Finite Group Databasebeta

← C2×#10594487 #11901722

Subgroups — C2×#10594487 #11901722

Order 1152.

2409 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64097C211yesmaximal, characteristic, complemented
2C2×C3×#898C211yesmaximal, characteristic, complemented
3C2×C3×#894C211yesmaximal, characteristic, complemented
4C2×#63915C211yesmaximal, characteristic, complemented
5C2×#63913C211yesmaximal, characteristic, complemented
6C2×#63899C211yesmaximal, characteristic, complemented
7C2×#63896C211yesmaximal, characteristic, complemented
8C2×#63891C211yesmaximal, characteristic, complemented
9C2×#63885C211yesmaximal, characteristic
10C2×#63879C211yesmaximal, characteristic, complemented
11C2×#63878C211yesmaximal, characteristic, complemented
12C2×#63861C211yesmaximal, characteristic, complemented
13C2×#63860C211yesmaximal, characteristic, complemented
14C2×#63857C211yesmaximal, characteristic, complemented
15C2×#63837C211yesmaximal, characteristic, complemented
16#10594487C2116yesmaximal, direct product factor
17C2×#5710—31nomaximal
18C2×#5662—31nomaximal
19C22×#634C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#625C2211yescharacteristic
25C22×#625C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C4⋊C4C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×#3750C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33#64097C2218yescomplemented
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×C4⋊Dic3C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C3×#898C2218yescomplemented
45C3×#894C2218yescomplemented
46C2×#3724C2211yescharacteristic
47C2×Dic3⋊Dic3C2211yescharacteristic
48C2×Dic3⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×(C2×D3)⋊Dic3C2211yescharacteristic
51C2×(C2×D3)⋊Dic3C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63915C2218yescomplemented
58#63913C2218yescomplemented
59#63899C2218yescomplemented
60#63896C2218yescomplemented
61#63891C2218yescomplemented
62#63885C2218yes—
63#63879C2218yescomplemented
64#63878C2218yescomplemented
65#63861C2218yescomplemented
66#63860C2218yescomplemented
67#63857C2218yescomplemented
68#63837C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×#123—31no—
71C2×#939—31no—
72C2×#936—31no—
73C2×C4×#67—31no—
74C2×#924—31no—
75#5710—316no—
76#5662—316no—
77C2×#898—31no—
78C2×#898D311yescharacteristic, complemented
79C2×#897—31no—
80C2×#896—31no—
81C2×#896—31no—
82C2×#894D311yescharacteristic, complemented
83C2×#892—31no—
84C2×#888—31no—
85C2×#888—31no—
86C2×#888—61no—
87C2×#887—31no—
88C2×#886—31no—
89C2×#885—31no—
90C2×#885—31no—
91C2×#885—31no—
92C2×#885—31no—
93C2×#884—31no—
94C2×#883—31no—
95C2×#67⋊C4—31no—
96C2×#879—31no—
97C2×#878—31no—
98C2×#878—31no—
99C2×#877—31no—
100C2×#875—31no—
101C2×C4×Dic6—31no—
102C23×C3×D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C2×#634—42no—
