Finite Group Databasebeta

← #11884097

Subgroups — #11884097

Order 1152.

1117 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64151C211yesmaximal, characteristic, complemented
2C3×Q8×#67C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4#10595078C211yesmaximal, characteristic
5C3×#5227C211yesmaximal, characteristic, complemented
6#10591651C211yesmaximal, characteristic, complemented
7#10591605C211yesmaximal, characteristic, complemented
8#10591604C211yesmaximal, characteristic, complemented
9#10591596C211yesmaximal, characteristic, complemented
10#10591595C211yesmaximal, characteristic, complemented
11#10591565C211yesmaximal, characteristic, complemented
12#10591540C211yesmaximal, characteristic, complemented
13#10591184C211yesmaximal, characteristic, complemented
14#10591180C211yesmaximal, characteristic, complemented
15#10591151C211yesmaximal, characteristic, complemented
16#83559—31nomaximal
17#80061—31nomaximal
18C22×C32×Q8C2211yescharacteristic, complemented
19C2×#3828C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×D3×D12C2211yescharacteristic
22C2×#3756C2211yescharacteristic, complemented
23C2×#3756C2211yescharacteristic, complemented
24#64151—24no—
25C2×#3755C2211yescharacteristic
26C2×#3755C2211yescharacteristic
27C2×#3748C2211yescharacteristic, complemented
28C3×#946—21no—
29C3×#946C2211yescharacteristic
30C3×Q8×Dic3C2211yescharacteristic, complemented
31C3×#944—21no—
32C3×#944C2211yescharacteristic, complemented
33C2×C3×#215C2211yescharacteristic
34C2×C3×#215C2211yescharacteristic
35C3×#930C2211yescharacteristic
36C3×C4×#67—21no—
37C3×C4×#67C2211yescharacteristic
38C3×#924—21no—
39C3×#924C2211yescharacteristic, complemented
40#63983—21no—
41#63958—21no—
42D3×#215—24no—
43#63921—21no—
44#63894C2211yescharacteristic
45#63860C2211yescharacteristic
46#63857C2211yescharacteristic
47#63853—21no—
48C2×#3719C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63562C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C3×D4×Q8—31no—
64Q8×#67D311yescharacteristic, complemented
65C2×#942—31no—
66C2×#942—31no—
67C2×#942—61no—
68C22×#215—31no—
69C2×D3×SD16—31no—
70#5612—31no—
71#5550—31no—
72C3×#448—31no—
73#5228—31no—
74#5227D311yescharacteristic, complemented
75#5169—31no—
76#5167—31no—
77#5166—31no—
78#5086—31no—
79#5083—31no—
80#5051—31no—
81#5049—31no—
82#5047—31no—
83#5046—31no—
84#5042—31no—
85#5028—31no—
86#5026—31no—
87#5011—31no—
88#4818—31no—
89#4817—31no—
90#4813—31no—
91#4809—31no—
92#4733—31no—
93#4728—31no—
94C22×D32—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×#638—21no—
103#3828—22no—
104#3828—41no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—21no—
107C2×#634C2311yescharacteristic
108C2×C3×#67—21no—
109C2×C3×#67D411yescharacteristic
110C3×D3×Q8—22no—
111C3×D3×Q8—41no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6—21no—
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×#624—21no—
119D3×D12—22no—
120D3×D12—41no—
121#3756—22no—
122#3756—22no—
123#3755—22no—
124#3755D414yescomplemented
125#3748—22no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217—21no—
129C3×#217D411yescharacteristic
130C3×#215—22no—
131C3×#215—41no—
132C3×(C2×D3)⋊C4—21no—
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⋊C4D411yescharacteristic
143C3×C4×Dic3—21no—
