Finite Group Databasebeta

← C2×#10594230 #11901719

Subgroups — C2×#10594230 #11901719

Order 1152.

2429 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64094C211yesmaximal, characteristic, complemented
2C2×C3×#886C211yesmaximal, characteristic, complemented
3C2×C3×#879C211yesmaximal, characteristic, complemented
4C2×#63971C211yesmaximal, characteristic
5C2×#63964C211yesmaximal, characteristic, complemented
6C2×#63959C211yesmaximal, characteristic, complemented
7C2×#63952C211yesmaximal, characteristic, complemented
8C2×#63919C211yesmaximal, characteristic, complemented
9C2×#63896C211yesmaximal, characteristic, complemented
10C2×#63895C211yesmaximal, characteristic, complemented
11C2×#63878C211yesmaximal, characteristic, complemented
12C2×#63854C211yesmaximal, characteristic, complemented
13C2×#63852C211yesmaximal, characteristic, complemented
14C2×#63848C211yesmaximal, characteristic, complemented
15C2×#63844C211yesmaximal, characteristic, complemented
16#10594230C2116yesmaximal, direct product factor
17C2×#5710—31nomaximal
18C2×#5662—31nomaximal
19C22×#638C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C23×C3×Dic3C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#627C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×C4×C3⋊Dic3C2211yescharacteristic
33#64094C2218yescomplemented
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×C4⋊Dic3C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×C4⋊Dic3C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C3×#886C2218yescomplemented
45C3×#879C2218yescomplemented
46#63971C2218yes—
47C2×#3724C2211yescharacteristic
48C2×#3724C2211yescharacteristic
49C2×#3724C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52#63964C2218yescomplemented
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57#63959C2218yescomplemented
58C2×Dic32C2211yescharacteristic
59C2×Dic32C2211yescharacteristic
60#63952C2218yescomplemented
61#63919C2218yescomplemented
62#63896C2218yescomplemented
63#63895C2218yescomplemented
64#63878C2218yescomplemented
65#63854C2218yescomplemented
66#63852C2218yescomplemented
67#63848C2218yescomplemented
68#63844C2218yescomplemented
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×#898—31no—
79C2×#897—31no—
80C2×#896—31no—
81C2×#896—31no—
82C2×#894—31no—
83C2×#892—31no—
84C2×#888—31no—
85C2×#888—31no—
86C2×#887—31no—
87C2×#886D311yescharacteristic, complemented
88C2×#885—31no—
89C2×#885—31no—
90C2×#885—31no—
91C2×#885—31no—
92C2×#885—61no—
93C2×#884—31no—
94C2×#883—31no—
95C2×#67⋊C4—31no—
96C2×#879D311yescharacteristic, complemented
97C2×#878—31no—
98C2×#878—31no—
99C2×#877—31no—
100C2×#875—31no—
101C2×C4×Dic6—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C2×#638—24no—
108C2×#638C2314yes—
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C2×#634—24no—
113C2×#634C2314yes—
114C2×C3×#67—42no—
115C2×C3×#67C2314yes—
116C22×C3×Dic3—42no—
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2314yes—
125C2×#627—42no—
126C2×#627—42no—
127C2×#627C2314yes—
128C2×#627C2314yes—
129C2×#626—42no—
130C2×#626C2314yes—
131C2×#624—42no—
132C2×#624C2314yes—
133C2×D3×Dic3—24no—
134C2×D3×Dic3C2314yes—
135C32×C22⋊C4C2314yes—
136#3757C2314yes—
