Finite Group Databasebeta

← C2×#10594660 #11901343

Subgroups — C2×#10594660 #11901343

Order 1152.

2833 conjugacy classes of subgroups.

The subgroup lattice has 1000 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×#895C211yesmaximal, characteristic, complemented
4C2×#63922C211yesmaximal, characteristic, complemented
5C2×#63922C211yesmaximal, characteristic, complemented
6C2×#63921C211yesmaximal, characteristic, complemented
7C2×#63916C211yesmaximal, characteristic, complemented
8C2×#63913C211yesmaximal, characteristic, complemented
9C2×#63905C211yesmaximal, characteristic, complemented
10C2×#63904C211yesmaximal, characteristic, complemented
11C2×#63885C211yesmaximal, characteristic, complemented
12C2×#63884C211yesmaximal, characteristic, complemented
13C2×#63880C211yesmaximal, characteristic, complemented
14C2×#63860C211yesmaximal, characteristic, complemented
15C2×#63858C211yesmaximal, characteristic, complemented
16#10594660C2116yesmaximal, direct product factor
17C2×#5704—31nomaximal
18C2×#5613—31nomaximal
19C23×D32C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×#634C2211yescharacteristic, complemented
22C22×C3×D12C2211yescharacteristic
23C22×C3×D12C2211yescharacteristic
24C22×C3×D12C2211yescharacteristic, complemented
25C22×C3×C4×D3C2211yescharacteristic, complemented
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#625C2211yescharacteristic
29C22×#625C2211yescharacteristic
30C22×#624C2211yescharacteristic
31C22×D3×Dic3C2211yescharacteristic, complemented
32C2×C32×C4⋊C4C2211yescharacteristic, complemented
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3750C2211yescharacteristic, complemented
36C2×#3750C2211yescharacteristic, complemented
37#64105C2218yescomplemented
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
44C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
45C2×C3×C4×Dic3C2211yescharacteristic, complemented
46C3×#898C2218yescomplemented
47C3×#895C2218yescomplemented
48C2×Dic3⋊Dic3C2211yescharacteristic, complemented
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×(C2×D3)⋊Dic3C2211yescharacteristic
51C2×(C2×D3)⋊Dic3C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
55C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
56C2×Dic32C2211yescharacteristic, complemented
57#63922C2218yescomplemented
58#63922C2218yescomplemented
59#63921C2218yescomplemented
60#63916C2218yescomplemented
61#63913C2218yescomplemented
62#63905C2218yescomplemented
63#63904C2218yescomplemented
64#63885C2218yescomplemented
65#63884C2218yescomplemented
66#63880C2218yescomplemented
67#63860C2218yescomplemented
68#63858C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×#121—31no—
71C2×#939—31no—
72C2×#938—31no—
73C2×#937—31no—
74C2×#937—31no—
75C2×#936—31no—
