Finite Group Databasebeta

← C2×#10594503 #11910319

Subgroups — C2×#10594503 #11910319

Order 1152.

2209 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64105C211yesmaximal, characteristic, complemented
2C2×C3×#898C211yesmaximal, characteristic, complemented
3C2×C3×#888C211yesmaximal, characteristic, complemented
4C2×#63907C211yesmaximal, characteristic
5C2×#63896C211yesmaximal, characteristic, complemented
6C2×#63890C211yesmaximal, characteristic
7C2×#63887C211yesmaximal, characteristic, complemented
8C2×#63871C211yesmaximal, characteristic, complemented
9C2×#63868C211yesmaximal, characteristic, complemented
10C2×#63868C211yesmaximal, characteristic, complemented
11C2×#63866C211yesmaximal, characteristic, complemented
12C2×#63859C211yesmaximal, characteristic, complemented
13C2×#63853C211yesmaximal, characteristic
14C2×#63847C211yesmaximal, characteristic, complemented
15C2×#63846C211yesmaximal, characteristic, complemented
16#10594503C2116yesmaximal, direct product factor
17C2×#5735—31nomaximal
18C2×#5712—31nomaximal
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30#64105C2218yescomplemented
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C3×#898C2218yescomplemented
42C3×#888C2218yescomplemented
43C2×#3724C2211yescharacteristic
44C2×#3724C2211yescharacteristic
45C2×Dic3⋊Dic3C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63907C2218yes—
58#63896C2218yescomplemented
59#63890C2218yes—
60#63887C2218yescomplemented
61#63871C2218yescomplemented
62#63868C2218yescomplemented
63#63868C2218yescomplemented
64#63866C2218yescomplemented
65#63859C2218yescomplemented
66#63853C2218yes—
67#63847C2218yescomplemented
68#63846C2218yescomplemented
69C2×C3×C4⋊Q8—31no—
70C2×C3×#126—31no—
71C2×#947—31no—
72C2×#946—31no—
73C2×#946—31no—
74C2×#944—31no—
75#5735—316no—
76#5712—316no—
77C2×#898—31no—
78C2×#898—31no—
79C2×#898D311yescharacteristic, complemented
80C2×#897—31no—
81C2×#896—31no—
82C2×#896—31no—
83C2×#896—31no—
84C2×#896—61no—
85C2×#894—31no—
86C2×#894—31no—
87C2×#890—31no—
88C2×#889—31no—
89C2×#889—31no—
90C2×#889—31no—
91C2×#888D311yescharacteristic, complemented
92C2×#886—31no—
93C2×#885—31no—
94C2×#883—31no—
95C2×#879—31no—
96C2×#878—31no—
97C2×#878—31no—
98C2×#876—31no—
99C2×#876—31no—
100C2×#876—31no—
101C2×#869—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
110C2×C4×C3⋊D3—42no—
111C2×C4×C3⋊D3C2314yes—
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×Dic6—42no—
122C2×C3×Dic6—42no—
123C2×C3×Dic6C2314yes—
124C2×C3×Dic6C2314yes—
125C2×#626—42no—
126C2×#626C2314yes—
127C2×D3×Dic3—42no—
128C2×D3×Dic3C2314yes—
129C32×C4⋊C4C2314yes—
130#3752C2314yes—
131#3752C2314yes—
132#3750C2314yes—
133#3750C2314yes—
134C3×(C2×D3)⋊C4C2314yes—
135C3×(C2×D3)⋊C4C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×C4⋊Dic3C2314yes—
138C3×C4⋊Dic3C2314yes—
139C3×Dic3⋊C4C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×Dic3⋊C4C2314yes—
142C3×C4×Dic3C2314yes—
143C3×C4×Dic3C2314yes—
144#3724C2314yes—
145#3724C2314yes—
146Dic3⋊Dic3C2314yes—
147Dic3⋊Dic3C2314yes—
