Finite Group Databasebeta

← C2×#10594225 #11901322

Subgroups — C2×#10594225 #11901322

Order 1152.

3009 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#885C211yesmaximal, characteristic, complemented
3C2×C3×#883C211yesmaximal, characteristic, complemented
4C2×#63981C211yesmaximal, characteristic, complemented
5C2×#63981C211yesmaximal, characteristic, complemented
6C2×#63970C211yesmaximal, characteristic, complemented
7C2×#63956C211yesmaximal, characteristic, complemented
8C2×#63912C211yesmaximal, characteristic, complemented
9C2×#63907C211yesmaximal, characteristic, complemented
10C2×#63906C211yesmaximal, characteristic, complemented
11C2×C4×#626C211yesmaximal, characteristic, complemented
12C2×#63890C211yesmaximal, characteristic, complemented
13C2×#63881C211yesmaximal, characteristic, complemented
14C2×#63871C211yesmaximal, characteristic, complemented
15C2×#63868C211yesmaximal, characteristic, complemented
16#10594225C2116yesmaximal, direct product factor
17C2×#5678—31nomaximal
18C2×#5657—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic, complemented
25C22×C3×Dic6C2211yescharacteristic, complemented
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#625C2211yescharacteristic, complemented
31C22×D3×Dic3C2211yescharacteristic, complemented
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×#3757C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3752C2211yescharacteristic
36C22⋊C4×C3⋊D3C2218yescomplemented
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
43C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
44C2×C3×C4×Dic3C2211yescharacteristic, complemented
45C3×#885C2218yescomplemented
46C3×#883C2218yescomplemented
47#63981C2218yescomplemented
48#63981C2218yescomplemented
49#63970C2218yescomplemented
50C2×#3724C2211yescharacteristic, complemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52C2×Dic3⋊Dic3C2211yescharacteristic, complemented
53C2×Dic3⋊Dic3C2211yescharacteristic, complemented
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57C2×#3722C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
59#63956C2218yescomplemented
60C2×Dic32C2211yescharacteristic, complemented
61#63912C2218yescomplemented
62#63907C2218yescomplemented
63#63906C2218yescomplemented
64C4×#626C2218yescomplemented
65#63890C2218yescomplemented
66#63881C2218yescomplemented
67#63871C2218yescomplemented
68#63868C2218yescomplemented
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×#886—31no—
86C2×#885—31no—
87C2×#885D311yescharacteristic, complemented
88C2×#884—31no—
89C2×#884—31no—
90C2×#884—31no—
91C2×#883D311yescharacteristic, complemented
92C2×#882—31no—
93C2×#882—31no—
94C2×#67⋊C4—31no—
95C2×D3×C22⋊C4—31no—
96C2×D3×C22⋊C4—31no—
97C2×D3×C22⋊C4—61no—
98C2×#879—31no—
99C2×#879—31no—
100C2×#876—31no—
101C2×C4×D12—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3—24no—
104C23×C3⋊D3—42no—
105C23×C3⋊D3—42no—
106C23×C3⋊D3C2311yescharacteristic
