Finite Group Databasebeta

← #11900195

Subgroups — #11900195

Order 1152.

3467 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic
2#10595975C211yesmaximal, characteristic, complemented
3C3×#5504C211yesmaximal, characteristic, complemented
4C2×C3×#893C211yesmaximal, characteristic, complemented
5#10595056C214yesmaximal, complemented
6C4×D3×#67C214yesmaximal, complemented
7#10594982C211yesmaximal, characteristic, complemented
8#10594954C211yesmaximal, characteristic, complemented
9Dic3×#235C211yesmaximal, characteristic, complemented
10#10594606C212yesmaximal, complemented
11#10594605C212yesmaximal, complemented
12#10594604C212yesmaximal, complemented
13D3×#893C212yesmaximal, complemented
14#10594361C212yesmaximal, complemented
15#10594360C212yesmaximal, complemented
16#10594359C212yesmaximal, complemented
17#10594358C212yesmaximal, complemented
18#85886—31nomaximal
19C4×#1004—31nomaximal
20C2×#3828C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C22×C3×C4×D3C2212yescomplemented
24C2×D3×#67C2214yes—
25#64307C4116yescomplemented
26C2×#3802C2212yes—
27C2×D3×D12C2212yes—
28C2×C4×D32C2214yescomplemented
29C2×#3796C2212yes—
30C2×#3795C2212yes—
31C2×C32×C4⋊C4C2211yescharacteristic, complemented
32C4×#638C2214yescomplemented
33#64135C2211yescharacteristic, complemented
34#64102C2212yescomplemented
35#64101C2212yescomplemented
36C4⋊C4×C3⋊D3C2212yescomplemented
37#64096C2212yescomplemented
38C3×C4×#67C2214yescomplemented
39C2×C3×(C2×D3)⋊C4C2212yescomplemented
40C3×#926C2211yescharacteristic, complemented
41C2×C3×C4×Dic3C2211yescharacteristic, complemented
42C3×#893C2212yescomplemented
43C3×#893C2212yescomplemented
44C3×#893C2212yescomplemented
45C3×#893C2212yescomplemented
46C3×#893C2212yescomplemented
47C3×#892C2212yescomplemented
48C3×D3×C4⋊C4C2212yescomplemented
49C3×#887C2212yescomplemented
50Dic3×#67C2212yescomplemented
51Dic3×#67C2212yescomplemented
52D3×#217C2214yescomplemented
53#63952C2212yescomplemented
54#63952C2212yescomplemented
55#63921C2214yescomplemented
56D3×(C2×D3)⋊C4C2214yescomplemented
57D3×(C2×D3)⋊C4C2214yescomplemented
58#63904C2214yescomplemented
59C4×#626C2214yescomplemented
60#63902C2214yescomplemented
61C4×#625C2214yescomplemented
62#63898C2212yescomplemented
63#63898C2212yescomplemented
64#63894C2211yescharacteristic, complemented
65#63894C2211yescharacteristic, complemented
66Dic3×D12C2211yescharacteristic, complemented
67Dic3×D12C2212yescomplemented
68Dic3×D12C2211yescharacteristic, complemented
69Dic3×D12C2212yescomplemented
70C4×#624C2212yescomplemented
71#63881C2214yescomplemented
72#63880C2214yescomplemented
73#63879C2214yescomplemented
74#63879C2214yescomplemented
75#63878C2214yescomplemented
76#63877C2214yescomplemented
77D3×Dic3⋊C4C2214yescomplemented
78C4×D3×Dic3C2212yescomplemented
79C4×D3×Dic3C2214yescomplemented
80#63874C2212yescomplemented
81#63855C2212yescomplemented
82#63844C2211yescharacteristic, complemented
83#63844C2211yescharacteristic, complemented
84Dic3×Dic6C2211yescharacteristic, complemented
85Dic3×Dic6C2211yescharacteristic, complemented
86C2×#1009—31no—
87C2×#1004—31no—
88C3×#520—31no—
89C2×C3×C4×D4—31no—
90Dic3×#41—31no—
91#5798—31no—
92C2×C4×#67—34no—
93#5574—32no—
94C4×#239—32no—
