Finite Group Databasebeta

← C2×#10594944 #11903152

Subgroups — C2×#10594944 #11903152

Order 1152.

2717 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic, complemented
2C2×C3×#929C211yesmaximal, characteristic, complemented
3C2×C3×C4×#67C211yesmaximal, characteristic, complemented
4C2×#63971C211yesmaximal, characteristic, complemented
5C2×#63971C211yesmaximal, characteristic, complemented
6C2×#63970C211yesmaximal, characteristic, complemented
7C2×#63956C211yesmaximal, characteristic, complemented
8C2×#63906C211yesmaximal, characteristic, complemented
9C2×#63902C211yesmaximal, characteristic, complemented
10#10594944C2116yesmaximal, direct product factor
11C2×#63881C211yesmaximal, characteristic, complemented
12C2×#63877C211yesmaximal, characteristic, complemented
13C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
14C2×#63870C211yesmaximal, characteristic, complemented
15C2×#63868C211yesmaximal, characteristic, complemented
16C2×#63853C211yesmaximal, characteristic, complemented
17C2×#5661—31nomaximal
18C2×#5540—31nomaximal
19C23×C32×C4C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#625C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C22×D3×Dic3C2211yescharacteristic
30C22×D3×Dic3C2211yescharacteristic
31C2×#3757C2211yescharacteristic
32C4×#638C2218yescomplemented
33C2×#3752C2211yescharacteristic
34C2×#3750C2211yescharacteristic
35C2×C4×C3⋊Dic3C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C3×#929C2218yescomplemented
39C3×C4×#67C2218yescomplemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C2×C3×Dic3⋊C4C2211yescharacteristic
46C2×C3×C4×Dic3C2211yescharacteristic
47#63971C2218yescomplemented
48#63971C2218yescomplemented
49#63970C2218yescomplemented
50C2×#3724C2211yescharacteristic
51C2×#3724C2211yescharacteristic
52C2×#3724C2211yescharacteristic
53C2×Dic3⋊Dic3C2211yescharacteristic
54C2×Dic3⋊Dic3C2211yescharacteristic
55C2×Dic3⋊Dic3C2211yescharacteristic
56C2×#3722C2211yescharacteristic
57C2×#3722C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59#63956C2218yescomplemented
60C2×Dic32C2211yescharacteristic
61#63906C2218yescomplemented
62#63902C2218yescomplemented
63#63881C2218yescomplemented
64#63877C2218yescomplemented
65D3×Dic3⋊C4C2218yescomplemented
66#63870C2218yescomplemented
67#63868C2218yescomplemented
68#63853C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×C4×D4—31no—
71C2×#939—31no—
72C2×#939—31no—
73C2×#939—31no—
74C2×#938—31no—
75C2×#930—31no—
76C2×#929D311yescharacteristic, complemented
77C2×C4×#67—31no—
78C2×C4×#67—31no—
79C2×C4×#67—61no—
80C2×C4×#67D311yescharacteristic, complemented
81C22×Dic3⋊C4—31no—
82#5661—316no—
83#5540—316no—
84C2×#898—31no—
85C2×#894—31no—
86C2×#893—31no—
87C2×D3×C4⋊C4—31no—
88C2×#889—31no—
89C2×#889—31no—
90C2×#884—31no—
91C2×#884—31no—
92C2×#884—31no—
93C2×#883—31no—
94C2×#67⋊C4—31no—
95C2×#67⋊C4—31no—
96C2×#67⋊C4—31no—
97C2×#879—31no—
98C2×#879—31no—
99C2×#877—31no—
100C2×#876—31no—
101C2×#872—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C22×C32×C4—42no—
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2314yes—