137#3752C2314yes—
138#3752C2314yes—
139C4×C3⋊Dic3C2314yes—
140C3×#217C2314yes—
141C3×#217C2314yes—
142C3×(C2×D3)⋊C4C2314yes—
143C3×(C2×D3)⋊C4C2314yes—
144C3×C4⋊Dic3C2314yes—
145C3×C4⋊Dic3C2314yes—
146C3×C4⋊Dic3C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×Dic3⋊C4C2314yes—
149C3×C4×Dic3C2314yes—
150#3724C2314yes—
151#3724C2314yes—
152#3724C2314yes—
153Dic3⋊Dic3C2314yes—
154Dic3⋊Dic3C2314yes—
155#3722C2314yes—
156#3722C2314yes—
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—61no—
168C22×#67C2×D311yescharacteristic
169C23×Dic3—31no—
170C23×Dic3C2×D311yescharacteristic
171C22×D12—31no—
172C22×C4×D3—31no—
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C22×Dic6—31no—
176C22×Dic6—31no—
177C22×Dic6—31no—
178C22×Dic6—31no—
179C22×Dic6—31no—
180C22×Dic6—31no—
181C22×Dic6—61no—
182C3×#126—38no—
183C3×#123—38no—
184C2×C3×C4⋊C4—31no—
185C2×C3×C4⋊C4—31no—
186C2×C3×C4⋊C4—31no—
187C2×C3×C4⋊C4—31no—
188C2×C3×C4⋊C4—31no—
189C2×C3×C22⋊C4—21no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4C2×D311yescharacteristic
195C2×C3×C22⋊C4C2×D311yescharacteristic
196C2×C3×C42—31no—
197C2×#217—31no—
198C2×#217—31no—
199C2×#217—31no—
200C2×#217—31no—
201C2×#217—61no—
202C2×#217C2×D311yescharacteristic
203C2×#217C2×D311yescharacteristic
204#939—38no—
205#936—38no—
206C4×#67—38no—
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)⋊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—61no—
218C2×(C2×D3)⋊C4—61no—
219C2×(C2×D3)⋊C4C2×D311yescharacteristic
220C2×(C2×D3)⋊C4C2×D311yescharacteristic
221C2×C4⋊Dic3—31no—
222C2×C4⋊Dic3—31no—
223C2×C4⋊Dic3C2×D311yescharacteristic
224C2×C4⋊Dic3C2×D311yescharacteristic
225C2×C4⋊Dic3C2×D311yescharacteristic
226#924—38no—
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⋊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#898—38no—
247#897—38no—
248#896—38no—
249#896—38no—
250#894—38no—
251#892—38no—
252#888—38no—
253#888—38no—
254#887—38no—
255#886C2×D318yescomplemented
256#885—38no—
257#885—38no—
258#885—38no—
259#885—38no—
260#885—68no—
261#884—38no—
262#883—38no—
263#67⋊C4—38no—
264#879C2×D318yescomplemented
265#878—38no—
266#878—38no—
267#877—38no—
268#875—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⋊D3C2412yes—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3C2412yes—
283C2×C32×C4—22no—
284C2×C32×C4—22no—
285C2×C32×C4C2412yes—
286C2×C32×C4C2412yes—
287#638—28no—
288C2×C3⋊Dic3—22no—
289C2×C3⋊Dic3—22no—
290C2×C3⋊Dic3#4114yes—
291C2×C3⋊Dic3C2412yes—
292C2×C3⋊Dic3C2412yes—
293C2×C3⋊Dic3C2412yes—
294#634—28no—
295C3×#67—44no—
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—
311#627—44no—
312#627—44no—
313#626—44no—
314#624—44no—
315D3×Dic3—28no—
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—21no—
333C24×C3—31no—
334C24×C3C22×D311yescharacteristic
335C24×C3C22×D311yescharacteristic
336C23×D3—31no—
337C23×D3—31no—
338C23×D3—61no—
339C23×D3C22×D311yescharacteristic
340C2×C3×D4—34no—
341C2×C3×D4—122no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—34no—
352C22×C3×C4—122no—
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C22×C3×C4C22×D311yescharacteristic
357C2×#67—34no—
358C2×#67—34no—
359C2×#67—34no—
360C2×#67—42no—
361C2×#67—64no—
