Finite Group Databasebeta

← C2×#10594540 #11901417

Subgroups — C2×#10594540 #11901417

Order 1152.

2411 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64107C211yesmaximal, characteristic, complemented
2C2×C3×#896C211yesmaximal, characteristic, complemented
3C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×#63906C211yesmaximal, characteristic
5C2×#63905C211yesmaximal, characteristic, complemented
6C2×#63904C211yesmaximal, characteristic, complemented
7C2×C4×#625C211yesmaximal, characteristic, complemented
8C2×#63888C211yesmaximal, characteristic, complemented
9C2×#63870C211yesmaximal, characteristic, complemented
10C2×#63861C211yesmaximal, characteristic, complemented
11C2×#63856C211yesmaximal, characteristic, complemented
12C2×#63854C211yesmaximal, characteristic, complemented
13C2×#63850C211yesmaximal, characteristic, complemented
14C2×#63850C211yesmaximal, characteristic, complemented
15C2×#63847C211yesmaximal, characteristic, complemented
16#10594540C2116yesmaximal, direct product factor
17C2×#5638—31nomaximal
18C2×#5515—31nomaximal
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#625C2211yescharacteristic
27C22×#624C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×C4×C3⋊Dic3C2211yescharacteristic
35#64107C2218yescomplemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C3×#896C2218yescomplemented
44C3×D3×C4⋊C4C2218yescomplemented
45C2×#3724C2211yescharacteristic
46C2×#3724C2211yescharacteristic
47C2×#3724C2211yescharacteristic
48C2×#3724C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63906C2218yes—
58#63905C2218yescomplemented
59#63904C2218yescomplemented
60C4×#625C2218yescomplemented
61#63888C2218yescomplemented
62#63870C2218yescomplemented
63#63861C2218yescomplemented
64#63856C2218yescomplemented
65#63854C2218yescomplemented
66#63850C2218yescomplemented
67#63850C2218yescomplemented
68#63847C2218yescomplemented
69C2×C3×C22⋊Q8—31no—
70C22×C3×C4⋊C4—31no—
71C2×#946—31no—
72C2×#946—31no—
73C2×#930—31no—
74C2×#929—31no—
75C2×#929—31no—
76C2×#929—31no—
77C2×C4×#67—31no—
78C2×C4×#67—31no—
79C2×C4×#67—31no—
80C2×#924—31no—
81#5638—316no—
82#5515—316no—
83C2×#898—31no—
84C2×#898—31no—
85C2×#898—31no—
86C2×#898—61no—
87C2×#896—31no—
88C2×#896D311yescharacteristic, complemented
89C2×#894—31no—
90C2×#894—31no—
91C2×#894—31no—
92C2×#893—31no—
93C2×D3×C4⋊C4D311yescharacteristic, complemented
94C2×#889—31no—
95C2×#889—31no—
96C2×#889—31no—
97C2×#889—31no—
98C2×#884—31no—
99C2×#883—31no—
100C2×#883—31no—
101C2×#879—31no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
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×D3—42no—
119C2×C3×C4×D3—42no—
120C2×C3×C4×D3—42no—
121C2×C3×C4×D3C2314yes—
122C2×C3×C4×D3C2314yes—
123C2×C3×C4×D3C2314yes—
124C2×C3×C4×D3C2314yes—
125C2×C3×Dic6—42no—
126C2×C3×Dic6C2314yes—
127C2×#626—24no—
128C2×#626—42no—
129C2×#626C2314yes—
