Finite Group Databasebeta

← C2×#10594160 #11901671

Subgroups — C2×#10594160 #11901671

Order 1152.

2425 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64087C211yesmaximal, characteristic, complemented
2C2×C3×#885C211yesmaximal, characteristic, complemented
3C2×C3×#883C211yesmaximal, characteristic, complemented
4C2×#63980C211yesmaximal, characteristic
5C2×#63969C211yesmaximal, characteristic, complemented
6C2×#63959C211yesmaximal, characteristic, complemented
7C2×#63957C211yesmaximal, characteristic, complemented
8C2×#63913C211yesmaximal, characteristic, complemented
9C2×#63899C211yesmaximal, characteristic, complemented
10C2×#63879C211yesmaximal, characteristic, complemented
11C2×#63861C211yesmaximal, characteristic, complemented
12C2×#63859C211yesmaximal, characteristic, complemented
13C2×#63856C211yesmaximal, characteristic, complemented
14C2×#63844C211yesmaximal, characteristic, complemented
15C2×#63839C211yesmaximal, characteristic, complemented
16#10594160C2116yesmaximal, direct product factor
17C2×#5669—31nomaximal
18C2×#5662—31nomaximal
19C23×C3⋊Dic3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C22×#627C2211yescharacteristic
26C22×#625C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33#64087C2218yescomplemented
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×Dic3⋊C4C2211yescharacteristic
41C2×C3×C4×Dic3C2211yescharacteristic
42C3×#885C2218yescomplemented
43C3×#883C2218yescomplemented
44#63980C2218yes—
45#63969C2218yescomplemented
46C2×#3724C2211yescharacteristic
47C2×#3724C2211yescharacteristic
48C2×#3724C2211yescharacteristic
49C2×#3724C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×(C2×D3)⋊Dic3C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56#63959C2218yescomplemented
57#63957C2218yescomplemented
58C2×Dic32C2211yescharacteristic
59C2×Dic32C2211yescharacteristic
60C2×Dic32C2211yescharacteristic
61#63913C2218yescomplemented
62#63899C2218yescomplemented
63#63879C2218yescomplemented
64#63861C2218yescomplemented
65#63859C2218yescomplemented
66#63856C2218yescomplemented
67#63844C2218yescomplemented
68#63839C2218yescomplemented
69C2×C3×#124—31no—
70C2×C3×#123—31no—
71C2×#946—31no—
72C2×#944—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#936—31no—
76C2×#935—31no—
77C2×C4×#67—31no—
78C2×#924—31no—
79#5669—316no—
80#5662—316no—
81C2×#898—31no—
82C2×#896—31no—
83C2×#888—31no—
84C2×#887—31no—
85C2×#885—31no—
86C2×#885—31no—
87C2×#885—31no—
88C2×#885D311yescharacteristic, complemented
89C2×#883—31no—
90C2×#883D311yescharacteristic, complemented
91C2×#67⋊C4—31no—
92C2×#879—31no—
93C2×#879—31no—
94C2×#878—31no—
95C2×#878—31no—
96C2×#878—31no—
97C2×#878—61no—
98C2×#877—31no—
99C2×#877—31no—
100C2×#876—31no—
101C2×C4×Dic6—31no—
102C24×C32C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C3⋊Dic3—24no—
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2314yes—
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C2×#634—24no—
114C2×#634C2314yes—
115C2×C3×#67—42no—
116C2×C3×#67—42no—
117C2×C3×#67C2314yes—
118C2×C3×#67C2314yes—
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×C3×C4×D3—42no—
126C2×C3×C4×D3C2314yes—
127C2×C3×Dic6—42no—
128C2×C3×Dic6C2314yes—
129C2×#627—42no—
130C2×#627C2314yes—
131C2×#625—24no—
132C2×#625C2314yes—
133C2×D3×Dic3—42no—
134C2×D3×Dic3C2314yes—
135C32×C22⋊C4C2314yes—
136#3757C2314yes—
137C4⋊(C3⋊Dic3)C2314yes—
