Finite Group Databasebeta

← C2×#10594039 #11903048

Subgroups — C2×#10594039 #11903048

Order 1152.

2413 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64086C211yesmaximal, characteristic, complemented
2C2×C3×#67⋊C4C211yesmaximal, characteristic
3C2×C3×#877C211yesmaximal, characteristic, complemented
4C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5C2×#63964C211yesmaximal, characteristic, complemented
6C2×#63962C211yesmaximal, characteristic
7C2×#63961C211yesmaximal, characteristic
8C2×C4×#627C211yesmaximal, characteristic, complemented
9C2×#63870C211yesmaximal, characteristic, complemented
10C2×#63867C211yesmaximal, characteristic, complemented
11C2×#63867C211yesmaximal, characteristic, complemented
12C2×#63862C211yesmaximal, characteristic, complemented
13C2×#63859C211yesmaximal, characteristic, complemented
14C2×#63855C211yesmaximal, characteristic, complemented
15C2×#63851C211yesmaximal, characteristic, complemented
16#10594039C2116yesmaximal, direct product factor
17C2×#5541—31nomaximal
18C2×#5531—31nomaximal
19C23×C3⋊Dic3C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×#627C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C2×C4×C3⋊Dic3C2211yescharacteristic
31#64086C2218yescomplemented
32C2×C3×#217C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C3×#67⋊C4C2218yes—
41C3×#877C2218yescomplemented
42C2×#3724C2211yescharacteristic
43C2×#3724C2211yescharacteristic
44C2×#3724C2211yescharacteristic
45C2×Dic3⋊Dic3C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2218yescomplemented
54#63964C2218yescomplemented
55#63962C2218yes—
56#63961C2218yes—
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61C4×#627C2218yescomplemented
62#63870C2218yescomplemented
63#63867C2218yescomplemented
64#63867C2218yescomplemented
65#63862C2218yescomplemented
66#63859C2218yescomplemented
67#63855C2218yescomplemented
68#63851C2218yescomplemented
69C2×C3×C4×D4—31no—
70C2×C3×#117—31no—
71C2×#935—31no—
72C2×#935—31no—
73C2×#929—31no—
74C2×#926—31no—
75C22×C4⋊Dic3—31no—
76C2×#924—31no—
77C2×#924—31no—
78C22×Dic3⋊C4—31no—
79#5541—316no—
80#5531—316no—
81C2×#898—31no—
82C2×#896—31no—
83C2×#889—31no—
84C2×#889—31no—
85C2×#889—31no—
86C2×#889—31no—
87C2×#886—31no—
88C2×#67⋊C4D311yescharacteristic
89C2×#879—31no—
90C2×#879—31no—
91C2×#878—31no—
92C2×#877—31no—
93C2×#877—31no—
94C2×#877—61no—
95C2×#877D311yescharacteristic, complemented
96C2×#876—31no—
97C2×#872—31no—
98C2×#870—31no—
99C2×#870—31no—
100C2×C4×Dic6—31no—
101C2×C4×Dic6—31no—
102C24×C32C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C3⋊Dic3—24no—
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2314yes—
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C2×C3×#67—24no—
113C2×C3×#67C2314yes—
114C22×C3×Dic3—24no—
115C22×C3×Dic3—24no—
116C22×C3×Dic3C2314yes—
117C22×C3×Dic3C2314yes—
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×C3×C4×D3—24no—
126C2×C3×C4×D3C2314yes—
127C2×#627—24no—
128C2×#627C2314yes—
129C32×C22⋊C4C2314yes—
130#3757C2314yes—
131#3750C2314yes—
132#3750C2314yes—
133C4×C3⋊Dic3C2314yes—
134C4×C3⋊Dic3C2314yes—
135C3×#217C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×Dic3⋊C4C2314yes—
138C3×Dic3⋊C4C2314yes—
