Finite Group Databasebeta

← C2×#10594045 #11903051

Subgroups — C2×#10594045 #11903051

Order 1152.

2419 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64095C211yesmaximal, characteristic
2C2×C3×#878C211yesmaximal, characteristic, complemented
3C2×C3×#877C211yesmaximal, characteristic, complemented
4C2×#63966C211yesmaximal, characteristic
5C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
6C2×#63957C211yesmaximal, characteristic, complemented
7C2×#63952C211yesmaximal, characteristic
8C2×#63888C211yesmaximal, characteristic, complemented
9C2×#63869C211yesmaximal, characteristic, complemented
10C2×#63868C211yesmaximal, characteristic, complemented
11C2×#63848C211yesmaximal, characteristic, complemented
12C2×#63845C211yesmaximal, characteristic, complemented
13C2×#63845C211yesmaximal, characteristic, complemented
14C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
15C2×#63836C211yesmaximal, characteristic, complemented
16#10594045C2116yesmaximal, direct product factor
17C2×#5642—31nomaximal
18C2×#5531—31nomaximal
19C22×#638C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30#64095C2218yes—
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C3×#878C2218yescomplemented
41C3×#877C2218yescomplemented
42C2×#3724C2211yescharacteristic
43C2×#3724C2211yescharacteristic
44C2×#3724C2211yescharacteristic
45#63966C2218yes—
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2218yescomplemented
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56#63957C2218yescomplemented
57C2×Dic32C2211yescharacteristic
58C2×Dic32C2211yescharacteristic
59C2×Dic32C2211yescharacteristic
60#63952C2218yes—
61#63888C2218yescomplemented
62#63869C2218yescomplemented
63#63868C2218yescomplemented
64#63848C2218yescomplemented
65#63845C2218yescomplemented
66#63845C2218yescomplemented
67Dic3×Dic6C2218yescomplemented
68#63836C2218yescomplemented
69C2×C3×C22⋊Q8—31no—
70C2×C3×#117—31no—
71C2×#946—31no—
72C2×Q8×Dic3—31no—
73C2×#929—31no—
74C2×C4×#67—31no—
75C22×C4⋊Dic3—31no—
76C22×Dic3⋊C4—31no—
77#5642—316no—
78#5531—316no—
79C2×#898—31no—
80C2×#898—31no—
81C2×#898—31no—
82C2×#896—31no—
83C2×#892—31no—
84C2×#890—31no—
85C2×#890—31no—
86C2×#890—31no—
87C2×#889—31no—
88C2×#889—31no—
89C2×#886—31no—
90C2×#886—31no—
91C2×#886—31no—
92C2×#886—61no—
93C2×#67⋊C4—31no—
94C2×#878D311yescharacteristic, complemented
95C2×#877—31no—
96C2×#877—31no—
97C2×#877D311yescharacteristic, complemented
98C2×#876—31no—
99C2×#872—31no—
100C2×#870—31no—
101C2×C4×Dic6—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C2×#638—24no—
107C2×#638C2314yes—
108C22×C3⋊Dic3—24no—
109C22×C3⋊Dic3C2314yes—
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3×Dic3—24no—
114C22×C3×Dic3—24no—
115C22×C3×Dic3C2314yes—
116C22×C3×Dic3C2314yes—
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×C3×Dic6—24no—
126C2×C3×Dic6C2314yes—
127C2×#624—24no—
128C2×#624C2314yes—
129C32×C22⋊C4C2314yes—
130#3752C2314yes—
131#3752C2314yes—
132C4⋊(C3⋊Dic3)C2314yes—
133C4⋊(C3⋊Dic3)C2314yes—
134C3×#217C2314yes—
135C3×#217C2314yes—
136C3×C4⋊Dic3C2314yes—
137C3×Dic3⋊C4C2314yes—
138C3×Dic3⋊C4C2314yes—
139C3×Dic3⋊C4C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×C4×Dic3C2314yes—
