Finite Group Databasebeta

← C2×#10594590 #11910260

Subgroups — C2×#10594590 #11910260

Order 1152.

2465 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64106C211yesmaximal, characteristic, complemented
2C2×C3×#896C211yesmaximal, characteristic, complemented
3C2×C3×#894C211yesmaximal, characteristic, complemented
4C2×#63913C211yesmaximal, characteristic, complemented
5C2×#63912C211yesmaximal, characteristic, complemented
6C2×#63908C211yesmaximal, characteristic, complemented
7C2×#63907C211yesmaximal, characteristic, complemented
8C2×#63906C211yesmaximal, characteristic, complemented
9C2×#63896C211yesmaximal, characteristic, complemented
10C2×#63891C211yesmaximal, characteristic, complemented
11C2×#63886C211yesmaximal, characteristic, complemented
12C2×#63856C211yesmaximal, characteristic, complemented
13C2×#63853C211yesmaximal, characteristic, complemented
14C2×#63850C211yesmaximal, characteristic, complemented
15C2×#63845C211yesmaximal, characteristic, complemented
16#10594590C2116yesmaximal, direct product factor
17C2×#5667—31nomaximal
18C2×#5647—31nomaximal
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#625C2211yescharacteristic
29C22×#625C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C2×C32×C4⋊C4C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
36#64106C2218yescomplemented
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C3×#896C2218yescomplemented
46C3×#894C2218yescomplemented
47C2×#3724C2211yescharacteristic
48C2×#3724C2211yescharacteristic
49C2×Dic3⋊Dic3C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63913C2218yescomplemented
58#63912C2218yescomplemented
59#63908C2218yescomplemented
60#63907C2218yescomplemented
61#63906C2218yescomplemented
62#63896C2218yescomplemented
63#63891C2218yescomplemented
64#63886C2218yescomplemented
65#63856C2218yescomplemented
66#63853C2218yescomplemented
67#63850C2218yescomplemented
68#63845C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×C22⋊Q8—31no—
71C2×#947—31no—
72C2×#946—31no—
73C2×#939—31no—
74C2×#938—31no—
75C2×#930—31no—
76C2×#930—31no—
77C2×#929—31no—
78C2×#924—31no—
79#5667—316no—
80#5647—316no—
81C2×#897—31no—
82C2×#897—31no—
83C2×#897—61no—
84C2×#896—31no—
85C2×#896D311yescharacteristic, complemented
86C2×#895—31no—
87C2×#894—31no—
88C2×#894—31no—
89C2×#894D311yescharacteristic, complemented
90C2×#890—31no—
91C2×#889—31no—
92C2×#886—31no—
93C2×#885—31no—
94C2×#885—31no—
95C2×#885—31no—
96C2×#884—31no—
97C2×#884—31no—
98C2×#884—31no—
99C2×#883—31no—
100C2×#883—31no—
101C2×#878—31no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C22×C32×C4C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C2×C4×C3⋊D3—42no—
113C2×C4×C3⋊D3C2314yes—
114C2×#634—42no—
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×D3—42no—
125C2×C3×C4×D3C2314yes—
126C2×C3×C4×D3C2314yes—
127C2×C3×Dic6—42no—
128C2×C3×Dic6C2314yes—
129C2×#626—42no—
130C2×#626—42no—
131C2×#626—42no—
132C2×#626C2314yes—
133C2×#626C2314yes—
