Finite Group Databasebeta

← C2×#10594331 #11903032

Subgroups — C2×#10594331 #11903032

Order 1152.

2371 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64107C211yesmaximal, characteristic, complemented
2C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#889C211yesmaximal, characteristic, complemented
4C2×#63904C211yesmaximal, characteristic
5C2×#63895C211yesmaximal, characteristic, complemented
6C2×#63855C211yesmaximal, characteristic, complemented
7C2×#63851C211yesmaximal, characteristic, complemented
8C2×#63850C211yesmaximal, characteristic
9C2×#63850C211yesmaximal, characteristic
10C2×#63848C211yesmaximal, characteristic, complemented
11C2×#63847C211yesmaximal, characteristic, complemented
12C2×#63845C211yesmaximal, characteristic, complemented
13C2×#63841C211yesmaximal, characteristic, complemented
14C2×#63838C211yesmaximal, characteristic, complemented
15C2×#63836C211yesmaximal, characteristic, complemented
16#10594331C2116yesmaximal, direct product factor
17C2×#5693—31nomaximal
18C2×#5513—31nomaximal
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#627C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×C4×C3⋊Dic3C2211yescharacteristic
32#64107C2218yescomplemented
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×Dic3⋊C4C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C3×D3×C4⋊C4C2218yescomplemented
43C3×#889C2218yescomplemented
44C2×#3724C2211yescharacteristic
45C2×#3724C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×#3722C2211yescharacteristic
50C2×#3722C2211yescharacteristic
51C2×(C2×D3)⋊Dic3C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×Dic32C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63904C2218yes—
58#63895C2218yescomplemented
59#63855C2218yescomplemented
60#63851C2218yescomplemented
61#63850C2218yes—
62#63850C2218yes—
63#63848C2218yescomplemented
64#63847C2218yescomplemented
65#63845C2218yescomplemented
66#63841C2218yescomplemented
67#63838C2218yescomplemented
68#63836C2218yescomplemented
69C2×C3×#125—31no—
70C22×C3×C4⋊C4—31no—
71C2×#929—31no—
72C2×#929—31no—
73C2×C4×#67—31no—
74C2×#926—31no—
75C2×#926—31no—
76C2×#924—31no—
77#5693—316no—
78#5513—316no—
79C2×#898—31no—
80C2×#898—31no—
81C2×#898—31no—
82C2×#898—31no—
83C2×#898—61no—
84C2×#897—31no—
85C2×#896—31no—
86C2×#896—31no—
87C2×#894—31no—
88C2×#894—31no—
89C2×#893—31no—
90C2×#892—31no—
91C2×#892—31no—
92C2×D3×C4⋊C4D311yescharacteristic, complemented
93C2×#890—31no—
94C2×#889—31no—
95C2×#889—31no—
96C2×#889—31no—
97C2×#889D311yescharacteristic, complemented
98C2×#887—31no—
99C2×#887—31no—
100C2×#872—31no—
101C2×#872—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
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C2×C3×C4×D3—24no—
118C2×C3×C4×D3—24no—
119C2×C3×C4×D3—24no—
120C2×C3×C4×D3C2314yes—
121C2×C3×C4×D3C2314yes—
122C2×C3×C4×D3C2314yes—
123C2×#627—24no—
124C2×#627C2314yes—
125C2×#626—24no—
126C2×#626C2314yes—
127C2×#624—24no—
128C2×#624C2314yes—
129C32×C4⋊C4C2314yes—
130#3752C2314yes—
131#3752C2314yes—
132#3752C2314yes—
133C4⋊(C3⋊Dic3)C2314yes—
134#3750C2314yes—
135C4×C3⋊Dic3C2314yes—
136C3×C4⋊Dic3C2314yes—
137C3×C4⋊Dic3C2314yes—
138C3×Dic3⋊C4C2314yes—
