Finite Group Databasebeta

← C2×#10595345 #11910322

Subgroups — C2×#10595345 #11910322

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×#64155C211yesmaximal, characteristic, complemented
2C2×C3×#946C211yesmaximal, characteristic, complemented
3C2×C3×#944C211yesmaximal, characteristic, complemented
4#10595345C2116yesmaximal, direct product factor
5C2×#63907C211yesmaximal, characteristic
6C2×#63868C211yesmaximal, characteristic, complemented
7C2×#63865C211yesmaximal, characteristic, complemented
8C2×#63861C211yesmaximal, characteristic, complemented
9C2×#63859C211yesmaximal, characteristic, complemented
10C2×#63853C211yesmaximal, characteristic
11C2×#63851C211yesmaximal, characteristic, complemented
12C2×#63850C211yesmaximal, characteristic
13C2×#63848C211yesmaximal, characteristic, complemented
14C2×#63847C211yesmaximal, characteristic, complemented
15C2×#63845C211yesmaximal, characteristic, complemented
16C2×#63839C211yesmaximal, characteristic, complemented
17C2×#5735—31nomaximal
18C2×#5646—31nomaximal
19C22×C32×Q8C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#626C2211yescharacteristic
25#64155C2218yescomplemented
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C3×#946C2218yescomplemented
32C3×#944C2218yescomplemented
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C2×#3724C2211yescharacteristic
44C2×#3724C2211yescharacteristic
45C2×#3724C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×#3722C2211yescharacteristic
50C2×#3722C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63907C2218yes—
58#63868C2218yescomplemented
59#63865C2218yescomplemented
60#63861C2218yescomplemented
61#63859C2218yescomplemented
62#63853C2218yes—
63#63851C2218yescomplemented
64#63850C2218yes—
65#63848C2218yescomplemented
66#63847C2218yescomplemented
67#63845C2218yescomplemented
68#63839C2218yescomplemented
69C2×C3×C4⋊Q8—31no—
70C2×C3×C22⋊Q8—31no—
71C2×#947—31no—
72C2×#946—31no—
73C2×#946—31no—
74C2×#946—61no—
75C2×#946D311yescharacteristic, complemented
76C2×#944—31no—
77C2×#944D311yescharacteristic, complemented
78C2×#929—31no—
79C2×#924—31no—
80#5735—316no—
81#5646—316no—
82C2×#898—31no—
83C2×#898—31no—
84C2×#898—31no—
85C2×#898—31no—
86C2×#896—31no—
87C2×#896—31no—
88C2×#896—31no—
89C2×#894—31no—
90C2×#894—31no—
91C2×#890—31no—
92C2×#889—31no—
93C2×#889—31no—
94C2×#889—31no—
95C2×#888—31no—
96C2×#885—31no—
97C2×#883—31no—
98C2×#879—31no—
99C2×#879—31no—
100C2×#876—31no—
101C2×#876—31no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C2×C32×Q8—42no—
105C2×C32×Q8C2314yes—
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C2×C4×C3⋊D3—42no—
113C2×C4×C3⋊D3C2314yes—
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×#626—42no—
128C2×#626C2314yes—
129#3752C2314yes—
130#3752C2314yes—
131C4⋊(C3⋊Dic3)C2314yes—
132#3750C2314yes—
133#3750C2314yes—
134C3×(C2×D3)⋊C4C2314yes—
135C3×(C2×D3)⋊C4C2314yes—
136C3×C4⋊Dic3C2314yes—
137C3×Dic3⋊C4C2314yes—
138C3×Dic3⋊C4C2314yes—
139C3×Dic3⋊C4C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×Dic3⋊C4C2314yes—
142C3×Dic3⋊C4C2314yes—
143C3×C4×Dic3C2314yes—
144#3724C2314yes—
145#3724C2314yes—
146#3724C2314yes—