134C2×#626C2314yes—
135C2×#625—42no—
136C2×#625—42no—
137C2×#625C2314yes—
138C2×#625C2314yes—
139C2×D3×Dic3—42no—
140C2×D3×Dic3C2314yes—
141C32×C4⋊C4C2314yes—
142#3752C2314yes—
143#3752C2314yes—
144C4⋊(C3⋊Dic3)C2314yes—
145C4⋊(C3⋊Dic3)C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×Dic3⋊C4C2314yes—
152C3×Dic3⋊C4C2314yes—
153C3×Dic3⋊C4C2314yes—
154#3724C2314yes—
155#3724C2314yes—
156Dic3⋊Dic3C2314yes—
157Dic3⋊Dic3C2314yes—
158#3722C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163Dic32C2314yes—
164C2×#562—91noSylow
165C22×C3×Q8—31no—
166C22×C3×D4—31no—
167C23×C3×C4—31no—
168C23×C3×C4—31no—
169C22×#67—31no—
170C22×#67—31no—
171C22×#67—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C23×Dic3—31no—
177C22×D12—31no—
178C22×D12—31no—
179C22×D12—31no—
180C22×D12C2×D311yescharacteristic
181C22×C4×D3—31no—
182C22×C4×D3—31no—
183C22×C4×D3—31no—
184C22×C4×D3—61no—
185C22×C4×D3C2×D311yescharacteristic
186C22×C4×D3C2×D311yescharacteristic
187C22×Dic6—31no—
188C22×Dic6—31no—
189C22×Dic6—61no—
190C22×Dic6C2×D311yescharacteristic
191C3×#123—38no—
192C3×C22⋊Q8—38no—
193C2×C3×C4⋊C4—21no—
194C2×C3×C4⋊C4—31no—
195C2×C3×C4⋊C4—31no—
196C2×C3×C4⋊C4—31no—
197C2×C3×C4⋊C4C2×D311yescharacteristic
198C2×C3×C4⋊C4C2×D311yescharacteristic
199C2×C3×C22⋊C4—31no—
200C2×C3×C22⋊C4—31no—
201C2×C3×C22⋊C4—31no—
202C2×C3×C22⋊C4—31no—
203C2×C3×C22⋊C4—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—31no—
207C2×#217—31no—
208#947—38no—
209#946—38no—
210#939—38no—
211#938—38no—
212#930—38no—
213#930—38no—
214#929—38no—
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—31no—
223C2×(C2×D3)⋊C4—31no—
224C2×(C2×D3)⋊C4—31no—
225C2×(C2×D3)⋊C4—61no—
226C2×(C2×D3)⋊C4—61no—
227C2×(C2×D3)⋊C4C2×D311yescharacteristic
228C2×(C2×D3)⋊C4C2×D311yescharacteristic
229C2×(C2×D3)⋊C4C2×D311yescharacteristic
230C2×(C2×D3)⋊C4C2×D311yescharacteristic
231C2×(C2×D3)⋊C4C2×D311yescharacteristic
232C2×C4⋊Dic3—31no—
233C2×C4⋊Dic3—31no—
234C2×C4⋊Dic3—31no—
235C2×C4⋊Dic3—31no—
236C2×C4⋊Dic3—31no—
237C2×C4⋊Dic3—31no—
238C2×C4⋊Dic3—61no—
239C2×C4⋊Dic3—61no—
240#924—38no—
241C2×Dic3⋊C4—31no—
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—31no—
244C2×Dic3⋊C4—31no—
245C2×Dic3⋊C4—31no—
246C2×Dic3⋊C4—31no—
247C2×Dic3⋊C4C2×D311yescharacteristic
248C2×Dic3⋊C4C2×D311yescharacteristic
249C2×Dic3⋊C4C2×D311yescharacteristic
250C2×C4×Dic3—31no—
251C2×C4×Dic3—31no—
252#897—38no—
253#897—38no—
254#897—68no—
255#896—38no—
256#896C2×D318yescomplemented
257#895—38no—
258#894—38no—
259#894—38no—
260#894C2×D318yescomplemented
261#890—38no—
262#889—38no—
263#886—38no—
264#885—38no—
265#885—38no—
266#885—38no—
267#884—38no—
268#884—38no—
269#884—38no—
270#883—38no—
271#883—38no—
272#878—38no—
273C23×C32C2411yescharacteristic
274C22×C3⋊D3—22no—
275C22×C3⋊D3—22no—
276C22×C3⋊D3—22no—
277C22×C3⋊D3C2412yes—
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3C2412yes—
288C22×C3×D3C2412yes—
289C22×C3×D3C2412yes—
290C2×C32×C4—22no—
291C2×C32×C4—22no—