107C23×C3⋊D3C2311yescharacteristic
108C23×C3⋊D3C2314yes—
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C2×C4×C3⋊D3—42no—
116C2×C4×C3⋊D3—42no—
117C2×C4×C3⋊D3C2314yes—
118C2×C4×C3⋊D3C2314yes—
119C2×C3×#67—42no—
120C2×C3×#67—42no—
121C2×C3×#67C2314yes—
122C2×C3×#67C2314yes—
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×C4×D3—42no—
130C2×C3×C4×D3C2314yescomplemented
131C2×C3×Dic6—42no—
132C2×C3×Dic6C2314yescomplemented
133C2×#626—24no—
134C2×#626—24no—
135C2×#626—42no—
136C2×#626—42no—
137C2×#626C2314yes—
138C2×#626C2314yes—
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#625—42no—
142C2×#625C2314yescomplemented
143C2×D3×Dic3—42no—
144C2×D3×Dic3C2314yescomplemented
145C32×C22⋊C4C2314yes—
146#3757C2314yes—
147#3752C2314yes—
148#3752C2314yes—
149C3×#217C2314yes—
150C3×#217C2314yes—
151C3×(C2×D3)⋊C4C2314yescomplemented
152C3×(C2×D3)⋊C4C2314yescomplemented
153C3×(C2×D3)⋊C4C2314yescomplemented
154C3×C4⋊Dic3C2314yescomplemented
155C3×Dic3⋊C4C2314yescomplemented
156C3×C4×Dic3C2314yescomplemented
157#3724C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159Dic3⋊Dic3C2314yescomplemented
160Dic3⋊Dic3C2314yescomplemented
161#3722C2314yes—
162#3722C2314yes—
163#3722C2314yes—
164#3722C2314yes—
165(C2×D3)⋊Dic3C2314yescomplemented
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C24×D3—61no—
171C22×C3×Q8—31no—
172C22×C3×D4—31no—
173C22×C3×D4—31no—
174C23×C3×C4—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67C2×D311yescharacteristic
182C22×#67C2×D311yescharacteristic
183C23×Dic3—31no—
184C22×D12—31no—
185C22×D12—31no—
186C22×D12—31no—
187C22×D12—31no—
188C22×C4×D3—31no—
189C22×C4×D3—31no—
190C22×C4×D3—31no—
191C22×C4×D3—31no—
192C22×C4×D3—31no—
193C22×C4×D3—61no—
194C22×C4×D3—61no—
195C22×C4×D3C2×D311yescharacteristic, complemented
196C22×Dic6C2×D311yescharacteristic, complemented
197C3×#124—38no—
198C3×#123—38no—
199C2×C3×C4⋊C4—31no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C22⋊C4—21no—
202C2×C3×C22⋊C4—31no—
203C2×C3×C22⋊C4—31no—
204C2×C3×C22⋊C4—31no—
205C2×C3×C22⋊C4—31no—
206C2×C3×C22⋊C4—31no—
207C2×C3×C22⋊C4C2×D311yescharacteristic
208C2×C3×C22⋊C4C2×D311yescharacteristic
209C2×C3×C42—31no—
210C2×#217—31no—
211C2×#217—31no—
212C2×#217—31no—
213C2×#217—61no—
214C2×#217C2×D311yescharacteristic
215C2×#217C2×D311yescharacteristic
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—31no—
237C2×(C2×D3)⋊C4—61no—
238C2×(C2×D3)⋊C4—61no—
239C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
240C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
241C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
242C2×C4⋊Dic3—31no—
243C2×C4⋊Dic3—31no—
244C2×C4⋊Dic3—31no—
245C2×C4⋊Dic3C2×D311yescharacteristic, complemented
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4C2×D311yescharacteristic, complemented
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#886—38no—
260#885—38no—
261#885C2×D318yescomplemented
262#884—38no—
263#884—38no—
264#884—38no—
265#883C2×D318yescomplemented
