Finite Group Databasebeta

← C2×#10594467 #11901522

Subgroups — C2×#10594467 #11901522

Order 1152.

2733 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic, complemented
2C2×C3×#894C211yesmaximal, characteristic, complemented
3C2×C3×#889C211yesmaximal, characteristic, complemented
4C2×#63911C211yesmaximal, characteristic, complemented
5C2×#63910C211yesmaximal, characteristic, complemented
6C2×#63910C211yesmaximal, characteristic, complemented
7C2×#63910C211yesmaximal, characteristic, complemented
8C2×#63909C211yesmaximal, characteristic, complemented
9C2×#63904C211yesmaximal, characteristic, complemented
10C2×#63897C211yesmaximal, characteristic, complemented
11C2×#63890C211yesmaximal, characteristic, complemented
12C2×#63886C211yesmaximal, characteristic, complemented
13C2×#63881C211yesmaximal, characteristic, complemented
14C2×#63853C211yesmaximal, characteristic, complemented
15C2×#63836C211yesmaximal, characteristic, complemented
16#10594467C2116yesmaximal, direct product factor
17C2×#5697—31nomaximal
18C2×#5663—31nomaximal
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#626C2211yescharacteristic
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#624C2211yescharacteristic
32C22×#624C2211yescharacteristic
33C22×D3×Dic3C2211yescharacteristic
34C2×C32×C4⋊C4C2211yescharacteristic
35C2×#3752C2211yescharacteristic
36C2×#3752C2211yescharacteristic
37#64104C2218yescomplemented
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×C4⋊Dic3C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C2×C3×Dic3⋊C4C2211yescharacteristic
46C2×C3×Dic3⋊C4C2211yescharacteristic
47C2×C3×C4×Dic3C2211yescharacteristic
48C3×#894C2218yescomplemented
49C3×#889C2218yescomplemented
50C2×Dic3⋊Dic3C2211yescharacteristic
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×Dic32C2211yescharacteristic
57#63911C2218yescomplemented
58#63910C2218yescomplemented
59#63910C2218yescomplemented
60#63910C2218yescomplemented
61#63909C2218yescomplemented
62#63904C2218yescomplemented
63#63897C2218yescomplemented
64#63890C2218yescomplemented
65#63886C2218yescomplemented
66#63881C2218yescomplemented
67#63853C2218yescomplemented
68#63836C2218yescomplemented
69C2×C3×#125—31no—
70C2×C3×#123—31no—
71C2×#940—31no—
72C2×#939—31no—
73C2×#930—31no—
74C2×C4×#67—31no—
75#5697—316no—
76#5663—316no—
77C2×#895—31no—
78C2×#895—31no—
79C2×#895—31no—
80C2×#895—31no—
81C2×#895—31no—
82C2×#895—31no—
83C2×#895—31no—
84C2×#895—61no—
85C2×#894—31no—
86C2×#894—31no—
87C2×#894—31no—
88C2×#894—31no—
89C2×#894D311yescharacteristic, complemented
90C2×#893—31no—
91C2×#893—31no—
92C2×#892—31no—
93C2×#889D311yescharacteristic, complemented
94C2×#886—31no—
95C2×#884—31no—
96C2×#884—31no—
97C2×#884—31no—
98C2×#883—31no—
99C2×#67⋊C4—31no—
100C2×#874—31no—
101C2×#872—31no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C22×C32×C4C2311yescharacteristic
