Finite Group Databasebeta

← C2×#10594307 #11901348

Subgroups — C2×#10594307 #11901348

Order 1152.

2885 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64093C211yesmaximal, characteristic, complemented
2C2×C3×#886C211yesmaximal, characteristic, complemented
3C2×C3×#885C211yesmaximal, characteristic, complemented
4C2×#63983C211yesmaximal, characteristic, complemented
5C2×#63978C211yesmaximal, characteristic, complemented
6C2×#63958C211yesmaximal, characteristic, complemented
7C2×#63952C211yesmaximal, characteristic, complemented
8C2×#63923C211yesmaximal, characteristic, complemented
9C2×#63921C211yesmaximal, characteristic, complemented
10C2×#63907C211yesmaximal, characteristic, complemented
11C2×#63894C211yesmaximal, characteristic, complemented
12C2×#63871C211yesmaximal, characteristic, complemented
13C2×#63859C211yesmaximal, characteristic, complemented
14C2×#63858C211yesmaximal, characteristic, complemented
15C2×#63854C211yesmaximal, characteristic, complemented
16#10594307C2116yesmaximal, direct product factor
17C2×#5678—31nomaximal
18C2×#5657—31nomaximal
19C23×D32C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic, complemented
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C23×C3×Dic3C2211yescharacteristic, complemented
27C22×C3×Dic6C2211yescharacteristic, complemented
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#624C2211yescharacteristic
31C22×#624C2211yescharacteristic, complemented
32C2×C32×C22⋊C4C2211yescharacteristic, complemented
33C2×#3752C2211yescharacteristic, complemented
34C2×#3750C2211yescharacteristic, complemented
35#64093C2218yescomplemented
36C2×C3×#217C2211yescharacteristic, complemented
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
42C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
43C2×C3×C4×Dic3C2211yescharacteristic, complemented
44C3×#886C2218yescomplemented
45C3×#885C2218yescomplemented
46#63983C2218yescomplemented
47#63978C2218yescomplemented
48C2×#3724C2211yescharacteristic, complemented
49C2×Dic3⋊Dic3C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic, complemented
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58#63958C2218yescomplemented
59C2×Dic32C2211yescharacteristic, complemented
60#63952C2218yescomplemented
61#63923C2218yescomplemented
62#63921C2218yescomplemented
63#63907C2218yescomplemented
64#63894C2218yescomplemented
65#63871C2218yescomplemented
66#63859C2218yescomplemented
67#63858C2218yescomplemented
68#63854C2218yescomplemented
69C2×C3×#124—31no—
70C2×C3×#123—31no—
71C2×#947—31no—
72C2×#946—31no—
73C2×#939—31no—
74C2×#938—31no—
75C2×#937—31no—
76C2×#937—31no—
77C2×#930—31no—
78C2×C4×#67—31no—
79#5678—316no—
80#5657—316no—
81C2×#898—31no—
82C2×#897—31no—
83C2×#894—31no—
84C2×#893—31no—
85C2×#886D311yescharacteristic, complemented
86C2×#885—31no—
87C2×#885D311yescharacteristic, complemented
88C2×#884—31no—
89C2×#884—31no—
90C2×#884—31no—
91C2×#884—61no—
92C2×#883—31no—
93C2×#882—31no—
94C2×#882—31no—