142C3×C4×Dic3C2314yes—
143#3724C2314yes—
144#3724C2314yes—
145#3724C2314yes—
146Dic3⋊Dic3C2314yes—
147Dic3⋊Dic3C2314yes—
148Dic3⋊Dic3C2314yes—
149Dic3⋊Dic3C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152#3722C2314yes—
153#3722C2314yes—
154#3722C2314yes—
155Dic32C2314yes—
156Dic32C2314yes—
157Dic32C2314yes—
158C2×#552—91noSylow
159C22×C3×Q8—31no—
160C23×C3×C4—31no—
161C23×C3×C4—31no—
162C22×#67—31no—
163C22×#67—31no—
164C22×#67—61no—
165C23×Dic3—31no—
166C23×Dic3—31no—
167C23×Dic3—61no—
168C23×Dic3C2×D311yescharacteristic
169C23×Dic3C2×D311yescharacteristic
170C22×C4×D3—31no—
171C22×C4×D3—31no—
172C22×Dic6C2×D311yescharacteristic
173C3×C22⋊Q8—38no—
174C3×#117—38no—
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×C22⋊C4—21no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4C2×D311yescharacteristic
184C2×C3×C22⋊C4C2×D311yescharacteristic
185C2×C3×C42—31no—
186C2×C3×C42—31no—
187C2×#217C2×D311yescharacteristic
188C2×#217C2×D311yescharacteristic
189#946—38no—
190Q8×Dic3—38no—
191#929—38no—
192C4×#67—38no—
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—61no—
204C2×(C2×D3)⋊C4—61no—
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—38no—
210C2×C4⋊Dic3—31no—
211C2×C4⋊Dic3—31no—
212C2×C4⋊Dic3—31no—
213C2×C4⋊Dic3—31no—
214C2×C4⋊Dic3—31no—
215C2×C4⋊Dic3—31no—
216C2×C4⋊Dic3—61no—
217C2×C4⋊Dic3—61no—
218C2×C4⋊Dic3C2×D311yescharacteristic
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—31no—
228C2×Dic3⋊C4—31no—
229C2×Dic3⋊C4—31no—
230C2×Dic3⋊C4—31no—
231C2×Dic3⋊C4—38no—
232C2×Dic3⋊C4C2×D311yescharacteristic
233C2×Dic3⋊C4C2×D311yescharacteristic
234C2×Dic3⋊C4C2×D311yescharacteristic
235C2×Dic3⋊C4C2×D311yescharacteristic
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×Dic3C2×D311yescharacteristic
243C2×C4×Dic3C2×D311yescharacteristic
244#898—38no—
245#898—38no—
246#898—38no—
247#896—38no—
248#892—38no—
249#890—38no—
250#890—38no—
251#890—38no—
252#889—38no—
253#889—38no—
254#886—38no—
255#886—38no—
256#886—38no—
257#886—68no—
258#67⋊C4—38no—
259#878C2×D318yescomplemented
260#877—38no—
261#877—38no—
262#877C2×D318yescomplemented
263#876—38no—
264#872—38no—
265#870—38no—
266C4×Dic6—38no—
267C23×C32—22no—
268C23×C32—22no—
269C23×C32#4114yes—
270C23×C32C2412yes—
271C23×C32C2411yescharacteristic
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×C4C2412yes—
279C2×C32×C4C2412yes—
280#638—28no—
281C2×C3⋊Dic3—28no—
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—28no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3—22no—
296C2×C3×Dic3—28no—
297C2×C3×Dic3#4114yes—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C3×Dic6—28no—
307#624—28no—
308#552—916no—
309C2×#126—91no—
310C2×#126—91no—
311C2×#125—91no—
312C2×#125—91no—
313C2×#125—91no—
314C2×#123—91no—
315C2×#123—91no—
316C2×C22⋊Q8—31no—
317C2×C22⋊Q8—91no—
318C2×C4×Q8—91no—
319C2×C4×D4—91no—
320C2×#117—31no—
321C2×#117—91no—
322C2×#117—91no—
323C22×C4⋊C4—91no—
324C24×C3—21no—
325C24×C3C22×D311yescharacteristic
326C24×C3C22×D311yescharacteristic
327C23×D3—31no—
328C23×D3—31no—
329C23×D3—61no—
330C2×C3×Q8—34no—
