Finite Group Databasebeta

← C2×#10593922 #11903150

Subgroups — C2×#10593922 #11903150

Order 1152.

2627 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64085C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3C2×C3×#872C211yesmaximal, characteristic, complemented
4C2×#63906C211yesmaximal, characteristic, complemented
5C2×#63906C211yesmaximal, characteristic, complemented
6C2×#63905C211yesmaximal, characteristic, complemented
7C2×#63904C211yesmaximal, characteristic, complemented
8C2×#63886C211yesmaximal, characteristic, complemented
9C2×#63885C211yesmaximal, characteristic, complemented
10C2×#63880C211yesmaximal, characteristic, complemented
11C2×#63879C211yesmaximal, characteristic, complemented
12C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
13C2×#63859C211yesmaximal, characteristic, complemented
14C2×#63854C211yesmaximal, characteristic, complemented
15C2×#63846C211yesmaximal, characteristic, complemented
16#10593922C2116yesmaximal, direct product factor
17C2×#5540—31nomaximal
18C2×#5530—31nomaximal
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#625C2211yescharacteristic
27C22×#625C2211yescharacteristic
28C22×#624C2211yescharacteristic
29C22×D3×Dic3C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C2×C32×C42C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3750C2211yescharacteristic
36C2×#3750C2211yescharacteristic
37C2×#3750C2211yescharacteristic
38#64085C2218yescomplemented
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×C4⋊Dic3C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C2×C3×Dic3⋊C4C2211yescharacteristic
46C2×C3×C4×Dic3C2211yescharacteristic
47C3×C4×D12C2218yescomplemented
48C3×#872C2218yescomplemented
49C2×#3724C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×Dic3⋊Dic3C2211yescharacteristic
52C2×Dic3⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63906C2218yescomplemented
58#63906C2218yescomplemented
59#63905C2218yescomplemented
60#63904C2218yescomplemented
61#63886C2218yescomplemented
62#63885C2218yescomplemented
63#63880C2218yescomplemented
64#63879C2218yescomplemented
65D3×Dic3⋊C4C2218yescomplemented
66#63859C2218yescomplemented
67#63854C2218yescomplemented
68#63846C2218yescomplemented
69C2×C3×C4×D4—31no—
70C2×C3×#117—31no—
71C2×#939—31no—
72C2×#939—31no—
73C2×#930—31no—
74C2×#930—31no—
75C2×#929—31no—
76C2×C4×#67—31no—
77C2×C4×#67—31no—
78C22×Dic3⋊C4—31no—
79#5540—316no—
80#5530—316no—
81C2×#895—31no—
82C2×#894—31no—
83C2×#893—31no—
84C2×D3×C4⋊C4—31no—
85C2×#890—31no—
86C2×#889—31no—
87C2×#884—31no—
88C2×#884—31no—
89C2×#884—31no—
90C2×#883—31no—
91C2×#883—31no—
92C2×#67⋊C4—31no—
93C2×#67⋊C4—31no—
94C2×#879—31no—
95C2×#876—31no—
96C2×#876—31no—
97C2×#876—31no—
98C2×#876—61no—
99C2×C4×D12—31no—
100C2×C4×D12D311yescharacteristic, complemented
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
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C2×C3×D12—24no—
118C2×C3×D12C2314yes—
119C2×C3×C4×D3—24no—
120C2×C3×C4×D3—42no—
121C2×C3×C4×D3—42no—
122C2×C3×C4×D3C2314yes—
123C2×C3×C4×D3C2314yes—
124C2×C3×C4×D3C2314yes—
125C2×#626—24no—
126C2×#626—24no—
127C2×#626—42no—
128C2×#626C2314yes—
129C2×#626C2314yes—
130C2×#626C2314yes—
131C2×#625—24no—
132C2×#625—42no—
133C2×#625C2314yes—
134C2×#625C2314yes—
135C2×#624—42no—
136C2×#624C2314yes—
137C2×D3×Dic3—24no—