108C22×C32×C4C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C3⋊Dic3C2311yescharacteristic
111C2×C4⋊(C3⋊D3)—42no—
112C2×C4⋊(C3⋊D3)—42no—
113C2×C4⋊(C3⋊D3)—42no—
114C2×C4⋊(C3⋊D3)C2314yes—
115C2×C4⋊(C3⋊D3)C2314yes—
116C2×C4⋊(C3⋊D3)C2314yes—
117C2×C4×C3⋊D3—42no—
118C2×C4×C3⋊D3C2314yes—
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C2×C3×D12—42no—
126C2×C3×D12C2314yes—
127C2×C3×C4×D3—42no—
128C2×C3×C4×D3C2314yes—
129C2×#626—24no—
130C2×#626—24no—
131C2×#626—42no—
132C2×#626—42no—
133C2×#626—42no—
134C2×#626—42no—
135C2×#626C2314yes—
136C2×#626C2314yes—
137C2×#626C2314yes—
138C2×#626C2314yes—
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#624—24no—
142C2×#624—42no—
143C2×#624C2314yes—
144C2×#624C2314yes—
145C2×D3×Dic3—42no—
146C2×D3×Dic3C2314yes—
147C32×C4⋊C4C2314yes—
148#3752C2314yes—
149#3752C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×C4⋊Dic3C2314yes—
154C3×Dic3⋊C4C2314yes—
155C3×Dic3⋊C4C2314yes—
156C3×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×C4×Dic3C2314yes—
160Dic3⋊Dic3C2314yes—
161#3722C2314yes—
162#3722C2314yes—
163#3722C2314yes—
164#3722C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166Dic32C2314yes—
167C2×#540—91noSylow
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—
176C23×Dic3—31no—
177C22×D12—31no—
178C22×D12—31no—
179C22×D12—31no—
180C22×D12—31no—
181C22×D12—31no—
182C22×D12—31no—
183C22×D12—31no—
184C22×D12—31no—
185C22×D12—31no—
186C22×D12—31no—
187C22×D12—31no—
188C22×D12—31no—
189C22×D12—61no—
190C22×D12—61no—
191C22×D12—61no—
192C22×D12C2×D311yescharacteristic
193C22×C4×D3—31no—
194C22×C4×D3—31no—
195C22×C4×D3—31no—
196C22×C4×D3—31no—
197C22×C4×D3—31no—
198C22×C4×D3—31no—
199C22×C4×D3—31no—
200C22×C4×D3—61no—
201C22×C4×D3C2×D311yescharacteristic
202C3×#125—38no—
203C3×#123—38no—
204C2×C3×C4⋊C4—21no—
205C2×C3×C4⋊C4—31no—
206C2×C3×C4⋊C4—31no—
207C2×C3×C4⋊C4—31no—
208C2×C3×C4⋊C4—31no—
209C2×C3×C4⋊C4—31no—
210C2×C3×C4⋊C4—31no—
211C2×C3×C4⋊C4C2×D311yescharacteristic
212C2×C3×C4⋊C4C2×D311yescharacteristic
213C2×C3×C22⋊C4—31no—
214C2×C3×C22⋊C4—31no—
215C2×C3×C22⋊C4—31no—
216C2×C3×C42—31no—
217C2×#217—31no—
218#940—38no—
219#939—38no—
220#930—38no—
221C4×#67—38no—
222C2×(C2×D3)⋊C4—31no—
223C2×(C2×D3)⋊C4—31no—
224C2×(C2×D3)⋊C4—31no—
225C2×(C2×D3)⋊C4—31no—
226C2×(C2×D3)⋊C4—31no—
227C2×(C2×D3)⋊C4—31no—
228C2×(C2×D3)⋊C4—31no—
229C2×(C2×D3)⋊C4—31no—
230C2×(C2×D3)⋊C4—31no—
231C2×(C2×D3)⋊C4—31no—
232C2×(C2×D3)⋊C4—31no—
233C2×(C2×D3)⋊C4—31no—
234C2×(C2×D3)⋊C4—31no—
235C2×(C2×D3)⋊C4—61no—
236C2×(C2×D3)⋊C4—61no—
237C2×(C2×D3)⋊C4C2×D311yescharacteristic
238C2×(C2×D3)⋊C4C2×D311yescharacteristic
239C2×(C2×D3)⋊C4C2×D311yescharacteristic
240C2×C4⋊Dic3—31no—
241C2×C4⋊Dic3C2×D311yescharacteristic
242C2×Dic3⋊C4—31no—
243C2×Dic3⋊C4C2×D311yescharacteristic
244C2×Dic3⋊C4C2×D311yescharacteristic
245C2×Dic3⋊C4C2×D311yescharacteristic
246C2×Dic3⋊C4C2×D311yescharacteristic
