Finite Group Databasebeta

← C2×#10594349 #11903034

Subgroups — C2×#10594349 #11903034

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×#64103C211yesmaximal, characteristic
2C2×C3×#889C211yesmaximal, characteristic, complemented
3C2×C3×#887C211yesmaximal, characteristic, complemented
4C2×#63897C211yesmaximal, characteristic
5C2×#63894C211yesmaximal, characteristic
6C2×#63888C211yesmaximal, characteristic, complemented
7C2×#63888C211yesmaximal, characteristic, complemented
8C2×#63883C211yesmaximal, characteristic, complemented
9C2×#63874C211yesmaximal, characteristic, complemented
10C2×#63868C211yesmaximal, characteristic, complemented
11C2×#63868C211yesmaximal, characteristic, complemented
12C2×#63867C211yesmaximal, characteristic, complemented
13C2×#63847C211yesmaximal, characteristic, complemented
14C2×#63836C211yesmaximal, characteristic, complemented
15C2×#63836C211yesmaximal, characteristic, complemented
16#10594349C2116yesmaximal, direct product factor
17C2×#5693—31nomaximal
18C2×#5581—31nomaximal
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C22×#624C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3752C2211yescharacteristic
29C2×#3750C2211yescharacteristic
30#64103C2218yes—
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2211yescharacteristic
40C2×C3×C4×Dic3C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C3×#889C2218yescomplemented
43C3×#887C2218yescomplemented
44C2×#3724C2211yescharacteristic
45C2×#3724C2211yescharacteristic
46C2×#3724C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63897C2218yes—
58#63894C2218yes—
59#63888C2218yescomplemented
60#63888C2218yescomplemented
61#63883C2218yescomplemented
62#63874C2218yescomplemented
63#63868C2218yescomplemented
64#63868C2218yescomplemented
65#63867C2218yescomplemented
66#63847C2218yescomplemented
67#63836C2218yescomplemented
68#63836C2218yescomplemented
69C2×C3×#125—31no—
70C2×C3×C4×Q8—31no—
71C2×#946—31no—
72C2×#946—31no—
73#5693—316no—
74#5581—316no—
75C2×#898—31no—
76C2×#898—31no—
77C2×#896—31no—
78C2×#896—31no—
79C2×#894—31no—
80C2×#894—31no—
81C2×#894—31no—
82C2×#894—31no—
83C2×#894—61no—
84C2×#893—31no—
85C2×#892—31no—
86C2×#892—31no—
87C2×D3×C4⋊C4—31no—
88C2×D3×C4⋊C4—31no—
89C2×#889—31no—
90C2×#889—31no—
91C2×#889—31no—
92C2×#889D311yescharacteristic, complemented
93C2×#887D311yescharacteristic, complemented
94C2×#876—31no—
95C2×#876—31no—
96C2×C4×D12—31no—
97C2×#872—31no—
98C2×#872—31no—
99C2×#872—31no—
100C2×#872—31no—
101C2×#870—31no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C2×C4⋊(C3⋊D3)—24no—
110C2×C4⋊(C3⋊D3)C2314yes—
111C2×C4×C3⋊D3—24no—
112C2×C4×C3⋊D3C2314yes—
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×C3×Dic6—24no—
122C2×C3×Dic6C2314yes—
123C2×#624—24no—
124C2×#624—24no—
125C2×#624—24no—
126C2×#624C2314yes—
127C2×#624C2314yes—
128C2×#624C2314yes—
129C32×C4⋊C4C2314yes—
130#3752C2314yes—
131#3752C2314yes—
132#3752C2314yes—
133#3750C2314yes—
134C3×C4⋊Dic3C2314yes—
135C3×Dic3⋊C4C2314yes—
136C3×Dic3⋊C4C2314yes—
137C3×Dic3⋊C4C2314yes—
138C3×Dic3⋊C4C2314yes—
139C3×Dic3⋊C4C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×C4×Dic3C2314yes—
142C3×C4×Dic3C2314yes—
143C3×C4×Dic3C2314yes—
144C3×C4×Dic3C2314yes—
145#3724C2314yes—
146#3724C2314yes—
147#3724C2314yes—
148Dic3⋊Dic3C2314yes—
149Dic3⋊Dic3C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152#3722C2314yes—
153#3722C2314yes—
154#3722C2314yes—
155#3722C2314yes—
156#3722C2314yes—
157Dic32C2314yes—
158C2×#552—91noSylow
159C22×C3×Q8—31no—
160C22×D12—31no—
161C22×D12—31no—
162C22×D12—61no—