139C3×Dic3⋊C4C2314yes—
140C3×C4×Dic3C2314yes—
141C3×C4×Dic3C2314yes—
142C3×C4×Dic3C2314yes—
143#3724C2314yes—
144#3724C2314yes—
145#3724C2314yes—
146Dic3⋊Dic3C2314yes—
147Dic3⋊Dic3C2314yes—
148Dic3⋊Dic3C2314yes—
149Dic3⋊Dic3C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154(C2×D3)⋊Dic3C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157(C2×D3)⋊Dic3C2314yes—
158C2×#552—91noSylow
159C22×C3×D4—31no—
160C23×C3×C4—31no—
161C23×C3×C4—31no—
162C23×C3×C4—31no—
163C22×#67C2×D311yescharacteristic
164C23×Dic3—31no—
165C23×Dic3—31no—
166C23×Dic3—61no—
167C23×Dic3C2×D311yescharacteristic
168C23×Dic3C2×D311yescharacteristic
169C22×C4×D3C2×D311yescharacteristic
170C22×Dic6—31no—
171C22×Dic6—31no—
172C3×C4×D4—38no—
173C3×#117—38no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C22⋊C4—21no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4C2×D311yescharacteristic
181C2×C3×C22⋊C4C2×D311yescharacteristic
182C2×C3×C42—31no—
183C2×C3×C42—31no—
184C2×C3×C42—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—31no—
189C2×#217—31no—
190C2×#217—31no—
191C2×#217—61no—
192C2×#217C2×D311yescharacteristic
193#935—38no—
194#935—38no—
195#929—38no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4C2×D311yescharacteristic
201#926—38no—
202C2×C4⋊Dic3—31no—
203C2×C4⋊Dic3—31no—
204C2×C4⋊Dic3—31no—
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3—38no—
211#924—38no—
212#924—38no—
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—31no—
227C2×Dic3⋊C4—31no—
228C2×Dic3⋊C4—31no—
229C2×Dic3⋊C4—31no—
230C2×Dic3⋊C4—31no—
231C2×Dic3⋊C4—38no—
232C2×Dic3⋊C4—61no—
233C2×Dic3⋊C4—61no—
234C2×Dic3⋊C4C2×D311yescharacteristic
235C2×Dic3⋊C4C2×D311yescharacteristic
236C2×Dic3⋊C4C2×D311yescharacteristic
237C2×C4×Dic3—31no—
238C2×C4×Dic3—31no—
239C2×C4×Dic3—31no—
240C2×C4×Dic3—31no—
241C2×C4×Dic3—61no—
242C2×C4×Dic3—61no—
243C2×C4×Dic3C2×D311yescharacteristic
244C2×C4×Dic3C2×D311yescharacteristic
245C2×C4×Dic3C2×D311yescharacteristic
246#898—38no—
247#896—38no—
248#889—38no—
249#889—38no—
250#889—38no—
251#889—38no—
252#886—38no—
253#67⋊C4C2×D318yes—
254#879—38no—
255#879—38no—
256#878—38no—
257#877—38no—
258#877—38no—
259#877—68no—
260#877C2×D318yescomplemented
261#876—38no—
262#872—38no—
263#870—38no—
264#870—38no—
265C4×Dic6—38no—
266C4×Dic6—38no—
267C23×C32—22no—
268C23×C32—22no—
269C23×C32#4114yes—
270C23×C32C2412yes—
271C23×C32C2411yescharacteristic
272C22×C3×D3—22no—
273C22×C3×D3—22no—
274C22×C3×D3—22no—
275C22×C3×D3C2412yes—
276C2×C32×C4—22no—
277C2×C32×C4—22no—
278C2×C32×C4C2412yes—
279C2×C32×C4C2412yes—
280C2×C3⋊Dic3—28no—
281C2×C3⋊Dic3—22no—
282C2×C3⋊Dic3—22no—
283C2×C3⋊Dic3—22no—
284C2×C3⋊Dic3—22no—
285C2×C3⋊Dic3C2412yes—
286C2×C3⋊Dic3C2412yes—
287C2×C3⋊Dic3C2412yes—
288C2×C3⋊Dic3C2412yes—
289C3×#67—28no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—28no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—22no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3—28no—
298C2×C3×Dic3#4114yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C3×C4×D3—28no—
307#627—28no—
308#552—916no—
309C2×#126—91no—
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—31no—
320C2×#117—31no—
321C2×#117—91no—