138#3750C2314yes—
139#3750C2314yes—
140C3×#217C2314yes—
141C3×#217C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×C4⋊Dic3C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×C4×Dic3C2314yes—
148#3724C2314yes—
149#3724C2314yes—
150#3724C2314yes—
151#3724C2314yes—
152Dic3⋊Dic3C2314yes—
153(C2×D3)⋊Dic3C2314yes—
154(C2×D3)⋊Dic3C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157(C2×D3)⋊Dic3C2314yes—
158Dic32C2314yes—
159Dic32C2314yes—
160Dic32C2314yes—
161C2×#542—91noSylow
162C22×C3×Q8—31no—
163C22×C3×D4—31no—
164C22×C3×D4—31no—
165C23×C3×C4—31no—
166C22×#67—31no—
167C22×#67—31no—
168C22×#67C2×D311yescharacteristic
169C22×#67C2×D311yescharacteristic
170C23×Dic3—31no—
171C23×Dic3—31no—
172C23×Dic3—31no—
173C23×Dic3—61no—
174C22×C4×D3—31no—
175C22×C4×D3C2×D311yescharacteristic
176C22×Dic6—31no—
177C22×Dic6—31no—
178C22×Dic6—31no—
179C22×Dic6—31no—
180C22×Dic6—61no—
181C22×Dic6C2×D311yescharacteristic
182C3×#124—38no—
183C3×#123—38no—
184C2×C3×C4⋊C4—31no—
185C2×C3×C4⋊C4—31no—
186C2×C3×C22⋊C4—21no—
187C2×C3×C22⋊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⋊C4C2×D311yescharacteristic
193C2×C3×C22⋊C4C2×D311yescharacteristic
194C2×C3×C42—31no—
195C2×#217—31no—
196C2×#217—31no—
197C2×#217—31no—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—31no—
201C2×#217—31no—
202C2×#217—61no—
203C2×#217C2×D311yescharacteristic
204C2×#217C2×D311yescharacteristic
205#946—38no—
206#944—38no—
207#939—38no—
208#939—38no—
209#936—38no—
210#935—38no—
211C4×#67—38no—
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)⋊C4C2×D311yescharacteristic
218C2×(C2×D3)⋊C4C2×D311yescharacteristic
219C2×(C2×D3)⋊C4C2×D311yescharacteristic
220C2×C4⋊Dic3—31no—
221C2×C4⋊Dic3—31no—
222C2×C4⋊Dic3—31no—
223C2×C4⋊Dic3—61no—
224C2×C4⋊Dic3C2×D311yescharacteristic
225#924—38no—
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—31no—
237C2×Dic3⋊C4—31no—
238C2×Dic3⋊C4—31no—
239C2×Dic3⋊C4—61no—
240C2×Dic3⋊C4—61no—
241C2×Dic3⋊C4C2×D311yescharacteristic
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#898—38no—
250#896—38no—
251#888—38no—
252#887—38no—
253#885—38no—
254#885—38no—
255#885—38no—
256#885C2×D318yescomplemented
257#883—38no—
258#883C2×D318yescomplemented
259#67⋊C4—38no—
260#879—38no—
261#879—38no—
262#878—38no—
263#878—38no—
264#878—38no—
265#878—68no—
266#877—38no—
267#877—38no—
268#876—38no—
269C4×Dic6—38no—
270C23×C32—22no—
271C23×C32—22no—
272C23×C32—22no—
273C23×C32C2412yes—
274C23×C32C2411yescharacteristic
275C22×C3×D3—22no—
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3C2412yes—
282C22×C3×D3C2412yes—
283C2×C32×C4—22no—
284C2×C32×C4—22no—
285C2×C32×C4C2412yes—
286C2×C32×C4C2412yes—
287C2×C3⋊Dic3—22no—
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⋊Dic3C2412yes—
296#634—28no—
297C3×#67—44no—
298C3×#67—44no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—22no—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C3×C4×D3—44no—
312C3×Dic6—44no—
313#627—44no—
314#625—28no—
315D3×Dic3—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—31no—
334C24×C3—31no—
335C24×C3C22×D311yescharacteristic
336C24×C3C22×D311yescharacteristic
337C23×D3C22×D311yescharacteristic
338C23×D3C22×D311yescharacteristic
339C2×C3×Q8—34no—
340C2×C3×Q8—122no—
341C2×C3×D4—34no—
342C2×C3×D4—34no—
343C2×C3×D4—122no—
344C2×C3×D4—122no—
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—34no—
354C22×C3×C4—122no—
