Finite Group Databasebeta

← C2×#10594471 #11903031

Subgroups — C2×#10594471 #11903031

Order 1152.

2457 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#898C211yesmaximal, characteristic, complemented
3C2×C3×#889C211yesmaximal, characteristic, complemented
4C2×#63899C211yesmaximal, characteristic, complemented
5C2×#63881C211yesmaximal, characteristic
6C2×#63877C211yesmaximal, characteristic, complemented
7C2×#63874C211yesmaximal, characteristic, complemented
8C2×#63865C211yesmaximal, characteristic, complemented
9C2×#63861C211yesmaximal, characteristic, complemented
10C2×#63853C211yesmaximal, characteristic
11C2×#63853C211yesmaximal, characteristic
12C2×#63849C211yesmaximal, characteristic, complemented
13C2×#63847C211yesmaximal, characteristic, complemented
14C2×#63845C211yesmaximal, characteristic, complemented
15C2×#63837C211yesmaximal, characteristic, complemented
16#10594471C2116yesmaximal, direct product factor
17C2×#5708—31nomaximal
18C2×#5693—31nomaximal
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×#627C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C4⋊C4×C3⋊D3C2218yescomplemented
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C3×#898C2218yescomplemented
43C3×#889C2218yescomplemented
44C2×#3724C2211yescharacteristic
45C2×#3724C2211yescharacteristic
46C2×#3724C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×#3722C2211yescharacteristic
50C2×#3722C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×Dic32C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63899C2218yescomplemented
58#63881C2218yes—
59#63877C2218yescomplemented
60#63874C2218yescomplemented
61#63865C2218yescomplemented
62#63861C2218yescomplemented
63#63853C2218yes—
64#63853C2218yes—
65#63849C2218yescomplemented
66#63847C2218yescomplemented
67#63845C2218yescomplemented
68#63837C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×#125—31no—
71#5708—316no—
72#5693—316no—
73C2×#898—31no—
74C2×#898D311yescharacteristic, complemented
75C2×#896—31no—
76C2×#896—31no—
77C2×#896—31no—
78C2×#894—31no—
79C2×#894—31no—
80C2×#893—31no—
81C2×#892—31no—
82C2×#892—31no—
83C2×D3×C4⋊C4—31no—
84C2×D3×C4⋊C4—31no—
85C2×D3×C4⋊C4—61no—
86C2×#890—31no—
87C2×#889—31no—
88C2×#889—31no—
89C2×#889—31no—
90C2×#889D311yescharacteristic, complemented
91C2×#887—31no—
92C2×#883—31no—
93C2×#883—31no—
94C2×#67⋊C4—31no—
95C2×#879—31no—
96C2×#878—31no—
97C2×#877—31no—
98C2×#872—31no—
99C2×#872—31no—
100C2×#872—31no—
101C2×C4×Dic6—31no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C2×C4×C3⋊D3—24no—
111C2×C4×C3⋊D3—24no—
112C2×C4×C3⋊D3—24no—
113C2×C4×C3⋊D3C2314yes—
114C2×C4×C3⋊D3C2314yes—
115C2×C4×C3⋊D3C2314yes—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C2×#627—24no—
124C2×#627C2314yes—
