Finite Group Databasebeta

← C2×#10593930 #11903329

Subgroups — C2×#10593930 #11903329

Order 1152.

2645 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic, complemented
2C2×C3×#875C211yesmaximal, characteristic, complemented
3C2×C3×#872C211yesmaximal, characteristic, complemented
4C2×#63915C211yesmaximal, characteristic, complemented
5C2×#63912C211yesmaximal, characteristic, complemented
6C2×#63907C211yesmaximal, characteristic, complemented
7C2×#63906C211yesmaximal, characteristic, complemented
8C2×#63886C211yesmaximal, characteristic, complemented
9C2×#63885C211yesmaximal, characteristic, complemented
10C2×#63881C211yesmaximal, characteristic, complemented
11C2×#63879C211yesmaximal, characteristic, complemented
12C2×#63878C211yesmaximal, characteristic, complemented
13C2×#63877C211yesmaximal, characteristic, complemented
14C2×#63852C211yesmaximal, characteristic, complemented
15C2×#63839C211yesmaximal, characteristic, complemented
16#10593930C2116yesmaximal, direct product factor
17C2×#5670—31nomaximal
18C2×#5532—31nomaximal
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#625C2211yescharacteristic
28C22×#625C2211yescharacteristic
29C22×D3×Dic3C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C2×C32×C42C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×#3750C2211yescharacteristic
35C2×#3750C2211yescharacteristic
36C2×C4×C3⋊Dic3C2211yescharacteristic
37#64081C2218yescomplemented
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
45C2×C3×Dic3⋊C4C2211yescharacteristic
46C2×C3×C4×Dic3C2211yescharacteristic
47C3×#875C2218yescomplemented
48C3×#872C2218yescomplemented
49C2×#3724C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63915C2218yescomplemented
58#63912C2218yescomplemented
59#63907C2218yescomplemented
60#63906C2218yescomplemented
61#63886C2218yescomplemented
62#63885C2218yescomplemented
63#63881C2218yescomplemented
64#63879C2218yescomplemented
65#63878C2218yescomplemented
66#63877C2218yescomplemented
67#63852C2218yescomplemented
68#63839C2218yescomplemented
69C2×C3×#124—31no—
70C2×C3×#117—31no—
71C2×#947—31no—
72C2×#944—31no—
73C2×#939—31no—
74C2×#939—31no—
75C2×#930—31no—
76C2×C4×#67—31no—
77#5670—316no—
78#5532—316no—
79C2×#895—31no—
80C2×#893—31no—
81C2×#892—31no—
82C2×#888—31no—
83C2×#885—31no—
84C2×#885—31no—
85C2×#885—31no—
86C2×#885—31no—
87C2×#884—31no—
88C2×#884—31no—
89C2×#884—31no—
90C2×#884—31no—
91C2×#67⋊C4—31no—
92C2×#67⋊C4—31no—
93C2×#877—31no—
94C2×#877—31no—
95C2×#875—31no—
96C2×#875D311yescharacteristic, complemented
97C2×#872—31no—
98C2×#872—31no—
99C2×#872—31no—
100C2×#872—61no—
101C2×#872D311yescharacteristic, complemented
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—24no—
113C2×C4×C3⋊D3C2314yes—
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
119C2×C3×D12—42no—
120C2×C3×D12C2314yes—
121C2×C3×C4×D3—24no—
122C2×C3×C4×D3C2314yes—
123C2×C3×Dic6—42no—
124C2×C3×Dic6C2314yes—
125C2×#627—42no—
126C2×#627C2314yes—
127C2×#626—24no—
128C2×#626—42no—
129C2×#626—42no—
130C2×#626C2314yes—
131C2×#626C2314yes—
132C2×#626C2314yes—
133C2×#625—24no—
134C2×#625—42no—
135C2×#625C2314yes—
136C2×#625C2314yes—
137C2×D3×Dic3—24no—
138C2×D3×Dic3—24no—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2314yes—
141C32×C42C2314yes—
142#3752C2314yes—
143#3752C2314yes—