95#5546—32no—
96#5546—32no—
97#5545—34no—
98#5545—32no—
99#5545—32no—
100#5545—32no—
101C4×D3×D4—34no—
102C4×D3×D4—32no—
103C4×D3×D4—32no—
104C4×D3×D4—32no—
105C4×#237—32no—
106C4×#237—32no—
107#5522—31no—
108#5522—32no—
109#5521—31no—
110#5521—32no—
111#5504—31no—
112#5504—31no—
113#5504—32no—
114#5504—61no—
115#5504D311yescharacteristic, complemented
116C2×#893—32no—
117C2×#893D311yescharacteristic, complemented
118#5486—34no—
119C4×#235—31no—
120C4×#235—31no—
121C23×C3×D3C2312yes—
122C22×D32C2314yes—
123C22×C32×C4C2312yes—
124C22×C32×C4C2311yescharacteristic
125C2×#638C2312yes—
126#3828C2×C418yescomplemented
127C2×C4⋊(C3⋊D3)C2311yescharacteristic
128C2×C4×C3⋊D3C2314yes—
129C2×C4×C3⋊D3C2312yes—
130C2×#634C2311yescharacteristic
131C2×C3×#67C2312yes—
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C3×#235C2×C418yescomplemented
135C2×C3×D12C2×C418yescomplemented
136C2×C3×D12C2312yes—
137C2×C3×D12C2312yes—
138C2×C3×D12C2311yescharacteristic
139C2×C3×C4×D3—44no—
140C2×C3×C4×D3C2314yes—
141C2×C3×C4×D3C2314yes—
142C2×C3×C4×D3C2314yes—
143C2×C3×C4×D3C2312yes—
144C2×C3×Dic6C2311yescharacteristic
145D3×#67C2×C4132yescomplemented
146C2×#626C2314yes—
147C2×#625C2314yes—
148C2×#624C2312yes—
149C2×#624C2312yes—
150C2×D3×Dic3C2312yes—
151C2×D3×Dic3C2314yes—
152C2×D3×Dic3C2314yes—
153C2×D3×Dic3C2312yes—
154C2×D3×Dic3C2314yes—
155#3802C2×C4116yescomplemented
156D3×D12C2×C4116yescomplemented
157C4×D32—48no—
158#3796C2×C4116yescomplemented
159#3795C2×C4116yescomplemented
160C32×C4⋊C4C2312yes—
161C32×C4⋊C4C2312yes—
162#3757C2312yes—
163#3752C2314yes—
164C4⋊(C3⋊Dic3)C2311yescharacteristic
165C4⋊(C3⋊Dic3)C2311yescharacteristic
166#3750C2314yes—
167C4×C3⋊Dic3C2314yes—
168C4×C3⋊Dic3C2312yes—
169C3×#217C2312yes—
170C3×(C2×D3)⋊C4C2314yes—
171C3×(C2×D3)⋊C4C2314yes—
172C3×(C2×D3)⋊C4C2314yes—
173C3×C4⋊Dic3C2311yescharacteristic
174C3×C4⋊Dic3C2311yescharacteristic
175C3×Dic3⋊C4C2314yes—
176C3×C4×Dic3C2314yes—
177C3×C4×Dic3C2312yes—
178C3×C4×Dic3C2311yescharacteristic
179C3×C4×Dic3C2311yescharacteristic
180C3×C4×Dic3C2311yescharacteristic
181C3×C4×Dic3C2311yescharacteristic
182#3724C2312yes—
183#3724C2312yes—
184Dic3⋊Dic3C2312yes—
185Dic3⋊Dic3C2312yes—
186#3722C2312yes—
187#3722C2312yes—
188(C2×D3)⋊Dic3C2312yes—
189(C2×D3)⋊Dic3C2312yes—
190(C2×D3)⋊Dic3C2314yes—
191(C2×D3)⋊Dic3C2314yes—
192Dic32C2312yes—
193Dic32C2312yes—
194Dic32C2312yes—
195Dic32C2312yes—
196C4×H(5,𝔽2)—91noSylow
197C2×C3×#41—31no—
198C22×C3×D4—31no—
199C23×C3×C4—32no—
200C22×#67—34no—
201#1009—316no—
202C2×#239—32no—
203#1004—316no—
204C2×#237—32no—
205C2×#237—32no—
206C2×D3×D4—34no—
207C2×D3×D4—32no—
208C2×D3×D4—32no—
209C2×D3×D4—32no—
210C2×#235—31no—
211C2×#235—31no—
212C2×#235—32no—
213C2×#235—61no—
214C2×#235C2×D311yescharacteristic
215C22×D12—32no—
216C22×D12C2×D311yescharacteristic
217C22×C4×D3—34no—
218C22×C4×D3—34no—
219C22×C4×D3C2×D312yescomplemented
220C3×C4×Q8—32no—
221C3×C4×D4—34no—
222C3×C4×D4—32no—
223C3×C4×D4—32no—
224C3×C4×D4—32no—
225C3×C4×D4—32no—
226C3×C4×D4—32no—
227C3×#117—31no—
228C3×#117—32no—
229C2×C3×C4⋊C4—21no—
230C2×C3×C4⋊C4—32no—
231C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
232C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
