22×SD16—91no—
305D4×Q8—31no—
306#546—91no—
307#497—91no—
308#468—91no—
309#467—91no—
310#464—91no—
311#461—91no—
312#452—91no—
313#451—31no—
314#450—91no—
315#448—91no—
316#440—91no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C23×D3—121no—
321C2×C3×Q8—21no—
322C2×C3×Q8—21no—
323C2×C3×Q8—24no—
324C2×C3×Q8—22no—
325C2×C3×Q8—22no—
326C2×C3×Q8—21no—
327C2×C3×Q8—21no—
328C2×C3×Q8—31no—
329C2×C3×Q8—31no—
330C2×C3×Q8—41no—
331C2×C3×Q8—41no—
332C2×C3×Q8—41no—
333C2×C3×Q8—42no—
334C2×C3×Q8—61no—
335C2×C3×Q8—62no—
336C2×C3×Q8—121no—
337C2×C3×Q8C22×D311yescharacteristic
338C2×C3×Q8C22×D311yescharacteristic
339C2×C3×Q8C22×D311yescharacteristic
340C2×C3×Q8C22×D311yescharacteristic
341C2×C3×D4—31no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—31no—
346C22×C3×C4—41no—
347C22×C3×C4—61no—
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C2×#67—61no—
351C2×#67—61no—
352C2×#67#6711yescharacteristic
353#239—62no—
354#239—121no—
355D3×Q8—22no—
356D3×Q8—41no—
357#235—62no—
358#235—121no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—31no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—64no—
368C2×D12—61no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—61no—
372C2×D12—121no—
373C2×D12—121no—
374C2×D12—121no—
375C2×D12—122no—
376C2×C4×D3—21no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3C22×D311yescharacteristic
382C2×Dic6—21no—
383C2×Dic6C22×D311yescharacteristic
384C2×Dic6C22×D311yescharacteristic
385C3×Q16—62no—
386C3×Q16—121no—
387C2×C3×C8—31no—
388C2×C3×C8—31no—
389C3×C4⋊C4—31no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—31no—
392C3×C4⋊C4—61no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4—61no—
395C3×C4⋊C4—61no—
396C3×C4⋊C4—61no—
397C3×C4⋊C4—61no—
398C3×C22⋊C4—31no—
399C3×C22⋊C4—31no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C22⋊C4—61no—
403C3×C42—31no—
404C3×C42—61no—
405#217—21no—
406#217—21no—
407#217#6711yescharacteristic
408#216—22no—
409#216—41no—
410#216—62no—
411#216—62no—
412#215—34no—
413#215—34no—
414#215—64no—
415#215—62no—
416#215—62no—
417#215—62no—
418#215—62no—
419#215—62no—
420#215—64no—
421#215—64no—
422#215—64no—
423#215—62no—
424#215—62no—
425#215—121no—
426(C2×D3)⋊C4—21no—
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#6711yescharacteristic
436C4⋊Dic3—21no—
437C4⋊Dic3C22×D311yescharacteristic
438C4⋊Dic3C22×D311yescharacteristic
439Dic3⋊C4—21no—
440Dic3⋊C4—21no—
441Dic3⋊C4—21no—
442Dic3⋊C4—21no—
443Dic3⋊C4—21no—
444Dic3⋊C4#6711yescharacteristic
445C4×Dic3—21no—
446C4×Dic3C22×D311yescharacteristic
447#208—62no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—61no—
453C2×C3⋊C8—61no—
454C2×C3⋊C8—62no—
455C2×C3⋊C8—62no—
456C2×C3⋊C8—64no—
457C2×C3⋊C8C22×D311yescharacteristic
458C2×C3⋊C8C22×D311yescharacteristic
459#204—62no—
460#204—121no—
461ΓL(1,𝔽25)—62no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32#13712yescomplemented
465C22×C32C22×D411yescharacteristic
466C2×C3⋊D3—22no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3⋊D3—41no—
471C2×C3⋊D3—41no—
472C2×C3⋊D3—84no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C32×C4—21no—
477C32×C4—22no—
478C32×C4—41no—
479C32×C4C22×D411yescharacteristic
480C32×C4H(5,𝔽2)11yescharacteristic
481C3×Dic3—21no—
482C3×Dic3—21no—
483C3×Dic3—21no—
484C3×Dic3—41no—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—91no—
489C22×Q8—31no—
490C22×Q8D3211yescharacteristic
491C22×D4—91no—
492#137—184no—
493C2×Q16—31no—
494C2×Q16—31no—
495C2×Q16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×SD16—91no—
502C2×SD16—184no—
503C2×M16—91no—
504C22×C8—91no—
505C4⋊Q8—31no—
506C4⋊Q8—61no—
507#124—91no—
508#123—181no—
509C22⋊Q8—31no—
510C22⋊Q8—31no—
511C22⋊Q8—31no—
512C22⋊Q8—61no—
513C22⋊Q8—61no—
514#121—91no—
515#121—181no—
516#120—181no—
517C4×Q8—31no—
518C4×D4—31no—
519C4×D4—61no—
520C4×D4—91no—
521C2×C22⋊C4—181no—
522#107—91no—
523C4⋊C8—91no—