144#3750C2314yes—
145#3750C2314yes—
146C4×C3⋊Dic3C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×Dic3⋊C4C2314yes—
154C3×Dic3⋊C4C2314yes—
155C3×C4×Dic3C2314yes—
156#3724C2314yes—
157Dic3⋊Dic3C2314yes—
158#3722C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162Dic32C2314yes—
163Dic32C2314yes—
164C2×#555—91noSylow
165C22×C3×Q8—31no—
166C22×C3×D4—31no—
167C23×C3×C4—31no—
168C22×#67—31no—
169C22×#67—31no—
170C22×#67—31no—
171C22×#67—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C23×Dic3—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—31no—
185C22×C4×D3—61no—
186C22×C4×D3C2×D311yescharacteristic
187C22×Dic6—31no—
188C22×Dic6—31no—
189C22×Dic6C2×D311yescharacteristic
190C3×#124—38no—
191C3×#117—38no—
192C2×C3×C4⋊C4—31no—
193C2×C3×C4⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4—31no—
200C2×C3×C42—21no—
201C2×C3×C42—31no—
202C2×C3×C42C2×D311yescharacteristic
203C2×C3×C42C2×D311yescharacteristic
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—31no—
207#947—38no—
208#944—38no—
209#939—38no—
210#939—38no—
211#930—38no—
212C4×#67—38no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4—31no—
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—61no—
223C2×(C2×D3)⋊C4—61no—
224C2×(C2×D3)⋊C4C2×D311yescharacteristic
225C2×(C2×D3)⋊C4C2×D311yescharacteristic
226C2×(C2×D3)⋊C4C2×D311yescharacteristic
227C2×(C2×D3)⋊C4C2×D311yescharacteristic
228C2×(C2×D3)⋊C4C2×D311yescharacteristic
229C2×(C2×D3)⋊C4C2×D311yescharacteristic
230C2×C4⋊Dic3—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—61no—
239C2×Dic3⋊C4—61no—
240C2×Dic3⋊C4C2×D311yescharacteristic
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×Dic3—61no—
249C2×C4×Dic3C2×D311yescharacteristic
250#895—38no—
251#893—38no—
252#892—38no—
253#888—38no—
254#885—38no—
255#885—38no—
256#885—38no—
257#885—38no—
258#884—38no—
259#884—38no—
260#884—38no—
261#884—38no—
262#67⋊C4—38no—
263#67⋊C4—38no—
264#877—38no—
265#877—38no—
266#875—38no—
267#875C2×D318yescomplemented
268#872—38no—
269#872—38no—
270#872—38no—
271#872—68no—
272#872C2×D318yescomplemented
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#4114yes—
299C2×C3⋊Dic3C2412yes—
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2412yes—
302C4×C3⋊D3—28no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—22no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3#4114yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C2×C3×Dic3C2412yes—
312C2×C3×Dic3C2412yes—
313C3×D12—44no—
314C3×C4×D3—28no—
315C3×Dic6—44no—
316#627—44no—
317#626—28no—
318#626—44no—
319#626—44no—
320#625—28no—
321#625—44no—
322D3×Dic3—28no—
323D3×Dic3—28no—
324#555—916no—
325C2×C4⋊Q8—91no—
326C2×#124—31no—
327C2×#124—91no—
328C2×#124—91no—
329C2×#124—91no—
330C2×#121—91no—
331C2×#121—91no—
332C2×#121—91no—
333C2×#121—91no—
334C2×C4×D4—91no—
335C2×C4×D4—91no—
336C2×#117—31no—
337C2×#117—91no—
338C2×#117—91no—
339C2×#117—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—64no—
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C22×C3×C4C22×D311yescharacteristic
369C2×#67—34no—
370C2×#67—34no—
371C2×#67—34no—
372C2×#67—34no—
373C2×#67—34no—
374C2×#67—34no—
375C2×#67—34no—
376C2×#67—64no—
377C2×#67—64no—
378C2×#67—64no—
379C2×#67—122no—
380C2×#67—122no—
381C2×#67—122no—
