Finite Group Databasebeta

← C2×#10595116 #11900627

Subgroups — C2×#10595116 #11900627

Order 1152.

2677 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64148C211yesmaximal, characteristic
2C2×C3×#935C211yesmaximal, characteristic, complemented
3C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
4C2×#63982C211yesmaximal, characteristic, complemented
5C2×#63966C211yesmaximal, characteristic, complemented
6C2×#63956C211yesmaximal, characteristic, complemented
7C2×#63955C211yesmaximal, characteristic, complemented
8C22×Dic32C211yesmaximal, characteristic, complemented
9C2×#63953C211yesmaximal, characteristic, complemented
10C2×#63952C211yesmaximal, characteristic, complemented
11C2×#63952C211yesmaximal, characteristic, complemented
12#10595116C2116yesmaximal, direct product factor
13C2×#63848C211yesmaximal, characteristic, complemented
14C2×#63847C211yesmaximal, characteristic, complemented
15C2×#63837C211yesmaximal, characteristic, complemented
16C2×#63836C211yesmaximal, characteristic, complemented
17C2×#5649—31nomaximal
18C2×#5538—31nomaximal
19C22×C32×D4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C23×C3×Dic3C2211yescharacteristic
26C22×#627C2211yescharacteristic
27C22×#624C2211yescharacteristic
28C2×#3757C2211yescharacteristic
29#64148C2218yes—
30C2×#3752C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×C3×#217C2211yescharacteristic
33C2×C3×#217C2211yescharacteristic
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C3×#935C2218yescomplemented
38C3×D4×Dic3C2218yescomplemented
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×C4×Dic3C2211yescharacteristic
43#63982C2218yescomplemented
44C2×#3724C2211yescharacteristic
45C2×#3724C2211yescharacteristic
46#63966C2218yescomplemented
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54#63956C2218yescomplemented
55#63955C2218yescomplemented
56C2×Dic32C2211yescharacteristic
57C2×Dic32C2211yescharacteristic
58C2×Dic32C2211yescharacteristic
59C2×Dic32C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61C2×Dic32C2218yescomplemented
62#63953C2218yescomplemented
63#63952C2218yescomplemented
64#63952C2218yescomplemented
65#63848C2218yescomplemented
66#63847C2218yescomplemented
67#63837C2218yescomplemented
68#63836C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×C4×D4—31no—
71C2×#939—31no—
72C2×#939—31no—
73C2×#939—61no—
74C2×#935D311yescharacteristic, complemented
75C2×D4×Dic3D311yescharacteristic, complemented
76C2×#929—31no—
77C2×C4×#67—31no—
78C2×C4×#67—31no—
79C2×#926—31no—
80C22×C4×Dic3—31no—
81C22×C4×Dic3—31no—
82#5649—316no—
83#5538—316no—
84C2×#898—31no—
85C2×#898—31no—
86C2×#892—31no—
87C2×#889—31no—
88C2×#889—31no—
89C2×#887—31no—
90C2×#886—31no—
91C2×#885—31no—
92C2×#885—31no—
93C2×#67⋊C4—31no—
94C2×#67⋊C4—31no—
95C2×#879—31no—
96C2×#879—31no—
97C2×#878—31no—
98C2×#878—31no—
99C2×#877—31no—
100C2×#872—31no—
101C2×C4×Dic6—31no—
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C2×C32×D4—24no—
106C2×C32×D4C2314yes—
