Finite Group Databasebeta

← C2×#10594167 #11901443

Subgroups — C2×#10594167 #11901443

Order 1152.

2501 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64093C211yesmaximal, characteristic
2C2×C3×#879C211yesmaximal, characteristic, complemented
3C2×C3×#878C211yesmaximal, characteristic, complemented
4C2×#63975C211yesmaximal, characteristic, complemented
5C2×#63975C211yesmaximal, characteristic, complemented
6C2×#63966C211yesmaximal, characteristic, complemented
7C2×#63952C211yesmaximal, characteristic, complemented
8C2×#63897C211yesmaximal, characteristic, complemented
9C2×#63894C211yesmaximal, characteristic, complemented
10C2×#63888C211yesmaximal, characteristic, complemented
11C2×#63883C211yesmaximal, characteristic, complemented
12C2×#63871C211yesmaximal, characteristic, complemented
13C2×#63867C211yesmaximal, characteristic, complemented
14C2×#63848C211yesmaximal, characteristic, complemented
15C2×#63846C211yesmaximal, characteristic, complemented
16#10594167C2116yesmaximal, direct product factor
17C2×#5707—31nomaximal
18C2×#5638—31nomaximal
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C22×#624C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×#624C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×#3752C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31#64093C2218yes—
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×C4⋊Dic3C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C3×#879C2218yescomplemented
43C3×#878C2218yescomplemented
44#63975C2218yescomplemented
45#63975C2218yescomplemented
46C2×#3724C2211yescharacteristic
47#63966C2218yescomplemented
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57C2×#3722C2211yescharacteristic
58C2×#3722C2211yescharacteristic
59C2×Dic32C2211yescharacteristic
60#63952C2218yescomplemented
61#63897C2218yescomplemented
62#63894C2218yescomplemented
63#63888C2218yescomplemented
64#63883C2218yescomplemented
65#63871C2218yescomplemented
66#63867C2218yescomplemented
67#63848C2218yescomplemented
68#63846C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×C22⋊Q8—31no—
71C2×#946—31no—
72C2×#946—31no—
73C2×#929—31no—
74C2×C4×#67—31no—
75#5707—316no—
76#5638—316no—
77C2×#898—31no—
78C2×#898—31no—
79C2×#897—31no—
80C2×#896—31no—
81C2×#894—31no—
82C2×#894—31no—
83C2×#893—31no—
84C2×D3×C4⋊C4—31no—
85C2×D3×C4⋊C4—31no—
86C2×#890—31no—
87C2×#889—31no—
88C2×#889—31no—
89C2×#886—31no—
90C2×#884—31no—
91C2×#884—31no—
92C2×#884—61no—
93C2×#883—31no—
94C2×#883—31no—
95C2×#883—31no—
96C2×#883—31no—
97C2×#67⋊C4—31no—
98C2×#879D311yescharacteristic, complemented
99C2×#878D311yescharacteristic, complemented
100C2×C4×D12—31no—
101C2×#870—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C2×#638—24no—
108C2×#638—42no—
109C2×#638C2314yes—
110C2×#638C2314yes—
