Finite Group Databasebeta

← C2×#10595085 #11901300

Subgroups — C2×#10595085 #11901300

Order 1152.

2885 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64139C211yesmaximal, characteristic, complemented
2C2×C3×#929C211yesmaximal, characteristic, complemented
3C2×C3×C4×#67C211yesmaximal, characteristic, complemented
4C2×#63983C211yesmaximal, characteristic, complemented
5C2×#63971C211yesmaximal, characteristic, complemented
6C2×#63958C211yesmaximal, characteristic, complemented
7C2×#63953C211yesmaximal, characteristic, complemented
8#10595085C2116yesmaximal, direct product factor
9C2×#63923C211yesmaximal, characteristic, complemented
10C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#63904C211yesmaximal, characteristic, complemented
12C2×#63897C211yesmaximal, characteristic, complemented
13C2×#63893C211yesmaximal, characteristic, complemented
14C2×#63868C211yesmaximal, characteristic, complemented
15C2×#63861C211yesmaximal, characteristic, complemented
16C2×#63852C211yesmaximal, characteristic, complemented
17C2×#5657—31nomaximal
18C2×#5560—31nomaximal
19C23×D32C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic, complemented
21C22×#638C2211yescharacteristic
22C22×#638C2211yescharacteristic, complemented
23C22×C4⋊(C3⋊D3)C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×#627C2211yescharacteristic, complemented
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#624C2211yescharacteristic, complemented
31C22×D3×Dic3C2211yescharacteristic
32#64139C2218yescomplemented
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic, complemented
35C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
36C2×C3×#217C2211yescharacteristic, complemented
37C2×C3×#217C2211yescharacteristic, complemented
38C3×#929C2218yescomplemented
39C3×C4×#67C2218yescomplemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic
42C2×C3×(C2×D3)⋊C4C2211yescharacteristic
43C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
44C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
45C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
46C2×C3×C4×Dic3C2211yescharacteristic, complemented
47#63983C2218yescomplemented
48#63971C2218yescomplemented
49C2×#3724C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×#3722C2211yescharacteristic
52C2×#3722C2211yescharacteristic
53C2×#3722C2211yescharacteristic
54C2×#3722C2211yescharacteristic, complemented
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58#63958C2218yescomplemented
59C2×Dic32C2211yescharacteristic, complemented
60#63953C2218yescomplemented
61#63923C2218yescomplemented
62D3×(C2×D3)⋊C4C2218yescomplemented
63#63904C2218yescomplemented
64#63897C2218yescomplemented
65#63893C2218yescomplemented
66#63868C2218yescomplemented
67#63861C2218yescomplemented
