Finite Group Databasebeta

← C2×#10593910 #11900645

Subgroups — C2×#10593910 #11900645

Order 1152.

2613 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3C2×C3×#872C211yesmaximal, characteristic, complemented
4C2×#63913C211yesmaximal, characteristic, complemented
5C2×C4×#625C211yesmaximal, characteristic, complemented
6C2×C4×#625C211yesmaximal, characteristic, complemented
7C2×#63896C211yesmaximal, characteristic, complemented
8C2×#63891C211yesmaximal, characteristic, complemented
9C2×#63885C211yesmaximal, characteristic
10C2×#63884C211yesmaximal, characteristic, complemented
11C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
12C2×#63861C211yesmaximal, characteristic, complemented
13C2×#63858C211yesmaximal, characteristic, complemented
14C2×#63855C211yesmaximal, characteristic, complemented
15C2×#63847C211yesmaximal, characteristic, complemented
16#10593910C2116yesmaximal, direct product factor
17C2×#5538—31nomaximal
18C2×#5528—31nomaximal
19C22×#634C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×#625C2211yescharacteristic
25C22×#625C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C42C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33C2×C4×C3⋊Dic3C2211yescharacteristic
34C4×#634C2218yescomplemented
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×C4×D12C2218yescomplemented
44C3×#872C2218yescomplemented
45C2×#3724C2211yescharacteristic
46C2×#3724C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×(C2×D3)⋊Dic3C2211yescharacteristic
51C2×(C2×D3)⋊Dic3C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63913C2218yescomplemented
58C4×#625C2218yescomplemented
59C4×#625C2218yescomplemented
60#63896C2218yescomplemented
61#63891C2218yescomplemented
62#63885C2218yes—
63#63884C2218yescomplemented
64C4×D3×Dic3C2218yescomplemented
65#63861C2218yescomplemented
66#63858C2218yescomplemented
67#63855C2218yescomplemented
68#63847C2218yescomplemented
69C2×C3×C4×D4—31no—
70C2×C3×#117—31no—
71C2×#939—31no—
72C2×#935—31no—
73C2×C4×#67—31no—
74C2×C4×#67—31no—
75C2×C4×#67—31no—
76C2×C4×#67—31no—
77C2×#926—31no—
78C22×C4×Dic3—31no—
79#5538—316no—
80#5528—316no—
81C2×#898—31no—
82C2×#898—31no—
83C2×#896—31no—
84C2×#894—31no—
85C2×#889—31no—
86C2×#889—31no—
87C2×#886—31no—
88C2×#885—31no—
89C2×#885—31no—
90C2×#884—31no—
91C2×#883—31no—
92C2×#879—31no—
93C2×#879—31no—
94C2×#878—31no—
95C2×C4×D12D311yescharacteristic, complemented
96C2×#872—31no—
97C2×#872D311yescharacteristic, complemented
98C2×C42×D3—31no—
99C2×C4×Dic6—31no—
100C2×C4×Dic6—31no—
101C2×C4×Dic6—61no—
102C23×C3×D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C2×#634—24no—
113C2×#634C2314yes—
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C2×C3×D12—24no—
120C2×C3×D12C2314yes—
121C2×C3×C4×D3—24no—
122C2×C3×C4×D3—24no—
123C2×C3×C4×D3—24no—
124C2×C3×C4×D3C2314yes—
125C2×C3×C4×D3C2314yes—
126C2×C3×C4×D3C2314yes—
127C2×#625—24no—
128C2×#625—24no—
129C2×#625C2314yes—