125C2×#626—24no—
126C2×#626C2314yes—
127C2×D3×Dic3—24no—
128C2×D3×Dic3C2314yes—
129C32×C4⋊C4C2314yes—
130C4⋊(C3⋊Dic3)C2314yes—
131#3750C2314yes—
132#3750C2314yes—
133C3×(C2×D3)⋊C4C2314yes—
134C3×(C2×D3)⋊C4C2314yes—
135C3×(C2×D3)⋊C4C2314yes—
136C3×C4⋊Dic3C2314yes—
137C3×C4⋊Dic3C2314yes—
138C3×Dic3⋊C4C2314yes—
139C3×Dic3⋊C4C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×Dic3⋊C4C2314yes—
142C3×Dic3⋊C4C2314yes—
143C3×C4×Dic3C2314yes—
144C3×C4×Dic3C2314yes—
145#3724C2314yes—
146#3724C2314yes—
147#3724C2314yes—
148Dic3⋊Dic3C2314yes—
149Dic3⋊Dic3C2314yes—
150#3722C2314yes—
151#3722C2314yes—
152#3722C2314yes—
153(C2×D3)⋊Dic3C2314yes—
154(C2×D3)⋊Dic3C2314yes—
155Dic32C2314yes—
156Dic32C2314yes—
157Dic32C2314yes—
158C2×#552—91noSylow
159C22×#67—31no—
160C23×Dic3—31no—
161C22×D12—31no—
162C22×C4×D3—31no—
163C22×C4×D3—31no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C22×C4×D3—31no—
167C22×C4×D3—31no—
168C22×C4×D3—31no—
169C22×C4×D3—61no—
170C22×C4×D3—61no—
171C22×C4×D3—61no—
172C22×Dic6—31no—
173C22×Dic6—31no—
174C3×#126—38no—
175C3×#125—38no—
176C2×C3×C4⋊C4—21no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C4⋊C4—31no—
182C2×C3×C4⋊C4—31no—
183C2×C3×C4⋊C4—31no—
184C2×C3×C4⋊C4C2×D311yescharacteristic
185C2×C3×C4⋊C4C2×D311yescharacteristic
186C2×C3×C22⋊C4—31no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C42—31no—
190C2×C3×C42—31no—
191C2×#217—31no—
192C2×#217—31no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—31no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4C2×D311yescharacteristic
202C2×(C2×D3)⋊C4C2×D311yescharacteristic
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×C4⋊Dic3—31no—
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—61no—
209C2×C4⋊Dic3C2×D311yescharacteristic
210C2×C4⋊Dic3C2×D311yescharacteristic
211C2×Dic3⋊C4—31no—
212C2×Dic3⋊C4—31no—
213C2×Dic3⋊C4—31no—
214C2×Dic3⋊C4—31no—
215C2×Dic3⋊C4—31no—
216C2×Dic3⋊C4—31no—
217C2×Dic3⋊C4—31no—
218C2×Dic3⋊C4—31no—
219C2×Dic3⋊C4—31no—
220C2×Dic3⋊C4—31no—
221C2×Dic3⋊C4—31no—
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—61no—
224C2×Dic3⋊C4—61no—
225C2×Dic3⋊C4C2×D311yescharacteristic
226C2×Dic3⋊C4C2×D311yescharacteristic
227C2×Dic3⋊C4C2×D311yescharacteristic
228C2×Dic3⋊C4C2×D311yescharacteristic
229C2×Dic3⋊C4C2×D311yescharacteristic
230C2×C4×Dic3—31no—
231C2×C4×Dic3—31no—
232C2×C4×Dic3—31no—
233C2×C4×Dic3—31no—
234C2×C4×Dic3—31no—
235C2×C4×Dic3—31no—
236C2×C4×Dic3C2×D311yescharacteristic
237C2×C4×Dic3C2×D311yescharacteristic
238#898—38no—
239#898C2×D318yescomplemented
240#896—38no—
241#896—38no—
242#896—38no—
243#894—38no—
244#894—38no—
245#893—38no—
246#892—38no—
247#892—38no—
248D3×C4⋊C4—38no—
249D3×C4⋊C4—38no—
250D3×C4⋊C4—68no—
251#890—38no—
252#889—38no—
253#889—38no—
