Finite Group Databasebeta

← #11900909

Subgroups — #11900909

Order 1152.

2579 conjugacy classes of subgroups.

The subgroup lattice has 1153 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic, complemented
2C3×C4×#235C212yesmaximal, complemented
3#10595076C211yesmaximal, characteristic, complemented
4#10595060C212yesmaximal, complemented
5#10595017C211yesmaximal, characteristic, complemented
6#10595003C212yesmaximal, complemented
7#10594934C212yesmaximal, complemented
8#10594933C212yesmaximal, complemented
9#10594836C212yesmaximal, complemented
10#10594006C211yesmaximal, characteristic, complemented
11#10593997C212yesmaximal, complemented
12C42×D32C211yesmaximal, characteristic, complemented
13C4×#3798C211yesmaximal, characteristic, complemented
14C4×#3798C212yesmaximal, complemented
15#10593935C211yesmaximal, characteristic, complemented
16#10593934C212yesmaximal, complemented
17#10593926C212yesmaximal, complemented
18#10593911C212yesmaximal, complemented
19#10593910C212yesmaximal, complemented
20#85836—32nomaximal
21C2×#3828C2211yescharacteristic
22C2×C3×#235C2212yes—
23C2×C4×D32C2211yescharacteristic
24C2×C4×D32C2212yes—
25C2×#3798C2212yes—
26C2×#3798C2211yescharacteristic
27C2×C32×C42C2211yescharacteristic, complemented
28C4×#638C2212yes—
29C4×#638C2212yescomplemented
30#64135C2211yescharacteristic, complemented
31C4×C4⋊(C3⋊D3)C2212yes—
32#64081C2211yescharacteristic
33#64081C2211yescharacteristic, complemented
34C42×C3⋊D3C2211yescharacteristic
35C42×C3⋊D3C2211yescharacteristic, complemented
36C4×#634C2212yescomplemented
37C3×C4×#67C2212yes—
38C3×C4×#67C2212yes—
39C3×C4×#67C2212yescomplemented
40C3×C4×#67C2212yescomplemented
41C3×#926C2212yescomplemented
42C3×C4×D12C2212yes—
43C3×C4×D12C2212yes—
44C3×#872C2212yes—
45C3×#872C2212yescomplemented
46C3×C42×D3C2212yes—
47C3×C42×D3C2212yescomplemented
48C3×C4×Dic6C2212yescomplemented
49C3×C4×Dic6C2212yescomplemented
50#63983C2211yescharacteristic
51#63979C2211yescharacteristic, complemented
52#63975C2211yescharacteristic
53#63971C2212yes—
54#63970C2212yes—
55#63969C2212yes—
56#63959C2212yescomplemented
57#63958C2212yes—
58#63956C2212yescomplemented
59#63953C2211yescharacteristic, complemented
60#63923C2211yescharacteristic
61#63922C2212yes—
62C4×#627C2212yescomplemented
63C4×#627C2212yescomplemented
64C4×#627C2212yescomplemented
65#63913C2211yescharacteristic, complemented
66#63910C2212yes—
67#63907C2212yescomplemented
68C4×#626C2212yes—
69C4×#626C2212yes—
70C4×#626C2212yes—
71C4×#626C2212yes—
72C4×#626C2212yescomplemented
73C4×#626C2212yescomplemented
74C4×#625C2212yes—
75C4×#625C2212yes—
76C4×#625C2212yescomplemented
77#63899C2212yes—
78#63897C2211yescharacteristic
79#63896C2212yes—
80#63895C2212yes—
81#63893C2212yes—
82#63891C2212yes—
83#63890C2212yes—
84#63888C2212yes—
85#63887C2212yes—
86#63886C2212yes—
87#63885C2212yes—
88#63884C2212yes—
89C4×#624C2212yes—
90C4×#624C2211yescharacteristic
91C4×D3×Dic3C2212yes—
92C4×D3×Dic3C2212yes—
93C4×D3×Dic3C2212yes—
94#63874C2211yescharacteristic