331C2×C3×Q8—64no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—31no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—31no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—34no—
342C22×C3×C4—31no—
343C22×C3×C4—34no—
344C22×C3×C4—64no—
345C22×C3×C4—64no—
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C2×#67—34no—
351C2×#67—34no—
352C2×#67—64no—
353C2×#67—64no—
354C2×#67—64no—
355C2×#67—124no—
356C22×Dic3—24no—
357C22×Dic3—24no—
358C22×Dic3—34no—
359C22×Dic3—34no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—64no—
367C22×Dic3—61no—
368C22×Dic3—61no—
369C22×Dic3—61no—
370C22×Dic3—64no—
371C22×Dic3—64no—
372C22×Dic3—124no—
373C22×Dic3C22×D314yes—
374C22×Dic3C22×D314yes—
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C2×C4×D3—34no—
384C2×C4×D3—34no—
385C2×C4×D3—64no—
386C2×C4×D3—64no—
387C2×Dic6—24no—
388C2×Dic6C22×D314yes—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—34no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—34no—
394C3×C22⋊C4—24no—
395C3×C22⋊C4—34no—
396C3×C22⋊C4—34no—
397C3×C22⋊C4C22×D314yes—
398C3×C22⋊C4C22×D314yes—
399C3×C42—34no—
400C3×C42—34no—
401#217C22×D314yes—
402#217C22×D314yes—
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—
415C4⋊Dic3—34no—
416C4⋊Dic3—34no—
417C4⋊Dic3—34no—
418C4⋊Dic3—34no—
419C4⋊Dic3—34no—
420C4⋊Dic3—34no—
421C4⋊Dic3—34no—
422C4⋊Dic3—34no—
423C4⋊Dic3—34no—
424C4⋊Dic3—34no—
425C4⋊Dic3—64no—
426C4⋊Dic3—64no—
427C4⋊Dic3C22×D314yes—
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—34no—
439Dic3⋊C4—34no—
440Dic3⋊C4C22×D314yes—
441Dic3⋊C4C22×D314yes—
442Dic3⋊C4C22×D314yes—
443Dic3⋊C4C22×D314yes—
444C4×Dic3—34no—
445C4×Dic3—34no—
446C4×Dic3—34no—
447C4×Dic3—34no—
448C4×Dic3—34no—
449C4×Dic3—34no—
450C4×Dic3C22×D314yes—
451C4×Dic3C22×D314yes—
452C22×C32—28no—
453C22×C32—22no—
454C22×C32—22no—
455C22×C32C2×#4114yes—
456C22×C32C2×#4112yes—
457C22×C32C2×#4112yes—
458C22×C322−1+412yes—
459C22×C32C2511yescharacteristic
460C2×C3⋊D3—22no—
461C2×C3⋊D3—22no—
462C2×C3⋊D3—22no—
463C2×C3⋊D3—44no—
464C32×C4—22no—
465C32×C4—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×Dic3—22no—
475C3×Dic3—22no—
476C3×Dic3C2×#4114yes—
477C22×Q8—31no—
478C22×D4—91no—
479C23×C4—31no—
480C23×C4—31no—
481C23×C4—91no—
482C23×C4—91no—
483#126—98no—
484#126—98no—
485#125—98no—
486#125—98no—
487#125—98no—
488#123—98no—
489#123—98no—
490C22⋊Q8—38no—
491C22⋊Q8—98no—
492C4×Q8—98no—
493C4×D4—98no—
494#117—38no—
495#117—98no—
496#117—98no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—91no—
503C2×C4⋊C4—91no—
504C2×C4⋊C4—91no—
505C2×C4⋊C4—91no—
506C2×C4⋊C4—98no—
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—91no—
514C2×C22⋊C4—31no—
515C2×C22⋊C4—31no—
516C2×C22⋊C4—91no—
517C2×C22⋊C4—91no—
518C2×C22⋊C4—91no—
519C2×C22⋊C4—91no—
520C2×C22⋊C4—91no—
521C2×C22⋊C4D3211yescharacteristic
522C2×C42—31no—
523C2×C42—31no—
524C2×C42—91no—
525C2×C42—91no—
526C2×C42—91no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—21no—
533C23×C3—24no—
534C23×C3—42no—
535C23×C3—42no—
536C23×C3#23514yes—
537C23×C3#23914yes—
538C23×C3C23×D312yes—
539C23×C3C23×D312yes—
540C23×C3C23×D311yescharacteristic
541C23×C3C23×D311yescharacteristic
542C22×D3—32no—
543C22×D3—32no—
544C22×D3—62no—