113C2×#634—42no—
114C2×#634C2314yes—
115C2×#634C2314yes—
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C2×C3×D12—42no—
122C2×C3×D12C2314yes—
123C2×C3×C4×D3—42no—
124C2×C3×C4×D3C2314yes—
125C2×#627—24no—
126C2×#627C2314yes—
127C2×#625—24no—
128C2×#625—42no—
129C2×#625C2314yes—
130C2×#625C2314yes—
131C2×D3×Dic3—24no—
132C2×D3×Dic3—42no—
133C2×D3×Dic3C2314yes—
134C2×D3×Dic3C2314yes—
135C32×C4⋊C4C2314yes—
136C4⋊(C3⋊Dic3)C2314yes—
137#3750C2314yes—
138#3750C2314yes—
139C4×C3⋊Dic3C2314yes—
140C3×(C2×D3)⋊C4C2314yes—
141C3×(C2×D3)⋊C4C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×(C2×D3)⋊C4C2314yes—
146C3×C4⋊Dic3C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×Dic3⋊C4C2314yes—
149C3×C4×Dic3C2314yes—
150#3724C2314yes—
151Dic3⋊Dic3C2314yes—
152Dic3⋊Dic3C2314yes—
153(C2×D3)⋊Dic3C2314yes—
154(C2×D3)⋊Dic3C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157(C2×D3)⋊Dic3C2314yes—
158(C2×D3)⋊Dic3C2314yes—
159Dic32C2314yes—
160Dic32C2314yes—
161C2×#542—91noSylow
162C22×C3×D4—31no—
163C23×C3×C4—31no—
164C22×#67—31no—
165C22×#67—31no—
166C22×#67—31no—
167C22×#67—31no—
168C23×Dic3—31no—
169C23×Dic3—31no—
170C22×D12C2×D311yescharacteristic
171C22×C4×D3—31no—
172C22×C4×D3—31no—
173C22×C4×D3C2×D311yescharacteristic
174C22×Dic6—31no—
175C22×Dic6—31no—
176C22×Dic6—31no—
177C22×Dic6—31no—
178C22×Dic6—31no—
179C22×Dic6—31no—
180C22×Dic6—61no—
181C22×Dic6—61no—
182C3×#126—38no—
183C3×#123—38no—
184C2×C3×C4⋊C4—21no—
185C2×C3×C4⋊C4—31no—
186C2×C3×C4⋊C4—31no—
187C2×C3×C4⋊C4—31no—
188C2×C3×C4⋊C4C2×D311yescharacteristic
189C2×C3×C4⋊C4C2×D311yescharacteristic
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×C22⋊C4—31no—
196C2×C3×C42—31no—
197C2×#217—31no—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—31no—
201C2×#217—31no—
202C2×#217—31no—
203#939—38no—
204#936—38no—
205C4×#67—38no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4C2×D311yescharacteristic
213C2×(C2×D3)⋊C4C2×D311yescharacteristic
214C2×(C2×D3)⋊C4C2×D311yescharacteristic
215C2×(C2×D3)⋊C4C2×D311yescharacteristic
216C2×(C2×D3)⋊C4C2×D311yescharacteristic
217C2×(C2×D3)⋊C4C2×D311yescharacteristic
218C2×C4⋊Dic3—31no—
219C2×C4⋊Dic3—31no—
220C2×C4⋊Dic3—31no—
221C2×C4⋊Dic3—31no—
222C2×C4⋊Dic3—61no—
223C2×C4⋊Dic3C2×D311yescharacteristic
224#924—38no—
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—61no—
234C2×Dic3⋊C4—61no—
235C2×Dic3⋊C4C2×D311yescharacteristic
236C2×Dic3⋊C4C2×D311yescharacteristic
237C2×C4×Dic3—31no—
238C2×C4×Dic3—31no—
239C2×C4×Dic3—31no—
240C2×C4×Dic3—31no—
241C2×C4×Dic3—31no—
242C2×C4×Dic3—31no—
243C2×C4×Dic3—61no—
244C2×C4×Dic3C2×D311yescharacteristic
245#898—38no—
246#898C2×D318yescomplemented
247#897—38no—
248#896—38no—
249#896—38no—
250#894C2×D318yescomplemented
251#892—38no—
252#888—38no—
253#888—38no—
254#888—68no—
255#887—38no—
256#886—38no—