139C3×Dic3⋊C4C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×Dic3⋊C4C2314yes—
142C3×Dic3⋊C4C2314yes—
143C3×Dic3⋊C4C2314yes—
144C3×C4×Dic3C2314yes—
145#3724C2314yes—
146#3724C2314yes—
147Dic3⋊Dic3C2314yes—
148Dic3⋊Dic3C2314yes—
149Dic3⋊Dic3C2314yes—
150#3722C2314yes—
151#3722C2314yes—
152(C2×D3)⋊Dic3C2314yes—
153(C2×D3)⋊Dic3C2314yes—
154(C2×D3)⋊Dic3C2314yes—
155Dic32C2314yes—
156Dic32C2314yes—
157Dic32C2314yes—
158C2×#552—91noSylow
159C23×C3×C4—31no—
160C23×C3×C4—31no—
161C23×C3×C4—31no—
162C22×#67—31no—
163C22×D12—31no—
164C22×C4×D3—31no—
165C22×C4×D3—31no—
166C22×C4×D3C2×D311yescharacteristic
167C22×C4×D3C2×D311yescharacteristic
168C22×C4×D3C2×D311yescharacteristic
169C22×Dic6—31no—
170C22×Dic6—31no—
171C3×#125—38no—
172C2×C3×C4⋊C4—21no—
173C2×C3×C4⋊C4—31no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C4⋊C4—31no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C4⋊C4—38no—
182C2×C3×C4⋊C4C2×D311yescharacteristic
183C2×C3×C4⋊C4C2×D311yescharacteristic
184C2×C3×C42—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—31no—
188#929—38no—
189#929—38no—
190C4×#67—38no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4—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)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—61no—
205C2×(C2×D3)⋊C4—61no—
206C2×(C2×D3)⋊C4—61no—
207#926—38no—
208#926—38no—
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3—31no—
211C2×C4⋊Dic3—31no—
212C2×C4⋊Dic3—31no—
213C2×C4⋊Dic3—31no—
214C2×C4⋊Dic3—61no—
215C2×C4⋊Dic3C2×D311yescharacteristic
216C2×C4⋊Dic3C2×D311yescharacteristic
217#924—38no—
218C2×Dic3⋊C4—31no—
219C2×Dic3⋊C4—31no—
220C2×Dic3⋊C4—31no—
221C2×Dic3⋊C4—31no—
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4—31no—
225C2×Dic3⋊C4—31no—
226C2×Dic3⋊C4—31no—
227C2×Dic3⋊C4—61no—
228C2×Dic3⋊C4C2×D311yescharacteristic
229C2×Dic3⋊C4C2×D311yescharacteristic
230C2×Dic3⋊C4C2×D311yescharacteristic
231C2×Dic3⋊C4C2×D311yescharacteristic
232C2×Dic3⋊C4C2×D311yescharacteristic
233C2×Dic3⋊C4C2×D311yescharacteristic
234C2×C4×Dic3—31no—
235C2×C4×Dic3—31no—
236C2×C4×Dic3—31no—
237C2×C4×Dic3—31no—
238C2×C4×Dic3—31no—
239C2×C4×Dic3—31no—
240C2×C4×Dic3—31no—
241C2×C4×Dic3—31no—
242C2×C4×Dic3—61no—
243C2×C4×Dic3C2×D311yescharacteristic
244#898—38no—
245#898—38no—
246#898—38no—
247#898—38no—
248#898—68no—
249#897—38no—
250#896—38no—
251#896—38no—
252#894—38no—
253#894—38no—
254#893—38no—
255#892—38no—
256#892—38no—
257D3×C4⋊C4C2×D318yescomplemented
258#890—38no—
259#889—38no—
260#889—38no—
261#889—38no—
262#889C2×D318yescomplemented
263#887—38no—
264#887—38no—
265#872—38no—
266#872—38no—
267C23×C32C2411yescharacteristic
268C22×C3⋊D3—22no—
269C22×C3⋊D3—22no—
270C22×C3⋊D3—22no—
271C22×C3⋊D3C2412yes—
272C22×C3×D3—22no—
273C22×C3×D3—22no—
274C22×C3×D3#4114yes—
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—22no—
285C2×C3⋊Dic3C2412yes—
286C2×C3⋊Dic3C2412yes—
287C2×C3⋊Dic3C2412yes—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3#4114yes—
295C2×C3×Dic3C2412yes—
296C2×C3×Dic3C2412yes—
297C2×C3×Dic3C2412yes—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C3×C4×D3—28no—
303C3×C4×D3—28no—
304C3×C4×D3—28no—
305#627—28no—
306#626—28no—
307#624—28no—
308#552—916no—
309C2×#126—91no—
