Finite Group Databasebeta

← #11904190

Subgroups — #11904190

Order 1152.

2299 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595941C211yesmaximal, characteristic, complemented
2C3×C4×#235C211yesmaximal, characteristic, complemented
3C3×C4×#235C211yesmaximal, characteristic, complemented
4#10594939C212yesmaximal, complemented
5#10594934C214yesmaximal, complemented
6#10594899C212yesmaximal, complemented
7#10594887C212yesmaximal, complemented
8#10594840C212yesmaximal, complemented
9#10593974C212yesmaximal, complemented
10#10593915C214yesmaximal, complemented
11Dic6×D12C211yesmaximal, characteristic, complemented
12#10593895C211yesmaximal, characteristic, complemented
13C4×#3795C212yesmaximal, complemented
14C4×D3×Dic6C212yesmaximal, complemented
15#10593879C211yesmaximal, characteristic, complemented
16#10593873C212yesmaximal, complemented
17#10593860C211yesmaximal, characteristic, complemented
18#85844—31nomaximal
19#85826—31nomaximal
20C2×C3×#235C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C2×#3795C2212yes—
23C2×D3×Dic6C2212yes—
24C2×C32×C42C2211yescharacteristic
25#64135C2212yes—
26#64133C2212yes—
27#64133C2212yes—
28#64079C2212yes—
29#64078C2211yescharacteristic
30#64078C2211yescharacteristic
31C4×#634C2212yes—
32C4×#634C2212yes—
33C3×C4×#67C2212yes—
34C3×C4×#67C2212yes—
35C3×C4×#67C2212yes—
36C3×C4×#67C2212yes—
37C3×#926C2211yescharacteristic
38C3×#926C2211yescharacteristic
39C3×C4×D12C2211yescharacteristic
40C3×C4×D12C2211yescharacteristic
41C3×C4×D12C2211yescharacteristic
42C3×C4×D12C2211yescharacteristic
43C3×#872C2212yes—
44C3×#872C2212yes—
45C3×C42×D3C2212yes—
46C3×C42×D3C2212yes—
47C3×C4×Dic6C2211yescharacteristic
48C3×C4×Dic6C2211yescharacteristic
49C3×C4×Dic6C2211yescharacteristic
50C3×C4×Dic6C2211yescharacteristic
51#63970C2214yes—
52#63969C2214yes—
53#63959C2214yes—
54#63956C2214yes—
55#63918C2212yes—
56C4×#627C2214yes—
57#63908C2212yes—
58#63905C2214yes—
59C4×#625C2214yes—
60#63893C2214yes—
61Dic3×D12C2212yes—
62#63891C2214yes—
63D3×C4⋊Dic3C2212yes—
64#63879C2214yes—
65#63877C2214yes—
66D3×Dic3⋊C4C2214yes—
67C4×D3×Dic3C2214yes—
68#63869C2212yes—
69#63867C2214yes—
70#63866C2212yes—
71#63861C2214yes—
72#63860C2212yes—
73#63859C2214yes—
74#63857C2212yes—
75#63857C2212yes—
76#63856C2212yes—
77#63855C2214yes—
78#63851C2214yes—
79#63845C2214yes—
80#63844C2212yes—
81#63844C2212yes—
82Dic3×Dic6C2212yes—
83#63841C2212yes—
84#63837C2214yes—
85C3×C4×#41—31no—
86C3×C4×#41—31no—
87#5831—32no—
88#5824—32no—
89#5584—31no—
90#5578—32no—
91Q8×D12—31no—
92C4×D3×Q8—32no—
93#5570—31no—
94#5567—31no—
95#5557—34no—
96#5557—32no—
97#5555—31no—
98#5552—32no—
99#5551—32no—
100#5551—31no—
101#5542—32no—
102#5542—31no—
103#5541—32no—
104#5538—34no—
105D4×Dic6—31no—
106C4×#237—32no—
107#5533—32no—