76C2×#935—31no—
77C2×#929—31no—
78C2×C4×#67—31no—
79#5704—316no—
80#5613—316no—
81C2×#898—31no—
82C2×#898D311yescharacteristic, complemented
83C2×#896—31no—
84C2×#896—31no—
85C2×#896—61no—
86C2×#895—31no—
87C2×#895D311yescharacteristic, complemented
88C2×#894—31no—
89C2×#893—31no—
90C2×#885—31no—
91C2×#885—31no—
92C2×#884—31no—
93C2×#883—31no—
94C2×#882—31no—
95C2×#882—31no—
96C2×#67⋊C4—31no—
97C2×D3×C22⋊C4—31no—
98C2×D3×C22⋊C4—31no—
99C2×#879—31no—
100C2×#875—31no—
101C2×C4×D12—31no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C22×D32—24no—
108C22×D32—42no—
109C22×D32—42no—
110C22×D32C2314yes—
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C2×C4×C3⋊D3—42no—
118C2×C4×C3⋊D3C2314yes—
119C2×#634—42no—
120C2×#634C2314yescomplemented
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×C3×D12—42no—
126C2×C3×D12—42no—
127C2×C3×D12—42no—
128C2×C3×D12C2314yes—
129C2×C3×D12C2314yes—
130C2×C3×D12C2314yescomplemented
131C2×C3×C4×D3—42no—
132C2×C3×C4×D3C2314yescomplemented
133C2×#626—24no—
134C2×#626—24no—
135C2×#626C2314yes—
136C2×#626C2314yes—
137C2×#625—42no—
138C2×#625—42no—
139C2×#625C2314yes—
140C2×#625C2314yes—
141C2×#624—42no—
142C2×#624C2314yes—
143C2×D3×Dic3—42no—
144C2×D3×Dic3C2314yescomplemented
145C32×C4⋊C4C2314yescomplemented
146#3752C2314yes—
147#3752C2314yes—
148#3750C2314yescomplemented
149#3750C2314yescomplemented
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×(C2×D3)⋊C4C2314yes—
154C3×(C2×D3)⋊C4C2314yescomplemented
155C3×C4⋊Dic3C2314yescomplemented
156C3×Dic3⋊C4C2314yescomplemented
157C3×C4×Dic3C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yescomplemented
164(C2×D3)⋊Dic3C2314yescomplemented
165(C2×D3)⋊Dic3C2314yescomplemented
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C22×C3×D4—31no—
171C22×C3×D4—31no—
172C22×C3×D4—31no—
173C23×C3×C4—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C23×Dic3—31no—
181C22×D12—31no—
182C22×D12—31no—
183C22×D12C2×D311yescharacteristic
184C22×D12C2×D311yescharacteristic
185C22×D12C2×D311yescharacteristic, complemented
186C22×C4×D3—31no—
187C22×C4×D3—31no—
188C22×C4×D3—31no—
189C22×C4×D3—31no—
190C22×C4×D3—31no—
191C22×C4×D3—61no—
192C22×C4×D3C2×D311yescharacteristic, complemented
193C22×Dic6—31no—
194C22×Dic6—31no—
195C22×Dic6—61no—
196C3×#126—38no—
197C3×#121—38no—
198C2×C3×C4⋊C4—21no—
199C2×C3×C4⋊C4—31no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
202C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
203C2×C3×C22⋊C4—31no—
204C2×C3×C22⋊C4—31no—
205C2×C3×C22⋊C4—31no—
206C2×C3×C22⋊C4—31no—
207C2×C3×C22⋊C4—31no—
208C2×C3×C42—31no—
209C2×#217—31no—
210C2×#217—31no—
211C2×#217—31no—
212C2×#217—31no—
213C2×#217—31no—
214C2×#217—31no—
215C2×#217—31no—
216#939—38no—
217#938—38no—
218#937—38no—