68#63852C2218yescomplemented
69C2×C3×#123—31no—
70C2×C3×C4×D4—31no—
71C2×#939—31no—
72C2×#938—31no—
73C2×#937—31no—
74C2×#937—31no—
75C2×#930—31no—
76C2×#930—31no—
77C2×#930—61no—
78C2×#929D311yescharacteristic, complemented
79C2×C4×#67—31no—
80C2×C4×#67D311yescharacteristic, complemented
81C22×(C2×D3)⋊C4—31no—
82#5657—316no—
83#5560—316no—
84C2×#898—31no—
85C2×#898—31no—
86C2×#897—31no—
87C2×#894—31no—
88C2×#894—31no—
89C2×#893—31no—
90C2×#885—31no—
91C2×#885—31no—
92C2×#885—31no—
93C2×#884—31no—
94C2×#884—31no—
95C2×#882—31no—
96C2×#882—31no—
97C2×D3×C22⋊C4—31no—
98C2×#879—31no—
99C2×#878—31no—
100C2×#876—31no—
101C2×#875—31no—
102C24×C32C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C22×D32—24no—
108C22×D32—42no—
109C22×D32—42no—
110C22×D32C2314yes—
111C22×C32×C4—42no—
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C22×C32×C4C2314yescomplemented
115C2×#638—42no—
116C2×#638—42no—
117C2×#638C2314yes—
118C2×#638C2314yescomplemented
119C22×C3⋊Dic3C2311yescharacteristic
120C22×C3⋊Dic3C2311yescharacteristic
121C2×C4⋊(C3⋊D3)—42no—
122C2×C4⋊(C3⋊D3)C2314yes—
123C2×C3×#67—24no—
124C2×C3×#67—42no—
125C2×C3×#67C2314yes—
126C2×C3×#67C2314yes—
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C2×C3×C4×D3—42no—
134C2×C3×C4×D3C2314yes—
135C2×#627—42no—
136C2×#627C2314yescomplemented
137C2×#626—24no—
138C2×#626—42no—
139C2×#626C2314yes—
140C2×#626C2314yes—
141C2×#624—42no—
142C2×#624C2314yescomplemented
143C2×D3×Dic3—42no—
144C2×D3×Dic3C2314yes—
145#3752C2314yes—
146#3752C2314yescomplemented
147C4⋊(C3⋊Dic3)C2314yescomplemented
148C3×#217C2314yescomplemented
149C3×#217C2314yescomplemented
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×Dic3⋊C4C2314yescomplemented
154C3×Dic3⋊C4C2314yescomplemented
155C3×Dic3⋊C4C2314yescomplemented
156C3×C4×Dic3C2314yescomplemented
157#3724C2314yescomplemented
158Dic3⋊Dic3C2314yescomplemented
159#3722C2314yes—
160#3722C2314yes—
161#3722C2314yes—
162#3722C2314yescomplemented
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166Dic32C2314yescomplemented
167C2×#538—91noSylow
168C24×D3—31no—
169C24×D3—31no—
170C22×C3×D4—31no—
171C22×C3×D4—31no—
172C23×C3×C4—21no—
173C23×C3×C4—31no—
174C23×C3×C4C2×D311yescharacteristic, complemented
175C23×C3×C4C2×D311yescharacteristic, complemented
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—31no—
180C22×#67—31no—
181C22×#67—31no—
182C22×#67—61no—
183C22×#67—61no—
184C22×#67C2×D311yescharacteristic
185C22×#67C2×D311yescharacteristic
186C23×Dic3—31no—
187C22×D12—31no—
188C22×D12—31no—
189C22×D12—31no—
190C22×D12—31no—
191C22×D12—61no—
192C22×C4×D3—31no—
193C22×C4×D3—31no—
194C22×C4×D3—31no—
195C22×C4×D3C2×D311yescharacteristic
196C22×Dic6—31no—
197C22×Dic6—31no—
198C3×#123—38no—
199C3×C4×D4—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×C3×C42—31no—