292C2×C32×C4—22no—
293C2×C32×C4C2412yes—
294C2×C32×C4C2412yes—
295C2×C32×C4C2412yes—
296C2×C3⋊Dic3—22no—
297C2×C3⋊Dic3—22no—
298C2×C3⋊Dic3—22no—
299C2×C3⋊Dic3C2412yes—
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2412yes—
302C4×C3⋊D3—44no—
303#634—44no—
304C2×C3×Dic3—22no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C2×C3×Dic3C2412yes—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314C3×D12—44no—
315C3×C4×D3—44no—
316C3×C4×D3—44no—
317C3×Dic6—44no—
318#626—44no—
319#626—44no—
320#626—44no—
321#625—44no—
322#625—44no—
323D3×Dic3—44no—
324#562—916no—
325C2×#125—91no—
326C2×#124—91no—
327C2×#124—91no—
328C2×#123—31no—
329C2×#123—91no—
330C2×#123—91no—
331C2×#123—91no—
332C2×C22⋊Q8—31no—
333C2×C22⋊Q8—91no—
334C2×C22⋊Q8—91no—
335C2×C22⋊Q8—91no—
336C2×#121—91no—
337C2×#121—91no—
338C2×#121—91no—
339C2×#121—91no—
340C24×C3—31no—
341C24×C3—31no—
342C24×C3—31no—
343C23×D3—31no—
344C23×D3—31no—
345C23×D3—61no—
346C23×D3C22×D311yescharacteristic
347C23×D3C22×D311yescharacteristic
348C23×D3C22×D311yescharacteristic
349C2×C3×Q8—34no—
350C2×C3×Q8—122no—
351C2×C3×D4—34no—
352C2×C3×D4—122no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—34no—
362C22×C3×C4—34no—
363C22×C3×C4—122no—
364C22×C3×C4—122no—
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C2×#67—34no—
372C2×#67—34no—
373C2×#67—34no—
374C2×#67—34no—
375C2×#67—34no—
376C2×#67—34no—
377C2×#67—34no—
378C2×#67—122no—
379C2×#67—122no—
380C2×#67—122no—
381C2×#67—122no—
382C2×#67—122no—
383C2×#67—122no—
384C2×#67—122no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—34no—
392C22×Dic3—61no—
393C22×Dic3—61no—
394C22×Dic3—61no—
395C22×Dic3—122no—
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D311yescharacteristic
401C2×D12—34no—
402C2×D12—34no—
403C2×D12—34no—
404C2×D12—42no—
405C2×D12—122no—
406C2×D12—122no—
407C2×D12—122no—
408C2×D12C22×D314yes—
409C2×C4×D3—34no—
410C2×C4×D3—34no—
411C2×C4×D3—34no—
412C2×C4×D3—42no—
413C2×C4×D3—42no—
414C2×C4×D3—64no—
415C2×C4×D3—122no—
416C2×C4×D3—122no—
417C2×C4×D3—122no—
418C2×C4×D3—124no—
419C2×C4×D3C22×D314yes—
420C2×C4×D3C22×D314yes—
421C2×Dic6—34no—
422C2×Dic6—34no—
423C2×Dic6—42no—
424C2×Dic6—64no—
425C2×Dic6—122no—
426C2×Dic6—122no—
427C2×Dic6—124no—
428C2×Dic6C22×D314yes—
429C3×C4⋊C4—24no—
430C3×C4⋊C4—34no—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—34no—
433C3×C4⋊C4C22×D314yes—
434C3×C4⋊C4C22×D314yes—
435C3×C22⋊C4—34no—
436C3×C22⋊C4—34no—
437C3×C22⋊C4—34no—
438C3×C22⋊C4—34no—
439C3×C22⋊C4—34no—
440#217—34no—
441#217—34no—
442#217—34no—
443#217—34no—
444(C2×D3)⋊C4—34no—
445(C2×D3)⋊C4—34no—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4—34no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4—64no—
455(C2×D3)⋊C4—64no—
456(C2×D3)⋊C4C22×D314yes—
457(C2×D3)⋊C4C22×D314yes—
458(C2×D3)⋊C4C22×D314yes—
459(C2×D3)⋊C4C22×D314yes—
460(C2×D3)⋊C4C22×D314yes—
461C4⋊Dic3—34no—
462C4⋊Dic3—34no—
463C4⋊Dic3—34no—
464C4⋊Dic3—34no—
465C4⋊Dic3—34no—
466C4⋊Dic3—34no—