322C2×#117—91no—
323C22×C4⋊C4—91no—
324C24×C3—21no—
325C24×C3—31no—
326C24×C3C22×D311yescharacteristic
327C24×C3C22×D311yescharacteristic
328C23×D3C22×D311yescharacteristic
329C2×C3×D4—34no—
330C2×C3×D4—64no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—34no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—34no—
342C22×C3×C4—34no—
343C22×C3×C4—64no—
344C22×C3×C4—64no—
345C22×C3×C4—64no—
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C2×#67—24no—
351C2×#67C22×D314yes—
352C22×Dic3—24no—
353C22×Dic3—24no—
354C22×Dic3—34no—
355C22×Dic3—34no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—64no—
365C22×Dic3—61no—
366C22×Dic3—61no—
367C22×Dic3—61no—
368C22×Dic3—61no—
369C22×Dic3—68no—
370C22×Dic3—64no—
371C22×Dic3—64no—
372C22×Dic3C22×D314yes—
373C22×Dic3C22×D314yes—
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C2×C4×D3—24no—
382C2×C4×D3C22×D314yes—
383C2×Dic6—34no—
384C2×Dic6—34no—
385C2×Dic6—64no—
386C2×Dic6—64no—
387C3×C4⋊C4—34no—
388C3×C4⋊C4—34no—
389C3×C4⋊C4—34no—
390C3×C22⋊C4—24no—
391C3×C22⋊C4—34no—
392C3×C22⋊C4—34no—
393C3×C22⋊C4C22×D314yes—
394C3×C22⋊C4C22×D314yes—
395C3×C42—34no—
396C3×C42—34no—
397C3×C42—34no—
398#217—34no—
399#217—34no—
400#217—34no—
401#217—34no—
402#217—34no—
403#217—34no—
404#217—64no—
405#217C22×D314yes—
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—34no—
408(C2×D3)⋊C4—34no—
409(C2×D3)⋊C4—34no—
410(C2×D3)⋊C4C22×D314yes—
411C4⋊Dic3—34no—
412C4⋊Dic3—34no—
413C4⋊Dic3—34no—
414C4⋊Dic3—34no—
415C4⋊Dic3—34no—
416C4⋊Dic3—34no—
417C4⋊Dic3—34no—
418C4⋊Dic3—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⋊C4C22×D314yes—
440Dic3⋊C4C22×D314yes—
441Dic3⋊C4C22×D314yes—
442C4×Dic3—34no—
443C4×Dic3—34no—
444C4×Dic3—34no—
445C4×Dic3—34no—
446C4×Dic3—64no—
447C4×Dic3—64no—
448C4×Dic3C22×D314yes—
449C4×Dic3C22×D314yes—
450C4×Dic3C22×D314yes—
451C22×C32—28no—
452C22×C32—22no—
453C22×C32—22no—
454C22×C32C2×#4114yes—
455C22×C32C2×#4112yes—
456C22×C32C2×#4112yes—
457C22×C322−1+412yes—
458C22×C32C2511yescharacteristic
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—44no—
463C32×C4—22no—
464C32×C4—22no—
465C3⋊Dic3—22no—
466C3⋊Dic3—22no—
467C3⋊Dic3—22no—
468C3⋊Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3—22no—
475C3×Dic3C2×#4114yes—
476C22×Q8—91no—
477C22×D4—31no—
478C23×C4—31no—
479C23×C4—31no—
480C23×C4—31no—
481C23×C4—91no—
482#126—98no—
483#126—98no—
484#125—98no—
485#125—98no—
486#125—98no—
487#123—98no—
488#123—98no—
489C22⋊Q8—98no—
490C22⋊Q8—98no—
491C4×Q8—98no—
492C4×D4—38no—
493#117—38no—
494#117—98no—
495#117—98no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—91no—
500C2×C4⋊C4—91no—
501C2×C4⋊C4—91no—
502C2×C4⋊C4—91no—
503C2×C4⋊C4—98no—
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⋊C4—91no—
512C2×C4⋊C4—91no—
513C2×C22⋊C4—31no—
514C2×C22⋊C4—31no—
515C2×C22⋊C4—91no—
516C2×C22⋊C4—91no—
517C2×C22⋊C4—91no—
518C2×C22⋊C4—91no—
519C2×C22⋊C4—91no—
520C2×C22⋊C4D3211yescharacteristic
521C2×C42—31no—
522C2×C42—31no—
523C2×C42—31no—
524C2×C42—91no—
525C2×C42—91no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—21no—
532C23×C3—24no—
533C23×C3—32no—
534C23×C3—42no—
535C23×C3—42no—
536C23×C3—62no—
537C23×C3—62no—
538C23×C3—62no—