148Dic3⋊Dic3C2314yes—
149Dic3⋊Dic3C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152#3722C2314yes—
153#3722C2314yes—
154#3722C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157Dic32C2314yes—
158C2×#563—91noSylow
159C22×C3×Q8—31no—
160C22×C3×Q8—31no—
161C22×#67—31no—
162C23×Dic3—31no—
163C22×D12—31no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C22×C4×D3—31no—
167C22×C4×D3—61no—
168C22×Dic6—31no—
169C22×Dic6—31no—
170C22×Dic6—61no—
171C22×Dic6C2×D311yescharacteristic
172C22×Dic6C2×D311yescharacteristic
173C3×C4⋊Q8—38no—
174C3×#126—38no—
175C2×C3×C4⋊C4—21no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C4⋊C4C2×D311yescharacteristic
182C2×C3×C4⋊C4C2×D311yescharacteristic
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C42—31no—
187C2×C3×C42—31no—
188C2×#217—31no—
189C2×#217—31no—
190#947—38no—
191#946—38no—
192#946—38no—
193#944—38no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—61no—
207C2×(C2×D3)⋊C4—61no—
208C2×(C2×D3)⋊C4C2×D311yescharacteristic
209C2×(C2×D3)⋊C4C2×D311yescharacteristic
210C2×(C2×D3)⋊C4C2×D311yescharacteristic
211C2×C4⋊Dic3—31no—
212C2×C4⋊Dic3—31no—
213C2×C4⋊Dic3—31no—
214C2×C4⋊Dic3—31no—
215C2×C4⋊Dic3—31no—
216C2×C4⋊Dic3—31no—
217C2×C4⋊Dic3C2×D311yescharacteristic
218C2×C4⋊Dic3C2×D311yescharacteristic
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—31no—
232C2×Dic3⋊C4—31no—
233C2×Dic3⋊C4—61no—
234C2×Dic3⋊C4—61no—
235C2×Dic3⋊C4C2×D311yescharacteristic
236C2×Dic3⋊C4C2×D311yescharacteristic
237C2×Dic3⋊C4C2×D311yescharacteristic
238C2×C4×Dic3—31no—
239C2×C4×Dic3—31no—
240C2×C4×Dic3C2×D311yescharacteristic
241C2×C4×Dic3C2×D311yescharacteristic
242#898—38no—
243#898—38no—
244#898C2×D318yescomplemented
245#897—38no—
246#896—38no—
247#896—38no—
248#896—38no—
249#896—68no—
250#894—38no—
251#894—38no—
252#890—38no—
253#889—38no—
254#889—38no—
255#889—38no—
256#888C2×D318yescomplemented
257#886—38no—
258#885—38no—
259#883—38no—
260#879—38no—
261#878—38no—
262#878—38no—
263#876—38no—
264#876—38no—
265#876—38no—
266#869—38no—
267C23×C32C2411yescharacteristic
268C22×C3⋊D3—22no—
269C22×C3⋊D3—22no—
270C22×C3⋊D3—22no—
271C22×C3⋊D3C2412yes—
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×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⋊Dic3C2412yes—
286C2×C3⋊Dic3C2412yes—
287C2×C3⋊Dic3C2412yes—
288C4×C3⋊D3—44no—
289#634—44no—
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×Dic3—22no—
297C2×C3×Dic3C2412yes—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2412yes—
304C3×Dic6—44no—
305C3×Dic6—44no—
306#626—44no—
307D3×Dic3—44no—
308#563—916no—
309C2×C4⋊Q8—31no—
310C2×C4⋊Q8—91no—
311C2×#126—31no—
312C2×#126—91no—
313C2×#126—91no—
314C2×#126—91no—
315C2×#125—91no—
316C2×#125—91no—
317C2×#124—91no—
318C2×#123—91no—
319C2×#123—91no—
320C2×C22⋊Q8—91no—
321C2×C22⋊Q8—91no—
322C2×C22⋊Q8—91no—
323C2×C22⋊Q8—91no—
324C24×C3—31no—
325C23×D3—31no—
326C23×D3—31no—
327C23×D3—61no—
328C23×D3C22×D311yescharacteristic
329C2×C3×Q8—34no—
330C2×C3×Q8—34no—
331C2×C3×Q8—122no—
332C2×C3×Q8—122no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—31no—