107C22×C32×C4C2311yescharacteristic
108C2×#638—24no—
109C2×#638—24no—
110C2×#638C2314yes—
111C2×#638C2314yes—
112C22×C3⋊Dic3—24no—
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2314yes—
115C22×C3⋊Dic3C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3×Dic3—24no—
118C22×C3×Dic3—24no—
119C22×C3×Dic3—24no—
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2314yes—
128C22×C3×Dic3C2314yes—
129C22×C3×Dic3C2314yes—
130C22×C3×Dic3C2311yescharacteristic
131C2×#627—24no—
132C2×#627C2314yes—
133C2×#624—24no—
134C2×#624C2314yes—
135#3757C2314yes—
136#3752C2314yes—
137#3750C2314yes—
138C3×#217C2314yes—
139C3×#217C2314yes—
140C3×#217C2314yes—
141C3×#217C2314yes—
142C3×#217C2314yes—
143C3×C4⋊Dic3C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×C4×Dic3C2314yes—
147#3724C2314yes—
148#3724C2314yes—
149Dic3⋊Dic3C2314yes—
150Dic3⋊Dic3C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153#3722C2314yes—
154#3722C2314yes—
155#3722C2314yes—
156Dic32C2314yes—
157Dic32C2314yes—
158Dic32C2314yes—
159Dic32C2314yes—
160Dic32C2314yes—
161C2×#529—91noSylow
162C22×C3×D4—21no—
163C22×C3×D4C2×D311yescharacteristic
164C22×C3×D4C2×D311yescharacteristic
165C23×C3×C4—31no—
166C23×C3×C4—31no—
167C23×C3×C4—31no—
168C22×#67—31no—
169C22×#67—31no—
170C22×#67—31no—
171C22×#67—31no—
172C22×#67—61no—
173C22×#67—61no—
174C23×Dic3—31no—
175C23×Dic3—31no—
176C23×Dic3—61no—
177C23×Dic3C2×D311yescharacteristic
178C23×Dic3C2×D311yescharacteristic
179C23×Dic3C2×D311yescharacteristic
180C22×C4×D3—31no—
181C22×C4×D3—31no—
182C22×Dic6—31no—
183C22×Dic6—31no—
184C3×#123—38no—
185C3×C4×D4—38no—
186C2×C3×C4⋊C4—31no—
187C2×C3×C4⋊C4—31no—
188C2×C3×C4⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C42—31no—
195C2×#217—31no—
196C2×#217—31no—
197C2×#217—61no—
198C2×#217C2×D311yescharacteristic
199C2×#217C2×D311yescharacteristic
200C2×#217C2×D311yescharacteristic
201C2×#217C2×D311yescharacteristic
202C2×#217C2×D311yescharacteristic
203#939—38no—
204#939—38no—
205#939—68no—
206#935C2×D318yescomplemented
207D4×Dic3C2×D318yescomplemented
208#929—38no—
209C4×#67—38no—
210C4×#67—38no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4—31no—
215C2×(C2×D3)⋊C4—31no—
216C2×(C2×D3)⋊C4—31no—
217C2×(C2×D3)⋊C4—31no—
218C2×(C2×D3)⋊C4—31no—
219C2×(C2×D3)⋊C4—61no—
220#926—38no—
221C2×C4⋊Dic3—31no—
222C2×C4⋊Dic3—31no—
223C2×C4⋊Dic3—31no—
224C2×C4⋊Dic3—31no—
225C2×C4⋊Dic3C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
238C2×Dic3⋊C4C2×D311yescharacteristic
239C2×C4×Dic3—38no—
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×Dic3—31no—
249C2×C4×Dic3—31no—
250C2×C4×Dic3—38no—
251C2×C4×Dic3C2×D311yescharacteristic
252#898—38no—
253#898—38no—
254#892—38no—
255#889—38no—
256#889—38no—
257#887—38no—
258#886—38no—
259#885—38no—
260#885—38no—
261#67⋊C4—38no—
262#67⋊C4—38no—
263#879—38no—
264#879—38no—
265#878—38no—
266#878—38no—
267#877—38no—
268#872—38no—
269C4×Dic6—38no—
270C23×C32—22no—
271C23×C32—22no—
272C23×C32—22no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32#4114yes—