362C2×#67—64no—
363C2×#67—64no—
364C2×#67—124no—
365C2×#67—122no—
366C2×#67C22×D314yes—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—31no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—34no—
374C22×Dic3—42no—
375C22×Dic3—61no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—64no—
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C22×Dic3C22×D311yescharacteristic
386C22×Dic3C22×D314yes—
387C2×D12—34no—
388C2×D12—122no—
389C2×C4×D3—34no—
390C2×C4×D3—34no—
391C2×C4×D3—34no—
392C2×C4×D3—64no—
393C2×C4×D3—122no—
394C2×C4×D3—122no—
395C2×Dic6—34no—
396C2×Dic6—34no—
397C2×Dic6—34no—
398C2×Dic6—34no—
399C2×Dic6—34no—
400C2×Dic6—34no—
401C2×Dic6—64no—
402C2×Dic6—64no—
403C2×Dic6—64no—
404C2×Dic6—124no—
405C2×Dic6—122no—
406C2×Dic6—122no—
407C2×Dic6—122no—
408C2×Dic6—122no—
409C3×C4⋊C4—34no—
410C3×C4⋊C4—34no—
411C3×C4⋊C4—34no—
412C3×C4⋊C4—34no—
413C3×C4⋊C4—34no—
414C3×C22⋊C4—24no—
415C3×C22⋊C4—34no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—34no—
418C3×C22⋊C4—34no—
419C3×C22⋊C4C22×D314yes—
420C3×C22⋊C4C22×D314yes—
421C3×C42—34no—
422#217—34no—
423#217—34no—
424#217—34no—
425#217—34no—
426#217—64no—
427#217C22×D314yes—
428#217C22×D314yes—
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)⋊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—64no—
440(C2×D3)⋊C4—64no—
441(C2×D3)⋊C4C22×D314yes—
442(C2×D3)⋊C4C22×D314yes—
443C4⋊Dic3—34no—
444C4⋊Dic3—34no—
445C4⋊Dic3C22×D314yes—
446C4⋊Dic3C22×D314yes—
447C4⋊Dic3C22×D314yes—
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⋊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×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—44no—
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—22no—
481C2×C3×D3—44no—
482C32×C4—22no—
483C32×C4—22no—
484C3⋊Dic3—22no—
485C3⋊Dic3—22no—
486C3⋊Dic3C2×#4114yes—
487C3×Dic3—22no—
488C3×Dic3—22no—
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—31no—
522C2×C4⋊C4—31no—
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—91no—
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—22no—
545C23×C3—22no—
546C23×C3—22no—
547C23×C3—22no—
548C23×C3—22no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—21no—
552C23×C3—32no—
553C23×C3—42no—
554C23×C3—42no—
555C23×C3—42no—
556C23×C3—62no—
557C23×C3—62no—
558C23×C3—62no—
559C23×C3C23×D312yes—
560C23×C3C23×D312yes—
561C23×C3C23×D311yescharacteristic
562C23×C3C23×D311yescharacteristic
563C22×D3—22no—
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—32no—
567C22×D3—32no—
568C22×D3—62no—
569C22×D3—62no—
570C22×D3—62no—
571C22×D3—62no—
572C22×D3—62no—
573C22×D3—62no—
574C22×D3—62no—
575C22×D3—122no—
576C22×D3—122no—
577C22×D3—122no—
578C22×D3C23×D312yes—
579C3×D4—124no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—32no—
587C2×C3×C4—32no—
588C2×C3×C4—32no—
589C2×C3×C4—32no—
590C2×C3×C4—32no—
591C2×C3×C4—32no—
592C2×C3×C4—32no—
593C2×C3×C4—42no—
594C2×C3×C4—42no—
595C2×C3×C4—62no—
596C2×C3×C4—62no—
597C2×C3×C4—62no—
598C2×C3×C4—62no—
599C2×C3×C4—62no—
600C2×C3×C4—62no—
601C2×C3×C4—62no—
602C2×C3×C4—124no—
603C2×C3×C4C23×D312yes—
604C2×C3×C4C23×D312yes—
605C2×C3×C4C23×D312yes—
606C2×C3×C4C23×D312yes—
607#67—44no—
608#67—68no—
609#67—68no—
