Finite Group Databasebeta

← C2×#10595255 #11901310

Subgroups — C2×#10595255 #11901310

Order 1152.

3003 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64146C211yesmaximal, characteristic, complemented
2C2×C3×#938C211yesmaximal, characteristic, complemented
3C2×C3×#935C211yesmaximal, characteristic, complemented
4C2×#63981C211yesmaximal, characteristic, complemented
5C2×#63978C211yesmaximal, characteristic, complemented
6C2×#63974C211yesmaximal, characteristic, complemented
7C2×#63959C211yesmaximal, characteristic, complemented
8C2×#63958C211yesmaximal, characteristic, complemented
9C2×#63956C211yesmaximal, characteristic, complemented
10C2×#63953C211yesmaximal, characteristic, complemented
11C2×#63952C211yesmaximal, characteristic, complemented
12#10595255C2116yesmaximal, direct product factor
13C2×#63904C211yesmaximal, characteristic, complemented
14C2×#63895C211yesmaximal, characteristic, complemented
15C2×#63850C211yesmaximal, characteristic, complemented
16C2×#63848C211yesmaximal, characteristic, complemented
17C2×#5657—31nomaximal
18C2×#5613—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C22×C32×D4C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic, complemented
25C23×C3×Dic3C2211yescharacteristic, complemented
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×#627C2211yescharacteristic, complemented
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#624C2211yescharacteristic
31C22×#624C2211yescharacteristic
32C2×#3757C2211yescharacteristic
33#64146C2218yescomplemented
34C2×#3752C2211yescharacteristic
35C2×#3752C2211yescharacteristic
36C2×C3×#217C2211yescharacteristic
37C2×C3×#217C2211yescharacteristic
38C2×C3×#217C2211yescharacteristic
39C2×C3×#217C2211yescharacteristic, complemented
40C2×C3×#217C2211yescharacteristic, complemented
41C3×#938C2218yescomplemented
42C3×#935C2218yescomplemented
43C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
44C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46#63981C2218yescomplemented
47#63978C2218yescomplemented
48#63974C2218yescomplemented
49C2×#3724C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×Dic3⋊Dic3C2211yescharacteristic, complemented
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic
55C2×#3722C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
58#63959C2218yescomplemented
59#63958C2218yescomplemented
60#63956C2218yescomplemented
61C2×Dic32C2211yescharacteristic, complemented
62C2×Dic32C2211yescharacteristic, complemented
63#63953C2218yescomplemented
64#63952C2218yescomplemented
65#63904C2218yescomplemented
66#63895C2218yescomplemented
67#63850C2218yescomplemented
68#63848C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×#121—31no—
71C2×#939—31no—
72C2×#938—31no—
73C2×#938D311yescharacteristic, complemented
74C2×#937—31no—
75C2×#937—31no—
76C2×#937—31no—
77C2×#937—61no—
78C2×#936—31no—