276C23×C32C2412yes—
277C23×C32C2412yes—
278C23×C32C2411yescharacteristic
279C22×C3⋊D3—22no—
280C22×C3⋊D3—22no—
281C22×C3⋊D3—22no—
282C22×C3⋊D3C2412yes—
283C32×D4—28no—
284C2×C32×C4—22no—
285C2×C32×C4C2412yes—
286#638—28no—
287#638—28no—
288C2×C3⋊Dic3—22no—
289C2×C3⋊Dic3—22no—
290C2×C3⋊Dic3—28no—
291C2×C3⋊Dic3#4114yes—
292C2×C3⋊Dic3C2412yes—
293C2×C3⋊Dic3C2412yes—
294C2×C3⋊Dic3C2412yes—
295C2×C3×Dic3—22no—
296C2×C3×Dic3—22no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—28no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—28no—
304C2×C3×Dic3—28no—
305C2×C3×Dic3#4114yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C2×C3×Dic3C2412yes—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314#627—28no—
315#624—28no—
316#529—916no—
317C2×#126—91no—
318C2×#126—91no—
319C2×#125—91no—
320C2×#124—91no—
321C2×#123—31no—
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—91no—
330C2×#117—91no—
331C22×C42—91no—
332C24×C3—21no—
333C24×C3—21no—
334C24×C3C22×D311yescharacteristic
335C24×C3C22×D311yescharacteristic
336C24×C3C22×D311yescharacteristic
337C24×C3C22×D311yescharacteristic
338C23×D3—31no—
339C23×D3—31no—
340C23×D3—61no—
341C2×C3×D4—24no—
342C2×C3×D4—24no—
343C2×C3×D4—24no—
344C2×C3×D4—44no—
345C2×C3×D4C22×D314yes—
346C2×C3×D4C22×D314yes—
347C22×C3×C4—21no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—34no—
353C22×C3×C4—34no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—34no—
359C22×C3×C4—64no—
360C22×C3×C4—64no—
361C22×C3×C4—64no—
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C2×#67—34no—
365C2×#67—34no—
366C2×#67—34no—
367C2×#67—34no—
368C2×#67—64no—
369C2×#67—64no—
370C2×#67—64no—
371C2×#67—64no—
372C2×#67—64no—
373C2×#67—64no—
374C2×#67—124no—
375C2×#67—124no—
376C22×Dic3—24no—
377C22×Dic3—24no—
378C22×Dic3—24no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—34no—
382C22×Dic3—34no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—61no—
388C22×Dic3—61no—
389C22×Dic3—61no—
390C22×Dic3—64no—
391C22×Dic3—64no—
392C22×Dic3—64no—
393C22×Dic3—124no—
394C22×Dic3C22×D314yes—
395C22×Dic3C22×D314yes—
396C22×Dic3C22×D314yes—
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C2×C4×D3—34no—
406C2×C4×D3—34no—
407C2×C4×D3—64no—
408C2×C4×D3—64no—
409C2×Dic6—34no—
410C2×Dic6—34no—
411C2×Dic6—64no—
412C2×Dic6—64no—
413C3×C4⋊C4—34no—
414C3×C4⋊C4—34no—
415C3×C4⋊C4—34no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—34no—
420C3×C22⋊C4—34no—
421C3×C42—34no—
422#217—34no—
423#217—34no—
424#217—64no—
425#217C22×D314yes—
426#217C22×D314yes—
427#217C22×D314yes—
428#217C22×D314yes—
429#217C22×D314yes—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—64no—
439C4⋊Dic3—34no—
440C4⋊Dic3—34no—
441C4⋊Dic3—34no—
442C4⋊Dic3—34no—
443C4⋊Dic3C22×D314yes—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—34no—
447Dic3⋊C4—34no—
448Dic3⋊C4—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4—34no—
451Dic3⋊C4—34no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—64no—
