Finite Group Databasebeta

← C2×#10593872 #11903025

Subgroups — C2×#10593872 #11903025

Order 1152.

2413 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic, complemented
2C2×C3×#872C211yesmaximal, characteristic, complemented
3C2×C3×#870C211yesmaximal, characteristic, complemented
4C2×#63904C211yesmaximal, characteristic
5C2×#63895C211yesmaximal, characteristic, complemented
6C2×#63883C211yesmaximal, characteristic, complemented
7C2×#63867C211yesmaximal, characteristic, complemented
8C2×#63862C211yesmaximal, characteristic, complemented
9C2×#63858C211yesmaximal, characteristic, complemented
10C2×#63854C211yesmaximal, characteristic
11C2×#63853C211yesmaximal, characteristic
12C2×#63851C211yesmaximal, characteristic, complemented
13C2×#63846C211yesmaximal, characteristic, complemented
14C2×#63838C211yesmaximal, characteristic, complemented
15C2×#63836C211yesmaximal, characteristic, complemented
16#10593872C2116yesmaximal, direct product factor
17C2×#5693—31nomaximal
18C2×#5529—31nomaximal
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C22×#626C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×C32×C42C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30C2×C4×C3⋊Dic3C2211yescharacteristic
31#64081C2218yescomplemented
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43C3×#872C2218yescomplemented
44C3×#870C2218yescomplemented
45C2×#3724C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63904C2218yes—
58#63895C2218yescomplemented
59#63883C2218yescomplemented
60#63867C2218yescomplemented
61#63862C2218yescomplemented
62#63858C2218yescomplemented
63#63854C2218yes—
64#63853C2218yes—
65#63851C2218yescomplemented
66#63846C2218yescomplemented
67#63838C2218yescomplemented
68#63836C2218yescomplemented
69C2×C3×#125—31no—
70C2×C3×#117—31no—
71C2×C4×#67—31no—
72C2×#924—31no—
73#5693—316no—
74#5529—316no—
75C2×#898—31no—
76C2×#898—31no—
77C2×#897—31no—
78C2×#896—31no—
79C2×#896—31no—
80C2×#894—31no—
81C2×#894—31no—
82C2×#893—31no—
83C2×#892—31no—
84C2×D3×C4⋊C4—31no—
85C2×D3×C4⋊C4—31no—
86C2×#890—31no—
87C2×#889—31no—
88C2×#889—31no—
89C2×#887—31no—
90C2×#887—31no—
91C2×#883—31no—
92C2×#883—31no—
93C2×#879—31no—
94C2×#879—31no—
95C2×#872—31no—
96C2×#872—31no—
97C2×#872—31no—
98C2×#872—61no—
99C2×#872D311yescharacteristic, complemented
100C2×#870—31no—
101C2×#870D311yescharacteristic, complemented
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⋊D3C2314yes—
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C2×C3×C4×D3—24no—
120C2×C3×C4×D3C2314yes—
121C2×#627—24no—
122C2×#627C2314yes—
123C2×#626—24no—
124C2×#626C2314yes—
125C2×#624—24no—
126C2×#624—24no—
127C2×#624C2314yes—
128C2×#624C2314yes—
129C32×C42C2314yes—
130#3752C2314yes—
131#3752C2314yes—
132#3750C2314yes—
133#3750C2314yes—
134C4×C3⋊Dic3C2314yes—
135C3×(C2×D3)⋊C4C2314yes—
136C3×(C2×D3)⋊C4C2314yes—
137C3×C4⋊Dic3C2314yes—
138C3×C4⋊Dic3C2314yes—
139C3×Dic3⋊C4C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×Dic3⋊C4C2314yes—
142C3×Dic3⋊C4C2314yes—
143C3×Dic3⋊C4C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×C4×Dic3C2314yes—
146#3724C2314yes—
147Dic3⋊Dic3C2314yes—
148Dic3⋊Dic3C2314yes—
149Dic3⋊Dic3C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152#3722C2314yes—
153(C2×D3)⋊Dic3C2314yes—
154(C2×D3)⋊Dic3C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156Dic32C2314yes—
157Dic32C2314yes—
158C2×#552—91noSylow
159C23×C3×C4—31no—
160C22×#67—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—61no—
169C22×C4×D3C2×D311yescharacteristic
170C22×Dic6—31no—
171C22×Dic6—31no—
