Finite Group Databasebeta

← C2×#10595417 #11910259

Subgroups — C2×#10595417 #11910259

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×#64155C211yesmaximal, characteristic, complemented
2C2×C3×#947C211yesmaximal, characteristic, complemented
3C2×C3×#946C211yesmaximal, characteristic, complemented
4#10595417C2116yesmaximal, direct product factor
5C2×#63912C211yesmaximal, characteristic, complemented
6C2×#63906C211yesmaximal, characteristic, complemented
7C2×#63905C211yesmaximal, characteristic, complemented
8C2×#63899C211yesmaximal, characteristic, complemented
9C2×#63893C211yesmaximal, characteristic, complemented
10C2×#63891C211yesmaximal, characteristic, complemented
11C2×#63890C211yesmaximal, characteristic, complemented
12C2×#63886C211yesmaximal, characteristic, complemented
13C2×#63885C211yesmaximal, characteristic, complemented
14C2×#63867C211yesmaximal, characteristic, complemented
15C2×#63853C211yesmaximal, characteristic, complemented
16C2×#63852C211yesmaximal, characteristic, complemented
17C2×#5684—31nomaximal
18C2×#5647—31nomaximal
19C22×C32×Q8C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#625C2211yescharacteristic
28C22×#625C2211yescharacteristic
29C22×D3×Dic3C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31#64155C2218yescomplemented
32C2×#3752C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
35C2×#3750C2211yescharacteristic
36C2×#3750C2211yescharacteristic
37C3×#947C2218yescomplemented
38C3×#946C2218yescomplemented
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×(C2×D3)⋊C4C2211yescharacteristic
44C2×C3×(C2×D3)⋊C4C2211yescharacteristic
45C2×C3×C4⋊Dic3C2211yescharacteristic
46C2×C3×Dic3⋊C4C2211yescharacteristic
47C2×C3×Dic3⋊C4C2211yescharacteristic
48C2×C3×C4×Dic3C2211yescharacteristic
49C2×#3724C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57#63912C2218yescomplemented
58#63906C2218yescomplemented
59#63905C2218yescomplemented
60#63899C2218yescomplemented
61#63893C2218yescomplemented
62#63891C2218yescomplemented
63#63890C2218yescomplemented
64#63886C2218yescomplemented
65#63885C2218yescomplemented
66#63867C2218yescomplemented
67#63853C2218yescomplemented
68#63852C2218yescomplemented
69C2×C3×#124—31no—
70C2×C3×C22⋊Q8—31no—
71C2×#947D311yescharacteristic, complemented
72C2×#946—31no—
73C2×#946—31no—
74C2×#946—61no—
75C2×#946D311yescharacteristic, complemented
76C2×#939—31no—
77C2×#939—31no—
78C2×#930—31no—
79C2×#929—31no—
80#5684—316no—
81#5647—316no—
82C2×#897—31no—
83C2×#896—31no—
84C2×#895—31no—
85C2×#894—31no—
86C2×#894—31no—
87C2×#889—31no—
88C2×#886—31no—
89C2×#886—31no—
90C2×#885—31no—
91C2×#884—31no—
92C2×#884—31no—
93C2×#884—31no—
94C2×#884—31no—
95C2×#883—31no—
96C2×#883—31no—
97C2×#883—31no—
98C2×#878—31no—
99C2×#878—31no—
100C2×#875—31no—
101C2×#870—31no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3×D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C2×C32×Q8—42no—
107C2×C32×Q8C2314yes—
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C32×C4C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C2×C4×C3⋊D3—42no—
115C2×C4×C3⋊D3C2314yes—
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—42no—
126C2×#627C2314yes—
127C2×#626—42no—