95#63874C2212yescomplemented
96#63861C2212yescomplemented
97#63858C2212yescomplemented
98#63855C2212yes—
99#63855C2212yescomplemented
100#63855C2212yescomplemented
101#63854C2212yes—
102#63848C2212yescomplemented
103#63847C2212yescomplemented
104#63846C2212yescomplemented
105#63845C2212yescomplemented
106#63840C2211yescharacteristic, complemented
107#63839C2212yescomplemented
108C3×C4×#41—32no—
109#5832—32no—
110#5828—32no—
111#5580—32no—
112#5580—32no—
113#5578—32no—
114#5578—32no—
115#5557—32no—
116#5557—32no—
117#5548—32no—
118#5548—32no—
119#5547—32no—
120#5547—32no—
121#5547—32no—
122#5547—32no—
123#5538—32no—
124#5538—32no—
125#5538—32no—
126#5538—32no—
127#5528—32no—
128#5528—32no—
129#5528—32no—
130#5528—32no—
131#5524—32no—
132#5517—32no—
133C4×#235—32no—
134C4×#235—32no—
135C4×#235—32no—
136C4×#235—32no—
137C4×#235—61no—
138C4×#235D312yescomplemented
139C2×C42×D3—32no—
140C22×D32C2311yescharacteristic
141C22×C32×C4C2312yes—
142C22×C32×C4C2311yescharacteristic
143C2×#638C2311yescharacteristic
144C2×#638C2311yescharacteristic
145#3828—24no—
146C2×C4⋊(C3⋊D3)C2311yescharacteristic
147C2×C4×C3⋊D3C2312yes—
148C2×C4×C3⋊D3C2312yes—
149C2×C4×C3⋊D3C2311yescharacteristic
150C2×C4×C3⋊D3C2311yescharacteristic
151C2×#634C2311yescharacteristic
152C2×C3×#67C2312yes—
153C2×C3×#67C2312yes—
154C3×#235—28no—
155C2×C3×D12C2312yes—
156C2×C3×C4×D3C2312yes—
157C2×C3×C4×D3C2312yes—
158C2×C3×C4×D3C2312yes—
159C2×C3×C4×D3C2312yes—
160C2×C3×C4×D3C2312yes—
161C2×C3×C4×D3C2312yes—
162C2×C3×Dic6C2312yes—
163C2×#627C2312yes—
164C2×#627C2311yescharacteristic
165C2×#626C2312yes—
166C2×#626C2312yes—
167C2×#626C2312yes—
168C2×#625C2311yescharacteristic
169C2×#625C2312yes—
170C2×#624C2311yescharacteristic
171C2×#624C2312yes—
172C2×D3×Dic3C2312yes—
173C2×D3×Dic3C2312yes—
174C2×D3×Dic3C2312yes—
175C4×D32—24no—
176C4×D32—28no—
177#3798—24no—
178#3798—28no—
179C32×C42C2312yes—
180C32×C42C2311yescharacteristic
181C32×C42C2311yescharacteristic
182#3757C2312yes—
183#3752C2312yes—
184#3752C2312yes—
185C4⋊(C3⋊Dic3)C2312yes—
186#3750C2312yes—
187#3750C2312yes—
188C4×C3⋊Dic3C2312yes—
189C4×C3⋊Dic3C2312yes—
190C4×C3⋊Dic3C2311yescharacteristic
191C4×C3⋊Dic3C2311yescharacteristic
192C3×#217C2312yes—
193C3×#217C2312yes—
194C3×(C2×D3)⋊C4C2312yes—
195C3×(C2×D3)⋊C4C2312yes—
196C3×(C2×D3)⋊C4C2312yes—
197C3×(C2×D3)⋊C4C2312yes—
198C3×C4⋊Dic3C2312yes—
199C3×C4⋊Dic3C2312yes—
200C3×Dic3⋊C4C2312yes—
201C3×Dic3⋊C4C2312yes—
202C3×Dic3⋊C4C2312yes—
203C3×Dic3⋊C4C2312yes—
204C3×C4×Dic3C2312yes—
205C3×C4×Dic3C2312yes—
206C3×C4×Dic3C2312yes—
207C3×C4×Dic3C2312yes—
208C3×C4×Dic3C2312yes—
209C3×C4×Dic3C2312yes—
210#3724C2312yes—
211#3724C2312yes—
212#3724C2312yes—
213Dic3⋊Dic3C2312yes—
214Dic3⋊Dic3C2312yes—
215Dic3⋊Dic3C2312yes—
216Dic3⋊Dic3C2312yes—
217Dic3⋊Dic3C2312yes—
218Dic3⋊Dic3C2312yes—
219#3722C2312yes—
220#3722C2312yes—
221#3722C2311yescharacteristic
222#3722C2311yescharacteristic
223(C2×D3)⋊Dic3C2312yes—
224(C2×D3)⋊Dic3C2312yes—
225(C2×D3)⋊Dic3C2312yes—
226(C2×D3)⋊Dic3C2312yes—
227(C2×D3)⋊Dic3C2312yes—
