Finite Group Databasebeta

← C2×#10594473 #11903200

Subgroups — C2×#10594473 #11903200

Order 1152.

2713 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#898C211yesmaximal, characteristic, complemented
3C2×C3×#894C211yesmaximal, characteristic, complemented
4C2×#63916C211yesmaximal, characteristic, complemented
5C2×#63912C211yesmaximal, characteristic, complemented
6C2×#63912C211yesmaximal, characteristic, complemented
7C2×C4×#626C211yesmaximal, characteristic, complemented
8C2×#63891C211yesmaximal, characteristic, complemented
9C2×#63885C211yesmaximal, characteristic, complemented
10C2×#63881C211yesmaximal, characteristic, complemented
11C2×#63881C211yesmaximal, characteristic, complemented
12C2×#63879C211yesmaximal, characteristic, complemented
13C2×#63877C211yesmaximal, characteristic, complemented
14C2×#63861C211yesmaximal, characteristic, complemented
15C2×#63847C211yesmaximal, characteristic, complemented
16#10594473C2116yesmaximal, direct product factor
17C2×#5709—31nomaximal
18C2×#5661—31nomaximal
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#625C2211yescharacteristic
28C22×#625C2211yescharacteristic
29C22×D3×Dic3C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C2×C32×C4⋊C4C2211yescharacteristic
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×#3750C2211yescharacteristic
35C4⋊C4×C3⋊D3C2218yescomplemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C2×C3×C4×Dic3C2211yescharacteristic
46C3×#898C2218yescomplemented
47C3×#894C2218yescomplemented
48C2×#3724C2211yescharacteristic
49C2×#3724C2211yescharacteristic
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×Dic32C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63916C2218yescomplemented
58#63912C2218yescomplemented
59#63912C2218yescomplemented
60C4×#626C2218yescomplemented
61#63891C2218yescomplemented
62#63885C2218yescomplemented
63#63881C2218yescomplemented
64#63881C2218yescomplemented
65#63879C2218yescomplemented
66#63877C2218yescomplemented
67#63861C2218yescomplemented
68#63847C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×#123—31no—
71C2×#939—31no—
72C2×#938—31no—
73C2×C4×#67—31no—
74C2×C4×#67—31no—
75#5709—316no—
76#5661—316no—
77C2×#898—31no—
78C2×#898D311yescharacteristic, complemented
79C2×#895—31no—
80C2×#894D311yescharacteristic, complemented
81C2×#893—31no—
82C2×#893—31no—
83C2×D3×C4⋊C4—31no—
84C2×D3×C4⋊C4—31no—
85C2×D3×C4⋊C4—61no—
86C2×#889—31no—
87C2×#889—31no—
88C2×#886—31no—
89C2×#884—31no—
90C2×#884—31no—
91C2×#884—31no—
92C2×#884—31no—
93C2×#884—31no—
94C2×#883—31no—
95C2×#67⋊C4—31no—
96C2×#67⋊C4—31no—
97C2×#67⋊C4—31no—
98C2×#879—31no—
99C2×#877—31no—
100C2×C4×D12—31no—
101C2×#872—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—24no—
113C2×C4×C3⋊D3—42no—
114C2×C4×C3⋊D3—42no—
115C2×C4×C3⋊D3C2314yes—
116C2×C4×C3⋊D3C2314yes—
117C2×C4×C3⋊D3C2314yes—
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C2×C3×D12—42no—
124C2×C3×D12C2314yes—
125C2×C3×C4×D3—42no—
126C2×C3×C4×D3C2314yes—
127C2×#626—24no—
128C2×#626—24no—
129C2×#626—24no—
130C2×#626C2314yes—
131C2×#626C2314yes—
132C2×#626C2314yes—
133C2×#625—24no—
134C2×#625—42no—
135C2×#625C2314yes—
136C2×#625C2314yes—
137C2×D3×Dic3—24no—
138C2×D3×Dic3—42no—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2314yes—
141C32×C4⋊C4C2314yes—
142C4⋊(C3⋊Dic3)C2314yes—