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C2×C4⋊(C3⋊D3)—24no—
114C2×C4⋊(C3⋊D3)C2314yes—
115C2×C4×C3⋊D3—42no—
116C2×C4×C3⋊D3C2314yes—
117C22×C3×Dic3—42no—
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2314yes—
127C2×C3×Dic6—42no—
128C2×C3×Dic6C2314yes—
129C2×#624—24no—
130C2×#624—42no—
131C2×#624—42no—
132C2×#624C2314yes—
133C2×#624C2314yes—
134C2×#624C2314yes—
135C32×C22⋊C4C2314yes—
136#3752C2314yes—
137#3750C2314yes—
138C3×#217C2314yes—
139C3×#217C2314yes—
140C3×#217C2314yes—
141C3×C4⋊Dic3C2314yes—
142C3×C4⋊Dic3C2314yes—
143C3×Dic3⋊C4C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×C4×Dic3C2314yes—
148#3724C2314yes—
149Dic3⋊Dic3C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155#3722C2314yes—
156#3722C2314yes—
157#3722C2314yes—
158#3722C2314yes—
159#3722C2314yes—
160Dic32C2314yes—
161C2×#539—91noSylow
162C22×C3×Q8—31no—
163C23×C3×C4—31no—
164C22×#67—31no—
165C22×#67—31no—
166C22×#67—31no—
167C22×#67—31no—
168C22×#67—61no—
169C22×#67—61no—
170C23×Dic3C2×D311yescharacteristic
171C22×D12—31no—
172C22×D12—31no—
173C22×D12—61no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—31no—
177C22×C4×D3—31no—
178C22×C4×D3—31no—
179C22×C4×D3—31no—
180C22×C4×D3—31no—
181C22×C4×D3—31no—
182C22×C4×D3—61no—
183C22×Dic6C2×D311yescharacteristic
184C3×#126—38no—
185C3×C22⋊Q8—38no—
186C2×C3×C4⋊C4—31no—
187C2×C3×C4⋊C4—31no—
188C2×C3×C4⋊C4—31no—
189C2×C3×C4⋊C4—31no—
190C2×C3×C4⋊C4—31no—
191C2×C3×C4⋊C4—31no—
192C2×C3×C22⋊C4—21no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4C2×D311yescharacteristic
197C2×C3×C22⋊C4C2×D311yescharacteristic
198C2×C3×C42—31no—
199C2×#217C2×D311yescharacteristic
200C2×#217C2×D311yescharacteristic
201C2×#217C2×D311yescharacteristic
202#946—38no—
203#946—38no—
204#929—38no—
205C4×#67—38no—
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—31no—
218C2×(C2×D3)⋊C4—61no—
219C2×C4⋊Dic3—31no—
220C2×C4⋊Dic3—31no—
221C2×C4⋊Dic3—31no—
222C2×C4⋊Dic3—31no—
223C2×C4⋊Dic3—31no—
224C2×C4⋊Dic3—31no—
225C2×C4⋊Dic3C2×D311yescharacteristic
226C2×C4⋊Dic3C2×D311yescharacteristic
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—31no—
235C2×Dic3⋊C4—31no—
236C2×Dic3⋊C4—31no—
237C2×Dic3⋊C4—61no—
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×Dic3C2×D311yescharacteristic
245#898—38no—
246#898—38no—
247#897—38no—
248#896—38no—
249#894—38no—
250#894—38no—
251#893—38no—
252D3×C4⋊C4—38no—
253D3×C4⋊C4—38no—
254#890—38no—
255#889—38no—
256#889—38no—
257#886—38no—
258#884—38no—
259#884—38no—
260#884—68no—
261#883—38no—
262#883—38no—
263#883—38no—
264#883—38no—
265#67⋊C4—38no—
266#879C2×D318yescomplemented
267#878C2×D318yescomplemented
268C4×D12—38no—
269#870—38no—
270C23×C32—22no—
271C23×C32—22no—
272C23×C32—22no—
273C23×C32C2412yes—
274C23×C32C2411yescharacteristic
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×C4C2412yes—