108#5531—34no—
109#5529—32no—
110#5529—34no—
111#5479—32no—
112C4×#235—32no—
113C4×#235D311yescharacteristic, complemented
114C4×#235D311yescharacteristic, complemented
115#5470—31no—
116#5470—31no—
117#5470—32no—
118#5470—61no—
119C2×C4×Dic6—32no—
120C22×C32×C4C2311yescharacteristic
121C22×C32×C4C2311yescharacteristic
122C22×C32×C4C2311yescharacteristic
123C2×#634C2312yes—
124C2×#634C2312yes—
125C2×C3×#67C2312yes—
126C2×C3×#67C2312yes—
127C3×#235—24no—
128C3×#235—24no—
129C2×C3×D12C2311yescharacteristic
130C2×C3×D12C2311yescharacteristic
131C2×C3×C4×D3C2312yes—
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2312yes—
134C2×C3×C4×D3C2312yes—
135C2×C3×C4×D3C2312yes—
136C2×C3×C4×D3C2312yes—
137C2×C3×Dic6C2311yescharacteristic
138C2×C3×Dic6C2311yescharacteristic
139C2×#627C2314yes—
140C2×#625C2314yes—
141C2×D3×Dic3C2314yes—
142C2×D3×Dic3C2314yes—
143#3795—28no—
144D3×Dic6—28no—
145C32×C42C2311yescharacteristic
146C32×C42C2311yescharacteristic
147C32×C42C2311yescharacteristic
148C32×C42C2311yescharacteristic
149#3757C2314yes—
150C4⋊(C3⋊Dic3)C2312yes—
151C4⋊(C3⋊Dic3)C2312yes—
152C4⋊(C3⋊Dic3)C2312yes—
153C4⋊(C3⋊Dic3)C2312yes—
154#3750C2314yes—
155#3750C2314yes—
156C4×C3⋊Dic3C2314yes—
157C3×#217C2312yes—
158C3×#217C2312yes—
159C3×(C2×D3)⋊C4C2312yes—
160C3×(C2×D3)⋊C4C2312yes—
161C3×(C2×D3)⋊C4C2312yes—
162C3×(C2×D3)⋊C4C2312yes—
163C3×C4⋊Dic3C2311yescharacteristic
164C3×C4⋊Dic3C2311yescharacteristic
165C3×C4⋊Dic3C2311yescharacteristic
166C3×C4⋊Dic3C2311yescharacteristic
167C3×Dic3⋊C4C2312yes—
168C3×Dic3⋊C4C2312yes—
169C3×Dic3⋊C4C2312yes—
170C3×Dic3⋊C4C2312yes—
171C3×C4×Dic3C2312yes—
172C3×C4×Dic3C2312yes—
173C3×C4×Dic3C2312yes—
174C3×C4×Dic3C2312yes—
175C3×C4×Dic3C2312yes—
176C3×C4×Dic3C2312yes—
177#3724C2314yes—
178#3724C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187Dic32C2314yes—
188Dic32C2314yes—
189#3482—91noSylow
190C2×C3×#41—31no—
191C2×C3×#41—31no—
192C2×D3×Q8—32no—
193C2×#237—32no—
194C2×#235—32no—
195C2×#235C2×D311yescharacteristic
196C2×#235C2×D311yescharacteristic
197C22×Dic6—32no—
198C3×C4×Q8—31no—
199C3×C4×Q8—31no—
200C3×C4×Q8—31no—
201C3×C4×Q8—31no—
202C3×C4×D4—32no—
203C3×C4×D4—32no—
204C3×C4×D4—32no—
205C3×C4×D4—32no—
206C3×C4×D4—31no—
207C3×C4×D4—31no—
208C3×C4×D4—31no—
209C3×C4×D4—31no—
210C3×#117—31no—
211C3×#117—31no—
212C3×#117—32no—
213C3×#117—32no—
214C2×C3×C42—21no—
215C2×C3×C42—32no—
216C2×C3×C42—32no—
217C2×C3×C42C2×D311yescharacteristic
218C2×C3×C42C2×D311yescharacteristic
219#946—32no—
220Q8×Dic3—32no—
221#944—32no—
222#939—34no—
223#938—34no—
224#938—32no—
225#936—34no—
226#936—32no—
227#935—34no—
228D4×Dic3—32no—
229#930—32no—
230#929—34no—
231C4×#67—34no—
232C4×#67—34no—
233C4×#67—34no—
234C4×#67C2×D312yes—
235C4×#67C2×D312yes—
236C4×#67C2×D312yes—
237C4×#67C2×D312yes—
238#926—32no—
