Finite Group Databasebeta

← #11864599

Subgroups — #11864599

Order 1152.

1604 conjugacy classes of subgroups.

The subgroup lattice has 1041 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic, complemented
2C3×#5629C211yesmaximal, characteristic, complemented
3C2×#63947C211yesmaximal, characteristic, complemented
4C2×#63939C211yesmaximal, characteristic, complemented
5#10592746C211yesmaximal, characteristic, complemented
6C3×#5046C211yesmaximal, characteristic, complemented
7#10591655C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591182C211yesmaximal, characteristic, complemented
10#10591160C211yesmaximal, characteristic, complemented
11#10591145C211yesmaximal, characteristic, complemented
12#10590613C211yesmaximal, characteristic, complemented
13#10590607C211yesmaximal, characteristic, complemented
14#10590595C211yesmaximal, characteristic, complemented
15D3×#809C211yesmaximal, characteristic, complemented
16#83424—31nomaximal
17#80149—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×#235C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C2×D3×#67—21no—
23C2×D3×#67—21no—
24#64307—24no—
25#64307—24no—
26C2×#3802—21no—
27C2×D3×D12C2211yescharacteristic
28C2×D3×D12C2211yescharacteristic
29C2×#3796—21no—
30C2×#3795C2211yescharacteristic
31C2×#3795C2211yescharacteristic
32C32×C22⋊Q8C2211yescharacteristic, complemented
33C2×#3756C2211yescharacteristic, complemented
34C2×#3755C2211yescharacteristic, complemented
35C3×#946C2211yescharacteristic, complemented
36C2×C3×#215C2211yescharacteristic, complemented
37C2×C3×#215C2211yescharacteristic, complemented
38C3×#930C2211yescharacteristic, complemented
39C3×#896—21no—
40C3×#895—21no—
41C3×#895C2211yescharacteristic, complemented
42C3×D3×C4⋊C4C2211yescharacteristic, complemented
43C3×#884—21no—
44C3×#884—21no—
45#63947—24no—
46#63939—24no—
47C2×#3716C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic, complemented
53#63657C2211yescharacteristic, complemented
54#63637C2211yescharacteristic, complemented
55#63636C2211yescharacteristic, complemented
56C3×#830C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63562C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×#1009—31no—
66C2×#1004—31no—
67C3×#537—31no—
68C2×#950—31no—
69C2×#949—31no—
70C2×#916—31no—
71C2×#914—31no—
72#5629D311yescharacteristic, complemented
73C3×#450—31no—
74#5234—31no—
75#5217—31no—
76#5173—31no—
77#5169—31no—
78#5047—31no—
79#5047—31no—
80#5047—31no—
81#5047—61no—
82#5046—31no—
83#5046D311yescharacteristic, complemented
84#5037—31no—
85#5037—31no—
86#5036—31no—
87#5036—31no—
88#4966—31no—
89C2×#809—31no—
90#4781—31no—
91#4773—31no—
92#4771—31no—
93D3×#102—31no—
94#4734—31no—
95#4727—31no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C22×D32—21no—
99C2×C32×Q8C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×#638—21no—
102#3828—22no—
103#3828—22no—
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—21no—
106C2×#634C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67D411yescharacteristic
109C2×C3×#67D411yescharacteristic
110C3×#239—22no—
111C3×#239—22no—
