Finite Group Databasebeta

← C2×#10594409 #11903069

Subgroups — C2×#10594409 #11903069

Order 1152.

2361 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64098C211yesmaximal, characteristic, complemented
2C2×C3×#898C211yesmaximal, characteristic, complemented
3C2×C3×#892C211yesmaximal, characteristic, complemented
4C2×C4×#627C211yesmaximal, characteristic, complemented
5C2×#63905C211yesmaximal, characteristic
6C2×#63902C211yesmaximal, characteristic
7C2×#63899C211yesmaximal, characteristic, complemented
8C2×#63899C211yesmaximal, characteristic, complemented
9C2×#63891C211yesmaximal, characteristic
10C2×#63877C211yesmaximal, characteristic, complemented
11C2×#63877C211yesmaximal, characteristic, complemented
12C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
13C2×#63869C211yesmaximal, characteristic, complemented
14C2×#63859C211yesmaximal, characteristic, complemented
15C2×#63847C211yesmaximal, characteristic, complemented
16#10594409C2116yesmaximal, direct product factor
17C2×#5708—31nomaximal
18C2×#5531—31nomaximal
19C22×C3×C4×D3C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×#625C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×C4×C3⋊Dic3C2211yescharacteristic
32#64098C2218yescomplemented
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C3×#898C2218yescomplemented
45C3×#892C2218yescomplemented
46C2×#3724C2211yescharacteristic
47C2×#3724C2211yescharacteristic
48C2×#3724C2211yescharacteristic
49C2×#3724C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57C4×#627C2218yescomplemented
58#63905C2218yes—
59#63902C2218yes—
60#63899C2218yescomplemented
61#63899C2218yescomplemented
62#63891C2218yes—
63#63877C2218yescomplemented
64#63877C2218yescomplemented
65D3×Dic3⋊C4C2218yescomplemented
66#63869C2218yescomplemented
67#63859C2218yescomplemented
68#63847C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×#117—31no—
71C2×#929—31no—
72C22×Dic3⋊C4—31no—
73#5708—316no—
74#5531—316no—
75C2×#898D311yescharacteristic, complemented
76C2×#896—31no—
77C2×#896—31no—
78C2×#892D311yescharacteristic, complemented
79C2×D3×C4⋊C4—31no—
80C2×#890—31no—
81C2×#889—31no—
82C2×#889—31no—
83C2×#889—31no—
84C2×#889—31no—
85C2×#889—61no—
86C2×#886—31no—
87C2×#883—31no—
88C2×#883—31no—
89C2×#67⋊C4—31no—
90C2×#67⋊C4—31no—
91C2×#879—31no—
92C2×#878—31no—
93C2×#878—31no—
94C2×#877—31no—
95C2×#877—31no—
96C2×#876—31no—
97C2×#872—31no—
98C2×#872—31no—
99C2×#870—31no—
100C2×C4×Dic6—31no—
101C2×C4×Dic6—31no—
102C23×C3×D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C2×C3×C4×D3—24no—
118C2×C3×C4×D3C2314yes—
119C2×#627—24no—
120C2×#627C2314yes—
121C2×#625—24no—
122C2×#625C2314yes—
123C2×D3×Dic3—24no—
124C2×D3×Dic3—24no—
125C2×D3×Dic3—24no—
