Finite Group Databasebeta

← C2×#10594273 #11902455

Subgroups — C2×#10594273 #11902455

Order 1152.

3965 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#67C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64094C211yesmaximal, characteristic, complemented
4C2×C3×#884C211yesmaximal, characteristic, complemented
5C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
6C2×#63976C211yesmaximal, characteristic, complemented
7C2×#63971C211yesmaximal, characteristic, complemented
8C2×#63969C211yesmaximal, characteristic, complemented
9C2×#63922C211yesmaximal, characteristic, complemented
10C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#63906C211yesmaximal, characteristic, complemented
12C2×#63902C211yesmaximal, characteristic, complemented
13C2×C4×#625C211yesmaximal, characteristic, complemented
14C2×#63896C211yesmaximal, characteristic, complemented
15C2×#63850C211yesmaximal, characteristic, complemented
16#10594273C2116yesmaximal, direct product factor
17C2×#5610—31nomaximal
18C2×#5490—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×#634C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic, complemented
25C22×C3×D12C2211yescharacteristic, complemented
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×C3×C4×D3C2211yescharacteristic, complemented
29C2×D3×#67—28no—
30C2×D3×#67C2218yescomplemented
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic, complemented
33C22×#625C2211yescharacteristic
34C22×#625C2211yescharacteristic
35C22×#625C2211yescharacteristic, complemented
36C22×D3×Dic3C2211yescharacteristic
37C22×D3×Dic3C2211yescharacteristic, complemented
38C22×D3×Dic3C2211yescharacteristic, complemented
39C2×#3795—28no—
40C2×#3795C2218yescomplemented
41C2×C32×C22⋊C4C2211yescharacteristic, complemented
42C2×#3757C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic, complemented
44C2×#3752C2211yescharacteristic, complemented
45C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
46#64094C2218yescomplemented
47C2×C3×#217C2211yescharacteristic, complemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
52C3×#884C2218yescomplemented
53C3×D3×C22⋊C4C2218yescomplemented
54#63976C2218yescomplemented
55#63971C2218yescomplemented
56#63969C2218yescomplemented
57C2×#3724C2211yescharacteristic, complemented
58C2×#3724C2211yescharacteristic, complemented
59C2×Dic3⋊Dic3C2211yescharacteristic, complemented
60C2×#3722C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
64#63922C2218yescomplemented
65D3×(C2×D3)⋊C4C2218yescomplemented
66#63906C2218yescomplemented
67#63902C2218yescomplemented
68C4×#625C2218yescomplemented
69#63896C2218yescomplemented
70#63850C2218yescomplemented
71C23×#67—31no—
72C22×#237—31no—
73C22×D3×D4—31no—
74C22×#235—31no—
75C2×C3×#121—31no—
76C22×C3×C22⋊C4—31no—
77C2×#953—31no—
78C2×#939—31no—
79C2×#937—31no—
80C2×#937—31no—
81C2×#935—31no—
82C2×#930—31no—
83C2×#929—31no—
84C2×C4×#67—31no—
85C2×C4×#67—31no—
86C22×(C2×D3)⋊C4—31no—
87#5610—316no—
88C2×#896—31no—
89C2×#894—31no—
90C2×#885—31no—
91C2×#885—31no—
92C2×#885—61no—
93#5490—316no—
94C2×#884—31no—
95C2×#884—31no—
96C2×#884D311yescharacteristic, complemented
97C2×#883—31no—
98C2×#882—31no—
99C2×#67⋊C4—31no—
100C2×#67⋊C4—31no—
101C2×D3×C22⋊C4—31no—
102C2×D3×C22⋊C4D311yescharacteristic, complemented
103C2×#878—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3×D3—24no—