257#885—38no—
258#885—38no—
259#885—38no—
260#885—38no—
261#884—38no—
262#883—38no—
263#67⋊C4—38no—
264#879—38no—
265#878—38no—
266#878—38no—
267#877—38no—
268#875—38no—
269C4×Dic6—38no—
270C23×C32C2411yescharacteristic
271C22×C3×D3—22no—
272C22×C3×D3—22no—
273C22×C3×D3—22no—
274C22×C3×D3—22no—
275C22×C3×D3—22no—
276C22×C3×D3—22no—
277C22×C3×D3—22no—
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3C2412yes—
281C22×C3×D3C2412yes—
282C22×C3×D3C2412yes—
283C2×C32×C4—22no—
284C2×C32×C4—22no—
285C2×C32×C4—22no—
286C2×C32×C4C2412yes—
287C2×C32×C4C2412yes—
288C2×C32×C4C2412yes—
289C2×C3⋊Dic3—22no—
290C2×C3⋊Dic3—22no—
291C2×C3⋊Dic3—22no—
292C2×C3⋊Dic3#4114yes—
293C2×C3⋊Dic3C2412yes—
294C2×C3⋊Dic3C2412yes—
295C2×C3⋊Dic3C2412yes—
296C2×C3⋊Dic3C2412yes—
297#634—44no—
298#634—44no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3C2412yes—
305C2×C3×Dic3C2412yes—
306C2×C3×Dic3C2412yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C3×D12—44no—
310C3×C4×D3—44no—
311#627—28no—
312#625—28no—
313#625—44no—
314D3×Dic3—28no—
315D3×Dic3—44no—
316#542—916no—
317C2×C4⋊Q8—91no—
318C2×#126—31no—
319C2×#126—91no—
320C2×#124—91no—
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—31no—
333C24×C3—31no—
334C24×C3—31no—
335C23×D3C22×D311yescharacteristic
336C23×D3C22×D311yescharacteristic
337C23×D3C22×D311yescharacteristic
338C2×C3×D4—34no—
339C2×C3×D4—122no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—34no—
349C22×C3×C4—122no—
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C2×#67—34no—
357C2×#67—34no—
358C2×#67—34no—
359C2×#67—34no—
360C2×#67—64no—
361C2×#67—64no—
362C2×#67—122no—
363C2×#67—122no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—34no—
373C22×Dic3—34no—
374C22×Dic3—61no—
375C22×Dic3—61no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—64no—
379C22×Dic3—122no—
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C2×D12—42no—
386C2×D12C22×D314yes—
387C2×C4×D3—34no—
388C2×C4×D3—34no—
389C2×C4×D3—42no—
390C2×C4×D3—64no—
391C2×C4×D3—122no—
392C2×C4×D3C22×D314yes—
393C2×Dic6—34no—
394C2×Dic6—34no—
395C2×Dic6—34no—
396C2×Dic6—34no—
397C2×Dic6—34no—
398C2×Dic6—34no—
399C2×Dic6—64no—
400C2×Dic6—64no—
401C2×Dic6—64no—
402C2×Dic6—64no—
403C2×Dic6—122no—
404C2×Dic6—122no—
405C2×Dic6—122no—
406C2×Dic6—122no—
407C2×Dic6—124no—
408C2×Dic6—124no—
409C3×C4⋊C4—24no—
410C3×C4⋊C4—34no—
411C3×C4⋊C4—34no—
412C3×C4⋊C4—34no—
413C3×C4⋊C4C22×D314yes—
414C3×C4⋊C4C22×D314yes—
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×C42—34no—
422#217—34no—
423#217—34no—
424#217—34no—
425#217—34no—
426#217—34no—
427#217—34no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—34no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4C22×D314yes—
435(C2×D3)⋊C4C22×D314yes—
436(C2×D3)⋊C4C22×D314yes—
437(C2×D3)⋊C4C22×D314yes—
438(C2×D3)⋊C4C22×D314yes—