110C2×#638—24no—
111C2×#638C2314yes—
112C22×C3⋊Dic3C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C2×C4×C3⋊D3—42no—
116C2×C4×C3⋊D3C2314yes—
117C2×C3×#67—24no—
118C2×C3×#67—42no—
119C2×C3×#67C2314yes—
120C2×C3×#67C2314yes—
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C2×C3×C4×D3—42no—
128C2×C3×C4×D3C2314yes—
129C2×#626—24no—
130C2×#626—42no—
131C2×#626C2314yes—
132C2×#626C2314yes—
133C2×#625—24no—
134C2×#625C2314yes—
135C2×D3×Dic3—24no—
136C2×D3×Dic3—24no—
137C2×D3×Dic3—42no—
138C2×D3×Dic3C2314yes—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2314yes—
141#3757C2314yes—
142#3752C2314yes—
143#3750C2314yes—
144C4×C3⋊Dic3C2314yes—
145C3×#217C2314yes—
146C3×#217C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×Dic3⋊C4C2314yes—
151C3×Dic3⋊C4C2314yes—
152C3×Dic3⋊C4C2314yes—
153C3×C4×Dic3C2314yes—
154#3724C2314yes—
155#3724C2314yes—
156#3724C2314yes—
157Dic3⋊Dic3C2314yes—
158Dic3⋊Dic3C2314yes—
159Dic3⋊Dic3C2314yes—
160#3722C2314yes—
161#3722C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163Dic32C2314yes—
164C2×#553—91noSylow
165C22×C3×D4—31no—
166C22×C3×D4—31no—
167C23×C3×C4—21no—
168C23×C3×C4—31no—
169C23×C3×C4C2×D311yescharacteristic
170C23×C3×C4C2×D311yescharacteristic
171C22×#67—31no—
172C22×#67—31no—
173C22×#67—31no—
174C22×#67—31no—
175C22×#67—31no—
176C22×#67—31no—
177C22×#67—61no—
178C22×#67C2×D311yescharacteristic
179C22×#67C2×D311yescharacteristic
180C23×Dic3—31no—
181C23×Dic3—31no—
182C23×Dic3—31no—
183C22×D12—31no—
184C22×D12—31no—
185C22×C4×D3—31no—
186C22×C4×D3—31no—
187C22×C4×D3—31no—
188C22×C4×D3—31no—
189C22×C4×D3—31no—
190C22×C4×D3—61no—
191C22×C4×D3C2×D311yescharacteristic
192C3×#123—38no—
193C3×C4×D4—38no—
194C2×C3×C4⋊C4—31no—
195C2×C3×C4⋊C4—31no—
196C2×C3×C4⋊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—
206C2×#217—61no—
207C2×#217C2×D311yescharacteristic
208C2×#217C2×D311yescharacteristic
209#939—38no—
210#939—38no—
211#939—38no—
212#938—38no—
213#930—38no—
214#929C2×D318yescomplemented
215C4×#67—38no—
216C4×#67—38no—
217C4×#67—68no—
218C4×#67C2×D318yescomplemented
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—31no—
226C2×(C2×D3)⋊C4—61no—
227C2×(C2×D3)⋊C4C2×D311yescharacteristic
228C2×(C2×D3)⋊C4C2×D311yescharacteristic
229C2×(C2×D3)⋊C4C2×D311yescharacteristic
230C2×C4⋊Dic3—31no—
231C2×C4⋊Dic3—31no—
232C2×C4⋊Dic3—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—31no—
244C2×Dic3⋊C4—38no—
245C2×Dic3⋊C4—61no—
246C2×Dic3⋊C4C2×D311yescharacteristic
247C2×Dic3⋊C4C2×D311yescharacteristic
248C2×Dic3⋊C4C2×D311yescharacteristic
249C2×C4×Dic3—31no—
250C2×C4×Dic3—31no—
251C2×C4×Dic3—31no—
252C2×C4×Dic3—31no—
253C2×C4×Dic3—61no—
254C2×C4×Dic3C2×D311yescharacteristic
255#898—38no—
256#894—38no—
257#893—38no—
258D3×C4⋊C4—38no—
259#889—38no—
260#889—38no—
261#884—38no—
262#884—38no—
263#884—38no—
264#883—38no—
265#67⋊C4—38no—
266#67⋊C4—38no—
267#67⋊C4—38no—
268#879—38no—
269#879—38no—
270#877—38no—
271#876—38no—
272#872—38no—
273C23×C32—22no—
274C23×C32—22no—
275C23×C32—22no—
276C23×C32C2412yes—
277C23×C32C2411yescharacteristic
