Finite Group Databasebeta

← C2×#10594226 #11901313

Subgroups — C2×#10594226 #11901313

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×#884C211yesmaximal, characteristic, complemented
3C2×C3×#879C211yesmaximal, characteristic, complemented
4C2×#63981C211yesmaximal, characteristic, complemented
5C2×#63981C211yesmaximal, characteristic, complemented
6C2×#63969C211yesmaximal, characteristic, complemented
7C2×#63959C211yesmaximal, characteristic, complemented
8C2×#63916C211yesmaximal, characteristic, complemented
9C2×C4×#626C211yesmaximal, characteristic, complemented
10C2×#63886C211yesmaximal, characteristic, complemented
11C2×#63881C211yesmaximal, characteristic, complemented
12C2×#63865C211yesmaximal, characteristic, complemented
13C2×#63852C211yesmaximal, characteristic, complemented
14C2×#63850C211yesmaximal, characteristic, complemented
15C2×#63848C211yesmaximal, characteristic, complemented
16#10594226C2116yesmaximal, direct product factor
17C2×#5704—31nomaximal
18C2×#5613—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×D12C2211yescharacteristic, complemented
25C22×C3×C4×D3C2211yescharacteristic, complemented
26C22×#627C2211yescharacteristic, complemented
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic, complemented
41C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
42C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
43C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
44C2×C3×C4×Dic3C2211yescharacteristic, complemented
45C3×#884C2218yescomplemented
46C3×#879C2218yescomplemented
47#63981C2218yescomplemented
48#63981C2218yescomplemented
49#63969C2218yescomplemented
50C2×#3724C2211yescharacteristic, complemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
59#63959C2218yescomplemented
60C2×Dic32C2211yescharacteristic, complemented
61#63916C2218yescomplemented
62C4×#626C2218yescomplemented
63#63886C2218yescomplemented
64#63881C2218yescomplemented
65#63865C2218yescomplemented
66#63852C2218yescomplemented
67#63850C2218yescomplemented
68#63848C2218yescomplemented
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×#898—31no—
83C2×#896—31no—
84C2×#896—31no—
85C2×#895—31no—
86C2×#895—31no—
87C2×#894—31no—
88C2×#893—31no—
89C2×#885—31no—
90C2×#885—31no—
91C2×#884D311yescharacteristic, complemented
92C2×#883—31no—
93C2×#882—31no—
94C2×#882—31no—
95C2×#67⋊C4—31no—
96C2×D3×C22⋊C4—31no—
97C2×D3×C22⋊C4—31no—
98C2×D3×C22⋊C4—61no—
99C2×#879D311yescharacteristic, complemented
100C2×#875—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×D12—42no—
130C2×C3×D12C2314yescomplemented
131C2×C3×C4×D3—42no—
132C2×C3×C4×D3C2314yescomplemented
133C2×#627—42no—
134C2×#627C2314yescomplemented
135C2×#626—24no—
136C2×#626—24no—
137C2×#626—42no—
138C2×#626—42no—
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#626C2314yes—
142C2×#626C2314yes—
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×C4⋊Dic3C2314yescomplemented
153C3×Dic3⋊C4C2314yescomplemented
154C3×Dic3⋊C4C2314yescomplemented
155C3×Dic3⋊C4C2314yescomplemented
156C3×C4×Dic3C2314yescomplemented
157#3724C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159#3722C2314yes—