172C3×#125—38no—
173C3×#117—38no—
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—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C42—21no—
185C2×C3×C42—31no—
186C2×C3×C42C2×D311yescharacteristic
187C2×C3×C42C2×D311yescharacteristic
188C2×#217—31no—
189C2×#217—31no—
190C2×#217—31no—
191C4×#67—38no—
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—61no—
202C2×(C2×D3)⋊C4—61no—
203C2×(C2×D3)⋊C4C2×D311yescharacteristic
204C2×(C2×D3)⋊C4C2×D311yescharacteristic
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3C2×D311yescharacteristic
211C2×C4⋊Dic3C2×D311yescharacteristic
212#924—38no—
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—31no—
224C2×Dic3⋊C4—61no—
225C2×Dic3⋊C4—61no—
226C2×Dic3⋊C4C2×D311yescharacteristic
227C2×Dic3⋊C4C2×D311yescharacteristic
228C2×Dic3⋊C4C2×D311yescharacteristic
229C2×Dic3⋊C4C2×D311yescharacteristic
230C2×Dic3⋊C4C2×D311yescharacteristic
231C2×Dic3⋊C4C2×D311yescharacteristic
232C2×C4×Dic3—31no—
233C2×C4×Dic3—31no—
234C2×C4×Dic3—31no—
235C2×C4×Dic3—31no—
236C2×C4×Dic3—31no—
237C2×C4×Dic3—31no—
238C2×C4×Dic3—61no—
239C2×C4×Dic3C2×D311yescharacteristic
240#898—38no—
241#898—38no—
242#897—38no—
243#896—38no—
244#896—38no—
245#894—38no—
246#894—38no—
247#893—38no—
248#892—38no—
249D3×C4⋊C4—38no—
250D3×C4⋊C4—38no—
251#890—38no—
252#889—38no—
253#889—38no—
254#887—38no—
255#887—38no—
256#883—38no—
257#883—38no—
258#879—38no—
259#879—38no—
260#872—38no—
261#872—38no—
262#872—38no—
263#872—68no—
264#872C2×D318yescomplemented
265#870—38no—
266#870C2×D318yescomplemented
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—22no—
285C2×C3⋊Dic3C2412yes—
286C2×C3⋊Dic3C2412yes—
287C2×C3⋊Dic3C2412yes—
288C4×C3⋊D3—28no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—22no—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—22no—
294C2×C3×Dic3—22no—
295C2×C3×Dic3#4114yes—
296C2×C3×Dic3C2412yes—
297C2×C3×Dic3C2412yes—
298C2×C3×Dic3C2412yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2412yes—
303C3×C4×D3—28no—
304#627—28no—
305#626—28no—
306#624—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—31no—
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×C4—34no—
340C22×C3×C4—64no—
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C2×#67—34no—
348C2×#67—64no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—61no—
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—24no—
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—68no—
381C2×C4×D3—64no—
382C2×C4×D3C22×D314yes—
383C2×Dic6—34no—
384C2×Dic6—34no—
385C2×Dic6—64no—
386C2×Dic6—64no—
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⋊C4—34no—
395C3×C22⋊C4—34no—
396C3×C22⋊C4—34no—
397C3×C42—24no—
398C3×C42—34no—
399C3×C42C22×D314yes—
400C3×C42C22×D314yes—
401#217—34no—
402#217—34no—
403#217—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)⋊C4C22×D314yes—
416(C2×D3)⋊C4C22×D314yes—
417C4⋊Dic3—34no—
418C4⋊Dic3—34no—
419C4⋊Dic3—34no—
420C4⋊Dic3—34no—
421C4⋊Dic3—34no—
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—34no—
434Dic3⋊C4—34no—
435Dic3⋊C4—64no—
436Dic3⋊C4—64no—
437Dic3⋊C4C22×D314yes—
438Dic3⋊C4C22×D314yes—
439Dic3⋊C4C22×D314yes—
440Dic3⋊C4C22×D314yes—
441Dic3⋊C4C22×D314yes—
442Dic3⋊C4C22×D314yes—
443C4×Dic3—34no—
444C4×Dic3—34no—
445C4×Dic3—34no—
446C4×Dic3—34no—
447C4×Dic3—34no—
448C4×Dic3—34no—
449C4×Dic3—64no—
450C4×Dic3C22×D314yes—
451C22×C32C2×#4112yes—
452C22×C32C2×#4112yes—
453C22×C322−1+412yes—
454C22×C32C2511yescharacteristic
455C2×C3⋊D3—28no—
456C2×C3⋊D3—22no—
457C2×C3⋊D3—22no—
458C2×C3⋊D3C2×#4114yes—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—44no—