278C22×C3⋊D3—22no—
279C22×C3⋊D3—22no—
280C22×C3⋊D3—22no—
281C22×C3⋊D3C2412yes—
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3#4114yes—
288C22×C3×D3C2412yes—
289C22×C3×D3C2412yes—
290C2×C32×C4—22no—
291C2×C32×C4—22no—
292C2×C32×C4—44no—
293C2×C32×C4C2412yes—
294C2×C32×C4C2412yes—
295#638—28no—
296C2×C3⋊Dic3—22no—
297C2×C3⋊Dic3—22no—
298C2×C3⋊Dic3#4114yes—
299C2×C3⋊Dic3C2412yes—
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2412yes—
302C4×C3⋊D3—44no—
303C3×#67—28no—
304C3×#67—44no—
305C2×C3×Dic3—22no—
306C2×C3×Dic3—22no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3C2412yes—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C3×C4×D3—44no—
318#626—28no—
319#626—44no—
320#625—28no—
321D3×Dic3—28no—
322D3×Dic3—28no—
323D3×Dic3—44no—
324#553—916no—
325C2×#126—91no—
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—31no—
335C2×C4×D4—91no—
336C2×C4×D4—91no—
337C2×C4×D4—91no—
338C2×#117—91no—
339C22×C4⋊C4—91no—
340C24×C3—21no—
341C24×C3—31no—
342C24×C3—31no—
343C24×C3C22×D311yescharacteristic
344C24×C3C22×D311yescharacteristic
345C23×D3—31no—
346C23×D3—31no—
347C23×D3—61no—
348C23×D3C22×D311yescharacteristic
349C23×D3C22×D311yescharacteristic
350C2×C3×D4—34no—
351C2×C3×D4—34no—
352C2×C3×D4—64no—
353C2×C3×D4—122no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—24no—
357C22×C3×C4—31no—
358C22×C3×C4—31no—
359C22×C3×C4—31no—
360C22×C3×C4—31no—
361C22×C3×C4—31no—
362C22×C3×C4—31no—
363C22×C3×C4—34no—
364C22×C3×C4—42no—
365C22×C3×C4—42no—
366C22×C3×C4—44no—
367C22×C3×C4—122no—
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D314yes—
373C22×C3×C4C22×D314yes—
374C2×#67—24no—
375C2×#67—34no—
376C2×#67—34no—
377C2×#67—34no—
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—34no—
381C2×#67—42no—
382C2×#67—64no—
383C2×#67—64no—
384C2×#67—64no—
385C2×#67—64no—
386C2×#67—64no—
387C2×#67—68no—
388C2×#67—64no—
389C2×#67—122no—
390C2×#67C22×D314yes—
391C2×#67C22×D314yes—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—31no—
397C22×Dic3—31no—
398C22×Dic3—34no—
399C22×Dic3—34no—
400C22×Dic3—34no—
401C22×Dic3—61no—
402C22×Dic3—61no—
403C22×Dic3—61no—
404C22×Dic3—64no—
405C22×Dic3—64no—
406C22×Dic3—122no—
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C22×Dic3C22×D311yescharacteristic
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C2×D12—34no—
414C2×D12—34no—
415C2×D12—64no—
416C2×D12—122no—
417C2×C4×D3—34no—
418C2×C4×D3—34no—
419C2×C4×D3—34no—
420C2×C4×D3—34no—
421C2×C4×D3—34no—
422C2×C4×D3—42no—
423C2×C4×D3—64no—
424C2×C4×D3—64no—
425C2×C4×D3—64no—
426C2×C4×D3—122no—
427C2×C4×D3—122no—
428C2×C4×D3—122no—
429C2×C4×D3—124no—
430C2×C4×D3C22×D314yes—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—34no—
433C3×C4⋊C4—34no—
434C3×C22⋊C4—34no—
435C3×C22⋊C4—34no—
436C3×C22⋊C4—34no—
437C3×C22⋊C4—34no—
438C3×C22⋊C4—34no—
439C3×C42—34no—
440#217—34no—
441#217—34no—
442#217—34no—
443#217—64no—
444#217C22×D314yes—
445#217C22×D314yes—
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—64no—
454(C2×D3)⋊C4C22×D314yes—
455(C2×D3)⋊C4C22×D314yes—
456(C2×D3)⋊C4C22×D314yes—