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—31no—
170C22×C4×D3—31no—
171C22×C4×D3—61no—
172C22×Dic6C2×D311yescharacteristic
173C3×#125—38no—
174C3×C4×Q8—38no—
175C2×C3×C4⋊C4—21no—
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×C4⋊C4—31no—
183C2×C3×C4⋊C4C2×D311yescharacteristic
184C2×C3×C4⋊C4C2×D311yescharacteristic
185C2×C3×C42—31no—
186C2×C3×C42—31no—
187C2×C3×C42—31no—
188C2×C3×C42—31no—
189#946—38no—
190#946—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—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—61no—
208C2×(C2×D3)⋊C4—61no—
209C2×(C2×D3)⋊C4—61no—
210C2×C4⋊Dic3—31no—
211C2×C4⋊Dic3—31no—
212C2×C4⋊Dic3—31no—
213C2×C4⋊Dic3—31no—
214C2×C4⋊Dic3C2×D311yescharacteristic
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—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×Dic3C2×D311yescharacteristic
237C2×C4×Dic3C2×D311yescharacteristic
238C2×C4×Dic3C2×D311yescharacteristic
239C2×C4×Dic3C2×D311yescharacteristic
240#898—38no—
241#898—38no—
242#896—38no—
243#896—38no—
244#894—38no—
245#894—38no—
246#894—38no—
247#894—38no—
248#894—68no—
249#893—38no—
250#892—38no—
251#892—38no—
252D3×C4⋊C4—38no—
253D3×C4⋊C4—38no—
254#889—38no—
255#889—38no—
256#889—38no—
257#889C2×D318yescomplemented
258#887C2×D318yescomplemented
259#876—38no—
260#876—38no—
261C4×D12—38no—
262#872—38no—
263#872—38no—
264#872—38no—
265#872—38no—
266#870—38no—
267C23×C32C2411yescharacteristic
268C22×C3⋊D3—22no—
269C22×C3⋊D3—22no—
270C22×C3⋊D3—22no—
271C22×C3⋊D3—22no—
272C22×C3⋊D3—22no—
273C22×C3⋊D3#4114yes—
274C22×C3⋊D3C2412yes—
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⋊Dic3C2412yes—
285C2×C3⋊Dic3C2412yes—
286C4⋊(C3⋊D3)—28no—
287C4×C3⋊D3—28no—
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—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—
303C2×C3×Dic3C2412yes—
304C3×Dic6—28no—
305#624—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—31no—
319C2×C4×D4—91no—
320C2×#117—91no—
321C2×#117—91no—
322C2×#117—91no—
323C22×C4⋊C4—91no—
324C23×D3—31no—
325C23×D3—31no—
326C23×D3—31no—
327C23×D3—31no—
328C23×D3—61no—
329C23×D3—61no—
330C2×C3×Q8—34no—
331C2×C3×Q8—64no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—21no—
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—31no—
342C22×C3×C4—31no—
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3C22×D311yescharacteristic
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C2×D12—34no—
364C2×D12—34no—
365C2×D12—64no—
366C2×D12—64no—
367C2×D12—64no—
368C2×D12—124no—
369C2×C4×D3—34no—
370C2×C4×D3—34no—
371C2×C4×D3—34no—
372C2×C4×D3—34no—
373C2×C4×D3—34no—
374C2×C4×D3—34no—
375C2×C4×D3—34no—
376C2×C4×D3—34no—
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—64no—
385C2×C4×D3—64no—
386C2×C4×D3—124no—
387C2×Dic6—24no—
388C2×Dic6C22×D314yes—
389C3×C4⋊C4—24no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—34no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—34no—
395C3×C4⋊C4—34no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4C22×D314yes—
398C3×C4⋊C4C22×D314yes—
399C3×C42—34no—
400C3×C42—34no—
401C3×C42—34no—
402C3×C42—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—34no—
414(C2×D3)⋊C4—34no—
415(C2×D3)⋊C4—34no—
416(C2×D3)⋊C4—34no—
417(C2×D3)⋊C4—34no—
418(C2×D3)⋊C4—34no—
419(C2×D3)⋊C4—64no—
420(C2×D3)⋊C4—64no—
421(C2×D3)⋊C4—64no—
422C4⋊Dic3—34no—
423C4⋊Dic3—34no—
424C4⋊Dic3—34no—
425C4⋊Dic3—34no—
426C4⋊Dic3C22×D314yes—
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—34no—
439Dic3⋊C4—64no—
440Dic3⋊C4C22×D314yes—
441Dic3⋊C4C22×D314yes—
442Dic3⋊C4C22×D314yes—
443Dic3⋊C4C22×D314yes—
444Dic3⋊C4C22×D314yes—