147Dic3⋊Dic3C2314yes—
148Dic3⋊Dic3C2314yes—
149Dic3⋊Dic3C2314yes—
150#3722C2314yes—
151#3722C2314yes—
152#3722C2314yes—
153(C2×D3)⋊Dic3C2314yes—
154(C2×D3)⋊Dic3C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156Dic32C2314yes—
157Dic32C2314yes—
158C2×#563—91noSylow
159C22×C3×Q8—21no—
160C22×C3×Q8—31no—
161C22×C3×Q8C2×D311yescharacteristic
162C22×C3×Q8C2×D311yescharacteristic
163C23×C3×C4—31no—
164C22×#67—31no—
165C22×D12—31no—
166C22×C4×D3—31no—
167C22×C4×D3—31no—
168C22×C4×D3—61no—
169C22×C4×D3C2×D311yescharacteristic
170C22×Dic6—31no—
171C22×Dic6—31no—
172C22×Dic6C2×D311yescharacteristic
173C3×C4⋊Q8—38no—
174C3×C22⋊Q8—38no—
175C2×C3×C4⋊C4—31no—
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⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C42—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—31no—
188#947—38no—
189#946—38no—
190#946—38no—
191#946—68no—
192#946C2×D318yescomplemented
193#944—38no—
194#944C2×D318yescomplemented
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)⋊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—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4—61no—
210C2×(C2×D3)⋊C4—61no—
211C2×(C2×D3)⋊C4C2×D311yescharacteristic
212C2×(C2×D3)⋊C4C2×D311yescharacteristic
213C2×C4⋊Dic3—31no—
214C2×C4⋊Dic3—31no—
215C2×C4⋊Dic3—31no—
216C2×C4⋊Dic3—31no—
217C2×C4⋊Dic3—31no—
218C2×C4⋊Dic3—61no—
219C2×C4⋊Dic3C2×D311yescharacteristic
220#924—38no—
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—31no—
234C2×Dic3⋊C4—61no—
235C2×Dic3⋊C4—61no—
236C2×Dic3⋊C4C2×D311yescharacteristic
237C2×Dic3⋊C4C2×D311yescharacteristic
238C2×Dic3⋊C4C2×D311yescharacteristic
239C2×Dic3⋊C4C2×D311yescharacteristic
240C2×Dic3⋊C4C2×D311yescharacteristic
241C2×Dic3⋊C4C2×D311yescharacteristic
242C2×C4×Dic3—31no—
243C2×C4×Dic3—31no—
244C2×C4×Dic3—31no—
245C2×C4×Dic3—31no—
246C2×C4×Dic3C2×D311yescharacteristic
247#898—38no—
248#898—38no—
249#898—38no—
250#898—38no—
251#896—38no—
252#896—38no—
253#896—38no—
254#894—38no—
255#894—38no—
256#890—38no—
257#889—38no—
258#889—38no—
259#889—38no—
260#888—38no—
261#885—38no—
262#883—38no—
263#879—38no—
264#879—38no—
265#876—38no—
266#876—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—
276C32×Q8—44no—
277C2×C32×C4—22no—
278C2×C32×C4—22no—
279C2×C32×C4—22no—
280C2×C32×C4C2412yes—
281C2×C32×C4C2412yes—
282C2×C32×C4C2412yes—
283C2×C3⋊Dic3—22no—
284C2×C3⋊Dic3—22no—
285C2×C3⋊Dic3—22no—
286C2×C3⋊Dic3C2412yes—
287C2×C3⋊Dic3C2412yes—
288C2×C3⋊Dic3C2412yes—
289C4×C3⋊D3—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×C4×D3—44no—
305C3×Dic6—44no—
306#627—44no—
307#626—44no—
308#563—916no—
309C2×C4⋊Q8—31no—
310C2×C4⋊Q8—91no—
311C2×#126—91no—
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—31no—
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—24no—
330C2×C3×Q8—34no—
331C2×C3×Q8—42no—
332C2×C3×Q8—42no—
333C2×C3×Q8—44no—
334C2×C3×Q8—122no—
335C2×C3×Q8C22×D314yes—
336C2×C3×Q8C22×D314yes—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—34no—
348C22×C3×C4—122no—
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C2×#67—34no—
356C2×#67—122no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—61no—
