Finite Group Databasebeta

← C2×#10595211 #11901666

Subgroups — C2×#10595211 #11901666

Order 1152.

2477 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×#936C211yesmaximal, characteristic, complemented
3C2×C3×#935C211yesmaximal, characteristic, complemented
4C2×#63982C211yesmaximal, characteristic, complemented
5C2×#63975C211yesmaximal, characteristic, complemented
6C2×#63964C211yesmaximal, characteristic, complemented
7C2×#63957C211yesmaximal, characteristic, complemented
8C2×#63956C211yesmaximal, characteristic, complemented
9C2×#63953C211yesmaximal, characteristic, complemented
10C2×#63953C211yesmaximal, characteristic, complemented
11C2×#63952C211yesmaximal, characteristic, complemented
12#10595211C2116yesmaximal, direct product factor
13C2×#63888C211yesmaximal, characteristic, complemented
14C2×#63868C211yesmaximal, characteristic, complemented
15C2×#63839C211yesmaximal, characteristic, complemented
16C2×#63837C211yesmaximal, characteristic, complemented
17C2×#5669—31nomaximal
18C2×#5662—31nomaximal
19C22×C32×D4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C22×#627C2211yescharacteristic
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
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C3×#936C2218yescomplemented
40C3×#935C2218yescomplemented
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44#63982C2218yescomplemented
45#63975C2218yescomplemented
46C2×#3724C2211yescharacteristic
47C2×#3724C2211yescharacteristic
48C2×#3724C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53#63964C2218yescomplemented
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57#63957C2218yescomplemented
58#63956C2218yescomplemented
59C2×Dic32C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61C2×Dic32C2211yescharacteristic
62#63953C2218yescomplemented
63#63953C2218yescomplemented
64#63952C2218yescomplemented
65#63888C2218yescomplemented
66#63868C2218yescomplemented
67#63839C2218yescomplemented
68#63837C2218yescomplemented
69C2×C3×#124—31no—
70C2×C3×#123—31no—
71C2×#946—31no—
72C2×#944—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#939—61no—
76C2×#936D311yescharacteristic, complemented
77C2×#935D311yescharacteristic, complemented
78C2×C4×#67—31no—
79C2×#924—31no—
80#5669—316no—
81#5662—316no—
82C2×#898—31no—
83C2×#896—31no—
84C2×#888—31no—
85C2×#887—31no—
86C2×#885—31no—
87C2×#885—31no—
88C2×#885—31no—
89C2×#885—31no—
90C2×#883—31no—
91C2×#883—31no—
92C2×#67⋊C4—31no—
93C2×#879—31no—
94C2×#879—31no—
95C2×#878—31no—
96C2×#878—31no—
97C2×#878—31no—
98C2×#877—31no—
99C2×#877—31no—
100C2×#876—31no—
101C2×C4×Dic6—31no—
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C2×C32×D4—42no—
106C2×C32×D4C2314yes—
107C22×C32×C4C2311yescharacteristic
108C2×#638—24no—
109C2×#638—42no—
110C2×#638C2314yes—
111C2×#638C2314yes—
112C22×C3⋊Dic3—24no—
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C22×C3⋊Dic3C2314yes—
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3×Dic3—42no—
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2314yes—
127C2×C3×Dic6—42no—
128C2×C3×Dic6C2314yes—
129C2×#627—24no—
130C2×#627—42no—
131C2×#627C2314yes—
132C2×#627C2314yes—