228(C2×D3)⋊Dic3C2312yes—
229Dic32C2311yescharacteristic
230Dic32C2312yes—
231Dic32C2311yescharacteristic
232Dic32C2312yes—
233#3444—91noSylow
234C2×C3×#41—32no—
235C2×#235—32no—
236C2×#235—32no—
237C2×#235—32no—
238C2×#235—32no—
239C2×#235—61no—
240C2×#235C2×D312yes—
241C22×C4×D3—32no—
242C22×C4×D3—32no—
243C22×C4×D3—32no—
244C3×C4×Q8—32no—
245C3×C4×Q8—32no—
246C3×C4×D4—32no—
247C3×C4×D4—32no—
248C3×C4×D4—32no—
249C3×C4×D4—32no—
250C3×C4×D4—32no—
251C3×C4×D4—32no—
252C3×#117—32no—
253C3×#117—32no—
254C3×#117—32no—
255C2×C3×C42—21no—
256C2×C3×C42—32no—
257C2×C3×C42—32no—
258C2×C3×C42C2×D312yescomplemented
259#947—32no—
260#946—32no—
261#946—32no—
262#944—32no—
263#940—32no—
264#939—32no—
265#939—32no—
266#939—32no—
267#939—32no—
268#938—32no—
269#938—32no—
270#937—32no—
271#937—32no—
272#936—32no—
273#935—32no—
274#935—32no—
275C4×#67—32no—
276C4×#67—32no—
277C4×#67—32no—
278C4×#67—32no—
279C4×#67—32no—
280C4×#67—32no—
281C4×#67—32no—
282C4×#67—32no—
283C4×#67—32no—
284C4×#67—32no—
285C4×#67—32no—
286C4×#67—32no—
287C4×#67—32no—
288C4×#67—32no—
289C4×#67—32no—
290C4×#67—32no—
291C4×#67—62no—
292C4×#67—62no—
293C4×#67C2×D312yes—
294C4×#67C2×D312yes—
295C4×#67C2×D312yescomplemented
296C4×#67C2×D312yescomplemented
297#926—32no—
298#926—32no—
299#926—32no—
300#926—32no—
301#926—61no—
302#926C2×D312yescomplemented
303C2×C4×Dic3—32no—
304C2×C4×Dic3—32no—
305C2×C4×Dic3—32no—
306#898—32no—
307#898—32no—
308#898—32no—
309#898—32no—
310#897—32no—
311#897—32no—
312#896—32no—
313#896—32no—
314#896—32no—
315#896—32no—
316#895—32no—
317#895—32no—
318#894—32no—
319#894—32no—
320#894—32no—
321#894—32no—
322#890—32no—
323#890—32no—
324#889—32no—
325#889—32no—
326#889—32no—
327#889—32no—
328#888—32no—
329#888—32no—
330#886—32no—
331#886—32no—
332#885—32no—
333#885—32no—
334#885—32no—
335#885—32no—
336#884—32no—
337#884—32no—
338#884—32no—
339#884—32no—
340#883—32no—
341#883—32no—
342#883—32no—
343#883—32no—
344#882—32no—
345#882—32no—
346#879—32no—
347#879—32no—
348#879—32no—
349#879—32no—
350#878—32no—
351#878—32no—
352#878—32no—
353#878—32no—
354C4×D12—32no—
355C4×D12—32no—
356C4×D12—32no—
357C4×D12—32no—
358C4×D12—32no—
359C4×D12—32no—
360C4×D12—32no—
361C4×D12—32no—
362C4×D12—62no—
363C4×D12C2×D312yes—
364C4×D12C2×D312yes—
365#872—32no—
366#872—32no—
367#872—32no—
368#872—32no—
369#872—32no—
370#872—32no—
371#872—32no—
372#872—32no—
373#872—61no—
374#872—61no—
375#872C2×D312yes—
376#872C2×D312yescomplemented
377C42×D3—32no—
378C42×D3—32no—
379C42×D3—32no—
380C42×D3—32no—
381C42×D3—32no—
382C42×D3—32no—
383C42×D3—32no—
384C42×D3—32no—
385C42×D3—61no—
386C42×D3—61no—
387C42×D3C2×D312yes—
388C42×D3C2×D312yescomplemented
389C4×Dic6—32no—
390C4×Dic6—32no—
391C4×Dic6—32no—
392C4×Dic6—32no—
393C4×Dic6—32no—
394C4×Dic6—32no—
395C4×Dic6—32no—
396C4×Dic6—32no—
397C4×Dic6—62no—
398C4×Dic6C2×D312yescomplemented
399C4×Dic6C2×D312yescomplemented
400C23×C32C2411yescharacteristic
401C22×C3⋊D3C2411yescharacteristic
402C22×C3⋊D3C2411yescharacteristic
403C22×C3×D3C2412yes—