219#937—38no—
220#936—38no—
221#935—38no—
222#929—38no—
223C4×#67—38no—
224C2×(C2×D3)⋊C4—31no—
225C2×(C2×D3)⋊C4—31no—
226C2×(C2×D3)⋊C4—31no—
227C2×(C2×D3)⋊C4—31no—
228C2×(C2×D3)⋊C4—31no—
229C2×(C2×D3)⋊C4—31no—
230C2×(C2×D3)⋊C4—31no—
231C2×(C2×D3)⋊C4—31no—
232C2×(C2×D3)⋊C4—31no—
233C2×(C2×D3)⋊C4—31no—
234C2×(C2×D3)⋊C4—31no—
235C2×(C2×D3)⋊C4—61no—
236C2×(C2×D3)⋊C4—61no—
237C2×(C2×D3)⋊C4C2×D311yescharacteristic
238C2×(C2×D3)⋊C4C2×D311yescharacteristic
239C2×(C2×D3)⋊C4C2×D311yescharacteristic
240C2×(C2×D3)⋊C4C2×D311yescharacteristic
241C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
242C2×C4⋊Dic3—31no—
243C2×C4⋊Dic3C2×D311yescharacteristic, complemented
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—61no—
250C2×Dic3⋊C4—61no—
251C2×Dic3⋊C4C2×D311yescharacteristic, complemented
252C2×C4×Dic3—31no—
253C2×C4×Dic3—31no—
254C2×C4×Dic3C2×D311yescharacteristic, complemented
255#898—38no—
256#898C2×D318yescomplemented
257#896—38no—
258#896—38no—
259#896—68no—
260#895—38no—
261#895C2×D318yescomplemented
262#894—38no—
263#893—38no—
264#885—38no—
265#885—38no—
266#884—38no—
267#883—38no—
268#882—38no—
269#882—38no—
270#67⋊C4—38no—
271D3×C22⋊C4—38no—
272D3×C22⋊C4—38no—
273#879—38no—
274#875—38no—
275C4×D12—38no—
276C23×C32C2411yescharacteristic
277C22×C3⋊D3—22no—
278C22×C3⋊D3—22no—
279C22×C3⋊D3#4114yes—
280C22×C3⋊D3C2412yes—
281C22×C3×D3—22no—
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3—22no—
288C22×C3×D3—22no—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3C2412yes—
294C22×C3×D3C2412yes—
295C22×C3×D3C2412yes—
296C22×C3×D3C2412yes—
297C2×D32—28no—
298C2×D32—44no—
299C2×D32—44no—
300C2×D32—416no—
301C2×C32×C4—22no—
302C2×C32×C4—22no—
303C2×C32×C4—22no—
304C2×C32×C4C2412yes—
305C2×C32×C4C2412yes—
306C2×C32×C4C2412yes—
307C2×C3⋊Dic3—22no—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3—22no—
310C2×C3⋊Dic3C2412yes—
311C2×C3⋊Dic3C2412yes—
312C2×C3⋊Dic3C2412yes—
313C4×C3⋊D3—44no—
314#634—44no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C3×D12—44no—
324C3×D12—44no—
325C3×D12—44no—
326C3×C4×D3—44no—
327#626—28no—
328#626—28no—
329#625—44no—
330#625—44no—
331#624—44no—
332D3×Dic3—44no—
333#538—916no—
334C2×#126—31no—
335C2×#126—91no—
336C2×#124—91no—
337C2×#124—91no—
338C2×#123—91no—
339C2×#123—91no—
340C2×C22⋊Q8—91no—
341C2×#121—31no—
342C2×#121—91no—
343C2×#121—91no—
344C2×#120—91no—
345C2×#120—91no—
346C2×C4×D4—91no—
347C2×C4×D4—91no—
348C22×C22⋊C4—91no—
349C24×C3—31no—
350C24×C3—31no—
351C24×C3—31no—
352C24×C3—31no—
353C23×D3—31no—
354C23×D3—31no—
355C23×D3—34no—
356C23×D3—34no—
357C23×D3—61no—
358C23×D3—64no—
359C23×D3—64no—
360C23×D3—122no—
361C23×D3—122no—
362C23×D3—122no—
363C23×D3—122no—
364C23×D3C22×D311yescharacteristic
365C23×D3C22×D311yescharacteristic