133C2×#624—42no—
134C2×#624C2314yes—
135#3757C2314yes—
136#3752C2314yes—
137#3750C2314yes—
138C3×#217C2314yes—
139C3×#217C2314yes—
140C3×#217C2314yes—
141C3×#217C2314yes—
142C3×#217C2314yes—
143C3×#217C2314yes—
144C3×#217C2314yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×C4×Dic3C2314yes—
148#3724C2314yes—
149#3724C2314yes—
150#3724C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155#3722C2314yes—
156#3722C2314yes—
157#3722C2314yes—
158Dic32C2314yes—
159Dic32C2314yes—
160Dic32C2314yes—
161C2×#542—91noSylow
162C22×C3×Q8—31no—
163C22×C3×D4—21no—
164C22×C3×D4C2×D311yescharacteristic
165C22×C3×D4C2×D311yescharacteristic
166C23×C3×C4—31no—
167C22×#67—31no—
168C22×#67—31no—
169C22×#67—31no—
170C22×#67—31no—
171C22×#67—61no—
172C22×#67—61no—
173C23×Dic3—31no—
174C23×Dic3—31no—
175C23×Dic3—61no—
176C23×Dic3C2×D311yescharacteristic
177C22×C4×D3—31no—
178C22×C4×D3—31no—
179C22×Dic6—31no—
180C22×Dic6—31no—
181C22×Dic6—31no—
182C22×Dic6—31no—
183C22×Dic6C2×D311yescharacteristic
184C3×#124—38no—
185C3×#123—38no—
186C2×C3×C4⋊C4—31no—
187C2×C3×C4⋊C4—31no—
188C2×C3×C22⋊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×C22⋊C4—31no—
195C2×C3×C42—31no—
196C2×#217—31no—
197C2×#217—31no—
198C2×#217—61no—
199C2×#217C2×D311yescharacteristic
200C2×#217C2×D311yescharacteristic
201C2×#217C2×D311yescharacteristic
202C2×#217C2×D311yescharacteristic
203C2×#217C2×D311yescharacteristic
204C2×#217C2×D311yescharacteristic
205C2×#217C2×D311yescharacteristic
206#946—38no—
207#944—38no—
208#939—38no—
209#939—38no—
210#939—68no—
211#936C2×D318yescomplemented
212#935C2×D318yescomplemented
213C4×#67—38no—
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—31no—
220C2×(C2×D3)⋊C4—31no—
221C2×(C2×D3)⋊C4—31no—
222C2×(C2×D3)⋊C4—61no—
223C2×C4⋊Dic3—31no—
224C2×C4⋊Dic3—31no—
225C2×C4⋊Dic3—31no—
226C2×C4⋊Dic3—31no—
227#924—38no—
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—31no—
237C2×Dic3⋊C4—31no—
238C2×Dic3⋊C4—31no—
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—61no—
241C2×Dic3⋊C4C2×D311yescharacteristic
242C2×Dic3⋊C4C2×D311yescharacteristic
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×Dic3C2×D311yescharacteristic
250#898—38no—
251#896—38no—
252#888—38no—
253#887—38no—
254#885—38no—
255#885—38no—
256#885—38no—
257#885—38no—
258#883—38no—
259#883—38no—
260#67⋊C4—38no—
261#879—38no—
262#879—38no—
263#878—38no—
264#878—38no—
265#878—38no—
266#877—38no—
267#877—38no—
268#876—38no—
269C4×Dic6—38no—
270C23×C32—22no—
271C23×C32—22no—
272C23×C32—22no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32—22no—
276C23×C32C2412yes—
277C23×C32C2412yes—
278C23×C32C2411yescharacteristic
279C22×C3⋊D3—22no—
280C22×C3⋊D3—22no—
281C22×C3⋊D3—22no—
282C22×C3⋊D3C2412yes—
283C32×D4—44no—
284C2×C32×C4—22no—
285C2×C32×C4C2412yes—
286#638—28no—
287#638—44no—
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—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—44no—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C2×C3×Dic3C2412yes—
312C3×Dic6—44no—
313#627—28no—
314#627—44no—
315#624—44no—
316#542—916no—
317C2×C4⋊Q8—91no—
318C2×#126—91no—
319C2×#126—91no—
320C2×#124—31no—
321C2×#124—91no—