457C4⋊Dic3—34no—
458C4⋊Dic3—34no—
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—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—64no—
472Dic3⋊C4C22×D314yes—
473Dic3⋊C4C22×D314yes—
474Dic3⋊C4C22×D314yes—
475C4×Dic3—34no—
476C4×Dic3—34no—
477C4×Dic3—34no—
478C4×Dic3—34no—
479C4×Dic3—64no—
480C4×Dic3C22×D314yes—
481C22×C32—22no—
482C22×C32—22no—
483C22×C32—22no—
484C22×C32—44no—
485C22×C32C2×#4112yes—
486C22×C32C2×#4112yes—
487C22×C32H(5,𝔽2)12yes—
488C22×C32C2511yescharacteristic
489C2×C3⋊D3—22no—
490C2×C3⋊D3—22no—
491C2×C3⋊D3—22no—
492C2×C3⋊D3—44no—
493C2×C3×D3—28no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—44no—
500C2×C3×D3C2×#4114yes—
501C32×C4—22no—
502C32×C4—22no—
503C3⋊Dic3—22no—
504C3⋊Dic3—22no—
505C3⋊Dic3C2×#4114yes—
506C3×Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C22×D4—31no—
513C22×D4—31no—
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×C4D3211yescharacteristic
524#126—98no—
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—38no—
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—98no—
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×C4⋊C4—91no—
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×C42—31no—
560C2×C42—91no—
561C2×C42—91no—
562C23×C3—24no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—22no—
566C23×C3—22no—
567C23×C3—22no—
568C23×C3—22no—
569C23×C3—22no—
570C23×C3—21no—
571C23×C3—34no—
572C23×C3—32no—
573C23×C3—32no—
574C23×C3—42no—
575C23×C3—42no—
576C23×C3—62no—
577C23×C3—62no—
578C23×C3—62no—
579C23×C3—62no—
580C23×C3—62no—
581C23×C3C23×D312yes—
582C23×C3C23×D312yes—
583C23×C3C23×D311yescharacteristic
584C23×C3C23×D311yescharacteristic
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—32no—
591C22×D3—32no—
592C22×D3—62no—
593C22×D3—64no—
594C22×D3—62no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3—62no—
599C22×D3—62no—
600C22×D3—122no—
601C22×D3—122no—
602C22×D3#23514yes—
603C22×D3C23×D312yes—
604C22×D3C23×D312yes—
605C3×D4—68no—
606C3×D4—124no—
607C2×C3×C4—24no—
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—32no—
620C2×C3×C4—42no—
621C2×C3×C4—44no—
622C2×C3×C4—44no—
623C2×C3×C4—48no—
624C2×C3×C4—62no—
625C2×C3×C4—62no—
626C2×C3×C4—62no—
627C2×C3×C4—62no—
628C2×C3×C4—62no—
629C2×C3×C4—62no—
630C2×C3×C4—124no—
631C2×C3×C4C23×D312yes—
632C2×C3×C4C23×D312yes—
633C2×C3×C4C23×D312yes—
634C2×C3×C4C23×D312yes—
635#67—28no—
636#67—44no—
637#67—68no—
638#67—68no—
639#67—68no—
640#67—68no—
641#67—616no—
642#67—68no—
643#67—124no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—22no—
648C2×Dic3—22no—
649C2×Dic3—22no—
650C2×Dic3—34no—
651C2×Dic3—34no—
652C2×Dic3—32no—
653C2×Dic3—32no—
654C2×Dic3—32no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—32no—
658C2×Dic3—64no—
659C2×Dic3—62no—
660C2×Dic3—62no—
661C2×Dic3—62no—
662C2×Dic3—68no—
663C2×Dic3—68no—
664C2×Dic3—62no—
665C2×Dic3—62no—
666C2×Dic3—62no—
667C2×Dic3—62no—
668C2×Dic3—122no—
669C2×Dic3—122no—
670C2×Dic3—124no—
671C2×Dic3C23×D312yes—
672C2×Dic3C23×D312yes—
673C2×Dic3C23×D312yes—
674C2×Dic3C23×D312yes—
675C2×Dic3C23×D312yes—