366C23×D3C22×D311yescharacteristic
367C23×D3C22×D311yescharacteristic
368C2×C3×D4—34no—
369C2×C3×D4—34no—
370C2×C3×D4—34no—
371C2×C3×D4—122no—
372C2×C3×D4—122no—
373C2×C3×D4—122no—
374C22×C3×C4—21no—
375C22×C3×C4—21no—
376C22×C3×C4—21no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—34no—
382C22×C3×C4—122no—
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C2×#67—34no—
390C2×#67—34no—
391C2×#67—34no—
392C2×#67—34no—
393C2×#67—34no—
394C2×#67—34no—
395C2×#67—64no—
396C2×#67—64no—
397C2×#67—122no—
398C2×#67—122no—
399C2×#67—122no—
400C2×#67—122no—
401C22×Dic3—31no—
402C22×Dic3—31no—
403C22×Dic3—31no—
404C22×Dic3—31no—
405C22×Dic3—31no—
406C22×Dic3—31no—
407C22×Dic3—34no—
408C22×Dic3—61no—
409C22×Dic3—61no—
410C22×Dic3—61no—
411C22×Dic3—122no—
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415C22×Dic3C22×D311yescharacteristic
416C2×D12—34no—
417C2×D12—34no—
418C2×D12—42no—
419C2×D12—42no—
420C2×D12—42no—
421C2×D12—64no—
422C2×D12—64no—
423C2×D12C22×D314yes—
424C2×D12C22×D314yes—
425C2×D12C22×D314yescomplemented
426C2×C4×D3—34no—
427C2×C4×D3—34no—
428C2×C4×D3—34no—
429C2×C4×D3—34no—
430C2×C4×D3—34no—
431C2×C4×D3—42no—
432C2×C4×D3—64no—
433C2×C4×D3—122no—
434C2×C4×D3—122no—
435C2×C4×D3—122no—
436C2×C4×D3—122no—
437C2×C4×D3—124no—
438C2×C4×D3—122no—
439C2×C4×D3C22×D314yescomplemented
440C2×Dic6—34no—
441C2×Dic6—34no—
442C2×Dic6—64no—
443C2×Dic6—122no—
444C2×Dic6—122no—
445C2×Dic6—124no—
446C3×C4⋊C4—24no—
447C3×C4⋊C4—34no—
448C3×C4⋊C4—34no—
449C3×C4⋊C4C22×D314yescomplemented
450C3×C4⋊C4C22×D314yescomplemented
451C3×C22⋊C4—34no—
452C3×C22⋊C4—34no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C42—34no—
457#217—34no—
458#217—34no—
459#217—34no—
460#217—34no—
461#217—34no—
462#217—34no—
463#217—34no—
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4—34no—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4—34no—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—34no—
471(C2×D3)⋊C4—34no—
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4—34no—
474(C2×D3)⋊C4—34no—
475(C2×D3)⋊C4—64no—
476(C2×D3)⋊C4—64no—
477(C2×D3)⋊C4C22×D314yes—
478(C2×D3)⋊C4C22×D314yes—
479(C2×D3)⋊C4C22×D314yes—
480(C2×D3)⋊C4C22×D314yes—
481(C2×D3)⋊C4C22×D314yescomplemented
482C4⋊Dic3—34no—
483C4⋊Dic3C22×D314yescomplemented
484Dic3⋊C4—34no—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—64no—
490Dic3⋊C4—64no—
491Dic3⋊C4C22×D314yescomplemented
492C4×Dic3—34no—
493C4×Dic3—34no—
494C4×Dic3C22×D314yescomplemented
495C22×C32C2×#4112yes—
496C22×C32H(5,𝔽2)12yes—
497C22×C32H(5,𝔽2)12yes—
498C22×C32C2511yescharacteristic
499C2×C3⋊D3—28no—
500C2×C3⋊D3—22no—
501C2×C3⋊D3—22no—
502C2×C3⋊D3C2×#4114yes—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—22no—
509C2×C3×D3—22no—
510C2×C3×D3—22no—