322C2×#124—91no—
323C2×#123—31no—
324C2×#123—91no—
325C2×C22⋊Q8—91no—
326C2×C22⋊Q8—91no—
327C2×C22⋊Q8—91no—
328C2×#121—91no—
329C2×C4×Q8—91no—
330C2×C4×D4—91no—
331C2×#117—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×Q8—34no—
342C2×C3×Q8—122no—
343C2×C3×D4—24no—
344C2×C3×D4—42no—
345C2×C3×D4—42no—
346C2×C3×D4—44no—
347C2×C3×D4C22×D314yes—
348C2×C3×D4C22×D314yes—
349C22×C3×C4—21no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—34no—
359C22×C3×C4—122no—
360C22×C3×C4C22×D311yescharacteristic
361C22×C3×C4C22×D311yescharacteristic
362C2×#67—34no—
363C2×#67—34no—
364C2×#67—34no—
365C2×#67—34no—
366C2×#67—64no—
367C2×#67—64no—
368C2×#67—64no—
369C2×#67—64no—
370C2×#67—124no—
371C2×#67—122no—
372C2×#67—122no—
373C2×#67—124no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—34no—
377C22×Dic3—34no—
378C22×Dic3—31no—
379C22×Dic3—31no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—42no—
383C22×Dic3—61no—
384C22×Dic3—61no—
385C22×Dic3—61no—
386C22×Dic3—64no—
387C22×Dic3—64no—
388C22×Dic3—64no—
389C22×Dic3—124no—
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D314yes—
399C2×C4×D3—34no—
400C2×C4×D3—34no—
401C2×C4×D3—122no—
402C2×C4×D3—122no—
403C2×Dic6—34no—
404C2×Dic6—34no—
405C2×Dic6—34no—
406C2×Dic6—34no—
407C2×Dic6—42no—
408C2×Dic6—64no—
409C2×Dic6—64no—
410C2×Dic6—122no—
411C2×Dic6—122no—
412C2×Dic6C22×D314yes—
413C3×C4⋊C4—34no—
414C3×C4⋊C4—34no—
415C3×C22⋊C4—34no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4—34no—
420C3×C22⋊C4—34no—
421C3×C22⋊C4—34no—
422C3×C42—34no—
423#217—34no—
424#217—34no—
425#217—64no—
426#217C22×D314yes—
427#217C22×D314yes—
428#217C22×D314yes—
429#217C22×D314yes—
430#217C22×D314yes—
431#217C22×D314yes—
432#217C22×D314yes—
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—34no—
439(C2×D3)⋊C4—34no—
440(C2×D3)⋊C4—34no—
441(C2×D3)⋊C4—64no—
442C4⋊Dic3—34no—
443C4⋊Dic3—34no—
444C4⋊Dic3—34no—
445C4⋊Dic3—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—34no—
455Dic3⋊C4—34no—
456Dic3⋊C4—34no—
457Dic3⋊C4—34no—
458Dic3⋊C4—64no—
459Dic3⋊C4C22×D314yes—
460Dic3⋊C4C22×D314yes—
461C4×Dic3—34no—
462C4×Dic3—34no—
463C4×Dic3—34no—
464C4×Dic3—34no—
465C4×Dic3—34no—
466C4×Dic3—34no—
467C4×Dic3C22×D314yes—
468C22×C32—22no—
469C22×C32—22no—
470C22×C32—22no—
471C22×C32—22no—
472C22×C32—22no—
473C22×C32—22no—
474C22×C32—44no—
475C22×C32—44no—
476C22×C32C2×#4112yes—
477C22×C32H(5,𝔽2)12yes—
478C22×C322−1+412yes—
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×Dic3—22no—
496C22×Q8—31no—
497C22×Q8—91no—
498C22×Q8—91no—
499C22×D4—91no—
500C22×D4—91no—
501C22×D4D3211yescharacteristic
502C23×C4—31no—
503C23×C4—91no—
504C23×C4—91no—
505C4⋊Q8—98no—
506#126—98no—
507#126—98no—
508#124—38no—
509#124—98no—
510#124—98no—
511#123—38no—
512#123—98no—
513C22⋊Q8—98no—
514C22⋊Q8—98no—
515C22⋊Q8—98no—
516#121—98no—
517C4×Q8—98no—
518C4×D4—98no—
519#117—98no—
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×C4⋊C4—91no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—31no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—91no—
542C2×C42—31no—
543C2×C42—91no—
544C2×C42—91no—
545C2×C42—91no—
546C23×C3—24no—
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—22no—