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×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C2×#67—34no—
350C2×#67—122no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—34no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—122no—
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C2×D12—34no—
370C2×D12—122no—
371C2×C4×D3—34no—
372C2×C4×D3—34no—
373C2×C4×D3—34no—
374C2×C4×D3—64no—
375C2×C4×D3—122no—
376C2×C4×D3—122no—
377C2×C4×D3—124no—
378C2×C4×D3—122no—
379C2×Dic6—34no—
380C2×Dic6—34no—
381C2×Dic6—42no—
382C2×Dic6—42no—
383C2×Dic6—64no—
384C2×Dic6—122no—
385C2×Dic6—122no—
386C2×Dic6—124no—
387C2×Dic6C22×D314yes—
388C2×Dic6C22×D314yes—
389C3×C4⋊C4—24no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—34no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—34no—
395C3×C4⋊C4C22×D314yes—
396C3×C4⋊C4C22×D314yes—
397C3×C22⋊C4—34no—
398C3×C22⋊C4—34no—
399C3×C22⋊C4—34no—
400C3×C42—34no—
401C3×C42—34no—
402#217—34no—
403#217—34no—
404(C2×D3)⋊C4—34no—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—34no—
408(C2×D3)⋊C4—34no—
409(C2×D3)⋊C4—34no—
410(C2×D3)⋊C4—34no—
411(C2×D3)⋊C4—34no—
412(C2×D3)⋊C4—34no—
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4—34no—
415(C2×D3)⋊C4—34no—
416(C2×D3)⋊C4—64no—
417(C2×D3)⋊C4—64no—
418(C2×D3)⋊C4C22×D314yes—
419(C2×D3)⋊C4C22×D314yes—
420(C2×D3)⋊C4C22×D314yes—
421C4⋊Dic3—34no—
422C4⋊Dic3—34no—
423C4⋊Dic3—34no—
424C4⋊Dic3—34no—
425C4⋊Dic3—34no—
426C4⋊Dic3—34no—
427C4⋊Dic3C22×D314yes—
428C4⋊Dic3C22×D314yes—
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—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—34no—
440Dic3⋊C4—34no—
441Dic3⋊C4—34no—
442Dic3⋊C4—34no—
443Dic3⋊C4—64no—
444Dic3⋊C4—64no—
445Dic3⋊C4C22×D314yes—
446Dic3⋊C4C22×D314yes—
447Dic3⋊C4C22×D314yes—
448C4×Dic3—34no—
449C4×Dic3—34no—
450C4×Dic3C22×D314yes—
451C4×Dic3C22×D314yes—
452C22×C32H(5,𝔽2)12yes—
453C22×C322−1+412yes—
454C22×C322−1+412yes—
455C22×C32C2511yescharacteristic
456C2×C3⋊D3—22no—
457C2×C3⋊D3—22no—
458C2×C3⋊D3—22no—
459C2×C3⋊D3—44no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—44no—
464C32×C4—22no—
465C32×C4—22no—
466C32×C4—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×Dic3—22no—
476C3×Dic3—22no—
477C22×Q8—31no—
478C22×Q8—31no—
479C22×Q8—91no—
480C22×D4—91no—
481C23×C4—91no—
482C23×C4—91no—
483C4⋊Q8—38no—
484C4⋊Q8—98no—
485#126—38no—
486#126—98no—
487#126—98no—
488#126—98no—
489#125—98no—
490#125—98no—
491#124—98no—
492#123—98no—
493#123—98no—
494C22⋊Q8—98no—
495C22⋊Q8—98no—
496C22⋊Q8—98no—
497C22⋊Q8—98no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—31no—
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⋊C4—91no—
512C2×C4⋊C4—91no—
513C2×C4⋊C4D3211yescharacteristic
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×C22⋊C4—91no—
521C2×C22⋊C4—91no—
522C2×C22⋊C4—91no—
523C2×C22⋊C4—91no—
524C2×C42—31no—
525C2×C42—31no—
526C2×C42—91no—
527C23×C3—21no—
528C23×C3—32no—
529C23×C3—62no—
530C23×C3—62no—
531C23×C3—62no—
532C23×C3C23×D311yescharacteristic