455Dic3⋊C4C22×D314yes—
456Dic3⋊C4C22×D314yes—
457C4×Dic3—34no—
458C4×Dic3—34no—
459C4×Dic3—34no—
460C4×Dic3—34no—
461C4×Dic3—34no—
462C4×Dic3—34no—
463C4×Dic3—34no—
464C4×Dic3—34no—
465C4×Dic3—34no—
466C4×Dic3—34no—
467C4×Dic3C22×D314yes—
468C22×C32—28no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32—22no—
473C22×C32—22no—
474C22×C32—44no—
475C22×C32C2×#4114yes—
476C22×C32C2×#4112yes—
477C22×C32C2×#4112yes—
478C22×C32C2×#4112yes—
479C22×C32C2511yescharacteristic
480C2×C3⋊D3—22no—
481C2×C3⋊D3—22no—
482C2×C3⋊D3—22no—
483C2×C3⋊D3—44no—
484C32×C4—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—
493C3×Dic3—22no—
494C3×Dic3—22no—
495C3×Dic3C2×#4114yes—
496C22×Q8—91no—
497C22×D4—91no—
498C22×D4—91no—
499C22×D4D3211yescharacteristic
500C23×C4—31no—
501C23×C4—31no—
502C23×C4—31no—
503C23×C4—91no—
504C23×C4—91no—
505#126—98no—
506#126—98no—
507#125—98no—
508#124—98no—
509#123—38no—
510#123—98no—
511C22⋊Q8—98no—
512#121—98no—
513C4×Q8—98no—
514C4×D4—38no—
515C4×D4—98no—
516C4×D4—98no—
517#117—98no—
518#117—98no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—31no—
521C2×C4⋊C4—31no—
522C2×C4⋊C4—91no—
523C2×C4⋊C4—91no—
524C2×C4⋊C4—91no—
525C2×C4⋊C4—91no—
526C2×C4⋊C4—91no—
527C2×C4⋊C4—91no—
528C2×C4⋊C4—91no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C42—31no—
540C2×C42—91no—
541C2×C42—91no—
542C2×C42—91no—
543C2×C42—91no—
544C2×C42—91no—
545C2×C42—98no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—22no—
553C23×C3—22no—
554C23×C3—22no—
555C23×C3—22no—
556C23×C3—22no—
557C23×C3—22no—
558C23×C3—21no—
559C23×C3—24no—
560C23×C3—42no—
561C23×C3—42no—
562C23×C3—42no—
563C23×C3—42no—
564C23×C3—42no—
565C23×C3#23514yes—
566C23×C3#23714yes—
567C23×C3C23×D312yes—
568C23×C3C23×D312yes—
569C23×C3C23×D312yes—
570C23×C3C23×D312yes—
571C23×C3C23×D311yescharacteristic
572C23×C3C23×D311yescharacteristic
573C22×D3—32no—
574C22×D3—32no—
575C22×D3—62no—
576C22×D3—62no—
577C22×D3—62no—
578C22×D3—62no—
579C22×D3—62no—
580C22×D3—62no—
581C22×D3—62no—
582C22×D3—122no—
583C22×D3—122no—
584C22×D3—122no—
585C3×D4—28no—
586C3×D4—28no—
587C3×D4—48no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—34no—
592C2×C3×C4—32no—
593C2×C3×C4—32no—
594C2×C3×C4—32no—
595C2×C3×C4—32no—
596C2×C3×C4—32no—
597C2×C3×C4—32no—
598C2×C3×C4—32no—
599C2×C3×C4—32no—
600C2×C3×C4—42no—
601C2×C3×C4—68no—
602C2×C3×C4—68no—
603C2×C3×C4—68no—
604C2×C3×C4—62no—
605C2×C3×C4—62no—
606C2×C3×C4—62no—
607C2×C3×C4—62no—
608C2×C3×C4—62no—
609C2×C3×C4—62no—
610C2×C3×C4—62no—
611C2×C3×C4C23×D312yes—
612C2×C3×C4C23×D312yes—
613#67—68no—
614#67—68no—
615#67—68no—
616#67—68no—
617#67—128no—
618#67—128no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—28no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—28no—
628C2×Dic3—28no—
629C2×Dic3—34no—
630C2×Dic3—34no—
631C2×Dic3—32no—
632C2×Dic3—32no—
633C2×Dic3—32no—
634C2×Dic3—32no—
635C2×Dic3—32no—
636C2×Dic3—32no—
637C2×Dic3—64no—
638C2×Dic3—62no—
639C2×Dic3—62no—
640C2×Dic3—62no—