559C23×C3—22no—
560C23×C3—22no—
561C23×C3—21no—
562C23×C3—42no—
563C23×C3—42no—
564C23×C3—42no—
565C23×C3—42no—
566C23×C3—42no—
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×Q8—124no—
586C3×D4—44no—
587C3×D4—44no—
588C3×D4—48no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
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—62no—
602C2×C3×C4—62no—
603C2×C3×C4—62no—
604C2×C3×C4—62no—
605C2×C3×C4—62no—
606C2×C3×C4—62no—
607C2×C3×C4—62no—
608C2×C3×C4—62no—
609C2×C3×C4—124no—
610C2×C3×C4C23×D312yes—
611C2×C3×C4C23×D312yes—
612#67—68no—
613#67—68no—
614#67—128no—
615#67—124no—
616#67—124no—
617#67—128no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—34no—
627C2×Dic3—34no—
628C2×Dic3—32no—
629C2×Dic3—32no—
630C2×Dic3—32no—
631C2×Dic3—32no—
632C2×Dic3—32no—
633C2×Dic3—32no—
634C2×Dic3—44no—
635C2×Dic3—64no—
636C2×Dic3—62no—
637C2×Dic3—62no—
638C2×Dic3—62no—
639C2×Dic3—68no—
640C2×Dic3—68no—
641C2×Dic3—62no—
642C2×Dic3—62no—
643C2×Dic3—62no—
644C2×Dic3—62no—
645C2×Dic3—128no—
646C2×Dic3—122no—
647C2×Dic3—122no—
648C2×Dic3C23×D312yes—
649C2×Dic3C23×D312yes—
650C2×Dic3C23×D312yes—
651C2×Dic3C23×D312yes—
652C2×Dic3C23×D312yes—
653C2×Dic3C23×D312yes—
654C2×Dic3C23×D312yes—
655C2×Dic3C23×D312yes—
656C4×D3—124no—
657C4×D3—124no—
658Dic6—44no—
659Dic6—68no—
660Dic6—68no—
661Dic6—124no—
662Dic6—124no—
663C2×C32—42no—
664C2×C32—42no—
665C2×C32#54214yescomplemented
666C2×C32C22×#4111yescharacteristic
667C2×C32C2×H(5,𝔽2)11yescharacteristic
668C2×C32C2×2−1+411yescharacteristic
669C3⋊D3—42no—
670C24—91no—
671C24C2×D3211yescharacteristic
672C24C2×D3211yescharacteristic
673C2×Q8—34no—
674C2×Q8—94no—
675C2×Q8—94no—
676C2×Q8—122no—
677C2×Q8—184no—
678C2×Q8—362no—
679C2×D4—42no—
680C2×D4—94no—
681C2×D4—94no—
682C2×D4—184no—
683C2×D4—362no—
684C2×D4C2×D3214yes—
685C22×C4—31no—
686C22×C4—31no—
687C22×C4—31no—
688C22×C4—31no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—34no—
694C22×C4—94no—
695C22×C4—91no—
696C22×C4—94no—
697C22×C4—91no—
698C22×C4—91no—
699C22×C4—122no—
700C22×C4—184no—
701C22×C4—362no—
702C22×C4C2×D3211yescharacteristic
703C4⋊C4—34no—
704C4⋊C4—34no—
705C4⋊C4—94no—
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—34no—
719C22⋊C4—34no—
720C22⋊C4—94no—
721C22⋊C4—94no—
722C22⋊C4—94no—
723C22⋊C4—94no—
724C22⋊C4—94no—
725C42—34no—
726C42—94no—
727C42—94no—
728C42—94no—
729C22×C3—24no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
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—22no—
745C22×C3—21no—
746C22×C3—42no—
747C22×C3—42no—
748C22×C3—42no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—48no—
752C22×C3—44no—
753C22×C3—44no—
754C22×C3—44no—
755C22×C3—44no—
756C22×C3—84no—
757C22×C3#100412yes—
758C22×C3#100412yes—
759C22×C3D3×#4112yes—
760C22×C3D3×#4112yes—
761C22×C3#101012yes—
762C22×C3#101012yes—
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—42no—
780C3×C4—62no—
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—22no—
796Dic3—34no—
797Dic3—34no—
798Dic3—64no—
799Dic3—62no—
800Dic3—62no—
801Dic3—62no—
802Dic3—62no—
803Dic3—122no—
804Dic3—122no—
805C32C2×#54211yescharacteristic, complemented, Sylow
