Finite Group Databasebeta

← C2×#10595117 #11903057

Subgroups — C2×#10595117 #11903057

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×#64144C211yesmaximal, characteristic
2C2×C3×#935C211yesmaximal, characteristic
3C2×C3×D4×Dic3C211yesmaximal, characteristic
4C22×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
5C2×#63964C211yesmaximal, characteristic, complemented
6C2×#63964C211yesmaximal, characteristic, complemented
7C2×#63957C211yesmaximal, characteristic, complemented
8C2×#63956C211yesmaximal, characteristic, complemented
9C2×#63956C211yesmaximal, characteristic, complemented
10C2×#63955C211yesmaximal, characteristic, complemented
11C2×#63955C211yesmaximal, characteristic, complemented
12#10595117C2116yesmaximal, direct product factor
13C2×#63867C211yesmaximal, characteristic, complemented
14C2×#63847C211yesmaximal, characteristic, complemented
15C2×#63846C211yesmaximal, characteristic, complemented
16C2×#63837C211yesmaximal, characteristic, complemented
17C2×#5650—31nomaximal
18C2×#5541—31nomaximal
19C22×C32×D4C2211yescharacteristic
20C23×C3⋊Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C22×#627C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28#64144C2218yes—
29C2×#3750C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C3×#935C2218yes—
37C3×D4×Dic3C2218yes—
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×#3724C2211yescharacteristic
43C2×#3724C2211yescharacteristic
44C2×#3724C2211yescharacteristic
45C2×Dic3⋊Dic3C2211yescharacteristic
46C2×Dic3⋊Dic3C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×Dic3⋊Dic3C2218yescomplemented
54#63964C2218yescomplemented
55#63964C2218yescomplemented
56#63957C2218yescomplemented
57#63956C2218yescomplemented
58#63956C2218yescomplemented
59#63955C2218yescomplemented
60#63955C2218yescomplemented
61C2×Dic32C2211yescharacteristic
62C2×Dic32C2211yescharacteristic
63C2×Dic32C2211yescharacteristic
64C2×Dic32C2211yescharacteristic
65#63867C2218yescomplemented
66#63847C2218yescomplemented
67#63846C2218yescomplemented
68#63837C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×C4×D4—31no—
71C2×#935—31no—
72C2×#935—31no—
73C2×#935—61no—
74C2×#935D311yescharacteristic
75C2×D4×Dic3D311yescharacteristic
76C2×#926—31no—
77C2×#926—31no—
78C22×C4⋊Dic3—31no—
79C2×#924—31no—
80C2×#924—31no—
81C22×Dic3⋊C4—31no—
82#5650—316no—
83#5541—316no—
84C2×#890—31no—
85C2×#889—31no—
86C2×#889—31no—
87C2×#889—31no—
88C2×#889—31no—
89C2×#887—31no—
90C2×#879—31no—
91C2×#879—31no—
92C2×#879—31no—
93C2×#879—31no—
94C2×#878—31no—
95C2×#878—31no—
96C2×#877—31no—
97C2×#877—31no—
98C2×#877—31no—
99C2×#877—31no—
100C2×#870—31no—
101C2×C4×Dic6—31no—
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C2×C32×D4—24no—
105C2×C32×D4C2314yes—
106C22×C32×C4C2311yescharacteristic
107C22×C3⋊Dic3—24no—
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2314yes—
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3×Dic3—24no—
114C22×C3×Dic3—24no—
115C22×C3×Dic3—24no—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2314yes—
124C22×C3×Dic3C2314yes—
125C22×C3×Dic3C2314yes—
126C22×C3×Dic3C2311yescharacteristic
127C2×#627—24no—
128C2×#627C2314yes—
129#3757C2314yes—
130#3757C2314yes—