404C22×C3×D3C2412yes—
405C2×D32—22no—
406C2×D32—24no—
407C2×C32×C4—22no—
408C2×C32×C4—24no—
409C2×C32×C4C2411yescharacteristic
410C2×C32×C4C2412yes—
411C2×C32×C4C2412yes—
412C2×C32×C4C2411yescharacteristic
413#638—22no—
414#638—22no—
415C2×C3⋊Dic3C2412yes—
416C2×C3⋊Dic3C2411yescharacteristic
417C2×C3⋊Dic3C2412yes—
418C2×C3⋊Dic3C2411yescharacteristic
419C4⋊(C3⋊D3)—22no—
420C4×C3⋊D3—22no—
421C4×C3⋊D3—24no—
422C4×C3⋊D3—24no—
423C4×C3⋊D3#4114yescomplemented
424#634—22no—
425C3×#67—24no—
426C3×#67—24no—
427C2×C3×Dic3C2412yes—
428C2×C3×Dic3C2412yes—
429C2×C3×Dic3C2412yes—
430C2×C3×Dic3C2412yes—
431C2×C3×Dic3C2412yes—
432C2×C3×Dic3C2412yes—
433C3×D12—24no—
434C3×C4×D3—24no—
435C3×C4×D3—24no—
436C3×C4×D3—24no—
437C3×C4×D3—24no—
438C3×C4×D3—24no—
439C3×C4×D3#4118yescomplemented
440C3×Dic6—24no—
441#627—22no—
442#627—24no—
443#626—24no—
444#626—24no—
445#626—24no—
446#625—24no—
447#625—22no—
448#624—22no—
449#624—24no—
450D3×Dic3—24no—
451D3×Dic3—24no—
452D3×Dic3—24no—
453#533—92no—
454#533—91no—
455#532—91no—
456#532—92no—
457#529—92no—
458#529—92no—
459#529—92no—
460#529—92no—
461#529—92no—
462#529—92no—
463#525—92no—
464#525—91no—
465#525—91no—
466#525—92no—
467C4×#41—32no—
468C4×#41—91no—
469C4×#41—92no—
470C4×#41—91no—
471C22×C42—91no—
472C23×D3—32no—
473C3×#41—68no—
474C2×C3×Q8—32no—
475C2×C3×D4—32no—
476C2×C3×D4—32no—
477C2×C3×D4—32no—
478C22×C3×C4—21no—
479C22×C3×C4—22no—
480C22×C3×C4—32no—
481C22×C3×C4—32no—
482C22×C3×C4—32no—
483C22×C3×C4—32no—
484C22×C3×C4—32no—
485C22×C3×C4—32no—
486C22×C3×C4C22×D312yes—
487C22×C3×C4C22×D312yes—
488C22×C3×C4C22×D312yes—
489C2×#67—32no—
490C2×#67—32no—
491C2×#67—32no—
492C2×#67—32no—
493C2×#67—32no—
494C2×#67—32no—
495C2×#67—32no—
496C2×#67—32no—
497C2×#67—61no—
498C2×#67—61no—
499C2×#67C22×D312yes—
500C2×#67C22×D312yes—
501C22×Dic3—32no—
502C22×Dic3—32no—
503C22×Dic3—32no—
504#235—28no—
505#235—68no—
506#235—68no—
507#235—68no—
508#235—68no—
509#235—68no—
510C2×D12—32no—
511C2×D12—32no—
512C2×D12—32no—
513C2×D12—32no—
514C2×D12—61no—
515C2×D12C22×D312yes—
516C2×C4×D3—32no—
517C2×C4×D3—32no—
518C2×C4×D3—32no—
519C2×C4×D3—32no—
520C2×C4×D3—32no—
521C2×C4×D3—32no—
522C2×C4×D3—32no—
523C2×C4×D3—32no—
524C2×C4×D3—32no—
525C2×C4×D3—32no—
526C2×C4×D3—32no—
527C2×C4×D3—32no—
528C2×C4×D3—61no—
529C2×C4×D3—61no—
530C2×C4×D3—62no—
531C2×C4×D3—62no—
532C2×C4×D3—68no—
533C2×C4×D3—68no—
534C2×C4×D3—68no—
535C2×C4×D3C22×D312yes—
536C2×C4×D3C22×D312yes—
537C2×C4×D3C22×D312yes—
538C2×C4×D3C22×D312yes—
539C2×C4×D3C22×D312yes—
540C2×C4×D3C22×D312yes—
541C2×Dic6—32no—
542C2×Dic6—32no—
543C2×Dic6—32no—
544C2×Dic6—32no—
545C2×Dic6—61no—
546C2×Dic6C22×D312yes—
547C3×C4⋊C4—32no—
548C3×C4⋊C4—32no—
549C3×C4⋊C4—32no—
550C3×C4⋊C4—32no—
551C3×C4⋊C4—32no—
552C3×C4⋊C4—32no—
553C3×C22⋊C4—32no—
554C3×C22⋊C4—32no—
555C3×C22⋊C4—32no—
556C3×C22⋊C4—32no—
557C3×C22⋊C4—32no—
558C3×C22⋊C4—32no—
559C3×C42—22no—
560C3×C42—21no—
561C3×C42—21no—
562C3×C42—32no—
563C3×C42—32no—
564C3×C42—32no—
565C3×C42—32no—
566C3×C42—32no—
567C3×C42—32no—
568C3×C42C22×D312yes—