130C2×#626C2314yes—
131C2×#625—24no—
132C2×#625C2314yes—
133C2×#624—42no—
134C2×#624C2314yes—
135C32×C4⋊C4C2314yes—
136#3752C2314yes—
137#3752C2314yes—
138#3752C2314yes—
139C4⋊(C3⋊Dic3)C2314yes—
140#3750C2314yes—
141C4×C3⋊Dic3C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×C4⋊Dic3C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×Dic3⋊C4C2314yes—
149#3724C2314yes—
150#3724C2314yes—
151#3724C2314yes—
152#3724C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155#3722C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157(C2×D3)⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160Dic32C2314yes—
161C2×#539—91noSylow
162C22×C3×Q8—31no—
163C23×C3×C4—31no—
164C23×C3×C4—31no—
165C23×C3×C4—31no—
166C23×C3×C4—31no—
167C22×#67—31no—
168C22×#67—31no—
169C22×#67—31no—
170C22×#67—31no—
171C22×D12—31no—
172C22×D12—31no—
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C22×C4×D3C2×D311yescharacteristic
176C22×C4×D3C2×D311yescharacteristic
177C22×C4×D3C2×D311yescharacteristic
178C22×C4×D3C2×D311yescharacteristic
179C22×Dic6C2×D311yescharacteristic
180C3×C22⋊Q8—38no—
181C2×C3×C4⋊C4—21no—
182C2×C3×C4⋊C4—31no—
183C2×C3×C4⋊C4—31no—
184C2×C3×C4⋊C4—31no—
185C2×C3×C4⋊C4—31no—
186C2×C3×C4⋊C4—31no—
187C2×C3×C4⋊C4—38no—
188C2×C3×C4⋊C4C2×D311yescharacteristic
189C2×C3×C4⋊C4C2×D311yescharacteristic
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×#217—31no—
193C2×#217—31no—
194C2×#217—31no—
195C2×#217—31no—
196#946—38no—
197#946—38no—
198#930—38no—
199#929—38no—
200#929—38no—
201#929—38no—
202C4×#67—38no—
203C4×#67—38no—
204C4×#67—38no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4—31no—
215C2×(C2×D3)⋊C4—31no—
216C2×(C2×D3)⋊C4—31no—
217C2×(C2×D3)⋊C4—61no—
218C2×(C2×D3)⋊C4—61no—
219C2×(C2×D3)⋊C4—61no—
220C2×(C2×D3)⋊C4C2×D311yescharacteristic
221C2×(C2×D3)⋊C4C2×D311yescharacteristic
222C2×C4⋊Dic3—31no—
223C2×C4⋊Dic3—31no—
224C2×C4⋊Dic3—31no—
225C2×C4⋊Dic3—31no—
226C2×C4⋊Dic3—61no—
227C2×C4⋊Dic3C2×D311yescharacteristic
228#924—38no—
229C2×Dic3⋊C4—31no—
230C2×Dic3⋊C4—31no—
231C2×Dic3⋊C4—31no—
232C2×Dic3⋊C4—31no—
233C2×Dic3⋊C4—31no—
234C2×Dic3⋊C4—31no—
235C2×Dic3⋊C4—31no—
236C2×Dic3⋊C4—31no—
237C2×Dic3⋊C4—31no—
238C2×Dic3⋊C4—31no—
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—31no—
241C2×Dic3⋊C4—61no—
242C2×Dic3⋊C4C2×D311yescharacteristic
243C2×Dic3⋊C4C2×D311yescharacteristic
244C2×Dic3⋊C4C2×D311yescharacteristic
245C2×Dic3⋊C4C2×D311yescharacteristic
246C2×C4×Dic3—31no—
247C2×C4×Dic3—31no—
248C2×C4×Dic3—31no—
249C2×C4×Dic3—31no—
250C2×C4×Dic3—61no—
251#898—38no—
252#898—38no—
253#898—38no—
254#898—68no—
255#896—38no—
256#896C2×D318yescomplemented
257#894—38no—
258#894—38no—
259#894—38no—
260#893—38no—
261D3×C4⋊C4C2×D318yescomplemented
262#889—38no—
263#889—38no—
264#889—38no—
265#889—38no—
266#884—38no—
267#883—38no—
268#883—38no—
269#879—38no—
270C23×C32C2411yescharacteristic