126C2×D3×Dic3C2314yes—
127C2×D3×Dic3C2314yes—
128C2×D3×Dic3C2314yes—
129C32×C4⋊C4C2314yes—
130C4⋊(C3⋊Dic3)C2314yes—
131#3750C2314yes—
132#3750C2314yes—
133#3750C2314yes—
134#3750C2314yes—
135C4×C3⋊Dic3C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×(C2×D3)⋊C4C2314yes—
138C3×(C2×D3)⋊C4C2314yes—
139C3×(C2×D3)⋊C4C2314yes—
140C3×(C2×D3)⋊C4C2314yes—
141C3×C4⋊Dic3C2314yes—
142C3×C4⋊Dic3C2314yes—
143C3×Dic3⋊C4C2314yes—
144C3×C4×Dic3C2314yes—
145C3×C4×Dic3C2314yes—
146C3×C4×Dic3C2314yes—
147#3724C2314yes—
148#3724C2314yes—
149#3724C2314yes—
150#3724C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154(C2×D3)⋊Dic3C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157Dic32C2314yes—
158C2×#552—91noSylow
159C23×C3×C4—31no—
160C22×#67—31no—
161C22×#67—31no—
162C23×Dic3—31no—
163C23×Dic3—31no—
164C23×Dic3—31no—
165C22×C4×D3—31no—
166C22×C4×D3—31no—
167C22×C4×D3—31no—
168C22×C4×D3C2×D311yescharacteristic
169C22×Dic6—31no—
170C22×Dic6—31no—
171C3×#126—38no—
172C3×#117—38no—
173C2×C3×C4⋊C4—21no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4C2×D311yescharacteristic
178C2×C3×C4⋊C4C2×D311yescharacteristic
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C42—31no—
185C2×C3×C42—31no—
186C2×C3×C42—31no—
187C2×#217—31no—
188C2×#217—31no—
189C2×#217—31no—
190#929—38no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4C2×D311yescharacteristic
195C2×(C2×D3)⋊C4C2×D311yescharacteristic
196C2×(C2×D3)⋊C4C2×D311yescharacteristic
197C2×(C2×D3)⋊C4C2×D311yescharacteristic
198C2×(C2×D3)⋊C4C2×D311yescharacteristic
199C2×C4⋊Dic3—31no—
200C2×C4⋊Dic3—31no—
201C2×C4⋊Dic3—31no—
202C2×C4⋊Dic3—31no—
203C2×C4⋊Dic3—31no—
204C2×C4⋊Dic3—61no—
205C2×C4⋊Dic3C2×D311yescharacteristic
206C2×C4⋊Dic3C2×D311yescharacteristic
207C2×Dic3⋊C4—31no—
208C2×Dic3⋊C4—31no—
209C2×Dic3⋊C4—31no—
210C2×Dic3⋊C4—31no—
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4—31no—
218C2×Dic3⋊C4—31no—
219C2×Dic3⋊C4—31no—
220C2×Dic3⋊C4—31no—
221C2×Dic3⋊C4—31no—
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4—31no—
225C2×Dic3⋊C4—31no—
226C2×Dic3⋊C4—38no—
227C2×Dic3⋊C4—61no—
228C2×Dic3⋊C4—61no—
229C2×Dic3⋊C4—61no—
230C2×Dic3⋊C4—61no—
231C2×Dic3⋊C4C2×D311yescharacteristic
232C2×C4×Dic3—31no—
233C2×C4×Dic3—31no—
234C2×C4×Dic3—31no—
235C2×C4×Dic3—31no—
236C2×C4×Dic3—61no—
237C2×C4×Dic3C2×D311yescharacteristic
238C2×C4×Dic3C2×D311yescharacteristic
239C2×C4×Dic3C2×D311yescharacteristic
240#898C2×D318yescomplemented
241#896—38no—
242#896—38no—
243#892C2×D318yescomplemented
244D3×C4⋊C4—38no—
245#890—38no—
246#889—38no—
247#889—38no—
248#889—38no—
249#889—38no—
250#889—68no—
251#886—38no—
252#883—38no—
253#883—38no—
254#67⋊C4—38no—
255#67⋊C4—38no—
256#879—38no—
257#878—38no—
258#878—38no—
259#877—38no—