254#889—38no—
255#889C2×D318yescomplemented
256#887—38no—
257#883—38no—
258#883—38no—
259#67⋊C4—38no—
260#879—38no—
261#878—38no—
262#877—38no—
263#872—38no—
264#872—38no—
265#872—38no—
266C4×Dic6—38no—
267C23×C32C2411yescharacteristic
268C22×C3⋊D3—22no—
269C22×C3⋊D3—22no—
270C22×C3⋊D3#4114yes—
271C22×C3⋊D3C2412yes—
272C22×C3×D3—22no—
273C22×C3×D3—22no—
274C22×C3×D3—22no—
275C22×C3×D3C2412yes—
276C2×C32×C4—22no—
277C2×C32×C4—22no—
278C2×C32×C4—22no—
279C2×C32×C4C2412yes—
280C2×C32×C4C2412yes—
281C2×C32×C4C2412yes—
282C2×C3⋊Dic3—22no—
283C2×C3⋊Dic3—22no—
284C2×C3⋊Dic3#4114yes—
285C2×C3⋊Dic3C2412yes—
286C2×C3⋊Dic3C2412yes—
287C2×C3⋊Dic3C2412yes—
288C4×C3⋊D3—28no—
289C4×C3⋊D3—28no—
290C4×C3⋊D3—28no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—22no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2412yes—
305#627—28no—
306#626—28no—
307D3×Dic3—28no—
308#552—916no—
309C2×#126—31no—
310C2×#126—91no—
311C2×#125—31no—
312C2×#125—91no—
313C2×#125—91no—
314C2×#123—91no—
315C2×#123—91no—
316C2×C22⋊Q8—91no—
317C2×C22⋊Q8—91no—
318C2×C4×Q8—91no—
319C2×C4×D4—91no—
320C2×#117—91no—
321C2×#117—91no—
322C2×#117—91no—
323C22×C4⋊C4—91no—
324C24×C3—31no—
325C23×D3—31no—
326C23×D3—31no—
327C23×D3—61no—
328C23×D3C22×D311yescharacteristic
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C2×#67—34no—
346C2×#67—64no—
347C22×Dic3—31no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—34no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—64no—
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C2×D12—34no—
366C2×D12—64no—
367C2×C4×D3—34no—
368C2×C4×D3—34no—
369C2×C4×D3—34no—
370C2×C4×D3—34no—
371C2×C4×D3—34no—
372C2×C4×D3—34no—
373C2×C4×D3—34no—
374C2×C4×D3—64no—
375C2×C4×D3—64no—
376C2×C4×D3—64no—
377C2×C4×D3—64no—
378C2×C4×D3—64no—
379C2×C4×D3—64no—
380C2×C4×D3—64no—
381C2×C4×D3—64no—
382C2×C4×D3—64no—
383C2×C4×D3—64no—
384C2×C4×D3—68no—
385C2×C4×D3—124no—
386C2×C4×D3—124no—
387C2×Dic6—34no—
388C2×Dic6—34no—
389C2×Dic6—64no—
390C2×Dic6—64no—
391C3×C4⋊C4—24no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—34no—
395C3×C4⋊C4—34no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4—34no—
398C3×C4⋊C4—34no—
399C3×C4⋊C4C22×D314yes—
400C3×C4⋊C4C22×D314yes—
401C3×C22⋊C4—34no—
402C3×C22⋊C4—34no—
403C3×C22⋊C4—34no—
404C3×C42—34no—
405C3×C42—34no—
406#217—34no—
407#217—34no—
408(C2×D3)⋊C4—34no—
409(C2×D3)⋊C4—34no—
410(C2×D3)⋊C4—34no—
411(C2×D3)⋊C4—34no—
412(C2×D3)⋊C4—34no—
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4—34no—
415(C2×D3)⋊C4—34no—
416(C2×D3)⋊C4C22×D314yes—
417(C2×D3)⋊C4C22×D314yes—
418(C2×D3)⋊C4C22×D314yes—
419C4⋊Dic3—34no—
420C4⋊Dic3—34no—
421C4⋊Dic3—34no—
422C4⋊Dic3—34no—
423C4⋊Dic3—64no—
424C4⋊Dic3C22×D314yes—
425C4⋊Dic3C22×D314yes—
426Dic3⋊C4—34no—