79C2×#935D311yescharacteristic, complemented
80C2×#930—31no—
81C2×#929—31no—
82C2×C4×#67—31no—
83C2×C4×#67—31no—
84#5657—316no—
85#5613—316no—
86C2×#898—31no—
87C2×#898—31no—
88C2×#897—31no—
89C2×#896—31no—
90C2×#894—31no—
91C2×#893—31no—
92C2×#885—31no—
93C2×#885—31no—
94C2×#885—31no—
95C2×#884—31no—
96C2×#882—31no—
97C2×#67⋊C4—31no—
98C2×D3×C22⋊C4—31no—
99C2×D3×C22⋊C4—31no—
100C2×#879—31no—
101C2×#879—31no—
102C24×C32C2311yescharacteristic
103C24×C32C2311yescharacteristic
104C23×C3⋊D3—24no—
105C23×C3⋊D3—42no—
106C23×C3⋊D3—42no—
107C23×C3⋊D3C2311yescharacteristic
108C23×C3⋊D3C2311yescharacteristic
109C23×C3⋊D3C2314yes—
110C23×C3×D3C2311yescharacteristic
111C2×C32×D4—42no—
112C2×C32×D4C2314yes—
113C22×C32×C4C2311yescharacteristic
114C2×#638—24no—
115C2×#638—42no—
116C2×#638C2314yes—
117C2×#638C2314yes—
118C22×C3⋊Dic3C2311yescharacteristic
119C22×C3⋊Dic3C2311yescharacteristic
120C2×C3×#67—42no—
121C2×C3×#67—42no—
122C2×C3×#67C2314yes—
123C2×C3×#67C2314yescomplemented
124C22×C3×Dic3—42no—
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2314yescomplemented
133C2×C3×C4×D3—42no—
134C2×C3×C4×D3C2314yescomplemented
135C2×#627—42no—
136C2×#627C2314yescomplemented
137C2×#626—24no—
138C2×#626—42no—
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#624—42no—
142C2×#624—42no—
143C2×#624C2314yes—
144C2×#624C2314yes—
145#3757C2314yes—
146#3752C2314yes—
147#3752C2314yes—
148C3×#217C2314yes—
149C3×#217C2314yes—
150C3×#217C2314yes—
151C3×#217C2314yescomplemented
152C3×#217C2314yescomplemented
153C3×C4⋊Dic3C2314yescomplemented
154C3×Dic3⋊C4C2314yescomplemented
155C3×Dic3⋊C4C2314yescomplemented
156#3724C2314yescomplemented
157Dic3⋊Dic3C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159#3722C2314yes—
160#3722C2314yes—
161#3722C2314yes—
162#3722C2314yes—
163(C2×D3)⋊Dic3C2314yescomplemented
164(C2×D3)⋊Dic3C2314yescomplemented
165Dic32C2314yescomplemented
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C24×D3—61no—
171C22×C3×D4—21no—
172C22×C3×D4—31no—
173C22×C3×D4—31no—
174C22×C3×D4C2×D311yescharacteristic
175C22×C3×D4C2×D311yescharacteristic
176C23×C3×C4—31no—
177C23×C3×C4—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—31no—
183C22×#67—31no—
184C22×#67—61no—
185C22×#67—61no—
186C22×#67C2×D311yescharacteristic
187C22×#67C2×D311yescharacteristic, complemented
188C23×Dic3C2×D311yescharacteristic, complemented
189C22×D12—31no—
190C22×D12—31no—
191C22×C4×D3—31no—
192C22×C4×D3—31no—
193C22×C4×D3—31no—
194C22×C4×D3—31no—
195C22×C4×D3C2×D311yescharacteristic, complemented
196C22×Dic6—31no—
197C22×Dic6—31no—
198C3×#123—38no—
199C3×#121—38no—
200C2×C3×C4⋊C4—31no—
201C2×C3×C4⋊C4—31no—
202C2×C3×C4⋊C4—31no—
203C2×C3×C22⋊C4—31no—
204C2×C3×C22⋊C4—31no—
205C2×C3×C22⋊C4—31no—
206C2×C3×C22⋊C4—31no—
207C2×C3×C22⋊C4—31no—
208C2×#217—31no—
209C2×#217—31no—
210C2×#217—31no—
211C2×#217—31no—
212C2×#217—61no—