143#3750C2314yes—
144#3750C2314yes—
145C3×(C2×D3)⋊C4C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×C4⋊Dic3C2314yes—
152C3×Dic3⋊C4C2314yes—
153C3×Dic3⋊C4C2314yes—
154C3×C4×Dic3C2314yes—
155#3724C2314yes—
156#3724C2314yes—
157Dic3⋊Dic3C2314yes—
158#3722C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162Dic32C2314yes—
163Dic32C2314yes—
164C2×#553—91noSylow
165C22×C3×D4—31no—
166C23×C3×C4—31no—
167C22×#67—31no—
168C22×#67—31no—
169C22×#67—31no—
170C22×#67—31no—
171C22×#67—31no—
172C22×#67—31no—
173C22×#67—31no—
174C23×Dic3—31no—
175C23×Dic3—31no—
176C22×D12—31no—
177C22×D12—31no—
178C22×D12—31no—
179C22×D12C2×D311yescharacteristic
180C22×C4×D3—31no—
181C22×C4×D3—31no—
182C22×C4×D3—31no—
183C22×C4×D3—31no—
184C22×C4×D3—31no—
185C22×C4×D3—31no—
186C22×C4×D3—31no—
187C22×C4×D3—31no—
188C22×C4×D3—61no—
189C22×C4×D3—61no—
190C22×C4×D3—61no—
191C22×C4×D3C2×D311yescharacteristic
192C3×#126—38no—
193C3×#123—38no—
194C2×C3×C4⋊C4—21no—
195C2×C3×C4⋊C4—31no—
196C2×C3×C4⋊C4—31no—
197C2×C3×C4⋊C4—31no—
198C2×C3×C4⋊C4C2×D311yescharacteristic
199C2×C3×C4⋊C4C2×D311yescharacteristic
200C2×C3×C22⋊C4—31no—
201C2×C3×C22⋊C4—31no—
202C2×C3×C22⋊C4—31no—
203C2×C3×C22⋊C4—31no—
204C2×C3×C22⋊C4—31no—
205C2×C3×C22⋊C4—31no—
206C2×C3×C42—31no—
207C2×#217—31no—
208C2×#217—31no—
209C2×#217—31no—
210#939—38no—
211#938—38no—
212C4×#67—38no—
213C4×#67—38no—
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)⋊C4C2×D311yescharacteristic
220C2×(C2×D3)⋊C4C2×D311yescharacteristic
221C2×(C2×D3)⋊C4C2×D311yescharacteristic
222C2×(C2×D3)⋊C4C2×D311yescharacteristic
223C2×(C2×D3)⋊C4C2×D311yescharacteristic
224C2×(C2×D3)⋊C4C2×D311yescharacteristic
225C2×C4⋊Dic3—31no—
226C2×C4⋊Dic3—31no—
227C2×C4⋊Dic3—31no—
228C2×C4⋊Dic3—61no—
229C2×C4⋊Dic3C2×D311yescharacteristic
230C2×Dic3⋊C4—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—31no—
239C2×Dic3⋊C4—61no—
240C2×Dic3⋊C4—61no—
241C2×Dic3⋊C4C2×D311yescharacteristic
242C2×Dic3⋊C4C2×D311yescharacteristic
243C2×C4×Dic3—31no—
244C2×C4×Dic3—31no—
245C2×C4×Dic3—31no—
246C2×C4×Dic3—31no—
247C2×C4×Dic3C2×D311yescharacteristic
248#898—38no—
249#898C2×D318yescomplemented
250#895—38no—
251#894C2×D318yescomplemented
252#893—38no—
253#893—38no—
254D3×C4⋊C4—38no—
255D3×C4⋊C4—38no—
256D3×C4⋊C4—68no—
257#889—38no—
258#889—38no—
259#886—38no—
260#884—38no—
261#884—38no—
262#884—38no—
263#884—38no—
264#884—38no—
265#883—38no—
266#67⋊C4—38no—
267#67⋊C4—38no—
268#67⋊C4—38no—
269#879—38no—
270#877—38no—
271C4×D12—38no—
272#872—38no—
273C23×C32C2411yescharacteristic
274C22×C3⋊D3—22no—
275C22×C3⋊D3—22no—
276C22×C3⋊D3#4114yes—
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—
303C4×C3⋊D3—44no—
304C4×C3⋊D3—44no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3C2412yes—
311C2×C3×Dic3C2412yes—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C3×D12—44no—
316C3×C4×D3—44no—
317#626—28no—
318#626—28no—
319#626—28no—
320#625—28no—
321#625—44no—
322D3×Dic3—28no—
323D3×Dic3—44no—
324#553—916no—
325C2×#126—31no—
326C2×#126—91no—
327C2×#125—91no—
328C2×#123—31no—
329C2×#123—91no—
330C2×#121—91no—
331C2×#121—91no—
332C2×#121—91no—
333C2×#121—91no—
334C2×C4×D4—91no—
335C2×C4×D4—91no—
336C2×C4×D4—91no—
337C2×C4×D4—91no—
338C2×#117—91no—
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—122no—
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—122no—