95C2×#67⋊C4—31no—
96C2×D3×C22⋊C4—31no—
97C2×D3×C22⋊C4—31no—
98C2×#879—31no—
99C2×#879—31no—
100C2×#876—31no—
101C2×C4×D12—31no—
102C24×C32C2311yescharacteristic
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
113C2×#638—24no—
114C2×#638—42no—
115C2×#638C2314yes—
116C2×#638C2314yescomplemented
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2311yescharacteristic
119C2×C4⋊(C3⋊D3)—24no—
120C2×C4⋊(C3⋊D3)C2314yes—
121C2×C4×C3⋊D3—42no—
122C2×C4×C3⋊D3C2314yes—
123C2×C3×#67—42no—
124C2×C3×#67—42no—
125C2×C3×#67C2314yes—
126C2×C3×#67C2314yes—
127C22×C3×Dic3—42no—
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2314yescomplemented
135C2×C3×Dic6—42no—
136C2×C3×Dic6C2314yescomplemented
137C2×#626—42no—
138C2×#626—42no—
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#624—42no—
142C2×#624—42no—
143C2×#624C2314yes—
144C2×#624C2314yescomplemented
145C32×C22⋊C4C2314yescomplemented
146#3752C2314yescomplemented
147#3750C2314yescomplemented
148C3×#217C2314yescomplemented
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×C4⋊Dic3C2314yescomplemented
154C3×C4⋊Dic3C2314yescomplemented
155C3×C4×Dic3C2314yescomplemented
156#3724C2314yescomplemented
157Dic3⋊Dic3C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159#3722C2314yes—
160#3722C2314yes—
161#3722C2314yescomplemented
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C22×C3×Q8—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—
180C22×#67—61no—
181C22×#67—61no—
182C22×#67C2×D311yescharacteristic
183C22×#67C2×D311yescharacteristic
184C23×Dic3C2×D311yescharacteristic, complemented
185C22×D12—31no—
186C22×D12—31no—
187C22×D12—31no—
188C22×D12—31no—
189C22×D12—61no—
190C22×C4×D3—31no—
191C22×C4×D3—31no—
192C22×C4×D3—31no—
193C22×C4×D3—31no—
194C22×C4×D3—31no—
195C22×C4×D3—31no—
196C22×C4×D3—61no—
197C22×Dic6C2×D311yescharacteristic, complemented
198C3×#124—38no—
199C3×#123—38no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C4⋊C4—31no—
202C2×C3×C22⋊C4—21no—
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×C22⋊C4C2×D311yescharacteristic, complemented
209C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
210C2×C3×C42—31no—
211C2×#217—31no—
212C2×#217—31no—
213C2×#217—31no—
214C2×#217—31no—
215C2×#217C2×D311yescharacteristic, complemented
216#947—38no—
217#946—38no—
218#939—38no—
219#938—38no—
220#937—38no—
221#937—38no—
222#930—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—31no—
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×C4⋊Dic3—31no—
242C2×C4⋊Dic3—31no—
243C2×C4⋊Dic3C2×D311yescharacteristic, complemented
244C2×C4⋊Dic3C2×D311yescharacteristic, complemented
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—61no—
252C2×C4×Dic3—31no—
253C2×C4×Dic3—31no—
254C2×C4×Dic3C2×D311yescharacteristic, complemented
255#898—38no—
256#897—38no—
257#894—38no—
258#893—38no—
259#886C2×D318yescomplemented
260#885—38no—
261#885C2×D318yescomplemented
262#884—38no—
263#884—38no—
264#884—38no—
265#884—68no—
266#883—38no—