467C4⋊Dic3—64no—
468C4⋊Dic3—64no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—34no—
474Dic3⋊C4—34no—
475Dic3⋊C4C22×D314yes—
476Dic3⋊C4C22×D314yes—
477Dic3⋊C4C22×D314yes—
478C4×Dic3—34no—
479C4×Dic3—34no—
480C22×C32H(5,𝔽2)12yes—
481C22×C32H(5,𝔽2)12yes—
482C22×C322−1+412yes—
483C22×C32C2511yescharacteristic
484C2×C3⋊D3—22no—
485C2×C3⋊D3—22no—
486C2×C3⋊D3—22no—
487C2×C3⋊D3—44no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—44no—
498C2×C3×D3—44no—
499C2×C3×D3—44no—
500C32×C4—22no—
501C32×C4—22no—
502C32×C4—22no—
503C3⋊Dic3—22no—
504C3⋊Dic3—22no—
505C3⋊Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C22×Q8—31no—
512C22×Q8—91no—
513C22×D4—31no—
514C22×D4—91no—
515C22×D4—91no—
516C22×D4—91no—
517C22×D4—91no—
518C22×D4—91no—
519C23×C4—31no—
520C23×C4—31no—
521C23×C4—91no—
522C23×C4—91no—
523#125—98no—
524#124—98no—
525#124—98no—
526#123—38no—
527#123—98no—
528#123—98no—
529#123—98no—
530C22⋊Q8—38no—
531C22⋊Q8—98no—
532C22⋊Q8—98no—
533C22⋊Q8—98no—
534#121—98no—
535#121—98no—
536#121—98no—
537#121—98no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545C2×C4⋊C4—91no—
546C2×C4⋊C4—91no—
547C2×C4⋊C4D3211yescharacteristic
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—91no—
560C2×C42—91no—
561C23×C3—21no—
562C23×C3—32no—
563C23×C3—32no—
564C23×C3—32no—
565C23×C3—62no—
566C23×C3—62no—
567C23×C3—62no—
568C23×C3—62no—
569C23×C3—62no—
570C23×C3—62no—
571C23×C3—62no—
572C23×C3—62no—
573C23×C3—62no—
574C23×C3C23×D311yescharacteristic
575C23×C3C23×D311yescharacteristic
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—22no—
585C22×D3—32no—
586C22×D3—32no—
587C22×D3—62no—
588C22×D3—64no—
589C22×D3—62no—
590C22×D3—62no—
591C22×D3—62no—
592C22×D3—62no—
593C22×D3—62no—
594C22×D3—62no—
595C22×D3—122no—
596C22×D3—122no—
597C22×D3C23×D312yes—
598C22×D3C23×D312yes—
599C22×D3C23×D312yes—
600C3×Q8—124no—
601C3×D4—124no—
602C2×C3×C4—24no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—22no—
606C2×C3×C4—22no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—22no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—32no—
613C2×C3×C4—32no—
614C2×C3×C4—32no—
615C2×C3×C4—32no—
616C2×C3×C4—32no—
617C2×C3×C4—42no—
618C2×C3×C4—42no—
619C2×C3×C4—62no—
620C2×C3×C4—62no—
621C2×C3×C4—62no—
622C2×C3×C4—62no—
623C2×C3×C4—62no—
624C2×C3×C4—124no—
625C2×C3×C4—124no—
626C2×C3×C4C23×D312yes—
627C2×C3×C4C23×D312yes—
628C2×C3×C4C23×D312yes—
629C2×C3×C4C23×D312yes—
630C2×C3×C4C23×D312yes—
631C2×C3×C4C23×D312yes—
632#67—124no—
633#67—124no—
634#67—124no—
635#67—124no—
636#67—124no—
637#67—124no—
638#67—124no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—32no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—62no—
651C2×Dic3—62no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—122no—
660C2×Dic3—122no—
661C2×Dic3—122no—
662C2×Dic3—124no—
663C2×Dic3C23×D312yes—
664C2×Dic3C23×D312yes—
665C2×Dic3C23×D312yes—
666C2×Dic3C23×D312yes—
667C2×Dic3C23×D312yes—
668D12—44no—
669D12—124no—