130C2×#625C2314yes—
131C2×D3×Dic3—24no—
132C2×D3×Dic3—24no—
133C2×D3×Dic3C2314yes—
134C2×D3×Dic3C2314yes—
135C32×C42C2314yes—
136C4⋊(C3⋊Dic3)C2314yes—
137#3750C2314yes—
138#3750C2314yes—
139C4×C3⋊Dic3C2314yes—
140C4×C3⋊Dic3C2314yes—
141C3×(C2×D3)⋊C4C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×C4⋊Dic3C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×C4×Dic3C2314yes—
149#3724C2314yes—
150#3724C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153(C2×D3)⋊Dic3C2314yes—
154(C2×D3)⋊Dic3C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157(C2×D3)⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159Dic32C2314yes—
160Dic32C2314yes—
161C2×#529—91noSylow
162C22×C3×D4—31no—
163C23×C3×C4—31no—
164C23×C3×C4—31no—
165C23×C3×C4—31no—
166C22×#67—31no—
167C22×#67—31no—
168C22×#67—31no—
169C22×#67—31no—
170C23×Dic3—31no—
171C23×Dic3—31no—
172C22×D12C2×D311yescharacteristic
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C22×C4×D3C2×D311yescharacteristic
176C22×C4×D3C2×D311yescharacteristic
177C22×C4×D3C2×D311yescharacteristic
178C22×Dic6—31no—
179C22×Dic6—31no—
180C22×Dic6—61no—
181C3×C4×D4—38no—
182C3×#117—38no—
183C2×C3×C4⋊C4—31no—
184C2×C3×C4⋊C4—31no—
185C2×C3×C4⋊C4—31no—
186C2×C3×C22⋊C4—31no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C42—21no—
191C2×C3×C42—31no—
192C2×C3×C42C2×D311yescharacteristic
193C2×C3×C42C2×D311yescharacteristic
194C2×#217—31no—
195C2×#217—31no—
196C2×#217—31no—
197C2×#217—31no—
198C2×#217—31no—
199C2×#217—31no—
200#939—38no—
201#935—38no—
202C4×#67—38no—
203C4×#67—38no—
204C4×#67—38no—
205C4×#67—38no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4C2×D311yescharacteristic
213C2×(C2×D3)⋊C4C2×D311yescharacteristic
214C2×(C2×D3)⋊C4C2×D311yescharacteristic
215C2×(C2×D3)⋊C4C2×D311yescharacteristic
216#926—38no—
217C2×C4⋊Dic3—31no—
218C2×C4⋊Dic3—31no—
219C2×C4⋊Dic3—31no—
220C2×C4⋊Dic3—31no—
221C2×C4⋊Dic3—61no—
222C2×C4⋊Dic3C2×D311yescharacteristic
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4—31no—
225C2×Dic3⋊C4—31no—
226C2×Dic3⋊C4—31no—
227C2×Dic3⋊C4—31no—
228C2×Dic3⋊C4—31no—
229C2×Dic3⋊C4—31no—
230C2×Dic3⋊C4—31no—
231C2×Dic3⋊C4—31no—
232C2×Dic3⋊C4—31no—
233C2×Dic3⋊C4—61no—
234C2×Dic3⋊C4—61no—
235C2×Dic3⋊C4C2×D311yescharacteristic
236C2×Dic3⋊C4C2×D311yescharacteristic
237C2×C4×Dic3—31no—
238C2×C4×Dic3—31no—
239C2×C4×Dic3—31no—
240C2×C4×Dic3—31no—
241C2×C4×Dic3—31no—
242C2×C4×Dic3—31no—
243C2×C4×Dic3—31no—
244C2×C4×Dic3—31no—
245C2×C4×Dic3—38no—
246C2×C4×Dic3—61no—
247C2×C4×Dic3—61no—
248C2×C4×Dic3C2×D311yescharacteristic
249#898—38no—
250#898—38no—
251#896—38no—
252#894—38no—
253#889—38no—
254#889—38no—
255#886—38no—
256#885—38no—
257#885—38no—
258#884—38no—
259#883—38no—
260#879—38no—
261#879—38no—
262#878—38no—
263C4×D12C2×D318yescomplemented
264#872—38no—
265#872C2×D318yescomplemented
266C42×D3—38no—
267C4×Dic6—38no—
268C4×Dic6—38no—
269C4×Dic6—68no—
270C23×C32C2411yescharacteristic
271C22×C3×D3—22no—