439(C2×D3)⋊C4C22×D314yes—
440C4⋊Dic3—34no—
441C4⋊Dic3—34no—
442C4⋊Dic3—34no—
443C4⋊Dic3—34no—
444C4⋊Dic3—64no—
445C4⋊Dic3C22×D314yes—
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⋊C4—64no—
456Dic3⋊C4C22×D314yes—
457Dic3⋊C4C22×D314yes—
458C4×Dic3—34no—
459C4×Dic3—34no—
460C4×Dic3—34no—
461C4×Dic3—34no—
462C4×Dic3—34no—
463C4×Dic3—34no—
464C4×Dic3—64no—
465C4×Dic3C22×D314yes—
466C22×C32C2×#4112yes—
467C22×C32H(5,𝔽2)12yes—
468C22×C322−1+412yes—
469C22×C32C2511yescharacteristic
470C2×C3×D3—22no—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—44no—
480C2×C3×D3—44no—
481C2×C3×D3—44no—
482C32×C4—22no—
483C32×C4—22no—
484C32×C4—22no—
485C3⋊Dic3—22no—
486C3⋊Dic3—22no—
487C3⋊Dic3—22no—
488C3⋊Dic3C2×#4114yes—
489C3×Dic3—22no—
490C3×Dic3—22no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3—22no—
494C22×Q8—91no—
495C22×Q8—91no—
496C22×Q8—91no—
497C22×D4—31no—
498C22×D4—91no—
499C22×D4—91no—
500C23×C4—31no—
501C23×C4—91no—
502C23×C4—91no—
503C4⋊Q8—98no—
504#126—38no—
505#126—98no—
506#124—98no—
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—31no—
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⋊C4D3211yescharacteristic
528C2×C22⋊C4—31no—
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×C22⋊C4—91no—
540C2×C42—31no—
541C2×C42—91no—
542C2×C42—91no—
543C2×C42—91no—
544C23×C3—21no—
545C23×C3—32no—
546C23×C3—32no—
547C23×C3—32no—
548C23×C3—62no—
549C23×C3—62no—
550C23×C3—62no—
551C23×C3—62no—
552C23×C3—62no—
553C23×C3—62no—
554C23×C3—62no—
555C23×C3—62no—
556C23×C3—62no—
557C23×C3C23×D311yescharacteristic
558C23×C3C23×D311yescharacteristic
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3—22no—
568C22×D3C23×D312yes—
569C22×D3C23×D312yes—
570C22×D3C23×D312yes—
571C3×D4—124no—
572C2×C3×C4—24no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—32no—
583C2×C3×C4—32no—
584C2×C3×C4—32no—
585C2×C3×C4—32no—
586C2×C3×C4—32no—
587C2×C3×C4—42no—
588C2×C3×C4—42no—
589C2×C3×C4—62no—
590C2×C3×C4—62no—
591C2×C3×C4—62no—
592C2×C3×C4—62no—
593C2×C3×C4—62no—
594C2×C3×C4—124no—
595C2×C3×C4C23×D312yes—
596C2×C3×C4C23×D312yes—
597C2×C3×C4C23×D312yes—
598C2×C3×C4C23×D312yes—
599C2×C3×C4C23×D312yes—
600C2×C3×C4C23×D312yes—
601#67—68no—
602#67—68no—
603#67—124no—
604#67—124no—
605C2×Dic3—22no—
606C2×Dic3—22no—
607C2×Dic3—22no—
608C2×Dic3—22no—
609C2×Dic3—22no—
610C2×Dic3—34no—
611C2×Dic3—34no—
612C2×Dic3—32no—
613C2×Dic3—32no—
614C2×Dic3—32no—
615C2×Dic3—32no—
616C2×Dic3—32no—
617C2×Dic3—32no—
618C2×Dic3—32no—
619C2×Dic3—32no—
620C2×Dic3—64no—
621C2×Dic3—62no—
622C2×Dic3—62no—
623C2×Dic3—62no—
624C2×Dic3—62no—
625C2×Dic3—68no—
626C2×Dic3—64no—
627C2×Dic3—62no—
628C2×Dic3—62no—
629C2×Dic3—62no—
630C2×Dic3—62no—
631C2×Dic3—62no—
632C2×Dic3—62no—
633C2×Dic3—122no—
634C2×Dic3—122no—
635C2×Dic3—124no—
636C2×Dic3C23×D312yes—
637C2×Dic3C23×D312yes—
638C2×Dic3C23×D312yes—