239#926—32no—
240#926—32no—
241#926—34no—
242#926—62no—
243#926C2×D311yescharacteristic
244#926C2×D311yescharacteristic
245C2×C4⋊Dic3—32no—
246#924—32no—
247#924—32no—
248#924—32no—
249#924—32no—
250#924—32no—
251#924—32no—
252#924—32no—
253#924—34no—
254#924—62no—
255#924—62no—
256C2×Dic3⋊C4—34no—
257C2×C4×Dic3—34no—
258#898—34no—
259#897—32no—
260#897—32no—
261#897—34no—
262#896—34no—
263#892—32no—
264D3×C4⋊C4—34no—
265D3×C4⋊C4—32no—
266#890—34no—
267#890—32no—
268#889—34no—
269#889—34no—
270#888—32no—
271#887—34no—
272#887—32no—
273#887—32no—
274#886—34no—
275#885—34no—
276#883—34no—
277#883—34no—
278#883—34no—
279#67⋊C4—34no—
280#879—34no—
281#879—34no—
282#879—34no—
283#879—34no—
284#878—34no—
285#877—34no—
286#876—34no—
287#875—32no—
288C4×D12—32no—
289C4×D12C2×D311yescharacteristic
290C4×D12C2×D311yescharacteristic
291C4×D12C2×D311yescharacteristic
292C4×D12C2×D311yescharacteristic
293#872—34no—
294#872—34no—
295#872C2×D312yes—
296#872C2×D312yes—
297C42×D3—34no—
298C42×D3C2×D312yes—
299C42×D3C2×D312yes—
300#870—32no—
301#870—32no—
302#870—32no—
303#870—34no—
304#870—62no—
305#869—32no—
306#869—31no—
307#869—31no—
308#869—31no—
309#869—31no—
310#869—32no—
311#869—61no—
312#869—61no—
313C4×Dic6—32no—
314C4×Dic6—32no—
315C4×Dic6—32no—
316C4×Dic6—32no—
317C4×Dic6—32no—
318C4×Dic6—32no—
319C4×Dic6—32no—
320C4×Dic6—34no—
321C4×Dic6—34no—
322C4×Dic6—34no—
323C4×Dic6—62no—
324C4×Dic6—62no—
325C4×Dic6C2×D311yescharacteristic
326C4×Dic6C2×D311yescharacteristic
327C4×Dic6C2×D311yescharacteristic
328C4×Dic6C2×D311yescharacteristic
329C23×C32C2411yescharacteristic
330C22×C3×D3C2412yes—
331C22×C3×D3C2412yes—
332C2×C32×C4—22no—
333C2×C32×C4—22no—
334C2×C32×C4—22no—
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C32×C4C2411yescharacteristic
341C2×C3⋊Dic3C2414yes—
342C2×C3⋊Dic3C2414yes—
343#634—24no—
344#634—24no—
345C3×#67—24no—
346C3×#67—24no—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C3×D12—22no—
354C3×D12#4114yescomplemented
355C3×C4×D3—24no—
356C3×C4×D3—24no—
357C3×C4×D3—24no—
358C3×C4×D3—24no—
359C3×C4×D3—24no—
360C3×C4×D3—24no—
361C3×Dic6—22no—
362C3×Dic6#4114yescomplemented
363#627—28no—
364#625—28no—
365D3×Dic3—28no—
366D3×Dic3—28no—
367#557—91no—
368#556—92no—
369#556—91no—
370#552—94no—
371#552—92no—
372D4×Q8—91no—
373#548—92no—
374#547—91no—
375#547—92no—
376#533—92no—
377#533—91no—
378#529—92no—
379#529—94no—
380C4×#41—31no—
381C4×#41—31no—
382C4×#41—92no—
383C2×C4×Q8—92no—
384C3×#41—64no—
385C3×#41—64no—
386C2×C3×Q8—31no—
387C2×C3×Q8—31no—
388C2×C3×D4—32no—
389C2×C3×D4—32no—
390C2×C3×D4—31no—
391C2×C3×D4—31no—
392C22×C3×C4—21no—
393C22×C3×C4—21no—
394C22×C3×C4—21no—
395C22×C3×C4—32no—
396C22×C3×C4—32no—
397C22×C3×C4—32no—
398C22×C3×C4—32no—
399C22×C3×C4—32no—
400C22×C3×C4—32no—