209C2×#217—31no—
210C2×#217—31no—
211C2×#217—31no—
212C2×#217C2×D311yescharacteristic, complemented
213C2×#217C2×D311yescharacteristic, complemented
214#939—38no—
215#938—38no—
216#937—38no—
217#937—38no—
218#930—38no—
219#930—38no—
220#930—68no—
221#929C2×D318yescomplemented
222C4×#67—38no—
223C4×#67C2×D318yescomplemented
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—31no—
236C2×(C2×D3)⋊C4—31no—
237C2×(C2×D3)⋊C4—31no—
238C2×(C2×D3)⋊C4—31no—
239C2×(C2×D3)⋊C4—38no—
240C2×(C2×D3)⋊C4—61no—
241C2×(C2×D3)⋊C4—61no—
242C2×(C2×D3)⋊C4C2×D311yescharacteristic
243C2×(C2×D3)⋊C4C2×D311yescharacteristic
244C2×(C2×D3)⋊C4C2×D311yescharacteristic
245C2×C4⋊Dic3—31no—
246C2×C4⋊Dic3—31no—
247C2×C4⋊Dic3—31no—
248C2×C4⋊Dic3—61no—
249C2×Dic3⋊C4—31no—
250C2×Dic3⋊C4—31no—
251C2×Dic3⋊C4—31no—
252C2×Dic3⋊C4C2×D311yescharacteristic, complemented
253C2×Dic3⋊C4C2×D311yescharacteristic, complemented
254C2×Dic3⋊C4C2×D311yescharacteristic, complemented
255C2×C4×Dic3—31no—
256C2×C4×Dic3—31no—
257C2×C4×Dic3C2×D311yescharacteristic, complemented
258#898—38no—
259#898—38no—
260#897—38no—
261#894—38no—
262#894—38no—
263#893—38no—
264#885—38no—
265#885—38no—
266#885—38no—
267#884—38no—
268#884—38no—
269#882—38no—
270#882—38no—
271D3×C22⋊C4—38no—
272#879—38no—
273#878—38no—
274#876—38no—
275#875—38no—
276C23×C32—22no—
277C23×C32—22no—
278C23×C32—22no—
279C23×C32C2412yes—
280C23×C32C2411yescharacteristic
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×D3—22no—
290C22×C3×D3—22no—
291C22×C3×D3—22no—
292C22×C3×D3—22no—
293C22×C3×D3—22no—
294C22×C3×D3#4114yes—
295C22×C3×D3C2412yes—
296C22×C3×D3C2412yes—
297C2×D32—28no—
298C2×D32—44no—
299C2×D32—44no—
300C2×D32—416no—
301C2×C32×C4—22no—
302C2×C32×C4—22no—
303C2×C32×C4—44no—
304C2×C32×C4C2412yes—
305C2×C32×C4C2412yes—
306#638—44no—
307#638—44no—
308C2×C3⋊Dic3—22no—
309C2×C3⋊Dic3—22no—
310C2×C3⋊Dic3C2412yes—
311C2×C3⋊Dic3C2412yes—
312C4⋊(C3⋊D3)—44no—
313C3×#67—28no—
314C3×#67—44no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—22no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—22no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—22no—
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—
332D3×Dic3—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—91no—
342C2×#121—91no—
343C2×#121—91no—
344C2×#120—91no—
345C2×#120—91no—
346C2×C4×D4—31no—
347C2×C4×D4—91no—
348C22×C22⋊C4—91no—
349C24×C3—21no—
350C24×C3—31no—
351C24×C3—31no—
352C24×C3C22×D311yescharacteristic
353C24×C3C22×D311yescharacteristic
354C23×D3—31no—
355C23×D3—31no—
356C23×D3—31no—
357C23×D3—31no—
358C23×D3—34no—
359C23×D3—34no—
360C23×D3—61no—
361C23×D3—61no—
362C23×D3—64no—
363C23×D3—64no—
364C23×D3—122no—
365C23×D3—122no—
366C23×D3—122no—
367C23×D3—122no—
368C23×D3C22×D311yescharacteristic