511C2×C3×D3—22no—
512C2×C3×D3—22no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—44no—
516C2×C3×D3—44no—
517C2×C3×D3—44no—
518C2×C3×D3—44no—
519D32—416no—
520C32×C4—22no—
521C32×C4—22no—
522C32×C4—22no—
523C3⋊Dic3—22no—
524C3⋊Dic3—22no—
525C3⋊Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C25—91no—
531C22×Q8—91no—
532C22×D4—31no—
533C22×D4—31no—
534C22×D4—31no—
535C22×D4—91no—
536C22×D4—91no—
537C22×D4—91no—
538C22×D4—91no—
539C23×C4—31no—
540C23×C4—91no—
541C23×C4—91no—
542C23×C4—91no—
543#126—38no—
544#126—98no—
545#124—98no—
546#124—98no—
547#123—98no—
548#123—98no—
549C22⋊Q8—98no—
550#121—38no—
551#121—98no—
552#121—98no—
553#120—98no—
554#120—98no—
555C4×D4—98no—
556C4×D4—98no—
557C2×C4⋊C4—31no—
558C2×C4⋊C4—31no—
559C2×C4⋊C4—91no—
560C2×C4⋊C4—91no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4D3211yescharacteristic, complemented
563C2×C22⋊C4—31no—
564C2×C22⋊C4—31no—
565C2×C22⋊C4—31no—
566C2×C22⋊C4—31no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—98no—
569C2×C22⋊C4—91no—
570C2×C22⋊C4—91no—
571C2×C22⋊C4—91no—
572C2×C22⋊C4—91no—
573C2×C22⋊C4—91no—
574C2×C22⋊C4—91no—
575C2×C22⋊C4—91no—
576C2×C22⋊C4—91no—
577C2×C22⋊C4—91no—
578C2×C42—31no—
579C2×C42—91no—
580C23×C3—21no—
581C23×C3—32no—
582C23×C3—32no—
583C23×C3—32no—
584C23×C3—32no—
585C23×C3—62no—
586C23×C3—62no—
587C23×C3—62no—
588C23×C3—62no—
589C23×C3—62no—
590C23×C3—62no—
591C23×C3—62no—
592C23×C3—62no—
593C23×C3—62no—
594C23×C3—62no—
595C23×C3—62no—
596C23×C3—62no—
597C23×C3C23×D311yescharacteristic
598C23×C3C23×D311yescharacteristic
599C22×D3—22no—
600C22×D3—22no—
601C22×D3—22no—
602C22×D3—22no—
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—22no—
611C22×D3—34no—
612C22×D3—34no—
613C22×D3—32no—
614C22×D3—32no—
615C22×D3—64no—
616C22×D3—62no—
617C22×D3—68no—
618C22×D3—68no—
619C22×D3—62no—
620C22×D3—62no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—122no—
624C22×D3—122no—
625C22×D3—124no—
626C22×D3—124no—
627C22×D3—124no—
628C22×D3—124no—
629C22×D3—1216no—
630C22×D3—1216no—
631C22×D3C23×D312yes—
632C22×D3C23×D312yes—
633C22×D3C23×D312yes—
634C22×D3C23×D312yes—
635C3×D4—124no—
636C3×D4—124no—
637C3×D4—124no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—22no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—42no—
652C2×C3×C4—42no—
653C2×C3×C4—42no—
654C2×C3×C4—62no—
655C2×C3×C4—62no—
656C2×C3×C4—62no—
657C2×C3×C4—62no—
658C2×C3×C4—124no—
659C2×C3×C4C23×D312yes—
660C2×C3×C4C23×D312yes—
661C2×C3×C4C23×D312yes—
662C2×C3×C4C23×D312yes—
663C2×C3×C4C23×D312yes—
664C2×C3×C4C23×D312yes—
665#67—68no—
666#67—68no—
667#67—124no—
668#67—124no—
669#67—124no—
670#67—124no—
671C2×Dic3—22no—
672C2×Dic3—22no—
673C2×Dic3—22no—
674C2×Dic3—22no—
675C2×Dic3—32no—
676C2×Dic3—32no—