213C2×#217C2×D311yescharacteristic
214C2×#217C2×D311yescharacteristic
215C2×#217C2×D311yescharacteristic
216C2×#217C2×D311yescharacteristic, complemented
217C2×#217C2×D311yescharacteristic, complemented
218#939—38no—
219#938—38no—
220#938C2×D318yescomplemented
221#937—38no—
222#937—38no—
223#937—38no—
224#937—68no—
225#936—38no—
226#935C2×D318yescomplemented
227#930—38no—
228#929—38no—
229C4×#67—38no—
230C4×#67—38no—
231C2×(C2×D3)⋊C4—31no—
232C2×(C2×D3)⋊C4—31no—
233C2×(C2×D3)⋊C4—31no—
234C2×(C2×D3)⋊C4—31no—
235C2×(C2×D3)⋊C4—31no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—31no—
240C2×(C2×D3)⋊C4—31no—
241C2×(C2×D3)⋊C4—31no—
242C2×(C2×D3)⋊C4—31no—
243C2×(C2×D3)⋊C4—31no—
244C2×(C2×D3)⋊C4—31no—
245C2×(C2×D3)⋊C4—61no—
246C2×(C2×D3)⋊C4—61no—
247C2×C4⋊Dic3—31no—
248C2×C4⋊Dic3—31no—
249C2×C4⋊Dic3C2×D311yescharacteristic, complemented
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4—31no—
253C2×Dic3⋊C4—31no—
254C2×Dic3⋊C4C2×D311yescharacteristic, complemented
255C2×Dic3⋊C4C2×D311yescharacteristic, complemented
256C2×C4×Dic3—31no—
257C2×C4×Dic3—31no—
258C2×C4×Dic3—31no—
259C2×C4×Dic3—31no—
260#898—38no—
261#898—38no—
262#897—38no—
263#896—38no—
264#894—38no—
265#893—38no—
266#885—38no—
267#885—38no—
268#885—38no—
269#884—38no—
270#882—38no—
271#67⋊C4—38no—
272D3×C22⋊C4—38no—
273D3×C22⋊C4—38no—
274#879—38no—
275#879—38no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32—22no—
279C23×C32—22no—
280C23×C32—22no—
281C23×C32—22no—
282C23×C32C2412yes—
283C23×C32C2412yes—
284C23×C32C2411yescharacteristic
285C22×C3⋊D3—22no—
286C22×C3⋊D3—22no—
287C22×C3⋊D3—22no—
288C22×C3⋊D3—22no—
289C22×C3⋊D3—22no—
290C22×C3⋊D3—28no—
291C22×C3⋊D3—44no—
292C22×C3⋊D3—44no—
293C22×C3⋊D3—416no—
294C22×C3⋊D3#4114yes—
295C22×C3⋊D3C2412yes—
296C22×C3⋊D3C2412yes—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
300C22×C3×D3C2412yes—
301C32×D4—44no—
302C2×C32×C4—22no—
303C2×C32×C4C2412yes—
304#638—28no—
305#638—44no—
306C2×C3⋊Dic3—22no—
307C2×C3⋊Dic3—22no—
308C2×C3⋊Dic3C2412yes—
309C2×C3⋊Dic3C2412yes—
310C3×#67—44no—
311C3×#67—44no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3—22no—
314C2×C3×Dic3—22no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—44no—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C3×C4×D3—44no—
328#627—44no—
329#626—28no—
330#626—44no—
331#624—44no—
332#624—44no—
333#538—916no—
334C2×#126—91no—
335C2×#126—91no—
336C2×#124—91no—
337C2×#124—91no—
338C2×#123—31no—
339C2×#123—91no—
340C2×C22⋊Q8—91no—
341C2×#121—31no—
342C2×#121—91no—
343C2×#121—91no—
344C2×#120—91no—
345C2×#120—91no—
346C2×C4×D4—91no—
347C2×C4×D4—91no—
348C22×C22⋊C4—91no—
349C24×C3—21no—
350C24×C3—21no—
351C24×C3—31no—
352C24×C3C22×D311yescharacteristic
353C24×C3C22×D311yescharacteristic
354C24×C3C22×D311yescharacteristic
355C24×C3C22×D311yescharacteristic
356C23×D3—31no—
357C23×D3—31no—
358C23×D3—31no—