569C3×C42C22×D312yes—
570C3×C42C22×D312yes—
571C3×C42C22×D312yes—
572#217—32no—
573#217—32no—
574#217—32no—
575#217—32no—
576#217—32no—
577#217—32no—
578#217—32no—
579#217—32no—
580#217—62no—
581#217C22×D312yes—
582#217C22×D312yes—
583(C2×D3)⋊C4—32no—
584(C2×D3)⋊C4—32no—
585(C2×D3)⋊C4—32no—
586(C2×D3)⋊C4—32no—
587(C2×D3)⋊C4—32no—
588(C2×D3)⋊C4—32no—
589(C2×D3)⋊C4—32no—
590(C2×D3)⋊C4—32no—
591(C2×D3)⋊C4—32no—
592(C2×D3)⋊C4—32no—
593(C2×D3)⋊C4—32no—
594(C2×D3)⋊C4—32no—
595(C2×D3)⋊C4—32no—
596(C2×D3)⋊C4—32no—
597(C2×D3)⋊C4—32no—
598(C2×D3)⋊C4—32no—
599(C2×D3)⋊C4—62no—
600(C2×D3)⋊C4—62no—
601(C2×D3)⋊C4C22×D312yes—
602(C2×D3)⋊C4C22×D312yes—
603(C2×D3)⋊C4C22×D312yes—
604(C2×D3)⋊C4C22×D312yes—
605C4⋊Dic3—32no—
606C4⋊Dic3—32no—
607C4⋊Dic3—32no—
608C4⋊Dic3—32no—
609C4⋊Dic3—32no—
610C4⋊Dic3—32no—
611C4⋊Dic3—32no—
612C4⋊Dic3—32no—
613C4⋊Dic3—62no—
614C4⋊Dic3C22×D312yes—
615C4⋊Dic3C22×D312yes—
616Dic3⋊C4—32no—
617Dic3⋊C4—32no—
618Dic3⋊C4—32no—
619Dic3⋊C4—32no—
620Dic3⋊C4—32no—
621Dic3⋊C4—32no—
622Dic3⋊C4—32no—
623Dic3⋊C4—32no—
624Dic3⋊C4—32no—
625Dic3⋊C4—32no—
626Dic3⋊C4—32no—
627Dic3⋊C4—32no—
628Dic3⋊C4—32no—
629Dic3⋊C4—32no—
630Dic3⋊C4—32no—
631Dic3⋊C4—32no—
632Dic3⋊C4—62no—
633Dic3⋊C4—62no—
634Dic3⋊C4C22×D312yes—
635Dic3⋊C4C22×D312yes—
636Dic3⋊C4C22×D312yes—
637Dic3⋊C4C22×D312yes—
638C4×Dic3—32no—
639C4×Dic3—32no—
640C4×Dic3—32no—
641C4×Dic3—32no—
642C4×Dic3—32no—
643C4×Dic3—32no—
644C4×Dic3—32no—
645C4×Dic3—32no—
646C4×Dic3—32no—
647C4×Dic3—32no—
648C4×Dic3—32no—
649C4×Dic3—32no—
650C4×Dic3—62no—
651C4×Dic3—62no—
652C4×Dic3—61no—
653C4×Dic3—61no—
654C4×Dic3C22×D312yes—
655C4×Dic3C22×D312yes—
656C4×Dic3C22×D312yes—
657C4×Dic3C22×D312yes—
658C4×Dic3C22×D312yes—
659C4×Dic3C22×D312yes—
660C22×C32—21no—
661C22×C32—22no—
662C22×C32C2511yescharacteristic
663C2×C3⋊D3—21no—
664C2×C3⋊D3—22no—
665C2×C3⋊D3—22no—
666C2×C3⋊D3C2×#4112yes—
667C2×C3×D3—22no—
668C2×C3×D3—22no—
669C2×C3×D3—22no—
670C2×C3×D3—22no—
671C2×C3×D3—22no—
672C2×C3×D3C2×#4114yes—
673D32—28no—
674C32×C4—21no—
675C32×C4—22no—
676C32×C4C2×#4114yes—
677C32×C4C2×#4112yes—
678C3⋊Dic3—21no—
679C3⋊Dic3—22no—
680C3⋊Dic3—22no—
681C3⋊Dic3C2×#4112yes—
682C3×Dic3—22no—
683C3×Dic3—22no—
684C3×Dic3—22no—
685C3×Dic3—22no—
686C3×Dic3—22no—
687C3×Dic3C2×#4114yes—
688C2×#41—32no—
689C2×#41—92no—
690C2×#41—91no—
691C2×#41—91no—
692C23×C4—92no—
693C23×C4—91no—
694C4⋊Q8—91no—
695C4⋊Q8—92no—
696#127—91no—
697#126—92no—
698#126—92no—
699#126—92no—
700#126—92no—
701#125—92no—
702#125—92no—
703#125—92no—
704#124—91no—
705#124—91no—
706#124—92no—
707#124—92no—
708#123—91no—
709#123—92no—
710#123—92no—
711#123—92no—
712#123—92no—
713#123—91no—
714#123—92no—
715C22⋊Q8—92no—
716C22⋊Q8—92no—
717C22⋊Q8—92no—
718C22⋊Q8—92no—
719C22⋊Q8—92no—
720C22⋊Q8—92no—
721#121—92no—
722#121—92no—
723#121—92no—
724#121—92no—
725#121—92no—
726#121—92no—
727#120—91no—
728#120—92no—
729#120—91no—
730C4×Q8—32no—
731C4×Q8—32no—
732C4×Q8—92no—
733C4×Q8—92no—
734C4×Q8—92no—
735C4×Q8—92no—
736C4×D4—32no—
737C4×D4—32no—
738C4×D4—32no—
739C4×D4—32no—