107C23×C3×D3—24no—
108C23×C3×D3—42no—
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2314yes—
111C23×C3×D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C22×D32—24no—
115C22×D32—24no—
116C22×D32—42no—
117C22×D32C2314yes—
118C22×C32×C4C2311yescharacteristic
119C22×C32×C4C2311yescharacteristic
120C2×#638—24no—
121C2×#638C2314yes—
122C22×C3⋊Dic3C2311yescharacteristic
123C22×C3⋊Dic3C2311yescharacteristic
124C22×C3⋊Dic3C2311yescharacteristic
125C2×#634—24no—
126C2×#634C2314yescomplemented
127C2×C3×#67—24no—
128C2×C3×#67—42no—
129C2×C3×#67C2314yes—
130C2×C3×#67C2314yescomplemented
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C2×C3×D12—24no—
136C2×C3×D12C2314yescomplemented
137C2×C3×C4×D3—24no—
138C2×C3×C4×D3—42no—
139C2×C3×C4×D3—42no—
140C2×C3×C4×D3C2314yescomplemented
141C2×C3×C4×D3C2314yescomplemented
142C2×C3×C4×D3C2314yescomplemented
143D3×#67—232no—
144C2×#626—24no—
145C2×#626—42no—
146C2×#626C2314yes—
147C2×#626C2314yescomplemented
148C2×#625—24no—
149C2×#625—24no—
150C2×#625D418yescomplemented
151C2×#625C2314yes—
152C2×#625C2314yes—
153C2×#625C2314yescomplemented
154C2×D3×Dic3—24no—
155C2×D3×Dic3—24no—
156C2×D3×Dic3—24no—
157C2×D3×Dic3C2314yes—
158C2×D3×Dic3C2314yescomplemented
159C2×D3×Dic3C2314yescomplemented
160#3795—232no—
161C32×C22⋊C4C2314yescomplemented
162#3757C2314yescomplemented
163#3752C2314yescomplemented
164#3752C2314yescomplemented
165C4×C3⋊Dic3C2314yescomplemented
166C3×#217C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yes—
168C3×(C2×D3)⋊C4C2314yes—
169C3×(C2×D3)⋊C4C2314yescomplemented
170C3×Dic3⋊C4C2314yescomplemented
171#3724C2314yescomplemented
172#3724C2314yescomplemented
173Dic3⋊Dic3C2314yescomplemented
174#3722C2314yescomplemented
175(C2×D3)⋊Dic3C2314yes—
176(C2×D3)⋊Dic3C2314yescomplemented
177(C2×D3)⋊Dic3C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3C2×D311yescharacteristic
183C22×C3×D4—31no—
184C22×C3×D4—31no—
185C22×C3×D4—31no—
186C23×C3×C4—31no—
187C23×C3×C4—31no—
188C23×C3×C4—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—38no—
198C22×#67—31no—
199C22×#67—31no—
200C22×#67—61no—
201C22×#67—68no—
202C22×#67C2×D311yescharacteristic
203C22×#67C2×D311yescharacteristic, complemented
204C23×Dic3—31no—
205C23×Dic3—31no—
206C23×Dic3—31no—
207C2×#237—38no—
208C2×#237—68no—
209C2×D3×D4—38no—
210C2×D3×D4—68no—
211C2×#235—38no—
212C2×#235—68no—
213C22×D12—31no—
214C22×D12—31no—
215C22×D12C2×D311yescharacteristic, complemented
216C22×C4×D3—31no—
217C22×C4×D3—31no—
218C22×C4×D3—31no—
219C22×C4×D3C2×D311yescharacteristic, complemented
220C22×C4×D3C2×D311yescharacteristic, complemented
221C22×C4×D3C2×D311yescharacteristic, complemented
222C22×Dic6—31no—
223C22×Dic6—31no—
224C22×Dic6—61no—
225C3×#121—38no—
226C2×C3×C4⋊C4—31no—
227C2×C3×C22⋊C4—21no—
228C2×C3×C22⋊C4—31no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—38no—
233C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
234C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
235#953—38no—
236C2×#217—31no—
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217—31no—
241C2×#217—61no—
242C2×#217C2×D311yescharacteristic, complemented
243#939—38no—
244#937—38no—
245#937—38no—
246#935—38no—
247#930—38no—
248#929—38no—
249C4×#67—38no—
250C4×#67—38no—
251C2×(C2×D3)⋊C4—31no—
252C2×(C2×D3)⋊C4—31no—
253C2×(C2×D3)⋊C4—31no—
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4—31no—