112C3×#235—22no—
113C3×#235—22no—
114C2×C3×D12—21no—
115C2×C3×D12—22no—
116C2×C3×D12—22no—
117C2×C3×D12—21no—
118C2×C3×D12—21no—
119C2×C3×D12D411yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×D12C2311yescharacteristic
122C2×C3×D12C2311yescharacteristic
123C2×C3×C4×D3—21no—
124C2×C3×C4×D3—21no—
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×Dic6D411yescharacteristic
128D3×#67—28no—
129D3×#67—28no—
130C2×#626—21no—
131C2×#626—21no—
132C2×#625—21no—
133C2×#625—21no—
134C2×D3×Dic3—21no—
135C2×D3×Dic3—21no—
136#3802—28no—
137D3×D12—22no—
138D3×D12—22no—
139D3×D12—22no—
140D3×D12D414yescomplemented
141#3796—28no—
142#3795—22no—
143#3795—22no—
144#3795—22no—
145#3795D414yescomplemented
146C32×C4⋊C4—21no—
147C32×C4⋊C4C2311yescharacteristic
148C32×C22⋊C4—21no—
149#3756—22no—
150#3755—22no—
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152C2×C3⋊(C3⋊C8)C2311yescharacteristic
153C3×#215—22no—
154C3×#215—22no—
155C3×(C2×D3)⋊C4—21no—
156C3×(C2×D3)⋊C4—21no—
157C3×(C2×D3)⋊C4—21no—
158C3×C4⋊Dic3C2311yescharacteristic
159C3×Dic3⋊C4—21no—
160C3×Dic3⋊C4—21no—
161C2×C3×C3⋊C8C2311yescharacteristic
162C2×C3×C3⋊C8C2311yescharacteristic
163#3716—22no—
164#3714—22no—
165#3713—22no—
166#3713—22no—
167#3711—22no—
168D3×C3⋊C8—22no—
169#3012—91noSylow
170C2×C3×#41—31no—
171C2×C3×#41—31no—
172C22×C3×D4—31no—
173C22×#67—61no—
174C22×#67—61no—
175#1009—64no—
176#1009—64no—
177C2×#239—61no—
178C2×#239C2×D311yescharacteristic, complemented
179#1004—64no—
180#1004—64no—
181C2×#237—31no—
182C2×#237—31no—
183C2×#237—61no—
184C2×D3×D4—31no—
185C2×D3×D4—31no—
186C2×D3×D4—61no—
187C2×D3×D4—61no—
188C2×D3×D4—61no—
189C2×D3×D4—61no—
190C2×#235—31no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—31no—
194C2×#235—61no—
195C2×#235C2×D311yescharacteristic
196C22×D12—31no—
197C22×D12—31no—
198C22×D12C2×D311yescharacteristic
199C2×C3×SD16—31no—
200C2×C3×SD16—31no—
201C3×C22⋊Q8—21no—
202C3×C22⋊Q8—31no—
203C3×C22⋊Q8—61no—
204C3×C22⋊Q8C2×D311yescharacteristic, complemented
205C3×C22⋊Q8C2×D311yescharacteristic, complemented
206C3×#121—31no—
207C3×#121—31no—
208C3×#121—61no—
209C3×#121—61no—
210C3×#121—61no—
211C2×C3×C4⋊C4—31no—
212#950—64no—
213#949—64no—
214#946C2×D311yescharacteristic, complemented
215C2×#216—31no—
216C2×#216—31no—
217C2×#216—61no—
218C2×#215—31no—
219C2×#215—31no—
220C2×#215—61no—
221C2×#215C2×D311yescharacteristic, complemented
222C2×#215C2×D311yescharacteristic, complemented
223C2×#214—31no—
224C2×#213—31no—
225C2×#213—31no—
226C2×#213—31no—
227C2×#213—31no—
228C2×#213—31no—
229#930C2×D311yescharacteristic, complemented
230C2×#208—31no—
231C22×C3⋊C8—31no—
232#916—64no—
233#914—64no—
234C2×D24—31no—
235C2×#204—31no—
236C2×ΓL(1,𝔽25)—31no—
237C2×D3×C8—31no—
238#896—21no—
239#895—21no—
240#895C2×D311yescharacteristic, complemented
241D3×C4⋊C4C2×D311yescharacteristic, complemented
242#884—21no—
243#884—21no—
244C3×#102—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#832—31no—
248#832—31no—
249#830—31no—
250#830—31no—
251#830—31no—
252#830—31no—
253#830—61no—
254#830C2×D311yescharacteristic, complemented