359C23×D3—31no—
360C23×D3—34no—
361C23×D3—34no—
362C23×D3—61no—
363C23×D3—61no—
364C23×D3—64no—
365C23×D3—64no—
366C23×D3—64no—
367C23×D3—124no—
368C23×D3—122no—
369C23×D3—122no—
370C23×D3—122no—
371C23×D3—122no—
372C23×D3—124no—
373C23×D3—124no—
374C23×D3C22×D311yescharacteristic
375C2×C3×D4—24no—
376C2×C3×D4—34no—
377C2×C3×D4—34no—
378C2×C3×D4—42no—
379C2×C3×D4—42no—
380C2×C3×D4—44no—
381C2×C3×D4—122no—
382C2×C3×D4—122no—
383C2×C3×D4C22×D314yes—
384C2×C3×D4C22×D314yes—
385C22×C3×C4—21no—
386C22×C3×C4—31no—
387C22×C3×C4—31no—
388C22×C3×C4—31no—
389C22×C3×C4—31no—
390C22×C3×C4—31no—
391C22×C3×C4—31no—
392C22×C3×C4—31no—
393C22×C3×C4—34no—
394C22×C3×C4—34no—
395C22×C3×C4—122no—
396C22×C3×C4—122no—
397C22×C3×C4C22×D311yescharacteristic
398C22×C3×C4C22×D311yescharacteristic
399C2×#67—34no—
400C2×#67—34no—
401C2×#67—34no—
402C2×#67—34no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—42no—
406C2×#67—42no—
407C2×#67—64no—
408C2×#67—64no—
409C2×#67—64no—
410C2×#67—64no—
411C2×#67—64no—
412C2×#67—124no—
413C2×#67—122no—
414C2×#67—122no—
415C2×#67—122no—
416C2×#67—124no—
417C2×#67C22×D314yes—
418C2×#67C22×D314yescomplemented
419C22×Dic3—31no—
420C22×Dic3—31no—
421C22×Dic3—31no—
422C22×Dic3—31no—
423C22×Dic3—42no—
424C22×Dic3—61no—
425C22×Dic3—61no—
426C22×Dic3C22×D311yescharacteristic
427C22×Dic3C22×D311yescharacteristic
428C22×Dic3C22×D311yescharacteristic
429C22×Dic3C22×D311yescharacteristic
430C22×Dic3C22×D311yescharacteristic
431C22×Dic3C22×D311yescharacteristic
432C22×Dic3C22×D311yescharacteristic
433C22×Dic3C22×D314yescomplemented
434C2×D12—34no—
435C2×D12—34no—
436C2×D12—64no—
437C2×D12—122no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—34no—
441C2×C4×D3—34no—
442C2×C4×D3—42no—
443C2×C4×D3—122no—
444C2×C4×D3—122no—
445C2×C4×D3—122no—
446C2×C4×D3—122no—
447C2×C4×D3C22×D314yescomplemented
448C2×Dic6—34no—
449C2×Dic6—34no—
450C2×Dic6—122no—
451C2×Dic6—122no—
452C3×C4⋊C4—34no—
453C3×C4⋊C4—34no—
454C3×C4⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4—34no—
457C3×C22⋊C4—34no—
458C3×C22⋊C4—34no—
459C3×C22⋊C4—34no—
460#217—34no—
461#217—34no—
462#217—34no—
463#217—34no—
464#217—64no—
465#217C22×D314yes—
466#217C22×D314yes—
467#217C22×D314yes—
468#217C22×D314yescomplemented
469#217C22×D314yescomplemented
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—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—64no—
485(C2×D3)⋊C4—64no—
486C4⋊Dic3—34no—
487C4⋊Dic3—34no—
488C4⋊Dic3C22×D314yescomplemented
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4C22×D314yescomplemented
494Dic3⋊C4C22×D314yescomplemented
495C4×Dic3—34no—
496C4×Dic3—34no—
497C4×Dic3—34no—
498C4×Dic3—34no—
499C22×C32—22no—
500C22×C32—22no—
501C22×C32—22no—
502C22×C32—22no—
503C22×C32—22no—
504C22×C32—22no—
505C22×C32—44no—
506C22×C32—44no—
507C22×C32C2×#4112yes—
508C22×C32H(5,𝔽2)12yes—
509C22×C32H(5,𝔽2)12yes—