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—31no—
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×C4—34no—
340C22×C3×C4—34no—
341C22×C3×C4—34no—
342C22×C3×C4—64no—
343C22×C3×C4—64no—
344C22×C3×C4—64no—
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C2×#67—34no—
352C2×#67—64no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361C22×Dic3—61no—
362C22×Dic3C22×D311yescharacteristic
363C22×Dic3C22×D311yescharacteristic
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C2×D12—34no—
370C2×D12—64no—
371C2×C4×D3—24no—
372C2×C4×D3—24no—
373C2×C4×D3—24no—
374C2×C4×D3—34no—
375C2×C4×D3—34no—
376C2×C4×D3—64no—
377C2×C4×D3—64no—
378C2×C4×D3C22×D314yes—
379C2×C4×D3C22×D314yes—
380C2×C4×D3C22×D314yes—
381C2×Dic6—34no—
382C2×Dic6—34no—
383C2×Dic6—64no—
384C2×Dic6—64no—
385C3×C4⋊C4—24no—
386C3×C4⋊C4—34no—
387C3×C4⋊C4—34no—
388C3×C4⋊C4—34no—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—34no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—34no—
394C3×C4⋊C4C22×D314yes—
395C3×C4⋊C4C22×D314yes—
396C3×C42—34no—
397#217—34no—
398#217—34no—
399#217—34no—
400(C2×D3)⋊C4—34no—
401(C2×D3)⋊C4—34no—
402(C2×D3)⋊C4—34no—
403(C2×D3)⋊C4—34no—
404(C2×D3)⋊C4—34no—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—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—64no—
414(C2×D3)⋊C4—64no—
415(C2×D3)⋊C4—64no—
416C4⋊Dic3—34no—
417C4⋊Dic3—34no—
418C4⋊Dic3—34no—
419C4⋊Dic3—34no—
420C4⋊Dic3—34no—
421C4⋊Dic3—64no—
422C4⋊Dic3C22×D314yes—
423C4⋊Dic3C22×D314yes—
424Dic3⋊C4—34no—
425Dic3⋊C4—34no—
426Dic3⋊C4—34no—
427Dic3⋊C4—34no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—34no—
431Dic3⋊C4—34no—
432Dic3⋊C4—34no—
433Dic3⋊C4—64no—
434Dic3⋊C4C22×D314yes—
435Dic3⋊C4C22×D314yes—
436Dic3⋊C4C22×D314yes—
437Dic3⋊C4C22×D314yes—
438Dic3⋊C4C22×D314yes—
439Dic3⋊C4C22×D314yes—
440C4×Dic3—34no—
441C4×Dic3—34no—
442C4×Dic3—34no—
443C4×Dic3—34no—
444C4×Dic3—34no—
445C4×Dic3—34no—
446C4×Dic3—34no—
447C4×Dic3—34no—
448C4×Dic3—64no—
449C4×Dic3C22×D314yes—
450C22×C32C2×#4112yes—
451C22×C32C2×#4112yes—
452C22×C322−1+412yes—
453C22×C32C2511yescharacteristic
454C2×C3⋊D3—22no—
455C2×C3⋊D3—22no—
456C2×C3⋊D3—22no—
457C2×C3⋊D3—44no—
458C2×C3×D3—28no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3C2×#4114yes—
462C32×C4—22no—
463C32×C4—22no—
464C32×C4—22no—
465C3⋊Dic3—22no—
466C3⋊Dic3—22no—
467C3⋊Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3C2×#4114yes—
475C22×Q8—91no—
476C22×D4—91no—
477C23×C4—31no—
478C23×C4—31no—
479C23×C4—31no—
480C23×C4—91no—
481#126—98no—
482#126—98no—
483#125—38no—
484#125—98no—
485#125—98no—
486#123—98no—
487#123—98no—
488C22⋊Q8—98no—
489C22⋊Q8—98no—
490C4×Q8—98no—
491C4×D4—98no—
492#117—98no—
493#117—98no—
494#117—98no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—31no—
503C2×C4⋊C4—38no—
504C2×C4⋊C4—91no—
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⋊C4D3211yescharacteristic
512C2×C22⋊C4—91no—
513C2×C22⋊C4—91no—
514C2×C22⋊C4—91no—
515C2×C22⋊C4—91no—
516C2×C22⋊C4—91no—
517C2×C22⋊C4—91no—
518C2×C22⋊C4—91no—
519C2×C22⋊C4—91no—
520C2×C42—31no—
521C2×C42—91no—
522C2×C42—91no—
523C2×C42—91no—
524C2×C42—91no—
525C23×C3—21no—
526C23×C3—34no—
527C23×C3—32no—
528C23×C3—62no—