286C2×C32×C4C2412yes—
287#638—28no—
288#638—44no—
289C2×C3⋊Dic3—22no—
290C2×C3⋊Dic3—22no—
291C2×C3⋊Dic3C2412yes—
292C2×C3⋊Dic3C2412yes—
293C4⋊(C3⋊D3)—28no—
294C4×C3⋊D3—44no—
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×Dic3—22no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—44no—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C2×C3×Dic3C2412yes—
312C3×Dic6—44no—
313#624—28no—
314#624—44no—
315#624—44no—
316#539—916no—
317C2×#126—31no—
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—91no—
332C24×C3—21no—
333C24×C3C22×D311yescharacteristic
334C24×C3C22×D311yescharacteristic
335C23×D3—31no—
336C23×D3—31no—
337C23×D3—31no—
338C23×D3—31no—
339C23×D3—61no—
340C23×D3—61no—
341C2×C3×Q8—34no—
342C2×C3×Q8—122no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—34no—
354C22×C3×C4—122no—
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C2×#67—34no—
360C2×#67—34no—
361C2×#67—34no—
362C2×#67—34no—
363C2×#67—64no—
364C2×#67—64no—
365C2×#67—64no—
366C2×#67—64no—
367C2×#67—124no—
368C2×#67—122no—
369C2×#67—122no—
370C2×#67—124no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—42no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D314yes—
387C2×D12—34no—
388C2×D12—34no—
389C2×D12—64no—
390C2×D12—64no—
391C2×D12—64no—
392C2×D12—124no—
393C2×C4×D3—34no—
394C2×C4×D3—34no—
395C2×C4×D3—34no—
396C2×C4×D3—34no—
397C2×C4×D3—34no—
398C2×C4×D3—34no—
399C2×C4×D3—34no—
400C2×C4×D3—34no—
401C2×C4×D3—64no—
402C2×C4×D3—64no—
403C2×C4×D3—64no—
404C2×C4×D3—122no—
405C2×C4×D3—122no—
406C2×C4×D3—122no—
407C2×C4×D3—122no—
408C2×C4×D3—122no—
409C2×C4×D3—122no—
410C2×C4×D3—124no—
411C2×Dic6—42no—
412C2×Dic6C22×D314yes—
413C3×C4⋊C4—34no—
414C3×C4⋊C4—34no—
415C3×C4⋊C4—34no—
416C3×C4⋊C4—34no—
417C3×C4⋊C4—34no—
418C3×C4⋊C4—34no—
419C3×C22⋊C4—24no—
420C3×C22⋊C4—34no—
421C3×C22⋊C4—34no—
422C3×C22⋊C4—34no—
423C3×C22⋊C4C22×D314yes—
424C3×C22⋊C4C22×D314yes—
425C3×C42—34no—
426#217C22×D314yes—
427#217C22×D314yes—
428#217C22×D314yes—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—34no—
439(C2×D3)⋊C4—34no—
440(C2×D3)⋊C4—34no—
441(C2×D3)⋊C4—64no—
442C4⋊Dic3—34no—
443C4⋊Dic3—34no—
444C4⋊Dic3—34no—
445C4⋊Dic3—34no—
446C4⋊Dic3—34no—
447C4⋊Dic3—34no—
448C4⋊Dic3C22×D314yes—
449C4⋊Dic3C22×D314yes—
450Dic3⋊C4—34no—
451Dic3⋊C4—34no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—34no—
455Dic3⋊C4—34no—
456Dic3⋊C4—34no—
457Dic3⋊C4—34no—
458Dic3⋊C4—34no—
459Dic3⋊C4—34no—
460Dic3⋊C4—64no—
461Dic3⋊C4C22×D314yes—
462Dic3⋊C4C22×D314yes—
463Dic3⋊C4C22×D314yes—
464Dic3⋊C4C22×D314yes—
465C4×Dic3—34no—
466C4×Dic3—34no—
467C4×Dic3C22×D314yes—
468C22×C32—22no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—44no—
472C22×C32C2×#4112yes—
473C22×C32H(5,𝔽2)12yes—
474C22×C322−1+412yes—
475C22×C32C2511yescharacteristic
476C2×C3⋊D3—28no—
477C2×C3⋊D3—22no—