131#3757C2314yes—
132#3750C2314yes—
133#3750C2314yes—
134C3×#217C2314yes—
135C3×#217C2314yes—
136C3×#217C2314yes—
137C3×#217C2314yes—
138C3×#217C2314yes—
139C3×C4⋊Dic3C2314yes—
140C3×Dic3⋊C4C2314yes—
141C3×Dic3⋊C4C2314yes—
142C3×C4×Dic3C2314yes—
143#3724C2314yes—
144#3724C2314yes—
145#3724C2314yes—
146Dic3⋊Dic3C2314yes—
147Dic3⋊Dic3C2314yes—
148Dic3⋊Dic3C2314yes—
149Dic3⋊Dic3C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic32C2314yes—
155Dic32C2314yes—
156Dic32C2314yes—
157Dic32C2314yes—
158C2×#552—91noSylow
159C22×C3×D4—21no—
160C22×C3×D4C2×D311yescharacteristic
161C22×C3×D4C2×D311yescharacteristic
162C23×C3×C4—31no—
163C23×C3×C4—31no—
164C23×C3×C4—31no—
165C23×Dic3—31no—
166C23×Dic3—31no—
167C23×Dic3—61no—
168C23×Dic3C2×D311yescharacteristic
169C23×Dic3C2×D311yescharacteristic
170C23×Dic3C2×D311yescharacteristic
171C22×Dic6—31no—
172C22×Dic6—31no—
173C3×#123—38no—
174C3×C4×D4—38no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C42—31no—
184C2×#217—31no—
185C2×#217—31no—
186C2×#217—31no—
187C2×#217—31no—
188C2×#217—31no—
189C2×#217—31no—
190C2×#217—61no—
191C2×#217—61no—
192C2×#217—61no—
193C2×#217C2×D311yescharacteristic
194C2×#217C2×D311yescharacteristic
195C2×#217C2×D311yescharacteristic
196C2×#217C2×D311yescharacteristic
197C2×#217C2×D311yescharacteristic
198#935—38no—
199#935—38no—
200#935—68no—
201#935C2×D318yes—
202D4×Dic3C2×D318yes—
203#926—38no—
204#926—38no—
205C2×C4⋊Dic3—31no—
206C2×C4⋊Dic3—31no—
207C2×C4⋊Dic3—31no—
208C2×C4⋊Dic3—31no—
209C2×C4⋊Dic3—31no—
210C2×C4⋊Dic3—31no—
211C2×C4⋊Dic3—31no—
212C2×C4⋊Dic3—31no—
213C2×C4⋊Dic3—38no—
214C2×C4⋊Dic3C2×D311yescharacteristic
215#924—38no—
216#924—38no—
217C2×Dic3⋊C4—31no—
218C2×Dic3⋊C4—31no—
219C2×Dic3⋊C4—31no—
220C2×Dic3⋊C4—31no—
221C2×Dic3⋊C4—38no—
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—31no—
232C2×Dic3⋊C4—31no—
233C2×Dic3⋊C4—31no—
234C2×Dic3⋊C4—31no—
235C2×Dic3⋊C4—31no—
236C2×Dic3⋊C4—61no—
237C2×Dic3⋊C4—61no—
238C2×Dic3⋊C4C2×D311yescharacteristic
239C2×Dic3⋊C4C2×D311yescharacteristic
240C2×C4×Dic3—31no—
241C2×C4×Dic3—31no—
242C2×C4×Dic3—31no—
243C2×C4×Dic3—31no—
244C2×C4×Dic3—31no—
245C2×C4×Dic3—31no—
246C2×C4×Dic3—31no—
247C2×C4×Dic3—31no—
248C2×C4×Dic3C2×D311yescharacteristic
249#890—38no—
250#889—38no—
251#889—38no—
252#889—38no—
253#889—38no—
254#887—38no—
255#879—38no—
256#879—38no—
257#879—38no—
258#879—38no—
259#878—38no—
260#878—38no—
261#877—38no—
262#877—38no—
263#877—38no—
264#877—38no—
265#870—38no—
266C4×Dic6—38no—
267C23×C32—22no—
268C23×C32—22no—
269C23×C32—22no—
270C23×C32—22no—
271C23×C32—22no—
272C23×C32#4114yes—
273C23×C32C2412yes—
274C23×C32C2412yes—
275C23×C32C2411yescharacteristic
276C32×D4—28no—
277C2×C32×C4—22no—
278C2×C32×C4C2412yes—
279C2×C3⋊Dic3—22no—
280C2×C3⋊Dic3—28no—
281C2×C3⋊Dic3—22no—
282C2×C3⋊Dic3—22no—
283C2×C3⋊Dic3—22no—
284C2×C3⋊Dic3C2412yes—
285C2×C3⋊Dic3C2412yes—
286C2×C3⋊Dic3C2412yes—
287C2×C3⋊Dic3C2412yes—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—28no—
290C2×C3×Dic3—22no—
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—28no—
298C2×C3×Dic3#4114yes—
299C2×C3×Dic3C2412yes—
300C2×C3×Dic3C2412yes—
301C2×C3×Dic3C2412yes—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307#627—28no—