267#882—38no—
268#882—38no—
269#67⋊C4—38no—
270D3×C22⋊C4—38no—
271D3×C22⋊C4—38no—
272#879—38no—
273#879—38no—
274#876—38no—
275C4×D12—38no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32—22no—
279C23×C32C2412yes—
280C23×C32C2411yescharacteristic
281C22×C3⋊D3—22no—
282C22×C3⋊D3—22no—
283C22×C3⋊D3—22no—
284C22×C3⋊D3—22no—
285C22×C3⋊D3—22no—
286C22×C3⋊D3#4114yes—
287C22×C3⋊D3C2412yes—
288C22×C3⋊D3C2412yes—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3—22no—
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×C4C2412yes—
304C2×C32×C4C2412yes—
305#638—28no—
306#638—44no—
307C2×C3⋊Dic3—22no—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3C2412yes—
310C2×C3⋊Dic3C2412yes—
311C4⋊(C3⋊D3)—28no—
312C4×C3⋊D3—44no—
313C3×#67—44no—
314C3×#67—44no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—22no—
321C2×C3×Dic3—44no—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C3×Dic6—44no—
329#626—44no—
330#626—44no—
331#624—44no—
332#624—44no—
333#538—916no—
334C2×#126—91no—
335C2×#126—91no—
336C2×#124—31no—
337C2×#124—91no—
338C2×#123—31no—
339C2×#123—91no—
340C2×C22⋊Q8—91no—
341C2×#121—91no—
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—21no—
350C24×C3—31no—
351C24×C3—31no—
352C24×C3C22×D311yescharacteristic
353C24×C3C22×D311yescharacteristic
354C23×D3—31no—
355C23×D3—31no—
356C23×D3—31no—
357C23×D3—31no—
358C23×D3—34no—
359C23×D3—34no—
360C23×D3—61no—
361C23×D3—61no—
362C23×D3—64no—
363C23×D3—64no—
364C23×D3—122no—
365C23×D3—122no—
366C23×D3—122no—
367C23×D3—122no—
368C23×D3C22×D311yescharacteristic
369C23×D3C22×D311yescharacteristic
370C2×C3×Q8—34no—
371C2×C3×Q8—122no—
372C2×C3×D4—34no—
373C2×C3×D4—34no—
374C2×C3×D4—122no—
375C2×C3×D4—122no—
376C22×C3×C4—21no—
377C22×C3×C4—21no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—34no—
385C22×C3×C4—122no—
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C2×#67—34no—
391C2×#67—34no—
392C2×#67—34no—
393C2×#67—34no—
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—42no—
397C2×#67—42no—
398C2×#67—64no—
399C2×#67—64no—
400C2×#67—64no—
401C2×#67—64no—
402C2×#67—124no—
403C2×#67—122no—
404C2×#67—122no—
405C2×#67—122no—
406C2×#67—122no—
407C2×#67—124no—
408C2×#67C22×D314yes—
409C2×#67C22×D314yes—
410C22×Dic3—31no—
411C22×Dic3—31no—
412C22×Dic3—31no—
413C22×Dic3—31no—
414C22×Dic3—42no—
415C22×Dic3—61no—
416C22×Dic3—61no—
417C22×Dic3C22×D311yescharacteristic
418C22×Dic3C22×D311yescharacteristic
419C22×Dic3C22×D311yescharacteristic
420C22×Dic3C22×D311yescharacteristic
421C22×Dic3C22×D311yescharacteristic
422C22×Dic3C22×D311yescharacteristic
423C22×Dic3C22×D314yescomplemented
424C2×D12—34no—
425C2×D12—34no—
426C2×D12—34no—
427C2×D12—34no—
428C2×D12—64no—
429C2×D12—64no—
430C2×D12—64no—
431C2×D12—124no—
432C2×D12—122no—
433C2×D12—122no—
434C2×C4×D3—34no—
435C2×C4×D3—34no—
436C2×C4×D3—34no—
437C2×C4×D3—34no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—64no—
441C2×C4×D3—122no—
442C2×C4×D3—122no—
443C2×C4×D3—122no—
444C2×C4×D3—122no—