266#882—38no—
267#882—38no—
268#67⋊C4—38no—
269D3×C22⋊C4—38no—
270D3×C22⋊C4—38no—
271D3×C22⋊C4—68no—
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—28no—
285C22×C3⋊D3—22no—
286C22×C3⋊D3—22no—
287C22×C3⋊D3—44no—
288C22×C3⋊D3—44no—
289C22×C3⋊D3—416no—
290C22×C3⋊D3#4114yes—
291C22×C3⋊D3C2412yes—
292C22×C3⋊D3C2412yes—
293C22×C3×D3—22no—
294C22×C3×D3—22no—
295C22×C3×D3—22no—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3C2412yes—
300C22×C3×D3C2412yes—
301C2×C32×C4—22no—
302C2×C32×C4—22no—
303C2×C32×C4C2412yes—
304C2×C32×C4C2412yes—
305C2×C3⋊Dic3—22no—
306C2×C3⋊Dic3—22no—
307C2×C3⋊Dic3C2412yes—
308C2×C3⋊Dic3C2412yes—
309C4×C3⋊D3—44no—
310C4×C3⋊D3—44no—
311C3×#67—44no—
312C3×#67—44no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—22no—
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—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C3×C4×D3—44no—
326C3×Dic6—44no—
327#626—28no—
328#626—28no—
329#626—44no—
330#626—44no—
331#625—44no—
332D3×Dic3—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—64no—
362C23×D3—61no—
363C23×D3—64no—
364C23×D3—64no—
365C23×D3—68no—
366C23×D3—122no—
367C23×D3—122no—
368C23×D3—122no—
369C23×D3—122no—
370C23×D3—124no—
371C23×D3—124no—
372C23×D3C22×D311yescharacteristic
373C23×D3C22×D311yescharacteristic
374C2×C3×Q8—34no—
375C2×C3×Q8—122no—
376C2×C3×D4—34no—
377C2×C3×D4—34no—
378C2×C3×D4—122no—
379C2×C3×D4—122no—
380C22×C3×C4—21no—
381C22×C3×C4—21no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—31no—
385C22×C3×C4—31no—
386C22×C3×C4—31no—
387C22×C3×C4—31no—
388C22×C3×C4—34no—
389C22×C3×C4—122no—
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C22×D311yescharacteristic
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—34no—
398C2×#67—34no—
399C2×#67—34no—
400C2×#67—42no—
401C2×#67—42no—
402C2×#67—64no—
403C2×#67—64no—
404C2×#67—122no—
405C2×#67—122no—
406C2×#67—122no—
407C2×#67—122no—
408C2×#67C22×D314yes—
409C2×#67C22×D314yes—
410C22×Dic3—31no—
411C22×Dic3—31no—
412C22×Dic3—31no—
413C22×Dic3—31no—
414C22×Dic3—34no—
415C22×Dic3—61no—
416C22×Dic3—61no—
417C22×Dic3—122no—
418C22×Dic3C22×D311yescharacteristic
419C22×Dic3C22×D311yescharacteristic
420C22×Dic3C22×D311yescharacteristic
421C22×Dic3C22×D311yescharacteristic
422C22×Dic3C22×D311yescharacteristic
423C22×Dic3C22×D311yescharacteristic
424C2×D12—34no—
425C2×D12—34no—
426C2×D12—34no—
427C2×D12—34no—
428C2×D12—64no—
429C2×D12—64no—
430C2×D12—122no—
431C2×D12—122no—
432C2×C4×D3—34no—
433C2×C4×D3—34no—
434C2×C4×D3—34no—
435C2×C4×D3—34no—
436C2×C4×D3—34no—
437C2×C4×D3—42no—
438C2×C4×D3—64no—
439C2×C4×D3—64no—
440C2×C4×D3—122no—
441C2×C4×D3—122no—
442C2×C4×D3—122no—
443C2×C4×D3—122no—
444C2×C4×D3—122no—
445C2×C4×D3—124no—
446C2×C4×D3—124no—
447C2×C4×D3C22×D314yescomplemented
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×D314yes—
459C3×C22⋊C4C22×D314yes—
460C3×C42—34no—
461#217—34no—
462#217—34no—
463#217—34no—
464#217—64no—
465#217C22×D314yes—