308#552—916no—
309C2×#126—91no—
310C2×#126—91no—
311C2×#125—91no—
312C2×#125—91no—
313C2×#125—91no—
314C2×#123—31no—
315C2×#123—91no—
316C2×C22⋊Q8—91no—
317C2×C22⋊Q8—91no—
318C2×C4×Q8—91no—
319C2×C4×D4—31no—
320C2×#117—91no—
321C2×#117—91no—
322C2×#117—91no—
323C22×C4⋊C4—91no—
324C24×C3—21no—
325C24×C3—21no—
326C24×C3C22×D311yescharacteristic
327C24×C3C22×D311yescharacteristic
328C24×C3C22×D311yescharacteristic
329C24×C3C22×D311yescharacteristic
330C2×C3×D4—24no—
331C2×C3×D4—24no—
332C2×C3×D4—24no—
333C2×C3×D4—44no—
334C2×C3×D4C22×D314yes—
335C2×C3×D4C22×D314yes—
336C22×C3×C4—21no—
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×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—34no—
346C22×C3×C4—34no—
347C22×C3×C4—34no—
348C22×C3×C4—64no—
349C22×C3×C4—64no—
350C22×C3×C4—64no—
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C22×Dic3—24no—
354C22×Dic3—24no—
355C22×Dic3—24no—
356C22×Dic3—34no—
357C22×Dic3—34no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—61no—
367C22×Dic3—61no—
368C22×Dic3—61no—
369C22×Dic3—61no—
370C22×Dic3—64no—
371C22×Dic3—64no—
372C22×Dic3—64no—
373C22×Dic3—124no—
374C22×Dic3C22×D314yes—
375C22×Dic3C22×D314yes—
376C22×Dic3C22×D314yes—
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C2×Dic6—34no—
386C2×Dic6—34no—
387C2×Dic6—64no—
388C2×Dic6—64no—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—34no—
392C3×C22⋊C4—34no—
393C3×C22⋊C4—34no—
394C3×C22⋊C4—34no—
395C3×C22⋊C4—34no—
396C3×C22⋊C4—34no—
397C3×C42—34no—
398#217—34no—
399#217—34no—
400#217—34no—
401#217—34no—
402#217—34no—
403#217—34no—
404#217—64no—
405#217—64no—
406#217—64no—
407#217C22×D314yes—
408#217C22×D314yes—
409#217C22×D314yes—
410#217C22×D314yes—
411#217C22×D314yes—
412C4⋊Dic3—34no—
413C4⋊Dic3—34no—
414C4⋊Dic3—34no—
415C4⋊Dic3—34no—
416C4⋊Dic3—34no—
417C4⋊Dic3—34no—
418C4⋊Dic3—34no—
419C4⋊Dic3—34no—
420C4⋊Dic3C22×D314yes—
421Dic3⋊C4—34no—
422Dic3⋊C4—34no—
423Dic3⋊C4—34no—
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—34no—
436Dic3⋊C4—34no—
437Dic3⋊C4—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—64no—
440Dic3⋊C4—64no—
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—34no—
450C4×Dic3—34no—
451C4×Dic3C22×D314yes—
452C22×C32—28no—
453C22×C32—22no—
454C22×C32—22no—
455C22×C32—22no—
456C22×C32—22no—
457C22×C32—22no—
458C22×C32—44no—
459C22×C32C2×#4114yes—
460C22×C32C2×#4112yes—
461C22×C32C2×#4112yes—
462C22×C322−1+412yes—
463C22×C32C2511yescharacteristic
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×Dic3—22no—
475C3×Dic3—22no—
476C3×Dic3C2×#4114yes—
477C22×Q8—91no—
478C22×D4D3211yescharacteristic
479C23×C4—31no—
480C23×C4—31no—
481C23×C4—31no—
482C23×C4—91no—
483#126—98no—
484#126—98no—
485#125—98no—
486#125—98no—
487#125—98no—
488#123—38no—
489#123—98no—
490C22⋊Q8—98no—
491C22⋊Q8—98no—
492C4×Q8—98no—
493C4×D4—38no—
494#117—98no—
495#117—98no—
496#117—98no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—91no—
501C2×C4⋊C4—91no—
502C2×C4⋊C4—91no—
503C2×C4⋊C4—91no—
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⋊C4—91no—
514C2×C22⋊C4—31no—
515C2×C22⋊C4—31no—
516C2×C22⋊C4—31no—
517C2×C22⋊C4—31no—
518C2×C22⋊C4—31no—
519C2×C22⋊C4—91no—
520C2×C22⋊C4—91no—