445Dic3⋊C4C22×D314yes—
446C4×Dic3—34no—
447C4×Dic3—34no—
448C4×Dic3C22×D314yes—
449C4×Dic3C22×D314yes—
450C4×Dic3C22×D314yes—
451C4×Dic3C22×D314yes—
452C22×C32C2×#4112yes—
453C22×C32C2×#4112yes—
454C22×C322−1+412yes—
455C22×C32C2511yescharacteristic
456C2×C3⋊D3—28no—
457C2×C3⋊D3—22no—
458C2×C3⋊D3—22no—
459C2×C3⋊D3—22no—
460C2×C3⋊D3—22no—
461C2×C3⋊D3—22no—
462C2×C3⋊D3—44no—
463C2×C3⋊D3C2×#4114yes—
464C32×C4—22no—
465C32×C4—22no—
466C32×C4—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—91no—
480C23×C4—91no—
481C23×C4—91no—
482C23×C4—91no—
483#126—98no—
484#126—98no—
485#125—38no—
486#125—98no—
487#125—98no—
488#123—98no—
489#123—98no—
490C22⋊Q8—98no—
491C22⋊Q8—98no—
492C4×Q8—38no—
493C4×D4—98no—
494#117—98no—
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—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×C4⋊C4D3211yescharacteristic
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×C22⋊C4—91no—
521C2×C22⋊C4—91no—
522C2×C42—31no—
523C2×C42—31no—
524C2×C42—31no—
525C2×C42—31no—
526C2×C42—91no—
527C23×C3—21no—
528C23×C3C23×D311yescharacteristic
529C23×C3C23×D311yescharacteristic
530C22×D3—34no—
531C22×D3—34no—
532C22×D3—32no—
533C22×D3—32no—
534C22×D3—32no—
535C22×D3—32no—
536C22×D3—64no—
537C22×D3—62no—
538C22×D3—62no—
539C22×D3—62no—
540C22×D3—62no—
541C22×D3—62no—
542C22×D3—62no—
543C22×D3—62no—
544C22×D3—62no—
545C22×D3—62no—
546C22×D3—62no—
547C22×D3—62no—
548C22×D3—62no—
549C22×D3—122no—
550C22×D3—122no—
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—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—34no—
565C2×C3×C4—32no—
566C2×C3×C4—32no—
567C2×C3×C4—32no—
568C2×C3×C4—32no—
569C2×C3×C4—32no—
570C2×C3×C4—32no—
571C2×C3×C4—32no—
572C2×C3×C4—32no—
573C2×C3×C4—42no—
574C2×C3×C4—42no—
575C2×C3×C4—42no—
576C2×C3×C4—62no—
577C2×C3×C4—62no—
578C2×C3×C4—62no—
579C2×C3×C4—62no—
580C2×C3×C4—62no—
581C2×C3×C4—62no—
582C2×C3×C4—62no—
583C2×C3×C4C23×D312yes—
584C2×C3×C4C23×D312yes—
585C2×C3×C4C23×D312yes—
586C2×C3×C4C23×D312yes—
587C2×C3×C4C23×D312yes—
588C2×C3×C4C23×D312yes—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—22no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—32no—
597C2×Dic3—32no—
598C2×Dic3—32no—
599C2×Dic3—32no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—62no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3—62no—
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—
616C2×Dic3C23×D312yes—
617D12—68no—
618D12—68no—
619D12—128no—
620C4×D3—68no—
621C4×D3—68no—
622C4×D3—68no—
623C4×D3—68no—
624C4×D3—68no—
625C4×D3—68no—
626C4×D3—68no—
627C4×D3—68no—
628C4×D3—128no—
629Dic6—28no—
630C2×C32#55214yescomplemented
631C2×C32C22×#4111yescharacteristic
632C2×C32C22×#4111yescharacteristic
633C2×C32C2×2−1+411yescharacteristic
634C3⋊D3—24no—
635C3⋊D3—42no—
636C24—91no—
637C24—91no—
638C2×Q8—34no—
639C2×Q8—64no—
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—31no—
650C22×C4—94no—
651C22×C4—94no—
652C22×C4—94no—
653C22×C4—91no—
654C22×C4—91no—
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—94no—
680C22⋊C4—94no—
681C22⋊C4—94no—
682C22⋊C4—94no—
683C22⋊C4—94no—
684C22⋊C4—94no—
685C22⋊C4—94no—
686C22⋊C4—94no—
687C42—34no—
688C42—34no—
689C42—34no—
690C42—34no—
691C42—94no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—21no—
696C22×C3C2×#23512yes—
697C22×C3#100712yes—
698C22×C3#100712yes—
699C22×C3D3×#4112yes—
700C22×C3D3×#4112yes—
701C22×C3D3×#4112yes—
702C22×C3C24×D311yescharacteristic
703C22×C3C24×D311yescharacteristic
704C2×D3—34no—
705C2×D3—34no—
706C2×D3—64no—
707C2×D3—68no—
708C2×D3—62no—
709C2×D3—62no—
710C2×D3—62no—