382C2×#67—122no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—34no—
390C22×Dic3—34no—
391C22×Dic3—61no—
392C22×Dic3—61no—
393C22×Dic3—61no—
394C22×Dic3—64no—
395C22×Dic3—64no—
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—64no—
406C2×D12—122no—
407C2×D12—122no—
408C2×D12C22×D314yes—
409C2×C4×D3—24no—
410C2×C4×D3—34no—
411C2×C4×D3—34no—
412C2×C4×D3—34no—
413C2×C4×D3—34no—
414C2×C4×D3—64no—
415C2×C4×D3—64no—
416C2×C4×D3—64no—
417C2×C4×D3—64no—
418C2×C4×D3—68no—
419C2×C4×D3—64no—
420C2×C4×D3C22×D314yes—
421C2×Dic6—34no—
422C2×Dic6—34no—
423C2×Dic6—42no—
424C2×Dic6—122no—
425C2×Dic6—122no—
426C2×Dic6C22×D314yes—
427C3×C4⋊C4—34no—
428C3×C4⋊C4—34no—
429C3×C22⋊C4—34no—
430C3×C22⋊C4—34no—
431C3×C22⋊C4—34no—
432C3×C22⋊C4—34no—
433C3×C22⋊C4—34no—
434C3×C22⋊C4—34no—
435C3×C42—24no—
436C3×C42—34no—
437C3×C42C22×D314yes—
438C3×C42C22×D314yes—
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—
460Dic3⋊C4—34no—
461Dic3⋊C4—34no—
462Dic3⋊C4—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—64no—
468Dic3⋊C4—64no—
469Dic3⋊C4C22×D314yes—
470Dic3⋊C4C22×D314yes—
471C4×Dic3—34no—
472C4×Dic3—34no—
473C4×Dic3—34no—
474C4×Dic3—34no—
475C4×Dic3—34no—
476C4×Dic3—34no—
477C4×Dic3—64no—
478C4×Dic3C22×D314yes—
479C22×C32C2×#4112yes—
480C22×C32C2×#4112yes—
481C22×C32H(5,𝔽2)12yes—
482C22×C32C2511yescharacteristic
483C2×C3⋊D3—22no—
484C2×C3⋊D3—22no—
485C2×C3⋊D3—22no—
486C2×C3⋊D3—44no—
487C2×C3×D3—22no—
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—44no—
497C2×C3×D3—44no—
498C2×C3×D3—44no—
499C32×C4—22no—
500C32×C4—22no—
501C32×C4—22no—
502C3⋊Dic3—22no—
503C3⋊Dic3—22no—
504C3⋊Dic3C2×#4114yes—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3C2×#4114yes—
510C22×Q8—31no—
511C22×Q8—91no—
512C22×D4—31no—
513C22×D4—91no—
514C22×D4—91no—
515C22×D4—91no—
516C22×D4—91no—
517C22×D4—91no—
518C23×C4—31no—
519C23×C4—91no—
520C23×C4—91no—
521C23×C4—91no—
522C4⋊Q8—98no—
523#124—38no—
524#124—98no—
525#124—98no—
526#124—98no—
527#121—98no—
528#121—98no—
529#121—98no—
530#121—98no—
531C4×D4—98no—
532C4×D4—98no—
533#117—38no—
534#117—98no—
535#117—98no—
536#117—98no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—91no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C22⋊C4—31no—
544C2×C22⋊C4—31no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—91no—
550C2×C22⋊C4—91no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C42—31no—
556C2×C42—91no—
557C2×C42—91no—
558C2×C42—91no—
559C2×C42D3211yescharacteristic
560C23×C3—21no—
561C23×C3—32no—
562C23×C3—32no—
563C23×C3—32no—
564C23×C3—62no—
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×C3C23×D311yescharacteristic
574C23×C3C23×D311yescharacteristic
575C22×D3—22no—
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—32no—
585C22×D3—32no—
586C22×D3—62no—
587C22×D3—64no—
588C22×D3—62no—
589C22×D3—62no—
590C22×D3—62no—
591C22×D3—62no—
592C22×D3—62no—
593C22×D3—62no—
594C22×D3—122no—
595C22×D3—122no—
596C22×D3C23×D312yes—
597C22×D3C23×D312yes—
598C22×D3C23×D312yes—
599C3×Q8—124no—
600C3×D4—124no—
601C2×C3×C4—24no—
602C2×C3×C4—22no—
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—34no—
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—68no—
620C2×C3×C4—62no—
621C2×C3×C4—62no—
622C2×C3×C4—62no—
623C2×C3×C4—62no—
624C2×C3×C4C23×D312yes—
625C2×C3×C4C23×D312yes—
626C2×C3×C4C23×D312yes—