445C2×C4×D3—122no—
446C2×C4×D3—122no—
447C2×C4×D3—124no—
448C2×Dic6—42no—
449C2×Dic6C22×D314yescomplemented
450C3×C4⋊C4—34no—
451C3×C4⋊C4—34no—
452C3×C22⋊C4—24no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4—34no—
457C3×C22⋊C4—34no—
458C3×C22⋊C4C22×D314yescomplemented
459C3×C22⋊C4C22×D314yescomplemented
460C3×C42—34no—
461#217—34no—
462#217—34no—
463#217—34no—
464#217—34no—
465#217C22×D314yescomplemented
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—34no—
476(C2×D3)⋊C4—34no—
477(C2×D3)⋊C4—34no—
478(C2×D3)⋊C4—64no—
479(C2×D3)⋊C4C22×D314yes—
480(C2×D3)⋊C4C22×D314yes—
481(C2×D3)⋊C4C22×D314yes—
482(C2×D3)⋊C4C22×D314yes—
483C4⋊Dic3—34no—
484C4⋊Dic3—34no—
485C4⋊Dic3C22×D314yescomplemented
486C4⋊Dic3C22×D314yescomplemented
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4—64no—
494C4×Dic3—34no—
495C4×Dic3—34no—
496C4×Dic3C22×D314yescomplemented
497C22×C32—22no—
498C22×C32—22no—
499C22×C32—22no—
500C22×C32—44no—
501C22×C32C2×#4112yes—
502C22×C32H(5,𝔽2)12yes—
503C22×C32H(5,𝔽2)12yes—
504C22×C32C2511yescharacteristic
505C2×C3⋊D3—28no—
506C2×C3⋊D3—22no—
507C2×C3⋊D3—22no—
508C2×C3⋊D3—22no—
509C2×C3⋊D3—22no—
510C2×C3⋊D3—22no—
511C2×C3⋊D3—44no—
512C2×C3⋊D3C2×#4114yes—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—22no—
519C2×C3×D3—44no—
520C2×C3×D3—44no—
521D32—416no—
522C32×C4—22no—
523C32×C4—22no—
524C3⋊Dic3—22no—
525C3⋊Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—22no—
531C3×Dic3—22no—
532C25—91no—
533C22×Q8—31no—
534C22×D4—31no—
535C22×D4—31no—
536C22×D4—91no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4—91no—
540C22×D4—91no—
541C23×C4—31no—
542C23×C4—91no—
543C23×C4—91no—
544C23×C4—91no—
545#126—98no—
546#126—98no—
547#124—38no—
548#124—98no—
549#123—38no—
550#123—98no—
551C22⋊Q8—98no—
552#121—98no—
553#121—98no—
554#121—98no—
555#120—98no—
556#120—98no—
557C4×D4—98no—
558C4×D4—98no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—31no—
561C2×C4⋊C4—91no—
562C2×C4⋊C4—91no—
563C2×C4⋊C4—91no—
564C2×C4⋊C4—91no—
565C2×C22⋊C4—31no—
566C2×C22⋊C4—31no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—98no—
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×C22⋊C4—91no—
579C2×C22⋊C4D3211yescharacteristic, complemented
580C2×C42—31no—
581C2×C42—91no—
582C23×C3—22no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—21no—
590C23×C3—32no—
591C23×C3—32no—
592C23×C3—42no—
593C23×C3—42no—
594C23×C3—42no—
595C23×C3—62no—
596C23×C3—62no—
597C23×C3—62no—
598C23×C3—62no—
599C23×C3—62no—
600C23×C3—62no—
601C23×C3C23×D312yes—
602C23×C3C23×D312yes—
603C23×C3C23×D311yescharacteristic
604C23×C3C23×D311yescharacteristic
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—32no—
616C22×D3—32no—
617C22×D3—64no—
618C22×D3—62no—
619C22×D3—62no—
620C22×D3—68no—
621C22×D3—68no—
622C22×D3—62no—
623C22×D3—62no—
624C22×D3—62no—
625C22×D3—62no—
626C22×D3—62no—
627C22×D3—62no—
628C22×D3—62no—
629C22×D3—62no—
630C22×D3—62no—
631C22×D3—62no—
632C22×D3—122no—
633C22×D3—122no—