138C2×D3×Dic3—42no—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2314yes—
141C32×C42C2314yes—
142#3752C2314yes—
143#3752C2314yes—
144#3752C2314yes—
145#3750C2314yes—
146#3750C2314yes—
147#3750C2314yes—
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(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163Dic32C2314yes—
164C2×#553—91noSylow
165C22×C3×D4—31no—
166C23×C3×C4—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—
177C23×Dic3—31no—
178C22×D12—31no—
179C22×D12—31no—
180C22×D12—31no—
181C22×D12C2×D311yescharacteristic
182C22×C4×D3—31no—
183C22×C4×D3—31no—
184C22×C4×D3—31no—
185C22×C4×D3—31no—
186C22×C4×D3C2×D311yescharacteristic
187C22×C4×D3C2×D311yescharacteristic
188C22×C4×D3C2×D311yescharacteristic
189C3×C4×D4—38no—
190C3×#117—38no—
191C2×C3×C4⋊C4—31no—
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×C42—21no—
199C2×C3×C42—31no—
200C2×C3×C42C2×D311yescharacteristic
201C2×C3×C42C2×D311yescharacteristic
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—31no—
205#939—38no—
206#939—38no—
207#930—38no—
208#930—38no—
209#929—38no—
210C4×#67—38no—
211C4×#67—38no—
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—31no—
218C2×(C2×D3)⋊C4—31no—
219C2×(C2×D3)⋊C4—31no—
220C2×(C2×D3)⋊C4—31no—
221C2×(C2×D3)⋊C4—61no—
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×C4⋊Dic3—31no—
229C2×C4⋊Dic3—31no—
230C2×C4⋊Dic3—31no—
231C2×C4⋊Dic3C2×D311yescharacteristic
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—31no—
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—31no—
241C2×Dic3⋊C4—31no—
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4—38no—
244C2×Dic3⋊C4—61no—
245C2×Dic3⋊C4—61no—
246C2×Dic3⋊C4—61no—
247C2×Dic3⋊C4C2×D311yescharacteristic
248C2×Dic3⋊C4C2×D311yescharacteristic
249C2×C4×Dic3—31no—
250C2×C4×Dic3—31no—
251C2×C4×Dic3C2×D311yescharacteristic
252#895—38no—
253#894—38no—
254#893—38no—
255D3×C4⋊C4—38no—
256#890—38no—
257#889—38no—
258#884—38no—
259#884—38no—
260#884—38no—
261#883—38no—
262#883—38no—
263#67⋊C4—38no—
264#67⋊C4—38no—
265#879—38no—
266#876—38no—
267#876—38no—
268#876—38no—
269#876—68no—
270C4×D12—38no—
271C4×D12C2×D318yescomplemented
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#4114yes—
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—
302C2×C3×Dic3—22no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—22no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3#4114yes—
307C2×C3×Dic3C2412yes—
308C2×C3×Dic3C2412yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C2×C3×Dic3C2412yes—
312C3×D12—28no—
313C3×C4×D3—28no—
314C3×C4×D3—44no—
315C3×C4×D3—44no—
316#626—28no—
317#626—28no—
318#626—44no—
319#625—28no—
320#625—44no—
321#624—44no—
322D3×Dic3—28no—
323D3×Dic3—44no—
324#553—916no—
325C2×#126—91no—
326C2×#126—91no—
327C2×#125—91no—
328C2×#123—91no—
329C2×#123—91no—
330C2×#121—91no—
331C2×#121—91no—
332C2×#121—91no—
333C2×#121—91no—
334C2×C4×D4—31no—
335C2×C4×D4—91no—
336C2×C4×D4—91no—
337C2×C4×D4—91no—
338C2×#117—31no—
339C22×C4⋊C4—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×D4—34no—
350C2×C3×D4—64no—
351C22×C3×C4—21no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—34no—
360C22×C3×C4—34no—
361C22×C3×C4—34no—
362C22×C3×C4—64no—
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—64no—
379C2×#67—64no—
380C2×#67—64no—
381C2×#67—64no—
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—34no—