401C22×C3×C4C22×D311yescharacteristic
402C22×C3×C4C22×D311yescharacteristic
403C22×C3×C4C22×D311yescharacteristic
404C22×C3×C4C22×D311yescharacteristic
405C22×C3×C4C22×D311yescharacteristic
406C22×C3×C4C22×D311yescharacteristic
407C2×#67—34no—
408C2×#67—34no—
409C2×#67C22×D312yes—
410C2×#67C22×D312yes—
411C22×Dic3—34no—
412C22×Dic3—34no—
413D3×Q8—68no—
414#237—68no—
415#235—24no—
416#235—24no—
417#235—68no—
418C2×D12C22×D311yescharacteristic
419C2×D12C22×D311yescharacteristic
420C2×C4×D3—34no—
421C2×C4×D3—34no—
422C2×C4×D3C22×D312yes—
423C2×C4×D3C22×D312yes—
424C2×C4×D3C22×D312yes—
425C2×C4×D3C22×D312yes—
426C2×C4×D3C22×D312yes—
427C2×C4×D3C22×D312yes—
428C2×Dic6—32no—
429C2×Dic6—32no—
430C2×Dic6—32no—
431C2×Dic6—32no—
432C2×Dic6—34no—
433C2×Dic6—34no—
434C2×Dic6—62no—
435C2×Dic6—62no—
436C2×Dic6—68no—
437C2×Dic6C22×D311yescharacteristic
438C2×Dic6C22×D311yescharacteristic
439C3×C4⋊C4—32no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—31no—
443C3×C4⋊C4—32no—
444C3×C4⋊C4—32no—
445C3×C4⋊C4—32no—
446C3×C4⋊C4—31no—
447C3×C22⋊C4—32no—
448C3×C22⋊C4—32no—
449C3×C22⋊C4—32no—
450C3×C22⋊C4—32no—
451C3×C22⋊C4—32no—
452C3×C22⋊C4—32no—
453C3×C42—21no—
454C3×C42—21no—
455C3×C42—21no—
456C3×C42—21no—
457C3×C42—32no—
458C3×C42—32no—
459C3×C42—32no—
460C3×C42—32no—
461C3×C42—32no—
462C3×C42—32no—
463C3×C42C22×D311yescharacteristic
464C3×C42C22×D311yescharacteristic
465C3×C42C22×D311yescharacteristic
466C3×C42C22×D311yescharacteristic
467C3×C42C22×D311yescharacteristic
468C3×C42C22×D311yescharacteristic
469C3×C42C22×D311yescharacteristic
470C3×C42C22×D311yescharacteristic
471#217—34no—
472#217—34no—
473#217—34no—
474#217—34no—
475#217—34no—
476#217—34no—
477#217—64no—
478#217C22×D312yes—
479#217C22×D312yes—
480(C2×D3)⋊C4—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4C22×D312yes—
485(C2×D3)⋊C4C22×D312yes—
486(C2×D3)⋊C4C22×D312yes—
487(C2×D3)⋊C4C22×D312yes—
488C4⋊Dic3—32no—
489C4⋊Dic3—32no—
490C4⋊Dic3—32no—
491C4⋊Dic3—32no—
492C4⋊Dic3—32no—
493C4⋊Dic3—32no—
494C4⋊Dic3—32no—
495C4⋊Dic3—32no—
496C4⋊Dic3—34no—
497C4⋊Dic3—34no—
498C4⋊Dic3—34no—
499C4⋊Dic3—34no—
500C4⋊Dic3—62no—
501C4⋊Dic3—62no—
502C4⋊Dic3—62no—
503C4⋊Dic3—62no—
504C4⋊Dic3C22×D311yescharacteristic
505C4⋊Dic3C22×D311yescharacteristic
506C4⋊Dic3C22×D311yescharacteristic
507C4⋊Dic3C22×D311yescharacteristic
508Dic3⋊C4—34no—
509Dic3⋊C4—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—34no—
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—34no—
519Dic3⋊C4—34no—
520Dic3⋊C4—64no—
521Dic3⋊C4—64no—
522Dic3⋊C4C22×D312yes—
523Dic3⋊C4C22×D312yes—
524Dic3⋊C4C22×D312yes—
525Dic3⋊C4C22×D312yes—
526C4×Dic3—34no—
527C4×Dic3—34no—
528C4×Dic3—34no—
529C4×Dic3—34no—
530C4×Dic3—34no—
531C4×Dic3—34no—
532C4×Dic3—64no—
533C4×Dic3C22×D312yes—
534C4×Dic3C22×D312yes—