634C22×D3—122no—
635C22×D3—122no—
636C22×D3—122no—
637C22×D3—124no—
638C22×D3—124no—
639C22×D3—124no—
640C22×D3—124no—
641C22×D3—1216no—
642C22×D3—1216no—
643C22×D3C23×D312yes—
644C22×D3C23×D312yes—
645C3×Q8—124no—
646C3×D4—124no—
647C3×D4—124no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—32no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—42no—
661C2×C3×C4—42no—
662C2×C3×C4—62no—
663C2×C3×C4—62no—
664C2×C3×C4—62no—
665C2×C3×C4—62no—
666C2×C3×C4—62no—
667C2×C3×C4—62no—
668C2×C3×C4—124no—
669C2×C3×C4C23×D312yes—
670C2×C3×C4C23×D312yes—
671C2×C3×C4C23×D312yes—
672C2×C3×C4C23×D312yes—
673#67—44no—
674#67—44no—
675#67—68no—
676#67—68no—
677#67—128no—
678#67—124no—
679#67—124no—
680#67—124no—
681#67—124no—
682#67—128no—
683C2×Dic3—22no—
684C2×Dic3—22no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—32no—
690C2×Dic3—32no—
691C2×Dic3—32no—
692C2×Dic3—32no—
693C2×Dic3—44no—
694C2×Dic3—62no—
695C2×Dic3—62no—
696C2×Dic3—64no—
697C2×Dic3—62no—
698C2×Dic3—62no—
699C2×Dic3—62no—
700C2×Dic3—62no—
701C2×Dic3—122no—
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D312yes—
706C2×Dic3C23×D312yes—
707C2×Dic3C23×D312yes—
708D12—68no—
709D12—68no—
710D12—128no—
711D12—124no—
712D12—124no—
713C4×D3—124no—
714C4×D3—124no—
715C4×D3—124no—
716C4×D3—124no—
717C4×D3—124no—
718C4×D3—124no—
719C4×D3—128no—
720Dic6—44no—
721C2×C32—42no—
722C2×C32#53814yescomplemented
723C2×C32C22×#4111yescharacteristic
724C2×C32C2×H(5,𝔽2)11yescharacteristic
725C2×C32C2×H(5,𝔽2)11yescharacteristic
726C3⋊D3—24no—
727C3⋊D3—42no—
728C3×D3—42no—
729C3×D3—42no—
730C24—31no—
731C24—31no—
732C24—94no—
733C24—91no—
734C24—91no—
735C24—184no—
736C24—362no—
737C24—362no—
738C24C2×D3211yescharacteristic
739C2×Q8—34no—
740C2×Q8—122no—
741C2×D4—34no—
742C2×D4—34no—
743C2×D4—94no—
744C2×D4—94no—
745C2×D4—94no—
746C2×D4—94no—
747C2×D4—94no—
748C2×D4—122no—
749C2×D4—122no—
750C2×D4—184no—
751C2×D4—184no—
752C2×D4—362no—
753C2×D4—362no—
754C2×D4—362no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—34no—
762C22×C4—94no—
763C22×C4—94no—
764C22×C4—91no—
765C22×C4—91no—
766C22×C4—94no—
767C22×C4—122no—
768C22×C4—362no—
769C22×C4—362no—
770C22×C4—362no—
771C22×C4C2×D3211yescharacteristic
772C22×C4C2×D3211yescharacteristic
773C4⋊C4—34no—
774C4⋊C4—34no—
775C4⋊C4—94no—
776C4⋊C4—94no—
777C4⋊C4—94no—
778C4⋊C4—94no—
779C22⋊C4—34no—
780C22⋊C4—34no—
781C22⋊C4—34no—
782C22⋊C4—34no—
783C22⋊C4—34no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C22⋊C4—94no—
790C22⋊C4—94no—
791C22⋊C4—94no—
792C22⋊C4C2×D3214yescomplemented
793C42—34no—
794C42—94no—
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—21no—
805C22×C3—42no—
806C22×C3—42no—
807C22×C3—42no—
808C22×C3—44no—
809C22×C3—44no—
810C22×C3—62no—
811C22×C3—62no—
812C22×C3—62no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—84no—
817C22×C3—124no—
818C22×C3—124no—
819C22×C3#100412yes—
820C22×C3#100412yes—
821C22×C3D3×#4112yes—
822C22×C3D3×#4112yes—
823C22×C3#100912yes—
824C22×C3#100912yes—