427Dic3⋊C4—34no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4—34no—
432Dic3⋊C4—34no—
433Dic3⋊C4—34no—
434Dic3⋊C4—34no—
435Dic3⋊C4—34no—
436Dic3⋊C4—34no—
437Dic3⋊C4—34no—
438Dic3⋊C4—64no—
439Dic3⋊C4—64no—
440Dic3⋊C4C22×D314yes—
441Dic3⋊C4C22×D314yes—
442Dic3⋊C4C22×D314yes—
443Dic3⋊C4C22×D314yes—
444Dic3⋊C4C22×D314yes—
445C4×Dic3—34no—
446C4×Dic3—34no—
447C4×Dic3—34no—
448C4×Dic3—34no—
449C4×Dic3—34no—
450C4×Dic3—34no—
451C4×Dic3C22×D314yes—
452C4×Dic3C22×D314yes—
453C22×C32C2×#4112yes—
454C22×C32C2×#4112yes—
455C22×C322−1+412yes—
456C22×C32C2511yescharacteristic
457C2×C3⋊D3—28no—
458C2×C3⋊D3—22no—
459C2×C3⋊D3—22no—
460C2×C3⋊D3C2×#4114yes—
461C2×C3×D3—22no—
462C2×C3×D3—22no—
463C2×C3×D3—22no—
464C2×C3×D3—44no—
465C32×C4—22no—
466C32×C4—22no—
467C32×C4—22no—
468C3⋊Dic3—22no—
469C3⋊Dic3—22no—
470C3⋊Dic3C2×#4114yes—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3—22no—
475C3×Dic3—22no—
476C3×Dic3—22no—
477C3×Dic3—22no—
478C22×Q8—91no—
479C22×D4—91no—
480C23×C4—91no—
481C23×C4—91no—
482C23×C4—91no—
483C23×C4—91no—
484#126—38no—
485#126—98no—
486#125—38no—
487#125—98no—
488#125—98no—
489#123—98no—
490#123—98no—
491C22⋊Q8—98no—
492C22⋊Q8—98no—
493C4×Q8—98no—
494C4×D4—98no—
495#117—98no—
496#117—98no—
497#117—98no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—31no—
503C2×C4⋊C4—31no—
504C2×C4⋊C4—31no—
505C2×C4⋊C4—91no—
506C2×C4⋊C4—91no—
507C2×C4⋊C4—91no—
508C2×C4⋊C4—91no—
509C2×C4⋊C4—91no—
510C2×C4⋊C4—91no—
511C2×C4⋊C4—91no—
512C2×C4⋊C4—91no—
513C2×C4⋊C4—98no—
514C2×C4⋊C4D3211yescharacteristic
515C2×C22⋊C4—31no—
516C2×C22⋊C4—31no—
517C2×C22⋊C4—31no—
518C2×C22⋊C4—91no—
519C2×C22⋊C4—91no—
520C2×C22⋊C4—91no—
521C2×C22⋊C4—91no—
522C2×C22⋊C4—91no—
523C2×C42—31no—
524C2×C42—31no—
525C2×C42—91no—
526C2×C42—91no—
527C2×C42—91no—
528C23×C3—21no—
529C23×C3—32no—
530C23×C3—62no—
531C23×C3—62no—
532C23×C3—62no—
533C23×C3C23×D311yescharacteristic
534C23×C3C23×D311yescharacteristic
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—22no—
538C22×D3—34no—
539C22×D3—34no—
540C22×D3—32no—
541C22×D3—32no—
542C22×D3—64no—
543C22×D3—62no—
544C22×D3—64no—
545C22×D3—64no—
546C22×D3—62no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—62no—
550C22×D3C23×D312yes—
551C2×C3×C4—24no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—32no—
564C2×C3×C4—32no—
565C2×C3×C4—32no—
566C2×C3×C4—32no—
567C2×C3×C4—32no—
568C2×C3×C4—42no—
569C2×C3×C4—42no—
570C2×C3×C4—62no—
571C2×C3×C4—62no—
572C2×C3×C4—62no—
573C2×C3×C4—62no—
574C2×C3×C4—62no—
575C2×C3×C4—62no—
576C2×C3×C4—62no—
577C2×C3×C4C23×D312yes—
578C2×C3×C4C23×D312yes—
579C2×C3×C4C23×D312yes—
580C2×C3×C4C23×D312yes—
581C2×C3×C4C23×D312yes—
582C2×C3×C4C23×D312yes—
583#67—68no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—34no—