641C2×Dic3—68no—
642C2×Dic3—68no—
643C2×Dic3—62no—
644C2×Dic3—62no—
645C2×Dic3—62no—
646C2×Dic3—62no—
647C2×Dic3—128no—
648C2×Dic3—122no—
649C2×Dic3—122no—
650C2×Dic3#23714yes—
651C2×Dic3C23×D312yes—
652C2×Dic3C23×D312yes—
653C2×Dic3C23×D312yes—
654C2×Dic3C23×D312yes—
655C2×Dic3C23×D312yes—
656C2×Dic3C23×D312yes—
657C2×Dic3C23×D312yes—
658C2×Dic3C23×D312yes—
659C4×D3—68no—
660C4×D3—68no—
661Dic6—68no—
662Dic6—68no—
663C2×C32—24no—
664C2×C32—42no—
665C2×C32#52914yescomplemented
666C2×C32C22×#4111yescharacteristic
667C2×C32C22×#4111yescharacteristic
668C2×C32C22×#4111yescharacteristic
669C3⋊D3—42no—
670C24—91no—
671C24C2×D3211yescharacteristic
672C24C2×D3211yescharacteristic
673C2×Q8—94no—
674C2×Q8—184no—
675C2×D4—24no—
676C2×D4—94no—
677C2×D4—94no—
678C2×D4—184no—
679C2×D4—184no—
680C2×D4C2×D3214yes—
681C22×C4—31no—
682C22×C4—34no—
683C22×C4—34no—
684C22×C4—34no—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—64no—
693C22×C4—64no—
694C22×C4—64no—
695C22×C4—94no—
696C22×C4—91no—
697C22×C4—94no—
698C22×C4—91no—
699C22×C4—91no—
700C22×C4—184no—
701C22×C4—184no—
702C22×C4C2×D3211yescharacteristic
703C4⋊C4—34no—
704C4⋊C4—34no—
705C4⋊C4—34no—
706C4⋊C4—94no—
707C4⋊C4—94no—
708C4⋊C4—94no—
709C4⋊C4—94no—
710C4⋊C4—94no—
711C4⋊C4—94no—
712C4⋊C4—94no—
713C22⋊C4—34no—
714C22⋊C4—34no—
715C22⋊C4—34no—
716C22⋊C4—34no—
717C22⋊C4—34no—
718C22⋊C4—94no—
719C22⋊C4—94no—
720C22⋊C4—94no—
721C22⋊C4—94no—
722C22⋊C4—94no—
723C42—34no—
724C42—94no—
725C42—94no—
726C42—94no—
727C42—94no—
728C42—94no—
729C22×C3—28no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—28no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—24no—
745C22×C3—21no—
746C22×C3—42no—
747C22×C3—48no—
748C22×C3—42no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—44no—
753C22×C3—44no—
754C22×C3—84no—
755C22×C3C2×#23514yes—
756C22×C3C2×#23512yes—
757C22×C3C2×#23712yes—
758C22×C3C2×#23714yes—
759C22×C3C2×#23712yes—
760C22×C3D3×#4112yes—
761C22×C3D3×#4112yes—
762C22×C3D3×#4112yes—
763C22×C3C24×D311yescharacteristic
764C22×C3C24×D311yescharacteristic
765C2×D3—62no—
766C2×D3—62no—
767C2×D3—62no—
768C2×D3—62no—
769C2×D3—62no—
770C2×D3—62no—
771C2×D3—122no—
772C2×D3—122no—
773C2×D3—122no—
774C2×D3—124no—
775C2×D3—124no—
776C2×D3—244no—
777C3×C4—22no—
778C3×C4—22no—
779C3×C4—34no—
780C3×C4—42no—
781C3×C4—62no—
782C3×C4—62no—
783C3×C4—62no—
784C3×C4—62no—
785C3×C4—62no—
786C3×C4—62no—
787C3×C4—62no—
788Dic3—22no—
789Dic3—22no—
790Dic3—22no—
791Dic3—22no—
792Dic3—22no—
793Dic3—22no—
794Dic3—22no—
795Dic3—34no—
796Dic3—34no—
797Dic3—64no—
798Dic3—62no—
799Dic3—62no—
800Dic3—62no—
801Dic3—62no—
802Dic3—122no—
803Dic3—122no—
804Dic3C2×#23714yes—
805C32C2×#52911yescharacteristic, complemented, Sylow
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—92no—
812C23—182no—
813C23—182no—
814C23—182no—
815C23#380414yes—
816C23C22×D3212yes—
817C23C22×D3212yes—
818C23C22×D3211yescharacteristic
819Q8—188no—
820D4—28no—
821D4—188no—
822D4—188no—
823C2×C4—22no—
824C2×C4—34no—