533C23×C3C23×D311yescharacteristic
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—32no—
538C22×D3—32no—
539C22×D3—62no—
540C22×D3—64no—
541C22×D3—62no—
542C22×D3—62no—
543C22×D3—62no—
544C22×D3—62no—
545C22×D3—62no—
546C22×D3—62no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3C23×D312yes—
550C3×Q8—124no—
551C3×Q8—124no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—32no—
564C2×C3×C4—32no—
565C2×C3×C4—32no—
566C2×C3×C4—32no—
567C2×C3×C4—32no—
568C2×C3×C4—42no—
569C2×C3×C4—42no—
570C2×C3×C4—42no—
571C2×C3×C4—62no—
572C2×C3×C4—62no—
573C2×C3×C4—62no—
574C2×C3×C4—62no—
575C2×C3×C4—62no—
576C2×C3×C4—62no—
577C2×C3×C4—62no—
578C2×C3×C4C23×D312yes—
579C2×C3×C4C23×D312yes—
580C2×C3×C4C23×D312yes—
581C2×C3×C4C23×D312yes—
582C2×C3×C4C23×D312yes—
583C2×C3×C4C23×D312yes—
584#67—124no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—32no—
596C2×Dic3—32no—
597C2×Dic3—32no—
598C2×Dic3—62no—
599C2×Dic3—62no—
600C2×Dic3—62no—
601C2×Dic3—64no—
602C2×Dic3—62no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—62no—
606C2×Dic3—62no—
607C2×Dic3—62no—
608C2×Dic3—122no—
609C2×Dic3—122no—
610C2×Dic3—124no—
611C2×Dic3C23×D312yes—
612C2×Dic3C23×D312yes—
613C2×Dic3C23×D312yes—
614C2×Dic3C23×D312yes—
615C2×Dic3C23×D312yes—
616C2×Dic3C23×D312yes—
617C2×Dic3C23×D312yes—
618D12—124no—
619C4×D3—124no—
620C4×D3—124no—
621C4×D3—128no—
622C4×D3—124no—
623Dic6—44no—
624Dic6—44no—
625Dic6—124no—
626Dic6—124no—
627Dic6—128no—
628C2×C32#56314yescomplemented
629C2×C32C2×H(5,𝔽2)11yescharacteristic
630C2×C32C2×2−1+411yescharacteristic
631C2×C32C2×2−1+411yescharacteristic
632C3⋊D3—42no—
633C3×D3—42no—
634C24—31no—
635C24—91no—
636C2×Q8—34no—
637C2×Q8—34no—
638C2×Q8—94no—
639C2×Q8—122no—
640C2×Q8—122no—
641C2×Q8—362no—
642C2×D4—94no—
643C2×D4—362no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—94no—
652C22×C4—91no—
653C22×C4—91no—
654C22×C4—91no—
655C22×C4—94no—
656C22×C4—362no—
657C22×C4—362no—
658C22×C4C2×D3211yescharacteristic
659C22×C4C2×D3211yescharacteristic
660C22×C4C2×D3211yescharacteristic
661C4⋊C4—34no—
662C4⋊C4—34no—
663C4⋊C4—34no—
664C4⋊C4—34no—
665C4⋊C4—34no—
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⋊C4C2×D3214yes—
677C22⋊C4—34no—
678C22⋊C4—34no—
679C22⋊C4—34no—
680C22⋊C4—94no—
681C22⋊C4—94no—
682C22⋊C4—94no—
683C22⋊C4—94no—
684C22⋊C4—94no—
685C22⋊C4—94no—
686C22⋊C4—94no—
687C42—34no—
688C42—34no—
689C42—94no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—21no—
694C22×C3—62no—
695C22×C3—62no—
696C22×C3—62no—
697C22×C3—124no—
698C22×C3#100412yes—
699C22×C3#100712yes—
700C22×C3#100712yes—
701C22×C3#100912yes—
702C22×C3#101012yes—
703C22×C3#101012yes—
704C22×C3C24×D311yescharacteristic
705C22×C3C24×D311yescharacteristic
706C2×D3—22no—
707C2×D3—22no—
708C2×D3—22no—
709C2×D3—44no—
710C2×D3—64no—
711C2×D3—62no—
712C2×D3—62no—
713C2×D3—62no—
714C2×D3—62no—
715C2×D3—62no—
716C2×D3—62no—
717C2×D3—122no—
718C2×D3—122no—
719C2×D3—128no—
720C2×D3—124no—
721C2×D3—124no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—42no—
731C3×C4—62no—
732C3×C4—62no—
733C3×C4—62no—