272C22×C3×D3—22no—
273C22×C3×D3—22no—
274C22×C3×D3—22no—
275C22×C3×D3—22no—
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C22×C3×D3—22no—
279C22×C3×D3#4114yes—
280C22×C3×D3C2412yes—
281C22×C3×D3C2412yes—
282C22×C3×D3C2412yes—
283C2×C32×C4—22no—
284C2×C32×C4—22no—
285C2×C32×C4#4114yes—
286C2×C32×C4C2412yes—
287C2×C32×C4C2412yes—
288C2×C32×C4C2412yes—
289C2×C3⋊Dic3—22no—
290C2×C3⋊Dic3—22no—
291C2×C3⋊Dic3—22no—
292C2×C3⋊Dic3#4114yes—
293C2×C3⋊Dic3C2412yes—
294C2×C3⋊Dic3C2412yes—
295C2×C3⋊Dic3C2412yes—
296C2×C3⋊Dic3C2412yes—
297#634—28no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C3×D12—28no—
309C3×C4×D3—28no—
310C3×C4×D3—28no—
311C3×C4×D3—28no—
312#625—28no—
313#625—28no—
314D3×Dic3—28no—
315D3×Dic3—28no—
316#529—916no—
317C2×#126—91no—
318C2×#126—91no—
319C2×#125—91no—
320C2×#124—91no—
321C2×#123—91no—
322C2×#123—91no—
323C2×C22⋊Q8—91no—
324C2×#121—91no—
325C2×C4×Q8—91no—
326C2×C4×D4—31no—
327C2×C4×D4—91no—
328C2×C4×D4—91no—
329C2×#117—31no—
330C2×#117—91no—
331C22×C42—91no—
332C24×C3—31no—
333C24×C3—31no—
334C24×C3—31no—
335C23×D3C22×D311yescharacteristic
336C23×D3C22×D311yescharacteristic
337C23×D3C22×D311yescharacteristic
338C2×C3×D4—34no—
339C2×C3×D4—64no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—34no—
349C22×C3×C4—34no—
350C22×C3×C4—34no—
351C22×C3×C4—64no—
352C22×C3×C4—64no—
353C22×C3×C4—64no—
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C22×C3×C4C22×D311yescharacteristic
360C2×#67—34no—
361C2×#67—34no—
362C2×#67—34no—
363C2×#67—34no—
364C2×#67—64no—
365C2×#67—64no—
366C2×#67—64no—
367C2×#67—64no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—34no—
377C22×Dic3—34no—
378C22×Dic3—61no—
379C22×Dic3—61no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—64no—
383C22×Dic3—64no—
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D311yescharacteristic
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C2×D12—24no—
390C2×D12C22×D314yes—
391C2×C4×D3—24no—
392C2×C4×D3—24no—
393C2×C4×D3—24no—
394C2×C4×D3—34no—
395C2×C4×D3—34no—
396C2×C4×D3—64no—
397C2×C4×D3—64no—
398C2×C4×D3C22×D314yes—
399C2×C4×D3C22×D314yes—
400C2×C4×D3C22×D314yes—
401C2×Dic6—34no—
402C2×Dic6—34no—
403C2×Dic6—64no—
404C2×Dic6—64no—
405C2×Dic6—64no—
406C2×Dic6—68no—
407C3×C4⋊C4—34no—
408C3×C4⋊C4—34no—
409C3×C4⋊C4—34no—
410C3×C22⋊C4—34no—
411C3×C22⋊C4—34no—
412C3×C22⋊C4—34no—
413C3×C22⋊C4—34no—
414C3×C42—24no—
415C3×C42—34no—
416C3×C42C22×D314yes—
417C3×C42C22×D314yes—
418#217—34no—
419#217—34no—
420#217—34no—
421#217—34no—
422#217—34no—
423#217—34no—
424(C2×D3)⋊C4—34no—
425(C2×D3)⋊C4—34no—
426(C2×D3)⋊C4—34no—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4C22×D314yes—
431(C2×D3)⋊C4C22×D314yes—
432(C2×D3)⋊C4C22×D314yes—
433(C2×D3)⋊C4C22×D314yes—
434C4⋊Dic3—34no—
435C4⋊Dic3—34no—
436C4⋊Dic3—34no—
437C4⋊Dic3—34no—
438C4⋊Dic3—64no—
439C4⋊Dic3C22×D314yes—
440Dic3⋊C4—34no—
441Dic3⋊C4—34no—
442Dic3⋊C4—34no—