128C2×#626—42no—
129C2×#626—42no—
130C2×#626C2314yes—
131C2×#626C2314yes—
132C2×#626C2314yes—
133C2×#625—42no—
134C2×#625—42no—
135C2×#625C2314yes—
136C2×#625C2314yes—
137C2×D3×Dic3—42no—
138C2×D3×Dic3—42no—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2314yes—
141#3752C2314yes—
142#3752C2314yes—
143C4⋊(C3⋊Dic3)C2314yes—
144#3750C2314yes—
145#3750C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×C4⋊Dic3C2314yes—
153C3×Dic3⋊C4C2314yes—
154C3×Dic3⋊C4C2314yes—
155C3×C4×Dic3C2314yes—
156#3724C2314yes—
157Dic3⋊Dic3C2314yes—
158Dic3⋊Dic3C2314yes—
159Dic3⋊Dic3C2314yes—
160#3722C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164C2×#562—91noSylow
165C22×C3×Q8—21no—
166C22×C3×Q8C2×D311yescharacteristic
167C22×C3×Q8C2×D311yescharacteristic
168C22×C3×D4—31no—
169C23×C3×C4—31no—
170C22×#67—31no—
171C22×#67—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C23×Dic3—31no—
178C23×Dic3—31no—
179C22×D12—31no—
180C22×D12—31no—
181C22×D12—31no—
182C22×D12C2×D311yescharacteristic
183C22×C4×D3—31no—
184C22×C4×D3—31no—
185C22×C4×D3—31no—
186C22×C4×D3—31no—
187C22×C4×D3—61no—
188C22×C4×D3C2×D311yescharacteristic
189C22×Dic6—31no—
190C22×Dic6—31no—
191C3×#124—38no—
192C3×C22⋊Q8—38no—
193C2×C3×C4⋊C4—31no—
194C2×C3×C4⋊C4—31no—
195C2×C3×C4⋊C4—31no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4—31no—
200C2×C3×C22⋊C4—31no—
201C2×C3×C22⋊C4—31no—
202C2×C3×C42—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—31no—
206#947C2×D318yescomplemented
207#946—38no—
208#946—38no—
209#946—68no—
210#946C2×D318yescomplemented
211#939—38no—
212#939—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—61no—
225C2×(C2×D3)⋊C4—61no—
226C2×(C2×D3)⋊C4C2×D311yescharacteristic
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—61no—
238C2×C4⋊Dic3C2×D311yescharacteristic
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—31no—
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⋊C4—31no—
248C2×Dic3⋊C4—61no—
249C2×Dic3⋊C4—61no—
250C2×Dic3⋊C4C2×D311yescharacteristic
251C2×Dic3⋊C4C2×D311yescharacteristic
252C2×C4×Dic3C2×D311yescharacteristic
253#897—38no—
254#896—38no—
255#895—38no—
256#894—38no—
257#894—38no—
258#889—38no—
259#886—38no—
260#886—38no—
261#885—38no—
262#884—38no—
263#884—38no—
264#884—38no—
265#884—38no—
266#883—38no—
267#883—38no—
268#883—38no—
269#878—38no—
270#878—38no—
271#875—38no—
272#870—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—
290C32×Q8—44no—
291C2×C32×C4—22no—
292C2×C32×C4—22no—
293C2×C32×C4—22no—
294C2×C32×C4C2412yes—
295C2×C32×C4C2412yes—
296C2×C32×C4C2412yes—
297C2×C3⋊Dic3—22no—
298C2×C3⋊Dic3—22no—
299C2×C3⋊Dic3—22no—
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2412yes—
302C2×C3⋊Dic3C2412yes—
303C4×C3⋊D3—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—
316#627—44no—
317#626—44no—
318#626—44no—
319#626—44no—
320#625—44no—
321#625—44no—
322D3×Dic3—44no—
323D3×Dic3—44no—
324#562—916no—
325C2×#125—91no—
326C2×#124—31no—
327C2×#124—91no—
328C2×#123—91no—
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—24no—
350C2×C3×Q8—42no—
351C2×C3×Q8—42no—
352C2×C3×Q8—44no—
353C2×C3×Q8C22×D314yes—
354C2×C3×Q8C22×D314yes—
355C2×C3×D4—34no—