144C3×C4×Dic3C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147Dic3⋊Dic3—21no—
148#3722—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3719—41no—
153#3717—22no—
154#3715—22no—
155D3×C3⋊C8—22no—
156#3266—91noSylow
157C22×C3×Q8—21no—
158C22×C3×Q8—31no—
159C22×C3×Q8C2×D311yescharacteristic, complemented
160C22×C3×Q8C2×D311yescharacteristic, complemented
161C2×D3×Q8C2×D311yescharacteristic
162C2×D3×D4—31no—
163C2×#235—31no—
164C2×#235—31no—
165C2×#235—61no—
166C22×D12—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C3×C4⋊Q8—31no—
170C3×C4⋊Q8—61no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8—61no—
174C3×C22⋊Q8—61no—
175C3×#121—31no—
176C3×C4×Q8—31no—
177C3×C4×D4—31no—
178C3×C4×D4—61no—
179#946—21no—
180#946C2×D311yescharacteristic
181Q8×Dic3C2×D311yescharacteristic, complemented
182#944—21no—
183#944C2×D311yescharacteristic, complemented
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—31no—
188C2×#216—31no—
189C2×#216—61no—
190C2×#216—61no—
191#942—64no—
192#942—64no—
193#942—68no—
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—64no—
203C2×#215C2×D311yescharacteristic
204C2×#215C2×D311yescharacteristic
205#938—61no—
206#937—61no—
207#937—61no—
208#936—31no—
209C2×#214—31no—
210#930C2×D311yescharacteristic
211C4×#67—21no—
212C4×#67C2×D311yescharacteristic
213#924—21no—
214#924—31no—
215#924C2×D311yescharacteristic, complemented
216C2×#208—31no—
217C2×#208—31no—
218C2×#208—61no—
219C22×C3⋊C8—31no—
220D3×SD16—64no—
221C2×Dic12—31no—
222C2×#204—31no—
223C2×D3×C8—31no—
224#897—31no—
225#894—61no—
226#893—31no—
227#884—61no—
228#883—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#835C2×D311yescharacteristic, complemented
238#835C2×D311yescharacteristic, complemented
239#832—31no—
240#830—31no—
241#830C2×D311yescharacteristic, complemented
242#821—31no—
243(C2×D3)⋊C8—31no—
244#816—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×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
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
274#638—42no—
275C2×C3⋊Dic3—21no—
276C4⋊(C3⋊D3)—21no—
277C4⋊(C3⋊D3)C2×D412yes—
278C4×C3⋊D3—42no—
279#634—21no—
280#634—21no—
281C3×#67—22no—
282C3×#67—81no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D411yescharacteristic
288C2×C3×Dic3C2×D411yescharacteristic
289C3×D12—21no—
290C3×D12—21no—
291C3×C4×D3—21no—
292C3×C4×D3—21no—
293C3×C4×D3—42no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—42no—
297#626—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—91no—
314#450—91no—
315#448—31no—
316#440—91no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C2×C3×Q8—21no—
321C2×C3×Q8—21no—
322C2×C3×Q8—24no—
323C2×C3×Q8—22no—
324C2×C3×Q8—22no—
325C2×C3×Q8—21no—
326C2×C3×Q8—21no—
327C2×C3×Q8—31no—
328C2×C3×Q8—41no—
329C2×C3×Q8—41no—
330C2×C3×Q8—41no—
331C2×C3×Q8—42no—
332C2×C3×Q8—61no—
333C2×C3×Q8—62no—
334C2×C3×Q8—121no—
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×Q8C22×D311yescharacteristic
337C2×C3×Q8C22×D311yescharacteristic
338C2×C3×Q8C22×D311yescharacteristic
339C2×C3×D4—31no—
340C2×C3×D4—31no—
341C2×C3×D4—61no—
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—21no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—121no—
355C2×#67#6711yescharacteristic
356D3×Q8—22no—
357D3×Q8—41no—
358D3×D4—62no—