510C22×C32C2511yescharacteristic
511C2×C3⋊D3—22no—
512C2×C3⋊D3—28no—
513C2×C3⋊D3—22no—
514C2×C3⋊D3—22no—
515C2×C3⋊D3—22no—
516C2×C3⋊D3—22no—
517C2×C3⋊D3—416no—
518C2×C3⋊D3—44no—
519C2×C3⋊D3C2×#4114yes—
520C2×C3×D3—22no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—44no—
524C32×C4—22no—
525C3⋊Dic3—22no—
526C3⋊Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—22no—
531C3×Dic3—22no—
532C3×Dic3—22no—
533C3×Dic3—22no—
534C25—91no—
535C22×Q8—91no—
536C22×D4—31no—
537C22×D4—31no—
538C22×D4—91no—
539C22×D4—91no—
540C22×D4—91no—
541C22×D4—91no—
542C22×D4D3211yescharacteristic
543C23×C4—31no—
544C23×C4—31no—
545C23×C4—91no—
546C23×C4—91no—
547#126—98no—
548#126—98no—
549#124—98no—
550#124—98no—
551#123—38no—
552#123—98no—
553C22⋊Q8—98no—
554#121—38no—
555#121—98no—
556#121—98no—
557#120—98no—
558#120—98no—
559C4×D4—98no—
560C4×D4—98no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—31no—
563C2×C4⋊C4—31no—
564C2×C4⋊C4—91no—
565C2×C4⋊C4—91no—
566C2×C4⋊C4—91no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—31no—
572C2×C22⋊C4—98no—
573C2×C22⋊C4—91no—
574C2×C22⋊C4—91no—
575C2×C22⋊C4—91no—
576C2×C22⋊C4—91no—
577C2×C22⋊C4—91no—
578C2×C22⋊C4—91no—
579C2×C22⋊C4—91no—
580C2×C22⋊C4—91no—
581C2×C22⋊C4—91no—
582C2×C42—91no—
583C2×C42—91no—
584C23×C3—24no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—22no—
590C23×C3—22no—
591C23×C3—22no—
592C23×C3—22no—
593C23×C3—22no—
594C23×C3—22no—
595C23×C3—22no—
596C23×C3—22no—
597C23×C3—22no—
598C23×C3—22no—
599C23×C3—21no—
600C23×C3—32no—
601C23×C3—42no—
602C23×C3—42no—
603C23×C3—42no—
604C23×C3—42no—
605C23×C3—42no—
606C23×C3—62no—
607C23×C3—62no—
608C23×C3—62no—
609C23×C3C23×D312yes—
610C23×C3C23×D312yes—
611C23×C3C23×D312yes—
612C23×C3C23×D312yes—
613C23×C3C23×D311yescharacteristic
614C23×C3C23×D311yescharacteristic
615C22×D3—22no—
616C22×D3—22no—
617C22×D3—22no—
618C22×D3—34no—
619C22×D3—34no—
620C22×D3—32no—
621C22×D3—32no—
622C22×D3—32no—
623C22×D3—32no—
624C22×D3—64no—
625C22×D3—62no—
626C22×D3—62no—
627C22×D3—68no—
628C22×D3—68no—
629C22×D3—62no—
630C22×D3—62no—
631C22×D3—62no—
632C22×D3—62no—
633C22×D3—64no—
634C22×D3—62no—
635C22×D3—62no—
636C22×D3—62no—
637C22×D3—62no—
638C22×D3—62no—
639C22×D3—62no—
640C22×D3—128no—
641C22×D3—122no—
642C22×D3—122no—
643C22×D3—122no—
644C22×D3—122no—
645C22×D3—124no—
646C22×D3—124no—
647C22×D3—124no—
648C22×D3—124no—
649C22×D3—128no—
650C22×D3—1216no—
651C22×D3—1216no—
652C22×D3—128no—
653C22×D3—1232no—
654C22×D3C23×D312yes—
655C3×D4—44no—
656C3×D4—44no—
657C3×D4—48no—
658C3×D4—124no—
659C3×D4—124no—
660C2×C3×C4—22no—
661C2×C3×C4—22no—
662C2×C3×C4—22no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—32no—
666C2×C3×C4—32no—
667C2×C3×C4—32no—
668C2×C3×C4—32no—
669C2×C3×C4—32no—
670C2×C3×C4—42no—
671C2×C3×C4—62no—
672C2×C3×C4—62no—
673C2×C3×C4—62no—
674C2×C3×C4—62no—
675C2×C3×C4—62no—
676C2×C3×C4—62no—