443Dic3⋊C4—34no—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
448Dic3⋊C4—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4—64no—
451Dic3⋊C4—64no—
452Dic3⋊C4C22×D314yes—
453Dic3⋊C4C22×D314yes—
454C4×Dic3—34no—
455C4×Dic3—34no—
456C4×Dic3—34no—
457C4×Dic3—34no—
458C4×Dic3—34no—
459C4×Dic3—34no—
460C4×Dic3—34no—
461C4×Dic3—34no—
462C4×Dic3—64no—
463C4×Dic3—64no—
464C4×Dic3C22×D314yes—
465C22×C32C2×#4112yes—
466C22×C32C2×#4112yes—
467C22×C32C2×#4112yes—
468C22×C32C2511yescharacteristic
469C2×C3×D3—28no—
470C2×C3×D3—22no—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—44no—
479C2×C3×D3—44no—
480C2×C3×D3C2×#4114yes—
481C32×C4—22no—
482C32×C4—22no—
483C32×C4C2×#4114yes—
484C3⋊Dic3—22no—
485C3⋊Dic3—22no—
486C3⋊Dic3—22no—
487C3⋊Dic3C2×#4114yes—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C22×Q8—91no—
494C22×D4—31no—
495C22×D4—91no—
496C22×D4—91no—
497C23×C4—31no—
498C23×C4—31no—
499C23×C4—31no—
500C23×C4—91no—
501C23×C4—91no—
502#126—98no—
503#126—98no—
504#125—98no—
505#124—98no—
506#123—98no—
507#123—98no—
508C22⋊Q8—98no—
509#121—98no—
510C4×Q8—98no—
511C4×D4—38no—
512C4×D4—98no—
513C4×D4—98no—
514#117—38no—
515#117—98no—
516C2×C4⋊C4—31no—
517C2×C4⋊C4—31no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—91no—
520C2×C4⋊C4—91no—
521C2×C4⋊C4—91no—
522C2×C4⋊C4—91no—
523C2×C4⋊C4—91no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—91no—
531C2×C22⋊C4—91no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C42—31no—
537C2×C42—98no—
538C2×C42—91no—
539C2×C42—91no—
540C2×C42—91no—
541C2×C42—91no—
542C2×C42D3211yescharacteristic
543C23×C3—21no—
544C23×C3—34no—
545C23×C3—32no—
546C23×C3—32no—
547C23×C3—32no—
548C23×C3—62no—
549C23×C3—62no—
550C23×C3—62no—
551C23×C3—62no—
552C23×C3—62no—
553C23×C3—62no—
554C23×C3—62no—
555C23×C3—62no—
556C23×C3C23×D311yescharacteristic
557C23×C3C23×D311yescharacteristic
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3#23514yes—
567C22×D3C23×D312yes—
568C22×D3C23×D312yes—
569C22×D3C23×D312yes—
570C3×D4—68no—
571C2×C3×C4—24no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—24no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—32no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—42no—
586C2×C3×C4—62no—
587C2×C3×C4—62no—
588C2×C3×C4—62no—
589C2×C3×C4—62no—
590C2×C3×C4—62no—
591C2×C3×C4—68no—
592C2×C3×C4—68no—
593C2×C3×C4—68no—
594C2×C3×C4#23514yes—
595C2×C3×C4#23714yes—
596C2×C3×C4C23×D312yes—
597C2×C3×C4C23×D312yes—
598C2×C3×C4C23×D312yes—
599C2×C3×C4C23×D312yes—
600C2×C3×C4C23×D312yes—
601C2×C3×C4C23×D312yes—
602#67—68no—
603#67—68no—
604#67—68no—
605#67—68no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—34no—
612C2×Dic3—34no—
613C2×Dic3—32no—
614C2×Dic3—32no—
615C2×Dic3—32no—
616C2×Dic3—32no—
617C2×Dic3—32no—
618C2×Dic3—32no—
619C2×Dic3—32no—
620C2×Dic3—32no—
621C2×Dic3—64no—
622C2×Dic3—62no—
623C2×Dic3—62no—
624C2×Dic3—62no—
625C2×Dic3—62no—
626C2×Dic3—68no—
627C2×Dic3—68no—
628C2×Dic3—64no—
629C2×Dic3—62no—