260#877—38no—
261#876—38no—
262#872—38no—
263#872—38no—
264#870—38no—
265C4×Dic6—38no—
266C4×Dic6—38no—
267C23×C32C2411yescharacteristic
268C22×C3×D3—22no—
269C22×C3×D3—22no—
270C22×C3×D3—22no—
271C22×C3×D3—22no—
272C22×C3×D3—22no—
273C22×C3×D3#4114yes—
274C22×C3×D3C2412yes—
275C22×C3×D3C2412yes—
276C2×C32×C4—22no—
277C2×C32×C4—22no—
278C2×C32×C4—22no—
279C2×C32×C4C2412yes—
280C2×C32×C4C2412yes—
281C2×C32×C4C2412yes—
282C2×C3⋊Dic3—22no—
283C2×C3⋊Dic3—22no—
284C2×C3⋊Dic3—22no—
285C2×C3⋊Dic3#4114yes—
286C2×C3⋊Dic3C2412yes—
287C2×C3⋊Dic3C2412yes—
288C2×C3⋊Dic3C2412yes—
289C2×C3⋊Dic3C2412yes—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—22no—
296C2×C3×Dic3C2412yes—
297C2×C3×Dic3C2412yes—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C3×C4×D3—28no—
303#627—28no—
304#625—28no—
305D3×Dic3—28no—
306D3×Dic3—28no—
307D3×Dic3—28no—
308#552—916no—
309C2×#126—31no—
310C2×#126—91no—
311C2×#125—91no—
312C2×#125—91no—
313C2×#125—91no—
314C2×#123—91no—
315C2×#123—91no—
316C2×C22⋊Q8—91no—
317C2×C22⋊Q8—91no—
318C2×C4×Q8—91no—
319C2×C4×D4—91no—
320C2×#117—31no—
321C2×#117—91no—
322C2×#117—91no—
323C22×C4⋊C4—91no—
324C24×C3—31no—
325C24×C3—31no—
326C23×D3C22×D311yescharacteristic
327C23×D3C22×D311yescharacteristic
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—34no—
338C22×C3×C4—64no—
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C2×#67—34no—
346C2×#67—34no—
347C2×#67—64no—
348C2×#67—64no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—34no—
358C22×Dic3—34no—
359C22×Dic3—34no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3—61no—
363C22×Dic3—61no—
364C22×Dic3—64no—
365C22×Dic3—64no—
366C22×Dic3—64no—
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C2×C4×D3—24no—
374C2×C4×D3—34no—
375C2×C4×D3—34no—
376C2×C4×D3—34no—
377C2×C4×D3—64no—
378C2×C4×D3—64no—
379C2×C4×D3—64no—
380C2×C4×D3C22×D314yes—
381C2×Dic6—34no—
382C2×Dic6—34no—
383C2×Dic6—64no—
384C2×Dic6—64no—
385C3×C4⋊C4—24no—
386C3×C4⋊C4—34no—
387C3×C4⋊C4—34no—
388C3×C4⋊C4—34no—
389C3×C4⋊C4C22×D314yes—
390C3×C4⋊C4C22×D314yes—
391C3×C22⋊C4—34no—
392C3×C22⋊C4—34no—
393C3×C22⋊C4—34no—
394C3×C22⋊C4—34no—
395C3×C22⋊C4—34no—
396C3×C42—34no—
397C3×C42—34no—
398C3×C42—34no—
399#217—34no—
400#217—34no—
401#217—34no—
402(C2×D3)⋊C4—34no—
403(C2×D3)⋊C4—34no—
404(C2×D3)⋊C4—34no—
405(C2×D3)⋊C4C22×D314yes—
406(C2×D3)⋊C4C22×D314yes—
407(C2×D3)⋊C4C22×D314yes—
408(C2×D3)⋊C4C22×D314yes—
409(C2×D3)⋊C4C22×D314yes—
410C4⋊Dic3—34no—
411C4⋊Dic3—34no—
412C4⋊Dic3—34no—
413C4⋊Dic3—34no—
414C4⋊Dic3—34no—
415C4⋊Dic3—64no—
416C4⋊Dic3C22×D314yes—
417C4⋊Dic3C22×D314yes—
418Dic3⋊C4—34no—
419Dic3⋊C4—34no—
420Dic3⋊C4—34no—
421Dic3⋊C4—34no—
422Dic3⋊C4—34no—
423Dic3⋊C4—34no—
424Dic3⋊C4—34no—
425Dic3⋊C4—34no—