369C23×D3C22×D311yescharacteristic
370C2×C3×D4—34no—
371C2×C3×D4—34no—
372C2×C3×D4—64no—
373C2×C3×D4—122no—
374C22×C3×C4—21no—
375C22×C3×C4—21no—
376C22×C3×C4—24no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—34no—
384C22×C3×C4—42no—
385C22×C3×C4—42no—
386C22×C3×C4—44no—
387C22×C3×C4—122no—
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D314yescomplemented
393C22×C3×C4C22×D314yescomplemented
394C2×#67—24no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—34no—
398C2×#67—34no—
399C2×#67—34no—
400C2×#67—34no—
401C2×#67—42no—
402C2×#67—64no—
403C2×#67—64no—
404C2×#67—64no—
405C2×#67—122no—
406C2×#67—122no—
407C2×#67—122no—
408C2×#67—122no—
409C2×#67—122no—
410C2×#67—124no—
411C2×#67—124no—
412C2×#67C22×D314yes—
413C2×#67C22×D314yes—
414C22×Dic3—31no—
415C22×Dic3—31no—
416C22×Dic3—31no—
417C22×Dic3—31no—
418C22×Dic3—34no—
419C22×Dic3—61no—
420C22×Dic3—61no—
421C22×Dic3—122no—
422C22×Dic3C22×D311yescharacteristic
423C22×Dic3C22×D311yescharacteristic
424C22×Dic3C22×D311yescharacteristic
425C22×Dic3C22×D311yescharacteristic
426C22×Dic3C22×D311yescharacteristic
427C22×Dic3C22×D311yescharacteristic
428C2×D12—34no—
429C2×D12—34no—
430C2×D12—34no—
431C2×D12—34no—
432C2×D12—64no—
433C2×D12—64no—
434C2×D12—122no—
435C2×D12—122no—
436C2×D12—124no—
437C2×D12—122no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—34no—
441C2×C4×D3—42no—
442C2×C4×D3—122no—
443C2×C4×D3—122no—
444C2×C4×D3—122no—
445C2×C4×D3C22×D314yes—
446C2×Dic6—34no—
447C2×Dic6—34no—
448C2×Dic6—122no—
449C2×Dic6—122no—
450C3×C4⋊C4—34no—
451C3×C4⋊C4—34no—
452C3×C4⋊C4—34no—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—34no—
455C3×C22⋊C4—34no—
456C3×C22⋊C4—34no—
457C3×C22⋊C4—34no—
458C3×C42—34no—
459#217—34no—
460#217—34no—
461#217—34no—
462#217C22×D314yescomplemented
463#217C22×D314yescomplemented
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4—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—64no—
480(C2×D3)⋊C4—64no—
481(C2×D3)⋊C4C22×D314yes—
482(C2×D3)⋊C4C22×D314yes—
483(C2×D3)⋊C4C22×D314yes—
484C4⋊Dic3—34no—
485C4⋊Dic3—34no—
486C4⋊Dic3—34no—
487C4⋊Dic3—64no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4C22×D314yescomplemented
492Dic3⋊C4C22×D314yescomplemented
493Dic3⋊C4C22×D314yescomplemented
494C4×Dic3—34no—
495C4×Dic3—34no—
496C4×Dic3C22×D314yescomplemented
497C22×C32—22no—
498C22×C32—22no—
499C22×C32—22no—
500C22×C32—44no—
501C22×C32C2×#4112yes—
502C22×C32H(5,𝔽2)12yes—
503C22×C32H(5,𝔽2)12yes—
504C22×C32C2511yescharacteristic
505C2×C3⋊D3—22no—
506C2×C3⋊D3—22no—
507C2×C3⋊D3—22no—
508C2×C3⋊D3—22no—
509C2×C3⋊D3—22no—
510C2×C3⋊D3—22no—
511C2×C3⋊D3—44no—
512C2×C3⋊D3—44no—
513C2×C3×D3—28no—
514C2×C3×D3—22no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—22no—
519C2×C3×D3—44no—
520C2×C3×D3C2×#4114yes—