676C2×Dic3C23×D312yes—
677D12—68no—
678D12—124no—
679C4×D3—44no—
680C4×D3—68no—
681C4×D3—68no—
682C4×D3—124no—
683C4×D3—124no—
684C4×D3—124no—
685C4×D3—128no—
686C2×C32—42no—
687C2×C32#55314yescomplemented
688C2×C32C22×#4111yescharacteristic
689C2×C32C22×#4111yescharacteristic
690C2×C32C2×H(5,𝔽2)11yescharacteristic
691C3⋊D3—42no—
692C3×D3—24no—
693C3×D3—42no—
694C24—31no—
695C24—31no—
696C24—91no—
697C24C2×D3211yescharacteristic
698C2×D4—34no—
699C2×D4—34no—
700C2×D4—64no—
701C2×D4—94no—
702C2×D4—94no—
703C2×D4—94no—
704C2×D4—94no—
705C2×D4—122no—
706C2×D4—184no—
707C2×D4—184no—
708C2×D4—184no—
709C2×D4—362no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—31no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—34no—
717C22×C4—42no—
718C22×C4—94no—
719C22×C4—94no—
720C22×C4—94no—
721C22×C4—91no—
722C22×C4—91no—
723C22×C4—91no—
724C22×C4—94no—
725C22×C4—122no—
726C22×C4—184no—
727C22×C4—184no—
728C22×C4—362no—
729C22×C4—362no—
730C22×C4C2×D3211yescharacteristic
731C22×C4C2×D3211yescharacteristic
732C22×C4C2×D3214yes—
733C4⋊C4—34no—
734C4⋊C4—34no—
735C4⋊C4—34no—
736C4⋊C4—94no—
737C4⋊C4—94no—
738C4⋊C4—94no—
739C4⋊C4—94no—
740C4⋊C4—94no—
741C4⋊C4—94no—
742C4⋊C4—94no—
743C22⋊C4—34no—
744C22⋊C4—34no—
745C22⋊C4—34no—
746C22⋊C4—34no—
747C22⋊C4—34no—
748C22⋊C4—94no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C22⋊C4—94no—
752C22⋊C4—94no—
753C42—34no—
754C42—94no—
755C42—94no—
756C22×C3—24no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—22no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—21no—
767C22×C3—34no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3—48no—
771C22×C3—44no—
772C22×C3—44no—
773C22×C3—68no—
774C22×C3—62no—
775C22×C3—62no—
776C22×C3—62no—
777C22×C3—62no—
778C22×C3—62no—
779C22×C3—124no—
780C22×C3C2×#23512yes—
781C22×C3#100412yes—
782C22×C3#100412yes—
783C22×C3D3×#4112yes—
784C22×C3D3×#4112yes—
785C22×C3D3×#4112yes—
786C22×C3C24×D311yescharacteristic
787C22×C3C24×D311yescharacteristic
788C2×D3—22no—
789C2×D3—22no—
790C2×D3—28no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—44no—
795C2×D3—64no—
796C2×D3—62no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—62no—
801C2×D3—62no—
802C2×D3—122no—
803C2×D3—122no—
804C2×D3—128no—
805C2×D3—124no—
806C2×D3—124no—
807C2×D3C2×#23514yes—
808C3×C4—24no—
809C3×C4—22no—
810C3×C4—22no—
811C3×C4—22no—
812C3×C4—22no—
813C3×C4—42no—
814C3×C4—62no—
815C3×C4—62no—
816C3×C4—62no—
817C3×C4—62no—
818C3×C4—62no—
819C3×C4—62no—
820Dic3—22no—
821Dic3—22no—
822Dic3—22no—
823Dic3—22no—
824Dic3—22no—
825Dic3—22no—
826Dic3—34no—
827Dic3—34no—
828Dic3—64no—
829Dic3—62no—
830Dic3—62no—
831Dic3—62no—
832Dic3—62no—
833Dic3—122no—
834Dic3—122no—
835C32C2×#55311yescharacteristic, complemented, Sylow
836C23—22no—
837C23—22no—
838C23—22no—
839C23—34no—
840C23—32no—
841C23—32no—
842C23—62no—
843C23—62no—
844C23—62no—
845C23—62no—
846C23—62no—
847C23—92no—
848C23—182no—
849C23—182no—
850C23—182no—
851C23C22×D3212yes—
852C23C22×D3211yescharacteristic
853D4—68no—
854D4—124no—
855D4—188no—
856D4—188no—
857D4—188no—