535C4×Dic3C22×D312yes—
536C4×Dic3C22×D312yes—
537C4×Dic3C22×D312yes—
538C4×Dic3C22×D312yes—
539C22×C32—21no—
540C22×C32—21no—
541C22×C32—21no—
542C22×C32C2511yescharacteristic
543C2×C3×D3—22no—
544C2×C3×D3—22no—
545C2×C3×D3—22no—
546C2×C3×D3—22no—
547C2×C3×D3—22no—
548C2×C3×D3C2×#4114yes—
549C32×C4—21no—
550C32×C4—21no—
551C32×C4—21no—
552C32×C4C2×#4112yes—
553C32×C4C2×#4112yes—
554C32×C42−1+412yes—
555C3⋊Dic3—24no—
556C3⋊Dic3—24no—
557C3×Dic3—22no—
558C3×Dic3—22no—
559C3×Dic3—22no—
560C3×Dic3—22no—
561C3×Dic3—22no—
562C3×Dic3C2×#4114yes—
563C2×#41—31no—
564C2×#41—31no—
565C2×#41—92no—
566C22×Q8—92no—
567C4⋊Q8—92no—
568C4⋊Q8—92no—
569C4⋊Q8—91no—
570C4⋊Q8—91no—
571#126—94no—
572#126—94no—
573#126—94no—
574#125—92no—
575#125—94no—
576#125—94no—
577#125—92no—
578#124—92no—
579#124—94no—
580#123—94no—
581#123—94no—
582#123—94no—
583C22⋊Q8—94no—
584C22⋊Q8—92no—
585C22⋊Q8—92no—
586C22⋊Q8—94no—
587C22⋊Q8—92no—
588C22⋊Q8—92no—
589C22⋊Q8—92no—
590#121—92no—
591#121—94no—
592C4×Q8—31no—
593C4×Q8—31no—
594C4×Q8—31no—
595C4×Q8—31no—
596C4×Q8—94no—
597C4×Q8—94no—
598C4×Q8—92no—
599C4×Q8—92no—
600C4×Q8—92no—
601C4×Q8—92no—
602C4×Q8—92no—
603C4×D4—32no—
604C4×D4—32no—
605C4×D4—32no—
606C4×D4—32no—
607C4×D4—31no—
608C4×D4—31no—
609C4×D4—31no—
610C4×D4—31no—
611C4×D4—92no—
612C4×D4—94no—
613C4×D4—94no—
614#117—31no—
615#117—31no—
616#117—32no—
617#117—32no—
618#117—94no—
619#117—94no—
620#117—92no—
621#117—92no—
622C2×C4⋊C4—94no—
623C2×C4⋊C4—92no—
624C2×C42—32no—
625C2×C42—32no—
626C2×C42—94no—
627C2×C42D3211yescharacteristic
628C23×C3—21no—
629C23×C3—32no—
630C23×C3—32no—
631C23×C3C23×D311yescharacteristic
632C23×C3C23×D311yescharacteristic
633C22×D3C23×D312yes—
634C22×D3C23×D312yes—
635C3×Q8—34no—
636C3×Q8—62no—
637C3×D4—34no—
638C3×D4—64no—
639C3×D4—64no—
640C3×D4—62no—
641C2×C3×C4—24no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
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—32no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—32no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—42no—
661C2×C3×C4—42no—
662C2×C3×C4—64no—
663C2×C3×C4—64no—
664C2×C3×C4—64no—
665C2×C3×C4—64no—
666C2×C3×C4—64no—
667C2×C3×C4—64no—
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D311yescharacteristic
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C23×D311yescharacteristic
672C2×C3×C4C23×D311yescharacteristic
673C2×C3×C4C23×D311yescharacteristic
674C2×C3×C4C23×D311yescharacteristic
675C2×C3×C4C23×D311yescharacteristic
676C2×C3×C4C23×D311yescharacteristic
677C2×C3×C4C23×D311yescharacteristic
678C2×C3×C4C23×D311yescharacteristic
679C2×C3×C4C23×D311yescharacteristic
680#67—24no—
681#67—24no—
682#67—68no—
683#67—68no—
684C2×Dic3—34no—
685C2×Dic3—34no—
686C2×Dic3—34no—
687C2×Dic3—34no—
688C2×Dic3—64no—
689C2×Dic3—64no—