521D32—416no—
522C32×C4—22no—
523C32×C4—22no—
524C3⋊Dic3—22no—
525C3⋊Dic3—22no—
526C3×Dic3—22no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—22no—
531C3×Dic3—22no—
532C25—91no—
533C22×Q8—91no—
534C22×D4—31no—
535C22×D4—31no—
536C22×D4—91no—
537C22×D4—91no—
538C22×D4—91no—
539C22×D4—91no—
540C22×D4—91no—
541C23×C4—31no—
542C23×C4—91no—
543C23×C4—91no—
544C23×C4D3211yescharacteristic, complemented
545#126—98no—
546#126—98no—
547#124—98no—
548#124—98no—
549#123—38no—
550#123—98no—
551C22⋊Q8—98no—
552#121—98no—
553#121—98no—
554#121—98no—
555#120—98no—
556#120—98no—
557C4×D4—38no—
558C4×D4—98no—
559C2×C4⋊C4—31no—
560C2×C4⋊C4—31no—
561C2×C4⋊C4—31no—
562C2×C4⋊C4—91no—
563C2×C4⋊C4—91no—
564C2×C4⋊C4—91no—
565C2×C22⋊C4—31no—
566C2×C22⋊C4—31no—
567C2×C22⋊C4—31no—
568C2×C22⋊C4—31no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—98no—
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×C22⋊C4—91no—
579C2×C22⋊C4—91no—
580C2×C42—31no—
581C2×C42—91no—
582C23×C3—24no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—22no—
586C23×C3—22no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—22no—
590C23×C3—21no—
591C23×C3—34no—
592C23×C3—32no—
593C23×C3—32no—
594C23×C3—42no—
595C23×C3—42no—
596C23×C3—62no—
597C23×C3—62no—
598C23×C3—62no—
599C23×C3—62no—
600C23×C3—62no—
601C23×C3C23×D312yes—
602C23×C3C23×D312yes—
603C23×C3C23×D311yescharacteristic
604C23×C3C23×D311yescharacteristic
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—22no—
609C22×D3—22no—
610C22×D3—32no—
611C22×D3—32no—
612C22×D3—32no—
613C22×D3—32no—
614C22×D3—62no—
615C22×D3—62no—
616C22×D3—68no—
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—62no—
626C22×D3—62no—
627C22×D3—62no—
628C22×D3—62no—
629C22×D3—68no—
630C22×D3—122no—
631C22×D3—122no—
632C22×D3—122no—
633C22×D3—122no—
634C22×D3—122no—
635C22×D3—122no—
636C22×D3—124no—
637C22×D3—124no—
638C22×D3—124no—
639C22×D3—124no—
640C22×D3—1216no—
641C22×D3—1216no—
642C22×D3#23514yes—
643C22×D3C23×D312yes—
644C22×D3C23×D312yes—
645C3×D4—68no—
646C3×D4—124no—
647C2×C3×C4—24no—
648C2×C3×C4—22no—
649C2×C3×C4—22no—
650C2×C3×C4—22no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—32no—
655C2×C3×C4—32no—
656C2×C3×C4—32no—
657C2×C3×C4—32no—
658C2×C3×C4—32no—
659C2×C3×C4—32no—
660C2×C3×C4—42no—
661C2×C3×C4—44no—
662C2×C3×C4—44no—
663C2×C3×C4—48no—
664C2×C3×C4—62no—
665C2×C3×C4—62no—
666C2×C3×C4—62no—
667C2×C3×C4—62no—
668C2×C3×C4—62no—
669C2×C3×C4—62no—
670C2×C3×C4—124no—
671C2×C3×C4C23×D312yes—
672C2×C3×C4C23×D312yes—
673C2×C3×C4C23×D312yes—
674C2×C3×C4C23×D312yes—
675#67—28no—
676#67—44no—
677#67—68no—
678#67—124no—
679#67—124no—
680#67—124no—
681#67—124no—
682#67—124no—
683#67—128no—
684#67—128no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—22no—
690C2×Dic3—22no—
691C2×Dic3—32no—