255#821—31no—
256(C2×D3)⋊C8—31no—
257(C2×D3)⋊C8—31no—
258#816—31no—
259#810—31no—
260#810—31no—
261#810—31no—
262#810—61no—
263#809—31no—
264#809—31no—
265#809—31no—
266#809—31no—
267#809—31no—
268#809—61no—
269#809C2×D311yescharacteristic, complemented
270#809C2×D311yescharacteristic, complemented
271C23×C32C2×D411yescharacteristic
272C22×C3⋊D3—21no—
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3—24no—
276C22×C3×D3—21no—
277C22×C3×D3—81no—
278C22×C3×D3—81no—
279C22×C3×D3C2×D411yescharacteristic
280C22×C3×D3C2×D411yescharacteristic
281C2×D32—24no—
282C2×D32—24no—
283C2×D32—81no—
284C2×D32—81no—
285C2×D32—81no—
286C2×D32—81no—
287C32×Q8—21no—
288C32×Q8—21no—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4C2×D411yescharacteristic
294C2×C32×C4C2411yescharacteristic
295#638—24no—
296C2×C3⋊Dic3—21no—
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)C2×D412yes—
299C4×C3⋊D3—24no—
300#634—21no—
301#634C2×D412yes—
302C3×#67—22no—
303C3×#67—22no—
304C3×#67—81no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3C2×D411yescharacteristic
307C2×C3×Dic3C2×D411yescharacteristic
308C3×D12—24no—
309C3×D12—22no—
310C3×D12—21no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—21no—
314C3×D12—42no—
315C3×D12—81no—
316C3×D12C2×D412yes—
317C3×D12C2×D412yes—
318C3×C4×D3—21no—
319C3×C4×D3—21no—
320C3×C4×D3—42no—
321C3×C4×D3—81no—
322C3×C4×D3C2×D412yes—
323C3×C4×D3C2×D412yes—
324C3×Dic6—22no—
325#626—24no—
326#626—24no—
327#625—24no—
328#625—24no—
329D3×Dic3—24no—
330D3×Dic3—24no—
331C3⋊(C3⋊C8)—21no—
332C3⋊(C3⋊C8)—21no—
333C3×C3⋊C8—21no—
334C3×C3⋊C8—21no—
335C2×H(5,𝔽2)—91no—
336C2×AGL(1,ℤ/8)—91no—
337C2×#135—91no—
338#537—31no—
339#452—91no—
340#452—91no—
341#450—31no—
342#450—91no—
343#449—91no—
344#449—91no—
345#447—91no—
346#447—91no—
347#417—91no—
348C2×#102—91no—
349#408—91no—
350C24×C3—61no—
351C23×D3—21no—
352C23×D3—61no—
353C23×D3—61no—
354C23×D3—61no—
355C23×D3—61no—
356C3×#41—62no—
357C3×#41—62no—
358C3×#41—62no—
359C3×#41—62no—
360C2×C3×Q8—21no—
361C2×C3×Q8—31no—
362C2×C3×Q8C22×D311yescharacteristic
363C2×C3×Q8C22×D311yescharacteristic
364C2×C3×D4—31no—
365C2×C3×D4—31no—
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C2×C3×D4—31no—
369C2×C3×D4—31no—
370C2×C3×D4—62no—
371C2×C3×D4—62no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C2×C3×D4—61no—
375C2×C3×D4—61no—
376C22×C3×C4—21no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—61no—
380C22×C3×C4—61no—
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C2×#67—21no—
384C2×#67—68no—
385C2×#67—68no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—61no—
391C2×#67—61no—
392C2×#67—61no—
393C2×#67—61no—
394C2×#67—121no—
395C2×#67#6711yescharacteristic
396C2×#67#6711yescharacteristic
397C22×Dic3—61no—
398C22×Dic3—61no—
399#239—22no—
400#239—22no—
401#239—68no—
402#237—34no—
403#237—68no—
404#237—62no—
405#237—62no—
406#237—62no—
407D3×D4—34no—
408D3×D4—62no—
409D3×D4—62no—
410D3×D4—68no—
411D3×D4—68no—
412D3×D4—68no—
413D3×D4—68no—
414D3×D4—62no—
415#235—22no—
416#235—22no—
417#235—34no—
418#235—62no—
419#235—62no—
420#235—62no—