466#217C22×D314yes—
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—34no—
479(C2×D3)⋊C4—34no—
480(C2×D3)⋊C4—64no—
481(C2×D3)⋊C4—64no—
482(C2×D3)⋊C4C22×D314yescomplemented
483(C2×D3)⋊C4C22×D314yescomplemented
484(C2×D3)⋊C4C22×D314yescomplemented
485C4⋊Dic3—34no—
486C4⋊Dic3—34no—
487C4⋊Dic3—34no—
488C4⋊Dic3C22×D314yescomplemented
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4—34no—
494Dic3⋊C4C22×D314yescomplemented
495C4×Dic3—34no—
496C4×Dic3—34no—
497C4×Dic3C22×D314yescomplemented
498C22×C32—22no—
499C22×C32—22no—
500C22×C32—22no—
501C22×C32—44no—
502C22×C32C2×#4112yes—
503C22×C32H(5,𝔽2)12yes—
504C22×C32H(5,𝔽2)12yes—
505C22×C32C2511yescharacteristic
506C2×C3⋊D3—28no—
507C2×C3⋊D3—22no—
508C2×C3⋊D3—22no—
509C2×C3⋊D3—22no—
510C2×C3⋊D3—22no—
511C2×C3⋊D3—22no—
512C2×C3⋊D3—416no—
513C2×C3⋊D3—44no—
514C2×C3⋊D3C2×#4114yes—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—22no—
519C2×C3×D3—22no—
520C2×C3×D3—22no—
521C2×C3×D3—44no—
522C2×C3×D3—44no—
523C32×C4—22no—
524C32×C4—22no—
525C3⋊Dic3—22no—
526C3⋊Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—22no—
531C3×Dic3—22no—
532C3×Dic3—22no—
533C25—91no—
534C22×Q8—31no—
535C22×D4—31no—
536C22×D4—31no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4—91no—
540C22×D4—91no—
541C22×D4—91no—
542C23×C4—31no—
543C23×C4—91no—
544C23×C4—91no—
545C23×C4—91no—
546#126—98no—
547#126—98no—
548#124—38no—
549#124—98no—
550#123—38no—
551#123—98no—
552C22⋊Q8—98no—
553#121—98no—
554#121—98no—
555#121—98no—
556#120—98no—
557#120—98no—
558C4×D4—98no—
559C4×D4—98no—
560C2×C4⋊C4—31no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—91no—
563C2×C4⋊C4—91no—
564C2×C4⋊C4—91no—
565C2×C4⋊C4—91no—
566C2×C22⋊C4—31no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
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⋊C4—98no—
580C2×C22⋊C4D3211yescharacteristic
581C2×C42—31no—
582C2×C42—91no—
583C23×C3—24no—
584C23×C3—22no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—22no—
590C23×C3—22no—
591C23×C3—21no—
592C23×C3—32no—
593C23×C3—32no—
594C23×C3—42no—
595C23×C3—42no—
596C23×C3—62no—
597C23×C3—62no—
598C23×C3—62no—
599C23×C3—62no—
600C23×C3—62no—
601C23×C3—62no—
602C23×C3C23×D312yes—
603C23×C3C23×D312yes—
604C23×C3C23×D311yescharacteristic
605C23×C3C23×D311yescharacteristic
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—22no—
611C22×D3—22no—
612C22×D3—34no—
613C22×D3—34no—
614C22×D3—32no—
615C22×D3—32no—
616C22×D3—32no—
617C22×D3—32no—
618C22×D3—64no—
619C22×D3—62no—
620C22×D3—62no—
621C22×D3—68no—
622C22×D3—68no—
623C22×D3—64no—
624C22×D3—64no—
625C22×D3—62no—
626C22×D3—62no—
627C22×D3—62no—
628C22×D3—62no—
629C22×D3—616no—
630C22×D3—64no—
631C22×D3—62no—
632C22×D3—62no—
633C22×D3—62no—
634C22×D3—62no—
635C22×D3—62no—
636C22×D3—62no—
637C22×D3—122no—
638C22×D3—122no—
639C22×D3—124no—
640C22×D3—124no—
641C22×D3—124no—
642C22×D3—124no—
643C22×D3—128no—
644C22×D3—128no—
645C22×D3—1232no—
646C22×D3—1216no—
647C22×D3—1216no—