478C2×C3⋊D3—22no—
479C2×C3⋊D3—22no—
480C2×C3⋊D3—22no—
481C2×C3⋊D3—22no—
482C2×C3⋊D3—44no—
483C2×C3⋊D3C2×#4114yes—
484C32×C4—22no—
485C32×C4—22no—
486C3⋊Dic3—22no—
487C3⋊Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3—22no—
494C3×Dic3—22no—
495C3×Dic3—22no—
496C22×Q8—31no—
497C22×D4—91no—
498C22×D4—91no—
499C22×D4—91no—
500C23×C4—31no—
501C23×C4—91no—
502C23×C4—91no—
503C23×C4—91no—
504C23×C4—91no—
505#126—38no—
506#126—98no—
507#125—98no—
508#125—98no—
509#123—98no—
510#123—98no—
511#123—98no—
512#123—98no—
513C22⋊Q8—38no—
514C22⋊Q8—98no—
515C22⋊Q8—98no—
516#121—98no—
517C4×D4—98no—
518C4×D4—98no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4—31no—
523C2×C4⋊C4—31no—
524C2×C4⋊C4—31no—
525C2×C4⋊C4—98no—
526C2×C4⋊C4—91no—
527C2×C4⋊C4—91no—
528C2×C4⋊C4—91no—
529C2×C4⋊C4—91no—
530C2×C4⋊C4—91no—
531C2×C4⋊C4—91no—
532C2×C4⋊C4—91no—
533C2×C4⋊C4—91no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542C2×C22⋊C4—91no—
543C2×C22⋊C4D3211yescharacteristic
544C2×C42—31no—
545C2×C42—91no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—21no—
554C23×C3—42no—
555C23×C3—42no—
556C23×C3—42no—
557C23×C3C23×D312yes—
558C23×C3C23×D312yes—
559C23×C3C23×D311yescharacteristic
560C23×C3C23×D311yescharacteristic
561C22×D3—34no—
562C22×D3—34no—
563C22×D3—32no—
564C22×D3—32no—
565C22×D3—32no—
566C22×D3—32no—
567C22×D3—64no—
568C22×D3—62no—
569C22×D3—62no—
570C22×D3—62no—
571C22×D3—62no—
572C22×D3—62no—
573C22×D3—62no—
574C22×D3—62no—
575C22×D3—62no—
576C22×D3—62no—
577C22×D3—62no—
578C22×D3—62no—
579C22×D3—62no—
580C22×D3—122no—
581C22×D3—122no—
582C22×D3—122no—
583C22×D3—122no—
584C22×D3—122no—
585C3×Q8—124no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—32no—
593C2×C3×C4—32no—
594C2×C3×C4—32no—
595C2×C3×C4—32no—
596C2×C3×C4—32no—
597C2×C3×C4—32no—
598C2×C3×C4—32no—
599C2×C3×C4—32no—
600C2×C3×C4—42no—
601C2×C3×C4—42no—
602C2×C3×C4—62no—
603C2×C3×C4—62no—
604C2×C3×C4—62no—
605C2×C3×C4—62no—
606C2×C3×C4—62no—
607C2×C3×C4—62no—
608C2×C3×C4—62no—
609C2×C3×C4—62no—
610C2×C3×C4—124no—
611C2×C3×C4C23×D312yes—
612C2×C3×C4C23×D312yes—
613C2×C3×C4C23×D312yes—
614C2×C3×C4C23×D312yes—
615#67—68no—
616#67—68no—
617#67—128no—
618#67—124no—
619#67—124no—
620#67—128no—
621C2×Dic3—22no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—32no—
630C2×Dic3—32no—
631C2×Dic3—32no—
632C2×Dic3—32no—
633C2×Dic3—44no—
634C2×Dic3—62no—
635C2×Dic3—62no—
636C2×Dic3—64no—
637C2×Dic3—62no—
638C2×Dic3—62no—
639C2×Dic3—62no—
640C2×Dic3—62no—
641C2×Dic3—122no—
642C2×Dic3C23×D312yes—
643C2×Dic3C23×D312yes—
644C2×Dic3C23×D312yes—
645C2×Dic3C23×D312yes—
646C2×Dic3C23×D312yes—
647C2×Dic3C23×D312yes—
648C2×Dic3C23×D312yes—
649C2×Dic3C23×D312yes—
650D12—68no—
651D12—68no—
652D12—128no—
653C4×D3—68no—
654C4×D3—68no—
655C4×D3—124no—
656C4×D3—124no—
657C4×D3—124no—
658C4×D3—124no—