359D3×D4—121no—
360#235—62no—
361#235—62no—
362#235—64no—
363#235—121no—
364#235—121no—
365#235—122no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—61no—
369C2×D12—62no—
370C2×D12—61no—
371C2×D12—121no—
372C2×D12C22×D311yescharacteristic
373C2×C4×D3—21no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—61no—
377C2×C4×D3—61no—
378C2×C4×D3—121no—
379C2×C4×D3C22×D311yescharacteristic
380C2×Dic6—21no—
381C2×Dic6—31no—
382C2×Dic6—31no—
383C2×Dic6—61no—
384C2×Dic6C22×D311yescharacteristic
385C3×SD16—62no—
386C3×SD16—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×C22⋊C4—31no—
398C3×C22⋊C4—31no—
399C3×C22⋊C4—61no—
400C3×C22⋊C4—61no—
401C3×C22⋊C4—61no—
402C3×C42—31no—
403C3×C42—61no—
404#217—21no—
405#217—61no—
406#217—61no—
407#217—61no—
408#217#6711yescharacteristic
409#216—62no—
410#216—62no—
411#216—64no—
412#216—64no—
413#216—62no—
414#216—62no—
415#216—121no—
416#215—22no—
417#215—34no—
418#215—34no—
419#215—41no—
420#215—64no—
421#215—62no—
422#215—62no—
423#215—62no—
424#215—62no—
425#215—64no—
426#214—62no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—21no—
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#6711yescharacteristic
435C4⋊Dic3—21no—
436C4⋊Dic3—61no—
437C4⋊Dic3C22×D311yescharacteristic
438C4⋊Dic3C22×D311yescharacteristic
439Dic3⋊C4—21no—
440Dic3⋊C4—21no—
441Dic3⋊C4—21no—
442Dic3⋊C4—21no—
443Dic3⋊C4—61no—
444Dic3⋊C4#6711yescharacteristic
445C4×Dic3—21no—
446C4×Dic3C22×D311yescharacteristic
447#208—62no—
448#208—62no—
449#208—64no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—61no—
455C2×C3⋊C8—61no—
456C2×C3⋊C8—62no—
457C2×C3⋊C8C22×D311yescharacteristic
458C2×C3⋊C8C22×D311yescharacteristic
459Dic12—121no—
460#204—62no—
461D3×C8—62no—
462C22×C32—21no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32C22×D411yescharacteristic
466C2×C3⋊D3—22no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3#13712yescomplemented
475D32—84no—
476C32×C4—21no—
477C32×C4—22no—
478C32×C4—41no—
479C32×C4C22×D411yescharacteristic
480C32×C4H(5,𝔽2)11yescharacteristic
481C3⋊Dic3—41no—
482C3×Dic3—21no—
483C3×Dic3—21no—
484C3×Dic3—21no—
485C3×Dic3—41no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C2×#41—91no—
489C22×Q8—31no—
490C22×Q8D3211yescharacteristic, complemented
491C22×D4—91no—
492#137—184no—
493C2×Q16—91no—
494C2×Q16—91no—
495C2×Q16—91no—
496C2×SD16—31no—
497C2×SD16—31no—
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—61no—
512C22⋊Q8—61no—
513C22⋊Q8—91no—
514#121—31no—
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×C3—61no—
536C23×C3D3×D411yescharacteristic
537C23×C3C2×#6711yescharacteristic
538C22×D3—21no—
539C22×D3—61no—
540C22×D3—61no—
541C22×D3—121no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3C2×#6711yescharacteristic
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—22no—
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—21no—
556C3×Q8—22no—
557C3×Q8—41no—
558C3×Q8—41no—
559C3×Q8—42no—
560C3×Q8—42no—
561C3×Q8—44no—
562C3×Q8—61no—
563C3×Q8—61no—
564C3×Q8—122no—
565C3×Q8D3×D412yes—
566C3×Q8D3×D412yes—
567C3×D4—62no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—241no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
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—31no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—42no—