256C2×(C2×D3)⋊C4—31no—
257C2×(C2×D3)⋊C4—31no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—31no—
260C2×(C2×D3)⋊C4—38no—
261C2×(C2×D3)⋊C4—61no—
262C2×(C2×D3)⋊C4—61no—
263C2×(C2×D3)⋊C4C2×D311yescharacteristic
264C2×(C2×D3)⋊C4C2×D311yescharacteristic
265C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
266C2×C4⋊Dic3—31no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4—31no—
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4—31no—
271C2×Dic3⋊C4—31no—
272C2×Dic3⋊C4C2×D311yescharacteristic, complemented
273C2×C4×Dic3—31no—
274C2×C4×Dic3—31no—
275C2×C4×Dic3—61no—
276#896—38no—
277#894—38no—
278#885—38no—
279#885—38no—
280#885—68no—
281#884—38no—
282#884—38no—
283#884C2×D318yescomplemented
284#883—38no—
285#882—38no—
286#67⋊C4—38no—
287#67⋊C4—38no—
288D3×C22⋊C4—38no—
289D3×C22⋊C4C2×D318yescomplemented
290#878—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32C2412yes—
295C23×C32C2411yescharacteristic
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3C2412yes—
300C22×C3×D3—22no—
301C22×C3×D3—22no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
306C22×C3×D3—22no—
307C22×C3×D3—22no—
308C22×C3×D3—22no—
309C22×C3×D3—28no—
310C22×C3×D3—28no—
311C22×C3×D3—44no—
312C22×C3×D3—416no—
313C22×C3×D3C2×D414yes—
314C22×C3×D3C2×D414yes—
315C22×C3×D3#4114yescomplemented
316C22×C3×D3C2412yes—
317C22×C3×D3C2412yes—
318C22×C3×D3C2412yes—
319C22×C3×D3C2412yes—
320C2×D32—28no—
321C2×D32—28no—
322C2×D32—44no—
323C2×D32—416no—
324C2×C32×C4—22no—
325C2×C32×C4—22no—
326C2×C32×C4C2412yes—
327C2×C32×C4C2412yes—
328#638—28no—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3C2×D414yes—
332C2×C3⋊Dic3C2412yes—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335#634—28no—
336C3×#67—28no—
337C3×#67—44no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C3×D12—28no—
347C3×C4×D3—28no—
348C3×C4×D3—44no—
349C3×C4×D3—44no—
350#626—28no—
351#626—44no—
352#625—28no—
353#625—28no—
354#625C2×D4116yescomplemented
355D3×Dic3—28no—
356D3×Dic3—28no—
357D3×Dic3—28no—
358C22×#41—91no—
359C23×D4—91no—
360#546—916no—
361C2×#124—91no—
362C2×#123—91no—
363C2×#123—91no—
364C2×C22⋊Q8—91no—
365C2×#121—31no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—91no—
369C2×#120—91no—
370C2×C4×D4—91no—
371C2×C4×D4—91no—
372C22×C22⋊C4—31no—
373C22×C22⋊C4—91no—
374C24×C3—21no—
375C24×C3—31no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3—31no—
379C24×C3—34no—
380C24×C3—64no—
381C24×C3—64no—
382C24×C3—122no—
383C24×C3C22×D311yescharacteristic
384C24×C3C22×D311yescharacteristic
385C23×D3—24no—
386C23×D3—24no—
387C23×D3—31no—
388C23×D3—31no—
389C23×D3—34no—
390C23×D3—34no—
391C23×D3—42no—
392C23×D3—61no—
393C23×D3—64no—
394C23×D3—64no—
395C23×D3—64no—
396C23×D3—64no—
397C23×D3—122no—
398C23×D3—122no—
399C23×D3C22×D311yescharacteristic
400C23×D3C22×D314yes—
401C23×D3C22×D311yescharacteristic
402C23×D3C22×D311yescharacteristic
403C23×D3C22×D311yescharacteristic
404C2×C3×D4—34no—
405C2×C3×D4—34no—
406C2×C3×D4—34no—
407C2×C3×D4—64no—
408C2×C3×D4—64no—
409C2×C3×D4—122no—
410C22×C3×C4—21no—
411C22×C3×C4—21no—
412C22×C3×C4—31no—
413C22×C3×C4—31no—
414C22×C3×C4—31no—
415C22×C3×C4—31no—
416C22×C3×C4—34no—
417C22×C3×C4—34no—
418C22×C3×C4—34no—
419C22×C3×C4—64no—
420C22×C3×C4—122no—
421C22×C3×C4—122no—
422C22×C3×C4C22×D311yescharacteristic
423C22×C3×C4C22×D311yescharacteristic
424C22×C3×C4C22×D311yescharacteristic