825C22×C3C24×D311yescharacteristic
826C22×C3C24×D311yescharacteristic
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—34no—
834C2×D3—34no—
835C2×D3—44no—
836C2×D3—44no—
837C2×D3—64no—
838C2×D3—68no—
839C2×D3—68no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—62no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—62no—
847C2×D3—62no—
848C2×D3—62no—
849C2×D3—62no—
850C2×D3—122no—
851C2×D3—128no—
852C2×D3—122no—
853C2×D3—122no—
854C2×D3—122no—
855C2×D3—122no—
856C2×D3—1216no—
857C2×D3—1216no—
858C2×D3—124no—
859C2×D3—124no—
860C2×D3—244no—
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—22no—
865C3×C4—42no—
866C3×C4—42no—
867C3×C4—62no—
868C3×C4—62no—
869C3×C4—62no—
870C3×C4—62no—
871C3×C4—62no—
872C3×C4—62no—
873Dic3—22no—
874Dic3—22no—
875Dic3—22no—
876Dic3—22no—
877Dic3—22no—
878Dic3—22no—
879Dic3—64no—
880Dic3—62no—
881Dic3—62no—
882Dic3—62no—
883Dic3—62no—
884Dic3—122no—
885C32C2×#53811yescharacteristic, complemented, Sylow
886C23—22no—
887C23—22no—
888C23—22no—
889C23—32no—
890C23—32no—
891C23—62no—
892C23—62no—
893C23—62no—
894C23—62no—
895C23—62no—
896C23—62no—
897C23—94no—
898C23—92no—
899C23—92no—
900C23—188no—
901C23—182no—
902C23—182no—
903C23—182no—
904C23—182no—
905C23—182no—
906C23—364no—
907C23—364no—
908C23—3616no—
909C23C22×D3212yes—
910C23C22×D3211yescharacteristic
911Q8—124no—
912D4—124no—
913D4—124no—
914D4—188no—
915D4—188no—
916D4—364no—
917D4—364no—
918D4—364no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—32no—
922C2×C4—32no—
923C2×C4—32no—
924C2×C4—32no—
925C2×C4—32no—
926C2×C4—32no—
927C2×C4—62no—
928C2×C4—62no—
929C2×C4—62no—
930C2×C4—62no—
931C2×C4—62no—
932C2×C4—62no—
933C2×C4—92no—
934C2×C4—92no—
935C2×C4—124no—
936C2×C4—182no—
937C2×C4—182no—
938C2×C4—364no—
939C2×C4—364no—
940C2×C4—364no—
941C2×C4C22×D3212yes—
942C2×C4C22×D3212yes—
943C2×C3—24no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—42no—
948C2×C3—42no—
949C2×C3—82no—
950C2×C3—122no—
951C2×C3—122no—
952C2×C3#565714yescomplemented
953C2×C3#567814yescomplemented
954C2×C3C2×#100411yescharacteristic
955C2×C3C2×#100411yescharacteristic
956C2×C3C2×D3×#4111yescharacteristic
957C2×C3C2×D3×#4111yescharacteristic
958C2×C3C2×#100911yescharacteristic
959C2×C3C2×#100911yescharacteristic
960D3—42no—
961D3—42no—
962D3—64no—
963D3—64no—
964D3—124no—
965D3—122no—
966D3—122no—
967D3—242no—
968C22—22no—
969C22—22no—
970C22—22no—
971C22—44no—
972C22—62no—
973C22—62no—
974C22—62no—
975C22—62no—
976C22—62no—
977C22—62no—
978C22—94no—
979C22—124no—
980C22—124no—
981C22—188no—
982C22—182no—
983C22—182no—
984C22—182no—
985C22—182no—
986C22—182no—
987C22—3616no—
988C22—364no—
989C22#6430712yes—
990C22#6431212yes—
991C22#6431412yes—
992C22C23×D3211yescharacteristic
993C4—22no—
994C4—22no—
995C4—62no—
996C4—62no—
997C4—62no—
998C4—62no—
999C4—62no—
1000C4—62no—
1001C4—182no—
1002C4—182no—
1003C3—21no—
1004C3C2×#565711yescharacteristic, complemented
1005C3C2×#567811yescharacteristic, complemented