426Dic3⋊C4—34no—
427Dic3⋊C4—34no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4—34no—
432Dic3⋊C4—34no—
433Dic3⋊C4—34no—
434Dic3⋊C4—34no—
435Dic3⋊C4—34no—
436Dic3⋊C4—34no—
437Dic3⋊C4—64no—
438Dic3⋊C4—64no—
439Dic3⋊C4—64no—
440Dic3⋊C4—64no—
441Dic3⋊C4C22×D314yes—
442C4×Dic3—34no—
443C4×Dic3—34no—
444C4×Dic3—34no—
445C4×Dic3—34no—
446C4×Dic3—64no—
447C4×Dic3C22×D314yes—
448C4×Dic3C22×D314yes—
449C4×Dic3C22×D314yes—
450C22×C32C2×#4112yes—
451C22×C32C2×#4112yes—
452C22×C322−1+412yes—
453C22×C32C2511yescharacteristic
454C2×C3×D3—28no—
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—44no—
461C2×C3×D3C2×#4114yes—
462C32×C4—22no—
463C32×C4—22no—
464C32×C4—22no—
465C3⋊Dic3—22no—
466C3⋊Dic3—22no—
467C3⋊Dic3—22no—
468C3⋊Dic3C2×#4114yes—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3—22no—
475C22×Q8—91no—
476C22×D4—91no—
477C23×C4—31no—
478C23×C4—91no—
479C23×C4—91no—
480C23×C4—91no—
481#126—38no—
482#126—98no—
483#125—98no—
484#125—98no—
485#125—98no—
486#123—98no—
487#123—98no—
488C22⋊Q8—98no—
489C22⋊Q8—98no—
490C4×Q8—98no—
491C4×D4—98no—
492#117—38no—
493#117—98no—
494#117—98no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—98no—
499C2×C4⋊C4—91no—
500C2×C4⋊C4—91no—
501C2×C4⋊C4—91no—
502C2×C4⋊C4—91no—
503C2×C4⋊C4—91no—
504C2×C4⋊C4—91no—
505C2×C4⋊C4—91no—
506C2×C4⋊C4—91no—
507C2×C4⋊C4—91no—
508C2×C4⋊C4—91no—
509C2×C4⋊C4—91no—
510C2×C4⋊C4—91no—
511C2×C4⋊C4D3211yescharacteristic
512C2×C22⋊C4—31no—
513C2×C22⋊C4—31no—
514C2×C22⋊C4—31no—
515C2×C22⋊C4—31no—
516C2×C22⋊C4—31no—
517C2×C22⋊C4—91no—
518C2×C22⋊C4—91no—
519C2×C22⋊C4—91no—
520C2×C42—31no—
521C2×C42—31no—
522C2×C42—31no—
523C2×C42—91no—
524C2×C42—91no—
525C23×C3—21no—
526C23×C3—34no—
527C23×C3—32no—
528C23×C3—32no—
529C23×C3—62no—
530C23×C3—62no—
531C23×C3—62no—
532C23×C3—62no—
533C23×C3—62no—
534C23×C3C23×D311yescharacteristic
535C23×C3C23×D311yescharacteristic
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3#23514yes—
542C22×D3C23×D312yes—
543C22×D3C23×D312yes—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—32no—
554C2×C3×C4—32no—
555C2×C3×C4—32no—
556C2×C3×C4—32no—
557C2×C3×C4—32no—
558C2×C3×C4—32no—
559C2×C3×C4—42no—
560C2×C3×C4—42no—
561C2×C3×C4—42no—
562C2×C3×C4—68no—
563C2×C3×C4—62no—
564C2×C3×C4—62no—
565C2×C3×C4—62no—
566C2×C3×C4—62no—
567C2×C3×C4—62no—
568C2×C3×C4—62no—
569C2×C3×C4C23×D312yes—
570C2×C3×C4C23×D312yes—
571C2×C3×C4C23×D312yes—
572C2×C3×C4C23×D312yes—
573C2×C3×C4C23×D312yes—
574C2×C3×C4C23×D312yes—
575#67—68no—
576#67—68no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—34no—
584C2×Dic3—34no—
585C2×Dic3—32no—
586C2×Dic3—32no—
587C2×Dic3—32no—
588C2×Dic3—32no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—64no—
594C2×Dic3—62no—