364C22×Dic3—61no—
365C22×Dic3—61no—
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371C22×Dic3C22×D311yescharacteristic
372C22×Dic3C22×D311yescharacteristic
373C2×D12—34no—
374C2×D12—122no—
375C2×C4×D3—34no—
376C2×C4×D3—34no—
377C2×C4×D3—42no—
378C2×C4×D3—64no—
379C2×C4×D3—122no—
380C2×C4×D3—122no—
381C2×C4×D3—124no—
382C2×C4×D3C22×D314yes—
383C2×Dic6—34no—
384C2×Dic6—34no—
385C2×Dic6—42no—
386C2×Dic6—122no—
387C2×Dic6—122no—
388C2×Dic6C22×D314yes—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—34no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—34no—
395C3×C4⋊C4—34no—
396C3×C22⋊C4—34no—
397C3×C22⋊C4—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)⋊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—64no—
416(C2×D3)⋊C4—64no—
417(C2×D3)⋊C4C22×D314yes—
418(C2×D3)⋊C4C22×D314yes—
419C4⋊Dic3—34no—
420C4⋊Dic3—34no—
421C4⋊Dic3—34no—
422C4⋊Dic3—34no—
423C4⋊Dic3—34no—
424C4⋊Dic3—64no—
425C4⋊Dic3C22×D314yes—
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—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—64no—
440Dic3⋊C4—64no—
441Dic3⋊C4C22×D314yes—
442Dic3⋊C4C22×D314yes—
443Dic3⋊C4C22×D314yes—
444Dic3⋊C4C22×D314yes—
445Dic3⋊C4C22×D314yes—
446Dic3⋊C4C22×D314yes—
447C4×Dic3—34no—
448C4×Dic3—34no—
449C4×Dic3—34no—
450C4×Dic3—34no—
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—91no—
479C22×Q8D3211yescharacteristic
480C22×D4—91no—
481C23×C4—31no—
482C23×C4—91no—
483C4⋊Q8—38no—
484C4⋊Q8—98no—
485#126—98no—
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—38no—
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—31no—
504C2×C4⋊C4—31no—
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×C22⋊C4—31no—
515C2×C22⋊C4—31no—
516C2×C22⋊C4—91no—
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—91no—
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—44no—
551C3×Q8—44no—
552C3×Q8—48no—
553C3×Q8—124no—
554C2×C3×C4—24no—
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—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—32no—
565C2×C3×C4—32no—
566C2×C3×C4—32no—
567C2×C3×C4—32no—
568C2×C3×C4—32no—
569C2×C3×C4—32no—
570C2×C3×C4—32no—
571C2×C3×C4—42no—
572C2×C3×C4—42no—
573C2×C3×C4—62no—
574C2×C3×C4—62no—
575C2×C3×C4—62no—
576C2×C3×C4—62no—
577C2×C3×C4—62no—
578C2×C3×C4—62no—
579C2×C3×C4—62no—
580C2×C3×C4—124no—
581C2×C3×C4C23×D312yes—
582C2×C3×C4C23×D312yes—
583C2×C3×C4C23×D312yes—
584C2×C3×C4C23×D312yes—
585C2×C3×C4C23×D312yes—
586C2×C3×C4C23×D312yes—
587#67—124no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—32no—
596C2×Dic3—32no—
597C2×Dic3—32no—
598C2×Dic3—32no—
599C2×Dic3—32no—
600C2×Dic3—32no—
601C2×Dic3—62no—
602C2×Dic3—62no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—62no—
606C2×Dic3—62no—
607C2×Dic3—62no—
608C2×Dic3—62no—
609C2×Dic3—62no—
610C2×Dic3—122no—
611C2×Dic3—122no—
612C2×Dic3—122no—
613C2×Dic3C23×D312yes—
614C2×Dic3C23×D312yes—
615C2×Dic3C23×D312yes—
616C2×Dic3C23×D312yes—
617C2×Dic3C23×D312yes—
618C2×Dic3C23×D312yes—
619C2×Dic3C23×D312yes—
620D12—124no—
621C4×D3—44no—
622C4×D3—124no—
623C4×D3—124no—
624C4×D3—128no—
625Dic6—44no—
626Dic6—124no—
627Dic6—124no—
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—42no—