524#103—31no—
525#103—31no—
526#103—91no—
527#103—91no—
528#102—91no—
529#102—91no—
530C22⋊C8—31no—
531C22⋊C8—91no—
532#97—91no—
533C23×C3—21no—
534C23×C3—31no—
535C23×C3D3×D411yescharacteristic
536C23×C3C2×#6711yescharacteristic
537C22×D3—61no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—121no—
542C22×D3—121no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—124no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3—242no—
549C22×D3—241no—
550C22×D3—241no—
551C22×D3—242no—
552C22×D3C2×#6711yescharacteristic
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—22no—
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—21no—
560C3×Q8—22no—
561C3×Q8—41no—
562C3×Q8—41no—
563C3×Q8—42no—
564C3×Q8—42no—
565C3×Q8—44no—
566C3×Q8—61no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×Q8—61no—
570C3×Q8—122no—
571C3×Q8D3×D412yes—
572C3×Q8D3×D412yes—
573C3×D4—62no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—31no—
587C2×C3×C4—31no—
588C2×C3×C4—31no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—42no—
592C2×C3×C4—42no—
593C2×C3×C4—44no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—122no—
601C2×C3×C4D3×D411yescharacteristic
602C2×C3×C4C2×#6711yescharacteristic
603C2×C3×C4C23×D311yescharacteristic
604C2×C3×C4C23×D311yescharacteristic
605#67—22no—
606#67—122no—
607#67—241no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3C2×#6711yescharacteristic
613C2×Dic3C2×#6711yescharacteristic
614C2×Dic3C2×#6711yescharacteristic
615D12—32no—
616D12—32no—
617D12—62no—
618D12—62no—
619D12—61no—
620D12—61no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—61no—
625D12—121no—
626D12—121no—
627D12—122no—
628D12—122no—
629D12—124no—
630D12—122no—
631D12—241no—
632C4×D3—21no—
633C4×D3—21no—
634C4×D3—42no—
635C4×D3—122no—
636C4×D3—122no—
637C4×D3—241no—
638C4×D3—241no—
639Dic6—21no—
640Dic6—21no—
641Dic6—21no—
642Dic6—21no—
643Dic6—42no—
644C3×C8—61no—
645C3×C8—61no—
646C3⋊C8—21no—
647C3⋊C8—21no—
648C3⋊C8—32no—
649C3⋊C8—32no—
650C3⋊C8—62no—
651C3⋊C8—62no—
652C3⋊C8—61no—
653C3⋊C8—61no—
654C2×C32—22no—
655C2×C32D4211yescharacteristic
656C2×C32C2×#13711yescharacteristic
657C2×C32#57711yescharacteristic
658C3⋊D3—42no—
659C3⋊D3—81no—
660C3×D3—41no—
661C24—181no—
662#41—182no—
663#41—361no—
664C2×Q8—21no—
665C2×Q8—22no—
666C2×Q8—31no—
667C2×Q8—31no—
668C2×Q8—41no—
669C2×Q8—61no—
670C2×Q8—62no—
671C2×Q8—121no—
672C2×Q8C2×D3211yescharacteristic
673C2×Q8C2×D3211yescharacteristic
674C2×D4—31no—
675C2×D4—91no—
676C2×D4—91no—
677C2×D4—182no—
678C2×D4—181no—
679C2×D4—181no—
680C2×D4—181no—
681C2×D4—361no—
682C22×C4—21no—
683C22×C4—31no—
684C22×C4—61no—
685C22×C4—181no—
686C22×C4—181no—
687C22×C4C2×D3211yescharacteristic
688Q16—62no—
689Q16—121no—
690Q16—182no—
691SD16—94no—
692SD16—182no—
693SD16—182no—
694SD16—182no—
695SD16—182no—
696SD16—361no—
697M16—182no—
698C2×C8—31no—
699C2×C8—31no—
700C2×C8—91no—
701C2×C8—91no—
702C2×C8—182no—
703C4⋊C4—31no—
704C4⋊C4—31no—
705C4⋊C4—31no—
706C4⋊C4—61no—
707C4⋊C4—61no—
708C4⋊C4—61no—
709C4⋊C4—61no—
710C4⋊C4—61no—
711C4⋊C4—61no—
712C22⋊C4—31no—
713C22⋊C4—31no—
714C22⋊C4—61no—
715C22⋊C4—61no—
716C22⋊C4—61no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C42—31no—
722C42—61no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—22no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3#91812yescomplemented
735C22×C3#94212yescomplemented
736C22×C3C2×D3×D411yescharacteristic
737C22×C3C22×#6711yescharacteristic
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—62no—
742C2×D3—62no—
743C2×D3—122no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—122no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—121no—
755C2×D3—241no—
756C2×D3—241no—
757C2×D3—241no—
758C2×D3—241no—
759C2×D3—244no—
760C2×D3—244no—
761C2×D3—248no—
762C3×C4—22no—
763C3×C4—22no—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—22no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—42no—