595C2×Dic3—62no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—68no—
599C2×Dic3—68no—
600C2×Dic3—68no—
601C2×Dic3—62no—
602C2×Dic3—62no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—62no—
606C2×Dic3—62no—
607C2×Dic3—122no—
608C2×Dic3—122no—
609C2×Dic3—122no—
610C2×Dic3C23×D312yes—
611C2×Dic3C23×D312yes—
612C2×Dic3C23×D312yes—
613C2×Dic3C23×D312yes—
614C2×Dic3C23×D312yes—
615C2×Dic3C23×D312yes—
616C4×D3—28no—
617C4×D3—68no—
618C4×D3—68no—
619C4×D3—68no—
620Dic6—68no—
621Dic6—68no—
622C2×C32#55214yescomplemented
623C2×C32C22×#4111yescharacteristic
624C2×C32C22×#4111yescharacteristic
625C2×C32C2×2−1+411yescharacteristic
626C3×D3—24no—
627C3×D3—42no—
628C24—31no—
629C24—31no—
630C2×Q8—94no—
631C2×Q8—184no—
632C2×D4—94no—
633C2×D4—184no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—34no—
641C22×C4—64no—
642C22×C4—94no—
643C22×C4—94no—
644C22×C4—94no—
645C22×C4—91no—
646C22×C4—91no—
647C22×C4—91no—
648C22×C4—91no—
649C22×C4—184no—
650C22×C4—184no—
651C22×C4—184no—
652C22×C4C2×D3211yescharacteristic
653C22×C4C2×D3211yescharacteristic
654C22×C4C2×D3211yescharacteristic
655C4⋊C4—34no—
656C4⋊C4—34no—
657C4⋊C4—34no—
658C4⋊C4—94no—
659C4⋊C4—94no—
660C4⋊C4—94no—
661C4⋊C4—94no—
662C4⋊C4—94no—
663C4⋊C4—94no—
664C4⋊C4—94no—
665C4⋊C4—94no—
666C4⋊C4—94no—
667C4⋊C4—94no—
668C4⋊C4—94no—
669C4⋊C4—94no—
670C4⋊C4C2×D3214yes—
671C22⋊C4—34no—
672C22⋊C4—34no—
673C22⋊C4—34no—
674C22⋊C4—34no—
675C22⋊C4—34no—
676C22⋊C4—94no—
677C22⋊C4—94no—
678C22⋊C4—94no—
679C42—34no—
680C42—34no—
681C42—34no—
682C42—94no—
683C42—94no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—21no—
688C22×C3—34no—
689C22×C3—62no—
690C22×C3—62no—
691C22×C3—68no—
692C22×C3—62no—
693C22×C3—62no—
694C22×C3—62no—
695C22×C3—124no—
696C22×C3C2×#23512yes—
697C22×C3D3×#4112yes—
698C22×C3D3×#4112yes—
699C22×C3D3×#4112yes—
700C22×C3#101012yes—
701C22×C3#101012yes—
702C22×C3C24×D311yescharacteristic
703C22×C3C24×D311yescharacteristic
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—28no—
707C2×D3—22no—
708C2×D3—22no—
709C2×D3—22no—
710C2×D3—44no—
711C2×D3C2×#23514yes—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—42no—
719C3×C4—42no—
720C3×C4—42no—
721C3×C4—62no—
722C3×C4—62no—
723C3×C4—62no—
724C3×C4—62no—
725C3×C4—62no—
726C3×C4—62no—
727Dic3—22no—
728Dic3—22no—
729Dic3—22no—
730Dic3—22no—
731Dic3—22no—
732Dic3—22no—
733Dic3—34no—
734Dic3—34no—
735Dic3—64no—
736Dic3—62no—
737Dic3—62no—
738Dic3—62no—
739Dic3—62no—
740Dic3—62no—
741Dic3—62no—
742Dic3—122no—
743Dic3—122no—
744Dic3—122no—
745C32C2×#55211yescharacteristic, complemented, Sylow
746C23—34no—
747C23—32no—
748C23—32no—
749C23—62no—
750C23—62no—
751C23—62no—
752C23—62no—
753C23—62no—
754C23C22×D3211yescharacteristic
755Q8—188no—