648C22×D3C23×D312yes—
649C22×D3C23×D312yes—
650C3×Q8—124no—
651C3×D4—124no—
652C3×D4—124no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—32no—
660C2×C3×C4—32no—
661C2×C3×C4—32no—
662C2×C3×C4—32no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—42no—
666C2×C3×C4—42no—
667C2×C3×C4—62no—
668C2×C3×C4—62no—
669C2×C3×C4—62no—
670C2×C3×C4—62no—
671C2×C3×C4—62no—
672C2×C3×C4—62no—
673C2×C3×C4—124no—
674C2×C3×C4C23×D312yes—
675C2×C3×C4C23×D312yes—
676C2×C3×C4C23×D312yes—
677C2×C3×C4C23×D312yes—
678#67—44no—
679#67—44no—
680#67—68no—
681#67—68no—
682#67—124no—
683#67—124no—
684#67—124no—
685#67—124no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—32no—
693C2×Dic3—32no—
694C2×Dic3—32no—
695C2×Dic3—32no—
696C2×Dic3—62no—
697C2×Dic3—62no—
698C2×Dic3—62no—
699C2×Dic3—62no—
700C2×Dic3—62no—
701C2×Dic3—62no—
702C2×Dic3—122no—
703C2×Dic3—122no—
704C2×Dic3—124no—
705C2×Dic3C23×D312yes—
706C2×Dic3C23×D312yes—
707C2×Dic3C23×D312yes—
708C2×Dic3C23×D312yes—
709C2×Dic3C23×D312yes—
710C2×Dic3C23×D312yes—
711D12—68no—
712D12—68no—
713D12—124no—
714D12—124no—
715C4×D3—44no—
716C4×D3—124no—
717C4×D3—124no—
718C4×D3—124no—
719C4×D3—124no—
720C4×D3—124no—
721C4×D3—128no—
722C4×D3—128no—
723Dic6—44no—
724C2×C32—42no—
725C2×C32#53814yescomplemented
726C2×C32C22×#4111yescharacteristic
727C2×C32C2×H(5,𝔽2)11yescharacteristic
728C2×C32C2×H(5,𝔽2)11yescharacteristic
729C3⋊D3—24no—
730C3⋊D3—42no—
731C3×D3—42no—
732C3×D3—42no—
733C24—31no—
734C24—31no—
735C24—91no—
736C24—91no—
737C24—94no—
738C24—184no—
739C24—362no—
740C24—362no—
741C24C2×D3211yescharacteristic
742C2×Q8—34no—
743C2×Q8—122no—
744C2×D4—34no—
745C2×D4—34no—
746C2×D4—94no—
747C2×D4—94no—
748C2×D4—94no—
749C2×D4—94no—
750C2×D4—94no—
751C2×D4—122no—
752C2×D4—122no—
753C2×D4—184no—
754C2×D4—184no—
755C2×D4—362no—
756C2×D4—362no—
757C2×D4—362no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—31no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—34no—
765C22×C4—94no—
766C22×C4—91no—
767C22×C4—91no—
768C22×C4—94no—
769C22×C4—94no—
770C22×C4—122no—
771C22×C4—362no—
772C22×C4—362no—
773C22×C4—362no—
774C22×C4C2×D3211yescharacteristic
775C22×C4C2×D3211yescharacteristic
776C4⋊C4—34no—
777C4⋊C4—34no—
778C4⋊C4—94no—
779C4⋊C4—94no—
780C4⋊C4—94no—
781C4⋊C4—94no—
782C22⋊C4—34no—
783C22⋊C4—34no—
784C22⋊C4—34no—
785C22⋊C4—34no—
786C22⋊C4—34no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C22⋊C4—94no—
790C22⋊C4—94no—
791C22⋊C4—94no—
792C22⋊C4—94no—
793C22⋊C4—94no—
794C22⋊C4—94no—
795C22⋊C4C2×D3214yes—
796C42—34no—
797C42—94no—
798C22×C3—24no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—21no—
809C22×C3—42no—
810C22×C3—42no—
811C22×C3—48no—
812C22×C3—44no—
813C22×C3—44no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—124no—
821C22×C3—124no—
822C22×C3#100412yes—
823C22×C3#100412yes—
824C22×C3D3×#4112yes—
825C22×C3D3×#4112yes—
826C22×C3#100912yes—
827C22×C3#100912yes—
828C22×C3C24×D311yescharacteristic
829C22×C3C24×D311yescharacteristic