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C22×C3×C4C22×D311yescharacteristic
359C2×#67—34no—
360C2×#67—34no—
361C2×#67—42no—
362C2×#67—42no—
363C2×#67—64no—
364C2×#67—64no—
365C2×#67C22×D314yes—
366C2×#67C22×D314yes—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—34no—
370C22×Dic3—34no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—31no—
377C22×Dic3—34no—
378C22×Dic3—61no—
379C22×Dic3—64no—
380C22×Dic3—61no—
381C22×Dic3—61no—
382C22×Dic3—61no—
383C22×Dic3—64no—
384C22×Dic3—64no—
385C22×Dic3—124no—
386C22×Dic3—122no—
387C22×Dic3C22×D311yescharacteristic
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C2×C4×D3—34no—
394C2×C4×D3—42no—
395C2×C4×D3—122no—
396C2×C4×D3C22×D314yes—
397C2×Dic6—34no—
398C2×Dic6—34no—
399C2×Dic6—34no—
400C2×Dic6—34no—
401C2×Dic6—42no—
402C2×Dic6—64no—
403C2×Dic6—64no—
404C2×Dic6—64no—
405C2×Dic6—124no—
406C2×Dic6—122no—
407C2×Dic6—122no—
408C2×Dic6C22×D314yes—
409C3×C4⋊C4—34no—
410C3×C4⋊C4—34no—
411C3×C22⋊C4—24no—
412C3×C22⋊C4—34no—
413C3×C22⋊C4—34no—
414C3×C22⋊C4—34no—
415C3×C22⋊C4—34no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4C22×D314yes—
418C3×C22⋊C4C22×D314yes—
419C3×C42—34no—
420#217—34no—
421#217—34no—
422#217—34no—
423#217—34no—
424#217—34no—
425#217—34no—
426#217—34no—
427#217—64no—
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)⋊C4C22×D314yes—
436(C2×D3)⋊C4C22×D314yes—
437(C2×D3)⋊C4C22×D314yes—
438C4⋊Dic3—34no—
439C4⋊Dic3—34no—
440C4⋊Dic3—34no—
441C4⋊Dic3—64no—
442C4⋊Dic3C22×D314yes—
443Dic3⋊C4—34no—
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—34no—
455Dic3⋊C4—34no—
456Dic3⋊C4—64no—
457Dic3⋊C4—64no—
458Dic3⋊C4C22×D314yes—
459C4×Dic3—34no—
460C4×Dic3—34no—
461C4×Dic3—34no—
462C4×Dic3—34no—
463C4×Dic3—34no—
464C4×Dic3—34no—
465C4×Dic3C22×D314yes—
466C22×C32—22no—
467C22×C32—22no—
468C22×C32—22no—
469C22×C32—44no—
470C22×C32C2×#4112yes—
471C22×C32H(5,𝔽2)12yes—
472C22×C322−1+412yes—
473C22×C32C2511yescharacteristic
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—44no—
481C2×C3×D3—44no—
482C32×C4—22no—
483C32×C4—22no—
484C3⋊Dic3—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—
494C22×Q8—31no—
495C22×Q8—91no—
496C22×Q8—91no—
497C22×D4—31no—
498C22×D4—31no—
499C22×D4—91no—
500C23×C4—31no—
501C23×C4—91no—
502C23×C4—91no—
503C4⋊Q8—98no—
504#126—98no—
505#126—98no—
506#124—38no—
507#124—98no—
508#124—98no—
509#123—38no—
510#123—98no—
511C22⋊Q8—98no—
512C22⋊Q8—98no—
513C22⋊Q8—98no—
514#121—98no—
515C4×Q8—98no—
516C4×D4—98no—
517#117—98no—
518C2×C4⋊C4—31no—
519C2×C4⋊C4—31no—
520C2×C4⋊C4—91no—
521C2×C4⋊C4—91no—
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×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—31no—
532C2×C22⋊C4—31no—
533C2×C22⋊C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C2×C22⋊C4—91no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4D3211yescharacteristic
540C2×C42—31no—
541C2×C42—91no—
542C2×C42—91no—
543C2×C42—91no—
544C23×C3—24no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—21no—
553C23×C3—32no—
554C23×C3—32no—
555C23×C3—42no—
556C23×C3—42no—
557C23×C3—62no—
558C23×C3—62no—
559C23×C3—62no—
560C23×C3—62no—
561C23×C3—62no—
562C23×C3—62no—
563C23×C3C23×D312yes—
564C23×C3C23×D312yes—
565C23×C3C23×D311yescharacteristic
566C23×C3C23×D311yescharacteristic
567C22×D3—22no—
568C22×D3—22no—
569C22×D3—22no—
570C22×D3—22no—
571C22×D3—22no—
572C22×D3—22no—