589C2×C3×C4—42no—
590C2×C3×C4—44no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—122no—
597C2×C3×C4D3×D411yescharacteristic
598C2×C3×C4C2×#6711yescharacteristic
599C2×C3×C4C23×D311yescharacteristic
600C2×C3×C4C23×D311yescharacteristic
601#67—22no—
602#67—81no—
603#67—122no—
604#67—122no—
605#67—122no—
606#67—124no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—121no—
613C2×Dic3C2×#6711yescharacteristic
614C2×Dic3C2×#6711yescharacteristic
615C2×Dic3C2×#6711yescharacteristic
616D12—21no—
617D12—21no—
618D12—32no—
619D12—32no—
620D12—62no—
621D12—61no—
622D12—61no—
623D12—121no—
624D12—122no—
625C4×D3—21no—
626C4×D3—21no—
627C4×D3—42no—
628C4×D3—122no—
629C4×D3—122no—
630C4×D3—124no—
631C4×D3—241no—
632C4×D3—241no—
633Dic6—21no—
634Dic6—21no—
635Dic6—42no—
636Dic6—62no—
637Dic6—61no—
638Dic6—61no—
639Dic6—61no—
640Dic6—61no—
641Dic6—121no—
642C3×C8—61no—
643C3×C8—61no—
644C3⋊C8—21no—
645C3⋊C8—21no—
646C3⋊C8—32no—
647C3⋊C8—32no—
648C3⋊C8—62no—
649C3⋊C8—62no—
650C3⋊C8—61no—
651C3⋊C8—61no—
652C2×C32—41no—
653C2×C32D4211yescharacteristic
654C2×C32C2×#13711yescharacteristic
655C2×C32#57711yescharacteristic
656C3⋊D3—42no—
657C3×D3—22no—
658C3×D3—81no—
659C24—181no—
660#41—182no—
661#41—361no—
662C2×Q8—21no—
663C2×Q8—22no—
664C2×Q8—31no—
665C2×Q8—41no—
666C2×Q8—61no—
667C2×Q8—62no—
668C2×Q8—91no—
669C2×Q8—121no—
670C2×Q8C2×D3211yescharacteristic
671C2×Q8C2×D3211yescharacteristic
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—61no—
675C2×D4—91no—
676C2×D4—181no—
677C2×D4—182no—
678C2×D4—181no—
679C2×D4—361no—
680C22×C4—21no—
681C22×C4—31no—
682C22×C4—61no—
683C22×C4—181no—
684C22×C4—181no—
685C22×C4C2×D3211yescharacteristic
686Q16—182no—
687Q16—182no—
688Q16—361no—
689SD16—62no—
690SD16—94no—
691SD16—121no—
692SD16—182no—
693SD16—182no—
694SD16—182no—
695M16—182no—
696C2×C8—31no—
697C2×C8—31no—
698C2×C8—91no—
699C2×C8—91no—
700C2×C8—182no—
701C4⋊C4—31no—
702C4⋊C4—31no—
703C4⋊C4—31no—
704C4⋊C4—61no—
705C4⋊C4—61no—
706C4⋊C4—61no—
707C4⋊C4—61no—
708C4⋊C4—61no—
709C4⋊C4—181no—
710C22⋊C4—31no—
711C22⋊C4—31no—
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—61no—
715C22⋊C4—181no—
716C22⋊C4—181no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C42—31no—
720C42—61no—
721C22×C3—22no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—32no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3C2×D3×D411yescharacteristic
738C22×C3C22×#6711yescharacteristic
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—41no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—62no—
745C2×D3—62no—
746C2×D3—122no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—241no—
752C2×D3—241no—
753C2×D3—244no—
754C2×D3—244no—
755C2×D3#94212yescomplemented
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—22no—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—42no—
764C3×C4—42no—
765C3×C4—41no—
766C3×C4—41no—
767C3×C4—61no—
768C3×C4—61no—
769C3×C4—61no—
770C3×C4—121no—
771C3×C4—121no—
772C3×C4—121no—
773C3×C4C2×D3×D411yescharacteristic
774C3×C4C2×D3×D411yescharacteristic
775C3×C4#100411yescharacteristic
776C3×C4#100411yescharacteristic
777Dic3—21no—
778Dic3—21no—
779Dic3—21no—
780Dic3—41no—
781Dic3—41no—
782Dic3—41no—
783Dic3—122no—
784Dic3—121no—
785Dic3—121no—