639C2×Dic3C23×D312yes—
640C2×Dic3C23×D312yes—
641D12—44no—
642C4×D3—44no—
643C4×D3—68no—
644C4×D3—124no—
645Dic6—68no—
646Dic6—68no—
647Dic6—124no—
648Dic6—124no—
649Dic6—124no—
650Dic6—124no—
651Dic6—128no—
652Dic6—128no—
653C2×C32#54214yescomplemented
654C2×C32C22×#4111yescharacteristic
655C2×C32C2×H(5,𝔽2)11yescharacteristic
656C2×C32C2×2−1+411yescharacteristic
657C3×D3—42no—
658C3×D3—42no—
659C3×D3—42no—
660C24—31no—
661C24—31no—
662C24—31no—
663C2×Q8—94no—
664C2×Q8—94no—
665C2×Q8—94no—
666C2×Q8—184no—
667C2×Q8—362no—
668C2×Q8—362no—
669C2×D4—34no—
670C2×D4—94no—
671C2×D4—94no—
672C2×D4—122no—
673C2×D4—184no—
674C2×D4—362no—
675C22×C4—31no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—34no—
681C22×C4—94no—
682C22×C4—94no—
683C22×C4—91no—
684C22×C4—91no—
685C22×C4—91no—
686C22×C4—91no—
687C22×C4—122no—
688C22×C4—184no—
689C22×C4—362no—
690C22×C4C2×D3211yescharacteristic
691C22×C4C2×D3211yescharacteristic
692C22×C4C2×D3211yescharacteristic
693C4⋊C4—34no—
694C4⋊C4—34no—
695C4⋊C4—34no—
696C4⋊C4—94no—
697C4⋊C4—94no—
698C4⋊C4—94no—
699C4⋊C4—94no—
700C4⋊C4—94no—
701C4⋊C4—94no—
702C4⋊C4C2×D3214yes—
703C22⋊C4—34no—
704C22⋊C4—34no—
705C22⋊C4—34no—
706C22⋊C4—34no—
707C22⋊C4—34no—
708C22⋊C4—34no—
709C22⋊C4—94no—
710C22⋊C4—94no—
711C22⋊C4—94no—
712C22⋊C4—94no—
713C22⋊C4—94no—
714C22⋊C4—94no—
715C42—34no—
716C42—94no—
717C42—94no—
718C42—94no—
719C22×C3—22no—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—21no—
723C22×C3—62no—
724C22×C3—62no—
725C22×C3—62no—
726C22×C3—62no—
727C22×C3—62no—
728C22×C3—62no—
729C22×C3—62no—
730C22×C3—62no—
731C22×C3—62no—
732C22×C3—124no—
733C22×C3—124no—
734C22×C3—124no—
735C22×C3#100412yes—
736C22×C3D3×#4112yes—
737C22×C3D3×#4112yes—
738C22×C3#100912yes—
739C22×C3#101012yes—
740C22×C3#101012yes—
741C22×C3C24×D311yescharacteristic
742C22×C3C24×D311yescharacteristic
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—44no—
753C2×D3—44no—
754C2×D3—44no—
755C3×C4—24no—
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—42no—
763C3×C4—42no—
764C3×C4—62no—
765C3×C4—62no—
766C3×C4—62no—
767C3×C4—62no—
768C3×C4—62no—
769Dic3—22no—
770Dic3—22no—
771Dic3—22no—
772Dic3—22no—
773Dic3—22no—
774Dic3—34no—
775Dic3—34no—
776Dic3—64no—
777Dic3—64no—
778Dic3—62no—
779Dic3—62no—
780Dic3—62no—
781Dic3—62no—
782Dic3—62no—
783Dic3—62no—
784Dic3—122no—
785Dic3—122no—
786C32C2×#54211yescharacteristic, complemented, Sylow
787C23—32no—
788C23—32no—
789C23—32no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23—62no—
794C23—62no—
795C23—62no—
796C23—62no—
797C23—62no—
798C23—62no—
799C23C22×D3211yescharacteristic
800Q8—188no—
801Q8—364no—
802Q8—364no—
803D4—124no—
804D4—188no—
805D4—364no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—32no—
810C2×C4—32no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—32no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—94no—