545C22×D3—62no—
546C22×D3—62no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—62no—
550C22×D3—62no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C3×Q8—68no—
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—34no—
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—32no—
569C2×C3×C4—32no—
570C2×C3×C4—42no—
571C2×C3×C4—42no—
572C2×C3×C4—68no—
573C2×C3×C4—62no—
574C2×C3×C4—68no—
575C2×C3×C4—62no—
576C2×C3×C4—62no—
577C2×C3×C4—62no—
578C2×C3×C4—62no—
579C2×C3×C4—62no—
580C2×C3×C4—62no—
581C2×C3×C4C23×D312yes—
582C2×C3×C4C23×D312yes—
583C2×C3×C4C23×D312yes—
584C2×C3×C4C23×D312yes—
585#67—68no—
586#67—68no—
587#67—128no—
588C2×Dic3—28no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—28no—
597C2×Dic3—32no—
598C2×Dic3—32no—
599C2×Dic3—32no—
600C2×Dic3—32no—
601C2×Dic3—32no—
602C2×Dic3—32no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—62no—
606C2×Dic3—68no—
607C2×Dic3—62no—
608C2×Dic3—62no—
609C2×Dic3—62no—
610C2×Dic3—68no—
611C2×Dic3—62no—
612C2×Dic3—62no—
613C2×Dic3—62no—
614C2×Dic3—122no—
615C2×Dic3—122no—
616C2×Dic3—128no—
617C2×Dic3—122no—
618C2×Dic3#23714yes—
619C2×Dic3C23×D312yes—
620C2×Dic3C23×D312yes—
621C2×Dic3C23×D312yes—
622C2×Dic3C23×D312yes—
623C2×Dic3C23×D312yes—
624C2×Dic3C23×D312yes—
625C2×Dic3C23×D312yes—
626C2×Dic3C23×D312yes—
627C4×D3—68no—
628C4×D3—68no—
629Dic6—28no—
630C2×C32—24no—
631C2×C32#55214yescomplemented
632C2×C32C22×#4111yescharacteristic
633C2×C32C22×#4111yescharacteristic
634C2×C32C2×2−1+411yescharacteristic
635C3⋊D3—42no—
636C24—91no—
637C24C2×D3211yescharacteristic
638C2×Q8—34no—
639C2×Q8—64no—
640C2×D4—94no—
641C2×D4—184no—
642C22×C4—31no—
643C22×C4—34no—
644C22×C4—34no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—64no—
653C22×C4—64no—
654C22×C4—94no—
655C22×C4—94no—
656C22×C4—91no—
657C22×C4—91no—
658C22×C4—91no—
659C22×C4—184no—
660C22×C4—184no—
661C22×C4C2×D3211yescharacteristic
662C22×C4C2×D3211yescharacteristic
663C4⋊C4—34no—
664C4⋊C4—34no—
665C4⋊C4—34no—
666C4⋊C4—34no—
667C4⋊C4—34no—
668C4⋊C4—94no—
669C4⋊C4—94no—
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⋊C4—94no—
679C22⋊C4—34no—
680C22⋊C4—34no—
681C22⋊C4—94no—
682C22⋊C4—94no—
683C22⋊C4—94no—
684C22⋊C4—94no—
685C22⋊C4—94no—
686C22⋊C4C2×D3214yes—
687C42—34no—
688C42—34no—
689C42—94no—
690C42—94no—
691C42—94no—
692C22×C3—28no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—28no—
698C22×C3—22no—
699C22×C3—24no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—21no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—48no—
706C22×C3C2×#23514yes—
707C22×C3C2×#23512yes—
708C22×C3C2×#23712yes—
709C22×C3C2×#23914yes—
710C22×C3C2×#23912yes—
711C22×C3D3×#4112yes—
712C22×C3#101012yes—
713C22×C3#101012yes—
714C22×C3C24×D311yescharacteristic
715C22×C3C24×D311yescharacteristic
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—62no—
721C2×D3—62no—
722C2×D3—122no—
723C2×D3—122no—
724C2×D3—122no—
725C2×D3—124no—
726C2×D3—124no—
727C2×D3—244no—
728C3×C4—22no—
729C3×C4—22no—
730C3×C4—22no—
731C3×C4—22no—
732C3×C4—34no—
733C3×C4—42no—
734C3×C4—42no—
735C3×C4—62no—
736C3×C4—62no—
737C3×C4—62no—
738C3×C4—62no—
739C3×C4—62no—
740C3×C4—62no—
741C3×C4—62no—
