Finite Group Databasebeta

← C2×#10595369 #11901913

Subgroups — C2×#10595369 #11901913

Order 1152.

2305 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64153C211yesmaximal, characteristic, complemented
2C2×C3×#946C211yesmaximal, characteristic
3C2×C3×#944C211yesmaximal, characteristic, complemented
4#10595369C2116yesmaximal, direct product factor
5C2×#63896C211yesmaximal, characteristic
6C2×#63887C211yesmaximal, characteristic
7C2×#63878C211yesmaximal, characteristic
8C2×#63877C211yesmaximal, characteristic
9C2×D3×Dic3⋊C4C211yesmaximal, characteristic
10C2×#63870C211yesmaximal, characteristic, complemented
11C2×#63867C211yesmaximal, characteristic, complemented
12C2×#63851C211yesmaximal, characteristic
13C2×#63847C211yesmaximal, characteristic, complemented
14C2×#63846C211yesmaximal, characteristic, complemented
15C2×#63840C211yesmaximal, characteristic, complemented
16C2×#63839C211yesmaximal, characteristic, complemented
17C2×#5729—31nomaximal
18C2×#5623—31nomaximal
19C22×C32×Q8C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C22×D3×Dic3C2211yescharacteristic
26#64153C2218yescomplemented
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×C4×C3⋊Dic3C2211yescharacteristic
32C3×#946C2218yes—
33C3×#944C2218yescomplemented
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C2×#3724C2211yescharacteristic
45C2×#3724C2211yescharacteristic
46C2×#3724C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63896C2218yes—
58#63887C2218yes—
59#63878C2218yes—
60#63877C2218yes—
61D3×Dic3⋊C4C2218yes—
62#63870C2218yescomplemented
63#63867C2218yescomplemented
64#63851C2218yes—
65#63847C2218yescomplemented
66#63846C2218yescomplemented
67#63840C2218yescomplemented
68#63839C2218yescomplemented
69C2×C3×C4⋊Q8—31no—
70C2×C3×C22⋊Q8—31no—
71C2×#946—31no—
72C2×#946D311yescharacteristic
73C2×#944—31no—
74C2×#944—31no—
75C2×#944—31no—
76C2×#944—61no—
77C2×#944D311yescharacteristic, complemented
78C2×#924—31no—
79C22×Dic3⋊C4—31no—
80#5729—316no—
81#5623—316no—
82C2×#896—31no—
83C2×#896—31no—
84C2×#892—31no—
85C2×D3×C4⋊C4—31no—
86C2×#890—31no—
87C2×#889—31no—
88C2×#889—31no—
89C2×#889—31no—
90C2×#889—31no—
91C2×#889—31no—
92C2×#889—31no—
93C2×#888—31no—
94C2×#888—31no—
95C2×#888—31no—
96C2×#878—31no—
97C2×#878—31no—
98C2×#877—31no—
99C2×#877—31no—
100C2×#872—31no—
101C2×#870—31no—
102C23×C3×D3C2311yescharacteristic
103C2×C32×Q8—42no—
104C2×C32×Q8C2314yes—
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C2×#634—42no—
113C2×#634C2314yes—
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×C3×C4×D3—42no—
122C2×C3×C4×D3C2314yes—
123C2×C3×Dic6—42no—
124C2×C3×Dic6C2314yes—
125C2×#627—42no—
126C2×#627C2314yes—
127C2×D3×Dic3—42no—
128C2×D3×Dic3Q818yescomplemented
129C2×D3×Dic3C2314yes—
130C2×D3×Dic3C2314yes—
131#3750C2314yes—
132#3750C2314yes—
133#3750C2314yes—
134#3750C2314yes—
135C4×C3⋊Dic3C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×(C2×D3)⋊C4C2314yes—
138C3×C4⋊Dic3C2314yes—
139C3×Dic3⋊C4C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×Dic3⋊C4C2314yes—
142C3×Dic3⋊C4C2314yes—