247C2×Dic3⋊C4C2×D311yescharacteristic
248C2×C4×Dic3—31no—
249C2×C4×Dic3—31no—
250C2×C4×Dic3C2×D311yescharacteristic
251#895—38no—
252#895—38no—
253#895—38no—
254#895—38no—
255#895—38no—
256#895—38no—
257#895—38no—
258#895—68no—
259#894—38no—
260#894—38no—
261#894—38no—
262#894—38no—
263#894C2×D318yescomplemented
264#893—38no—
265#893—38no—
266#892—38no—
267#889C2×D318yescomplemented
268#886—38no—
269#884—38no—
270#884—38no—
271#884—38no—
272#883—38no—
273#67⋊C4—38no—
274#874—38no—
275#872—38no—
276C23×C32C2411yescharacteristic
277C22×C3⋊D3—22no—
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⋊D3C2412yes—
287C22×C3⋊D3C2412yes—
288C22×C3⋊D3C2412yes—
289C22×C3×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3—22no—
295C22×C3×D3C2412yes—
296C22×C3×D3C2412yes—
297C2×C32×C4—22no—
298C2×C32×C4—22no—
299C2×C32×C4—22no—
300C2×C32×C4C2412yes—
301C2×C32×C4C2412yes—
302C2×C32×C4C2412yes—
303C2×C3⋊Dic3—22no—
304C2×C3⋊Dic3C2412yes—
305C4⋊(C3⋊D3)—44no—
306C4⋊(C3⋊D3)—44no—
307C4⋊(C3⋊D3)—44no—
308C4×C3⋊D3—44no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3#4114yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C3×D12—44no—
322C3×C4×D3—44no—
323#626—28no—
324#626—28no—
325#626—44no—
326#626—44no—
327#626—44no—
328#626—44no—
329#624—28no—
330#624—44no—
331D3×Dic3—44no—
332#540—916no—
333C2×#127—91no—
334C2×#125—31no—
335C2×#123—31no—
336C2×#123—91no—
337C2×#123—91no—
338C2×#123—91no—
339C2×#121—91no—
340C2×#121—91no—
341C2×#121—91no—
342C2×#121—91no—
343C2×#121—91no—
344C2×#121—91no—
345C2×C4×D4—91no—
346C2×C4×D4—91no—
347C2×#117—91no—
348C24×C3—31no—
349C24×C3—31no—
350C23×D3—31no—
351C23×D3—31no—
352C23×D3—31no—
353C23×D3—31no—
354C23×D3—31no—
355C23×D3—31no—
356C23×D3—61no—
357C23×D3—61no—
358C23×D3—61no—
359C23×D3C22×D311yescharacteristic
360C23×D3C22×D311yescharacteristic
361C2×C3×D4—34no—
362C2×C3×D4—122no—
363C22×C3×C4—21no—
364C22×C3×C4—21no—
365C22×C3×C4—21no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—34no—
373C22×C3×C4—122no—
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C22×C3×C4C22×D311yescharacteristic
378C22×C3×C4C22×D311yescharacteristic
379C22×C3×C4C22×D311yescharacteristic
380C2×#67—34no—
381C2×#67—34no—
382C2×#67—34no—
383C2×#67—34no—
384C2×#67—34no—
385C2×#67—34no—
386C2×#67—64no—
387C2×#67—64no—
388C2×#67—122no—
389C2×#67—122no—
390C2×#67—122no—
391C2×#67—122no—
392C22×Dic3—31no—
393C22×Dic3—31no—
394C22×Dic3—34no—
395C22×Dic3—61no—
396C22×Dic3—122no—
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C22×Dic3C22×D311yescharacteristic
403C2×D12—34no—
404C2×D12—34no—
405C2×D12—34no—
406C2×D12—34no—
407C2×D12—34no—
408C2×D12—34no—
409C2×D12—34no—
410C2×D12—34no—
411C2×D12—34no—
412C2×D12—34no—
413C2×D12—34no—
414C2×D12—34no—
415C2×D12—42no—
416C2×D12—64no—
417C2×D12—64no—
418C2×D12—64no—
419C2×D12—64no—
420C2×D12—64no—
421C2×D12—122no—
422C2×D12—122no—
423C2×D12—122no—