627C2×C3×C4C23×D312yes—
628C2×C3×C4C23×D312yes—
629C2×C3×C4C23×D312yes—
630#67—68no—
631#67—68no—
632#67—68no—
633#67—124no—
634#67—124no—
635#67—124no—
636#67—124no—
637C2×Dic3—22no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—34no—
642C2×Dic3—34no—
643C2×Dic3—32no—
644C2×Dic3—32no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—64no—
650C2×Dic3—62no—
651C2×Dic3—62no—
652C2×Dic3—62no—
653C2×Dic3—68no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—68no—
659C2×Dic3—122no—
660C2×Dic3—122no—
661C2×Dic3#23514yes—
662C2×Dic3C23×D312yes—
663C2×Dic3C23×D312yes—
664C2×Dic3C23×D312yes—
665C2×Dic3C23×D312yes—
666C2×Dic3C23×D312yes—
667D12—44no—
668D12—68no—
669D12—124no—
670D12—124no—
671C4×D3—28no—
672C4×D3—68no—
673C4×D3—68no—
674C4×D3—68no—
675C4×D3—616no—
676C4×D3—68no—
677Dic6—44no—
678Dic6—124no—
679Dic6—124no—
680C2×C32#55514yescomplemented
681C2×C32C22×#4111yescharacteristic
682C2×C32C22×#4111yescharacteristic
683C2×C32C2×H(5,𝔽2)11yescharacteristic
684C3⋊D3—42no—
685C3×D3—42no—
686C3×D3—42no—
687C3×D3—42no—
688C24—31no—
689C24—31no—
690C24—31no—
691C24—91no—
692C2×Q8—34no—
693C2×Q8—94no—
694C2×Q8—122no—
695C2×Q8—362no—
696C2×D4—34no—
697C2×D4—94no—
698C2×D4—94no—
699C2×D4—94no—
700C2×D4—94no—
701C2×D4—94no—
702C2×D4—122no—
703C2×D4—184no—
704C2×D4—184no—
705C2×D4—362no—
706C2×D4—362no—
707C2×D4—362no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—34no—
714C22×C4—64no—
715C22×C4—94no—
716C22×C4—94no—
717C22×C4—91no—
718C22×C4—91no—
719C22×C4—91no—
720C22×C4—94no—
721C22×C4—184no—
722C22×C4—184no—
723C22×C4—184no—
724C22×C4C2×D3211yescharacteristic
725C22×C4C2×D3211yescharacteristic
726C22×C4C2×D3211yescharacteristic
727C4⋊C4—34no—
728C4⋊C4—34no—
729C4⋊C4—94no—
730C4⋊C4—94no—
731C4⋊C4—94no—
732C4⋊C4—94no—
733C22⋊C4—34no—
734C22⋊C4—34no—
735C22⋊C4—34no—
736C22⋊C4—34no—
737C22⋊C4—34no—
738C22⋊C4—34no—
739C22⋊C4—94no—
740C22⋊C4—94no—
741C22⋊C4—94no—
742C22⋊C4—94no—
743C22⋊C4—94no—
744C22⋊C4—94no—
745C42—34no—
746C42—94no—
747C42—94no—
748C42—94no—
749C42C2×D3214yes—
750C22×C3—22no—
751C22×C3—22no—
752C22×C3—22no—
753C22×C3—21no—
754C22×C3—62no—
755C22×C3—62no—
756C22×C3—62no—
757C22×C3—62no—
758C22×C3—62no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—124no—
764C22×C3—124no—
765C22×C3—124no—
766C22×C3C2×#23512yes—
767C22×C3#100412yes—
768C22×C3D3×#4112yes—
769C22×C3D3×#4112yes—
770C22×C3D3×#4112yes—
771C22×C3#100912yes—
772C22×C3C24×D311yescharacteristic
773C22×C3C24×D311yescharacteristic
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—44no—
784C2×D3—44no—
785C2×D3—44no—
786C2×D3—64no—
787C2×D3—62no—
788C2×D3—62no—
789C2×D3—62no—
790C2×D3—62no—
791C2×D3—62no—
792C2×D3—62no—
793C2×D3—122no—
794C2×D3—122no—
795C2×D3—128no—
796C2×D3—124no—
797C2×D3—124no—
798C3×C4—24no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—22no—
802C3×C4—22no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—34no—
806C3×C4—42no—
807C3×C4—42no—
808C3×C4—62no—
809C3×C4—62no—
810C3×C4—62no—
811C3×C4—62no—
812Dic3—22no—
813Dic3—22no—
814Dic3—22no—
815Dic3—22no—
816Dic3—34no—
817Dic3—34no—
818Dic3—64no—
819Dic3—62no—
820Dic3—62no—
821Dic3—62no—
822Dic3—62no—
823Dic3—122no—
824Dic3—122no—
825Dic3C2×#23514yes—
826C32C2×#55511yescharacteristic, complemented, Sylow
827C23—32no—
828C23—32no—
829C23—32no—
830C23—62no—