160#3722C2314yes—
161#3722C2314yes—
162#3722C2314yes—
163(C2×D3)⋊Dic3C2314yescomplemented
164(C2×D3)⋊Dic3C2314yescomplemented
165(C2×D3)⋊Dic3C2314yescomplemented
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C24×D3—61no—
171C22×C3×D4—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×#67C2×D311yescharacteristic
180C22×#67C2×D311yescharacteristic
181C23×Dic3—31no—
182C22×D12—31no—
183C22×D12—31no—
184C22×D12—31no—
185C22×D12—31no—
186C22×D12C2×D311yescharacteristic, complemented
187C22×C4×D3—31no—
188C22×C4×D3—31no—
189C22×C4×D3—31no—
190C22×C4×D3—31no—
191C22×C4×D3—31no—
192C22×C4×D3—61no—
193C22×C4×D3—61no—
194C22×C4×D3C2×D311yescharacteristic, complemented
195C22×Dic6—31no—
196C22×Dic6—31no—
197C3×#126—38no—
198C3×#121—38no—
199C2×C3×C4⋊C4—31no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C4⋊C4—31no—
202C2×C3×C4⋊C4—31no—
203C2×C3×C22⋊C4—21no—
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—31no—
214C2×#217—31no—
215C2×#217—61no—
216C2×#217C2×D311yescharacteristic
217C2×#217C2×D311yescharacteristic
218#939—38no—
219#938—38no—
220#937—38no—
221#937—38no—
222#936—38no—
223#935—38no—
224#929—38no—
225C4×#67—38no—
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—31no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—31no—
240C2×(C2×D3)⋊C4—31no—
241C2×(C2×D3)⋊C4—61no—
242C2×(C2×D3)⋊C4—61no—
243C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
244C2×C4⋊Dic3—31no—
245C2×C4⋊Dic3C2×D311yescharacteristic, complemented
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4—31no—
248C2×Dic3⋊C4—31no—
249C2×Dic3⋊C4C2×D311yescharacteristic, complemented
250C2×Dic3⋊C4C2×D311yescharacteristic, complemented
251C2×Dic3⋊C4C2×D311yescharacteristic, complemented
252C2×C4×Dic3—31no—
253C2×C4×Dic3—31no—
254C2×C4×Dic3C2×D311yescharacteristic, complemented
255#898—38no—
256#898—38no—
257#896—38no—
258#896—38no—
259#895—38no—
260#895—38no—
261#894—38no—
262#893—38no—
263#885—38no—
264#885—38no—
265#884C2×D318yescomplemented
266#883—38no—
267#882—38no—
268#882—38no—
269#67⋊C4—38no—
270D3×C22⋊C4—38no—
271D3×C22⋊C4—38no—
272D3×C22⋊C4—68no—
273#879C2×D318yescomplemented
274#875—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×D12—44no—
326C3×C4×D3—44no—
327#627—44no—
328#626—28no—
329#626—28no—
330#626—44no—
331#626—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—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×D4—34no—
375C2×C3×D4—34no—
376C2×C3×D4—34no—
377C2×C3×D4—122no—
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—42no—
399C2×#67—42no—
400C2×#67—64no—
401C2×#67—64no—
402C2×#67—122no—
403C2×#67—122no—
404C2×#67C22×D314yes—
405C2×#67C22×D314yes—
406C22×Dic3—31no—
407C22×Dic3—31no—
408C22×Dic3—31no—
409C22×Dic3—31no—
410C22×Dic3—34no—
411C22×Dic3—61no—
412C22×Dic3—61no—
413C22×Dic3—122no—
414C22×Dic3C22×D311yescharacteristic
415C22×Dic3C22×D311yescharacteristic
416C22×Dic3C22×D311yescharacteristic
417C22×Dic3C22×D311yescharacteristic
418C22×Dic3C22×D311yescharacteristic
419C22×Dic3C22×D311yescharacteristic
420C2×D12—34no—
421C2×D12—34no—
422C2×D12—34no—