670D12—124no—
671D12—124no—
672C4×D3—44no—
673C4×D3—44no—
674C4×D3—124no—
675C4×D3—124no—
676C4×D3—124no—
677C4×D3—128no—
678Dic6—44no—
679Dic6—124no—
680Dic6—124no—
681Dic6—128no—
682C2×C32#56214yescomplemented
683C2×C32C2×H(5,𝔽2)11yescharacteristic
684C2×C32C2×H(5,𝔽2)11yescharacteristic
685C2×C32C2×2−1+411yescharacteristic
686C3⋊D3—42no—
687C3×D3—42no—
688C3×D3—42no—
689C3×D3—42no—
690C24—31no—
691C24—31no—
692C24—31no—
693C24—91no—
694C2×Q8—34no—
695C2×Q8—94no—
696C2×Q8—122no—
697C2×Q8—362no—
698C2×D4—34no—
699C2×D4—94no—
700C2×D4—94no—
701C2×D4—94no—
702C2×D4—94no—
703C2×D4—94no—
704C2×D4—122no—
705C2×D4—362no—
706C2×D4—362no—
707C2×D4—362no—
708C2×D4—362no—
709C2×D4—362no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—31no—
715C22×C4—34no—
716C22×C4—34no—
717C22×C4—94no—
718C22×C4—91no—
719C22×C4—91no—
720C22×C4—91no—
721C22×C4—94no—
722C22×C4—122no—
723C22×C4—122no—
724C22×C4—362no—
725C22×C4—362no—
726C22×C4C2×D3211yescharacteristic
727C22×C4C2×D3211yescharacteristic
728C22×C4C2×D3211yescharacteristic
729C4⋊C4—34no—
730C4⋊C4—34no—
731C4⋊C4—34no—
732C4⋊C4—94no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4C2×D3214yes—
739C22⋊C4—34no—
740C22⋊C4—34no—
741C22⋊C4—34no—
742C22⋊C4—34no—
743C22⋊C4—34no—
744C22⋊C4—94no—
745C22⋊C4—94no—
746C22⋊C4—94no—
747C22⋊C4—94no—
748C22⋊C4—94no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C42—94no—
752C22×C3—22no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—21no—
756C22×C3—62no—
757C22×C3—62no—
758C22×C3—62no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3—62no—
765C22×C3—124no—
766C22×C3—124no—
767C22×C3—124no—
768C22×C3#100412yes—
769C22×C3#100412yes—
770C22×C3#100712yes—
771C22×C3#100912yes—
772C22×C3#100912yes—
773C22×C3#101012yes—
774C22×C3C24×D311yescharacteristic
775C22×C3C24×D311yescharacteristic
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—44no—
786C2×D3—44no—
787C2×D3—44no—
788C2×D3—64no—
789C2×D3—62no—
790C2×D3—62no—
791C2×D3—62no—
792C2×D3—62no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—122no—
796C2×D3—122no—
797C2×D3—128no—
798C2×D3—124no—
799C2×D3—124no—
800C3×C4—24no—
801C3×C4—22no—
802C3×C4—22no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—42no—
808C3×C4—42no—
809C3×C4—62no—
810C3×C4—62no—
811C3×C4—62no—
812C3×C4—62no—
813C3×C4—62no—
814Dic3—22no—
815Dic3—22no—
816Dic3—22no—
817Dic3—22no—
818Dic3—22no—
819Dic3—62no—
820Dic3—62no—
821Dic3—62no—
822Dic3—62no—
823Dic3—62no—
824Dic3—62no—
825Dic3—122no—
826Dic3—122no—
827Dic3—122no—
828C32C2×#56211yescharacteristic, complemented, Sylow
829C23—32no—
830C23—32no—
831C23—32no—
832C23—62no—
833C23—62no—
834C23—62no—
835C23—62no—
836C23—62no—
837C23—62no—
838C23—62no—
839C23—62no—
840C23—62no—
841C23—92no—
842C23—182no—
843C23—182no—
844C23—182no—
845C23C22×D3211yescharacteristic
846Q8—124no—
847Q8—364no—
848D4—124no—
849D4—364no—
850D4—364no—
851D4—364no—
852D4—364no—