393C22×Dic3—61no—
394C22×Dic3—61no—
395C22×Dic3—61no—
396C22×Dic3—64no—
397C22×Dic3—122no—
398C22×Dic3C22×D311yescharacteristic
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C2×D12—24no—
404C2×D12—34no—
405C2×D12—34no—
406C2×D12—34no—
407C2×D12—64no—
408C2×D12—64no—
409C2×D12—122no—
410C2×D12C22×D314yes—
411C2×C4×D3—24no—
412C2×C4×D3—34no—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—34no—
416C2×C4×D3—42no—
417C2×C4×D3—42no—
418C2×C4×D3—64no—
419C2×C4×D3—122no—
420C2×C4×D3—122no—
421C2×C4×D3—122no—
422C2×C4×D3C22×D314yes—
423C2×C4×D3C22×D314yes—
424C2×C4×D3C22×D314yes—
425C3×C4⋊C4—34no—
426C3×C4⋊C4—34no—
427C3×C4⋊C4—34no—
428C3×C22⋊C4—34no—
429C3×C22⋊C4—34no—
430C3×C22⋊C4—34no—
431C3×C22⋊C4—34no—
432C3×C42—24no—
433C3×C42—34no—
434C3×C42C22×D314yes—
435C3×C42C22×D314yes—
436#217—34no—
437#217—34no—
438#217—34no—
439(C2×D3)⋊C4—34no—
440(C2×D3)⋊C4—34no—
441(C2×D3)⋊C4—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—64no—
449(C2×D3)⋊C4—64no—
450(C2×D3)⋊C4—64no—
451(C2×D3)⋊C4C22×D314yes—
452(C2×D3)⋊C4C22×D314yes—
453(C2×D3)⋊C4C22×D314yes—
454(C2×D3)⋊C4C22×D314yes—
455C4⋊Dic3—34no—
456C4⋊Dic3—34no—
457C4⋊Dic3—34no—
458C4⋊Dic3C22×D314yes—
459Dic3⋊C4—34no—
460Dic3⋊C4—34no—
461Dic3⋊C4—34no—
462Dic3⋊C4—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—64no—
471Dic3⋊C4—64no—
472Dic3⋊C4—64no—
473Dic3⋊C4C22×D314yes—
474Dic3⋊C4C22×D314yes—
475C4×Dic3—34no—
476C4×Dic3—34no—
477C4×Dic3C22×D314yes—
478C22×C32C2×#4112yes—
479C22×C32C2×#4112yes—
480C22×C32H(5,𝔽2)12yes—
481C22×C32C2511yescharacteristic
482C2×C3⋊D3—22no—
483C2×C3⋊D3—22no—
484C2×C3⋊D3—22no—
485C2×C3⋊D3—44no—
486C2×C3×D3—28no—
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—44no—
496C2×C3×D3—44no—
497C2×C3×D3C2×#4114yes—
498C32×C4—22no—
499C32×C4—22no—
500C32×C4—22no—
501C3⋊Dic3—22no—
502C3⋊Dic3—22no—
503C3⋊Dic3—22no—
504C3×Dic3—22no—
505C3×Dic3—22no—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3C2×#4114yes—
509C22×D4—31no—
510C22×D4—91no—
511C22×D4—91no—
512C22×D4—91no—
513C22×D4—91no—
514C22×D4—91no—
515C23×C4—31no—
516C23×C4—31no—
517C23×C4—31no—
518C23×C4—91no—
519C23×C4—91no—
520C23×C4—91no—
521#126—98no—
522#126—98no—
523#125—98no—
524#123—98no—
525#123—98no—
526#121—98no—
527#121—98no—
528#121—98no—
529#121—98no—
530C4×D4—38no—
531C4×D4—98no—
532C4×D4—98no—
533C4×D4—98no—
534#117—38no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4—31no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—98no—
539C2×C4⋊C4—91no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545C2×C4⋊C4—91no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—91no—
551C2×C22⋊C4—91no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C42—31no—
557C2×C42—91no—
558C2×C42D3211yescharacteristic
559C23×C3—21no—
560C23×C3—34no—
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×C3C23×D311yescharacteristic
573C23×C3C23×D311yescharacteristic
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—32no—
583C22×D3—32no—
584C22×D3—62no—
585C22×D3—62no—
586C22×D3—62no—
587C22×D3—62no—
588C22×D3—62no—
589C22×D3—62no—
590C22×D3—62no—
591C22×D3—122no—
592C22×D3—122no—
593C22×D3—122no—
594C22×D3#23514yes—
595C22×D3C23×D312yes—
596C22×D3C23×D312yes—
597C22×D3C23×D312yes—
598C3×D4—68no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
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—34no—
609C2×C3×C4—32no—