630C2×Dic3—62no—
631C2×Dic3—62no—
632C2×Dic3—62no—
633C2×Dic3—62no—
634C2×Dic3—62no—
635C2×Dic3—122no—
636C2×Dic3—122no—
637C2×Dic3C23×D312yes—
638C2×Dic3C23×D312yes—
639C2×Dic3C23×D312yes—
640C2×Dic3C23×D312yes—
641C2×Dic3C23×D312yes—
642D12—28no—
643C4×D3—28no—
644C4×D3—28no—
645C4×D3—28no—
646C4×D3—68no—
647C4×D3—68no—
648Dic6—68no—
649Dic6—68no—
650Dic6—616no—
651C2×C32#52914yescomplemented
652C2×C32C22×#4111yescharacteristic
653C2×C32C22×#4111yescharacteristic
654C2×C32C22×#4111yescharacteristic
655C3×D3—24no—
656C3×D3—42no—
657C3×D3—42no—
658C24—31no—
659C24—31no—
660C24—31no—
661C2×Q8—94no—
662C2×Q8—184no—
663C2×D4—34no—
664C2×D4—64no—
665C2×D4—94no—
666C2×D4—94no—
667C2×D4—184no—
668C2×D4—184no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—34no—
675C22×C4—34no—
676C22×C4—34no—
677C22×C4—64no—
678C22×C4—64no—
679C22×C4—64no—
680C22×C4—94no—
681C22×C4—94no—
682C22×C4—91no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—91no—
686C22×C4—184no—
687C22×C4—184no—
688C22×C4C2×D3211yescharacteristic
689C22×C4C2×D3211yescharacteristic
690C22×C4C2×D3211yescharacteristic
691C4⋊C4—34no—
692C4⋊C4—34no—
693C4⋊C4—34no—
694C4⋊C4—94no—
695C4⋊C4—94no—
696C4⋊C4—94no—
697C4⋊C4—94no—
698C4⋊C4—94no—
699C4⋊C4—94no—
700C4⋊C4—94no—
701C22⋊C4—34no—
702C22⋊C4—34no—
703C22⋊C4—34no—
704C22⋊C4—34no—
705C22⋊C4—94no—
706C22⋊C4—94no—
707C22⋊C4—94no—
708C22⋊C4—94no—
709C22⋊C4—94no—
710C22⋊C4—94no—
711C42—34no—
712C42—94no—
713C42—94no—
714C42—94no—
715C42—94no—
716C42C2×D3214yes—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—21no—
721C22×C3—34no—
722C22×C3—62no—
723C22×C3—62no—
724C22×C3—68no—
725C22×C3—62no—
726C22×C3—62no—
727C22×C3—62no—
728C22×C3—62no—
729C22×C3—62no—
730C22×C3—62no—
731C22×C3—124no—
732C22×C3—124no—
733C22×C3C2×#23512yes—
734C22×C3C2×#23512yes—
735C22×C3C2×#23712yes—
736C22×C3D3×#4112yes—
737C22×C3D3×#4112yes—
738C22×C3D3×#4112yes—
739C22×C3C24×D311yescharacteristic
740C22×C3C24×D311yescharacteristic
741C2×D3—22no—
742C2×D3—22no—
743C2×D3—28no—
744C2×D3—22no—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—44no—
751C2×D3—44no—
752C2×D3C2×#23514yes—
753C3×C4—24no—
754C3×C4—22no—
755C3×C4—22no—
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—24no—
759C3×C4—42no—
760C3×C4—62no—
761C3×C4—62no—
762C3×C4—62no—
763C3×C4—62no—
764C3×C4—62no—
765C3×C4C2×#23514yes—
766C3×C4C2×#23714yes—
767Dic3—22no—
768Dic3—22no—
769Dic3—22no—
770Dic3—22no—
771Dic3—22no—
772Dic3—34no—
773Dic3—34no—
774Dic3—64no—
775Dic3—64no—
776Dic3—62no—
777Dic3—62no—
778Dic3—62no—
779Dic3—62no—
780Dic3—62no—
781Dic3—62no—
782Dic3—122no—
783Dic3—122no—
784C32C2×#52911yescharacteristic, complemented, Sylow
785C23—34no—
786C23—32no—
787C23—32no—
788C23—32no—
789C23—62no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23—62no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23C22×D3211yescharacteristic
798Q8—188no—
799D4—68no—
800D4—188no—