786C32#326611yescharacteristic, complemented, Sylow
787C23—31no—
788C23—61no—
789C23—181no—
790C23—362no—
791C23—362no—
792C23—721no—
793C23D3×#6711yescharacteristic
794Q8—21no—
795Q8—21no—
796Q8—21no—
797Q8—42no—
798Q8—61no—
799Q8—61no—
800Q8—122no—
801Q8—181no—
802Q8—181no—
803Q8#381112yes—
804D4—62no—
805D4—61no—
806D4—61no—
807D4—92no—
808D4—181no—
809D4—241no—
810D4—362no—
811D4—362no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—31no—
817C2×C4—31no—
818C2×C4—31no—
819C2×C4—42no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—122no—
826C2×C4—181no—
827C2×C4—362no—
828C2×C4—721no—
829C2×C4D3×#6711yescharacteristic
830C2×C4C22×D3211yescharacteristic
831C8—61no—
832C8—61no—
833C8—92no—
834C8—181no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—42no—
839C2×C3—41no—
840C2×C3—41no—
841C2×C3—62no—
842C2×C3—241no—
843C2×C3#559011yescharacteristic
844C2×C3#576211yescharacteristic
845C2×C3D3×#13711yescharacteristic
846C2×C3D4×#6711yescharacteristic
847C2×C3C2×#94211yescharacteristic
848C2×C3#583711yescharacteristic
849D3—22no—
850D3—81no—
851D3—122no—
852D3—122no—
853D3—242no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—32no—
858C22—61no—
859C22—61no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—182no—
864C22—361no—
865C22—361no—
866C22—724no—
867C22C2×D3×#6711yescharacteristic
868C4—21no—
869C4—22no—
870C4—41no—
871C4—61no—
872C4—61no—
873C4—61no—
874C4—121no—
875C4—121no—
876C4—121no—
877C4—361no—
878C4C2×#381111yescharacteristic
879C4#6433011yescharacteristic
880C3—21no—
881C3#8006111yescharacteristic, complemented
882C3#8355911yescharacteristic, complemented
883C2—41no—
884C2—62no—
885C2—241no—
886C2—362no—
887C2D3×#94211yescharacteristic
888C2#1059531811yescharacteristic
889C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radical#10595078C2
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. C2×#64151C2semidirect
2. C3×Q8×#67C2semidirect
3. C2×D3×#215C2semidirect
5. C3×#5227C2semidirect
6. #10591651C2semidirect
7. #10591605C2semidirect
8. #10591604C2semidirect
9. #10591596C2semidirect
10. #10591595C2semidirect
11. #10591565C2semidirect
12. #10591540C2semidirect
13. #10591184C2semidirect
14. #10591180C2semidirect
15. #10591151C2semidirect
18. C22×C32×Q8C22semidirect
22. C2×#3756C22semidirect
23. C2×#3756C22semidirect
27. C2×#3748C22semidirect
30. C3×Q8×Dic3C22semidirect
32. C3×#944C22semidirect
39. C3×#924C22semidirect
48. C2×#3719C22semidirect
52. C3×#835C22semidirect
53. C3×#835C22semidirect
54. C3×#830C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
62. #63554C22semidirect
64. Q8×#67D3semidirect
74. #5227D3semidirect
124. #3755D4semidirect
159. C22×C3×Q8C2×D3semidirect
160. C22×C3×Q8C2×D3semidirect
181. Q8×Dic3C2×D3semidirect
183. #944C2×D3semidirect
215. #924C2×D3semidirect
237. #835C2×D3semidirect
238. #835C2×D3semidirect
241. #830C2×D3semidirect
474. C2×C3×D3#137semidirect
490. C22×Q8D32semidirect
755. C2×D3#942semidirect
786. C32#3266semidirect
881. C3#80061semidirect
882. C3#83559semidirect

Maximal subgroups

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

subgroupindex
C2×#641512
C3×Q8×#672
C2×D3×#2152
#105950782
C3×#52272
#105916512
#105916052
#105916042
#105915962
#105915952
#105915652
#105915402
#105911842
#105911802
#105911512
#835593
#800613