610C2×C3×C4—32no—
611C2×C3×C4—32no—
612C2×C3×C4—32no—
613C2×C3×C4—32no—
614C2×C3×C4—42no—
615C2×C3×C4—42no—
616C2×C3×C4—42no—
617C2×C3×C4—68no—
618C2×C3×C4—62no—
619C2×C3×C4—62no—
620C2×C3×C4—62no—
621C2×C3×C4—62no—
622C2×C3×C4—124no—
623C2×C3×C4—124no—
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—68no—
634#67—124no—
635#67—124no—
636#67—124no—
637C2×Dic3—22no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—32no—
642C2×Dic3—32no—
643C2×Dic3—32no—
644C2×Dic3—32no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—62no—
648C2×Dic3—62no—
649C2×Dic3—62no—
650C2×Dic3—62no—
651C2×Dic3—62no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—68no—
657C2×Dic3—122no—
658C2×Dic3—122no—
659C2×Dic3—122no—
660C2×Dic3—124no—
661C2×Dic3#23514yes—
662C2×Dic3C23×D312yes—
663C2×Dic3C23×D312yes—
664C2×Dic3C23×D312yes—
665C2×Dic3C23×D312yes—
666C2×Dic3C23×D312yes—
667D12—28no—
668D12—68no—
669D12—68no—
670D12—124no—
671C4×D3—28no—
672C4×D3—44no—
673C4×D3—44no—
674C4×D3—68no—
675C4×D3—124no—
676C4×D3—124no—
677C4×D3—124no—
678C2×C32#55314yescomplemented
679C2×C32C22×#4111yescharacteristic
680C2×C32C22×#4111yescharacteristic
681C2×C32C2×H(5,𝔽2)11yescharacteristic
682C3⋊D3—42no—
683C3×D3—24no—
684C3×D3—42no—
685C3×D3—42no—
686C24—31no—
687C24—31no—
688C24—31no—
689C24—91no—
690C2×D4—34no—
691C2×D4—64no—
692C2×D4—94no—
693C2×D4—94no—
694C2×D4—94no—
695C2×D4—94no—
696C2×D4—94no—
697C2×D4—184no—
698C2×D4—184no—
699C2×D4—184no—
700C2×D4—362no—
701C2×D4—362no—
702C22×C4—31no—
703C22×C4—31no—
704C22×C4—31no—
705C22×C4—31no—
706C22×C4—31no—
707C22×C4—34no—
708C22×C4—34no—
709C22×C4—34no—
710C22×C4—64no—
711C22×C4—94no—
712C22×C4—94no—
713C22×C4—94no—
714C22×C4—91no—
715C22×C4—91no—
716C22×C4—91no—
717C22×C4—122no—
718C22×C4—122no—
719C22×C4—184no—
720C22×C4—362no—
721C22×C4—362no—
722C22×C4C2×D3211yescharacteristic
723C22×C4C2×D3211yescharacteristic
724C22×C4C2×D3211yescharacteristic
725C4⋊C4—34no—
726C4⋊C4—34no—
727C4⋊C4—34no—
728C4⋊C4—94no—
729C4⋊C4—94no—
730C4⋊C4—94no—
731C4⋊C4—94no—
732C4⋊C4—94no—
733C4⋊C4—94no—
734C4⋊C4—94no—
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—
747C42C2×D3214yes—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—21no—
752C22×C3—34no—
753C22×C3—62no—
754C22×C3—62no—
755C22×C3—68no—
756C22×C3—62no—
757C22×C3—62no—
758C22×C3—62no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—124no—
763C22×C3—124no—
764C22×C3C2×#23512yes—
765C22×C3C2×#23512yes—
766C22×C3#100412yes—
767C22×C3D3×#4112yes—
768C22×C3D3×#4112yes—
769C22×C3#100912yes—
770C22×C3C24×D311yescharacteristic
771C22×C3C24×D311yescharacteristic
772C2×D3—22no—
773C2×D3—22no—
774C2×D3—28no—
775C2×D3—22no—
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—44no—
782C2×D3—44no—
783C2×D3—62no—
784C2×D3—62no—
785C2×D3—62no—
786C2×D3—62no—
787C2×D3—62no—
788C2×D3—62no—
789C2×D3—122no—
790C2×D3—122no—
791C2×D3—122no—
792C2×D3—124no—
793C2×D3—124no—
794C2×D3—244no—
795C2×D3C2×#23514yes—
796C3×C4—22no—
797C3×C4—22no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—22no—
802C3×C4—34no—
803C3×C4—42no—
804C3×C4—42no—
805C3×C4—42no—
806C3×C4—62no—
807C3×C4—62no—
808C3×C4—62no—
809C3×C4—62no—
810Dic3—22no—
811Dic3—22no—
812Dic3—22no—
813Dic3—22no—
814Dic3—62no—
815Dic3—62no—
816Dic3—62no—
817Dic3—62no—
818Dic3—62no—
819Dic3—62no—
820Dic3—122no—
821Dic3—122no—
822Dic3—122no—