539C23×C3#23514yes—
540C23×C3#23514yes—
541C23×C3C23×D312yes—
542C23×C3C23×D312yes—
543C23×C3C23×D311yescharacteristic
544C23×C3C23×D311yescharacteristic
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—22no—
548C22×D3C23×D312yes—
549C3×D4—68no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—34no—
557C2×C3×C4—32no—
558C2×C3×C4—32no—
559C2×C3×C4—32no—
560C2×C3×C4—32no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—32no—
564C2×C3×C4—42no—
565C2×C3×C4—42no—
566C2×C3×C4—68no—
567C2×C3×C4—68no—
568C2×C3×C4—68no—
569C2×C3×C4—62no—
570C2×C3×C4—62no—
571C2×C3×C4—62no—
572C2×C3×C4—62no—
573C2×C3×C4—62no—
574C2×C3×C4—62no—
575C2×C3×C4C23×D312yes—
576C2×C3×C4C23×D312yes—
577C2×C3×C4C23×D312yes—
578C2×C3×C4C23×D312yes—
579#67—28no—
580C2×Dic3—28no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—28no—
588C2×Dic3—32no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—32no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—62no—
599C2×Dic3—62no—
600C2×Dic3—64no—
601C2×Dic3—64no—
602C2×Dic3—616no—
603C2×Dic3—68no—
604C2×Dic3—68no—
605C2×Dic3—62no—
606C2×Dic3—62no—
607C2×Dic3—62no—
608C2×Dic3—62no—
609C2×Dic3—62no—
610C2×Dic3—62no—
611C2×Dic3—62no—
612C2×Dic3—62no—
613C2×Dic3—122no—
614C2×Dic3—122no—
615C2×Dic3#23714yes—
616C2×Dic3C23×D312yes—
617C2×Dic3C23×D312yes—
618C2×Dic3C23×D312yes—
619C2×Dic3C23×D312yes—
620C2×Dic3C23×D312yes—
621C2×Dic3C23×D312yes—
622C2×Dic3C23×D312yes—
623C4×D3—28no—
624Dic6—68no—
625Dic6—68no—
626C2×C32—24no—
627C2×C32#55214yescomplemented
628C2×C32C22×#4111yescharacteristic
629C2×C32C22×#4111yescharacteristic
630C2×C32C2×2−1+411yescharacteristic
631C3×D3—42no—
632C24—31no—
633C24C2×D3211yescharacteristic
634C2×Q8—94no—
635C2×Q8—184no—
636C2×D4—34no—
637C2×D4—64no—
638C22×C4—31no—
639C22×C4—34no—
640C22×C4—34no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—34no—
648C22×C4—64no—
649C22×C4—64no—
650C22×C4—64no—
651C22×C4—94no—
652C22×C4—91no—
653C22×C4—91no—
654C22×C4—91no—
655C22×C4—91no—
656C22×C4—184no—
657C22×C4C2×D3211yescharacteristic
658C22×C4C2×D3211yescharacteristic
659C4⋊C4—34no—
660C4⋊C4—34no—
661C4⋊C4—34no—
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⋊C4—94no—
671C4⋊C4—94no—
672C4⋊C4—94no—
673C4⋊C4—94no—
674C4⋊C4—94no—
675C22⋊C4—34no—
676C22⋊C4—34no—
677C22⋊C4—94no—
678C22⋊C4—94no—
679C22⋊C4—94no—
680C22⋊C4—94no—
681C22⋊C4—94no—
682C22⋊C4C2×D3214yes—
683C42—34no—
684C42—34no—
685C42—34no—
686C42—94no—
687C42—94no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—28no—
693C22×C3—28no—
694C22×C3—22no—
695C22×C3—24no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—21no—
699C22×C3—42no—
700C22×C3—42no—
701C22×C3—48no—
702C22×C3—62no—
703C22×C3—62no—
704C22×C3—62no—
705C22×C3—124no—
706C22×C3C2×#23514yes—
707C22×C3C2×#23514yes—
708C22×C3C2×#23512yes—
709C22×C3C2×#23512yes—
710C22×C3C2×#23712yes—
711C22×C3D3×#4112yes—
712C22×C3#101012yes—
713C22×C3#101012yes—
714C22×C3C24×D311yescharacteristic
715C22×C3C24×D311yescharacteristic
716C2×D3—22no—
717C2×D3—22no—
718C2×D3—22no—
719C2×D3—44no—
720C3×C4—22no—
721C3×C4—22no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—34no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—62no—