421#235—62no—
422#235—62no—
423#235—62no—
424#235—62no—
425#235—122no—
426#235—122no—
427C2×D12—21no—
428C2×D12—22no—
429C2×D12—22no—
430C2×D12—21no—
431C2×D12—21no—
432C2×D12—31no—
433C2×D12—31no—
434C2×D12—34no—
435C2×D12—61no—
436C2×D12—62no—
437C2×D12—62no—
438C2×D12—61no—
439C2×D12—61no—
440C2×D12—62no—
441C2×D12#6711yescharacteristic
442C2×D12C22×D311yescharacteristic
443C2×D12C22×D311yescharacteristic
444C2×D12C22×D311yescharacteristic
445C2×C4×D3—21no—
446C2×C4×D3—21no—
447C2×C4×D3—61no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3—121no—
452C2×C4×D3C22×D311yescharacteristic
453C2×C4×D3C22×D311yescharacteristic
454C2×Dic6—31no—
455C2×Dic6—31no—
456C2×Dic6—61no—
457C2×Dic6#6711yescharacteristic
458C3×SD16—62no—
459C3×SD16—62no—
460C2×C3×C8—31no—
461C2×C3×C8—31no—
462C3×C4⋊C4—21no—
463C3×C4⋊C4—21no—
464C3×C4⋊C4—21no—
465C3×C4⋊C4—31no—
466C3×C4⋊C4—41no—
467C3×C4⋊C4—61no—
468C3×C4⋊C4—61no—
469C3×C4⋊C4C22×D311yescharacteristic
470C3×C4⋊C4C22×D311yescharacteristic
471C3×C22⋊C4—21no—
472C3×C22⋊C4—21no—
473C3×C22⋊C4—41no—
474C3×C22⋊C4—61no—
475C3×C22⋊C4—61no—
476C3×C22⋊C4—61no—
477#216—62no—
478#216—62no—
479#216—122no—
480#215—22no—
481#215—22no—
482#215—62no—
483#215—62no—
484#215—122no—
485#214—62no—
486#213—62no—
487#213—62no—
488#213—62no—
489#213—62no—
490#213—62no—
491(C2×D3)⋊C4—21no—
492(C2×D3)⋊C4—21no—
493(C2×D3)⋊C4—21no—
494C4⋊Dic3C22×D311yescharacteristic
495Dic3⋊C4—21no—
496Dic3⋊C4—21no—
497#208—62no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—31no—
501C2×C3⋊C8—31no—
502C2×C3⋊C8—61no—
503C2×C3⋊C8—61no—
504C2×C3⋊C8—62no—
505C2×C3⋊C8C22×D311yescharacteristic
506C2×C3⋊C8C22×D311yescharacteristic
507D24—62no—
508#204—62no—
509ΓL(1,𝔽25)—62no—
510D3×C8—62no—
511C22×C32—21no—
512C22×C32—21no—
513C22×C32—21no—
514C22×C32C22×D411yescharacteristic
515C2×C3⋊D3—22no—
516C2×C3⋊D3—41no—
517C2×C3⋊D3—41no—
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—22no—
521C2×C3×D3—22no—
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527C2×C3×D3—41no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—84no—
533C2×C3×D3#12012yes—
534D32—84no—
535D32—84no—
536C32×C4—21no—
537C32×C4—41no—
538C32×C4—41no—
539C32×C4C22×D411yescharacteristic
540C32×C4C22×D411yescharacteristic
541C3⋊Dic3—22no—
542C3×Dic3—21no—
543C3×Dic3—41no—
544C3×Dic3#12012yes—
545H(5,𝔽2)—184no—
546H(5,𝔽2)—184no—
547C2×#41—31no—
548C2×#41—31no—
549C2×#41—91no—
550C2×#41—91no—
551C2×#41—91no—
552C2×#41—181no—
553C22×D4—31no—
554C22×D4—91no—
555C22×D4—91no—
556C22×D4—181no—
557C22×D4—181no—
558C22×D4—181no—
559AGL(1,ℤ/8)—184no—
560#135—184no—
561C2×Q16—91no—
562C2×SD16—31no—
563C2×SD16—31no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×D8—91no—
567C2×D8—91no—
568C2×D8—91no—
569C2×M16—91no—
570C22×C8—91no—
571C22⋊Q8—31no—
572C22⋊Q8—61no—
573C22⋊Q8D3211yescharacteristic, complemented
574#121—31no—
575#121—31no—
576#121—61no—
577#121—61no—
578#121—61no—
579C2×C4⋊C4—31no—
580#103—91no—
581#103—91no—
582#102—31no—
583#102—31no—
584#102—91no—
585#102—91no—
586#102—91no—
587#102—91no—
588C22⋊C8—31no—
589C22⋊C8—91no—
590C22⋊C8—91no—