143C3×Dic3⋊C4C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×C4×Dic3C2314yes—
146#3724C2314yes—
147#3724C2314yes—
148#3724C2314yes—
149Dic3⋊Dic3C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157Dic32C2314yes—
158Dic32C2314yes—
159C2×#544—91noSylow
160C22×C3×Q8—21no—
161C22×C3×Q8—31no—
162C22×C3×Q8C2×D311yescharacteristic
163C22×C3×Q8C2×D311yescharacteristic
164C23×C3×C4—31no—
165C23×Dic3—31no—
166C23×Dic3—31no—
167C22×C4×D3—31no—
168C22×C4×D3—31no—
169C22×C4×D3C2×D311yescharacteristic
170C22×Dic6—31no—
171C22×Dic6—31no—
172C22×Dic6—31no—
173C22×Dic6—31no—
174C22×Dic6—61no—
175C22×Dic6C2×D311yescharacteristic
176C3×C4⋊Q8—38no—
177C3×C22⋊Q8—38no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C4⋊C4—31no—
182C2×C3×C4⋊C4—31no—
183C2×C3×C4⋊C4—31no—
184C2×C3×C4⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C22⋊C4—31no—
187C2×C3×C42—31no—
188C2×#217—31no—
189C2×#217—31no—
190#946—38no—
191#946C2×D318yes—
192#944—38no—
193#944—38no—
194#944—38no—
195#944—68no—
196#944C2×D318yescomplemented
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4C2×D311yescharacteristic
200C2×(C2×D3)⋊C4C2×D311yescharacteristic
201C2×C4⋊Dic3—31no—
202C2×C4⋊Dic3—31no—
203C2×C4⋊Dic3—31no—
204C2×C4⋊Dic3—31no—
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3C2×D311yescharacteristic
208#924—38no—
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—31no—
227C2×Dic3⋊C4—31no—
228C2×Dic3⋊C4—31no—
229C2×Dic3⋊C4—38no—
230C2×Dic3⋊C4—61no—
231C2×Dic3⋊C4—61no—
232C2×Dic3⋊C4—61no—
233C2×Dic3⋊C4—61no—
234C2×Dic3⋊C4C2×D311yescharacteristic
235C2×Dic3⋊C4C2×D311yescharacteristic
236C2×Dic3⋊C4C2×D311yescharacteristic
237C2×Dic3⋊C4C2×D311yescharacteristic
238C2×Dic3⋊C4C2×D311yescharacteristic
239C2×Dic3⋊C4C2×D311yescharacteristic
240C2×C4×Dic3—31no—
241C2×C4×Dic3—31no—
242C2×C4×Dic3—31no—
243C2×C4×Dic3—31no—
244C2×C4×Dic3—31no—
245C2×C4×Dic3—31no—
246C2×C4×Dic3—61no—
247C2×C4×Dic3C2×D311yescharacteristic
248#896—38no—
249#896—38no—
250#892—38no—
251D3×C4⋊C4—38no—
252#890—38no—
253#889—38no—
254#889—38no—
255#889—38no—
256#889—38no—
257#889—38no—
258#889—38no—
259#888—38no—
260#888—38no—
261#888—38no—
262#878—38no—
263#878—38no—
264#877—38no—
265#877—38no—
266#872—38no—
267#870—38no—
268C23×C32C2411yescharacteristic
269C22×C3×D3—22no—
270C22×C3×D3—22no—
271C22×C3×D3C2×Q814yes—
272C22×C3×D3C2412yes—
273C32×Q8—44no—
274C2×C32×C4—22no—
275C2×C32×C4—22no—
276C2×C32×C4—22no—
277C2×C32×C4C2412yes—
278C2×C32×C4C2412yes—
279C2×C32×C4C2412yes—
280C2×C3⋊Dic3—22no—
281C2×C3⋊Dic3—22no—
282C2×C3⋊Dic3—22no—
283C2×C3⋊Dic3C2×Q814yes—
284C2×C3⋊Dic3C2412yes—
285C2×C3⋊Dic3C2412yes—
286C2×C3⋊Dic3C2412yes—
287C2×C3⋊Dic3C2412yes—
288#634—44no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3C2×Q814yes—
296C2×C3×Dic3C2412yes—
297C2×C3×Dic3C2412yes—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2412yes—
303C3×C4×D3—44no—
304C3×Dic6—44no—
305#627—44no—
306D3×Dic3—44no—
307D3×Dic3C2×Q8116yescomplemented
308#544—916no—
309C2×C4⋊Q8—31no—
310C2×C4⋊Q8—91no—
311C2×C4⋊Q8—91no—
312C2×C4⋊Q8—91no—
313C2×#125—91no—
314C2×#125—91no—
315C2×#125—91no—
316C2×#125—91no—