690C2×Dic3—68no—
691C2×Dic3—68no—
692C2×Dic3C23×D312yes—
693C2×Dic3C23×D312yes—
694C2×Dic3C23×D312yes—
695C2×Dic3C23×D312yes—
696C2×Dic3C23×D312yes—
697C2×Dic3C23×D312yes—
698D12—22no—
699D12#23514yescomplemented
700C4×D3—24no—
701C4×D3—24no—
702C4×D3—24no—
703C4×D3—24no—
704C4×D3—24no—
705C4×D3—24no—
706C4×D3—68no—
707C4×D3—68no—
708Dic6—22no—
709Dic6—68no—
710Dic6—64no—
711Dic6—64no—
712Dic6—64no—
713Dic6—64no—
714Dic6—68no—
715Dic6—124no—
716Dic6—124no—
717Dic6#23514yescomplemented
718C2×C32—41no—
719C2×C32C22×#4111yescharacteristic
720C2×C32C22×#4111yescharacteristic
721C2×C32C2×2−1+411yescharacteristic
722C3×D3—24no—
723C3×D3—42no—
724#41—64no—
725#41—64no—
726#41—188no—
727C2×Q8—31no—
728C2×Q8—31no—
729C2×Q8—94no—
730C2×Q8—92no—
731C2×Q8—92no—
732C2×Q8—188no—
733C2×D4—32no—
734C2×D4—32no—
735C2×D4—31no—
736C2×D4—31no—
737C2×D4—94no—
738C22×C4—32no—
739C22×C4—32no—
740C22×C4—32no—
741C22×C4—32no—
742C22×C4—32no—
743C22×C4—32no—
744C22×C4—94no—
745C22×C4—94no—
746C22×C4C2×D3211yescharacteristic
747C22×C4C2×D3211yescharacteristic
748C22×C4C2×D3211yescharacteristic
749C4⋊C4—32no—
750C4⋊C4—31no—
751C4⋊C4—31no—
752C4⋊C4—32no—
753C4⋊C4—32no—
754C4⋊C4—31no—
755C4⋊C4—31no—
756C4⋊C4—32no—
757C4⋊C4—94no—
758C4⋊C4—94no—
759C4⋊C4—94no—
760C4⋊C4—94no—
761C4⋊C4—94no—
762C4⋊C4—94no—
763C4⋊C4—92no—
764C4⋊C4—94no—
765C4⋊C4—94no—
766C4⋊C4—92no—
767C4⋊C4—92no—
768C4⋊C4—92no—
769C22⋊C4—32no—
770C22⋊C4—32no—
771C22⋊C4—32no—
772C22⋊C4—32no—
773C22⋊C4—32no—
774C22⋊C4—32no—
775C22⋊C4—94no—
776C22⋊C4—94no—
777C22⋊C4—94no—
778C22⋊C4—94no—
779C22⋊C4—94no—
780C42—32no—
781C42—32no—
782C42—32no—
783C42—32no—
784C42—32no—
785C42—32no—
786C42—94no—
787C42—94no—
788C42—94no—
789C42C2×D3211yescharacteristic
790C42C2×D3211yescharacteristic
791C42C2×D3211yescharacteristic
792C42C2×D3211yescharacteristic
793C22×C3—22no—
794C22×C3—21no—
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—21no—
798C22×C3—21no—
799C22×C3—21no—
800C22×C3—21no—
801C22×C3—34no—
802C22×C3—41no—
803C22×C3—41no—
804C22×C3—62no—
805C22×C3—62no—
806C22×C3—62no—
807C22×C3—62no—
808C22×C3—62no—
809C22×C3C24×D311yescharacteristic
810C22×C3C24×D311yescharacteristic
811C2×D3—22no—
812C2×D3—22no—
813C2×D3—22no—
814C2×D3—22no—
815C2×D3—22no—
816C2×D3C2×#23514yes—
817C3×C4—22no—
818C3×C4—21no—
819C3×C4—21no—
820C3×C4—21no—
821C3×C4—21no—
822C3×C4—21no—
823C3×C4—21no—
824C3×C4—22no—
825C3×C4—22no—
826C3×C4—22no—
827C3×C4—34no—
828C3×C4—41no—
829C3×C4—41no—
830C3×C4—62no—
831C3×C4—62no—
832C3×C4—62no—
833C3×C4—62no—
834C3×C4—62no—
835C3×C4C2×#23512yes—
836C3×C4C2×#23512yes—
837C3×C4D3×#4112yes—
838C3×C4D3×#4112yes—
839C3×C4#101012yes—
840C3×C4#101012yes—
841Dic3—22no—
842Dic3—22no—
843Dic3—22no—
844Dic3—22no—
845Dic3—22no—
846Dic3—64no—
847Dic3—64no—
848Dic3—64no—
849Dic3—64no—