677C2×C3×C4—62no—
678C2×C3×C4—124no—
679C2×C3×C4—124no—
680C2×C3×C4C23×D312yes—
681C2×C3×C4C23×D312yes—
682#67—44no—
683#67—44no—
684#67—68no—
685#67—68no—
686#67—68no—
687#67—128no—
688#67—124no—
689#67—124no—
690#67—124no—
691#67—128no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—22no—
699C2×Dic3—32no—
700C2×Dic3—32no—
701C2×Dic3—32no—
702C2×Dic3—32no—
703C2×Dic3—44no—
704C2×Dic3—62no—
705C2×Dic3—62no—
706C2×Dic3—62no—
707C2×Dic3—62no—
708C2×Dic3—62no—
709C2×Dic3—62no—
710C2×Dic3—122no—
711C2×Dic3—122no—
712C2×Dic3C23×D312yes—
713C2×Dic3C23×D312yes—
714C2×Dic3C23×D312yes—
715C2×Dic3C23×D312yes—
716C2×Dic3C23×D312yes—
717C2×Dic3C23×D312yes—
718C2×Dic3C23×D312yes—
719D12—68no—
720D12—124no—
721C4×D3—44no—
722C4×D3—124no—
723C4×D3—124no—
724C4×D3—124no—
725C4×D3—124no—
726Dic6—124no—
727Dic6—124no—
728C2×C32—42no—
729C2×C32—42no—
730C2×C32#53814yescomplemented
731C2×C32C22×#4111yescharacteristic
732C2×C32C2×H(5,𝔽2)11yescharacteristic
733C2×C32C2×H(5,𝔽2)11yescharacteristic
734C3⋊D3—24no—
735C3⋊D3—42no—
736C3×D3—42no—
737C24—31no—
738C24—91no—
739C24—91no—
740C24—94no—
741C24—184no—
742C24—362no—
743C24—362no—
744C24C2×D3211yescharacteristic
745C24C2×D3211yescharacteristic
746C2×Q8—94no—
747C2×Q8—362no—
748C2×D4—34no—
749C2×D4—34no—
750C2×D4—42no—
751C2×D4—94no—
752C2×D4—94no—
753C2×D4—94no—
754C2×D4—94no—
755C2×D4—122no—
756C2×D4—122no—
757C2×D4—184no—
758C2×D4—184no—
759C2×D4—362no—
760C2×D4—362no—
761C2×D4C2×D3214yes—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—31no—
766C22×C4—31no—
767C22×C4—31no—
768C22×C4—31no—
769C22×C4—34no—
770C22×C4—34no—
771C22×C4—94no—
772C22×C4—94no—
773C22×C4—91no—
774C22×C4—91no—
775C22×C4—122no—
776C22×C4—122no—
777C22×C4—362no—
778C22×C4—362no—
779C22×C4C2×D3211yescharacteristic
780C4⋊C4—34no—
781C4⋊C4—34no—
782C4⋊C4—34no—
783C4⋊C4—94no—
784C4⋊C4—94no—
785C4⋊C4—94no—
786C22⋊C4—34no—
787C22⋊C4—34no—
788C22⋊C4—34no—
789C22⋊C4—34no—
790C22⋊C4—34no—
791C22⋊C4—94no—
792C22⋊C4—94no—
793C22⋊C4—94no—
794C22⋊C4—94no—
795C22⋊C4—94no—
796C22⋊C4—94no—
797C22⋊C4—94no—
798C22⋊C4—94no—
799C22⋊C4—94no—
800C42—94no—
801C42—94no—
802C22×C3—24no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—22no—
806C22×C3—22no—
807C22×C3—22no—
808C22×C3—22no—
809C22×C3—22no—
810C22×C3—22no—
811C22×C3—22no—
812C22×C3—22no—
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—21no—
819C22×C3—42no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—48no—
825C22×C3—44no—
826C22×C3—44no—
827C22×C3—44no—
828C22×C3—44no—
829C22×C3—62no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—84no—
833C22×C3—124no—
834C22×C3#100412yes—
835C22×C3#100412yes—
836C22×C3#100412yes—
837C22×C3D3×#4112yes—
838C22×C3D3×#4112yes—
839C22×C3#100912yes—
840C22×C3C24×D311yescharacteristic
841C22×C3C24×D311yescharacteristic
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—22no—
845C2×D3—34no—