677C2×Dic3—32no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—32no—
681C2×Dic3—62no—
682C2×Dic3—62no—
683C2×Dic3—62no—
684C2×Dic3—64no—
685C2×Dic3—62no—
686C2×Dic3—62no—
687C2×Dic3—62no—
688C2×Dic3—62no—
689C2×Dic3—62no—
690C2×Dic3—62no—
691C2×Dic3—122no—
692C2×Dic3—122no—
693C2×Dic3—124no—
694C2×Dic3C23×D312yes—
695C2×Dic3C23×D312yes—
696C2×Dic3C23×D312yes—
697C2×Dic3C23×D312yes—
698D12—44no—
699D12—44no—
700D12—44no—
701D12—68no—
702D12—68no—
703C4×D3—44no—
704C4×D3—124no—
705C4×D3—124no—
706C4×D3—124no—
707C4×D3—124no—
708C4×D3—128no—
709C4×D3—124no—
710Dic6—124no—
711Dic6—124no—
712Dic6—128no—
713C2×C32#53814yescomplemented
714C2×C32C22×#4111yescharacteristic
715C2×C32C2×H(5,𝔽2)11yescharacteristic
716C2×C32C2×H(5,𝔽2)11yescharacteristic
717C3⋊D3—24no—
718C3×D3—42no—
719C3×D3—42no—
720C3×D3—42no—
721C3×D3—42no—
722C24—31no—
723C24—31no—
724C24—31no—
725C24—31no—
726C24—94no—
727C24—91no—
728C24—184no—
729C24—362no—
730C24—362no—
731C2×Q8—94no—
732C2×Q8—362no—
733C2×D4—34no—
734C2×D4—34no—
735C2×D4—34no—
736C2×D4—94no—
737C2×D4—94no—
738C2×D4—94no—
739C2×D4—94no—
740C2×D4—122no—
741C2×D4—122no—
742C2×D4—122no—
743C2×D4—184no—
744C2×D4—184no—
745C2×D4—362no—
746C2×D4—362no—
747C22×C4—31no—
748C22×C4—31no—
749C22×C4—31no—
750C22×C4—31no—
751C22×C4—34no—
752C22×C4—94no—
753C22×C4—94no—
754C22×C4—91no—
755C22×C4—91no—
756C22×C4—91no—
757C22×C4—94no—
758C22×C4—122no—
759C22×C4—362no—
760C22×C4—362no—
761C22×C4—362no—
762C22×C4C2×D3211yescharacteristic
763C22×C4C2×D3211yescharacteristic
764C22×C4C2×D3211yescharacteristic
765C4⋊C4—34no—
766C4⋊C4—34no—
767C4⋊C4—94no—
768C4⋊C4—94no—
769C4⋊C4—94no—
770C4⋊C4C2×D3214yescomplemented
771C22⋊C4—34no—
772C22⋊C4—34no—
773C22⋊C4—34no—
774C22⋊C4—34no—
775C22⋊C4—34no—
776C22⋊C4—94no—
777C22⋊C4—94no—
778C22⋊C4—94no—
779C22⋊C4—94no—
780C22⋊C4—94no—
781C22⋊C4—94no—
782C22⋊C4—94no—
783C22⋊C4—94no—
784C22⋊C4—94no—
785C42—34no—
786C42—94no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—21no—
791C22×C3—62no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3—62no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3—62no—
802C22×C3—62no—
803C22×C3—124no—
804C22×C3—124no—
805C22×C3—124no—
806C22×C3—124no—
807C22×C3#100412yes—
808C22×C3#100412yes—
809C22×C3D3×#4112yes—
810C22×C3D3×#4112yes—
811C22×C3#100912yes—
812C22×C3#100912yes—
813C22×C3C24×D311yescharacteristic
814C22×C3C24×D311yescharacteristic
815C2×D3—22no—
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—22no—
819C2×D3—22no—
820C2×D3—22no—
821C2×D3—22no—
822C2×D3—22no—
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—22no—
826C2×D3—22no—
827C2×D3—34no—
828C2×D3—34no—
829C2×D3—44no—
830C2×D3—44no—
831C2×D3—44no—
832C2×D3—44no—
833C2×D3—64no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—68no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—68no—