591C22⋊C8—91no—
592C23×C3—21no—
593C23×C3—31no—
594C23×C3—31no—
595C23×C3—64no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—241no—
600C23×C3—241no—
601C23×C3D3×D411yescharacteristic
602C23×C3C2×#6711yescharacteristic
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—24no—
606C22×D3—21no—
607C22×D3—64no—
608C22×D3—64no—
609C22×D3—64no—
610C22×D3—61no—
611C22×D3—61no—
612C22×D3—64no—
613C22×D3—81no—
614C22×D3—81no—
615C22×D3—121no—
616C22×D3—241no—
617C22×D3—241no—
618C22×D3—241no—
619C22×D3—241no—
620C22×D3—241no—
621C22×D3—241no—
622C22×D3—241no—
623C22×D3—241no—
624C22×D3C2×#6711yescharacteristic
625C22×D3C2×#6711yescharacteristic
626C3×Q8—21no—
627C3×Q8—21no—
628C3×Q8—21no—
629C3×Q8—21no—
630C3×Q8—41no—
631C3×Q8—41no—
632C3×Q8—62no—
633C3×D4—32no—
634C3×D4—32no—
635C3×D4—62no—
636C3×D4—64no—
637C3×D4—62no—
638C3×D4—62no—
639C3×D4—61no—
640C3×D4—61no—
641C3×D4—61no—
642C3×D4—61no—
643C3×D4—122no—
644C3×D4—241no—
645C3×D4—241no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—31no—
657C2×C3×C4—32no—
658C2×C3×C4—32no—
659C2×C3×C4—31no—
660C2×C3×C4—41no—
661C2×C3×C4—41no—
662C2×C3×C4—41no—
663C2×C3×C4—41no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—122no—
668C2×C3×C4—241no—
669C2×C3×C4D3×D411yescharacteristic
670C2×C3×C4C2×#6711yescharacteristic
671C2×C3×C4C23×D311yescharacteristic
672C2×C3×C4C23×D311yescharacteristic
673#67—22no—
674#67—22no—
675#67—64no—
676#67—64no—
677#67—64no—
678#67—64no—
679#67—64no—
680#67—64no—
681#67—64no—
682#67—64no—
683#67—81no—
684#67—124no—
685C2×Dic3—21no—
686C2×Dic3—64no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—64no—
690C2×Dic3—121no—
691C2×Dic3C2×#6711yescharacteristic
692C2×Dic3C2×#6711yescharacteristic
693D12—24no—
694D12—22no—
695D12—21no—
696D12—21no—
697D12—21no—
698D12—21no—
699D12—32no—
700D12—32no—
701D12—42no—
702D12—62no—
703D12—64no—
704D12—64no—
705D12—61no—
706D12—61no—
707D12—81no—
708D12—121no—
709D12D3×D412yes—
710D12D3×D412yes—
711C4×D3—21no—
712C4×D3—21no—
713C4×D3—42no—
714C4×D3—64no—
715C4×D3—64no—
716C4×D3—64no—
717C4×D3—64no—
718C4×D3—81no—
719C4×D3—124no—
720C4×D3D3×D412yes—
721C4×D3D3×D412yes—
722Dic6—22no—
723Dic6—32no—
724Dic6—32no—
725Dic6—62no—
726Dic6—61no—
727Dic6—61no—
728Dic6—121no—
729C3×C8—61no—
730C3×C8—61no—
731C3⋊C8—21no—
732C3⋊C8—21no—
733C3⋊C8—61no—
734C3⋊C8—61no—
735C3⋊C8—61no—
736C3⋊C8—61no—
737C3⋊C8—121no—
738C3⋊C8—121no—
739C2×C32—41no—
740C2×C32C2×#12011yescharacteristic
741C2×C32#57611yescharacteristic
742C2×C32#57711yescharacteristic
743C3⋊D3—42no—
744C3×D3—22no—
745C3×D3—41no—
746C3×D3—42no—
747C3×D3—42no—
748C3×D3—81no—
749C24—61no—
750C24—181no—
751C24—181no—
752#41—62no—
753#41—62no—
754#41—62no—
755#41—62no—
756#41—94no—
757#41—182no—
758#41—182no—
759#41—182no—
760#41—182no—
761#41—182no—
762#41—188no—
763C2×Q8—31no—
764C2×Q8—91no—
765C2×Q8C2×D3211yescharacteristic
766C2×D4—31no—
767C2×D4—31no—
768C2×D4—31no—
769C2×D4—31no—
770C2×D4—31no—
771C2×D4—31no—
772C2×D4—62no—
773C2×D4—62no—
774C2×D4—61no—
775C2×D4—61no—
776C2×D4—61no—
777C2×D4—61no—
778C2×D4—94no—
779C2×D4—91no—
780C2×D4—182no—