846C2×D3—34no—
847C2×D3—44no—
848C2×D3—64no—
849C2×D3—68no—
850C2×D3—62no—
851C2×D3—62no—
852C2×D3—62no—
853C2×D3—62no—
854C2×D3—68no—
855C2×D3—64no—
856C2×D3—62no—
857C2×D3—62no—
858C2×D3—62no—
859C2×D3—62no—
860C2×D3—62no—
861C2×D3—62no—
862C2×D3—122no—
863C2×D3—122no—
864C2×D3—128no—
865C2×D3—122no—
866C2×D3—122no—
867C2×D3—1216no—
868C2×D3—1216no—
869C2×D3—128no—
870C2×D3—1232no—
871C2×D3—124no—
872C2×D3—124no—
873C3×C4—22no—
874C3×C4—22no—
875C3×C4—42no—
876C3×C4—62no—
877C3×C4—62no—
878C3×C4—62no—
879C3×C4—62no—
880C3×C4—62no—
881C3×C4—62no—
882C3×C4—62no—
883Dic3—22no—
884Dic3—22no—
885Dic3—22no—
886Dic3—22no—
887Dic3—22no—
888Dic3—22no—
889Dic3—22no—
890Dic3—62no—
891Dic3—62no—
892Dic3—62no—
893Dic3—62no—
894Dic3—122no—
895Dic3—122no—
896C32C2×#53811yescharacteristic, complemented, Sylow
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—32no—
904C23—62no—
905C23—62no—
906C23—62no—
907C23—94no—
908C23—92no—
909C23—92no—
910C23—188no—
911C23—182no—
912C23—182no—
913C23—182no—
914C23—182no—
915C23—182no—
916C23—364no—
917C23—364no—
918C23—3616no—
919C23C22×D3212yes—
920C23C22×D3212yes—
921C23C22×D3211yescharacteristic
922Q8—364no—
923D4—44no—
924D4—124no—
925D4—124no—
926D4—188no—
927D4—188no—
928D4—364no—
929D4—364no—
930C2×C4—22no—
931C2×C4—32no—
932C2×C4—32no—
933C2×C4—32no—
934C2×C4—32no—
935C2×C4—32no—
936C2×C4—32no—
937C2×C4—32no—
938C2×C4—62no—
939C2×C4—62no—
940C2×C4—62no—
941C2×C4—62no—
942C2×C4—62no—
943C2×C4—62no—
944C2×C4—62no—
945C2×C4—92no—
946C2×C4—92no—
947C2×C4—124no—
948C2×C4—124no—
949C2×C4—182no—
950C2×C4—182no—
951C2×C4—364no—
952C2×C4—364no—
953C2×C4C22×D3212yes—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—21no—
957C2×C3—24no—
958C2×C3—44no—
959C2×C3—42no—
960C2×C3—42no—
961C2×C3—42no—
962C2×C3—42no—
963C2×C3—82no—
964C2×C3—122no—
965C2×C3#561314yescomplemented
966C2×C3#565714yescomplemented
967C2×C3C2×#100411yescharacteristic
968C2×C3C2×#100411yescharacteristic
969C2×C3C2×#100411yescharacteristic
970C2×C3C2×D3×#4111yescharacteristic
971C2×C3C2×D3×#4111yescharacteristic
972C2×C3C2×#100911yescharacteristic
973D3—42no—
974D3—64no—
975D3—64no—
976D3—124no—
977D3—124no—
978D3—122no—
979D3—122no—
980C22—22no—
981C22—22no—
982C22—22no—
983C22—22no—
984C22—22no—
985C22—22no—
986C22—44no—
987C22—44no—
988C22—62no—
989C22—62no—
990C22—62no—
991C22—94no—
992C22—124no—
993C22—182no—
994C22—182no—
995C22—188no—
996C22—182no—
997C22—182no—
998C22—182no—
999C22—3616no—
1000C22—364no—
1001C22#6431212yes—
1002C22#6431412yes—
1003C22#6433012yes—
1004C22C23×D3211yescharacteristic
1005C4—22no—
1006C4—62no—
1007C4—62no—
1008C4—62no—
1009C4—62no—
1010C4—62no—
1011C4—62no—
1012C4—62no—
1013C4—182no—
1014C4—182no—
1015C3—21no—
1016C3C2×#561311yescharacteristic, complemented
1017C3C2×#565711yescharacteristic, complemented
1018C2—42no—
1019C2—42no—
1020C2—122no—