271C22×C3⋊D3—22no—
272C22×C3⋊D3—22no—
273C22×C3⋊D3—22no—
274C22×C3⋊D3C2412yes—
275C22×C3×D3—22no—
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3#4114yes—
281C22×C3×D3C2412yes—
282C22×C3×D3C2412yes—
283C2×C32×C4—22no—
284C2×C32×C4—22no—
285C2×C32×C4—22no—
286C2×C32×C4C2412yes—
287C2×C32×C4C2412yes—
288C2×C32×C4C2412yes—
289C2×C3⋊Dic3—22no—
290C2×C3⋊Dic3—22no—
291C2×C3⋊Dic3—22no—
292C2×C3⋊Dic3C2412yes—
293C2×C3⋊Dic3C2412yes—
294C2×C3⋊Dic3C2412yes—
295C2×C3×Dic3—22no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C3×C4×D3—28no—
308C3×C4×D3—44no—
309C3×C4×D3—44no—
310C3×C4×D3—44no—
311C3×Dic6—44no—
312#626—28no—
313#626—44no—
314#625—28no—
315#624—44no—
316#539—916no—
317C2×#126—91no—
318C2×#126—91no—
319C2×#125—91no—
320C2×#125—91no—
321C2×#123—91no—
322C2×#123—91no—
323C2×#123—91no—
324C2×#123—91no—
325C2×C22⋊Q8—31no—
326C2×C22⋊Q8—91no—
327C2×C22⋊Q8—91no—
328C2×#121—91no—
329C2×C4×D4—91no—
330C2×C4×D4—91no—
331C22×C4⋊C4—31no—
332C24×C3—31no—
333C24×C3—31no—
334C23×D3—31no—
335C23×D3—31no—
336C23×D3—61no—
337C23×D3C22×D311yescharacteristic
338C23×D3C22×D311yescharacteristic
339C2×C3×Q8—34no—
340C2×C3×Q8—122no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—34no—
351C22×C3×C4—34no—
352C22×C3×C4—34no—
353C22×C3×C4—34no—
354C22×C3×C4—64no—
355C22×C3×C4—122no—
356C22×C3×C4—122no—
357C22×C3×C4—122no—
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C2×#67—34no—
365C2×#67—34no—
366C2×#67—34no—
367C2×#67—34no—
368C2×#67—64no—
369C2×#67—64no—
370C2×#67—64no—
371C2×#67—122no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—61no—
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C2×D12—34no—
388C2×D12—34no—
389C2×D12—64no—
390C2×D12—122no—
391C2×C4×D3—24no—
392C2×C4×D3—34no—
393C2×C4×D3—34no—
394C2×C4×D3—42no—
395C2×C4×D3—42no—
396C2×C4×D3—42no—
397C2×C4×D3—122no—
398C2×C4×D3—122no—
399C2×C4×D3C22×D314yes—
400C2×C4×D3C22×D314yes—
401C2×C4×D3C22×D314yes—
402C2×C4×D3C22×D314yes—
403C2×Dic6—42no—
404C2×Dic6C22×D314yes—
405C3×C4⋊C4—24no—
406C3×C4⋊C4—34no—
407C3×C4⋊C4—34no—
408C3×C4⋊C4—34no—
409C3×C4⋊C4—34no—
410C3×C4⋊C4—34no—
411C3×C4⋊C4C22×D314yes—
412C3×C4⋊C4C22×D314yes—
413C3×C22⋊C4—34no—
414C3×C22⋊C4—34no—
415#217—34no—
416#217—34no—
417#217—34no—
418#217—34no—
419(C2×D3)⋊C4—34no—
420(C2×D3)⋊C4—34no—
421(C2×D3)⋊C4—34no—
422(C2×D3)⋊C4—34no—
423(C2×D3)⋊C4—34no—
424(C2×D3)⋊C4—34no—
425(C2×D3)⋊C4—34no—
426(C2×D3)⋊C4—34no—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—64no—
432(C2×D3)⋊C4—64no—
433(C2×D3)⋊C4—64no—
434(C2×D3)⋊C4C22×D314yes—
435(C2×D3)⋊C4C22×D314yes—
436C4⋊Dic3—34no—
437C4⋊Dic3—34no—
438C4⋊Dic3—34no—
439C4⋊Dic3—34no—
440C4⋊Dic3—64no—
441C4⋊Dic3C22×D314yes—
442Dic3⋊C4—34no—
443Dic3⋊C4—34no—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
448Dic3⋊C4—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4—34no—
451Dic3⋊C4—34no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—64no—