734C3×C4—62no—
735C3×C4—62no—
736C3×C4—62no—
737C3×C4—62no—
738Dic3—22no—
739Dic3—22no—
740Dic3—22no—
741Dic3—22no—
742Dic3—22no—
743Dic3—22no—
744Dic3—22no—
745Dic3—64no—
746Dic3—62no—
747Dic3—62no—
748Dic3—62no—
749Dic3—62no—
750Dic3—62no—
751Dic3—62no—
752Dic3—122no—
753Dic3—122no—
754C32C2×#56311yescharacteristic, complemented, Sylow
755C23—32no—
756C23—62no—
757C23—62no—
758C23—62no—
759C23—92no—
760C23—182no—
761C23—182no—
762C23—182no—
763C23C22×D3211yescharacteristic
764Q8—124no—
765Q8—124no—
766Q8—364no—
767D4—364no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—92no—
786C2×C4—92no—
787C2×C4—92no—
788C2×C4—182no—
789C2×C4—182no—
790C2×C4—182no—
791C2×C4—364no—
792C2×C4—364no—
793C2×C4C22×D3212yes—
794C2×C4C22×D3212yes—
795C2×C4C22×D3212yes—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—24no—
800C2×C3—122no—
801C2×C3#571214yescomplemented
802C2×C3#573514yescomplemented
803C2×C3C2×#100411yescharacteristic
804C2×C3C2×#100711yescharacteristic
805C2×C3C2×#100711yescharacteristic
806C2×C3C2×#100911yescharacteristic
807C2×C3C2×#101011yescharacteristic
808C2×C3C2×#101011yescharacteristic
809D3—42no—
810D3—124no—
811D3—122no—
812D3—122no—
813C22—62no—
814C22—62no—
815C22—62no—
816C22—124no—
817C22—182no—
818C22—182no—
819C22—182no—
820C22—364no—
821C22#6429712yes—
822C22#6431412yes—
823C22#6431512yes—
824C22C23×D3211yescharacteristic
825C4—22no—
826C4—22no—
827C4—22no—
828C4—62no—
829C4—62no—
830C4—62no—
831C4—62no—
832C4—62no—
833C4—62no—
834C4—62no—
835C4—182no—
836C4—182no—
837C4—182no—
838C3—21no—
839C3C2×#571211yescharacteristic, complemented
840C3C2×#573511yescharacteristic, complemented
841C2—122no—
842C2—362no—
843C2#1059450314yesdirect product factor
844C2C2×#6429711yescharacteristic
845C2C2×#6431411yescharacteristic
846C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#563
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×#64105C2semidirect
2. C2×C3×#898C2semidirect
3. C2×C3×#888C2semidirect
5. C2×#63896C2semidirect
7. C2×#63887C2semidirect
8. C2×#63871C2semidirect
9. C2×#63868C2semidirect
10. C2×#63868C2semidirect
11. C2×#63866C2semidirect
12. C2×#63859C2semidirect
14. C2×#63847C2semidirect
15. C2×#63846C2semidirect
16. #10594503C2direct (N × H)
30. #64105C22semidirect
41. C3×#898C22semidirect
42. C3×#888C22semidirect
58. #63896C22semidirect
60. #63887C22semidirect
61. #63871C22semidirect
62. #63868C22semidirect
63. #63868C22semidirect
64. #63866C22semidirect
65. #63859C22semidirect
67. #63847C22semidirect
68. #63846C22semidirect
79. C2×#898D3semidirect
91. C2×#888D3semidirect
244. #898C2×D3semidirect
256. #888C2×D3semidirect
628. C2×C32#563semidirect
754. C32C2×#563semidirect
801. C2×C3#5712semidirect
802. C2×C3#5735semidirect
839. C3C2×#5712semidirect
840. C3C2×#5735semidirect
843. C2#10594503direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641052
C2×C3×#8982
C2×C3×#8882
C2×#639072
C2×#638962
C2×#638902
C2×#638872
C2×#638712
C2×#638682
C2×#638662
C2×#638592
C2×#638532
C2×#638472
C2×#638462
#105945032
C2×#57353
C2×#57123