801D4—188no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—62no—
810C2×C4—62no—
811C2×C4—62no—
812C2×C4—62no—
813C2×C4—62no—
814C2×C4—68no—
815C2×C4—68no—
816C2×C4—68no—
817C2×C4—94no—
818C2×C4—92no—
819C2×C4—92no—
820C2×C4—92no—
821C2×C4—92no—
822C2×C4—188no—
823C2×C4—188no—
824C2×C4—182no—
825C2×C4—182no—
826C2×C4—182no—
827C2×C4#379514yes—
828C2×C4C22×D3212yes—
829C2×C4C22×D3212yes—
830C2×C4C22×D3212yes—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—24no—
835C2×C3—64no—
836C2×C3—122no—
837C2×C3—122no—
838C2×C3#552814yescomplemented
839C2×C3#553814yescomplemented
840C2×C3C22×#23511yescharacteristic
841C2×C3C22×#23511yescharacteristic
842C2×C3C22×#23711yescharacteristic
843C2×C3C2×D3×#4111yescharacteristic
844C2×C3C2×D3×#4111yescharacteristic
845C2×C3C2×D3×#4111yescharacteristic
846D3—24no—
847D3—42no—
848D3—42no—
849C22—34no—
850C22—62no—
851C22—62no—
852C22—68no—
853C22—62no—
854C22—62no—
855C22—62no—
856C22—62no—
857C22—62no—
858C22—62no—
859C22—124no—
860C22—124no—
861C22C2×#379512yes—
862C22D3×#23512yes—
863C22#6430612yes—
864C22C23×D3211yescharacteristic
865C4—22no—
866C4—22no—
867C4—62no—
868C4—62no—
869C4—62no—
870C4—62no—
871C4—62no—
872C4—94no—
873C4—182no—
874C4—182no—
875C4—182no—
876C4C2×#379514yes—
877C3—21no—
878C3C2×#552811yescharacteristic, complemented
879C3C2×#553811yescharacteristic, complemented
880C2—64no—
881C2—122no—
882C2—122no—
883C2#1059391014yesdirect product factor
884C2C22×#379511yescharacteristic
885C2C2×D3×#23511yescharacteristic
886C2C2×#6430611yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC2×#63885C2
hypercenterC2×C42D32
hypocenterC32C2×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#634C2semidirect
2. C2×C3×C4×D12C2semidirect
3. C2×C3×#872C2semidirect
4. C2×#63913C2semidirect
5. C2×C4×#625C2semidirect
6. C2×C4×#625C2semidirect
7. C2×#63896C2semidirect
8. C2×#63891C2semidirect
10. C2×#63884C2semidirect
11. C2×C4×D3×Dic3C2semidirect
12. C2×#63861C2semidirect
13. C2×#63858C2semidirect
14. C2×#63855C2semidirect
15. C2×#63847C2semidirect
16. #10593910C2direct (N × H)
34. C4×#634C22semidirect
43. C3×C4×D12C22semidirect
44. C3×#872C22semidirect
57. #63913C22semidirect
58. C4×#625C22semidirect
59. C4×#625C22semidirect
60. #63896C22semidirect
61. #63891C22semidirect
63. #63884C22semidirect
64. C4×D3×Dic3C22semidirect
65. #63861C22semidirect
66. #63858C22semidirect
67. #63855C22semidirect
68. #63847C22semidirect
95. C2×C4×D12D3semidirect
97. C2×#872D3semidirect
263. C4×D12C2×D3semidirect
265. #872C2×D3semidirect
651. C2×C32#529semidirect
784. C32C2×#529semidirect
838. C2×C3#5528semidirect
839. C2×C3#5538semidirect
878. C3C2×#5528semidirect
879. C3C2×#5538semidirect
883. C2#10593910direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×C3×C4×D122
C2×C3×#8722
C2×#639132
C2×C4×#6252
C2×#638962
C2×#638912
C2×#638852
C2×#638842
C2×C4×D3×Dic32
C2×#638612
C2×#638582
C2×#638552
C2×#638472
#105939102
C2×#55383
C2×#55283