573C22×D3C23×D312yes—
574C22×D3C23×D312yes—
575C3×Q8—124no—
576C3×D4—124no—
577C3×D4—124no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—32no—
585C2×C3×C4—32no—
586C2×C3×C4—32no—
587C2×C3×C4—32no—
588C2×C3×C4—32no—
589C2×C3×C4—32no—
590C2×C3×C4—42no—
591C2×C3×C4—42no—
592C2×C3×C4—62no—
593C2×C3×C4—62no—
594C2×C3×C4—62no—
595C2×C3×C4—62no—
596C2×C3×C4—62no—
597C2×C3×C4—62no—
598C2×C3×C4—124no—
599C2×C3×C4C23×D312yes—
600C2×C3×C4C23×D312yes—
601C2×C3×C4C23×D312yes—
602C2×C3×C4C23×D312yes—
603#67—44no—
604#67—44no—
605#67—68no—
606#67—68no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—22no—
613C2×Dic3—34no—
614C2×Dic3—34no—
615C2×Dic3—32no—
616C2×Dic3—32no—
617C2×Dic3—32no—
618C2×Dic3—32no—
619C2×Dic3—32no—
620C2×Dic3—32no—
621C2×Dic3—32no—
622C2×Dic3—32no—
623C2×Dic3—64no—
624C2×Dic3—62no—
625C2×Dic3—62no—
626C2×Dic3—62no—
627C2×Dic3—62no—
628C2×Dic3—68no—
629C2×Dic3—68no—
630C2×Dic3—62no—
631C2×Dic3—62no—
632C2×Dic3—62no—
633C2×Dic3—62no—
634C2×Dic3—62no—
635C2×Dic3—62no—
636C2×Dic3—128no—
637C2×Dic3—122no—
638C2×Dic3—122no—
639C2×Dic3—122no—
640C2×Dic3—124no—
641C2×Dic3C23×D312yes—
642C2×Dic3C23×D312yes—
643C2×Dic3C23×D312yes—
644C2×Dic3C23×D312yes—
645C2×Dic3C23×D312yes—
646C2×Dic3C23×D312yes—
647C4×D3—44no—
648C4×D3—124no—
649Dic6—44no—
650Dic6—68no—
651Dic6—68no—
652Dic6—128no—
653Dic6—124no—
654Dic6—124no—
655C2×C32—42no—
656C2×C32#54214yescomplemented
657C2×C32C22×#4111yescharacteristic
658C2×C32C2×H(5,𝔽2)11yescharacteristic
659C2×C32C2×2−1+411yescharacteristic
660C3×D3—42no—
661C3×D3—42no—
662C24—31no—
663C24—31no—
664C24C2×D3211yescharacteristic
665C2×Q8—34no—
666C2×Q8—94no—
667C2×Q8—94no—
668C2×Q8—122no—
669C2×Q8—184no—
670C2×Q8—362no—
671C2×D4—34no—
672C2×D4—34no—
673C2×D4—94no—
674C2×D4—122no—
675C2×D4—122no—
676C2×D4—184no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—34no—
684C22×C4—94no—
685C22×C4—91no—
686C22×C4—94no—
687C22×C4—91no—
688C22×C4—91no—
689C22×C4—91no—
690C22×C4—122no—
691C22×C4—184no—
692C22×C4—362no—
693C22×C4C2×D3211yescharacteristic
694C22×C4C2×D3211yescharacteristic
695C4⋊C4—34no—
696C4⋊C4—34no—
697C4⋊C4—94no—
698C4⋊C4—94no—
699C4⋊C4—94no—
700C4⋊C4—94no—
701C4⋊C4—94no—
702C4⋊C4—94no—
703C4⋊C4—94no—
704C4⋊C4—94no—
705C22⋊C4—34no—
706C22⋊C4—34no—
707C22⋊C4—34no—
708C22⋊C4—34no—
709C22⋊C4—34no—
710C22⋊C4—94no—
711C22⋊C4—94no—
712C22⋊C4—94no—
713C22⋊C4—94no—
714C22⋊C4—94no—
715C22⋊C4—94no—
716C22⋊C4C2×D3214yes—
717C42—34no—
718C42—94no—
719C42—94no—
720C42—94no—
721C22×C3—24no—
722C22×C3—22no—
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—21no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—48no—
735C22×C3—44no—
736C22×C3—44no—
737C22×C3—62no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3—62no—
743C22×C3—124no—
744C22×C3—124no—
745C22×C3#100412yes—
746C22×C3#100412yes—
747C22×C3D3×#4112yes—
748C22×C3D3×#4112yes—
749C22×C3#101012yes—
750C22×C3#101012yes—
751C22×C3C24×D311yescharacteristic
752C22×C3C24×D311yescharacteristic
753C2×D3—22no—
754C2×D3—22no—
755C2×D3—22no—
756C2×D3—22no—
757C2×D3—22no—
758C2×D3—22no—
759C2×D3—44no—
760C2×D3—44no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—22no—
764C3×C4—22no—
765C3×C4—42no—
766C3×C4—42no—
767C3×C4—62no—
768C3×C4—62no—
769C3×C4—62no—
770C3×C4—62no—
771C3×C4—62no—
772C3×C4—62no—
773Dic3—22no—
774Dic3—22no—
775Dic3—22no—
776Dic3—22no—
777Dic3—22no—
778Dic3—22no—
779Dic3—34no—