424C2×D12—122no—
425C2×D12—122no—
426C2×D12—122no—
427C2×D12—124no—
428C2×D12—124no—
429C2×D12—124no—
430C2×D12—122no—
431C2×D12—122no—
432C2×D12—122no—
433C2×D12—122no—
434C2×D12C22×D314yes—
435C2×C4×D3—34no—
436C2×C4×D3—34no—
437C2×C4×D3—34no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—34no—
441C2×C4×D3—34no—
442C2×C4×D3—42no—
443C2×C4×D3—64no—
444C2×C4×D3—64no—
445C2×C4×D3—64no—
446C2×C4×D3—122no—
447C2×C4×D3—122no—
448C2×C4×D3—122no—
449C2×C4×D3—122no—
450C2×C4×D3—122no—
451C2×C4×D3—124no—
452C2×C4×D3C22×D314yes—
453C3×C4⋊C4—24no—
454C3×C4⋊C4—34no—
455C3×C4⋊C4—34no—
456C3×C4⋊C4—34no—
457C3×C4⋊C4—34no—
458C3×C4⋊C4—34no—
459C3×C4⋊C4—34no—
460C3×C4⋊C4C22×D314yes—
461C3×C4⋊C4C22×D314yes—
462C3×C22⋊C4—34no—
463C3×C22⋊C4—34no—
464C3×C22⋊C4—34no—
465C3×C42—34no—
466#217—34no—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4—34no—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—34no—
471(C2×D3)⋊C4—34no—
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4—34no—
474(C2×D3)⋊C4—34no—
475(C2×D3)⋊C4—34no—
476(C2×D3)⋊C4—34no—
477(C2×D3)⋊C4—34no—
478(C2×D3)⋊C4—34no—
479(C2×D3)⋊C4—34no—
480(C2×D3)⋊C4—64no—
481(C2×D3)⋊C4—64no—
482(C2×D3)⋊C4C22×D314yes—
483(C2×D3)⋊C4C22×D314yes—
484(C2×D3)⋊C4C22×D314yes—
485C4⋊Dic3—34no—
486C4⋊Dic3C22×D314yes—
487Dic3⋊C4—34no—
488Dic3⋊C4C22×D314yes—
489Dic3⋊C4C22×D314yes—
490Dic3⋊C4C22×D314yes—
491Dic3⋊C4C22×D314yes—
492Dic3⋊C4C22×D314yes—
493C4×Dic3—34no—
494C4×Dic3—34no—
495C4×Dic3C22×D314yes—
496C22×C32C2×#4112yes—
497C22×C32H(5,𝔽2)12yes—
498C22×C32H(5,𝔽2)12yes—
499C22×C32C2511yescharacteristic
500C2×C3⋊D3—22no—
501C2×C3⋊D3—22no—
502C2×C3⋊D3—22no—
503C2×C3⋊D3—22no—
504C2×C3⋊D3—22no—
505C2×C3⋊D3—22no—
506C2×C3⋊D3—22no—
507C2×C3⋊D3—22no—
508C2×C3⋊D3—22no—
509C2×C3⋊D3—44no—
510C2×C3⋊D3—44no—
511C2×C3⋊D3—44no—
512C2×C3×D3—22no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—44no—
519C2×C3×D3—44no—
520C32×C4—22no—
521C32×C4—22no—
522C32×C4—22no—
523C3⋊Dic3—22no—
524C3×Dic3—22no—
525C3×Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3C2×#4114yes—
530C22×D4—31no—
531C22×D4—91no—
532C22×D4—91no—
533C22×D4—91no—
534C22×D4—91no—
535C22×D4—91no—
536C22×D4—91no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4—91no—
540C23×C4—31no—
541C23×C4—91no—
542C23×C4—91no—
543C23×C4—91no—
544C23×C4—91no—
545#127—98no—
546#125—38no—
547#123—38no—
548#123—98no—
549#123—98no—
550#123—98no—
551#121—98no—
552#121—98no—
553#121—98no—
554#121—98no—
555#121—98no—
556#121—98no—
557C4×D4—98no—
558C4×D4—98no—
559#117—98no—
560C2×C4⋊C4—31no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—31no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—31no—
565C2×C4⋊C4—31no—
566C2×C4⋊C4—91no—
567C2×C4⋊C4D3211yescharacteristic
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—91no—
572C2×C22⋊C4—91no—
573C2×C22⋊C4—91no—
574C2×C22⋊C4—91no—
575C2×C22⋊C4—91no—
576C2×C22⋊C4—91no—