740C4×D4—32no—
741C4×D4—32no—
742C4×D4—92no—
743C4×D4—92no—
744C4×D4—92no—
745C4×D4—92no—
746C4×D4—92no—
747C4×D4—92no—
748C4×D4—92no—
749C4×D4—92no—
750C4×D4—92no—
751C4×D4—92no—
752C4×D4—92no—
753C4×D4—92no—
754#117—32no—
755#117—32no—
756#117—32no—
757#117—91no—
758#117—92no—
759#117—92no—
760#117—92no—
761#117—92no—
762#117—91no—
763#117—91no—
764#117—91no—
765C2×C42—32no—
766C2×C42—32no—
767C2×C42—92no—
768C2×C42—91no—
769C2×C42—92no—
770C2×C42—92no—
771C2×C42—92no—
772C2×C42—91no—
773C2×C42—91no—
774C2×C42D3211yescharacteristic, complemented
775C23×C3—21no—
776C23×C3—32no—
777C23×C3—32no—
778C23×C3C23×D312yes—
779C22×D3—32no—
780C22×D3—32no—
781C22×D3—61no—
782C22×D3—61no—
783C22×D3—64no—
784C22×D3—64no—
785C22×D3—64no—
786C22×D3C23×D312yes—
787C22×D3C23×D312yes—
788C3×Q8—64no—
789C3×D4—64no—
790C3×D4—64no—
791C3×D4—64no—
792C2×C3×C4—24no—
793C2×C3×C4—24no—
794C2×C3×C4—24no—
795C2×C3×C4—24no—
796C2×C3×C4—22no—
797C2×C3×C4—21no—
798C2×C3×C4—21no—
799C2×C3×C4—22no—
800C2×C3×C4—32no—
801C2×C3×C4—38no—
802C2×C3×C4—32no—
803C2×C3×C4—32no—
804C2×C3×C4—32no—
805C2×C3×C4—32no—
806C2×C3×C4—32no—
807C2×C3×C4—44no—
808C2×C3×C4—64no—
809C2×C3×C4—64no—
810C2×C3×C4—64no—
811C2×C3×C4—64no—
812C2×C3×C4—64no—
813C2×C3×C4C23×D312yes—
814C2×C3×C4C23×D312yes—
815C2×C3×C4C23×D312yes—
816C2×C3×C4C23×D312yes—
817C2×C3×C4C23×D312yes—
818C2×C3×C4C23×D312yes—
819#67—24no—
820#67—24no—
821#67—64no—
822#67—64no—
823#67—64no—
824#67—64no—
825#67—64no—
826#67—64no—
827#67—64no—
828#67—64no—
829#67—64no—
830#67—64no—
831C2×Dic3—32no—
832C2×Dic3—32no—
833C2×Dic3—32no—
834C2×Dic3—32no—
835C2×Dic3—32no—
836C2×Dic3—32no—
837C2×Dic3—61no—
838C2×Dic3—61no—
839C2×Dic3—62no—
840C2×Dic3—62no—
841C2×Dic3—64no—
842C2×Dic3—64no—
843C2×Dic3—64no—
844C2×Dic3C23×D312yes—
845C2×Dic3C23×D312yes—
846C2×Dic3C23×D312yes—
847C2×Dic3C23×D312yes—
848C2×Dic3C23×D312yes—
849C2×Dic3C23×D312yes—
850D12—24no—
851D12—64no—
852D12—64no—
853D12—64no—
854D12—64no—
855D12—64no—
856C4×D3—24no—
857C4×D3—24no—
858C4×D3—24no—
859C4×D3—24no—
860C4×D3—24no—
861C4×D3—38no—
862C4×D3—64no—
863C4×D3—64no—
864C4×D3—64no—
865C4×D3—64no—
866C4×D3—64no—
867C4×D3—64no—
868C4×D3—64no—
869C4×D3—64no—
870C4×D3—64no—
871C4×D3—64no—
872C4×D3—64no—
873C4×D3—64no—
874C4×D3—64no—
875C4×D3—124no—
876C4×D3—124no—
877C4×D3#23518yescomplemented
878Dic6—24no—
879Dic6—64no—
880Dic6—64no—
881Dic6—64no—
882Dic6—64no—
883Dic6—64no—
884C2×C32—41no—
885C2×C32C22×#4112yes—
886C2×C32C22×#4111yescharacteristic
887C3⋊D3—22no—
888C3⋊D3—41no—
889C3×D3—24no—
890C3×D3—42no—
891C24—91no—
892#41—68no—
893#41—184no—
894#41—188no—
895#41—184no—
896C2×Q8—32no—
897C2×Q8—92no—
898C2×Q8—91no—
899C2×Q8—91no—
900C2×D4—32no—
901C2×D4—32no—
902C2×D4—32no—
903C2×D4—92no—
904C2×D4—92no—
905C2×D4—92no—
906C2×D4—92no—
907C2×D4—91no—
908C2×D4—91no—
909C2×D4—91no—
910C2×D4—91no—
911C22×C4—32no—
912C22×C4—32no—
913C22×C4—32no—
914C22×C4—32no—
915C22×C4—32no—
916C22×C4—32no—
917C22×C4—92no—
918C22×C4—91no—
919C22×C4—92no—
920C22×C4—92no—
921C22×C4—92no—