463C32×C4—22no—
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×Dic3C2×#4114yes—
476C22×Q8—91no—
477C22×D4—91no—
478C23×C4—31no—
479C23×C4—91no—
480C23×C4—91no—
481C23×C4—91no—
482#126—98no—
483#126—98no—
484#125—38no—
485#125—98no—
486#125—98no—
487#123—98no—
488#123—98no—
489C22⋊Q8—98no—
490C22⋊Q8—98no—
491C4×Q8—98no—
492C4×D4—98no—
493#117—38no—
494#117—98no—
495#117—98no—
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—31no—
504C2×C4⋊C4—98no—
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×C22⋊C4—31no—
514C2×C22⋊C4—31no—
515C2×C22⋊C4—91no—
516C2×C22⋊C4—91no—
517C2×C22⋊C4—91no—
518C2×C22⋊C4—91no—
519C2×C22⋊C4—91no—
520C2×C22⋊C4—91no—
521C2×C42—31no—
522C2×C42—91no—
523C2×C42—91no—
524C2×C42—91no—
525C2×C42D3211yescharacteristic
526C23×C3—21no—
527C23×C3—32no—
528C23×C3—62no—
529C23×C3—62no—
530C23×C3—62no—
531C23×C3C23×D311yescharacteristic
532C23×C3C23×D311yescharacteristic
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—34no—
537C22×D3—34no—
538C22×D3—32no—
539C22×D3—32no—
540C22×D3—64no—
541C22×D3—62no—
542C22×D3—62no—
543C22×D3—62no—
544C22×D3—62no—
545C22×D3—62no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3C23×D312yes—
549C2×C3×C4—24no—
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—22no—
558C2×C3×C4—22no—
559C2×C3×C4—34no—
560C2×C3×C4—32no—
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—42no—
568C2×C3×C4—42no—
569C2×C3×C4—68no—
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×C4C23×D312yes—
577C2×C3×C4C23×D312yes—
578C2×C3×C4C23×D312yes—
579C2×C3×C4C23×D312yes—
580C2×C3×C4C23×D312yes—
581C2×C3×C4C23×D312yes—
582#67—68no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—62no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—64no—
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#23514yes—
608C2×Dic3C23×D312yes—
609C2×Dic3C23×D312yes—
610C2×Dic3C23×D312yes—
611C2×Dic3C23×D312yes—
612C2×Dic3C23×D312yes—
613C2×Dic3C23×D312yes—
614C2×Dic3C23×D312yes—
615D12—68no—
616C4×D3—28no—
617C4×D3—68no—
618C4×D3—68no—
619C4×D3—68no—
620C4×D3—68no—
621C4×D3—68no—
622C4×D3—616no—
623C4×D3—68no—
624Dic6—68no—
625Dic6—68no—
626C2×C32#55214yescomplemented
627C2×C32C22×#4111yescharacteristic
628C2×C32C22×#4111yescharacteristic
629C2×C32C2×2−1+411yescharacteristic
630C3⋊D3—24no—
631C3×D3—42no—
632C24—31no—
633C24—91no—
634C2×Q8—94no—
635C2×Q8—184no—
636C2×D4—94no—
637C2×D4—184no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—34no—
646C22×C4—64no—
647C22×C4—94no—
648C22×C4—94no—
649C22×C4—91no—
650C22×C4—91no—
651C22×C4—91no—
652C22×C4—94no—
653C22×C4—184no—
654C22×C4—184no—
655C22×C4—184no—
656C22×C4C2×D3211yescharacteristic
657C22×C4C2×D3211yescharacteristic
658C22×C4C2×D3211yescharacteristic
659C4⋊C4—34no—
660C4⋊C4—34no—
661C4⋊C4—34no—
662C4⋊C4—34no—
663C4⋊C4—34no—
664C4⋊C4—34no—
665C4⋊C4—34no—
666C4⋊C4—34no—
667C4⋊C4—94no—
668C4⋊C4—94no—
669C4⋊C4—94no—
670C4⋊C4—94no—
671C4⋊C4—94no—
672C4⋊C4—94no—
673C4⋊C4—94no—
674C4⋊C4—94no—
675C22⋊C4—34no—
676C22⋊C4—34no—
677C22⋊C4—94no—
678C22⋊C4—94no—
679C22⋊C4—94no—
680C22⋊C4—94no—
681C22⋊C4—94no—
682C22⋊C4—94no—
683C42—34no—
684C42—94no—
685C42—94no—
686C42—94no—
687C42C2×D3214yes—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—21no—
692C22×C3—62no—
693C22×C3—62no—
694C22×C3—62no—
695C22×C3—124no—
696C22×C3C2×#23512yes—
697C22×C3#100712yes—
698C22×C3D3×#4112yes—
699C22×C3D3×#4112yes—
700C22×C3D3×#4112yes—
701C22×C3#101012yes—
702C22×C3C24×D311yescharacteristic
703C22×C3C24×D311yescharacteristic
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—34no—