577C2×C22⋊C4—91no—
578C2×C42—31no—
579C2×C42—91no—
580C23×C3—21no—
581C23×C3—32no—
582C23×C3—32no—
583C23×C3—62no—
584C23×C3—62no—
585C23×C3—62no—
586C23×C3—62no—
587C23×C3—62no—
588C23×C3—62no—
589C23×C3C23×D311yescharacteristic
590C23×C3C23×D311yescharacteristic
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—32no—
598C22×D3—32no—
599C22×D3—32no—
600C22×D3—32no—
601C22×D3—32no—
602C22×D3—32no—
603C22×D3—62no—
604C22×D3—62no—
605C22×D3—62no—
606C22×D3—64no—
607C22×D3—62no—
608C22×D3—62no—
609C22×D3—62no—
610C22×D3—62no—
611C22×D3—62no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—62no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—62no—
620C22×D3—62no—
621C22×D3—62no—
622C22×D3—62no—
623C22×D3—62no—
624C22×D3—62no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—122no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3—122no—
631C22×D3—122no—
632C22×D3—122no—
633C22×D3C23×D312yes—
634C22×D3C23×D312yes—
635C3×D4—124no—
636C2×C3×C4—24no—
637C2×C3×C4—22no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—22no—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—22no—
644C2×C3×C4—22no—
645C2×C3×C4—22no—
646C2×C3×C4—34no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—42no—
654C2×C3×C4—42no—
655C2×C3×C4—62no—
656C2×C3×C4—62no—
657C2×C3×C4—62no—
658C2×C3×C4—62no—
659C2×C3×C4—62no—
660C2×C3×C4—124no—
661C2×C3×C4C23×D312yes—
662C2×C3×C4C23×D312yes—
663C2×C3×C4C23×D312yes—
664C2×C3×C4C23×D312yes—
665C2×C3×C4C23×D312yes—
666C2×C3×C4C23×D312yes—
667#67—68no—
668#67—68no—
669#67—124no—
670#67—124no—
671#67—124no—
672#67—124no—
673C2×Dic3—22no—
674C2×Dic3—22no—
675C2×Dic3—22no—
676C2×Dic3—22no—
677C2×Dic3—22no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—62no—
681C2×Dic3—62no—
682C2×Dic3—62no—
683C2×Dic3—122no—
684C2×Dic3—124no—
685C2×Dic3#23914yes—
686C2×Dic3C23×D312yes—
687C2×Dic3C23×D312yes—
688C2×Dic3C23×D312yes—
689C2×Dic3C23×D312yes—
690C2×Dic3C23×D312yes—
691C2×Dic3C23×D312yes—
692D12—44no—
693D12—68no—
694D12—68no—
695D12—124no—
696D12—124no—
697D12—124no—
698D12—124no—
699D12—124no—
700D12—124no—
701D12—128no—
702D12—128no—
703D12—128no—
704D12—124no—
705D12—124no—
706D12—124no—
707D12—124no—
708C4×D3—44no—
709C4×D3—68no—
710C4×D3—68no—
711C4×D3—124no—
712C4×D3—124no—
713C4×D3—124no—
714C4×D3—124no—
715C4×D3—124no—
716C4×D3—128no—
717C2×C32#54014yescomplemented
718C2×C32C22×#4111yescharacteristic
719C2×C32C2×H(5,𝔽2)11yescharacteristic
720C2×C32C2×H(5,𝔽2)11yescharacteristic
721C3⋊D3—42no—
722C3⋊D3—42no—
723C3⋊D3—42no—
724C3×D3—42no—
725C3×D3—42no—
726C24—31no—
727C24—31no—
728C24—91no—
729C24—91no—
730C24—91no—
731C2×D4—34no—
732C2×D4—94no—
733C2×D4—94no—
734C2×D4—94no—
735C2×D4—94no—
736C2×D4—94no—
737C2×D4—94no—
738C2×D4—94no—
739C2×D4—94no—
740C2×D4—94no—
741C2×D4—122no—
742C2×D4—184no—
743C2×D4—184no—
744C2×D4—362no—
745C2×D4—362no—
746C2×D4—362no—
747C2×D4—362no—