692C2×Dic3—32no—
693C2×Dic3—32no—
694C2×Dic3—32no—
695C2×Dic3—62no—
696C2×Dic3—62no—
697C2×Dic3—62no—
698C2×Dic3—62no—
699C2×Dic3—62no—
700C2×Dic3—62no—
701C2×Dic3—122no—
702C2×Dic3—122no—
703C2×Dic3—124no—
704C2×Dic3C23×D312yes—
705C2×Dic3C23×D312yes—
706C2×Dic3C23×D312yes—
707C2×Dic3C23×D312yes—
708C2×Dic3C23×D312yes—
709C2×Dic3C23×D312yes—
710D12—68no—
711D12—124no—
712D12—124no—
713D12—128no—
714D12—124no—
715C4×D3—44no—
716C4×D3—124no—
717C4×D3—124no—
718C4×D3—124no—
719Dic6—124no—
720Dic6—124no—
721C2×C32—42no—
722C2×C32#53814yescomplemented
723C2×C32C22×#4111yescharacteristic
724C2×C32C2×H(5,𝔽2)11yescharacteristic
725C2×C32C2×H(5,𝔽2)11yescharacteristic
726C3⋊D3—42no—
727C3⋊D3—42no—
728C3×D3—24no—
729C3×D3—42no—
730C24—31no—
731C24—31no—
732C24—94no—
733C24—91no—
734C24—91no—
735C24—184no—
736C24—362no—
737C24—362no—
738C24C2×D3211yescharacteristic
739C2×Q8—94no—
740C2×Q8—362no—
741C2×D4—34no—
742C2×D4—34no—
743C2×D4—64no—
744C2×D4—94no—
745C2×D4—94no—
746C2×D4—94no—
747C2×D4—94no—
748C2×D4—94no—
749C2×D4—122no—
750C2×D4—184no—
751C2×D4—362no—
752C2×D4—362no—
753C2×D4—362no—
754C2×D4—362no—
755C22×C4—31no—
756C22×C4—31no—
757C22×C4—31no—
758C22×C4—31no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—34no—
762C22×C4—42no—
763C22×C4—94no—
764C22×C4—94no—
765C22×C4—91no—
766C22×C4—91no—
767C22×C4—122no—
768C22×C4—362no—
769C22×C4—362no—
770C22×C4C2×D3211yescharacteristic
771C22×C4C2×D3211yescharacteristic
772C22×C4C2×D3214yescomplemented
773C4⋊C4—34no—
774C4⋊C4—34no—
775C4⋊C4—34no—
776C4⋊C4—94no—
777C4⋊C4—94no—
778C4⋊C4—94no—
779C22⋊C4—34no—
780C22⋊C4—34no—
781C22⋊C4—34no—
782C22⋊C4—34no—
783C22⋊C4—34no—
784C22⋊C4—94no—
785C22⋊C4—94no—
786C22⋊C4—94no—
787C22⋊C4—94no—
788C22⋊C4—94no—
789C22⋊C4—94no—
790C22⋊C4—94no—
791C22⋊C4—94no—
792C22⋊C4—94no—
793C42—34no—
794C42—94no—
795C22×C3—24no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—22no—
802C22×C3—22no—
803C22×C3—22no—
804C22×C3—22no—
805C22×C3—21no—
806C22×C3—34no—
807C22×C3—42no—
808C22×C3—42no—
809C22×C3—48no—
810C22×C3—44no—
811C22×C3—44no—
812C22×C3—68no—
813C22×C3—62no—
814C22×C3—62no—
815C22×C3—62no—
816C22×C3—62no—
817C22×C3—62no—
818C22×C3—124no—
819C22×C3C2×#23512yes—
820C22×C3#100412yes—
821C22×C3#100412yes—
822C22×C3D3×#4112yes—
823C22×C3#100912yes—
824C22×C3#100912yes—
825C22×C3C24×D311yescharacteristic
826C22×C3C24×D311yescharacteristic
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—28no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—44no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—62no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—62no—
844C2×D3—62no—
845C2×D3—62no—
846C2×D3—122no—
847C2×D3—122no—
848C2×D3—122no—
849C2×D3—122no—
850C2×D3—122no—
851C2×D3—122no—
852C2×D3—1216no—
853C2×D3—1216no—