780Dic3—34no—
781Dic3—64no—
782Dic3—62no—
783Dic3—62no—
784Dic3—62no—
785Dic3—62no—
786Dic3—62no—
787Dic3—62no—
788Dic3—122no—
789Dic3—122no—
790Dic3—122no—
791C32C2×#54211yescharacteristic, complemented, Sylow
792C23—22no—
793C23—22no—
794C23—22no—
795C23—32no—
796C23—32no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23C22×D3212yes—
804C23C22×D3211yescharacteristic
805Q8—124no—
806Q8—188no—
807Q8—364no—
808D4—124no—
809D4—124no—
810D4—188no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—32no—
817C2×C4—32no—
818C2×C4—32no—
819C2×C4—62no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—62no—
825C2×C4—94no—
826C2×C4—92no—
827C2×C4—92no—
828C2×C4—92no—
829C2×C4—92no—
830C2×C4—124no—
831C2×C4—188no—
832C2×C4—182no—
833C2×C4—182no—
834C2×C4—182no—
835C2×C4—364no—
836C2×C4C22×D3212yes—
837C2×C4C22×D3212yes—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—24no—
842C2×C3—44no—
843C2×C3—42no—
844C2×C3—42no—
845C2×C3—122no—
846C2×C3—122no—
847C2×C3#566214yescomplemented
848C2×C3#566914yescomplemented
849C2×C3C2×#100411yescharacteristic
850C2×C3C2×#100411yescharacteristic
851C2×C3C2×D3×#4111yescharacteristic
852C2×C3C2×D3×#4111yescharacteristic
853C2×C3C2×#101011yescharacteristic
854C2×C3C2×#101011yescharacteristic
855D3—42no—
856D3—42no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—44no—
861C22—62no—
862C22—62no—
863C22—62no—
864C22—62no—
865C22—62no—
866C22—62no—
867C22—124no—
868C22—124no—
869C22#6429812yes—
870C22#6431212yes—
871C22#6431312yes—
872C22C23×D3211yescharacteristic
873C4—22no—
874C4—22no—
875C4—62no—
876C4—62no—
877C4—62no—
878C4—62no—
879C4—62no—
880C4—62no—
881C4—94no—
882C4—182no—
883C4—182no—
884C4—182no—
885C3—21no—
886C3C2×#566211yescharacteristic, complemented
887C3C2×#566911yescharacteristic, complemented
888C2—42no—
889C2—122no—
890C2—122no—
891C2#1059416014yesdirect product factor
892C2C2×#6429811yescharacteristic
893C2C2×#6431211yescharacteristic
894C2C2×#6431311yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC2×#63980C2
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#542
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64087C2semidirect
2. C2×C3×#885C2semidirect
3. C2×C3×#883C2semidirect
5. C2×#63969C2semidirect
6. C2×#63959C2semidirect
7. C2×#63957C2semidirect
8. C2×#63913C2semidirect
9. C2×#63899C2semidirect
10. C2×#63879C2semidirect
11. C2×#63861C2semidirect
12. C2×#63859C2semidirect
13. C2×#63856C2semidirect
14. C2×#63844C2semidirect
15. C2×#63839C2semidirect
16. #10594160C2direct (N × H)
33. #64087C22semidirect
42. C3×#885C22semidirect
43. C3×#883C22semidirect
45. #63969C22semidirect
56. #63959C22semidirect
57. #63957C22semidirect
61. #63913C22semidirect
62. #63899C22semidirect
63. #63879C22semidirect
64. #63861C22semidirect
65. #63859C22semidirect
66. #63856C22semidirect
67. #63844C22semidirect
68. #63839C22semidirect
88. C2×#885D3semidirect
90. C2×#883D3semidirect
256. #885C2×D3semidirect
258. #883C2×D3semidirect
656. C2×C32#542semidirect
791. C32C2×#542semidirect
847. C2×C3#5662semidirect
848. C2×C3#5669semidirect
886. C3C2×#5662semidirect
887. C3C2×#5669semidirect
891. C2#10594160direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640872
C2×C3×#8852
C2×C3×#8832
C2×#639802
C2×#639692
C2×#639592
C2×#639572
C2×#639132
C2×#638992
C2×#638792
C2×#638612
C2×#638592
C2×#638562
C2×#638442
C2×#638392
#105941602
C2×#56693
C2×#56623