748C2×D4—362no—
749C2×D4—362no—
750C2×D4—362no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—31no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—34no—
758C22×C4—94no—
759C22×C4—94no—
760C22×C4—94no—
761C22×C4—91no—
762C22×C4—94no—
763C22×C4—122no—
764C22×C4—184no—
765C22×C4—362no—
766C22×C4—362no—
767C22×C4—362no—
768C22×C4C2×D3211yescharacteristic
769C22×C4C2×D3211yescharacteristic
770C22×C4C2×D3211yescharacteristic
771C4⋊C4—34no—
772C4⋊C4—34no—
773C4⋊C4—34no—
774C4⋊C4—34no—
775C4⋊C4—34no—
776C4⋊C4—34no—
777C4⋊C4—94no—
778C4⋊C4C2×D3214yes—
779C22⋊C4—34no—
780C22⋊C4—34no—
781C22⋊C4—34no—
782C22⋊C4—94no—
783C22⋊C4—94no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C42—34no—
790C42—94no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—22no—
794C22×C3—21no—
795C22×C3—62no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3—124no—
802C22×C3—124no—
803C22×C3#100412yes—
804C22×C3C2×#23912yes—
805C22×C3D3×#4112yes—
806C22×C3#100912yes—
807C22×C3#100912yes—
808C22×C3#100912yes—
809C22×C3C24×D311yescharacteristic
810C22×C3C24×D311yescharacteristic
811C2×D3—22no—
812C2×D3—22no—
813C2×D3—22no—
814C2×D3—22no—
815C2×D3—22no—
816C2×D3—22no—
817C2×D3—44no—
818C2×D3—44no—
819C2×D3—64no—
820C2×D3—62no—
821C2×D3—62no—
822C2×D3—62no—
823C2×D3—62no—
824C2×D3—62no—
825C2×D3—62no—
826C2×D3—62no—
827C2×D3—62no—
828C2×D3—62no—
829C2×D3—62no—
830C2×D3—62no—
831C2×D3—62no—
832C2×D3—62no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—62no—
837C2×D3—62no—
838C2×D3—122no—
839C2×D3—122no—
840C2×D3—122no—
841C2×D3—122no—
842C2×D3—122no—
843C2×D3—122no—
844C2×D3—122no—
845C2×D3—122no—
846C2×D3—128no—
847C2×D3—124no—
848C2×D3—124no—
849C2×D3—124no—
850C2×D3—124no—
851C2×D3—124no—
852C2×D3—124no—
853C2×D3—244no—
854C2×D3—244no—
855C3×C4—24no—
856C3×C4—22no—
857C3×C4—22no—
858C3×C4—22no—
859C3×C4—22no—
860C3×C4—22no—
861C3×C4—22no—
862C3×C4—34no—
863C3×C4—42no—
864C3×C4—42no—
865C3×C4—62no—
866C3×C4—62no—
867C3×C4—62no—
868C3×C4—62no—
869C3×C4—62no—
870Dic3—22no—
871Dic3—22no—
872Dic3—22no—
873Dic3—22no—
874Dic3—22no—
875Dic3—62no—
876Dic3—62no—
877Dic3—122no—
878Dic3C2×#23914yes—
879C32C2×#54011yescharacteristic, complemented, Sylow
880C23—32no—
881C23—32no—
882C23—62no—
883C23—62no—
884C23—62no—
885C23—62no—
886C23—62no—
887C23—62no—
888C23—92no—
889C23—92no—
890C23—92no—
891C23—182no—
892C23—182no—
893C23—182no—
894C23—182no—
895C23—182no—
896C23—182no—
897C23—182no—
898C23—182no—
899C23—182no—
900C23C22×D3211yescharacteristic
901D4—124no—
902D4—188no—
903D4—188no—
904D4—364no—
905D4—364no—
906D4—364no—
907D4—364no—
908D4—364no—
909D4—364no—
910D4—364no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—34no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—32no—
918C2×C4—32no—
919C2×C4—32no—
920C2×C4—32no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—62no—
924C2×C4—62no—
925C2×C4—62no—