529C23×C3—62no—
530C23×C3C23×D311yescharacteristic
531C23×C3C23×D311yescharacteristic
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—32no—
535C22×D3—32no—
536C22×D3—62no—
537C22×D3—62no—
538C22×D3—62no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—62no—
542C22×D3—62no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3#23714yes—
547C22×D3C23×D312yes—
548C2×C3×C4—22no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—22no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—34no—
558C2×C3×C4—32no—
559C2×C3×C4—32no—
560C2×C3×C4—32no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—32no—
564C2×C3×C4—32no—
565C2×C3×C4—42no—
566C2×C3×C4—42no—
567C2×C3×C4—42no—
568C2×C3×C4—68no—
569C2×C3×C4—68no—
570C2×C3×C4—68no—
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—32no—
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—32no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—62no—
599C2×Dic3—62no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—62no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—122no—
606C2×Dic3—122no—
607C2×Dic3—122no—
608C2×Dic3#23514yes—
609C2×Dic3C23×D312yes—
610C2×Dic3C23×D312yes—
611C2×Dic3C23×D312yes—
612C2×Dic3C23×D312yes—
613C2×Dic3C23×D312yes—
614C2×Dic3C23×D312yes—
615C2×Dic3C23×D312yes—
616D12—68no—
617C4×D3—28no—
618C4×D3—28no—
619C4×D3—28no—
620C4×D3—68no—
621C4×D3—68no—
622Dic6—68no—
623Dic6—68no—
624C2×C32#55214yescomplemented
625C2×C32C22×#4111yescharacteristic
626C2×C32C22×#4111yescharacteristic
627C2×C32C2×2−1+411yescharacteristic
628C3⋊D3—42no—
629C3×D3—24no—
630C24—31no—
631C24—91no—
632C2×Q8—94no—
633C2×Q8—184no—
634C2×D4—94no—
635C2×D4—184no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—34no—
644C22×C4—34no—
645C22×C4—34no—
646C22×C4—64no—
647C22×C4—64no—
648C22×C4—64no—
649C22×C4—94no—
650C22×C4—91no—
651C22×C4—91no—
652C22×C4—91no—
653C22×C4—184no—
654C22×C4C2×D3211yescharacteristic
655C22×C4C2×D3211yescharacteristic
656C22×C4C2×D3211yescharacteristic
657C4⋊C4—34no—
658C4⋊C4—34no—
659C4⋊C4—34no—
660C4⋊C4—34no—
661C4⋊C4—34no—
662C4⋊C4—34no—
663C4⋊C4—34no—
664C4⋊C4—34no—
665C4⋊C4—94no—
666C4⋊C4—94no—
667C4⋊C4—94no—
668C4⋊C4—94no—
669C4⋊C4—94no—
670C4⋊C4—94no—
671C4⋊C4—94no—
672C4⋊C4C2×D3214yes—
673C22⋊C4—94no—
674C22⋊C4—94no—
675C22⋊C4—94no—
676C22⋊C4—94no—
677C22⋊C4—94no—
678C22⋊C4—94no—
679C22⋊C4—94no—
680C22⋊C4—94no—
681C42—34no—
682C42—94no—
683C42—94no—
684C42—94no—
685C42—94no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—21no—
690C22×C3—34no—
691C22×C3—68no—
692C22×C3—62no—
693C22×C3—62no—
694C22×C3C2×#23512yes—
695C22×C3C2×#23712yes—
696C22×C3#100712yes—
697C22×C3#100712yes—
698C22×C3D3×#4112yes—
699C22×C3D3×#4112yes—
700C22×C3C24×D311yescharacteristic
701C22×C3C24×D311yescharacteristic
702C2×D3—22no—
703C2×D3—22no—
704C2×D3—28no—
705C2×D3—62no—
706C2×D3—62no—
707C2×D3—62no—
708C2×D3—62no—
709C2×D3—62no—
710C2×D3—62no—
711C2×D3—122no—
712C2×D3—122no—
713C2×D3—122no—
714C2×D3—124no—
715C2×D3—124no—
716C2×D3—244no—
717C2×D3C2×#23714yes—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—22no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—34no—
725C3×C4—42no—
726C3×C4—42no—
727C3×C4—42no—
728C3×C4—62no—