781C2×D4—181no—
782C2×D4—181no—
783C2×D4—182no—
784C2×D4—182no—
785C2×D4—188no—
786C2×D4—188no—
787C2×D4—188no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4—181no—
791C22×C4—31no—
792C22×C4—31no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—181no—
796C22×C4—181no—
797C22×C4—181no—
798C22×C4C2×D3211yescharacteristic
799Q16—182no—
800SD16—62no—
801SD16—62no—
802SD16—182no—
803SD16—182no—
804D8—182no—
805D8—182no—
806D8—182no—
807M16—182no—
808C2×C8—31no—
809C2×C8—31no—
810C2×C8—91no—
811C2×C8—91no—
812C2×C8—182no—
813C4⋊C4—21no—
814C4⋊C4—31no—
815C4⋊C4—61no—
816C4⋊C4—61no—
817C4⋊C4C2×D3211yescharacteristic
818C22⋊C4—21no—
819C22⋊C4—61no—
820C22⋊C4—61no—
821C22⋊C4—61no—
822C22×C3—21no—
823C22×C3—21no—
824C22×C3—21no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—32no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—61no—
834C22×C3—61no—
835C22×C3—61no—
836C22×C3—61no—
837C22×C3—62no—
838C22×C3—62no—
839C22×C3—61no—
840C22×C3—121no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3—121no—
847C22×C3—244no—
848C22×C3C2×D3×D411yescharacteristic
849C22×C3C22×#6711yescharacteristic
850C2×D3—21no—
851C2×D3—21no—
852C2×D3—21no—
853C2×D3—21no—
854C2×D3—21no—
855C2×D3—22no—
856C2×D3—22no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—41no—
863C2×D3—41no—
864C2×D3—62no—
865C2×D3—62no—
866C2×D3—84no—
867C2×D3—122no—
868C2×D3—121no—
869C2×D3—121no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—241no—
873C2×D3—241no—
874C2×D3—244no—
875C2×D3—244no—
876C2×D3—244no—
877C2×D3—244no—
878C2×D3#93712yes—
879C3×C4—21no—
880C3×C4—21no—
881C3×C4—21no—
882C3×C4—21no—
883C3×C4—32no—
884C3×C4—41no—
885C3×C4—41no—
886C3×C4—41no—
887C3×C4—41no—
888C3×C4—41no—
889C3×C4—61no—
890C3×C4—81no—
891C3×C4—81no—
892C3×C4—121no—
893C3×C4C2×D3×D411yescharacteristic
894C3×C4C2×D3×D411yescharacteristic
895C3×C4C2×D3×D411yescharacteristic
896C3×C4C2×D3×D411yescharacteristic
897Dic3—21no—
898Dic3—41no—
899Dic3—62no—
900Dic3—62no—
901Dic3—122no—
902Dic3#93712yes—
903C32#301211yescharacteristic, complemented, Sylow
904C23—31no—
905C23—31no—
906C23—64no—
907C23—61no—
908C23—61no—
909C23—61no—
910C23—184no—
911C23—184no—
912C23—181no—
913C23—241no—
914C23—241no—
915C23—721no—
916C23—721no—
917C23—721no—
918C23—721no—
919C23D3×#6711yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—62no—
923Q8—92no—
924Q8—181no—
925D4—32no—
926D4—32no—
927D4—62no—
928D4—64no—
929D4—62no—
930D4—62no—
931D4—61no—
932D4—61no—
933D4—61no—
934D4—61no—
935D4—92no—
936D4—122no—
937D4—184no—
938D4—184no—
939D4—184no—
940D4—184no—
941D4—184no—
942D4—181no—
943D4—241no—
944D4—241no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—31no—
950C2×C4—32no—
951C2×C4—32no—
952C2×C4—31no—
953C2×C4—61no—
954C2×C4—61no—
955C2×C4—61no—
956C2×C4—122no—
957C2×C4—184no—
958C2×C4—184no—
959C2×C4—184no—
960C2×C4—181no—
961C2×C4—241no—
962C2×C4D3×#6711yescharacteristic
963C2×C4C22×D3211yescharacteristic
964C8—61no—
965C8—61no—
966C8—181no—
967C8—181no—
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—41no—
972C2×C3—41no—
973C2×C3—62no—