659C4×D3—124no—
660C4×D3—124no—
661C4×D3—128no—
662Dic6—44no—
663C2×C32—42no—
664C2×C32#53914yescomplemented
665C2×C32C22×#4111yescharacteristic
666C2×C32C2×H(5,𝔽2)11yescharacteristic
667C2×C32C2×2−1+411yescharacteristic
668C3⋊D3—24no—
669C3⋊D3—42no—
670C24—91no—
671C24—91no—
672C24C2×D3211yescharacteristic
673C2×Q8—34no—
674C2×Q8—122no—
675C2×D4—94no—
676C2×D4—94no—
677C2×D4—94no—
678C2×D4—184no—
679C2×D4—184no—
680C2×D4—362no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—34no—
690C22×C4—94no—
691C22×C4—94no—
692C22×C4—94no—
693C22×C4—91no—
694C22×C4—91no—
695C22×C4—94no—
696C22×C4—122no—
697C22×C4—184no—
698C22×C4—362no—
699C22×C4—362no—
700C22×C4—362no—
701C22×C4C2×D3211yescharacteristic
702C22×C4C2×D3211yescharacteristic
703C4⋊C4—34no—
704C4⋊C4—34no—
705C4⋊C4—34no—
706C4⋊C4—34no—
707C4⋊C4—34no—
708C4⋊C4—34no—
709C4⋊C4—94no—
710C4⋊C4—94no—
711C4⋊C4—94no—
712C4⋊C4—94no—
713C4⋊C4—94no—
714C4⋊C4—94no—
715C4⋊C4—94no—
716C4⋊C4—94no—
717C22⋊C4—34no—
718C22⋊C4—34no—
719C22⋊C4—34no—
720C22⋊C4—94no—
721C22⋊C4—94no—
722C22⋊C4—94no—
723C22⋊C4—94no—
724C22⋊C4—94no—
725C22⋊C4—94no—
726C22⋊C4C2×D3214yes—
727C42—34no—
728C42—94no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—21no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—44no—
743C22×C3—44no—
744C22×C3—84no—
745C22×C3#100412yes—
746C22×C3#100712yes—
747C22×C3D3×#4112yes—
748C22×C3D3×#4112yes—
749C22×C3#100912yes—
750C22×C3#101012yes—
751C22×C3C24×D311yescharacteristic
752C22×C3C24×D311yescharacteristic
753C2×D3—34no—
754C2×D3—34no—
755C2×D3—64no—
756C2×D3—68no—
757C2×D3—62no—
758C2×D3—62no—
759C2×D3—62no—
760C2×D3—68no—
761C2×D3—62no—
762C2×D3—62no—
763C2×D3—62no—
764C2×D3—62no—
765C2×D3—62no—
766C2×D3—62no—
767C2×D3—62no—
768C2×D3—122no—
769C2×D3—122no—
770C2×D3—128no—
771C2×D3—122no—
772C2×D3—122no—
773C2×D3—122no—
774C2×D3—124no—
775C2×D3—124no—
776C2×D3—244no—
777C3×C4—22no—
778C3×C4—22no—
779C3×C4—22no—
780C3×C4—22no—
781C3×C4—42no—
782C3×C4—42no—
783C3×C4—62no—
784C3×C4—62no—
785C3×C4—62no—
786C3×C4—62no—
787C3×C4—62no—
788C3×C4—62no—
789C3×C4—62no—
790C3×C4—62no—
791Dic3—22no—
792Dic3—22no—
793Dic3—22no—
794Dic3—22no—
795Dic3—22no—
796Dic3—22no—
797Dic3—22no—
798Dic3—22no—
799Dic3—64no—
800Dic3—62no—
801Dic3—62no—
802Dic3—62no—
803Dic3—62no—
804Dic3—122no—
805C32C2×#53911yescharacteristic, complemented, Sylow
806C23—22no—
807C23—22no—
808C23—22no—
809C23—94no—
810C23—92no—
811C23—92no—
812C23—182no—
813C23—182no—
814C23—182no—
815C23—182no—
816C23—182no—
817C23C22×D3212yes—
818C23C22×D3211yescharacteristic
819Q8—124no—
820D4—188no—
821D4—188no—
822D4—364no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—32no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—32no—
830C2×C4—32no—
831C2×C4—32no—
832C2×C4—32no—