840C2×D3—122no—
841C2×D3—122no—
842C2×D3—128no—
843C2×D3—1216no—
844C2×D3—1216no—
845C3×C4—22no—
846C3×C4—22no—
847C3×C4—22no—
848C3×C4—22no—
849C3×C4—22no—
850C3×C4—22no—
851C3×C4—42no—
852C3×C4—42no—
853C3×C4—42no—
854C3×C4—62no—
855C3×C4—62no—
856C3×C4—62no—
857C3×C4—62no—
858Dic3—22no—
859Dic3—22no—
860Dic3—22no—
861Dic3—22no—
862Dic3—64no—
863Dic3—62no—
864Dic3—62no—
865Dic3—62no—
866Dic3—62no—
867Dic3—62no—
868Dic3—62no—
869Dic3—122no—
870Dic3—122no—
871C32C2×#53811yescharacteristic, complemented, Sylow
872C23—32no—
873C23—32no—
874C23—32no—
875C23—32no—
876C23—62no—
877C23—62no—
878C23—62no—
879C23—62no—
880C23—62no—
881C23—62no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—94no—
889C23—92no—
890C23—188no—
891C23—182no—
892C23—182no—
893C23—364no—
894C23—364no—
895C23—3616no—
896C23C22×D3211yescharacteristic
897Q8—364no—
898D4—124no—
899D4—124no—
900D4—124no—
901D4—188no—
902D4—188no—
903D4—364no—
904D4—364no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—32no—
909C2×C4—32no—
910C2×C4—32no—
911C2×C4—32no—
912C2×C4—62no—
913C2×C4—62no—
914C2×C4—62no—
915C2×C4—62no—
916C2×C4—92no—
917C2×C4—92no—
918C2×C4—92no—
919C2×C4—124no—
920C2×C4—182no—
921C2×C4—182no—
922C2×C4—182no—
923C2×C4—364no—
924C2×C4—364no—
925C2×C4—364no—
926C2×C4C22×D3212yes—
927C2×C4C22×D3212yes—
928C2×C4C22×D3212yes—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—24no—
933C2×C3—122no—
934C2×C3—122no—
935C2×C3—122no—
936C2×C3—122no—
937C2×C3#561314yescomplemented
938C2×C3#570414yescomplemented
939C2×C3C2×#100411yescharacteristic
940C2×C3C2×#100411yescharacteristic
941C2×C3C2×D3×#4111yescharacteristic
942C2×C3C2×D3×#4111yescharacteristic
943C2×C3C2×#100911yescharacteristic
944C2×C3C2×#100911yescharacteristic
945D3—42no—
946D3—42no—
947D3—42no—
948D3—42no—
949D3—64no—
950D3—64no—
951D3—124no—
952C22—62no—
953C22—62no—
954C22—62no—
955C22—62no—
956C22—62no—
957C22—62no—
958C22—62no—
959C22—62no—
960C22—62no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—94no—
965C22—124no—
966C22—124no—
967C22—124no—
968C22—124no—
969C22—182no—
970C22—182no—
971C22—188no—
972C22—3616no—
973C22#6430712yes—
974C22#6431412yes—
975C22#6431912yes—
976C22C23×D3211yescharacteristic
977C4—22no—
978C4—22no—
979C4—22no—
980C4—62no—
981C4—62no—
982C4—62no—
983C4—62no—
984C4—182no—
985C4—182no—
986C4—182no—
987C3—21no—
988C3C2×#561311yescharacteristic, complemented
989C3C2×#570411yescharacteristic, complemented
990C2—122no—
991C2—122no—
992C2—122no—
993C2—122no—
994C2—184no—
995C2#1059466014yesdirect product factor
996C2C2×#6430711yescharacteristic
997C2C2×#6431411yescharacteristic
998C2C2×#6431911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#538