922C22×C4—91no—
923C22×C4—92no—
924C22×C4—92no—
925C22×C4—91no—
926C22×C4—188no—
927C22×C4—184no—
928C22×C4C2×D3212yes—
929C22×C4C2×D3211yescharacteristic
930C4⋊C4—32no—
931C4⋊C4—32no—
932C4⋊C4—32no—
933C4⋊C4—32no—
934C4⋊C4—32no—
935C4⋊C4—32no—
936C4⋊C4—92no—
937C4⋊C4—92no—
938C4⋊C4—92no—
939C4⋊C4—92no—
940C4⋊C4—92no—
941C4⋊C4—92no—
942C4⋊C4—92no—
943C4⋊C4—92no—
944C4⋊C4—92no—
945C4⋊C4—92no—
946C4⋊C4—92no—
947C4⋊C4—92no—
948C22⋊C4—32no—
949C22⋊C4—32no—
950C22⋊C4—32no—
951C22⋊C4—32no—
952C22⋊C4—32no—
953C22⋊C4—32no—
954C22⋊C4—91no—
955C22⋊C4—91no—
956C22⋊C4—92no—
957C22⋊C4—92no—
958C22⋊C4—92no—
959C22⋊C4—92no—
960C22⋊C4—92no—
961C22⋊C4—92no—
962C22⋊C4—92no—
963C22⋊C4—92no—
964C22⋊C4—92no—
965C22⋊C4—92no—
966C22⋊C4—92no—
967C42—32no—
968C42—32no—
969C42—32no—
970C42—32no—
971C42—32no—
972C42—32no—
973C42—92no—
974C42—91no—
975C42—92no—
976C42—91no—
977C42—91no—
978C42—92no—
979C42—92no—
980C42—91no—
981C42C2×D3212yes—
982C42C2×D3211yescharacteristic
983C42C2×D3211yescharacteristic
984C22×C3—22no—
985C22×C3—22no—
986C22×C3—22no—
987C22×C3—22no—
988C22×C3—21no—
989C22×C3—34no—
990C22×C3—42no—
991C22×C3—62no—
992C22×C3—62no—
993C22×C3—62no—
994C22×C3—62no—
995C22×C3—62no—
996C22×C3C24×D312yes—
997C2×D3—22no—
998C2×D3—22no—
999C2×D3—22no—
1000C2×D3—22no—
1001C2×D3—22no—
1002C2×D3—34no—
1003C2×D3—62no—
1004C2×D3—616no—
1005C2×D3—62no—
1006C2×D3—62no—
1007C2×D3—62no—
1008C2×D3—62no—
1009C2×D3—62no—
1010C2×D3—62no—
1011C2×D3—122no—
1012C2×D3—122no—
1013C2×D3C2×#23514yes—
1014C3×C4—22no—
1015C3×C4—22no—
1016C3×C4—22no—
1017C3×C4—22no—
1018C3×C4—24no—
1019C3×C4—22no—
1020C3×C4—34no—
1021C3×C4—42no—
1022C3×C4—62no—
1023C3×C4—62no—
1024C3×C4—62no—
1025C3×C4—62no—
1026C3×C4—62no—
1027C3×C4C2×#23514yes—
1028C3×C4D3×#4114yes—
1029C3×C4D3×#4114yes—
1030Dic3—22no—
1031Dic3—22no—
1032Dic3—22no—
1033Dic3—22no—
1034Dic3—22no—
1035Dic3—34no—
1036Dic3—62no—
1037Dic3—62no—
1038Dic3—62no—
1039Dic3—62no—
1040Dic3—62no—
1041Dic3—62no—
1042Dic3—62no—
1043Dic3—122no—
1044Dic3—122no—
1045Dic3C2×#23514yes—
1046C32#344411yescharacteristic, complemented, Sylow
1047C23—32no—
1048C23—32no—
1049C23—91no—
1050C23—91no—
1051C23—184no—
1052C23—182no—
1053C23C22×D3211yescharacteristic
1054Q8—64no—
1055Q8—182no—
1056Q8—184no—
1057Q8—182no—
1058D4—64no—
1059D4—64no—
1060D4—64no—
1061D4—182no—
1062D4—184no—
1063D4—184no—
1064D4—184no—
1065D4—182no—
1066D4—182no—
1067D4—182no—
1068D4—184no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—32no—
1072C2×C4—38no—
1073C2×C4—32no—
1074C2×C4—32no—
1075C2×C4—32no—
1076C2×C4—32no—
1077C2×C4—32no—
1078C2×C4—64no—
1079C2×C4—64no—
1080C2×C4—64no—
1081C2×C4—64no—
1082C2×C4—64no—
1083C2×C4—91no—
1084C2×C4—94no—
1085C2×C4—92no—
1086C2×C4—92no—
1087C2×C4—91no—
1088C2×C4—184no—
1089C2×C4—184no—
1090C2×C4—182no—
1091C2×C4—184no—
1092C2×C4—184no—
1093C2×C4—184no—
1094C2×C4—184no—
1095C2×C4—182no—
1096C2×C4C22×D3211yescharacteristic
1097C2×C4C22×D3212yes—
1098C2×C4C22×D3212yes—
1099C2×C4C22×D3211yescharacteristic
1100C2×C3—22no—
1101C2×C3—21no—
1102C2×C3—42no—