233C2×C3×C22⋊C4—32no—
234C2×C3×C42—31no—
235C2×#217—34no—
236Q8×Dic3—31no—
237Q8×Dic3—31no—
238D4×Dic3—32no—
239D4×Dic3—32no—
240D4×Dic3—32no—
241D4×Dic3—32no—
242D4×Dic3—32no—
243D4×Dic3—32no—
244D4×Dic3—31no—
245D4×Dic3—31no—
246C4×#67—34no—
247C4×#67—34no—
248C4×#67—32no—
249C4×#67—32no—
250C4×#67—34no—
251C4×#67—34no—
252C4×#67—32no—
253C4×#67—32no—
254C4×#67—34no—
255C4×#67—34no—
256C4×#67—34no—
257C4×#67—34no—
258C4×#67—64no—
259C4×#67C2×D314yescomplemented
260C2×(C2×D3)⋊C4—34no—
261C2×(C2×D3)⋊C4—34no—
262C2×(C2×D3)⋊C4C2×D312yescomplemented
263#926—31no—
264#926—31no—
265#926—32no—
266#926—61no—
267#926C2×D311yescharacteristic, complemented
268C2×Dic3⋊C4—34no—
269C2×C4×Dic3—32no—
270C2×C4×Dic3—34no—
271C2×C4×Dic3C2×D311yescharacteristic, complemented
272#893—32no—
273#893—32no—
274#893—34no—
275#893—32no—
276#893—32no—
277#893—34no—
278#893—31no—
279#893—31no—
280#893—62no—
281#893C2×D312yescomplemented
282#893C2×D312yescomplemented
283#893C2×D312yescomplemented
284#893C2×D312yescomplemented
285#893C2×D312yescomplemented
286#892—32no—
287#892—32no—
288#892—34no—
289#892—62no—
290#892C2×D312yescomplemented
291D3×C4⋊C4—34no—
292D3×C4⋊C4—32no—
293D3×C4⋊C4—32no—
294D3×C4⋊C4—62no—
295D3×C4⋊C4C2×D312yescomplemented
296#887—32no—
297#887—32no—
298#887—31no—
299#887—31no—
300#887—62no—
301#887C2×D312yescomplemented
302#67⋊C4—32no—
303#67⋊C4—32no—
304#67⋊C4—34no—
305#67⋊C4—34no—
306#67⋊C4—34no—
307#67⋊C4—34no—
308#67⋊C4—34no—
309#67⋊C4—34no—
310D3×C22⋊C4—34no—
311D3×C22⋊C4—34no—
312D3×C22⋊C4—34no—
313D3×C22⋊C4—34no—
314D3×C22⋊C4—34no—
315#877—34no—
316#877—34no—
317C4×D12—31no—
318C4×D12—31no—
319C4×D12—32no—
320C4×D12—32no—
321C4×D12—34no—
322C4×D12—34no—
323C4×D12—31no—
324C4×D12—31no—
325#872—32no—
326#872—34no—
327#872—32no—
328#872—32no—
329C42×D3—32no—
330C42×D3—34no—
331C42×D3—32no—
332C42×D3—32no—
333C4×Dic6—31no—
334C4×Dic6—31no—
335C4×Dic6—31no—
336C4×Dic6—31no—
337C23×C32C2411yescharacteristic
338C22×C3⋊D3C2412yes—
339C22×C3×D3—42no—
340C22×C3×D3—42no—
341C22×C3×D3C22×C418yescomplemented
342C22×C3×D3C2412yes—
343C22×C3×D3C2414yes—
344C2×D32—44no—
345C2×D32—44no—
346C2×D32C22×C4116yescomplemented
347C2×C32×C4—42no—
348C2×C32×C4C22×C414yescomplemented
349C2×C32×C4C2414yes—
350C2×C32×C4C2411yescharacteristic
351C2×C32×C4C2411yescharacteristic
352#638C22×C418yescomplemented
353C2×C3⋊Dic3C2412yes—
354C2×C3⋊Dic3C2412yes—
355C2×C3⋊Dic3C2412yes—
356C4⋊(C3⋊D3)C22×C414yescomplemented
357C4×C3⋊D3—44no—
358C4×C3⋊D3C22×C418yescomplemented
359#634C22×C414yescomplemented
360C3×#67C22×C418yescomplemented
361C2×C3×Dic3—22no—
362C2×C3×Dic3—41no—
363C2×C3×Dic3C2411yescharacteristic
364C2×C3×Dic3C2411yescharacteristic
365C2×C3×Dic3C2412yes—
366C2×C3×Dic3C2412yes—
367C2×C3×Dic3C2411yescharacteristic
368C2×C3×Dic3C2412yes—
369C2×C3×Dic3C2411yescharacteristic
370C3×D12C22×C418yescomplemented
371C3×D12C22×C418yescomplemented
372C3×D12C22×C414yescomplemented
373C3×C4×D3—28no—
374C3×C4×D3—44no—
375C3×C4×D3—44no—
376C3×C4×D3C22×C418yescomplemented
377C3×Dic6C22×C414yescomplemented
378#626C22×C4116yescomplemented
379#625C22×C4116yescomplemented
380#624—24no—
381#624—42no—
382D3×Dic3—24no—
383D3×Dic3—44no—
384D3×Dic3—44no—
385D3×Dic3—42no—
386D3×Dic3C22×C4116yescomplemented