974C2×C3—81no—
975C2×C3—121no—
976C2×C3—122no—
977C2×C3—122no—
978C2×C3—241no—
979C2×C3D3×#12011yescharacteristic
980C2×C3#576211yescharacteristic
981C2×C3#577411yescharacteristic
982C2×C3C2×#93711yescharacteristic
983C2×C3#583511yescharacteristic
984C2×C3#583711yescharacteristic
985D3—22no—
986D3—42no—
987D3—42no—
988D3—41no—
989D3—81no—
990D3—122no—
991D3—122no—
992D3—242no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—32no—
997C22—61no—
998C22—61no—
999C22—61no—
1000C22—61no—
1001C22—62no—
1002C22—62no—
1003C22—61no—
1004C22—121no—
1005C22—121no—
1006C22—121no—
1007C22—121no—
1008C22—121no—
1009C22—121no—
1010C22—121no—
1011C22—182no—
1012C22—244no—
1013C22—361no—
1014C22—361no—
1015C22—724no—
1016C22—724no—
1017C22C2×D3×#6711yescharacteristic
1018C4—21no—
1019C4—32no—
1020C4—41no—
1021C4—41no—
1022C4—61no—
1023C4—121no—
1024C4—182no—
1025C4D32×D411yescharacteristic
1026C4D32×D411yescharacteristic
1027C3—21no—
1028C3#8014911yescharacteristic, complemented
1029C3#8342411yescharacteristic, complemented
1030C2—41no—
1031C2—62no—
1032C2—121no—
1033C2—122no—
1034C2—122no—
1035C2—241no—
1036C2—362no—
1037C2D3×#93711yescharacteristic
1038C2#1059531811yescharacteristic
1039C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3012
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×#64307C2semidirect
2. C3×#5629C2semidirect
3. C2×#63947C2semidirect
4. C2×#63939C2semidirect
5. #10592746C2semidirect
6. C3×#5046C2semidirect
7. #10591655C2semidirect
8. #10591651C2semidirect
9. #10591182C2semidirect
10. #10591160C2semidirect
11. #10591145C2semidirect
12. #10590613C2semidirect
13. #10590607C2semidirect
14. #10590595C2semidirect
15. D3×#809C2semidirect
19. C2×C3×#239C22semidirect
32. C32×C22⋊Q8C22semidirect
33. C2×#3756C22semidirect
34. C2×#3755C22semidirect
35. C3×#946C22semidirect
36. C2×C3×#215C22semidirect
37. C2×C3×#215C22semidirect
38. C3×#930C22semidirect
41. C3×#895C22semidirect
42. C3×D3×C4⋊C4C22semidirect
47. C2×#3716C22semidirect
48. C2×#3714C22semidirect
49. C2×#3713C22semidirect
50. C2×#3713C22semidirect
51. C2×#3711C22semidirect
52. C2×D3×C3⋊C8C22semidirect
53. #63657C22semidirect
54. #63637C22semidirect
55. #63636C22semidirect
56. C3×#830C22semidirect
57. C3×#809C22semidirect
58. C3×#809C22semidirect
59. #63567C22semidirect
60. #63564C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
72. #5629D3semidirect
83. #5046D3semidirect
140. D3×D12D4semidirect
145. #3795D4semidirect
178. C2×#239C2×D3semidirect
204. C3×C22⋊Q8C2×D3semidirect
205. C3×C22⋊Q8C2×D3semidirect
214. #946C2×D3semidirect
221. C2×#215C2×D3semidirect
222. C2×#215C2×D3semidirect
229. #930C2×D3semidirect
240. #895C2×D3semidirect
241. D3×C4⋊C4C2×D3semidirect
254. #830C2×D3semidirect
269. #809C2×D3semidirect
270. #809C2×D3semidirect
573. C22⋊Q8D32semidirect
903. C32#3012semidirect
1028. C3#80149semidirect
1029. C3#83424semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
C3×#56292
C2×#639472
C2×#639392
#105927462
C3×#50462
#105916552
#105916512
#105911822
#105911602
#105911452
#105906132
#105906072
#105905952
D3×#8092
#834243
#801493