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C22×C3×C4C22×D311yescharacteristic
365C22×C3×C4C22×D311yescharacteristic
366C22×C3×C4C22×D311yescharacteristic
367C2×#67—34no—
368C2×#67—34no—
369C2×#67—34no—
370C2×#67—34no—
371C2×#67—34no—
372C2×#67—34no—
373C2×#67—34no—
374C2×#67—64no—
375C2×#67—64no—
376C2×#67—64no—
377C2×#67—64no—
378C2×#67—64no—
379C2×#67—122no—
380C2×#67—122no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—34no—
388C22×Dic3—34no—
389C22×Dic3—61no—
390C22×Dic3—61no—
391C22×Dic3—61no—
392C22×Dic3—64no—
393C22×Dic3—122no—
394C22×Dic3C22×D311yescharacteristic
395C22×Dic3C22×D311yescharacteristic
396C22×Dic3C22×D311yescharacteristic
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C2×D12—34no—
400C2×D12—34no—
401C2×D12—34no—
402C2×D12—42no—
403C2×D12—64no—
404C2×D12—64no—
405C2×D12—64no—
406C2×D12C22×D314yes—
407C2×C4×D3—34no—
408C2×C4×D3—34no—
409C2×C4×D3—34no—
410C2×C4×D3—34no—
411C2×C4×D3—34no—
412C2×C4×D3—34no—
413C2×C4×D3—34no—
414C2×C4×D3—34no—
415C2×C4×D3—42no—
416C2×C4×D3—64no—
417C2×C4×D3—64no—
418C2×C4×D3—64no—
419C2×C4×D3—64no—
420C2×C4×D3—64no—
421C2×C4×D3—64no—
422C2×C4×D3—68no—
423C2×C4×D3—122no—
424C2×C4×D3—122no—
425C2×C4×D3—122no—
426C2×C4×D3—122no—
427C2×C4×D3—122no—
428C2×C4×D3—124no—
429C2×C4×D3—124no—
430C2×C4×D3C22×D314yes—
431C3×C4⋊C4—24no—
432C3×C4⋊C4—34no—
433C3×C4⋊C4—34no—
434C3×C4⋊C4—34no—
435C3×C4⋊C4C22×D314yes—
436C3×C4⋊C4C22×D314yes—
437C3×C22⋊C4—34no—
438C3×C22⋊C4—34no—
439C3×C22⋊C4—34no—
440C3×C22⋊C4—34no—
441C3×C22⋊C4—34no—
442C3×C22⋊C4—34no—
443C3×C42—34no—
444#217—34no—
445#217—34no—
446#217—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)⋊C4C22×D314yes—
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—
458C4⋊Dic3—34no—
459C4⋊Dic3—34no—
460C4⋊Dic3—34no—
461C4⋊Dic3—64no—
462C4⋊Dic3C22×D314yes—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—64no—
473Dic3⋊C4—64no—
474Dic3⋊C4C22×D314yes—
475Dic3⋊C4C22×D314yes—
476C4×Dic3—34no—
477C4×Dic3—34no—
478C4×Dic3—34no—
479C4×Dic3—34no—
480C4×Dic3C22×D314yes—
481C22×C32C2×#4112yes—
482C22×C32C2×#4112yes—
483C22×C32H(5,𝔽2)12yes—
484C22×C32C2511yescharacteristic
485C2×C3⋊D3—28no—
486C2×C3⋊D3—22no—
487C2×C3⋊D3—22no—
488C2×C3⋊D3C2×#4114yes—
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—22no—
498C2×C3×D3—44no—
499C2×C3×D3—44no—
500C2×C3×D3—44no—
501C32×C4—22no—
502C32×C4—22no—
503C32×C4—22no—
504C3⋊Dic3—22no—
505C3⋊Dic3—22no—
506C3⋊Dic3C2×#4114yes—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
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—
522C23×C4—91no—
523C23×C4—91no—
524#126—38no—
525#126—98no—
526#125—98no—
527#123—38no—
528#123—98no—
529#121—98no—
530#121—98no—
531#121—98no—
532#121—98no—
533C4×D4—98no—
534C4×D4—98no—
535C4×D4—98no—
536C4×D4—98no—
537#117—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—98no—
548C2×C4⋊C4D3211yescharacteristic
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—31no—
553C2×C22⋊C4—31no—
554C2×C22⋊C4—31no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C42—31no—
560C2×C42—91no—
561C2×C42—91no—
562C23×C3—21no—
563C23×C3—32no—
564C23×C3—32no—
565C23×C3—32no—
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×C3—62no—
575C23×C3C23×D311yescharacteristic
576C23×C3C23×D311yescharacteristic
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—22no—