711C2×D3—62no—
712C2×D3—68no—
713C2×D3—62no—
714C2×D3—62no—
715C2×D3—62no—
716C2×D3—62no—
717C2×D3—62no—
718C2×D3—62no—
719C2×D3—128no—
720C2×D3—122no—
721C2×D3—122no—
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—22no—
733C3×C4—22no—
734C3×C4—34no—
735C3×C4—42no—
736C3×C4—42no—
737C3×C4—42no—
738C3×C4—62no—
739C3×C4—62no—
740C3×C4—62no—
741C3×C4—62no—
742C3×C4—62no—
743C3×C4—62no—
744C3×C4—62no—
745Dic3—22no—
746Dic3—22no—
747Dic3—22no—
748Dic3—22no—
749Dic3—22no—
750Dic3—22no—
751Dic3—22no—
752Dic3—62no—
753Dic3—62no—
754Dic3—62no—
755Dic3—62no—
756Dic3—122no—
757Dic3—122no—
758Dic3C2×#23514yes—
759C32C2×#55211yescharacteristic, complemented, Sylow
760C23—94no—
761C23—92no—
762C23—92no—
763C23—182no—
764C23—182no—
765C23—182no—
766C23—182no—
767C23—182no—
768C23C22×D3211yescharacteristic
769Q8—68no—
770D4—188no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—34no—
775C2×C4—32no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—32no—
779C2×C4—32no—
780C2×C4—32no—
781C2×C4—32no—
782C2×C4—32no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—62no—
789C2×C4—62no—
790C2×C4—92no—
791C2×C4—92no—
792C2×C4—188no—
793C2×C4—188no—
794C2×C4—188no—
795C2×C4—188no—
796C2×C4—182no—
797C2×C4—182no—
798C2×C4C22×D3212yes—
799C2×C4C22×D3212yes—
800C2×C4C22×D3212yes—
801C2×C3—24no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3#558114yescomplemented
806C2×C3#569314yescomplemented
807C2×C3C22×#23511yescharacteristic
808C2×C3C2×#100711yescharacteristic
809C2×C3C2×#100711yescharacteristic
810C2×C3C2×D3×#4111yescharacteristic
811C2×C3C2×D3×#4111yescharacteristic
812C2×C3C2×D3×#4111yescharacteristic
813D3—64no—
814D3—64no—
815D3—124no—
816D3—122no—
817D3—122no—
818D3—242no—
819C22—94no—
820C22—188no—
821C22—182no—
822C22—182no—
823C22—182no—
824C22—182no—
825C22—182no—
826C22—364no—
827C22D3×#23512yes—
828C22#6431212yes—
829C22#6431612yes—
830C22C23×D3211yescharacteristic
831C4—22no—
832C4—22no—
833C4—22no—
834C4—34no—
835C4—62no—
836C4—62no—
837C4—62no—
838C4—62no—
839C4—62no—
840C4—62no—
841C4—62no—
842C4—182no—
843C4—182no—
844C3—21no—
845C3C2×#558111yescharacteristic, complemented
846C3C2×#569311yescharacteristic, complemented
847C2—184no—
848C2—362no—
849C2#1059434914yesdirect product factor
850C2C2×D3×#23511yescharacteristic
851C2C2×#6431211yescharacteristic
852C2C2×#6431611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
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
2. C2×C3×#889C2semidirect
3. C2×C3×#887C2semidirect
6. C2×#63888C2semidirect
7. C2×#63888C2semidirect
8. C2×#63883C2semidirect
9. C2×#63874C2semidirect
10. C2×#63868C2semidirect
11. C2×#63868C2semidirect
12. C2×#63867C2semidirect
13. C2×#63847C2semidirect
14. C2×#63836C2semidirect
15. C2×#63836C2semidirect
16. #10594349C2direct (N × H)
42. C3×#889C22semidirect
43. C3×#887C22semidirect
59. #63888C22semidirect
60. #63888C22semidirect
61. #63883C22semidirect
62. #63874C22semidirect
63. #63868C22semidirect
64. #63868C22semidirect
65. #63867C22semidirect
66. #63847C22semidirect
67. #63836C22semidirect
68. #63836C22semidirect
92. C2×#889D3semidirect
93. C2×#887D3semidirect
257. #889C2×D3semidirect
258. #887C2×D3semidirect
630. C2×C32#552semidirect
759. C32C2×#552semidirect
805. C2×C3#5581semidirect
806. C2×C3#5693semidirect
845. C3C2×#5581semidirect
846. C3C2×#5693semidirect
849. C2#10594349direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641032
C2×C3×#8892
C2×C3×#8872
C2×#638972
C2×#638942
C2×#638882
C2×#638832
C2×#638742
C2×#638682
C2×#638672
C2×#638472
C2×#638362
#105943492
C2×#56933
C2×#55813