825C2×C4—32no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—32no—
830C2×C4—32no—
831C2×C4—32no—
832C2×C4—32no—
833C2×C4—68no—
834C2×C4—68no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—62no—
839C2×C4—62no—
840C2×C4—68no—
841C2×C4—62no—
842C2×C4—62no—
843C2×C4—94no—
844C2×C4—92no—
845C2×C4—92no—
846C2×C4—92no—
847C2×C4—188no—
848C2×C4—188no—
849C2×C4—182no—
850C2×C4—182no—
851C2×C4C22×D3212yes—
852C2×C3—24no—
853C2×C3—24no—
854C2×C3—24no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—21no—
858C2×C3—44no—
859C2×C3—42no—
860C2×C3—42no—
861C2×C3—82no—
862C2×C3#553814yescomplemented
863C2×C3#564914yescomplemented
864C2×C3C22×#23511yescharacteristic
865C2×C3C22×#23711yescharacteristic
866C2×C3C22×#23711yescharacteristic
867C2×C3C2×D3×#4111yescharacteristic
868C2×C3C2×D3×#4111yescharacteristic
869C2×C3C2×D3×#4111yescharacteristic
870D3—122no—
871D3—122no—
872D3—242no—
873C22—28no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—44no—
880C22—182no—
881C22—182no—
882C22—182no—
883C22—364no—
884C22D3×#23712yes—
885C22#6431212yes—
886C22C2×#380414yes—
887C22C2×#380412yes—
888C22C23×D3211yescharacteristic
889C4—22no—
890C4—34no—
891C4—62no—
892C4—62no—
893C4—62no—
894C4—62no—
895C4—62no—
896C4—62no—
897C4—62no—
898C4—94no—
899C4—182no—
900C4—182no—
901C3—21no—
902C3C2×#553811yescharacteristic, complemented
903C3C2×#564911yescharacteristic, complemented
904C2—24no—
905C2—42no—
906C2—362no—
907C2#1059511614yesdirect product factor
908C2C2×D3×#23711yescharacteristic
909C2C2×#6431211yescharacteristic
910C2C22×#380411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
prime radicalC2×#64148C2
hypercenterC22×D4D32
hypocenterC32C2×#529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#935C2semidirect
3. C2×C3×D4×Dic3C2semidirect
4. C2×#63982C2semidirect
5. C2×#63966C2semidirect
6. C2×#63956C2semidirect
7. C2×#63955C2semidirect
8. C22×Dic32C2semidirect
9. C2×#63953C2semidirect
10. C2×#63952C2semidirect
11. C2×#63952C2semidirect
12. #10595116C2direct (N × H)
13. C2×#63848C2semidirect
14. C2×#63847C2semidirect
15. C2×#63837C2semidirect
16. C2×#63836C2semidirect
37. C3×#935C22semidirect
38. C3×D4×Dic3C22semidirect
43. #63982C22semidirect
46. #63966C22semidirect
54. #63956C22semidirect
55. #63955C22semidirect
61. C2×Dic32C22semidirect
62. #63953C22semidirect
63. #63952C22semidirect
64. #63952C22semidirect
65. #63848C22semidirect
66. #63847C22semidirect
67. #63837C22semidirect
68. #63836C22semidirect
74. C2×#935D3semidirect
75. C2×D4×Dic3D3semidirect
206. #935C2×D3semidirect
207. D4×Dic3C2×D3semidirect
665. C2×C32#529semidirect
805. C32C2×#529semidirect
862. C2×C3#5538semidirect
863. C2×C3#5649semidirect
902. C3C2×#5538semidirect
903. C3C2×#5649semidirect
907. C2#10595116direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641482
C2×C3×#9352
C2×C3×D4×Dic32
C2×#639822
C2×#639662
C2×#639562
C2×#639552
C22×Dic322
C2×#639532
C2×#639522
#105951162
C2×#638482
C2×#638472
C2×#638372
C2×#638362
C2×#56493
C2×#55383