1006C2—42no—
1007C2—122no—
1008C2—122no—
1009C2—184no—
1010C2—362no—
1011C2#1059430714yesdirect product factor
1012C2C2×#6430711yescharacteristic
1013C2C2×#6431211yescharacteristic
1014C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64093C2semidirect
2. C2×C3×#886C2semidirect
3. C2×C3×#885C2semidirect
4. C2×#63983C2semidirect
5. C2×#63978C2semidirect
6. C2×#63958C2semidirect
7. C2×#63952C2semidirect
8. C2×#63923C2semidirect
9. C2×#63921C2semidirect
10. C2×#63907C2semidirect
11. C2×#63894C2semidirect
12. C2×#63871C2semidirect
13. C2×#63859C2semidirect
14. C2×#63858C2semidirect
15. C2×#63854C2semidirect
16. #10594307C2direct (N × H)
21. C22×#638C22semidirect
26. C23×C3×Dic3C22semidirect
27. C22×C3×Dic6C22semidirect
31. C22×#624C22semidirect
32. C2×C32×C22⋊C4C22semidirect
33. C2×#3752C22semidirect
34. C2×#3750C22semidirect
35. #64093C22semidirect
36. C2×C3×#217C22semidirect
41. C2×C3×C4⋊Dic3C22semidirect
42. C2×C3×C4⋊Dic3C22semidirect
43. C2×C3×C4×Dic3C22semidirect
44. C3×#886C22semidirect
45. C3×#885C22semidirect
46. #63983C22semidirect
47. #63978C22semidirect
48. C2×#3724C22semidirect
49. C2×Dic3⋊Dic3C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
53. C2×#3722C22semidirect
58. #63958C22semidirect
59. C2×Dic32C22semidirect
60. #63952C22semidirect
61. #63923C22semidirect
62. #63921C22semidirect
63. #63907C22semidirect
64. #63894C22semidirect
65. #63871C22semidirect
66. #63859C22semidirect
67. #63858C22semidirect
68. #63854C22semidirect
85. C2×#886D3semidirect
87. C2×#885D3semidirect
116. C2×#638C23semidirect
134. C22×C3×Dic3C23semidirect
136. C2×C3×Dic6C23semidirect
144. C2×#624C23semidirect
145. C32×C22⋊C4C23semidirect
146. #3752C23semidirect
147. #3750C23semidirect
148. C3×#217C23semidirect
153. C3×C4⋊Dic3C23semidirect
154. C3×C4⋊Dic3C23semidirect
155. C3×C4×Dic3C23semidirect
156. #3724C23semidirect
157. Dic3⋊Dic3C23semidirect
158. Dic3⋊Dic3C23semidirect
161. #3722C23semidirect
166. Dic32C23semidirect
184. C23×Dic3C2×D3semidirect
197. C22×Dic6C2×D3semidirect
208. C2×C3×C22⋊C4C2×D3semidirect
209. C2×C3×C22⋊C4C2×D3semidirect
215. C2×#217C2×D3semidirect
243. C2×C4⋊Dic3C2×D3semidirect
244. C2×C4⋊Dic3C2×D3semidirect
254. C2×C4×Dic3C2×D3semidirect
259. #886C2×D3semidirect
261. #885C2×D3semidirect
423. C22×Dic3C22×D3semidirect
449. C2×Dic6C22×D3semidirect
458. C3×C22⋊C4C22×D3semidirect
459. C3×C22⋊C4C22×D3semidirect
465. #217C22×D3semidirect
485. C4⋊Dic3C22×D3semidirect
486. C4⋊Dic3C22×D3semidirect
496. C4×Dic3C22×D3semidirect
579. C2×C22⋊C4D32semidirect
722. C2×C32#538semidirect
792. C22⋊C4C2×D32semidirect
885. C32C2×#538semidirect
952. C2×C3#5657semidirect
953. C2×C3#5678semidirect
1004. C3C2×#5657semidirect
1005. C3C2×#5678semidirect
1011. C2#10594307direct (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×#8862
C2×C3×#8852
C2×#639832
C2×#639782
C2×#639582
C2×#639522
C2×#639232
C2×#639212
C2×#639072
C2×#638942
C2×#638712
C2×#638592
C2×#638582
C2×#638542
#105943072
C2×#56783
C2×#56573