728C3×C4—62no—
729C3×C4—62no—
730C3×C4—62no—
731C3×C4—62no—
732C3×C4—62no—
733Dic3—22no—
734Dic3—22no—
735Dic3—22no—
736Dic3—22no—
737Dic3—22no—
738Dic3—22no—
739Dic3—64no—
740Dic3—64no—
741Dic3—62no—
742Dic3—62no—
743Dic3—62no—
744Dic3—62no—
745Dic3—62no—
746Dic3—62no—
747Dic3—62no—
748Dic3—62no—
749Dic3—122no—
750Dic3—122no—
751Dic3C2×#23714yes—
752C32C2×#55211yescharacteristic, complemented, Sylow
753C23—22no—
754C23—22no—
755C23—32no—
756C23—62no—
757C23—62no—
758C23—62no—
759C23#379814yes—
760C23C22×D3212yes—
761C23C22×D3211yescharacteristic
762Q8—188no—
763D4—68no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—34no—
767C2×C4—32no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—68no—
775C2×C4—68no—
776C2×C4—68no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—92no—
784C2×C4—92no—
785C2×C4—92no—
786C2×C4—92no—
787C2×C4—188no—
788C2×C4—182no—
789C2×C4—182no—
790C2×C4—182no—
791C2×C4—182no—
792C2×C4C22×D3212yes—
793C2×C4C22×D3212yes—
794C2×C3—24no—
795C2×C3—24no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—24no—
800C2×C3—44no—
801C2×C3—122no—
802C2×C3#553114yescomplemented
803C2×C3#554114yescomplemented
804C2×C3C22×#23511yescharacteristic
805C2×C3C22×#23511yescharacteristic
806C2×C3C22×#23711yescharacteristic
807C2×C3C2×D3×#4111yescharacteristic
808C2×C3C2×#101011yescharacteristic
809C2×C3C2×#101011yescharacteristic
810D3—42no—
811C22—22no—
812C22—22no—
813C22—28no—
814C22—62no—
815C22—62no—
816C22—62no—
817C22—124no—
818C22C2×#379814yes—
819C22C2×#379812yes—
820C22#6430912yes—
821C22D3×#23712yes—
822C22C23×D3211yescharacteristic
823C4—22no—
824C4—22no—
825C4—34no—
826C4—62no—
827C4—62no—
828C4—62no—
829C4—62no—
830C4—62no—
831C4—62no—
832C4—182no—
833C4—182no—
834C4—182no—
835C4—182no—
836C3—21no—
837C3C2×#553111yescharacteristic, complemented
838C3C2×#554111yescharacteristic, complemented
839C2—24no—
840C2—122no—
841C2#1059403914yesdirect product factor
842C2C22×#379811yescharacteristic
843C2C2×#6430911yescharacteristic
844C2C2×D3×#23711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64086C2semidirect
3. C2×C3×#877C2semidirect
4. C22×Dic3⋊Dic3C2semidirect
5. C2×#63964C2semidirect
8. C2×C4×#627C2semidirect
9. C2×#63870C2semidirect
10. C2×#63867C2semidirect
11. C2×#63867C2semidirect
12. C2×#63862C2semidirect
13. C2×#63859C2semidirect
14. C2×#63855C2semidirect
15. C2×#63851C2semidirect
16. #10594039C2direct (N × H)
31. #64086C22semidirect
41. C3×#877C22semidirect
53. C2×Dic3⋊Dic3C22semidirect
54. #63964C22semidirect
61. C4×#627C22semidirect
62. #63870C22semidirect
63. #63867C22semidirect
64. #63867C22semidirect
65. #63862C22semidirect
66. #63859C22semidirect
67. #63855C22semidirect
68. #63851C22semidirect
95. C2×#877D3semidirect
260. #877C2×D3semidirect
627. C2×C32#552semidirect
752. C32C2×#552semidirect
802. C2×C3#5531semidirect
803. C2×C3#5541semidirect
837. C3C2×#5531semidirect
838. C3C2×#5541semidirect
841. C2#10594039direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640862
C2×C3×#67⋊C42
C2×C3×#8772
C22×Dic3⋊Dic32
C2×#639642
C2×#639622
C2×#639612
C2×C4×#6272
C2×#638702
C2×#638672
C2×#638622
C2×#638592
C2×#638552
C2×#638512
#105940392
C2×#55413
C2×#55313