756D4—188no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—32no—
761C2×C4—32no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—32no—
766C2×C4—68no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—94no—
774C2×C4—92no—
775C2×C4—92no—
776C2×C4—92no—
777C2×C4—92no—
778C2×C4—188no—
779C2×C4—188no—
780C2×C4—188no—
781C2×C4—182no—
782C2×C4—182no—
783C2×C4—182no—
784C2×C4C22×D3212yes—
785C2×C4C22×D3212yes—
786C2×C4C22×D3212yes—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—24no—
791C2×C3—64no—
792C2×C3—122no—
793C2×C3#553114yescomplemented
794C2×C3#570814yescomplemented
795C2×C3C22×#23511yescharacteristic
796C2×C3C2×D3×#4111yescharacteristic
797C2×C3C2×D3×#4111yescharacteristic
798C2×C3C2×D3×#4111yescharacteristic
799C2×C3C2×#101011yescharacteristic
800C2×C3C2×#101011yescharacteristic
801D3—24no—
802D3—42no—
803C22—34no—
804C22—62no—
805C22—62no—
806C22—68no—
807C22—62no—
808C22—62no—
809C22—62no—
810C22—124no—
811C22D3×#23512yes—
812C22#6430912yes—
813C22#6431912yes—
814C22C23×D3211yescharacteristic
815C4—22no—
816C4—22no—
817C4—22no—
818C4—62no—
819C4—62no—
820C4—62no—
821C4—62no—
822C4—62no—
823C4—62no—
824C4—94no—
825C4—182no—
826C4—182no—
827C4—182no—
828C3—21no—
829C3C2×#553111yescharacteristic, complemented
830C3C2×#570811yescharacteristic, complemented
831C2—64no—
832C2—122no—
833C2#1059440914yesdirect product factor
834C2C2×D3×#23511yescharacteristic
835C2C2×#6430911yescharacteristic
836C2C2×#6431911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#625C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64098C2semidirect
2. C2×C3×#898C2semidirect
3. C2×C3×#892C2semidirect
4. C2×C4×#627C2semidirect
7. C2×#63899C2semidirect
8. C2×#63899C2semidirect
10. C2×#63877C2semidirect
11. C2×#63877C2semidirect
12. C2×D3×Dic3⋊C4C2semidirect
13. C2×#63869C2semidirect
14. C2×#63859C2semidirect
15. C2×#63847C2semidirect
16. #10594409C2direct (N × H)
32. #64098C22semidirect
44. C3×#898C22semidirect
45. C3×#892C22semidirect
57. C4×#627C22semidirect
60. #63899C22semidirect
61. #63899C22semidirect
63. #63877C22semidirect
64. #63877C22semidirect
65. D3×Dic3⋊C4C22semidirect
66. #63869C22semidirect
67. #63859C22semidirect
68. #63847C22semidirect
75. C2×#898D3semidirect
78. C2×#892D3semidirect
240. #898C2×D3semidirect
243. #892C2×D3semidirect
622. C2×C32#552semidirect
745. C32C2×#552semidirect
793. C2×C3#5531semidirect
794. C2×C3#5708semidirect
829. C3C2×#5531semidirect
830. C3C2×#5708semidirect
833. C2#10594409direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640982
C2×C3×#8982
C2×C3×#8922
C2×C4×#6272
C2×#639052
C2×#639022
C2×#638992
C2×#638912
C2×#638772
C2×D3×Dic3⋊C42
C2×#638692
C2×#638592
C2×#638472
#105944092
C2×#57083
C2×#55313