850Dic3—124no—
851Dic3—124no—
852Dic3C2×#23514yes—
853C32#348211yescharacteristic, complemented, Sylow
854C23—32no—
855C23—32no—
856C23C22×D3211yescharacteristic
857Q8—34no—
858Q8—62no—
859Q8—188no—
860Q8—184no—
861Q8—184no—
862D4—34no—
863D4—64no—
864D4—64no—
865D4—62no—
866D4—188no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—32no—
871C2×C4—32no—
872C2×C4—32no—
873C2×C4—32no—
874C2×C4—32no—
875C2×C4—32no—
876C2×C4—64no—
877C2×C4—64no—
878C2×C4—64no—
879C2×C4—64no—
880C2×C4—64no—
881C2×C4—64no—
882C2×C4—94no—
883C2×C4—94no—
884C2×C4—188no—
885C2×C4—188no—
886C2×C4C22×D3211yescharacteristic
887C2×C4C22×D3211yescharacteristic
888C2×C4C22×D3211yescharacteristic
889C2×C4C22×D3211yescharacteristic
890C2×C4C22×D3211yescharacteristic
891C2×C4C22×D3211yescharacteristic
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—42no—
896C2×C3—41no—
897C2×C3—41no—
898C2×C3—64no—
899C2×C3—122no—
900C2×C3C22×#23511yescharacteristic
901C2×C3C22×#23511yescharacteristic
902C2×C3C2×D3×#4111yescharacteristic
903C2×C3C2×D3×#4111yescharacteristic
904C2×C3C2×#101011yescharacteristic
905C2×C3C2×#101011yescharacteristic
906D3—24no—
907D3—42no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—34no—
912C22—62no—
913C22—62no—
914C22—62no—
915C22—62no—
916C22—62no—
917C22C23×D3211yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—34no—
922C4—62no—
923C4—62no—
924C4—62no—
925C4—62no—
926C4—62no—
927C4—184no—
928C4—184no—
929C4#6429812yes—
930C4D3×#23512yes—
931C4D3×#23512yes—
932C3—21no—
933C3#8582611yescharacteristic, complemented
934C3#8584411yescharacteristic, complemented
935C2—41no—
936C2—64no—
937C2—122no—
938C2C2×#6429811yescharacteristic
939C2C2×D3×#23511yescharacteristic
940C2C2×D3×#23511yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3482
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595941C2semidirect
2. C3×C4×#235C2semidirect
3. C3×C4×#235C2semidirect
4. #10594939C2semidirect
5. #10594934C2semidirect
6. #10594899C2semidirect
7. #10594887C2semidirect
8. #10594840C2semidirect
9. #10593974C2semidirect
10. #10593915C2semidirect
11. Dic6×D12C2semidirect
12. #10593895C2semidirect
13. C4×#3795C2semidirect
14. C4×D3×Dic6C2semidirect
15. #10593879C2semidirect
16. #10593873C2semidirect
17. #10593860C2semidirect
113. C4×#235D3semidirect
114. C4×#235D3semidirect
354. C3×D12#41semidirect
362. C3×Dic6#41semidirect
699. D12#235semidirect
717. Dic6#235semidirect
853. C32#3482semidirect
933. C3#85826semidirect
934. C3#85844semidirect

Maximal subgroups

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

subgroupindex
#105959412
C3×C4×#2352
#105949392
#105949342
#105948992
#105948872
#105948402
#105939742
#105939152
Dic6×D122
#105938952
C4×#37952
C4×D3×Dic62
#105938792
#105938732
#105938602
#858443
#858263