853D4—364no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—32no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—32no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—62no—
867C2×C4—92no—
868C2×C4—92no—
869C2×C4—92no—
870C2×C4—124no—
871C2×C4—124no—
872C2×C4—182no—
873C2×C4—182no—
874C2×C4—182no—
875C2×C4—364no—
876C2×C4—364no—
877C2×C4C22×D3212yes—
878C2×C4C22×D3212yes—
879C2×C4C22×D3212yes—
880C2×C3—24no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—122no—
885C2×C3—122no—
886C2×C3—122no—
887C2×C3#564714yescomplemented
888C2×C3#566714yescomplemented
889C2×C3C2×#100411yescharacteristic
890C2×C3C2×#100411yescharacteristic
891C2×C3C2×#100711yescharacteristic
892C2×C3C2×#100911yescharacteristic
893C2×C3C2×#100911yescharacteristic
894C2×C3C2×#101011yescharacteristic
895D3—42no—
896D3—42no—
897D3—42no—
898D3—124no—
899D3—122no—
900D3—122no—
901C22—62no—
902C22—62no—
903C22—62no—
904C22—62no—
905C22—62no—
906C22—62no—
907C22—62no—
908C22—62no—
909C22—62no—
910C22—124no—
911C22—124no—
912C22—124no—
913C22—182no—
914C22—182no—
915C22—182no—
916C22—364no—
917C22#6430812yes—
918C22#6431312yes—
919C22#6431512yes—
920C22C23×D3211yescharacteristic
921C4—22no—
922C4—22no—
923C4—22no—
924C4—62no—
925C4—62no—
926C4—62no—
927C4—62no—
928C4—62no—
929C4—182no—
930C4—182no—
931C4—182no—
932C3—21no—
933C3C2×#564711yescharacteristic, complemented
934C3C2×#566711yescharacteristic, complemented
935C2—122no—
936C2—122no—
937C2—122no—
938C2—362no—
939C2#1059459014yesdirect product factor
940C2C2×#6430811yescharacteristic
941C2C2×#6431311yescharacteristic
942C2C2×#6431511yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#562
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×#64106C2semidirect
2. C2×C3×#896C2semidirect
3. C2×C3×#894C2semidirect
4. C2×#63913C2semidirect
5. C2×#63912C2semidirect
6. C2×#63908C2semidirect
7. C2×#63907C2semidirect
8. C2×#63906C2semidirect
9. C2×#63896C2semidirect
10. C2×#63891C2semidirect
11. C2×#63886C2semidirect
12. C2×#63856C2semidirect
13. C2×#63853C2semidirect
14. C2×#63850C2semidirect
15. C2×#63845C2semidirect
16. #10594590C2direct (N × H)
36. #64106C22semidirect
45. C3×#896C22semidirect
46. C3×#894C22semidirect
57. #63913C22semidirect
58. #63912C22semidirect
59. #63908C22semidirect
60. #63907C22semidirect
61. #63906C22semidirect
62. #63896C22semidirect
63. #63891C22semidirect
64. #63886C22semidirect
65. #63856C22semidirect
66. #63853C22semidirect
67. #63850C22semidirect
68. #63845C22semidirect
85. C2×#896D3semidirect
89. C2×#894D3semidirect
256. #896C2×D3semidirect
260. #894C2×D3semidirect
682. C2×C32#562semidirect
828. C32C2×#562semidirect
887. C2×C3#5647semidirect
888. C2×C3#5667semidirect
933. C3C2×#5647semidirect
934. C3C2×#5667semidirect
939. C2#10594590direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641062
C2×C3×#8962
C2×C3×#8942
C2×#639132
C2×#639122
C2×#639082
C2×#639072
C2×#639062
C2×#638962
C2×#638912
C2×#638862
C2×#638562
C2×#638532
C2×#638502
C2×#638452
#105945902
C2×#56673
C2×#56473