820C2×C4—92no—
821C2×C4—92no—
822C2×C4—92no—
823C2×C4—92no—
824C2×C4—124no—
825C2×C4—188no—
826C2×C4—182no—
827C2×C4—182no—
828C2×C4—182no—
829C2×C4—364no—
830C2×C4C22×D3212yes—
831C2×C4C22×D3212yes—
832C2×C4C22×D3212yes—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—24no—
837C2×C3—122no—
838C2×C3—122no—
839C2×C3—122no—
840C2×C3#566214yescomplemented
841C2×C3#571014yescomplemented
842C2×C3C2×#100411yescharacteristic
843C2×C3C2×D3×#4111yescharacteristic
844C2×C3C2×D3×#4111yescharacteristic
845C2×C3C2×#100911yescharacteristic
846C2×C3C2×#101011yescharacteristic
847C2×C3C2×#101011yescharacteristic
848D3—42no—
849D3—42no—
850D3—42no—
851C22—62no—
852C22—62no—
853C22—62no—
854C22—62no—
855C22—62no—
856C22—62no—
857C22—62no—
858C22—62no—
859C22—62no—
860C22—124no—
861C22—124no—
862C22—124no—
863C22#6429812yes—
864C22#6431412yes—
865C22#6431912yes—
866C22C23×D3211yescharacteristic
867C4—22no—
868C4—22no—
869C4—22no—
870C4—62no—
871C4—62no—
872C4—62no—
873C4—62no—
874C4—62no—
875C4—94no—
876C4—182no—
877C4—182no—
878C4—182no—
879C3—21no—
880C3C2×#566211yescharacteristic, complemented
881C3C2×#571011yescharacteristic, complemented
882C2—122no—
883C2—122no—
884C2—122no—
885C2#1059448714yesdirect product factor
886C2C2×#6429811yescharacteristic
887C2C2×#6431411yescharacteristic
888C2C2×#6431911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
prime radicalC2×#63885C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#542
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64097C2semidirect
2. C2×C3×#898C2semidirect
3. C2×C3×#894C2semidirect
4. C2×#63915C2semidirect
5. C2×#63913C2semidirect
6. C2×#63899C2semidirect
7. C2×#63896C2semidirect
8. C2×#63891C2semidirect
10. C2×#63879C2semidirect
11. C2×#63878C2semidirect
12. C2×#63861C2semidirect
13. C2×#63860C2semidirect
14. C2×#63857C2semidirect
15. C2×#63837C2semidirect
16. #10594487C2direct (N × H)
33. #64097C22semidirect
44. C3×#898C22semidirect
45. C3×#894C22semidirect
57. #63915C22semidirect
58. #63913C22semidirect
59. #63899C22semidirect
60. #63896C22semidirect
61. #63891C22semidirect
63. #63879C22semidirect
64. #63878C22semidirect
65. #63861C22semidirect
66. #63860C22semidirect
67. #63857C22semidirect
68. #63837C22semidirect
78. C2×#898D3semidirect
82. C2×#894D3semidirect
246. #898C2×D3semidirect
250. #894C2×D3semidirect
653. C2×C32#542semidirect
786. C32C2×#542semidirect
840. C2×C3#5662semidirect
841. C2×C3#5710semidirect
880. C3C2×#5662semidirect
881. C3C2×#5710semidirect
885. C2#10594487direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640972
C2×C3×#8982
C2×C3×#8942
C2×#639152
C2×#639132
C2×#638992
C2×#638962
C2×#638912
C2×#638852
C2×#638792
C2×#638782
C2×#638612
C2×#638602
C2×#638572
C2×#638372
#105944872
C2×#57103
C2×#56623