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—34no—
837C2×D3—34no—
838C2×D3—44no—
839C2×D3—44no—
840C2×D3—64no—
841C2×D3—64no—
842C2×D3—64no—
843C2×D3—616no—
844C2×D3—68no—
845C2×D3—68no—
846C2×D3—62no—
847C2×D3—62no—
848C2×D3—62no—
849C2×D3—62no—
850C2×D3—64no—
851C2×D3—62no—
852C2×D3—62no—
853C2×D3—62no—
854C2×D3—62no—
855C2×D3—62no—
856C2×D3—62no—
857C2×D3—122no—
858C2×D3—122no—
859C2×D3—1232no—
860C2×D3—1216no—
861C2×D3—1216no—
862C2×D3—128no—
863C2×D3—124no—
864C2×D3—124no—
865C3×C4—22no—
866C3×C4—22no—
867C3×C4—22no—
868C3×C4—22no—
869C3×C4—42no—
870C3×C4—42no—
871C3×C4—62no—
872C3×C4—62no—
873C3×C4—62no—
874C3×C4—62no—
875C3×C4—62no—
876C3×C4—62no—
877Dic3—22no—
878Dic3—22no—
879Dic3—22no—
880Dic3—22no—
881Dic3—22no—
882Dic3—22no—
883Dic3—62no—
884Dic3—62no—
885Dic3—62no—
886Dic3—62no—
887Dic3—122no—
888Dic3—122no—
889C32C2×#53811yescharacteristic, complemented, Sylow
890C23—22no—
891C23—22no—
892C23—22no—
893C23—32no—
894C23—32no—
895C23—62no—
896C23—62no—
897C23—62no—
898C23—62no—
899C23—62no—
900C23—62no—
901C23—94no—
902C23—92no—
903C23—92no—
904C23—188no—
905C23—182no—
906C23—182no—
907C23—182no—
908C23—182no—
909C23—182no—
910C23—364no—
911C23—364no—
912C23—3616no—
913C23C22×D3212yes—
914C23C22×D3211yescharacteristic
915Q8—124no—
916D4—124no—
917D4—124no—
918D4—188no—
919D4—188no—
920D4—364no—
921D4—364no—
922D4—364no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—32no—
926C2×C4—32no—
927C2×C4—32no—
928C2×C4—32no—
929C2×C4—32no—
930C2×C4—32no—
931C2×C4—62no—
932C2×C4—62no—
933C2×C4—62no—
934C2×C4—62no—
935C2×C4—62no—
936C2×C4—62no—
937C2×C4—92no—
938C2×C4—92no—
939C2×C4—124no—
940C2×C4—182no—
941C2×C4—182no—
942C2×C4—364no—
943C2×C4—364no—
944C2×C4—364no—
945C2×C4C22×D3212yes—
946C2×C4C22×D3212yes—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—21no—
950C2×C3—24no—
951C2×C3—44no—
952C2×C3—42no—
953C2×C3—42no—
954C2×C3—122no—
955C2×C3—122no—
956C2×C3#565714yescomplemented
957C2×C3#567814yescomplemented
958C2×C3C2×#100411yescharacteristic
959C2×C3C2×#100411yescharacteristic
960C2×C3C2×D3×#4111yescharacteristic
961C2×C3C2×D3×#4111yescharacteristic
962C2×C3C2×#100911yescharacteristic
963C2×C3C2×#100911yescharacteristic
964D3—42no—
965D3—42no—
966D3—68no—
967D3—64no—
968D3—64no—
969D3—124no—
970D3—122no—
971D3—122no—
972C22—22no—
973C22—22no—
974C22—22no—
975C22—44no—
976C22—62no—
977C22—62no—
978C22—62no—
979C22—62no—
980C22—62no—
981C22—62no—
982C22—94no—
983C22—124no—
984C22—124no—
985C22—182no—
986C22—182no—
987C22—188no—
988C22—182no—
989C22—182no—
990C22—182no—
991C22—3616no—
992C22—364no—
993C22#6430612yes—
994C22#6431412yes—
995C22#6431412yes—
996C22C23×D3211yescharacteristic
997C4—22no—
998C4—22no—
999C4—62no—
1000C4—62no—
1001C4—62no—
1002C4—62no—
1003C4—62no—
1004C4—62no—
1005C4—182no—
1006C4—182no—
1007C3—21no—
1008C3C2×#565711yescharacteristic, complemented
1009C3C2×#567811yescharacteristic, complemented
1010C2—42no—
1011C2—122no—