317C2×C22⋊Q8—31no—
318C2×C22⋊Q8—91no—
319C2×C22⋊Q8—91no—
320C2×C22⋊Q8—91no—
321C2×#117—91no—
322C2×#117—91no—
323C22×C4⋊C4—91no—
324C24×C3—31no—
325C23×D3C22×D311yescharacteristic
326C2×C3×Q8—24no—
327C2×C3×Q8—34no—
328C2×C3×Q8—42no—
329C2×C3×Q8—42no—
330C2×C3×Q8—44no—
331C2×C3×Q8—122no—
332C2×C3×Q8C22×D314yes—
333C2×C3×Q8C22×D314yes—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—34no—
345C22×C3×C4—122no—
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—38no—
355C22×Dic3—34no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—34no—
363C22×Dic3—61no—
364C22×Dic3—61no—
365C22×Dic3—61no—
366C22×Dic3—61no—
367C22×Dic3—122no—
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D311yescharacteristic
374C22×Dic3C22×D311yescharacteristic
375C2×C4×D3—38no—
376C2×C4×D3—34no—
377C2×C4×D3—34no—
378C2×C4×D3—42no—
379C2×C4×D3—122no—
380C2×C4×D3C22×D314yes—
381C2×Dic6—34no—
382C2×Dic6—34no—
383C2×Dic6—34no—
384C2×Dic6—34no—
385C2×Dic6—42no—
386C2×Dic6—64no—
387C2×Dic6—122no—
388C2×Dic6—122no—
389C2×Dic6—122no—
390C2×Dic6—122no—
391C2×Dic6—124no—
392C2×Dic6C22×D314yes—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—34no—
395C3×C4⋊C4—34no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4—34no—
398C3×C4⋊C4—34no—
399C3×C4⋊C4—34no—
400C3×C22⋊C4—34no—
401C3×C22⋊C4—34no—
402C3×C42—34no—
403#217—34no—
404#217—34no—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4C22×D314yes—
408(C2×D3)⋊C4C22×D314yes—
409C4⋊Dic3—34no—
410C4⋊Dic3—34no—
411C4⋊Dic3—34no—
412C4⋊Dic3—34no—
413C4⋊Dic3—34no—
414C4⋊Dic3—34no—
415C4⋊Dic3C22×D314yes—
416Dic3⋊C4—34no—
417Dic3⋊C4—34no—
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—64no—
437Dic3⋊C4—64no—
438Dic3⋊C4—64no—
439Dic3⋊C4—64no—
440Dic3⋊C4C22×D314yes—
441Dic3⋊C4C22×D314yes—
442Dic3⋊C4C22×D314yes—
443Dic3⋊C4C22×D314yes—
444Dic3⋊C4C22×D314yes—
445Dic3⋊C4C22×D314yes—
446C4×Dic3—34no—
447C4×Dic3—34no—
448C4×Dic3—34no—
449C4×Dic3—34no—
450C4×Dic3—34no—
451C4×Dic3—34no—
452C4×Dic3—64no—
453C4×Dic3C22×D314yes—
454C22×C32C22×Q812yes—
455C22×C32H(5,𝔽2)12yes—
456C22×C322−1+412yes—
457C22×C32C2511yescharacteristic
458C2×C3×D3—28no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3C22×Q814yes—
462C32×C4—22no—
463C32×C4—22no—
464C32×C4—22no—
465C3⋊Dic3—22no—
466C3⋊Dic3—22no—
467C3⋊Dic3—22no—
468C3⋊Dic3C22×Q814yes—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3—22no—
475C3×Dic3C22×Q814yes—
476C22×Q8—31no—
477C22×Q8—91no—
478C22×Q8—91no—
479C22×Q8D3211yescharacteristic
480C23×C4—31no—
481C23×C4—91no—
482C23×C4—91no—
483C4⋊Q8—38no—
484C4⋊Q8—98no—
485C4⋊Q8—98no—
486C4⋊Q8—98no—
487#125—98no—
488#125—98no—
489#125—98no—
490#125—98no—
491C22⋊Q8—38no—
492C22⋊Q8—98no—
493C22⋊Q8—98no—
494C22⋊Q8—98no—
495#117—98no—
496#117—98no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—31no—
503C2×C4⋊C4—31no—
504C2×C4⋊C4—98no—
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×C4⋊C4—91no—
514C2×C4⋊C4—91no—
515C2×C4⋊C4—91no—
516C2×C4⋊C4—91no—
517C2×C4⋊C4—91no—
518C2×C22⋊C4—31no—
519C2×C22⋊C4—31no—
520C2×C22⋊C4—91no—
521C2×C22⋊C4—91no—
522C2×C42—31no—
523C2×C42—91no—