854C2×D3—124no—
855C2×D3—124no—
856C2×D3—124no—
857C2×D3—124no—
858C2×D3—244no—
859C2×D3—244no—
860C2×D3C2×#23514yes—
861C3×C4—24no—
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—22no—
865C3×C4—22no—
866C3×C4—42no—
867C3×C4—62no—
868C3×C4—62no—
869C3×C4—62no—
870C3×C4—62no—
871C3×C4—62no—
872C3×C4—62no—
873Dic3—22no—
874Dic3—22no—
875Dic3—22no—
876Dic3—22no—
877Dic3—22no—
878Dic3—22no—
879Dic3—62no—
880Dic3—62no—
881Dic3—62no—
882Dic3—62no—
883Dic3—122no—
884Dic3—122no—
885C32C2×#53811yescharacteristic, complemented, Sylow
886C23—22no—
887C23—22no—
888C23—22no—
889C23—34no—
890C23—32no—
891C23—32no—
892C23—62no—
893C23—62no—
894C23—62no—
895C23—62no—
896C23—62no—
897C23—92no—
898C23—92no—
899C23—188no—
900C23—182no—
901C23—182no—
902C23—182no—
903C23—182no—
904C23—182no—
905C23—182no—
906C23—364no—
907C23—364no—
908C23—3616no—
909C23C22×D3212yes—
910C23C22×D3211yescharacteristic
911Q8—364no—
912D4—68no—
913D4—124no—
914D4—188no—
915D4—364no—
916D4—364no—
917D4—364no—
918D4—364no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—32no—
922C2×C4—32no—
923C2×C4—32no—
924C2×C4—32no—
925C2×C4—32no—
926C2×C4—32no—
927C2×C4—44no—
928C2×C4—62no—
929C2×C4—62no—
930C2×C4—62no—
931C2×C4—62no—
932C2×C4—62no—
933C2×C4—62no—
934C2×C4—92no—
935C2×C4—92no—
936C2×C4—124no—
937C2×C4—182no—
938C2×C4—182no—
939C2×C4—364no—
940C2×C4—364no—
941C2×C4C22×D3212yes—
942C2×C4C22×D3212yes—
943C2×C3—24no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—44no—
948C2×C3—42no—
949C2×C3—42no—
950C2×C3—64no—
951C2×C3—122no—
952C2×C3#556014yescomplemented
953C2×C3#565714yescomplemented
954C2×C3C22×#23511yescharacteristic
955C2×C3C2×#100411yescharacteristic
956C2×C3C2×#100411yescharacteristic
957C2×C3C2×D3×#4111yescharacteristic
958C2×C3C2×#100911yescharacteristic
959C2×C3C2×#100911yescharacteristic
960D3—24no—
961D3—42no—
962D3—122no—
963D3—122no—
964D3—122no—
965D3—122no—
966D3—242no—
967D3—242no—
968C22—22no—
969C22—22no—
970C22—22no—
971C22—34no—
972C22—44no—
973C22—68no—
974C22—62no—
975C22—62no—
976C22—62no—
977C22—62no—
978C22—62no—
979C22—124no—
980C22—182no—
981C22—182no—
982C22—182no—
983C22—182no—
984C22—182no—
985C22—182no—
986C22—3616no—
987C22—364no—
988C22—364no—
989C22D3×#23512yes—
990C22#6430812yes—
991C22#6433012yes—
992C22C23×D3211yescharacteristic
993C4—22no—
994C4—22no—
995C4—62no—
996C4—62no—
997C4—62no—
998C4—62no—
999C4—62no—
1000C4—62no—
1001C4—182no—
1002C4—182no—
1003C3—21no—
1004C3C2×#556011yescharacteristic, complemented
1005C3C2×#565711yescharacteristic, complemented
1006C2—42no—
1007C2—64no—
1008C2—122no—
1009C2—362no—
1010C2—362no—
1011C2#1059508514yesdirect product factor
1012C2C2×D3×#23511yescharacteristic
1013C2C2×#6430811yescharacteristic
1014C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64139C2semidirect