592C2×Dic3—34no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—32no—
596C2×Dic3—32no—
597C2×Dic3—32no—
598C2×Dic3—32no—
599C2×Dic3—64no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—62no—
603C2×Dic3—68no—
604C2×Dic3—62no—
605C2×Dic3—62no—
606C2×Dic3—62no—
607C2×Dic3—62no—
608C2×Dic3—122no—
609C2×Dic3—122no—
610C2×Dic3C23×D312yes—
611C2×Dic3C23×D312yes—
612C2×Dic3C23×D312yes—
613C2×Dic3C23×D312yes—
614C2×Dic3C23×D312yes—
615C2×Dic3C23×D312yes—
616C2×Dic3C23×D312yes—
617D12—68no—
618C4×D3—68no—
619C4×D3—68no—
620C4×D3—68no—
621C4×D3—68no—
622C4×D3—68no—
623C4×D3—68no—
624C4×D3—68no—
625C4×D3—616no—
626C4×D3—128no—
627C4×D3—128no—
628Dic6—68no—
629Dic6—68no—
630C2×C32#55214yescomplemented
631C2×C32C22×#4111yescharacteristic
632C2×C32C22×#4111yescharacteristic
633C2×C32C2×2−1+411yescharacteristic
634C3⋊D3—24no—
635C3×D3—42no—
636C24—31no—
637C24—91no—
638C2×Q8—94no—
639C2×Q8—184no—
640C2×D4—94no—
641C2×D4—184no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—94no—
650C22×C4—91no—
651C22×C4—91no—
652C22×C4—91no—
653C22×C4—94no—
654C22×C4—94no—
655C22×C4—94no—
656C22×C4—184no—
657C22×C4—184no—
658C22×C4—184no—
659C22×C4—184no—
660C22×C4C2×D3211yescharacteristic
661C22×C4C2×D3211yescharacteristic
662C22×C4C2×D3211yescharacteristic
663C4⋊C4—34no—
664C4⋊C4—34no—
665C4⋊C4—34no—
666C4⋊C4—34no—
667C4⋊C4—34no—
668C4⋊C4—34no—
669C4⋊C4—34no—
670C4⋊C4—94no—
671C4⋊C4—94no—
672C4⋊C4—94no—
673C4⋊C4—94no—
674C4⋊C4—94no—
675C4⋊C4—94no—
676C4⋊C4—94no—
677C4⋊C4—94no—
678C4⋊C4C2×D3214yes—
679C22⋊C4—34no—
680C22⋊C4—34no—
681C22⋊C4—34no—
682C22⋊C4—94no—
683C22⋊C4—94no—
684C22⋊C4—94no—
685C22⋊C4—94no—
686C22⋊C4—94no—
687C42—34no—
688C42—34no—
689C42—94no—
690C42—94no—
691C42—94no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—21no—
696C22×C3—62no—
697C22×C3—62no—
698C22×C3—62no—
699C22×C3—124no—
700C22×C3#100712yes—
701C22×C3D3×#4112yes—
702C22×C3D3×#4112yes—
703C22×C3D3×#4112yes—
704C22×C3D3×#4112yes—
705C22×C3#101012yes—
706C22×C3C24×D311yescharacteristic
707C22×C3C24×D311yescharacteristic
708C2×D3—22no—
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—34no—
712C2×D3—34no—
713C2×D3—44no—
714C2×D3—64no—
715C2×D3—64no—
716C2×D3—64no—
717C2×D3—616no—
718C2×D3—68no—
719C2×D3—62no—
720C2×D3—62no—
721C2×D3—62no—
722C2×D3—62no—
723C2×D3—68no—
724C3×C4—24no—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—22no—
730C3×C4—22no—
731C3×C4—42no—
732C3×C4—42no—
733C3×C4—62no—
734C3×C4—62no—
735C3×C4—62no—
736C3×C4—62no—
737C3×C4—62no—
738C3×C4—62no—
739C3×C4—62no—
740Dic3—22no—
741Dic3—22no—
742Dic3—22no—
743Dic3—22no—
744Dic3—22no—
745Dic3—22no—
746Dic3—22no—
747Dic3—34no—
748Dic3—34no—
749Dic3—64no—
750Dic3—62no—
751Dic3—62no—
752Dic3—62no—
753Dic3—62no—
754Dic3—122no—
755Dic3—122no—