387C2×H(5,𝔽2)—91no—
388#520—31no—
389#520—92no—
390#520—92no—
391#520—91no—
392#518—94no—
393#518—92no—
394#518—91no—
395#518—92no—
396C4×#41—91no—
397C4×#41—91no—
398C4×#41—92no—
399C4×#41—92no—
400C2×C4×D4—31no—
401C2×C4×D4—92no—
402C2×C4×D4—92no—
403C2×C4×D4—94no—
404C24×C3—32no—
405C23×D3—34no—
406C23×D3—34no—
407C23×D3C22×D312yes—
408C3×#41—38no—
409C2×C3×Q8—31no—
410C2×C3×D4—32no—
411C2×C3×D4—38no—
412C2×C3×D4—31no—
413C2×C3×D4—32no—
414C2×C3×D4—32no—
415C22×C3×C4—21no—
416C22×C3×C4—22no—
417C22×C3×C4—32no—
418C22×C3×C4—31no—
419C22×C3×C4—31no—
420C22×C3×C4—34no—
421C22×C3×C4—34no—
422C22×C3×C4—34no—
423C22×C3×C4—124no—
424C22×C3×C4C22×D312yes—
425C22×C3×C4C22×D312yes—
426C22×C3×C4C22×D311yescharacteristic
427C22×C3×C4C22×D311yescharacteristic
428C2×#67—32no—
429C2×#67—32no—
430C2×#67—34no—
431C2×#67—34no—
432C2×#67—332no—
433C2×#67—34no—
434C2×#67—62no—
435C2×#67C22×D312yes—
436C22×Dic3—34no—
437C22×Dic3—32no—
438C22×Dic3—32no—
439C22×Dic3—34no—
440C22×Dic3—34no—
441C22×Dic3C22×D311yescharacteristic
442C22×Dic3C22×D311yescharacteristic
443#239—316no—
444#237—316no—
445#237—316no—
446D3×D4—332no—
447D3×D4—316no—
448D3×D4—316no—
449D3×D4—316no—
450#235—38no—
451#235—38no—
452#235—316no—
453#235—68no—
454#235C4×D318yescomplemented
455C2×D12—34no—
456C2×D12—31no—
457C2×D12—31no—
458C2×D12—316no—
459C2×D12—61no—
460C2×D12C4×D318yescomplemented
461C2×D12C22×D312yes—
462C2×D12C22×D311yescharacteristic
463C2×D12C22×D312yes—
464C2×C4×D3—34no—
465C2×C4×D3—32no—
466C2×C4×D3—32no—
467C2×C4×D3—32no—
468C2×C4×D3—32no—
469C2×C4×D3—32no—
470C2×C4×D3—34no—
471C2×C4×D3—32no—
472C2×C4×D3—34no—
473C2×C4×D3—34no—
474C2×C4×D3—34no—
475C2×C4×D3—32no—
476C2×C4×D3—32no—
477C2×C4×D3—44no—
478C2×C4×D3—62no—
479C2×C4×D3—64no—
480C2×C4×D3—128no—
481C2×C4×D3—128no—
482C2×C4×D3C22×D314yes—
483C2×C4×D3C22×D314yes—
484C2×C4×D3C22×D314yes—
485C2×C4×D3C22×D312yes—
486C2×Dic6—31no—
487C2×Dic6—31no—
488C2×Dic6—61no—
489C2×Dic6C22×D311yescharacteristic
490C3×C4⋊C4—22no—
491C3×C4⋊C4—22no—
492C3×C4⋊C4—31no—
493C3×C4⋊C4—31no—
494C3×C4⋊C4—34no—
495C3×C4⋊C4C22×D312yes—
496C3×C4⋊C4C22×D312yes—
497C3×C4⋊C4C22×D312yes—
498C3×C4⋊C4C22×D312yes—
499C3×C22⋊C4—32no—
500C3×C22⋊C4—34no—
501C3×C22⋊C4—34no—
502C3×C22⋊C4—34no—
503C3×C42—31no—
504C3×C42—31no—
505C3×C42—31no—
506C3×C42—31no—
507C3×C42—34no—
508C3×C42—32no—
509#217—32no—
510#217—32no—
511#217—34no—
512#217—34no—
513#217—32no—
514#217—32no—
515#217—62no—
516#217C22×D312yes—
517(C2×D3)⋊C4—34no—
518(C2×D3)⋊C4—32no—
519(C2×D3)⋊C4—32no—
520(C2×D3)⋊C4—34no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—32no—
524(C2×D3)⋊C4—32no—
525(C2×D3)⋊C4—32no—
526(C2×D3)⋊C4—32no—
527(C2×D3)⋊C4—64no—
528(C2×D3)⋊C4C22×D314yes—
529(C2×D3)⋊C4C22×D314yes—
530(C2×D3)⋊C4C22×D314yes—
531C4⋊Dic3—31no—
532C4⋊Dic3—31no—
533C4⋊Dic3—31no—
534C4⋊Dic3—31no—
535C4⋊Dic3—32no—
536C4⋊Dic3—32no—
537C4⋊Dic3—61no—
538C4⋊Dic3—61no—
539C4⋊Dic3C22×D311yescharacteristic
540C4⋊Dic3C22×D311yescharacteristic
541Dic3⋊C4—34no—
542Dic3⋊C4—34no—
543Dic3⋊C4—32no—
544Dic3⋊C4—32no—
545Dic3⋊C4—32no—
546Dic3⋊C4—32no—
547Dic3⋊C4—32no—
548Dic3⋊C4—32no—
549Dic3⋊C4—64no—
550Dic3⋊C4C22×D314yes—
551C4×Dic3—32no—
552C4×Dic3—34no—
553C4×Dic3—34no—