770C3×C4—42no—
771C3×C4—41no—
772C3×C4—41no—
773C3×C4—61no—
774C3×C4—61no—
775C3×C4—61no—
776C3×C4—121no—
777C3×C4—121no—
778C3×C4—121no—
779C3×C4—121no—
780C3×C4C2×D3×D411yescharacteristic
781C3×C4C2×D3×D411yescharacteristic
782C3×C4#100411yescharacteristic
783C3×C4#100411yescharacteristic
784Dic3—21no—
785Dic3—21no—
786Dic3—21no—
787Dic3—41no—
788Dic3—41no—
789Dic3—41no—
790Dic3—41no—
791C32#326611yescharacteristic, complemented, Sylow
792C23—31no—
793C23—181no—
794C23—181no—
795C23—362no—
796C23—362no—
797C23—721no—
798C23D3×#6711yescharacteristic
799Q8—21no—
800Q8—21no—
801Q8—21no—
802Q8—42no—
803Q8—61no—
804Q8—61no—
805Q8—61no—
806Q8—61no—
807Q8—122no—
808Q8#381112yes—
809D4—62no—
810D4—92no—
811D4—181no—
812D4—181no—
813D4—181no—
814D4—362no—
815D4—362no—
816D4—721no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—31no—
822C2×C4—31no—
823C2×C4—31no—
824C2×C4—42no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—61no—
829C2×C4—61no—
830C2×C4—61no—
831C2×C4—122no—
832C2×C4—362no—
833C2×C4—721no—
834C2×C4D3×#6711yescharacteristic
835C2×C4C22×D3211yescharacteristic
836C8—61no—
837C8—61no—
838C8—92no—
839C8—181no—
840C2×C3—24no—
841C2×C3—22no—
842C2×C3—22no—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—121no—
847C2×C3#559011yescharacteristic
848C2×C3C2×#91811yescharacteristic
849C2×C3#577811yescharacteristic
850C2×C3D4×#6711yescharacteristic
851C2×C3C2×#94211yescharacteristic
852C2×C3#583711yescharacteristic
853D3—41no—
854D3—122no—
855D3—122no—
856D3—242no—
857D3—242no—
858D3—241no—
859D3—241no—
860C22—21no—
861C22—21no—
862C22—61no—
863C22—61no—
864C22—61no—
865C22—182no—
866C22—361no—
867C22—361no—
868C22—361no—
869C22—361no—
870C22—361no—
871C22—724no—
872C22#6394812yescomplemented
873C22C2×D3×#6711yescharacteristic
874C4—21no—
875C4—22no—
876C4—41no—
877C4—61no—
878C4—61no—
879C4—61no—
880C4—121no—
881C4—121no—
882C4—121no—
883C4—121no—
884C4C2×#381111yescharacteristic
885C4#6433011yescharacteristic
886C3—21no—
887C3#8020411yescharacteristic, complemented
888C3#8355911yescharacteristic, complemented
889C2—22no—
890C2—121no—
891C2—362no—
892C2—721no—
893C2#1059531911yescharacteristic
894C2C2×#6394811yescharacteristic
895C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radical#10595018C2
hypercenterC22×Q8D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3755C2semidirect
2. C3×Q8×#67C2semidirect
3. C2×#63948C2semidirect
5. C3×#5228C2semidirect
6. #10591657C2semidirect
7. #10591608C2semidirect
8. #10591607C2semidirect
9. #10591589C2semidirect
10. #10591584C2semidirect
11. #10591565C2semidirect
12. #10591540C2semidirect
13. #10591188C2semidirect
14. #10591183C2semidirect
15. #10591158C2semidirect
20. C2×C3×D3×Q8C22semidirect
29. C3×#946C22semidirect
30. C3×Q8×Dic3C22semidirect
32. C3×#944C22semidirect
33. C2×C3×#216C22semidirect
34. C2×C3×#216C22semidirect
48. C2×#3718C22semidirect
51. C2×#3711C22semidirect
52. C3×#835C22semidirect
53. C3×#835C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63565C22semidirect
58. #63565C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
64. Q8×#67D3semidirect
73. #5228D3semidirect
124. #3755D4semidirect
162. C2×D3×Q8C2×D3semidirect
181. #946C2×D3semidirect
182. Q8×Dic3C2×D3semidirect
184. #944C2×D3semidirect
187. C2×#216C2×D3semidirect
188. C2×#216C2×D3semidirect
238. #835C2×D3semidirect
239. #835C2×D3semidirect
464. C22×C32#137semidirect
734. C22×C3#918semidirect
735. C22×C3#942semidirect
791. C32#3266semidirect
872. C22#63948semidirect
887. C3#80204semidirect
888. C3#83559semidirect

Maximal subgroups

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

subgroupindex
C22×#37552
C3×Q8×#672
C2×#639482
#105950182
C3×#52282
#105916572
#105916082
#105916072
#105915892
#105915842
#105915652
#105915402
#105911882
#105911832
#105911582
#835593
#802043