1012C2—122no—
1013C2—184no—
1014C2—362no—
1015C2#1059422514yesdirect product factor
1016C2C2×#6430611yescharacteristic
1017C2C2×#6431411yescharacteristic
1018C2C2×#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×C22⋊C4×C3⋊D3C2semidirect
2. C2×C3×#885C2semidirect
3. C2×C3×#883C2semidirect
4. C2×#63981C2semidirect
5. C2×#63981C2semidirect
6. C2×#63970C2semidirect
7. C2×#63956C2semidirect
8. C2×#63912C2semidirect
9. C2×#63907C2semidirect
10. C2×#63906C2semidirect
11. C2×C4×#626C2semidirect
12. C2×#63890C2semidirect
13. C2×#63881C2semidirect
14. C2×#63871C2semidirect
15. C2×#63868C2semidirect
16. #10594225C2direct (N × H)
24. C22×C3×C4×D3C22semidirect
25. C22×C3×Dic6C22semidirect
30. C22×#625C22semidirect
31. C22×D3×Dic3C22semidirect
36. C22⋊C4×C3⋊D3C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C2×C3×(C2×D3)⋊C4C22semidirect
41. C2×C3×(C2×D3)⋊C4C22semidirect
42. C2×C3×C4⋊Dic3C22semidirect
43. C2×C3×Dic3⋊C4C22semidirect
44. C2×C3×C4×Dic3C22semidirect
45. C3×#885C22semidirect
46. C3×#883C22semidirect
47. #63981C22semidirect
48. #63981C22semidirect
49. #63970C22semidirect
50. C2×#3724C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
53. C2×Dic3⋊Dic3C22semidirect
58. C2×(C2×D3)⋊Dic3C22semidirect
59. #63956C22semidirect
60. C2×Dic32C22semidirect
61. #63912C22semidirect
62. #63907C22semidirect
63. #63906C22semidirect
64. C4×#626C22semidirect
65. #63890C22semidirect
66. #63881C22semidirect
67. #63871C22semidirect
68. #63868C22semidirect
87. C2×#885D3semidirect
91. C2×#883D3semidirect
130. C2×C3×C4×D3C23semidirect
132. C2×C3×Dic6C23semidirect
142. C2×#625C23semidirect
144. C2×D3×Dic3C23semidirect
151. C3×(C2×D3)⋊C4C23semidirect
152. C3×(C2×D3)⋊C4C23semidirect
153. C3×(C2×D3)⋊C4C23semidirect
154. C3×C4⋊Dic3C23semidirect
155. C3×Dic3⋊C4C23semidirect
156. C3×C4×Dic3C23semidirect
157. #3724C23semidirect
158. Dic3⋊Dic3C23semidirect
159. Dic3⋊Dic3C23semidirect
160. Dic3⋊Dic3C23semidirect
165. (C2×D3)⋊Dic3C23semidirect
166. Dic32C23semidirect
195. C22×C4×D3C2×D3semidirect
196. C22×Dic6C2×D3semidirect
239. C2×(C2×D3)⋊C4C2×D3semidirect
240. C2×(C2×D3)⋊C4C2×D3semidirect
241. C2×(C2×D3)⋊C4C2×D3semidirect
245. C2×C4⋊Dic3C2×D3semidirect
251. C2×Dic3⋊C4C2×D3semidirect
254. C2×C4×Dic3C2×D3semidirect
261. #885C2×D3semidirect
265. #883C2×D3semidirect
447. C2×C4×D3C22×D3semidirect
449. C2×Dic6C22×D3semidirect
482. (C2×D3)⋊C4C22×D3semidirect
483. (C2×D3)⋊C4C22×D3semidirect
484. (C2×D3)⋊C4C22×D3semidirect
488. C4⋊Dic3C22×D3semidirect
494. Dic3⋊C4C22×D3semidirect
497. C4×Dic3C22×D3semidirect
725. C2×C32#538semidirect
889. C32C2×#538semidirect
956. C2×C3#5657semidirect
957. C2×C3#5678semidirect
1008. C3C2×#5657semidirect
1009. C3C2×#5678semidirect
1015. C2#10594225direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C3⋊D32
C2×C3×#8852
C2×C3×#8832
C2×#639812
C2×#639702
C2×#639562
C2×#639122
C2×#639072
C2×#639062
C2×C4×#6262
C2×#638902
C2×#638812
C2×#638712
C2×#638682
#105942252
C2×#56783
C2×#56573