823Dic3C2×#23514yes—
824C32C2×#55311yescharacteristic, complemented, Sylow
825C23—34no—
826C23—32no—
827C23—32no—
828C23—32no—
829C23—62no—
830C23—62no—
831C23—62no—
832C23—62no—
833C23—62no—
834C23—62no—
835C23—62no—
836C23—62no—
837C23—92no—
838C23—182no—
839C23—182no—
840C23—182no—
841C23C22×D3211yescharacteristic
842D4—68no—
843D4—188no—
844D4—188no—
845D4—188no—
846D4—364no—
847D4—364no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—34no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—68no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—92no—
863C2×C4—92no—
864C2×C4—92no—
865C2×C4—124no—
866C2×C4—124no—
867C2×C4—188no—
868C2×C4—182no—
869C2×C4—182no—
870C2×C4—182no—
871C2×C4—364no—
872C2×C4—364no—
873C2×C4C22×D3212yes—
874C2×C4C22×D3212yes—
875C2×C4C22×D3212yes—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—24no—
880C2×C3—64no—
881C2×C3—122no—
882C2×C3—122no—
883C2×C3#553014yescomplemented
884C2×C3#554014yescomplemented
885C2×C3C22×#23511yescharacteristic
886C2×C3C22×#23511yescharacteristic
887C2×C3C2×#100411yescharacteristic
888C2×C3C2×D3×#4111yescharacteristic
889C2×C3C2×D3×#4111yescharacteristic
890C2×C3C2×#100911yescharacteristic
891D3—24no—
892D3—42no—
893D3—42no—
894D3—122no—
895D3—122no—
896D3—242no—
897C22—34no—
898C22—62no—
899C22—62no—
900C22—68no—
901C22—62no—
902C22—62no—
903C22—62no—
904C22—62no—
905C22—62no—
906C22—62no—
907C22—124no—
908C22—124no—
909C22—182no—
910C22—182no—
911C22—182no—
912C22—364no—
913C22D3×#23512yes—
914C22D3×#23512yes—
915C22#6430712yes—
916C22C23×D3211yescharacteristic
917C4—22no—
918C4—22no—
919C4—22no—
920C4—34no—
921C4—62no—
922C4—62no—
923C4—62no—
924C4—62no—
925C4—182no—
926C4—182no—
927C4—182no—
928C3—21no—
929C3C2×#553011yescharacteristic, complemented
930C3C2×#554011yescharacteristic, complemented
931C2—64no—
932C2—122no—
933C2—122no—
934C2—362no—
935C2#1059392214yesdirect product factor
936C2C2×D3×#23511yescharacteristic
937C2C2×D3×#23511yescharacteristic
938C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64085C2semidirect
2. C2×C3×C4×D12C2semidirect
3. C2×C3×#872C2semidirect
4. C2×#63906C2semidirect
5. C2×#63906C2semidirect
6. C2×#63905C2semidirect
7. C2×#63904C2semidirect
8. C2×#63886C2semidirect
9. C2×#63885C2semidirect
10. C2×#63880C2semidirect
11. C2×#63879C2semidirect
12. C2×D3×Dic3⋊C4C2semidirect
13. C2×#63859C2semidirect
14. C2×#63854C2semidirect
15. C2×#63846C2semidirect
16. #10593922C2direct (N × H)
38. #64085C22semidirect
47. C3×C4×D12C22semidirect
48. C3×#872C22semidirect
57. #63906C22semidirect
58. #63906C22semidirect
59. #63905C22semidirect
60. #63904C22semidirect
61. #63886C22semidirect
62. #63885C22semidirect
63. #63880C22semidirect
64. #63879C22semidirect
65. D3×Dic3⋊C4C22semidirect
66. #63859C22semidirect
67. #63854C22semidirect
68. #63846C22semidirect
100. C2×C4×D12D3semidirect
101. C2×#872D3semidirect
271. C4×D12C2×D3semidirect
272. #872C2×D3semidirect
678. C2×C32#553semidirect
824. C32C2×#553semidirect
883. C2×C3#5530semidirect
884. C2×C3#5540semidirect
929. C3C2×#5530semidirect
930. C3C2×#5540semidirect
935. C2#10593922direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640852
C2×C3×C4×D122
C2×C3×#8722
C2×#639062
C2×#639052
C2×#639042
C2×#638862
C2×#638852
C2×#638802
C2×#638792
C2×D3×Dic3⋊C42
C2×#638592
C2×#638542
C2×#638462
#105939222
C2×#55403
C2×#55303