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—92no—
813C23—182no—
814C23—182no—
815C23—182no—
816C23C22×D3212yes—
817C23C22×D3212yes—
818C23C22×D3211yescharacteristic
819Q8—124no—
820Q8—188no—
821Q8—364no—
822D4—44no—
823D4—188no—
824D4—364no—
825C2×C4—22no—
826C2×C4—32no—
827C2×C4—32no—
828C2×C4—32no—
829C2×C4—32no—
830C2×C4—32no—
831C2×C4—32no—
832C2×C4—32no—
833C2×C4—32no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—62no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—94no—
843C2×C4—92no—
844C2×C4—92no—
845C2×C4—92no—
846C2×C4—124no—
847C2×C4—188no—
848C2×C4—182no—
849C2×C4—182no—
850C2×C4—364no—
851C2×C4C22×D3212yes—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—24no—
856C2×C3—44no—
857C2×C3—42no—
858C2×C3—42no—
859C2×C3—42no—
860C2×C3—42no—
861C2×C3—82no—
862C2×C3#566214yescomplemented
863C2×C3#566914yescomplemented
864C2×C3C2×#100411yescharacteristic
865C2×C3C2×#100411yescharacteristic
866C2×C3C2×D3×#4111yescharacteristic
867C2×C3C2×D3×#4111yescharacteristic
868C2×C3C2×#101011yescharacteristic
869C2×C3C2×#101011yescharacteristic
870D3—122no—
871D3—122no—
872D3—242no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—44no—
880C22—44no—
881C22—182no—
882C22—182no—
883C22—182no—
884C22—364no—
885C22#6430912yes—
886C22#6431212yes—
887C22#6433012yes—
888C22C23×D3211yescharacteristic
889C4—22no—
890C4—62no—
891C4—62no—
892C4—62no—
893C4—62no—
894C4—62no—
895C4—62no—
896C4—62no—
897C4—62no—
898C4—94no—
899C4—182no—
900C4—182no—
901C3—21no—
902C3C2×#566211yescharacteristic, complemented
903C3C2×#566911yescharacteristic, complemented
904C2—42no—
905C2—42no—
906C2—362no—
907C2#1059521114yesdirect product factor
908C2C2×#6430911yescharacteristic
909C2C2×#6431211yescharacteristic
910C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
prime radicalC2×#64148C2
hypercenterC22×D4D32
hypocenterC32C2×#542
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×#936C2semidirect
3. C2×C3×#935C2semidirect
4. C2×#63982C2semidirect
5. C2×#63975C2semidirect
6. C2×#63964C2semidirect
7. C2×#63957C2semidirect
8. C2×#63956C2semidirect
9. C2×#63953C2semidirect
10. C2×#63953C2semidirect
11. C2×#63952C2semidirect
12. #10595211C2direct (N × H)
13. C2×#63888C2semidirect
14. C2×#63868C2semidirect
15. C2×#63839C2semidirect
16. C2×#63837C2semidirect
39. C3×#936C22semidirect
40. C3×#935C22semidirect
44. #63982C22semidirect
45. #63975C22semidirect
53. #63964C22semidirect
57. #63957C22semidirect
58. #63956C22semidirect
62. #63953C22semidirect
63. #63953C22semidirect
64. #63952C22semidirect
65. #63888C22semidirect
66. #63868C22semidirect
67. #63839C22semidirect
68. #63837C22semidirect
76. C2×#936D3semidirect
77. C2×#935D3semidirect
211. #936C2×D3semidirect
212. #935C2×D3semidirect
665. C2×C32#542semidirect
805. C32C2×#542semidirect
862. C2×C3#5662semidirect
863. C2×C3#5669semidirect
902. C3C2×#5662semidirect
903. C3C2×#5669semidirect
907. C2#10595211direct (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×#9362
C2×C3×#9352
C2×#639822
C2×#639752
C2×#639642
C2×#639572
C2×#639562
C2×#639532
C2×#639522
#105952112
C2×#638882
C2×#638682
C2×#638392
C2×#638372
C2×#56693
C2×#56623