833C2×C4—62no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—62no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—92no—
842C2×C4—92no—
843C2×C4—124no—
844C2×C4—188no—
845C2×C4—182no—
846C2×C4—182no—
847C2×C4—364no—
848C2×C4—364no—
849C2×C4—364no—
850C2×C4C22×D3212yes—
851C2×C4C22×D3212yes—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—24no—
856C2×C3—42no—
857C2×C3—42no—
858C2×C3—82no—
859C2×C3#563814yescomplemented
860C2×C3#570714yescomplemented
861C2×C3C2×#100411yescharacteristic
862C2×C3C2×#100711yescharacteristic
863C2×C3C2×D3×#4111yescharacteristic
864C2×C3C2×D3×#4111yescharacteristic
865C2×C3C2×#100911yescharacteristic
866C2×C3C2×#101011yescharacteristic
867D3—64no—
868D3—64no—
869D3—124no—
870D3—122no—
871D3—122no—
872D3—242no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—44no—
877C22—94no—
878C22—182no—
879C22—182no—
880C22—188no—
881C22—182no—
882C22—182no—
883C22—182no—
884C22—364no—
885C22#6429712yes—
886C22#6431212yes—
887C22#6431412yes—
888C22C23×D3211yescharacteristic
889C4—22no—
890C4—22no—
891C4—62no—
892C4—62no—
893C4—62no—
894C4—62no—
895C4—62no—
896C4—62no—
897C4—62no—
898C4—62no—
899C4—182no—
900C4—182no—
901C3—21no—
902C3C2×#563811yescharacteristic, complemented
903C3C2×#570711yescharacteristic, complemented
904C2—42no—
905C2—184no—
906C2—362no—
907C2#1059416714yesdirect product factor
908C2C2×#6429711yescharacteristic
909C2C2×#6431211yescharacteristic
910C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC2×#64093C2
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#539
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#879C2semidirect
3. C2×C3×#878C2semidirect
4. C2×#63975C2semidirect
5. C2×#63975C2semidirect
6. C2×#63966C2semidirect
7. C2×#63952C2semidirect
8. C2×#63897C2semidirect
9. C2×#63894C2semidirect
10. C2×#63888C2semidirect
11. C2×#63883C2semidirect
12. C2×#63871C2semidirect
13. C2×#63867C2semidirect
14. C2×#63848C2semidirect
15. C2×#63846C2semidirect
16. #10594167C2direct (N × H)
42. C3×#879C22semidirect
43. C3×#878C22semidirect
44. #63975C22semidirect
45. #63975C22semidirect
47. #63966C22semidirect
60. #63952C22semidirect
61. #63897C22semidirect
62. #63894C22semidirect
63. #63888C22semidirect
64. #63883C22semidirect
65. #63871C22semidirect
66. #63867C22semidirect
67. #63848C22semidirect
68. #63846C22semidirect
98. C2×#879D3semidirect
99. C2×#878D3semidirect
266. #879C2×D3semidirect
267. #878C2×D3semidirect
664. C2×C32#539semidirect
805. C32C2×#539semidirect
859. C2×C3#5638semidirect
860. C2×C3#5707semidirect
902. C3C2×#5638semidirect
903. C3C2×#5707semidirect
907. C2#10594167direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640932
C2×C3×#8792
C2×C3×#8782
C2×#639752
C2×#639662
C2×#639522
C2×#638972
C2×#638942
C2×#638882
C2×#638832
C2×#638712
C2×#638672
C2×#638482
C2×#638462
#105941672
C2×#57073
C2×#56383