554C4×Dic3—32no—
555C4×Dic3—32no—
556C4×Dic3—32no—
557C4×Dic3—32no—
558C4×Dic3—32no—
559C4×Dic3—32no—
560C4×Dic3—32no—
561C4×Dic3—32no—
562C4×Dic3—32no—
563C4×Dic3—64no—
564C4×Dic3—62no—
565C4×Dic3C22×D311yescharacteristic
566C4×Dic3C22×D312yes—
567C4×Dic3C22×D311yescharacteristic
568C4×Dic3C22×D314yes—
569C4×Dic3C22×D311yescharacteristic
570C4×Dic3C22×D311yescharacteristic
571C22×C32—21no—
572C22×C32—21no—
573C22×C32C23×C412yes—
574C22×C32C2511yescharacteristic
575C2×C3⋊D3—22no—
576C2×C3⋊D3—22no—
577C2×C3⋊D3C23×C414yes—
578C2×C3×D3—22no—
579C2×C3×D3—24no—
580C2×C3×D3—22no—
581C2×C3×D3—24no—
582C2×C3×D3—48no—
583C2×C3×D3C23×C418yes—
584C2×C3×D3C23×C414yes—
585D32—416no—
586C32×C4—24no—
587C32×C4C23×C412yes—
588C32×C4C23×C412yes—
589C3⋊Dic3—22no—
590C3⋊Dic3—22no—
591C3⋊Dic3C23×C414yes—
592C3×Dic3—22no—
593C3×Dic3—21no—
594C3×Dic3—22no—
595C3×Dic3—21no—
596C3×Dic3—21no—
597C3×Dic3C23×C414yes—
598C3×Dic3H(5,𝔽2)12yescomplemented
599H(5,𝔽2)—916no—
600C2×#41—31no—
601C2×#41—92no—
602C2×#41—92no—
603C2×#41—91no—
604C22×D4—31no—
605C22×D4—92no—
606C22×D4—92no—
607C22×D4—94no—
608C23×C4—32no—
609C23×C4—94no—
610C4×Q8—32no—
611C4×Q8—91no—
612C4×Q8—91no—
613C4×Q8—91no—
614C4×Q8—91no—
615C4×Q8—92no—
616C4×D4—34no—
617C4×D4—32no—
618C4×D4—32no—
619C4×D4—32no—
620C4×D4—32no—
621C4×D4—32no—
622C4×D4—94no—
623C4×D4—91no—
624C4×D4—91no—
625C4×D4—94no—
626C4×D4—91no—
627C4×D4—92no—
628C4×D4—91no—
629C4×D4—92no—
630C4×D4—94no—
631C4×D4—94no—
632C4×D4—92no—
633C4×D4—94no—
634C4×D4—94no—
635C4×D4—92no—
636C4×D4—94no—
637C4×D4—92no—
638C4×D4—92no—
639C4×D4—94no—
640C4×D4—92no—
641C4×D4—92no—
642C4×D4—94no—
643C4×D4—92no—
644#117—31no—
645#117—32no—
646#117—92no—
647#117—94no—
648#117—92no—
649#117—94no—
650#117—91no—
651#117—92no—
652C2×C4⋊C4—32no—
653C2×C4⋊C4—94no—
654C2×C4⋊C4—92no—
655C2×C4⋊C4D3211yescharacteristic, complemented
656C2×C22⋊C4—32no—
657C2×C22⋊C4—94no—
658C2×C22⋊C4—94no—
659C2×C22⋊C4—94no—
660C2×C22⋊C4—94no—
661C2×C42—31no—
662C2×C42—92no—
663C2×C42—92no—
664C2×C42—94no—
665C23×C3—21no—
666C23×C3—34no—
667C23×C3—32no—
668C23×C3—38no—
669C23×C3—122no—
670C23×C3—122no—
671C23×C3C23×D311yescharacteristic
672C23×C3C23×D311yescharacteristic
673C22×D3—32no—
674C22×D3—32no—
675C22×D3—316no—
676C22×D3—316no—
677C22×D3—42no—
678C22×D3—42no—
679C22×D3—62no—
680C22×D3—124no—
681C22×D3—124no—
682C22×D3—124no—
683C22×D3—124no—
684C22×D3C2×C4×D318yescomplemented
685C22×D3C23×D314yes—
686C22×D3C23×D312yes—
687C3×Q8—34no—
688C3×D4—38no—
689C3×D4—34no—
690C3×D4—38no—
691C3×D4—38no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
694C2×C3×C4—24no—
695C2×C3×C4—24no—
696C2×C3×C4—31no—
697C2×C3×C4—32no—
698C2×C3×C4—38no—
699C2×C3×C4—31no—
700C2×C3×C4—31no—
701C2×C3×C4—32no—
702C2×C3×C4—32no—
703C2×C3×C4—31no—
704C2×C3×C4—42no—
705C2×C3×C4—42no—
706C2×C3×C4—68no—
707C2×C3×C4—62no—
708C2×C3×C4—82no—
709C2×C3×C4—124no—
710C2×C3×C4—124no—
711C2×C3×C4—121no—
712C2×C3×C4C2×C4×D314yescomplemented
713C2×C3×C4C2×C4×D314yescomplemented
714C2×C3×C4C23×D314yes—
715C2×C3×C4C23×D314yes—
716C2×C3×C4C23×D311yescharacteristic
717C2×C3×C4C23×D311yescharacteristic
718C2×C3×C4C23×D311yescharacteristic
719C2×C3×C4C23×D311yescharacteristic
720#67—38no—
721#67—38no—
722#67—316no—