2. C2×C3×#929C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C2×#63983C2semidirect
5. C2×#63971C2semidirect
6. C2×#63958C2semidirect
7. C2×#63953C2semidirect
8. #10595085C2direct (N × H)
9. C2×#63923C2semidirect
10. C2×D3×(C2×D3)⋊C4C2semidirect
11. C2×#63904C2semidirect
12. C2×#63897C2semidirect
13. C2×#63893C2semidirect
14. C2×#63868C2semidirect
15. C2×#63861C2semidirect
16. C2×#63852C2semidirect
20. C23×C32×C4C22semidirect
22. C22×#638C22semidirect
27. C22×#627C22semidirect
30. C22×#624C22semidirect
32. #64139C22semidirect
34. C2×#3752C22semidirect
35. C2×C4⋊(C3⋊Dic3)C22semidirect
36. C2×C3×#217C22semidirect
37. C2×C3×#217C22semidirect
38. C3×#929C22semidirect
39. C3×C4×#67C22semidirect
43. C2×C3×Dic3⋊C4C22semidirect
44. C2×C3×Dic3⋊C4C22semidirect
45. C2×C3×Dic3⋊C4C22semidirect
46. C2×C3×C4×Dic3C22semidirect
47. #63983C22semidirect
48. #63971C22semidirect
49. C2×#3724C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
54. C2×#3722C22semidirect
58. #63958C22semidirect
59. C2×Dic32C22semidirect
60. #63953C22semidirect
61. #63923C22semidirect
62. D3×(C2×D3)⋊C4C22semidirect
63. #63904C22semidirect
64. #63897C22semidirect
65. #63893C22semidirect
66. #63868C22semidirect
67. #63861C22semidirect
68. #63852C22semidirect
78. C2×#929D3semidirect
80. C2×C4×#67D3semidirect
114. C22×C32×C4C23semidirect
118. C2×#638C23semidirect
136. C2×#627C23semidirect
142. C2×#624C23semidirect
146. #3752C23semidirect
147. C4⋊(C3⋊Dic3)C23semidirect
148. C3×#217C23semidirect
149. C3×#217C23semidirect
153. C3×Dic3⋊C4C23semidirect
154. C3×Dic3⋊C4C23semidirect
155. C3×Dic3⋊C4C23semidirect
156. C3×C4×Dic3C23semidirect
157. #3724C23semidirect
158. Dic3⋊Dic3C23semidirect
162. #3722C23semidirect
166. Dic32C23semidirect
174. C23×C3×C4C2×D3semidirect
175. C23×C3×C4C2×D3semidirect
212. C2×#217C2×D3semidirect
213. C2×#217C2×D3semidirect
221. #929C2×D3semidirect
223. C4×#67C2×D3semidirect
252. C2×Dic3⋊C4C2×D3semidirect
253. C2×Dic3⋊C4C2×D3semidirect
254. C2×Dic3⋊C4C2×D3semidirect
257. C2×C4×Dic3C2×D3semidirect
392. C22×C3×C4C22×D3semidirect
393. C22×C3×C4C22×D3semidirect
462. #217C22×D3semidirect
463. #217C22×D3semidirect
491. Dic3⋊C4C22×D3semidirect
492. Dic3⋊C4C22×D3semidirect
493. Dic3⋊C4C22×D3semidirect
496. C4×Dic3C22×D3semidirect
544. C23×C4D32semidirect
722. C2×C32#538semidirect
772. C22×C4C2×D32semidirect
885. C32C2×#538semidirect
952. C2×C3#5560semidirect
953. C2×C3#5657semidirect
1004. C3C2×#5560semidirect
1005. C3C2×#5657semidirect
1011. C2#10595085direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641392
C2×C3×#9292
C2×C3×C4×#672
C2×#639832
C2×#639712
C2×#639582
C2×#639532
#105950852
C2×#639232
C2×D3×(C2×D3)⋊C42
C2×#639042
C2×#638972
C2×#638932
C2×#638682
C2×#638612
C2×#638522
C2×#56573
C2×#55603