858D4—364no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—32no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—44no—
868C2×C4—62no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—62no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—94no—
875C2×C4—92no—
876C2×C4—92no—
877C2×C4—92no—
878C2×C4—124no—
879C2×C4—188no—
880C2×C4—188no—
881C2×C4—182no—
882C2×C4—182no—
883C2×C4—364no—
884C2×C4—364no—
885C2×C4C22×D3212yes—
886C2×C4C22×D3212yes—
887C2×C3—21no—
888C2×C3—21no—
889C2×C3—21no—
890C2×C3—24no—
891C2×C3—44no—
892C2×C3—42no—
893C2×C3—42no—
894C2×C3—64no—
895C2×C3—122no—
896C2×C3#554014yescomplemented
897C2×C3#566114yescomplemented
898C2×C3C22×#23511yescharacteristic
899C2×C3C2×#100411yescharacteristic
900C2×C3C2×#100411yescharacteristic
901C2×C3C2×D3×#4111yescharacteristic
902C2×C3C2×D3×#4111yescharacteristic
903C2×C3C2×D3×#4111yescharacteristic
904D3—24no—
905D3—42no—
906D3—124no—
907D3—122no—
908D3—122no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—34no—
913C22—44no—
914C22—62no—
915C22—62no—
916C22—68no—
917C22—62no—
918C22—62no—
919C22—62no—
920C22—124no—
921C22—182no—
922C22—182no—
923C22—182no—
924C22—364no—
925C22D3×#23512yes—
926C22#6430612yes—
927C22#6433012yes—
928C22C23×D3211yescharacteristic
929C4—22no—
930C4—22no—
931C4—62no—
932C4—62no—
933C4—62no—
934C4—62no—
935C4—62no—
936C4—62no—
937C4—94no—
938C4—182no—
939C4—182no—
940C3—21no—
941C3C2×#554011yescharacteristic, complemented
942C3C2×#566111yescharacteristic, complemented
943C2—42no—
944C2—64no—
945C2—122no—
946C2—362no—
947C2#1059494414yesdirect product factor
948C2C2×D3×#23511yescharacteristic
949C2C2×#6430611yescharacteristic
950C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#553
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#638C2semidirect
2. C2×C3×#929C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C2×#63971C2semidirect
5. C2×#63971C2semidirect
6. C2×#63970C2semidirect
7. C2×#63956C2semidirect
8. C2×#63906C2semidirect
9. C2×#63902C2semidirect
10. #10594944C2direct (N × H)
11. C2×#63881C2semidirect
12. C2×#63877C2semidirect
13. C2×D3×Dic3⋊C4C2semidirect
14. C2×#63870C2semidirect
15. C2×#63868C2semidirect
16. C2×#63853C2semidirect
32. C4×#638C22semidirect
38. C3×#929C22semidirect
39. C3×C4×#67C22semidirect
47. #63971C22semidirect
48. #63971C22semidirect
49. #63970C22semidirect
59. #63956C22semidirect
61. #63906C22semidirect
62. #63902C22semidirect
63. #63881C22semidirect
64. #63877C22semidirect
65. D3×Dic3⋊C4C22semidirect
66. #63870C22semidirect
67. #63868C22semidirect
68. #63853C22semidirect
76. C2×#929D3semidirect
80. C2×C4×#67D3semidirect
214. #929C2×D3semidirect
218. C4×#67C2×D3semidirect
687. C2×C32#553semidirect
835. C32C2×#553semidirect
896. C2×C3#5540semidirect
897. C2×C3#5661semidirect
941. C3C2×#5540semidirect
942. C3C2×#5661semidirect
947. C2#10594944direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×C3×#9292
C2×C3×C4×#672
C2×#639712
C2×#639702
C2×#639562
C2×#639062
C2×#639022
#105949442
C2×#638812
C2×#638772
C2×D3×Dic3⋊C42
C2×#638702
C2×#638682
C2×#638532
C2×#56613
C2×#55403