638C2×Q8—94no—
639C2×Q8—122no—
640C2×Q8—362no—
641C2×Q8C2×D3214yes—
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—34no—
652C22×C4—91no—
653C22×C4—91no—
654C22×C4—91no—
655C22×C4—94no—
656C22×C4—122no—
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—34no—
667C4⋊C4—34no—
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—
681C22⋊C4—94no—
682C22⋊C4—94no—
683C22⋊C4—94no—
684C22⋊C4—94no—
685C22⋊C4—94no—
686C22⋊C4—94no—
687C42—34no—
688C42—94no—
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#100412yes—
700C22×C3#100712yes—
701C22×C3#100712yes—
702C22×C3#100712yes—
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—24no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—22no—
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—62no—
746Dic3—62no—
747Dic3—62no—
748Dic3—62no—
749Dic3—62no—
750Dic3—62no—
751Dic3—122no—
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—44no—
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—124no—
789C2×C4—182no—
790C2×C4—182no—
791C2×C4—182no—
792C2×C4—364no—
793C2×C4C22×D3212yes—
794C2×C4C22×D3212yes—
795C2×C4C22×D3212yes—
796C2×C3—24no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—122no—
801C2×C3#564614yescomplemented
802C2×C3#573514yescomplemented
803C2×C3C2×#100411yescharacteristic
804C2×C3C2×#100411yescharacteristic
805C2×C3C2×#100711yescharacteristic
806C2×C3C2×#100711yescharacteristic
807C2×C3C2×#100711yescharacteristic
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#6431512yes—
822C22#6431612yes—
823C22#6433012yes—
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×#564611yescharacteristic, complemented
840C3C2×#573511yescharacteristic, complemented
841C2—122no—
842C2—362no—
843C2#1059534514yesdirect product factor
844C2C2×#6431511yescharacteristic
845C2C2×#6431611yescharacteristic
846C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC22×#626C22
hypercenterC22×Q8D32
hypocenterC32C2×#563
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64155C2semidirect
2. C2×C3×#946C2semidirect
3. C2×C3×#944C2semidirect
4. #10595345C2direct (N × H)
6. C2×#63868C2semidirect
7. C2×#63865C2semidirect
8. C2×#63861C2semidirect
9. C2×#63859C2semidirect
11. C2×#63851C2semidirect
13. C2×#63848C2semidirect
14. C2×#63847C2semidirect
15. C2×#63845C2semidirect
16. C2×#63839C2semidirect
25. #64155C22semidirect
31. C3×#946C22semidirect
32. C3×#944C22semidirect
58. #63868C22semidirect
59. #63865C22semidirect
60. #63861C22semidirect
61. #63859C22semidirect
63. #63851C22semidirect
65. #63848C22semidirect
66. #63847C22semidirect
67. #63845C22semidirect
68. #63839C22semidirect
75. C2×#946D3semidirect
77. C2×#944D3semidirect
192. #946C2×D3semidirect
194. #944C2×D3semidirect
628. C2×C32#563semidirect
754. C32C2×#563semidirect
801. C2×C3#5646semidirect
802. C2×C3#5735semidirect
839. C3C2×#5646semidirect
840. C3C2×#5735semidirect
843. C2#10595345direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641552
C2×C3×#9462
C2×C3×#9442
#105953452
C2×#639072
C2×#638682
C2×#638652
C2×#638612
C2×#638592
C2×#638532
C2×#638512
C2×#638502
C2×#638482
C2×#638472
C2×#638452
C2×#638392
C2×#57353
C2×#56463