610#67—128no—
611#67—124no—
612C2×Dic3—22no—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—34no—
620C2×Dic3—34no—
621C2×Dic3—32no—
622C2×Dic3—32no—
623C2×Dic3—32no—
624C2×Dic3—32no—
625C2×Dic3—32no—
626C2×Dic3—32no—
627C2×Dic3—44no—
628C2×Dic3—64no—
629C2×Dic3—62no—
630C2×Dic3—62no—
631C2×Dic3—62no—
632C2×Dic3—68no—
633C2×Dic3—62no—
634C2×Dic3—62no—
635C2×Dic3—62no—
636C2×Dic3—62no—
637C2×Dic3—122no—
638C2×Dic3—122no—
639C2×Dic3C23×D312yes—
640C2×Dic3C23×D312yes—
641C2×Dic3C23×D312yes—
642C2×Dic3C23×D312yes—
643C2×Dic3C23×D312yes—
644C2×Dic3C23×D312yes—
645C2×Dic3C23×D312yes—
646D12—124no—
647C4×D3—68no—
648C4×D3—124no—
649C4×D3—124no—
650Dic6—68no—
651Dic6—68no—
652Dic6—128no—
653Dic6—124no—
654Dic6—124no—
655Dic6—124no—
656Dic6—124no—
657C2×C32—42no—
658C2×C32#54214yescomplemented
659C2×C32C22×#4111yescharacteristic
660C2×C32C2×H(5,𝔽2)11yescharacteristic
661C2×C32C2×2−1+411yescharacteristic
662C3⋊D3—42no—
663C3×D3—42no—
664C24—31no—
665C24—91no—
666C24C2×D3211yescharacteristic
667C2×Q8—94no—
668C2×Q8—94no—
669C2×Q8—94no—
670C2×Q8—184no—
671C2×Q8—362no—
672C2×Q8—362no—
673C2×D4—34no—
674C2×D4—94no—
675C2×D4—94no—
676C2×D4—122no—
677C2×D4—184no—
678C2×D4—362no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—31no—
682C22×C4—31no—
683C22×C4—31no—
684C22×C4—31no—
685C22×C4—31no—
686C22×C4—34no—
687C22×C4—94no—
688C22×C4—94no—
689C22×C4—91no—
690C22×C4—91no—
691C22×C4—91no—
692C22×C4—122no—
693C22×C4—184no—
694C22×C4—362no—
695C22×C4C2×D3211yescharacteristic
696C22×C4C2×D3211yescharacteristic
697C4⋊C4—34no—
698C4⋊C4—34no—
699C4⋊C4—34no—
700C4⋊C4—34no—
701C4⋊C4—34no—
702C4⋊C4—94no—
703C4⋊C4—94no—
704C4⋊C4—94no—
705C4⋊C4—94no—
706C4⋊C4—94no—
707C22⋊C4—34no—
708C22⋊C4—34no—
709C22⋊C4—34no—
710C22⋊C4—34no—
711C22⋊C4—94no—
712C22⋊C4—94no—
713C22⋊C4—94no—
714C22⋊C4—94no—
715C22⋊C4—94no—
716C22⋊C4—94no—
717C22⋊C4—94no—
718C22⋊C4C2×D3214yes—
719C42—34no—
720C42—94no—
721C42—94no—
722C42—94no—
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—22no—
732C22×C3—21no—
733C22×C3—42no—
734C22×C3—42no—
735C22×C3—42no—
736C22×C3—44no—
737C22×C3—44no—
738C22×C3—62no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—84no—
742C22×C3—124no—
743C22×C3#100412yes—
744C22×C3D3×#4112yes—
745C22×C3D3×#4112yes—
746C22×C3#100912yes—
747C22×C3#101012yes—
748C22×C3#101012yes—
749C22×C3C24×D311yescharacteristic
750C22×C3C24×D311yescharacteristic
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—44no—
755C2×D3—62no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—62no—
759C2×D3—62no—
760C2×D3—62no—
761C2×D3—122no—
762C2×D3—122no—
763C2×D3—122no—
764C2×D3—124no—
765C2×D3—124no—
766C2×D3—244no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—42no—
772C3×C4—42no—
773C3×C4—62no—
774C3×C4—62no—
775C3×C4—62no—
776C3×C4—62no—
777C3×C4—62no—
778C3×C4—62no—
779C3×C4—62no—
780Dic3—22no—
781Dic3—22no—
782Dic3—22no—
783Dic3—22no—
784Dic3—22no—
785Dic3—22no—
786Dic3—22no—
787Dic3—34no—
788Dic3—34no—
789Dic3—64no—
790Dic3—62no—
791Dic3—62no—
792Dic3—62no—
793Dic3—62no—
794Dic3—122no—
795Dic3—122no—
796C32C2×#54211yescharacteristic, complemented, Sylow
797C23—22no—
798C23—22no—
799C23—22no—