455Dic3⋊C4C22×D314yes—
456Dic3⋊C4C22×D314yes—
457Dic3⋊C4C22×D314yes—
458Dic3⋊C4C22×D314yes—
459C4×Dic3—34no—
460C4×Dic3—34no—
461C4×Dic3—34no—
462C4×Dic3—34no—
463C4×Dic3—64no—
464C22×C32C2×#4112yes—
465C22×C32H(5,𝔽2)12yes—
466C22×C322−1+412yes—
467C22×C32C2511yescharacteristic
468C2×C3⋊D3—22no—
469C2×C3⋊D3—22no—
470C2×C3⋊D3—22no—
471C2×C3⋊D3—44no—
472C2×C3×D3—28no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—44no—
479C2×C3×D3C2×#4114yes—
480C32×C4—22no—
481C32×C4—22no—
482C32×C4—22no—
483C3⋊Dic3—22no—
484C3⋊Dic3—22no—
485C3⋊Dic3—22no—
486C3×Dic3—22no—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C22×Q8—31no—
493C22×D4—91no—
494C22×D4—91no—
495C22×D4—91no—
496C23×C4—31no—
497C23×C4—31no—
498C23×C4—31no—
499C23×C4—31no—
500C23×C4—91no—
501#126—98no—
502#126—98no—
503#125—98no—
504#125—98no—
505#123—98no—
506#123—98no—
507#123—98no—
508#123—98no—
509C22⋊Q8—38no—
510C22⋊Q8—98no—
511C22⋊Q8—98no—
512#121—98no—
513C4×D4—98no—
514C4×D4—98no—
515C2×C4⋊C4—31no—
516C2×C4⋊C4—31no—
517C2×C4⋊C4—31no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—38no—
521C2×C4⋊C4—91no—
522C2×C4⋊C4—91no—
523C2×C4⋊C4—91no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4—91no—
527C2×C4⋊C4—91no—
528C2×C4⋊C4—91no—
529C2×C4⋊C4D3211yescharacteristic
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C42—91no—
541C2×C42—91no—
542C23×C3—21no—
543C23×C3—34no—
544C23×C3—32no—
545C23×C3—32no—
546C23×C3—62no—
547C23×C3—62no—
548C23×C3—62no—
549C23×C3—62no—
550C23×C3—62no—
551C23×C3C23×D311yescharacteristic
552C23×C3C23×D311yescharacteristic
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—32no—
559C22×D3—32no—
560C22×D3—62no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—62no—
564C22×D3—62no—
565C22×D3—62no—
566C22×D3—62no—
567C22×D3—122no—
568C22×D3—122no—
569C22×D3—122no—
570C22×D3#23514yes—
571C22×D3C23×D312yes—
572C22×D3C23×D312yes—
573C3×Q8—124no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—32no—
586C2×C3×C4—32no—
587C2×C3×C4—32no—
588C2×C3×C4—32no—
589C2×C3×C4—42no—
590C2×C3×C4—42no—
591C2×C3×C4—42no—
592C2×C3×C4—68no—
593C2×C3×C4—62no—
594C2×C3×C4—62no—
595C2×C3×C4—62no—
596C2×C3×C4—62no—
597C2×C3×C4—62no—
598C2×C3×C4—62no—
599C2×C3×C4—124no—
600C2×C3×C4—124no—
601C2×C3×C4—124no—
602C2×C3×C4C23×D312yes—
603C2×C3×C4C23×D312yes—
604C2×C3×C4C23×D312yes—
605C2×C3×C4C23×D312yes—
606C2×C3×C4C23×D312yes—
607C2×C3×C4C23×D312yes—
608#67—68no—
609#67—68no—
610#67—68no—
611#67—124no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—32no—
619C2×Dic3—32no—
620C2×Dic3—32no—
621C2×Dic3—32no—
622C2×Dic3—32no—
623C2×Dic3—32no—
624C2×Dic3—62no—
625C2×Dic3—62no—
626C2×Dic3—62no—
627C2×Dic3—62no—
628C2×Dic3—62no—
629C2×Dic3—62no—
630C2×Dic3—62no—
631C2×Dic3—62no—
632C2×Dic3—62no—
633C2×Dic3—122no—
634C2×Dic3—122no—
635C2×Dic3—122no—
636C2×Dic3C23×D312yes—
637C2×Dic3C23×D312yes—