524C2×C42—91no—
525C2×C42—91no—
526C23×C3—21no—
527C23×C3—34no—
528C23×C3—32no—
529C23×C3—62no—
530C23×C3—62no—
531C23×C3C23×D311yescharacteristic
532C23×C3C23×D311yescharacteristic
533C22×D3—22no—
534C22×D3—22no—
535C22×D3D3×Q814yes—
536C22×D3C23×D312yes—
537C3×Q8—44no—
538C3×Q8—44no—
539C3×Q8—48no—
540C3×Q8—124no—
541C2×C3×C4—24no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
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—34no—
552C2×C3×C4—32no—
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—62no—
562C2×C3×C4—62no—
563C2×C3×C4—62no—
564C2×C3×C4—62no—
565C2×C3×C4—62no—
566C2×C3×C4—62no—
567C2×C3×C4—124no—
568C2×C3×C4C23×D312yes—
569C2×C3×C4C23×D312yes—
570C2×C3×C4C23×D312yes—
571C2×C3×C4C23×D312yes—
572C2×C3×C4C23×D312yes—
573C2×C3×C4C23×D312yes—
574C2×Dic3—22no—
575C2×Dic3—22no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—34no—
581C2×Dic3—34no—
582C2×Dic3—32no—
583C2×Dic3—32no—
584C2×Dic3—316no—
585C2×Dic3—32no—
586C2×Dic3—32no—
587C2×Dic3—32no—
588C2×Dic3—32no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—64no—
592C2×Dic3—62no—
593C2×Dic3—62no—
594C2×Dic3—62no—
595C2×Dic3—62no—
596C2×Dic3—64no—
597C2×Dic3—62no—
598C2×Dic3—62no—
599C2×Dic3—62no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—62no—
603C2×Dic3—122no—
604C2×Dic3—122no—
605C2×Dic3—124no—
606C2×Dic3D3×Q814yes—
607C2×Dic3C23×D312yes—
608C2×Dic3C23×D312yes—
609C2×Dic3C23×D312yes—
610C2×Dic3C23×D312yes—
611C2×Dic3C23×D312yes—
612C2×Dic3C23×D312yes—
613C2×Dic3C23×D312yes—
614C4×D3—316no—
615C4×D3—44no—
616C4×D3—124no—
617Dic6—44no—
618Dic6—124no—
619Dic6—124no—
620Dic6—124no—
621Dic6—124no—
622Dic6—128no—
623C2×C32#54414yescomplemented
624C2×C32C23×Q811yescharacteristic
625C2×C32C2×H(5,𝔽2)11yescharacteristic
626C2×C32C2×2−1+411yescharacteristic
627C3×D3—24no—
628C24—31no—
629C2×Q8—34no—
630C2×Q8—42no—
631C2×Q8—94no—
632C2×Q8—94no—
633C2×Q8—122no—
634C2×Q8—362no—
635C2×Q8—362no—
636C2×Q8C2×D3214yes—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—34no—
645C22×C4—94no—
646C22×C4—98no—
647C22×C4—94no—
648C22×C4—91no—
649C22×C4—91no—
650C22×C4—91no—
651C22×C4—91no—
652C22×C4—122no—
653C22×C4—362no—
654C22×C4C2×D3211yescharacteristic
655C22×C4C2×D3211yescharacteristic
656C22×C4C2×D3211yescharacteristic
657C4⋊C4—34no—
658C4⋊C4—34no—
659C4⋊C4—34no—
660C4⋊C4—34no—
661C4⋊C4—34no—
662C4⋊C4—34no—
663C4⋊C4—34no—
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—
675C4⋊C4—94no—
676C4⋊C4—94no—
677C22⋊C4—34no—
678C22⋊C4—34no—
679C22⋊C4—94no—
680C22⋊C4—94no—
681C42—34no—
682C42—94no—
683C42—94no—
684C42—94no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—21no—
689C22×C3—34no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—68no—
693C22×C3#100412yes—
694C22×C3#100412yes—
695C22×C3C2×D3×Q812yes—
696C22×C3C2×D3×Q812yes—
697C22×C3#100712yes—
698C22×C3#101012yes—
699C22×C3C24×D311yescharacteristic
700C22×C3C24×D311yescharacteristic
701C2×D3—22no—
702C2×D3—22no—
703C2×D3—28no—
704C2×D3C2×D3×Q814yes—
705C3×C4—24no—
706C3×C4—22no—
707C3×C4—22no—
708C3×C4—22no—
709C3×C4—22no—
710C3×C4—22no—
711C3×C4—22no—