723#67—316no—
724#67—316no—
725#67—68no—
726#67C2×C4×D318yescomplemented
727C2×Dic3—22no—
728C2×Dic3—32no—
729C2×Dic3—32no—
730C2×Dic3—316no—
731C2×Dic3—32no—
732C2×Dic3—32no—
733C2×Dic3—32no—
734C2×Dic3—32no—
735C2×Dic3—41no—
736C2×Dic3—62no—
737C2×Dic3—62no—
738C2×Dic3—62no—
739C2×Dic3—64no—
740C2×Dic3—124no—
741C2×Dic3—122no—
742C2×Dic3—124no—
743C2×Dic3C23×D311yescharacteristic
744C2×Dic3C23×D311yescharacteristic
745C2×Dic3C23×D312yes—
746C2×Dic3C23×D312yes—
747C2×Dic3C23×D311yescharacteristic
748C2×Dic3C23×D312yes—
749C2×Dic3C23×D311yescharacteristic
750D12—316no—
751D12—34no—
752D12—34no—
753D12—64no—
754D12C2×C4×D318yescomplemented
755D12C2×C4×D318yescomplemented
756D12C2×C4×D314yescomplemented
757C4×D3—28no—
758C4×D3—316no—
759C4×D3—38no—
760C4×D3—38no—
761C4×D3—44no—
762C4×D3—44no—
763C4×D3—68no—
764C4×D3—64no—
765C4×D3—64no—
766C4×D3—64no—
767C4×D3—122no—
768C4×D3—122no—
769C4×D3—124no—
770C4×D3—124no—
771C4×D3—124no—
772C4×D3—122no—
773C4×D3—124no—
774C4×D3—244no—
775C4×D3C2×C4×D318yescomplemented
776Dic6—34no—
777Dic6—34no—
778Dic6—64no—
779Dic6C2×C4×D314yescomplemented
780C2×C32—22no—
781C2×C32C24×C411yescharacteristic
782C2×C32C2×H(5,𝔽2)11yescharacteristic
783C2×C32#58511yescharacteristic
784C3⋊D3—24no—
785C3×D3—24no—
786C3×D3—28no—
787C24—32no—
788C24—94no—
789#41—38no—
790#41—916no—
791#41—916no—
792#41—98no—
793C2×Q8—31no—
794C2×Q8—91no—
795C2×D4—32no—
796C2×D4—32no—
797C2×D4—32no—
798C2×D4—31no—
799C2×D4—38no—
800C2×D4—916no—
801C2×D4—94no—
802C2×D4—916no—
803C2×D4—932no—
804C2×D4—94no—
805C2×D4—92no—
806C2×D4—91no—
807C22×C4—32no—
808C22×C4—31no—
809C22×C4—31no—
810C22×C4—34no—
811C22×C4—34no—
812C22×C4—34no—
813C22×C4—92no—
814C22×C4—92no—
815C22×C4—94no—
816C22×C4—92no—
817C22×C4—94no—
818C22×C4—92no—
819C22×C4—94no—
820C22×C4—92no—
821C22×C4—94no—
822C22×C4—124no—
823C22×C4—368no—
824C22×C4C2×D3212yes—
825C22×C4C2×D3211yescharacteristic
826C4⋊C4—31no—
827C4⋊C4—34no—
828C4⋊C4—31no—
829C4⋊C4—92no—
830C4⋊C4—92no—
831C4⋊C4—92no—
832C4⋊C4—92no—
833C4⋊C4—94no—
834C4⋊C4—91no—
835C4⋊C4—91no—
836C4⋊C4C2×D3212yes—
837C4⋊C4C2×D3212yes—
838C22⋊C4—32no—
839C22⋊C4—34no—
840C22⋊C4—34no—
841C22⋊C4—34no—
842C22⋊C4—92no—
843C22⋊C4—92no—
844C22⋊C4—94no—
845C22⋊C4—92no—
846C22⋊C4—92no—
847C22⋊C4—94no—
848C22⋊C4—92no—
849C22⋊C4—94no—
850C42—31no—
851C42—31no—
852C42—31no—
853C42—31no—
854C42—34no—
855C42—32no—
856C42—92no—
857C42—92no—
858C42—92no—
859C42—92no—
860C42—94no—
861C42—92no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—22no—
867C22×C3—21no—
868C22×C3—38no—
869C22×C3—34no—
870C22×C3—41no—
871C22×C3—41no—
872C22×C3—62no—
873C22×C3—62no—
874C22×C3—64no—
875C22×C3—64no—
876C22×C3—128no—
877C22×C3C22×C4×D312yes—
878C22×C3C22×C4×D312yes—
879C22×C3C24×D311yescharacteristic
880C22×C3C24×D311yescharacteristic
881C2×D3—24no—
882C2×D3—24no—
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—34no—
886C2×D3—34no—
887C2×D3—48no—
888C2×D3—64no—
889C2×D3—62no—
890C2×D3—62no—
891C2×D3—62no—
892C2×D3—62no—
893C2×D3—122no—
894C2×D3—122no—
895C2×D3—1216no—
896C2×D3—1216no—
897C2×D3C22×C4×D318yes—
898C2×D3C22×C4×D314yes—
899C3×C4—24no—
900C3×C4—24no—
901C3×C4—22no—
902C3×C4—22no—
903C3×C4—34no—
904C3×C4—32no—
905C3×C4—44no—