521C2×C22⋊C4—91no—
522C2×C42—31no—
523C2×C42—91no—
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—22no—
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—22no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—21no—
540C23×C3—24no—
541C23×C3—42no—
542C23×C3—42no—
543C23×C3—42no—
544C23×C3—42no—
545C23×C3—42no—
546C23×C3#23514yes—
547C23×C3#23714yes—
548C23×C3C23×D312yes—
549C23×C3C23×D312yes—
550C23×C3C23×D312yes—
551C23×C3C23×D312yes—
552C23×C3C23×D311yescharacteristic
553C23×C3C23×D311yescharacteristic
554C3×D4—28no—
555C3×D4—28no—
556C3×D4—48no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—34no—
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—32no—
568C2×C3×C4—32no—
569C2×C3×C4—42no—
570C2×C3×C4—68no—
571C2×C3×C4—68no—
572C2×C3×C4—68no—
573C2×C3×C4—62no—
574C2×C3×C4—62no—
575C2×C3×C4—62no—
576C2×C3×C4—62no—
577C2×C3×C4—62no—
578C2×C3×C4—62no—
579C2×C3×C4—62no—
580C2×C3×C4C23×D312yes—
581C2×C3×C4C23×D312yes—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—28no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—28no—
591C2×Dic3—28no—
592C2×Dic3—32no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—32no—
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—68no—
605C2×Dic3—62no—
606C2×Dic3—62no—
607C2×Dic3—62no—
608C2×Dic3—68no—
609C2×Dic3—62no—
610C2×Dic3—62no—
611C2×Dic3—62no—
612C2×Dic3—62no—
613C2×Dic3—62no—
614C2×Dic3—122no—
615C2×Dic3—122no—
616C2×Dic3—122no—
617C2×Dic3—122no—
618C2×Dic3—128no—
619C2×Dic3#23714yes—
620C2×Dic3C23×D312yes—
621C2×Dic3C23×D312yes—
622C2×Dic3C23×D312yes—
623C2×Dic3C23×D312yes—
624C2×Dic3C23×D312yes—
625C2×Dic3C23×D312yes—
626C2×Dic3C23×D312yes—
627C2×Dic3C23×D312yes—
628Dic6—68no—
629Dic6—68no—
630C2×C32—24no—
631C2×C32—42no—
632C2×C32#55214yescomplemented
633C2×C32C22×#4111yescharacteristic
634C2×C32C22×#4111yescharacteristic
635C2×C32C2×2−1+411yescharacteristic
636C24C2×D3211yescharacteristic
637C24C2×D3211yescharacteristic
638C2×Q8—94no—
639C2×Q8—184no—
640C2×D4—24no—
641C2×D4C2×D3214yes—
642C22×C4—31no—
643C22×C4—34no—
644C22×C4—34no—
645C22×C4—34no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—31no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—31no—
653C22×C4—64no—
654C22×C4—64no—
655C22×C4—64no—
656C22×C4—94no—
657C22×C4—91no—
658C22×C4—91no—
659C22×C4—91no—
660C22×C4—91no—
661C22×C4—184no—
662C22×C4C2×D3211yescharacteristic
663C4⋊C4—34no—
664C4⋊C4—34no—
665C4⋊C4—34no—
666C4⋊C4—94no—
667C4⋊C4—94no—
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—34no—
682C22⋊C4—34no—
683C22⋊C4—34no—
684C22⋊C4—94no—
685C22⋊C4—94no—
686C22⋊C4—94no—
687C42—34no—
688C42—94no—
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—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—22no—
706C22×C3—22no—
707C22×C3—24no—
708C22×C3—21no—
709C22×C3—48no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—44no—
716C22×C3—44no—
717C22×C3—84no—
718C22×C3C2×#23514yes—
719C22×C3C2×#23512yes—
720C22×C3C2×#23712yes—
721C22×C3C2×#23714yes—
722C22×C3C2×#23712yes—
723C22×C3D3×#4112yes—
724C22×C3#101012yes—
725C22×C3#101012yes—
726C22×C3C24×D311yescharacteristic
727C22×C3C24×D311yescharacteristic
728C3×C4—22no—
729C3×C4—22no—
730C3×C4—34no—