638C2×Dic3C23×D312yes—
639C2×Dic3C23×D312yes—
640C2×Dic3C23×D312yes—
641C2×Dic3C23×D312yes—
642D12—68no—
643D12—124no—
644C4×D3—28no—
645C4×D3—44no—
646C4×D3—44no—
647C4×D3—44no—
648C4×D3—124no—
649C4×D3—124no—
650Dic6—44no—
651C2×C32#53914yescomplemented
652C2×C32C22×#4111yescharacteristic
653C2×C32C2×H(5,𝔽2)11yescharacteristic
654C2×C32C2×2−1+411yescharacteristic
655C3⋊D3—42no—
656C3×D3—24no—
657C3×D3—42no—
658C24—31no—
659C24—31no—
660C24—91no—
661C2×Q8—34no—
662C2×Q8—122no—
663C2×D4—94no—
664C2×D4—94no—
665C2×D4—94no—
666C2×D4—184no—
667C2×D4—184no—
668C2×D4—362no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—34no—
676C22×C4—34no—
677C22×C4—34no—
678C22×C4—34no—
679C22×C4—64no—
680C22×C4—94no—
681C22×C4—91no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—122no—
685C22×C4—122no—
686C22×C4—122no—
687C22×C4—362no—
688C22×C4C2×D3211yescharacteristic
689C22×C4C2×D3211yescharacteristic
690C22×C4C2×D3211yescharacteristic
691C4⋊C4—34no—
692C4⋊C4—34no—
693C4⋊C4—34no—
694C4⋊C4—34no—
695C4⋊C4—34no—
696C4⋊C4—94no—
697C4⋊C4—94no—
698C4⋊C4—94no—
699C4⋊C4—94no—
700C4⋊C4—94no—
701C4⋊C4—94no—
702C4⋊C4—94no—
703C4⋊C4—94no—
704C4⋊C4C2×D3214yes—
705C22⋊C4—34no—
706C22⋊C4—34no—
707C22⋊C4—94no—
708C22⋊C4—94no—
709C22⋊C4—94no—
710C22⋊C4—94no—
711C22⋊C4—94no—
712C22⋊C4—94no—
713C22⋊C4—94no—
714C22⋊C4—94no—
715C42—94no—
716C42—94no—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—21no—
721C22×C3—34no—
722C22×C3—68no—
723C22×C3—62no—
724C22×C3—62no—
725C22×C3—62no—
726C22×C3—62no—
727C22×C3—62no—
728C22×C3—124no—
729C22×C3C2×#23512yes—
730C22×C3#100412yes—
731C22×C3#100412yes—
732C22×C3#100712yes—
733C22×C3#100712yes—
734C22×C3D3×#4112yes—
735C22×C3C24×D311yescharacteristic
736C22×C3C24×D311yescharacteristic
737C2×D3—22no—
738C2×D3—22no—
739C2×D3—28no—
740C2×D3—22no—
741C2×D3—22no—
742C2×D3—22no—
743C2×D3—44no—
744C2×D3—62no—
745C2×D3—62no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—62no—
750C2×D3—122no—
751C2×D3—122no—
752C2×D3—122no—
753C2×D3—124no—
754C2×D3—124no—
755C2×D3—244no—
756C2×D3C2×#23514yes—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—42no—
764C3×C4—42no—
765C3×C4—42no—
766C3×C4—62no—
767C3×C4—62no—
768C3×C4—62no—
769C3×C4—62no—
770C3×C4—62no—
771C3×C4—62no—
772Dic3—22no—
773Dic3—22no—
774Dic3—22no—
775Dic3—22no—
776Dic3—22no—
777Dic3—22no—
778Dic3—62no—
779Dic3—62no—
780Dic3—62no—
781Dic3—62no—
782Dic3—62no—
783Dic3—62no—
784Dic3—122no—
785Dic3—122no—
786Dic3—122no—
787C32C2×#53911yescharacteristic, complemented, Sylow
788C23—34no—
789C23—32no—
790C23—32no—
791C23—62no—
792C23—62no—
793C23—62no—
794C23—62no—
795C23—62no—
796C23—92no—
797C23—182no—
798C23—182no—
799C23—182no—
800C23C22×D3211yescharacteristic
801Q8—124no—
802D4—188no—
803D4—188no—
804D4—364no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—32no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—32no—