1021C2—184no—
1022C2—362no—
1023C2#1059525514yesdirect product factor
1024C2C2×#6431211yescharacteristic
1025C2C2×#6431411yescharacteristic
1026C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64146C2semidirect
2. C2×C3×#938C2semidirect
3. C2×C3×#935C2semidirect
4. C2×#63981C2semidirect
5. C2×#63978C2semidirect
6. C2×#63974C2semidirect
7. C2×#63959C2semidirect
8. C2×#63958C2semidirect
9. C2×#63956C2semidirect
10. C2×#63953C2semidirect
11. C2×#63952C2semidirect
12. #10595255C2direct (N × H)
13. C2×#63904C2semidirect
14. C2×#63895C2semidirect
15. C2×#63850C2semidirect
16. C2×#63848C2semidirect
24. C22×C3×#67C22semidirect
25. C23×C3×Dic3C22semidirect
26. C22×C3×C4×D3C22semidirect
27. C22×#627C22semidirect
33. #64146C22semidirect
39. C2×C3×#217C22semidirect
40. C2×C3×#217C22semidirect
41. C3×#938C22semidirect
42. C3×#935C22semidirect
43. C2×C3×C4⋊Dic3C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. #63981C22semidirect
47. #63978C22semidirect
48. #63974C22semidirect
49. C2×#3724C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
51. C2×Dic3⋊Dic3C22semidirect
56. C2×(C2×D3)⋊Dic3C22semidirect
57. C2×(C2×D3)⋊Dic3C22semidirect
58. #63959C22semidirect
59. #63958C22semidirect
60. #63956C22semidirect
61. C2×Dic32C22semidirect
62. C2×Dic32C22semidirect
63. #63953C22semidirect
64. #63952C22semidirect
65. #63904C22semidirect
66. #63895C22semidirect
67. #63850C22semidirect
68. #63848C22semidirect
73. C2×#938D3semidirect
79. C2×#935D3semidirect
123. C2×C3×#67C23semidirect
132. C22×C3×Dic3C23semidirect
134. C2×C3×C4×D3C23semidirect
136. C2×#627C23semidirect
151. C3×#217C23semidirect
152. C3×#217C23semidirect
153. C3×C4⋊Dic3C23semidirect
154. C3×Dic3⋊C4C23semidirect
155. C3×Dic3⋊C4C23semidirect
156. #3724C23semidirect
157. Dic3⋊Dic3C23semidirect
158. Dic3⋊Dic3C23semidirect
163. (C2×D3)⋊Dic3C23semidirect
164. (C2×D3)⋊Dic3C23semidirect
165. Dic32C23semidirect
166. Dic32C23semidirect
187. C22×#67C2×D3semidirect
188. C23×Dic3C2×D3semidirect
195. C22×C4×D3C2×D3semidirect
216. C2×#217C2×D3semidirect
217. C2×#217C2×D3semidirect
220. #938C2×D3semidirect
226. #935C2×D3semidirect
249. C2×C4⋊Dic3C2×D3semidirect
254. C2×Dic3⋊C4C2×D3semidirect
255. C2×Dic3⋊C4C2×D3semidirect
418. C2×#67C22×D3semidirect
433. C22×Dic3C22×D3semidirect
447. C2×C4×D3C22×D3semidirect
468. #217C22×D3semidirect
469. #217C22×D3semidirect
488. C4⋊Dic3C22×D3semidirect
493. Dic3⋊C4C22×D3semidirect
494. Dic3⋊C4C22×D3semidirect
730. C2×C32#538semidirect
896. C32C2×#538semidirect
965. C2×C3#5613semidirect
966. C2×C3#5657semidirect
1016. C3C2×#5613semidirect
1017. C3C2×#5657semidirect
1023. C2#10595255direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641462
C2×C3×#9382
C2×C3×#9352
C2×#639812
C2×#639782
C2×#639742
C2×#639592
C2×#639582
C2×#639562
C2×#639532
C2×#639522
#105952552
C2×#639042
C2×#638952
C2×#638502
C2×#638482
C2×#56573
C2×#56133