800C23—32no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—92no—
805C23—182no—
806C23—182no—
807C23—182no—
808C23C22×D3212yes—
809C23C22×D3211yescharacteristic
810Q8—188no—
811Q8—364no—
812Q8—364no—
813D4—124no—
814D4—188no—
815D4—364no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—32no—
819C2×C4—32no—
820C2×C4—32no—
821C2×C4—32no—
822C2×C4—32no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—62no—
826C2×C4—62no—
827C2×C4—62no—
828C2×C4—62no—
829C2×C4—62no—
830C2×C4—62no—
831C2×C4—62no—
832C2×C4—94no—
833C2×C4—92no—
834C2×C4—92no—
835C2×C4—92no—
836C2×C4—124no—
837C2×C4—188no—
838C2×C4—182no—
839C2×C4—182no—
840C2×C4—364no—
841C2×C4C22×D3212yes—
842C2×C4C22×D3212yes—
843C2×C3—21no—
844C2×C3—21no—
845C2×C3—21no—
846C2×C3—24no—
847C2×C3—42no—
848C2×C3—42no—
849C2×C3—82no—
850C2×C3—122no—
851C2×C3#566214yescomplemented
852C2×C3#571014yescomplemented
853C2×C3C2×#100411yescharacteristic
854C2×C3C2×D3×#4111yescharacteristic
855C2×C3C2×D3×#4111yescharacteristic
856C2×C3C2×#100911yescharacteristic
857C2×C3C2×#101011yescharacteristic
858C2×C3C2×#101011yescharacteristic
859D3—42no—
860D3—122no—
861D3—122no—
862D3—242no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—44no—
867C22—62no—
868C22—62no—
869C22—62no—
870C22—124no—
871C22—182no—
872C22—182no—
873C22—182no—
874C22—364no—
875C22#6430712yes—
876C22#6430912yes—
877C22#6431212yes—
878C22C23×D3211yescharacteristic
879C4—22no—
880C4—22no—
881C4—62no—
882C4—62no—
883C4—62no—
884C4—62no—
885C4—62no—
886C4—62no—
887C4—62no—
888C4—94no—
889C4—182no—
890C4—182no—
891C3—21no—
892C3C2×#566211yescharacteristic, complemented
893C3C2×#571011yescharacteristic, complemented
894C2—42no—
895C2—122no—
896C2—362no—
897C2#1059423014yesdirect product factor
898C2C2×#6430711yescharacteristic
899C2C2×#6430911yescharacteristic
900C2C2×#6431211yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
prime radicalC2×#63971C2
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×#64094C2semidirect
2. C2×C3×#886C2semidirect
3. C2×C3×#879C2semidirect
5. C2×#63964C2semidirect
6. C2×#63959C2semidirect
7. C2×#63952C2semidirect
8. C2×#63919C2semidirect
9. C2×#63896C2semidirect
10. C2×#63895C2semidirect
11. C2×#63878C2semidirect
12. C2×#63854C2semidirect
13. C2×#63852C2semidirect
14. C2×#63848C2semidirect
15. C2×#63844C2semidirect
16. #10594230C2direct (N × H)
33. #64094C22semidirect
44. C3×#886C22semidirect
45. C3×#879C22semidirect
52. #63964C22semidirect
57. #63959C22semidirect
60. #63952C22semidirect
61. #63919C22semidirect
62. #63896C22semidirect
63. #63895C22semidirect
64. #63878C22semidirect
65. #63854C22semidirect
66. #63852C22semidirect
67. #63848C22semidirect
68. #63844C22semidirect
87. C2×#886D3semidirect
96. C2×#879D3semidirect
255. #886C2×D3semidirect
264. #879C2×D3semidirect
658. C2×C32#542semidirect
796. C32C2×#542semidirect
851. C2×C3#5662semidirect
852. C2×C3#5710semidirect
892. C3C2×#5662semidirect
893. C3C2×#5710semidirect
897. C2#10594230direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640942
C2×C3×#8862
C2×C3×#8792
C2×#639712
C2×#639642
C2×#639592
C2×#639522
C2×#639192
C2×#638962
C2×#638952
C2×#638782
C2×#638542
C2×#638522
C2×#638482
C2×#638442
#105942302
C2×#57103
C2×#56623