423C2×D12—34no—
424C2×D12—42no—
425C2×D12—64no—
426C2×D12—64no—
427C2×D12—122no—
428C2×D12—122no—
429C2×D12C22×D314yescomplemented
430C2×C4×D3—34no—
431C2×C4×D3—34no—
432C2×C4×D3—34no—
433C2×C4×D3—34no—
434C2×C4×D3—34no—
435C2×C4×D3—42no—
436C2×C4×D3—64no—
437C2×C4×D3—64no—
438C2×C4×D3—122no—
439C2×C4×D3—122no—
440C2×C4×D3—122no—
441C2×C4×D3—122no—
442C2×C4×D3—122no—
443C2×C4×D3—124no—
444C2×C4×D3—124no—
445C2×C4×D3C22×D314yescomplemented
446C2×Dic6—34no—
447C2×Dic6—34no—
448C2×Dic6—122no—
449C2×Dic6—122no—
450C3×C4⋊C4—34no—
451C3×C4⋊C4—34no—
452C3×C4⋊C4—34no—
453C3×C4⋊C4—34no—
454C3×C22⋊C4—24no—
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—34no—
465#217—34no—
466#217—64no—
467#217C22×D314yes—
468#217C22×D314yes—
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—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—64no—
485(C2×D3)⋊C4—64no—
486(C2×D3)⋊C4C22×D314yescomplemented
487C4⋊Dic3—34no—
488C4⋊Dic3C22×D314yescomplemented
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4C22×D314yescomplemented
493Dic3⋊C4C22×D314yescomplemented
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—91no—
535C22×D4—31no—
536C22×D4—31no—
537C22×D4—31no—
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—38no—
547#126—98no—
548#124—98no—
549#124—98no—
550#123—98no—
551#123—98no—
552C22⋊Q8—98no—
553#121—38no—
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—31no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—91no—
565C2×C4⋊C4—91no—
566C2×C22⋊C4—31no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
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×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×D4—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—
684C2×Dic3—22no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—32no—
691C2×Dic3—32no—
692C2×Dic3—32no—
693C2×Dic3—32no—
694C2×Dic3—62no—
695C2×Dic3—62no—
696C2×Dic3—62no—
697C2×Dic3—62no—
698C2×Dic3—62no—
699C2×Dic3—62no—
700C2×Dic3—122no—
701C2×Dic3—122no—
702C2×Dic3—124no—
703C2×Dic3C23×D312yes—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D312yes—
706C2×Dic3C23×D312yes—
707C2×Dic3C23×D312yes—
708C2×Dic3C23×D312yes—
709D12—44no—
710D12—68no—
711D12—68no—
712D12—124no—
713D12—124no—
714C4×D3—44no—
715C4×D3—124no—
716C4×D3—124no—
717C4×D3—124no—
718C4×D3—124no—
719C4×D3—124no—
720C4×D3—128no—
721C4×D3—128no—
722Dic6—124no—
723Dic6—124no—
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—94no—
743C2×Q8—362no—
744C2×D4—34no—
745C2×D4—34no—
746C2×D4—34no—
747C2×D4—94no—
748C2×D4—94no—
749C2×D4—94no—
750C2×D4—94no—
751C2×D4—122no—
752C2×D4—122no—
753C2×D4—122no—
754C2×D4—184no—
755C2×D4—184no—
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—34no—
779C4⋊C4—34no—
780C4⋊C4—94no—
781C4⋊C4—94no—
782C22⋊C4—34no—
783C22⋊C4—34no—
784C22⋊C4—34no—
785C22⋊C4—94no—
786C22⋊C4—94no—
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—62no—
845C2×D3—62no—
846C2×D3—68no—
847C2×D3—62no—
848C2×D3—62no—
849C2×D3—68no—
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—364no—
916D4—124no—
917D4—124no—
918D4—124no—
919D4—188no—
920D4—188no—