731C3×C4—42no—
732C3×C4—62no—
733C3×C4—62no—
734C3×C4—62no—
735C3×C4—62no—
736C3×C4—62no—
737C3×C4—62no—
738C3×C4—62no—
739Dic3—22no—
740Dic3—22no—
741Dic3—22no—
742Dic3—22no—
743Dic3—22no—
744Dic3—22no—
745Dic3—22no—
746Dic3—62no—
747Dic3—62no—
748Dic3—62no—
749Dic3—62no—
750Dic3—62no—
751Dic3—62no—
752Dic3—62no—
753Dic3—62no—
754Dic3—122no—
755Dic3—122no—
756Dic3—122no—
757Dic3—122no—
758Dic3C2×#23714yes—
759C32C2×#55211yescharacteristic, complemented, Sylow
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23#380414yes—
766C23C22×D3212yes—
767C23C22×D3212yes—
768C23C22×D3211yescharacteristic
769Q8—188no—
770D4—28no—
771C2×C4—22no—
772C2×C4—34no—
773C2×C4—32no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—32no—
779C2×C4—32no—
780C2×C4—32no—
781C2×C4—68no—
782C2×C4—68no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4—62no—
787C2×C4—62no—
788C2×C4—68no—
789C2×C4—62no—
790C2×C4—62no—
791C2×C4—92no—
792C2×C4—92no—
793C2×C4—92no—
794C2×C4—92no—
795C2×C4—182no—
796C2×C4—182no—
797C2×C4—188no—
798C2×C4—182no—
799C2×C4—182no—
800C2×C4C22×D3212yes—
801C2×C3—24no—
802C2×C3—24no—
803C2×C3—24no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—44no—
808C2×C3—42no—
809C2×C3—42no—
810C2×C3—82no—
811C2×C3#554114yescomplemented
812C2×C3#565014yescomplemented
813C2×C3C22×#23511yescharacteristic
814C2×C3C22×#23711yescharacteristic
815C2×C3C22×#23711yescharacteristic
816C2×C3C2×D3×#4111yescharacteristic
817C2×C3C2×#101011yescharacteristic
818C2×C3C2×#101011yescharacteristic
819C22—28no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—44no—
826C22#6430912yes—
827C22D3×#23712yes—
828C22C2×#380414yes—
829C22C2×#380412yes—
830C22C23×D3211yescharacteristic
831C4—22no—
832C4—34no—
833C4—62no—
834C4—62no—
835C4—62no—
836C4—62no—
837C4—62no—
838C4—62no—
839C4—62no—
840C4—182no—
841C4—182no—
842C4—182no—
843C4—182no—
844C3—21no—
845C3C2×#554111yescharacteristic, complemented
846C3C2×#565011yescharacteristic, complemented
847C2—24no—
848C2—42no—
849C2#1059511714yesdirect product factor
850C2C2×#6430911yescharacteristic
851C2C2×D3×#23711yescharacteristic
852C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. C22×Dic3⋊Dic3C2semidirect
5. C2×#63964C2semidirect
6. C2×#63964C2semidirect
7. C2×#63957C2semidirect
8. C2×#63956C2semidirect
9. C2×#63956C2semidirect
10. C2×#63955C2semidirect
11. C2×#63955C2semidirect
12. #10595117C2direct (N × H)
13. C2×#63867C2semidirect
14. C2×#63847C2semidirect
15. C2×#63846C2semidirect
16. C2×#63837C2semidirect
53. C2×Dic3⋊Dic3C22semidirect
54. #63964C22semidirect
55. #63964C22semidirect
56. #63957C22semidirect
57. #63956C22semidirect
58. #63956C22semidirect
59. #63955C22semidirect
60. #63955C22semidirect
65. #63867C22semidirect
66. #63847C22semidirect
67. #63846C22semidirect
68. #63837C22semidirect
632. C2×C32#552semidirect
759. C32C2×#552semidirect
811. C2×C3#5541semidirect
812. C2×C3#5650semidirect
845. C3C2×#5541semidirect
846. C3C2×#5650semidirect
849. C2#10595117direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641442
C2×C3×#9352
C2×C3×D4×Dic32
C22×Dic3⋊Dic32
C2×#639642
C2×#639572
C2×#639562
C2×#639552
#105951172
C2×#638672
C2×#638472
C2×#638462
C2×#638372
C2×#56503
C2×#55413