831C23—62no—
832C23—62no—
833C23—62no—
834C23—62no—
835C23—62no—
836C23—62no—
837C23—62no—
838C23—62no—
839C23—92no—
840C23—182no—
841C23—182no—
842C23—182no—
843C23C22×D3211yescharacteristic
844Q8—124no—
845Q8—364no—
846D4—124no—
847D4—188no—
848D4—188no—
849D4—364no—
850D4—364no—
851D4—364no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—34no—
856C2×C4—32no—
857C2×C4—32no—
858C2×C4—32no—
859C2×C4—32no—
860C2×C4—32no—
861C2×C4—68no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—94no—
867C2×C4—92no—
868C2×C4—92no—
869C2×C4—92no—
870C2×C4—188no—
871C2×C4—188no—
872C2×C4—188no—
873C2×C4—182no—
874C2×C4—182no—
875C2×C4C22×D3212yes—
876C2×C4C22×D3212yes—
877C2×C4C22×D3212yes—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—24no—
882C2×C3—122no—
883C2×C3—122no—
884C2×C3—122no—
885C2×C3#553214yescomplemented
886C2×C3#567014yescomplemented
887C2×C3C22×#23511yescharacteristic
888C2×C3C2×#100411yescharacteristic
889C2×C3C2×D3×#4111yescharacteristic
890C2×C3C2×D3×#4111yescharacteristic
891C2×C3C2×D3×#4111yescharacteristic
892C2×C3C2×#100911yescharacteristic
893D3—42no—
894D3—42no—
895D3—42no—
896D3—124no—
897D3—122no—
898D3—122no—
899C22—62no—
900C22—62no—
901C22—62no—
902C22—62no—
903C22—62no—
904C22—62no—
905C22—62no—
906C22—62no—
907C22—62no—
908C22—124no—
909C22—124no—
910C22—124no—
911C22—182no—
912C22—182no—
913C22—182no—
914C22—364no—
915C22D3×#23512yes—
916C22#6430612yes—
917C22#6430712yes—
918C22C23×D3211yescharacteristic
919C4—22no—
920C4—22no—
921C4—22no—
922C4—34no—
923C4—62no—
924C4—62no—
925C4—62no—
926C4—62no—
927C4—94no—
928C4—182no—
929C4—182no—
930C3—21no—
931C3C2×#553211yescharacteristic, complemented
932C3C2×#567011yescharacteristic, complemented
933C2—122no—
934C2—122no—
935C2—122no—
936C2—362no—
937C2#1059393014yesdirect product factor
938C2C2×D3×#23511yescharacteristic
939C2C2×#6430611yescharacteristic
940C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#555
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64081C2semidirect
2. C2×C3×#875C2semidirect
3. C2×C3×#872C2semidirect
4. C2×#63915C2semidirect
5. C2×#63912C2semidirect
6. C2×#63907C2semidirect
7. C2×#63906C2semidirect
8. C2×#63886C2semidirect
9. C2×#63885C2semidirect
10. C2×#63881C2semidirect
11. C2×#63879C2semidirect
12. C2×#63878C2semidirect
13. C2×#63877C2semidirect
14. C2×#63852C2semidirect
15. C2×#63839C2semidirect
16. #10593930C2direct (N × H)
37. #64081C22semidirect
47. C3×#875C22semidirect
48. C3×#872C22semidirect
57. #63915C22semidirect
58. #63912C22semidirect
59. #63907C22semidirect
60. #63906C22semidirect
61. #63886C22semidirect
62. #63885C22semidirect
63. #63881C22semidirect
64. #63879C22semidirect
65. #63878C22semidirect
66. #63877C22semidirect
67. #63852C22semidirect
68. #63839C22semidirect
96. C2×#875D3semidirect
101. C2×#872D3semidirect
267. #875C2×D3semidirect
272. #872C2×D3semidirect
680. C2×C32#555semidirect
826. C32C2×#555semidirect
885. C2×C3#5532semidirect
886. C2×C3#5670semidirect
931. C3C2×#5532semidirect
932. C3C2×#5670semidirect
937. C2#10593930direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640812
C2×C3×#8752
C2×C3×#8722
C2×#639152
C2×#639122
C2×#639072
C2×#639062
C2×#638862
C2×#638852
C2×#638812
C2×#638792
C2×#638782
C2×#638772
C2×#638522
C2×#638392
#105939302
C2×#56703
C2×#55323