712C3×C4—34no—
713C3×C4—42no—
714C3×C4—42no—
715C3×C4—62no—
716C3×C4—62no—
717C3×C4—62no—
718C3×C4—62no—
719C3×C4—62no—
720C3×C4—62no—
721Dic3—22no—
722Dic3—22no—
723Dic3—22no—
724Dic3—22no—
725Dic3—22no—
726Dic3—22no—
727Dic3—34no—
728Dic3—34no—
729Dic3—64no—
730Dic3—64no—
731Dic3—62no—
732Dic3—62no—
733Dic3—62no—
734Dic3—62no—
735Dic3—62no—
736Dic3—62no—
737Dic3—122no—
738Dic3—122no—
739Dic3C2×D3×Q814yes—
740C32C2×#54411yescharacteristic, complemented, Sylow
741C23—34no—
742C23—32no—
743C23—62no—
744C23—62no—
745C23C22×D3211yescharacteristic
746Q8—44no—
747Q8—124no—
748Q8—364no—
749Q8—364no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—34no—
754C2×C4—32no—
755C2×C4—32no—
756C2×C4—32no—
757C2×C4—32no—
758C2×C4—32no—
759C2×C4—32no—
760C2×C4—32no—
761C2×C4—62no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—916no—
768C2×C4—94no—
769C2×C4—92no—
770C2×C4—92no—
771C2×C4—92no—
772C2×C4—92no—
773C2×C4—124no—
774C2×C4—182no—
775C2×C4—182no—
776C2×C4—182no—
777C2×C4—364no—
778C2×C4C22×D3212yes—
779C2×C4C22×D3212yes—
780C2×C4C22×D3212yes—
781C2×C3—24no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—64no—
786C2×C3#562314yescomplemented
787C2×C3#572914yescomplemented
788C2×C3C2×#100411yescharacteristic
789C2×C3C2×#100411yescharacteristic
790C2×C3C22×D3×Q811yescharacteristic
791C2×C3C22×D3×Q811yescharacteristic
792C2×C3C2×#100711yescharacteristic
793C2×C3C2×#101011yescharacteristic
794D3—24no—
795C22—34no—
796C22—68no—
797C22—62no—
798C22—62no—
799C22#6431512yes—
800C22D32×Q812yes—
801C22#6433012yes—
802C22C23×D3211yescharacteristic
803C4—22no—
804C4—22no—
805C4—22no—
806C4—34no—
807C4—62no—
808C4—62no—
809C4—62no—
810C4—62no—
811C4—62no—
812C4—62no—
813C4—94no—
814C4—182no—
815C4—182no—
816C4—182no—
817C3—21no—
818C3C2×#562311yescharacteristic, complemented
819C3C2×#572911yescharacteristic, complemented
820C2—64no—
821C2#1059536914yesdirect product factor
822C2C2×#6431511yescharacteristic
823C2C2×D32×Q811yescharacteristic
824C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC22×Q8D32
hypocenterC32C2×#544
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64153C2semidirect
3. C2×C3×#944C2semidirect
4. #10595369C2direct (N × H)
10. C2×#63870C2semidirect
11. C2×#63867C2semidirect
13. C2×#63847C2semidirect
14. C2×#63846C2semidirect
15. C2×#63840C2semidirect
16. C2×#63839C2semidirect
26. #64153C22semidirect
33. C3×#944C22semidirect
62. #63870C22semidirect
63. #63867C22semidirect
65. #63847C22semidirect
66. #63846C22semidirect
67. #63840C22semidirect
68. #63839C22semidirect
77. C2×#944D3semidirect
128. C2×D3×Dic3Q8semidirect
196. #944C2×D3semidirect
307. D3×Dic3C2×Q8semidirect
623. C2×C32#544semidirect
740. C32C2×#544semidirect
786. C2×C3#5623semidirect
787. C2×C3#5729semidirect
818. C3C2×#5623semidirect
819. C3C2×#5729semidirect
821. C2#10595369direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641532
C2×C3×#9462
C2×C3×#9442
#105953692
C2×#638962
C2×#638872
C2×#638782
C2×#638772
C2×D3×Dic3⋊C42
C2×#638702
C2×#638672
C2×#638512
C2×#638472
C2×#638462
C2×#638402
C2×#638392
C2×#57293
C2×#56233