729C3×C4—62no—
730C3×C4—62no—
731C3×C4—62no—
732C3×C4—62no—
733C3×C4—62no—
734Dic3—22no—
735Dic3—22no—
736Dic3—22no—
737Dic3—22no—
738Dic3—22no—
739Dic3—22no—
740Dic3—62no—
741Dic3—62no—
742Dic3—62no—
743Dic3—62no—
744Dic3—62no—
745Dic3—62no—
746Dic3—122no—
747Dic3—122no—
748Dic3—122no—
749Dic3C2×#23514yes—
750C32C2×#55211yescharacteristic, complemented, Sylow
751C23—34no—
752C23—32no—
753C23—62no—
754C23—62no—
755C23—92no—
756C23—182no—
757C23—182no—
758C23—182no—
759C23C22×D3211yescharacteristic
760Q8—188no—
761D4—188no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—34no—
766C2×C4—32no—
767C2×C4—32no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—68no—
774C2×C4—68no—
775C2×C4—68no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—92no—
783C2×C4—92no—
784C2×C4—92no—
785C2×C4—188no—
786C2×C4—182no—
787C2×C4—182no—
788C2×C4—182no—
789C2×C4C22×D3212yes—
790C2×C4C22×D3212yes—
791C2×C4C22×D3212yes—
792C2×C3—24no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—64no—
797C2×C3#551314yescomplemented
798C2×C3#569314yescomplemented
799C2×C3C22×#23511yescharacteristic
800C2×C3C22×#23711yescharacteristic
801C2×C3C2×#100711yescharacteristic
802C2×C3C2×#100711yescharacteristic
803C2×C3C2×D3×#4111yescharacteristic
804C2×C3C2×D3×#4111yescharacteristic
805D3—24no—
806D3—122no—
807D3—122no—
808D3—242no—
809C22—34no—
810C22—68no—
811C22—62no—
812C22—62no—
813C22—182no—
814C22—182no—
815C22—182no—
816C22—364no—
817C22D3×#23512yes—
818C22D3×#23712yes—
819C22#6431612yes—
820C22C23×D3211yescharacteristic
821C4—22no—
822C4—22no—
823C4—22no—
824C4—34no—
825C4—62no—
826C4—62no—
827C4—62no—
828C4—62no—
829C4—62no—
830C4—62no—
831C4—182no—
832C4—182no—
833C4—182no—
834C3—21no—
835C3C2×#551311yescharacteristic, complemented
836C3C2×#569311yescharacteristic, complemented
837C2—64no—
838C2—362no—
839C2#1059433114yesdirect product factor
840C2C2×D3×#23511yescharacteristic
841C2C2×D3×#23711yescharacteristic
842C2C2×#6431611yescharacteristic
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×#64107C2semidirect
2. C2×C3×D3×C4⋊C4C2semidirect
3. C2×C3×#889C2semidirect
5. C2×#63895C2semidirect
6. C2×#63855C2semidirect
7. C2×#63851C2semidirect
10. C2×#63848C2semidirect
11. C2×#63847C2semidirect
12. C2×#63845C2semidirect
13. C2×#63841C2semidirect
14. C2×#63838C2semidirect
15. C2×#63836C2semidirect
16. #10594331C2direct (N × H)
32. #64107C22semidirect
42. C3×D3×C4⋊C4C22semidirect
43. C3×#889C22semidirect
58. #63895C22semidirect
59. #63855C22semidirect
60. #63851C22semidirect
63. #63848C22semidirect
64. #63847C22semidirect
65. #63845C22semidirect
66. #63841C22semidirect
67. #63838C22semidirect
68. #63836C22semidirect
92. C2×D3×C4⋊C4D3semidirect
97. C2×#889D3semidirect
257. D3×C4⋊C4C2×D3semidirect
262. #889C2×D3semidirect
624. C2×C32#552semidirect
750. C32C2×#552semidirect
797. C2×C3#5513semidirect
798. C2×C3#5693semidirect
835. C3C2×#5513semidirect
836. C3C2×#5693semidirect
839. C2#10594331direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641072
C2×C3×D3×C4⋊C42
C2×C3×#8892
C2×#639042
C2×#638952
C2×#638552
C2×#638512
C2×#638502
C2×#638482
C2×#638472
C2×#638452
C2×#638412
C2×#638382
C2×#638362
#105943312
C2×#56933
C2×#55133