926C2×C4—92no—
927C2×C4—124no—
928C2×C4—188no—
929C2×C4—182no—
930C2×C4—364no—
931C2×C4—364no—
932C2×C4—364no—
933C2×C4C22×D3212yes—
934C2×C4C22×D3212yes—
935C2×C4C22×D3212yes—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—24no—
940C2×C3—122no—
941C2×C3—122no—
942C2×C3#566314yescomplemented
943C2×C3#569714yescomplemented
944C2×C3C2×#100411yescharacteristic
945C2×C3C22×#23911yescharacteristic
946C2×C3C2×D3×#4111yescharacteristic
947C2×C3C2×#100911yescharacteristic
948C2×C3C2×#100911yescharacteristic
949C2×C3C2×#100911yescharacteristic
950D3—42no—
951D3—42no—
952D3—124no—
953D3—122no—
954D3—122no—
955D3—122no—
956D3—122no—
957D3—122no—
958D3—122no—
959D3—242no—
960D3—242no—
961C22—62no—
962C22—62no—
963C22—62no—
964C22—62no—
965C22—62no—
966C22—62no—
967C22—124no—
968C22—124no—
969C22—182no—
970C22—182no—
971C22—182no—
972C22—182no—
973C22—182no—
974C22—182no—
975C22—182no—
976C22—182no—
977C22—182no—
978C22—364no—
979C22—364no—
980C22—364no—
981C22#6430812yes—
982C22#6431412yes—
983C22D3×#23912yes—
984C22C23×D3211yescharacteristic
985C4—22no—
986C4—22no—
987C4—22no—
988C4—34no—
989C4—62no—
990C4—62no—
991C4—62no—
992C4—62no—
993C4—62no—
994C4—182no—
995C3—21no—
996C3C2×#566311yescharacteristic, complemented
997C3C2×#569711yescharacteristic, complemented
998C2—122no—
999C2—122no—
1000C2—362no—
1001C2—362no—
1002C2—362no—
1003C2#1059446714yesdirect product factor
1004C2C2×#6430811yescharacteristic
1005C2C2×#6431411yescharacteristic
1006C2C2×D3×#23911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#540
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×#64104C2semidirect
2. C2×C3×#894C2semidirect
3. C2×C3×#889C2semidirect
4. C2×#63911C2semidirect
5. C2×#63910C2semidirect
6. C2×#63910C2semidirect
7. C2×#63910C2semidirect
8. C2×#63909C2semidirect
9. C2×#63904C2semidirect
10. C2×#63897C2semidirect
11. C2×#63890C2semidirect
12. C2×#63886C2semidirect
13. C2×#63881C2semidirect
14. C2×#63853C2semidirect
15. C2×#63836C2semidirect
16. #10594467C2direct (N × H)
37. #64104C22semidirect
48. C3×#894C22semidirect
49. C3×#889C22semidirect
57. #63911C22semidirect
58. #63910C22semidirect
59. #63910C22semidirect
60. #63910C22semidirect
61. #63909C22semidirect
62. #63904C22semidirect
63. #63897C22semidirect
64. #63890C22semidirect
65. #63886C22semidirect
66. #63881C22semidirect
67. #63853C22semidirect
68. #63836C22semidirect
89. C2×#894D3semidirect
93. C2×#889D3semidirect
263. #894C2×D3semidirect
267. #889C2×D3semidirect
717. C2×C32#540semidirect
879. C32C2×#540semidirect
942. C2×C3#5663semidirect
943. C2×C3#5697semidirect
996. C3C2×#5663semidirect
997. C3C2×#5697semidirect
1003. C2#10594467direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641042
C2×C3×#8942
C2×C3×#8892
C2×#639112
C2×#639102
C2×#639092
C2×#639042
C2×#638972
C2×#638902
C2×#638862
C2×#638812
C2×#638532
C2×#638362
#105944672
C2×#56973
C2×#56633