586C22×D3—34no—
587C22×D3—34no—
588C22×D3—32no—
589C22×D3—32no—
590C22×D3—64no—
591C22×D3—62no—
592C22×D3—64no—
593C22×D3—64no—
594C22×D3—62no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3C23×D312yes—
599C22×D3C23×D312yes—
600C22×D3C23×D312yes—
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×C4C23×D312yes—
626C2×C3×C4C23×D312yes—
627C2×C3×C4C23×D312yes—
628C2×C3×C4C23×D312yes—
629C2×C3×C4C23×D312yes—
630C2×C3×C4C23×D312yes—
631#67—68no—
632#67—68no—
633#67—68no—
634#67—68no—
635#67—68no—
636#67—124no—
637#67—124no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—34no—
644C2×Dic3—34no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—32no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—32no—
651C2×Dic3—64no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—68no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—62no—
659C2×Dic3—62no—
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—68no—
670D12—68no—
671D12—68no—
672C4×D3—44no—
673C4×D3—68no—
674C4×D3—68no—
675C4×D3—68no—
676C4×D3—616no—
677C4×D3—124no—
678C4×D3—124no—
679C4×D3—124no—
680C4×D3—124no—
681C4×D3—124no—
682C4×D3—128no—
683C4×D3—128no—
684C2×C32#55314yescomplemented
685C2×C32C22×#4111yescharacteristic
686C2×C32C22×#4111yescharacteristic
687C2×C32C2×H(5,𝔽2)11yescharacteristic
688C3⋊D3—24no—
689C3×D3—42no—
690C3×D3—42no—
691C3×D3—42no—
692C24—31no—
693C24—31no—
694C24—31no—
695C24—91no—
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—184no—
706C2×D4—184no—
707C2×D4—362no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—34no—
714C22×C4—94no—
715C22×C4—94no—
716C22×C4—91no—
717C22×C4—91no—
718C22×C4—91no—
719C22×C4—94no—
720C22×C4—94no—
721C22×C4—94no—
722C22×C4—122no—
723C22×C4—184no—
724C22×C4—184no—
725C22×C4—362no—
726C22×C4—362no—
727C22×C4—362no—
728C22×C4C2×D3211yescharacteristic
729C22×C4C2×D3211yescharacteristic
730C22×C4C2×D3211yescharacteristic
731C4⋊C4—34no—
732C4⋊C4—34no—
733C4⋊C4—34no—
734C4⋊C4—94no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—94no—
740C4⋊C4C2×D3214yes—
741C22⋊C4—34no—
742C22⋊C4—34no—
743C22⋊C4—34no—
744C22⋊C4—34no—
745C22⋊C4—34no—
746C22⋊C4—34no—
747C22⋊C4—94no—
748C22⋊C4—94no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C42—34no—
752C42—94no—
753C42—94no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—21no—
758C22×C3—62no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3—62no—
765C22×C3—62no—
766C22×C3—62no—
767C22×C3—124no—
768C22×C3—124no—
769C22×C3—124no—
770C22×C3#100412yes—
771C22×C3D3×#4112yes—
772C22×C3D3×#4112yes—
773C22×C3D3×#4112yes—
774C22×C3D3×#4112yes—
775C22×C3#100912yes—
776C22×C3C24×D311yescharacteristic
777C22×C3C24×D311yescharacteristic
778C2×D3—22no—
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—34no—
788C2×D3—34no—
789C2×D3—44no—
790C2×D3—44no—
791C2×D3—44no—
792C2×D3—64no—
793C2×D3—64no—
794C2×D3—64no—
795C2×D3—616no—
796C2×D3—68no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—62no—
801C2×D3—68no—
802C3×C4—24no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—22no—
809C3×C4—42no—
810C3×C4—42no—
811C3×C4—62no—
812C3×C4—62no—
813C3×C4—62no—
814C3×C4—62no—
815C3×C4—62no—
816Dic3—22no—
817Dic3—22no—
818Dic3—22no—
819Dic3—22no—
820Dic3—22no—
821Dic3—34no—
822Dic3—34no—
823Dic3—64no—
824Dic3—62no—
825Dic3—62no—