906C3×C4—62no—
907C3×C4—62no—
908C3×C4—61no—
909C3×C4—61no—
910C3×C4—61no—
911C3×C4C22×C4×D312yes—
912C3×C4C22×C4×D312yes—
913C3×C4C22×C4×D312yes—
914C3×C4C22×C4×D312yes—
915Dic3—21no—
916Dic3—21no—
917Dic3—21no—
918Dic3—22no—
919Dic3—22no—
920Dic3—34no—
921Dic3—34no—
922Dic3—64no—
923Dic3—62no—
924Dic3—62no—
925Dic3—62no—
926Dic3—62no—
927Dic3—122no—
928Dic3—122no—
929Dic3C22×C4×D314yes—
930Dic3#100412yescomplemented
931C32C4×H(5,𝔽2)11yescharacteristic, complemented, Sylow
932C23—32no—
933C23—34no—
934C23—38no—
935C23—916no—
936C23—92no—
937C23—122no—
938C23—122no—
939C23—364no—
940C23—364no—
941C23C22×D3211yescharacteristic
942Q8—34no—
943Q8—94no—
944D4—38no—
945D4—38no—
946D4—38no—
947D4—34no—
948D4—916no—
949D4—916no—
950D4—98no—
951D4—94no—
952C2×C4—31no—
953C2×C4—32no—
954C2×C4—38no—
955C2×C4—32no—
956C2×C4—31no—
957C2×C4—31no—
958C2×C4—31no—
959C2×C4—32no—
960C2×C4—42no—
961C2×C4—68no—
962C2×C4—62no—
963C2×C4—916no—
964C2×C4—92no—
965C2×C4—98no—
966C2×C4—92no—
967C2×C4—92no—
968C2×C4—124no—
969C2×C4—124no—
970C2×C4—121no—
971C2×C4—184no—
972C2×C4—184no—
973C2×C4—364no—
974C2×C4—362no—
975C2×C4—364no—
976C2×C4—362no—
977C2×C4—364no—
978C2×C4C4×D3214yescomplemented
979C2×C4C22×D3214yes—
980C2×C4C22×D3211yescharacteristic
981C2×C4C22×D3211yescharacteristic
982C2×C3—22no—
983C2×C3—22no—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—42no—
988C2×C3—68no—
989C2×C3—64no—
990C2×C3C23×C4×D311yescharacteristic
991C2×C3C23×C4×D311yescharacteristic
992C2×C3C2×#100411yescharacteristic
993C2×C3#596411yescharacteristic
994C2×C3D3×H(5,𝔽2)11yescharacteristic
995C2×C3#596811yescharacteristic
996D3—24no—
997D3—28no—
998D3—64no—
999D3—64no—
1000D3—124no—
1001C22—21no—
1002C22—21no—
1003C22—34no—
1004C22—38no—
1005C22—64no—
1006C22—62no—
1007C22—64no—
1008C22—62no—
1009C22—94no—
1010C22—128no—
1011C22—182no—
1012C22—182no—
1013C22—3616no—
1014C22C2×C4×D3212yes—
1015C22C23×D3211yescharacteristic
1016C4—24no—
1017C4—34no—
1018C4—32no—
1019C4—61no—
1020C4—62no—
1021C4—61no—
1022C4—61no—
1023C4—62no—
1024C4—94no—
1025C4—182no—
1026C4—182no—
1027C4C2×C4×D3212yes—
1028C4C2×C4×D3212yes—
1029C3—21no—
1030C3C4×#100411yescharacteristic, complemented
1031C3#8588611yescharacteristic, complemented
1032C2—22no—
1033C2—68no—
1034C2—64no—
1035C2—184no—
1036C2C22×C4×D3211yescharacteristic
1037C2D3×#100411yescharacteristic
1038C2#1059668811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutatorC2×C32C24×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC22×C32C25
prime radicalC2×#64307C2
hypercenterC2×C4⋊C4D32
hypocenterC32C4×H(5,𝔽2)
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10595975C2semidirect
3. C3×#5504C2semidirect
4. C2×C3×#893C2semidirect
5. #10595056C2semidirect
6. C4×D3×#67C2semidirect
7. #10594982C2semidirect
8. #10594954C2semidirect
9. Dic3×#235C2semidirect
10. #10594606C2semidirect
11. #10594605C2semidirect
12. #10594604C2semidirect
13. D3×#893C2semidirect
14. #10594361C2semidirect
15. #10594360C2semidirect
16. #10594359C2semidirect
17. #10594358C2semidirect
23. C22×C3×C4×D3C22semidirect
25. #64307C4semidirect
28. C2×C4×D32C22semidirect
31. C2×C32×C4⋊C4C22semidirect
32. C4×#638C22semidirect
33. #64135C22semidirect
34. #64102C22semidirect