356C2×C3×D4—122no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—34no—
366C22×C3×C4—122no—
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C2×#67—34no—
374C2×#67—34no—
375C2×#67—34no—
376C2×#67—34no—
377C2×#67—34no—
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—122no—
381C2×#67—122no—
382C2×#67—122no—
383C2×#67—122no—
384C2×#67—122no—
385C2×#67—122no—
386C2×#67—122no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—31no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—34no—
394C22×Dic3—34no—
395C22×Dic3—61no—
396C22×Dic3—61no—
397C22×Dic3—61no—
398C22×Dic3—122no—
399C22×Dic3—122no—
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C2×D12—34no—
406C2×D12—34no—
407C2×D12—34no—
408C2×D12—42no—
409C2×D12—122no—
410C2×D12—122no—
411C2×D12—122no—
412C2×D12C22×D314yes—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—34no—
417C2×C4×D3—42no—
418C2×C4×D3—64no—
419C2×C4×D3—122no—
420C2×C4×D3—122no—
421C2×C4×D3—122no—
422C2×C4×D3—122no—
423C2×C4×D3—124no—
424C2×C4×D3C22×D314yes—
425C2×Dic6—34no—
426C2×Dic6—34no—
427C2×Dic6—122no—
428C2×Dic6—122no—
429C3×C4⋊C4—34no—
430C3×C4⋊C4—34no—
431C3×C4⋊C4—34no—
432C3×C22⋊C4—34no—
433C3×C22⋊C4—34no—
434C3×C22⋊C4—34no—
435C3×C22⋊C4—34no—
436C3×C22⋊C4—34no—
437C3×C22⋊C4—34no—
438C3×C42—34no—
439#217—34no—
440#217—34no—
441#217—34no—
442(C2×D3)⋊C4—34no—
443(C2×D3)⋊C4—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—64no—
452(C2×D3)⋊C4—64no—
453(C2×D3)⋊C4C22×D314yes—
454(C2×D3)⋊C4C22×D314yes—
455(C2×D3)⋊C4C22×D314yes—
456(C2×D3)⋊C4C22×D314yes—
457(C2×D3)⋊C4C22×D314yes—
458(C2×D3)⋊C4C22×D314yes—
459C4⋊Dic3—34no—
460C4⋊Dic3—34no—
461C4⋊Dic3—34no—
462C4⋊Dic3—34no—
463C4⋊Dic3—34no—
464C4⋊Dic3—64no—
465C4⋊Dic3C22×D314yes—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—34no—
474Dic3⋊C4—34no—
475Dic3⋊C4—64no—
476Dic3⋊C4—64no—
477Dic3⋊C4C22×D314yes—
478Dic3⋊C4C22×D314yes—
479C4×Dic3C22×D314yes—
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—91no—
512C22×Q8D3211yescharacteristic
513C22×D4—31no—
514C22×D4—91no—
515C22×D4—91no—
516C22×D4—91no—
517C22×D4—91no—
518C22×D4—91no—
519C23×C4—31no—
520C23×C4—91no—
521C23×C4—91no—
522C23×C4—91no—
523#125—98no—
524#124—38no—
525#124—98no—
526#123—98no—
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⋊C4—91no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—31no—
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—31no—
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—44no—
601C3×Q8—44no—
602C3×Q8—48no—
603C3×D4—124no—
604C2×C3×C4—24no—
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—22no—
613C2×C3×C4—22no—
614C2×C3×C4—32no—
615C2×C3×C4—32no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—32no—
619C2×C3×C4—42no—
620C2×C3×C4—42no—
621C2×C3×C4—62no—
622C2×C3×C4—62no—
623C2×C3×C4—62no—
624C2×C3×C4—62no—
625C2×C3×C4—62no—
626C2×C3×C4—124no—
627C2×C3×C4C23×D312yes—
628C2×C3×C4C23×D312yes—
629C2×C3×C4C23×D312yes—
630C2×C3×C4C23×D312yes—
631C2×C3×C4C23×D312yes—
632C2×C3×C4C23×D312yes—
633#67—124no—
634#67—124no—
635#67—124no—
636#67—124no—
637#67—124no—
638#67—124no—
639#67—124no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—32no—
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—62no—
660C2×Dic3—122no—