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#561314yescomplemented
957C2×C3#570414yescomplemented
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×#561311yescharacteristic, complemented
1009C3C2×#570411yescharacteristic, complemented
1010C2—42no—
1011C2—122no—
1012C2—122no—
1013C2—184no—
1014C2—362no—
1015C2#1059422614yesdirect 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×#884C2semidirect
3. C2×C3×#879C2semidirect
4. C2×#63981C2semidirect
5. C2×#63981C2semidirect
6. C2×#63969C2semidirect
7. C2×#63959C2semidirect
8. C2×#63916C2semidirect
9. C2×C4×#626C2semidirect
10. C2×#63886C2semidirect
11. C2×#63881C2semidirect
12. C2×#63865C2semidirect
13. C2×#63852C2semidirect
14. C2×#63850C2semidirect
15. C2×#63848C2semidirect
16. #10594226C2direct (N × H)
24. C22×C3×D12C22semidirect
25. C22×C3×C4×D3C22semidirect
26. C22×#627C22semidirect
31. C22×D3×Dic3C22semidirect
36. C22⋊C4×C3⋊D3C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C2×C3×C4⋊Dic3C22semidirect
41. C2×C3×Dic3⋊C4C22semidirect
42. C2×C3×Dic3⋊C4C22semidirect
43. C2×C3×Dic3⋊C4C22semidirect
44. C2×C3×C4×Dic3C22semidirect
45. C3×#884C22semidirect
46. C3×#879C22semidirect
47. #63981C22semidirect
48. #63981C22semidirect
49. #63969C22semidirect
50. C2×#3724C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
56. C2×(C2×D3)⋊Dic3C22semidirect
57. C2×(C2×D3)⋊Dic3C22semidirect
58. C2×(C2×D3)⋊Dic3C22semidirect
59. #63959C22semidirect
60. C2×Dic32C22semidirect
61. #63916C22semidirect
62. C4×#626C22semidirect
63. #63886C22semidirect
64. #63881C22semidirect
65. #63865C22semidirect
66. #63852C22semidirect
67. #63850C22semidirect
68. #63848C22semidirect
91. C2×#884D3semidirect
99. C2×#879D3semidirect
130. C2×C3×D12C23semidirect
132. C2×C3×C4×D3C23semidirect
134. C2×#627C23semidirect
144. C2×D3×Dic3C23semidirect
151. C3×(C2×D3)⋊C4C23semidirect
152. C3×C4⋊Dic3C23semidirect
153. C3×Dic3⋊C4C23semidirect
154. C3×Dic3⋊C4C23semidirect
155. C3×Dic3⋊C4C23semidirect
156. C3×C4×Dic3C23semidirect
157. #3724C23semidirect
158. Dic3⋊Dic3C23semidirect
163. (C2×D3)⋊Dic3C23semidirect
164. (C2×D3)⋊Dic3C23semidirect
165. (C2×D3)⋊Dic3C23semidirect
166. Dic32C23semidirect
186. C22×D12C2×D3semidirect
194. C22×C4×D3C2×D3semidirect
243. C2×(C2×D3)⋊C4C2×D3semidirect
245. C2×C4⋊Dic3C2×D3semidirect
249. C2×Dic3⋊C4C2×D3semidirect
250. C2×Dic3⋊C4C2×D3semidirect
251. C2×Dic3⋊C4C2×D3semidirect
254. C2×C4×Dic3C2×D3semidirect
265. #884C2×D3semidirect
273. #879C2×D3semidirect
429. C2×D12C22×D3semidirect
445. C2×C4×D3C22×D3semidirect
486. (C2×D3)⋊C4C22×D3semidirect
488. C4⋊Dic3C22×D3semidirect
492. Dic3⋊C4C22×D3semidirect
493. Dic3⋊C4C22×D3semidirect
494. Dic3⋊C4C22×D3semidirect
497. C4×Dic3C22×D3semidirect
725. C2×C32#538semidirect
889. C32C2×#538semidirect
956. C2×C3#5613semidirect
957. C2×C3#5704semidirect
1008. C3C2×#5613semidirect
1009. C3C2×#5704semidirect
1015. C2#10594226direct (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×#8842
C2×C3×#8792
C2×#639812
C2×#639692
C2×#639592
C2×#639162
C2×C4×#6262
C2×#638862
C2×#638812
C2×#638652
C2×#638522
C2×#638502
C2×#638482
#105942262
C2×#57043
C2×#56133