1103C2×C3—42no—
1104C2×C3—64no—
1105C2×C3—122no—
1106C2×C3C22×#23512yes—
1107C2×C3C2×D3×#4112yes—
1108C2×C3C2×D3×#4112yes—
1109D3—24no—
1110D3—42no—
1111D3—64no—
1112D3—122no—
1113D3—122no—
1114D3—122no—
1115C22—22no—
1116C22—21no—
1117C22—34no—
1118C22—62no—
1119C22—62no—
1120C22—62no—
1121C22—62no—
1122C22—62no—
1123C22—92no—
1124C22—188no—
1125C22—182no—
1126C22—182no—
1127C22—181no—
1128C22C23×D3211yescharacteristic
1129C4—22no—
1130C4—21no—
1131C4—34no—
1132C4—62no—
1133C4—62no—
1134C4—62no—
1135C4—62no—
1136C4—62no—
1137C4—92no—
1138C4—182no—
1139C4—182no—
1140C4—181no—
1141C4D3×#23514yes—
1142C4#6430612yes—
1143C3—21no—
1144C3#8583612yescomplemented
1145C2—41no—
1146C2—64no—
1147C2—122no—
1148C2—182no—
1149C2—361no—
1150C2C2×D3×#23512yes—
1151C2C2×#6430611yescharacteristic
subgroupG/H
centerC42C2×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3444
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C42 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C4×#3828C2semidirect
2. C3×C4×#235C2semidirect
3. #10595076C2semidirect
4. #10595060C2semidirect
5. #10595017C2semidirect
6. #10595003C2semidirect
7. #10594934C2semidirect
8. #10594933C2semidirect
9. #10594836C2semidirect
10. #10594006C2semidirect
11. #10593997C2semidirect
12. C42×D32C2semidirect
13. C4×#3798C2semidirect
14. C4×#3798C2semidirect
15. #10593935C2semidirect
16. #10593934C2semidirect
17. #10593926C2semidirect
18. #10593911C2semidirect
19. #10593910C2semidirect
27. C2×C32×C42C22semidirect
29. C4×#638C22semidirect
30. #64135C22semidirect
33. #64081C22semidirect
35. C42×C3⋊D3C22semidirect
36. C4×#634C22semidirect
39. C3×C4×#67C22semidirect
40. C3×C4×#67C22semidirect
41. C3×#926C22semidirect
45. C3×#872C22semidirect
47. C3×C42×D3C22semidirect
48. C3×C4×Dic6C22semidirect
49. C3×C4×Dic6C22semidirect
51. #63979C22semidirect
56. #63959C22semidirect
58. #63956C22semidirect
59. #63953C22semidirect
62. C4×#627C22semidirect
63. C4×#627C22semidirect
64. C4×#627C22semidirect
65. #63913C22semidirect
67. #63907C22semidirect
72. C4×#626C22semidirect
73. C4×#626C22semidirect
76. C4×#625C22semidirect
95. #63874C22semidirect
96. #63861C22semidirect
97. #63858C22semidirect
99. #63855C22semidirect
100. #63855C22semidirect
102. #63848C22semidirect
103. #63847C22semidirect
104. #63846C22semidirect
105. #63845C22semidirect
106. #63840C22semidirect
107. #63839C22semidirect
138. C4×#235D3semidirect
258. C2×C3×C42C2×D3semidirect
295. C4×#67C2×D3semidirect
296. C4×#67C2×D3semidirect
302. #926C2×D3semidirect
376. #872C2×D3semidirect
388. C42×D3C2×D3semidirect
398. C4×Dic6C2×D3semidirect
399. C4×Dic6C2×D3semidirect
423. C4×C3⋊D3#41semidirect
439. C3×C4×D3#41semidirect
774. C2×C42D32semidirect
877. C4×D3#235semidirect
1046. C32#3444semidirect
1144. C3#85836semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C3×C4×#2352
#105950762
#105950602
#105950172
#105950032
#105949342
#105949332
#105948362
#105940062
#105939972
C42×D322
C4×#37982
#105939352
#105939342
#105939262
#105939112
#105939102
#858363