661C2×Dic3—122no—
662C2×Dic3—122no—
663C2×Dic3—124no—
664C2×Dic3—124no—
665C2×Dic3C23×D312yes—
666C2×Dic3C23×D312yes—
667C2×Dic3C23×D312yes—
668C2×Dic3C23×D312yes—
669C2×Dic3C23×D312yes—
670D12—44no—
671D12—124no—
672D12—124no—
673D12—124no—
674C4×D3—44no—
675C4×D3—124no—
676C4×D3—124no—
677C4×D3—124no—
678C4×D3—124no—
679C4×D3—128no—
680Dic6—124no—
681Dic6—124no—
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—42no—
695C2×Q8—94no—
696C2×Q8—362no—
697C2×Q8C2×D3214yes—
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—94no—
717C22×C4—94no—
718C22×C4—91no—
719C22×C4—91no—
720C22×C4—91no—
721C22×C4—94no—
722C22×C4—122no—
723C22×C4—362no—
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⋊C4—94no—
739C22⋊C4—34no—
740C22⋊C4—34no—
741C22⋊C4—34no—
742C22⋊C4—34no—
743C22⋊C4—34no—
744C22⋊C4—34no—
745C22⋊C4—94no—
746C22⋊C4—94no—
747C22⋊C4—94no—
748C22⋊C4—94no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C42—34no—
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—44no—
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—182no—
872C2×C4—182no—
873C2×C4—182no—
874C2×C4—364no—
875C2×C4—364no—
876C2×C4—364no—
877C2×C4C22×D3212yes—
878C2×C4C22×D3212yes—
879C2×C4C22×D3212yes—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—24no—
883C2×C3—21no—
884C2×C3—122no—
885C2×C3—122no—
886C2×C3—122no—
887C2×C3#564714yescomplemented
888C2×C3#568414yescomplemented
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#6431512yes—
918C22#6432012yes—
919C22#6433012yes—
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×#568411yescharacteristic, complemented
935C2—122no—
936C2—122no—
937C2—122no—
938C2—362no—
939C2#1059541714yesdirect product factor
940C2C2×#6431511yescharacteristic
941C2C2×#6432011yescharacteristic
942C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×#562
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64155C2semidirect
2. C2×C3×#947C2semidirect
3. C2×C3×#946C2semidirect
4. #10595417C2direct (N × H)
5. C2×#63912C2semidirect
6. C2×#63906C2semidirect
7. C2×#63905C2semidirect
8. C2×#63899C2semidirect
9. C2×#63893C2semidirect
10. C2×#63891C2semidirect
11. C2×#63890C2semidirect
12. C2×#63886C2semidirect
13. C2×#63885C2semidirect
14. C2×#63867C2semidirect
15. C2×#63853C2semidirect
16. C2×#63852C2semidirect
31. #64155C22semidirect
37. C3×#947C22semidirect
38. C3×#946C22semidirect
57. #63912C22semidirect
58. #63906C22semidirect
59. #63905C22semidirect
60. #63899C22semidirect
61. #63893C22semidirect
62. #63891C22semidirect
63. #63890C22semidirect
64. #63886C22semidirect
65. #63885C22semidirect
66. #63867C22semidirect
67. #63853C22semidirect
68. #63852C22semidirect
71. C2×#947D3semidirect
75. C2×#946D3semidirect
206. #947C2×D3semidirect
210. #946C2×D3semidirect
682. C2×C32#562semidirect
828. C32C2×#562semidirect
887. C2×C3#5647semidirect
888. C2×C3#5684semidirect
933. C3C2×#5647semidirect
934. C3C2×#5684semidirect
939. C2#10595417direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641552
C2×C3×#9472
C2×C3×#9462
#105954172
C2×#639122
C2×#639062
C2×#639052
C2×#638992
C2×#638932
C2×#638912
C2×#638902
C2×#638862
C2×#638852
C2×#638672
C2×#638532
C2×#638522
C2×#56843
C2×#56473