814C2×C4—68no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—62no—
821C2×C4—92no—
822C2×C4—92no—
823C2×C4—92no—
824C2×C4—124no—
825C2×C4—124no—
826C2×C4—124no—
827C2×C4—182no—
828C2×C4—182no—
829C2×C4—182no—
830C2×C4—364no—
831C2×C4C22×D3212yes—
832C2×C4C22×D3212yes—
833C2×C4C22×D3212yes—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—24no—
838C2×C3—64no—
839C2×C3—122no—
840C2×C3#551514yescomplemented
841C2×C3#563814yescomplemented
842C2×C3C22×#23511yescharacteristic
843C2×C3C2×#100411yescharacteristic
844C2×C3C2×#100411yescharacteristic
845C2×C3C2×#100711yescharacteristic
846C2×C3C2×#100711yescharacteristic
847C2×C3C2×D3×#4111yescharacteristic
848D3—24no—
849D3—42no—
850D3—122no—
851D3—122no—
852D3—242no—
853C22—34no—
854C22—62no—
855C22—62no—
856C22—68no—
857C22—62no—
858C22—62no—
859C22—62no—
860C22—124no—
861C22—182no—
862C22—182no—
863C22—182no—
864C22—364no—
865C22D3×#23512yes—
866C22#6431312yes—
867C22#6431612yes—
868C22C23×D3211yescharacteristic
869C4—22no—
870C4—22no—
871C4—22no—
872C4—62no—
873C4—62no—
874C4—62no—
875C4—62no—
876C4—62no—
877C4—62no—
878C4—182no—
879C4—182no—
880C4—182no—
881C3—21no—
882C3C2×#551511yescharacteristic, complemented
883C3C2×#563811yescharacteristic, complemented
884C2—64no—
885C2—122no—
886C2—362no—
887C2#1059454014yesdirect product factor
888C2C2×D3×#23511yescharacteristic
889C2C2×#6431311yescharacteristic
890C2C2×#6431611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC2×#63906C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#539
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×#64107C2semidirect
2. C2×C3×#896C2semidirect
3. C2×C3×D3×C4⋊C4C2semidirect
5. C2×#63905C2semidirect
6. C2×#63904C2semidirect
7. C2×C4×#625C2semidirect
8. C2×#63888C2semidirect
9. C2×#63870C2semidirect
10. C2×#63861C2semidirect
11. C2×#63856C2semidirect
12. C2×#63854C2semidirect
13. C2×#63850C2semidirect
14. C2×#63850C2semidirect
15. C2×#63847C2semidirect
16. #10594540C2direct (N × H)
35. #64107C22semidirect
43. C3×#896C22semidirect
44. C3×D3×C4⋊C4C22semidirect
58. #63905C22semidirect
59. #63904C22semidirect
60. C4×#625C22semidirect
61. #63888C22semidirect
62. #63870C22semidirect
63. #63861C22semidirect
64. #63856C22semidirect
65. #63854C22semidirect
66. #63850C22semidirect
67. #63850C22semidirect
68. #63847C22semidirect
88. C2×#896D3semidirect
93. C2×D3×C4⋊C4D3semidirect
256. #896C2×D3semidirect
261. D3×C4⋊C4C2×D3semidirect
651. C2×C32#539semidirect
787. C32C2×#539semidirect
840. C2×C3#5515semidirect
841. C2×C3#5638semidirect
882. C3C2×#5515semidirect
883. C3C2×#5638semidirect
887. C2#10594540direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641072
C2×C3×#8962
C2×C3×D3×C4⋊C42
C2×#639062
C2×#639052
C2×#639042
C2×C4×#6252
C2×#638882
C2×#638702
C2×#638612
C2×#638562
C2×#638542
C2×#638502
C2×#638472
#105945402
C2×#56383
C2×#55153