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×#895C2semidirect
4. C2×#63922C2semidirect
5. C2×#63922C2semidirect
6. C2×#63921C2semidirect
7. C2×#63916C2semidirect
8. C2×#63913C2semidirect
9. C2×#63905C2semidirect
10. C2×#63904C2semidirect
11. C2×#63885C2semidirect
12. C2×#63884C2semidirect
13. C2×#63880C2semidirect
14. C2×#63860C2semidirect
15. C2×#63858C2semidirect
16. #10594660C2direct (N × H)
21. C22×#634C22semidirect
24. C22×C3×D12C22semidirect
25. C22×C3×C4×D3C22semidirect
31. C22×D3×Dic3C22semidirect
32. C2×C32×C4⋊C4C22semidirect
35. C2×#3750C22semidirect
36. C2×#3750C22semidirect
37. #64105C22semidirect
42. C2×C3×(C2×D3)⋊C4C22semidirect
43. C2×C3×C4⋊Dic3C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
45. C2×C3×C4×Dic3C22semidirect
46. C3×#898C22semidirect
47. C3×#895C22semidirect
48. C2×Dic3⋊Dic3C22semidirect
53. C2×(C2×D3)⋊Dic3C22semidirect
54. C2×(C2×D3)⋊Dic3C22semidirect
55. C2×(C2×D3)⋊Dic3C22semidirect
56. C2×Dic32C22semidirect
57. #63922C22semidirect
58. #63922C22semidirect
59. #63921C22semidirect
60. #63916C22semidirect
61. #63913C22semidirect
62. #63905C22semidirect
63. #63904C22semidirect
64. #63885C22semidirect
65. #63884C22semidirect
66. #63880C22semidirect
67. #63860C22semidirect
68. #63858C22semidirect
82. C2×#898D3semidirect
87. C2×#895D3semidirect
120. C2×#634C23semidirect
130. C2×C3×D12C23semidirect
132. C2×C3×C4×D3C23semidirect
144. C2×D3×Dic3C23semidirect
145. C32×C4⋊C4C23semidirect
148. #3750C23semidirect
149. #3750C23semidirect
154. C3×(C2×D3)⋊C4C23semidirect
155. C3×C4⋊Dic3C23semidirect
156. C3×Dic3⋊C4C23semidirect
157. C3×C4×Dic3C23semidirect
158. Dic3⋊Dic3C23semidirect
163. (C2×D3)⋊Dic3C23semidirect
164. (C2×D3)⋊Dic3C23semidirect
165. (C2×D3)⋊Dic3C23semidirect
166. Dic32C23semidirect
185. C22×D12C2×D3semidirect
192. C22×C4×D3C2×D3semidirect
201. C2×C3×C4⋊C4C2×D3semidirect
202. C2×C3×C4⋊C4C2×D3semidirect
241. C2×(C2×D3)⋊C4C2×D3semidirect
243. C2×C4⋊Dic3C2×D3semidirect
251. C2×Dic3⋊C4C2×D3semidirect
254. C2×C4×Dic3C2×D3semidirect
256. #898C2×D3semidirect
261. #895C2×D3semidirect
425. C2×D12C22×D3semidirect
439. C2×C4×D3C22×D3semidirect
449. C3×C4⋊C4C22×D3semidirect
450. C3×C4⋊C4C22×D3semidirect
481. (C2×D3)⋊C4C22×D3semidirect
483. C4⋊Dic3C22×D3semidirect
491. Dic3⋊C4C22×D3semidirect
494. C4×Dic3C22×D3semidirect
562. C2×C4⋊C4D32semidirect
713. C2×C32#538semidirect
770. C4⋊C4C2×D32semidirect
871. C32C2×#538semidirect
937. C2×C3#5613semidirect
938. C2×C3#5704semidirect
988. C3C2×#5613semidirect
989. C3C2×#5704semidirect
995. C2#10594660direct (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×#8952
C2×#639222
C2×#639212
C2×#639162
C2×#639132
C2×#639052
C2×#639042
C2×#638852
C2×#638842
C2×#638802
C2×#638602
C2×#638582
#105946602
C2×#57043
C2×#56133