826Dic3—62no—
827Dic3—62no—
828Dic3—122no—
829Dic3—122no—
830C32C2×#55311yescharacteristic, complemented, Sylow
831C23—32no—
832C23—32no—
833C23—32no—
834C23—62no—
835C23—62no—
836C23—62no—
837C23—62no—
838C23—62no—
839C23—62no—
840C23—62no—
841C23—62no—
842C23—62no—
843C23—94no—
844C23—92no—
845C23—182no—
846C23—182no—
847C23C22×D3211yescharacteristic
848D4—124no—
849D4—188no—
850D4—188no—
851D4—188no—
852D4—188no—
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—94no—
868C2×C4—92no—
869C2×C4—92no—
870C2×C4—92no—
871C2×C4—124no—
872C2×C4—188no—
873C2×C4—188no—
874C2×C4—182no—
875C2×C4—182no—
876C2×C4—364no—
877C2×C4—364no—
878C2×C4—364no—
879C2×C4C22×D3212yes—
880C2×C4C22×D3212yes—
881C2×C4C22×D3212yes—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—24no—
886C2×C3—122no—
887C2×C3—122no—
888C2×C3—122no—
889C2×C3#566114yescomplemented
890C2×C3#570914yescomplemented
891C2×C3C2×#100411yescharacteristic
892C2×C3C2×D3×#4111yescharacteristic
893C2×C3C2×D3×#4111yescharacteristic
894C2×C3C2×D3×#4111yescharacteristic
895C2×C3C2×D3×#4111yescharacteristic
896C2×C3C2×#100911yescharacteristic
897D3—42no—
898D3—42no—
899D3—42no—
900D3—68no—
901D3—64no—
902D3—64no—
903C22—62no—
904C22—62no—
905C22—62no—
906C22—62no—
907C22—62no—
908C22—62no—
909C22—62no—
910C22—62no—
911C22—62no—
912C22—94no—
913C22—124no—
914C22—124no—
915C22—124no—
916C22—182no—
917C22—182no—
918C22—188no—
919C22#6430612yes—
920C22#6431412yes—
921C22#6431912yes—
922C22C23×D3211yescharacteristic
923C4—22no—
924C4—22no—
925C4—22no—
926C4—62no—
927C4—62no—
928C4—62no—
929C4—62no—
930C4—62no—
931C4—94no—
932C4—182no—
933C4—182no—
934C3—21no—
935C3C2×#566111yescharacteristic, complemented
936C3C2×#570911yescharacteristic, complemented
937C2—122no—
938C2—122no—
939C2—122no—
940C2—184no—
941C2#1059447314yesdirect product factor
942C2C2×#6430611yescharacteristic
943C2C2×#6431411yescharacteristic
944C2C2×#6431911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#553
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×C4⋊C4×C3⋊D3C2semidirect
2. C2×C3×#898C2semidirect
3. C2×C3×#894C2semidirect
4. C2×#63916C2semidirect
5. C2×#63912C2semidirect
6. C2×#63912C2semidirect
7. C2×C4×#626C2semidirect
8. C2×#63891C2semidirect
9. C2×#63885C2semidirect
10. C2×#63881C2semidirect
11. C2×#63881C2semidirect
12. C2×#63879C2semidirect
13. C2×#63877C2semidirect
14. C2×#63861C2semidirect
15. C2×#63847C2semidirect
16. #10594473C2direct (N × H)
35. C4⋊C4×C3⋊D3C22semidirect
46. C3×#898C22semidirect
47. C3×#894C22semidirect
57. #63916C22semidirect
58. #63912C22semidirect
59. #63912C22semidirect
60. C4×#626C22semidirect
61. #63891C22semidirect
62. #63885C22semidirect
63. #63881C22semidirect
64. #63881C22semidirect
65. #63879C22semidirect
66. #63877C22semidirect
67. #63861C22semidirect
68. #63847C22semidirect
78. C2×#898D3semidirect
80. C2×#894D3semidirect
249. #898C2×D3semidirect
251. #894C2×D3semidirect
684. C2×C32#553semidirect
830. C32C2×#553semidirect
889. C2×C3#5661semidirect
890. C2×C3#5709semidirect
935. C3C2×#5661semidirect
936. C3C2×#5709semidirect
941. C2#10594473direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×C3×#8982
C2×C3×#8942
C2×#639162
C2×#639122
C2×C4×#6262
C2×#638912
C2×#638852
C2×#638812
C2×#638792
C2×#638772
C2×#638612
C2×#638472
#105944732
C2×#57093
C2×#56613