35. #64101C22semidirect
36. C4⋊C4×C3⋊D3C22semidirect
37. #64096C22semidirect
38. C3×C4×#67C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C3×#926C22semidirect
41. C2×C3×C4×Dic3C22semidirect
42. C3×#893C22semidirect
43. C3×#893C22semidirect
44. C3×#893C22semidirect
45. C3×#893C22semidirect
46. C3×#893C22semidirect
47. C3×#892C22semidirect
48. C3×D3×C4⋊C4C22semidirect
49. C3×#887C22semidirect
50. Dic3×#67C22semidirect
51. Dic3×#67C22semidirect
52. D3×#217C22semidirect
53. #63952C22semidirect
54. #63952C22semidirect
55. #63921C22semidirect
56. D3×(C2×D3)⋊C4C22semidirect
57. D3×(C2×D3)⋊C4C22semidirect
58. #63904C22semidirect
59. C4×#626C22semidirect
60. #63902C22semidirect
61. C4×#625C22semidirect
62. #63898C22semidirect
63. #63898C22semidirect
64. #63894C22semidirect
65. #63894C22semidirect
66. Dic3×D12C22semidirect
67. Dic3×D12C22semidirect
68. Dic3×D12C22semidirect
69. Dic3×D12C22semidirect
70. C4×#624C22semidirect
71. #63881C22semidirect
72. #63880C22semidirect
73. #63879C22semidirect
74. #63879C22semidirect
75. #63878C22semidirect
76. #63877C22semidirect
77. D3×Dic3⋊C4C22semidirect
78. C4×D3×Dic3C22semidirect
79. C4×D3×Dic3C22semidirect
80. #63874C22semidirect
81. #63855C22semidirect
82. #63844C22semidirect
83. #63844C22semidirect
84. Dic3×Dic6C22semidirect
85. Dic3×Dic6C22semidirect
115. #5504D3semidirect
117. C2×#893D3semidirect
126. #3828C2×C4semidirect
134. C3×#235C2×C4semidirect
135. C2×C3×D12C2×C4semidirect
145. D3×#67C2×C4semidirect
155. #3802C2×C4semidirect
156. D3×D12C2×C4semidirect
158. #3796C2×C4semidirect
159. #3795C2×C4semidirect
219. C22×C4×D3C2×D3semidirect
231. C2×C3×C4⋊C4C2×D3semidirect
232. C2×C3×C4⋊C4C2×D3semidirect
259. C4×#67C2×D3semidirect
262. C2×(C2×D3)⋊C4C2×D3semidirect
267. #926C2×D3semidirect
271. C2×C4×Dic3C2×D3semidirect
281. #893C2×D3semidirect
282. #893C2×D3semidirect
283. #893C2×D3semidirect
284. #893C2×D3semidirect
285. #893C2×D3semidirect
290. #892C2×D3semidirect
295. D3×C4⋊C4C2×D3semidirect
301. #887C2×D3semidirect
341. C22×C3×D3C22×C4semidirect
346. C2×D32C22×C4semidirect
348. C2×C32×C4C22×C4semidirect
352. #638C22×C4semidirect
356. C4⋊(C3⋊D3)C22×C4semidirect
358. C4×C3⋊D3C22×C4semidirect
359. #634C22×C4semidirect
360. C3×#67C22×C4semidirect
370. C3×D12C22×C4semidirect
371. C3×D12C22×C4semidirect
372. C3×D12C22×C4semidirect
376. C3×C4×D3C22×C4semidirect
377. C3×Dic6C22×C4semidirect
378. #626C22×C4semidirect
379. #625C22×C4semidirect
386. D3×Dic3C22×C4semidirect
454. #235C4×D3semidirect
460. C2×D12C4×D3semidirect
598. C3×Dic3H(5,𝔽2)semidirect
655. C2×C4⋊C4D32semidirect
684. C22×D3C2×C4×D3semidirect
712. C2×C3×C4C2×C4×D3semidirect
713. C2×C3×C4C2×C4×D3semidirect
726. #67C2×C4×D3semidirect
754. D12C2×C4×D3semidirect
755. D12C2×C4×D3semidirect
756. D12C2×C4×D3semidirect
775. C4×D3C2×C4×D3semidirect
779. Dic6C2×C4×D3semidirect
930. Dic3#1004semidirect
931. C32C4×H(5,𝔽2)semidirect
978. C2×C4C4×D32semidirect
1030. C3C4×#1004semidirect
1031. C3#85886semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
#105959752
C3×#55042
C2×C3×#8932
#105950562
C4×D3×#672
#105949822
#105949542
Dic3×#2352
#105946062
#105946052
#105946042
D3×#8932
#105943612
#105943602
#105943592
#105943582
#858863
C4×#10043