708C2×D3—34no—
709C2×D3—44no—
710C2×D3—64no—
711C2×D3—68no—
712C2×D3—62no—
713C2×D3—62no—
714C2×D3—62no—
715C2×D3—62no—
716C2×D3—68no—
717C2×D3—122no—
718C2×D3—122no—
719C2×D3—128no—
720C3×C4—24no—
721C3×C4—22no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—34no—
728C3×C4—42no—
729C3×C4—42no—
730C3×C4—62no—
731C3×C4—62no—
732C3×C4—62no—
733C3×C4—62no—
734C3×C4—62no—
735C3×C4—62no—
736Dic3—22no—
737Dic3—22no—
738Dic3—22no—
739Dic3—22no—
740Dic3—22no—
741Dic3—22no—
742Dic3—64no—
743Dic3—62no—
744Dic3—62no—
745Dic3—62no—
746Dic3—62no—
747Dic3—62no—
748Dic3—62no—
749Dic3—122no—
750Dic3—122no—
751Dic3C2×#23514yes—
752C32C2×#55211yescharacteristic, complemented, Sylow
753C23—32no—
754C23—62no—
755C23—62no—
756C23—62no—
757C23—94no—
758C23—92no—
759C23—182no—
760C23—182no—
761C23C22×D3211yescharacteristic
762Q8—188no—
763D4—188no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—34no—
768C2×C4—32no—
769C2×C4—32no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—32no—
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—188no—
787C2×C4—188no—
788C2×C4—182no—
789C2×C4—182no—
790C2×C4—182no—
791C2×C4C22×D3212yes—
792C2×C4C22×D3212yes—
793C2×C4C22×D3212yes—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—24no—
798C2×C3—122no—
799C2×C3#552914yescomplemented
800C2×C3#569314yescomplemented
801C2×C3C22×#23511yescharacteristic
802C2×C3C2×#100711yescharacteristic
803C2×C3C2×D3×#4111yescharacteristic
804C2×C3C2×D3×#4111yescharacteristic
805C2×C3C2×D3×#4111yescharacteristic
806C2×C3C2×#101011yescharacteristic
807D3—42no—
808D3—64no—
809D3—64no—
810D3—124no—
811C22—62no—
812C22—62no—
813C22—62no—
814C22—94no—
815C22—124no—
816C22—182no—
817C22—182no—
818C22—188no—
819C22#6429712yes—
820C22D3×#23512yes—
821C22#6430612yes—
822C22C23×D3211yescharacteristic
823C4—22no—
824C4—22no—
825C4—22no—
826C4—34no—
827C4—62no—
828C4—62no—
829C4—62no—
830C4—62no—
831C4—62no—
832C4—62no—
833C4—182no—
834C4—182no—
835C4—182no—
836C3—21no—
837C3C2×#552911yescharacteristic, complemented
838C3C2×#569311yescharacteristic, complemented
839C2—122no—
840C2—184no—
841C2#1059387214yesdirect product factor
842C2C2×#6429711yescharacteristic
843C2C2×D3×#23511yescharacteristic
844C2C2×#6430611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×#626C22
hypercenterC2×C42D32
hypocenterC32C2×#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64081C2semidirect
2. C2×C3×#872C2semidirect
3. C2×C3×#870C2semidirect
5. C2×#63895C2semidirect
6. C2×#63883C2semidirect
7. C2×#63867C2semidirect
8. C2×#63862C2semidirect
9. C2×#63858C2semidirect
12. C2×#63851C2semidirect
13. C2×#63846C2semidirect
14. C2×#63838C2semidirect
15. C2×#63836C2semidirect
16. #10593872C2direct (N × H)
31. #64081C22semidirect
43. C3×#872C22semidirect
44. C3×#870C22semidirect
58. #63895C22semidirect
59. #63883C22semidirect
60. #63867C22semidirect
61. #63862C22semidirect
62. #63858C22semidirect
65. #63851C22semidirect
66. #63846C22semidirect
67. #63838C22semidirect
68. #63836C22semidirect
99. C2×#872D3semidirect
101. C2×#870D3semidirect
264. #872C2×D3semidirect
266. #870C2×D3semidirect
626. C2×C32#552semidirect
752. C32C2×#552semidirect
799. C2×C3#5529semidirect
800. C2×C3#5693semidirect
837. C3C2×#5529semidirect
838. C3C2×#5693semidirect
841. C2#10593872direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640812
C2×C3×#8722
C2×C3×#8702
C2×#639042
C2×#638952
C2×#638832
C2×#638672
C2×#638622
C2×#638582
C2×#638542
C2×#638532
C2×#638512
C2×#638462
C2×#638382
C2×#638362
#105938722
C2×#56933
C2×#55293