756C32C2×#55211yescharacteristic, complemented, Sylow
757C23—32no—
758C23—62no—
759C23—62no—
760C23—62no—
761C23—94no—
762C23—92no—
763C23—182no—
764C23—182no—
765C23C22×D3211yescharacteristic
766Q8—188no—
767D4—188no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—94no—
786C2×C4—92no—
787C2×C4—92no—
788C2×C4—92no—
789C2×C4—188no—
790C2×C4—188no—
791C2×C4—188no—
792C2×C4—188no—
793C2×C4—182no—
794C2×C4—182no—
795C2×C4C22×D3212yes—
796C2×C4C22×D3212yes—
797C2×C4C22×D3212yes—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—24no—
802C2×C3—122no—
803C2×C3#569314yescomplemented
804C2×C3#570814yescomplemented
805C2×C3C2×#100711yescharacteristic
806C2×C3C2×D3×#4111yescharacteristic
807C2×C3C2×D3×#4111yescharacteristic
808C2×C3C2×D3×#4111yescharacteristic
809C2×C3C2×D3×#4111yescharacteristic
810C2×C3C2×#101011yescharacteristic
811D3—42no—
812D3—68no—
813D3—64no—
814D3—64no—
815C22—62no—
816C22—62no—
817C22—62no—
818C22—94no—
819C22—124no—
820C22—182no—
821C22—182no—
822C22—188no—
823C22#6430612yes—
824C22#6431212yes—
825C22#6431512yes—
826C22C23×D3211yescharacteristic
827C4—22no—
828C4—22no—
829C4—22no—
830C4—62no—
831C4—62no—
832C4—62no—
833C4—62no—
834C4—62no—
835C4—62no—
836C4—62no—
837C4—94no—
838C4—182no—
839C4—182no—
840C3—21no—
841C3C2×#569311yescharacteristic, complemented
842C3C2×#570811yescharacteristic, complemented
843C2—122no—
844C2—184no—
845C2#1059447114yesdirect product factor
846C2C2×#6430611yescharacteristic
847C2C2×#6431211yescharacteristic
848C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#552
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×C4⋊C4×C3⋊D3C2semidirect
2. C2×C3×#898C2semidirect
3. C2×C3×#889C2semidirect
4. C2×#63899C2semidirect
6. C2×#63877C2semidirect
7. C2×#63874C2semidirect
8. C2×#63865C2semidirect
9. C2×#63861C2semidirect
12. C2×#63849C2semidirect
13. C2×#63847C2semidirect
14. C2×#63845C2semidirect
15. C2×#63837C2semidirect
16. #10594471C2direct (N × H)
29. C4⋊C4×C3⋊D3C22semidirect
42. C3×#898C22semidirect
43. C3×#889C22semidirect
57. #63899C22semidirect
59. #63877C22semidirect
60. #63874C22semidirect
61. #63865C22semidirect
62. #63861C22semidirect
65. #63849C22semidirect
66. #63847C22semidirect
67. #63845C22semidirect
68. #63837C22semidirect
74. C2×#898D3semidirect
90. C2×#889D3semidirect
239. #898C2×D3semidirect
255. #889C2×D3semidirect
630. C2×C32#552semidirect
756. C32C2×#552semidirect
803. C2×C3#5693semidirect
804. C2×C3#5708semidirect
841. C3C2×#5693semidirect
842. C3C2×#5708semidirect
845. C2#10594471direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×C3×#8982
C2×C3×#8892
C2×#638992
C2×#638812
C2×#638772
C2×#638742
C2×#638652
C2×#638612
C2×#638532
C2×#638492
C2×#638472
C2×#638452
C2×#638372
#105944712
C2×#57083
C2×#56933