742Dic3—22no—
743Dic3—22no—
744Dic3—22no—
745Dic3—22no—
746Dic3—22no—
747Dic3—22no—
748Dic3—22no—
749Dic3—62no—
750Dic3—62no—
751Dic3—62no—
752Dic3—62no—
753Dic3—62no—
754Dic3—62no—
755Dic3—122no—
756Dic3—122no—
757Dic3—122no—
758Dic3C2×#23714yes—
759C32C2×#55211yescharacteristic, complemented, Sylow
760C23—22no—
761C23—22no—
762C23—92no—
763C23—182no—
764C23—182no—
765C23—182no—
766C23#379914yes—
767C23C22×D3212yes—
768C23C22×D3211yescharacteristic
769Q8—68no—
770D4—188no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—34no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—32no—
779C2×C4—32no—
780C2×C4—32no—
781C2×C4—32no—
782C2×C4—68no—
783C2×C4—68no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—92no—
792C2×C4—92no—
793C2×C4—92no—
794C2×C4—188no—
795C2×C4—188no—
796C2×C4—182no—
797C2×C4—182no—
798C2×C4—182no—
799C2×C4C22×D3212yes—
800C2×C4C22×D3212yes—
801C2×C3—24no—
802C2×C3—24no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—24no—
807C2×C3—44no—
808C2×C3#553114yescomplemented
809C2×C3#564214yescomplemented
810C2×C3C22×#23511yescharacteristic
811C2×C3C22×#23711yescharacteristic
812C2×C3C22×#23911yescharacteristic
813C2×C3C2×D3×#4111yescharacteristic
814C2×C3C2×#101011yescharacteristic
815C2×C3C2×#101011yescharacteristic
816D3—122no—
817D3—122no—
818D3—242no—
819C22—22no—
820C22—22no—
821C22—28no—
822C22—182no—
823C22—182no—
824C22—182no—
825C22—364no—
826C22C2×#379914yes—
827C22C2×#379912yes—
828C22#6430912yes—
829C22D3×#23712yes—
830C22C23×D3211yescharacteristic
831C4—22no—
832C4—22no—
833C4—34no—
834C4—62no—
835C4—62no—
836C4—62no—
837C4—62no—
838C4—62no—
839C4—62no—
840C4—62no—
841C4—182no—
842C4—182no—
843C4—182no—
844C3—21no—
845C3C2×#553111yescharacteristic, complemented
846C3C2×#564211yescharacteristic, complemented
847C2—24no—
848C2—362no—
849C2#1059404514yesdirect product factor
850C2C22×#379911yescharacteristic
851C2C2×#6430911yescharacteristic
852C2C2×D3×#23711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#878C2semidirect
3. C2×C3×#877C2semidirect
5. C22×Dic3⋊Dic3C2semidirect
6. C2×#63957C2semidirect
8. C2×#63888C2semidirect
9. C2×#63869C2semidirect
10. C2×#63868C2semidirect
11. C2×#63848C2semidirect
12. C2×#63845C2semidirect
13. C2×#63845C2semidirect
14. C2×Dic3×Dic6C2semidirect
15. C2×#63836C2semidirect
16. #10594045C2direct (N × H)
40. C3×#878C22semidirect
41. C3×#877C22semidirect
52. C2×Dic3⋊Dic3C22semidirect
56. #63957C22semidirect
61. #63888C22semidirect
62. #63869C22semidirect
63. #63868C22semidirect
64. #63848C22semidirect
65. #63845C22semidirect
66. #63845C22semidirect
67. Dic3×Dic6C22semidirect
68. #63836C22semidirect
94. C2×#878D3semidirect
97. C2×#877D3semidirect
259. #878C2×D3semidirect
262. #877C2×D3semidirect
631. C2×C32#552semidirect
759. C32C2×#552semidirect
808. C2×C3#5531semidirect
809. C2×C3#5642semidirect
845. C3C2×#5531semidirect
846. C3C2×#5642semidirect
849. C2#10594045direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640952
C2×C3×#8782
C2×C3×#8772
C2×#639662
C22×Dic3⋊Dic32
C2×#639572
C2×#639522
C2×#638882
C2×#638692
C2×#638682
C2×#638482
C2×#638452
C2×Dic3×Dic62
C2×#638362
#105940452
C2×#56423
C2×#55313