425C22×C3×C4C22×D311yescharacteristic
426C2×#67—24no—
427C2×#67—38no—
428C2×#67—38no—
429C2×#67—34no—
430C2×#67—34no—
431C2×#67—34no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—34no—
439C2×#67—42no—
440C2×#67—64no—
441C2×#67—64no—
442C2×#67—64no—
443C2×#67—64no—
444C2×#67—632no—
445C2×#67—64no—
446C2×#67—64no—
447C2×#67—64no—
448C2×#67—64no—
449C2×#67—124no—
450C2×#67—122no—
451C2×#67C22×D314yes—
452C2×#67C22×D314yescomplemented
453C22×Dic3—31no—
454C22×Dic3—31no—
455C22×Dic3—31no—
456C22×Dic3—31no—
457C22×Dic3—31no—
458C22×Dic3—31no—
459C22×Dic3—34no—
460C22×Dic3—34no—
461C22×Dic3—34no—
462C22×Dic3—61no—
463C22×Dic3—61no—
464C22×Dic3—61no—
465C22×Dic3—64no—
466C22×Dic3—64no—
467C22×Dic3—64no—
468C22×Dic3C22×D311yescharacteristic
469C22×Dic3C22×D311yescharacteristic
470C22×Dic3C22×D311yescharacteristic
471C22×Dic3C22×D311yescharacteristic
472#237—632no—
473D3×D4—632no—
474#235—632no—
475C2×D12—24no—
476C2×D12—34no—
477C2×D12—34no—
478C2×D12—64no—
479C2×D12—122no—
480C2×D12C22×D314yescomplemented
481C2×C4×D3—24no—
482C2×C4×D3—34no—
483C2×C4×D3—34no—
484C2×C4×D3—34no—
485C2×C4×D3—42no—
486C2×C4×D3—42no—
487C2×C4×D3—64no—
488C2×C4×D3—64no—
489C2×C4×D3—64no—
490C2×C4×D3C22×D314yescomplemented
491C2×C4×D3C22×D314yescomplemented
492C2×C4×D3C22×D314yescomplemented
493C2×Dic6—34no—
494C2×Dic6—34no—
495C2×Dic6—64no—
496C2×Dic6—64no—
497C2×Dic6—64no—
498C2×Dic6—124no—
499C3×C4⋊C4—34no—
500C3×C22⋊C4—24no—
501C3×C22⋊C4—34no—
502C3×C22⋊C4—34no—
503C3×C22⋊C4—34no—
504C3×C22⋊C4—34no—
505C3×C22⋊C4C22×D314yescomplemented
506C3×C22⋊C4C22×D314yescomplemented
507#217—34no—
508#217—34no—
509#217—34no—
510#217—34no—
511#217—34no—
512#217—64no—
513#217C22×D314yescomplemented
514(C2×D3)⋊C4—34no—
515(C2×D3)⋊C4—34no—
516(C2×D3)⋊C4—34no—
517(C2×D3)⋊C4—34no—
518(C2×D3)⋊C4—34no—
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4—34no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—64no—
524(C2×D3)⋊C4—64no—
525(C2×D3)⋊C4C22×D314yes—
526(C2×D3)⋊C4C22×D314yes—
527(C2×D3)⋊C4C22×D314yescomplemented
528C4⋊Dic3—34no—
529Dic3⋊C4—34no—
530Dic3⋊C4—34no—
531Dic3⋊C4—34no—
532Dic3⋊C4—34no—
533Dic3⋊C4—34no—
534Dic3⋊C4C22×D314yescomplemented
535C4×Dic3—34no—
536C4×Dic3—34no—
537C4×Dic3—64no—
538C22×C32—22no—
539C22×C32—22no—
540C22×C32—22no—
541C22×C32—44no—
542C22×C32C22×D412yes—
543C22×C32C2×#4112yes—
544C22×C32H(5,𝔽2)12yes—
545C22×C32C2511yescharacteristic
546C2×C3⋊D3—22no—
547C2×C3⋊D3—22no—
548C2×C3⋊D3—22no—
549C2×C3⋊D3—44no—
550C2×C3×D3—28no—
551C2×C3×D3—28no—
552C2×C3×D3—28no—
553C2×C3×D3—22no—
554C2×C3×D3—22no—
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—22no—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—416no—
563C2×C3×D3—44no—
564C2×C3×D3C22×D414yes—
565C2×C3×D3C22×D414yes—
566C2×C3×D3C2×#4114yescomplemented
567D32—416no—
568C32×C4—22no—
569C32×C4—22no—
570C3⋊Dic3—22no—
571C3⋊Dic3—22no—
572C3⋊Dic3C22×D414yes—
573C3×Dic3—22no—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C25—31no—
578C25—91no—
579C2×#41—98no—
580C2×#41—188no—
581C22×Q8—91no—
582C22×D4—31no—
583C22×D4—31no—
584C22×D4—31no—
585C22×D4—91no—
586C22×D4—91no—
587C22×D4—98no—
588C22×D4—91no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—188no—
593C23×C4—31no—
594C23×C4—31no—
595C23×C4—31no—
596C23×C4—91no—
597C23×C4—91no—
598C23×C4—91no—
599#124—98no—
600#123—98no—
601#123—98no—
602C22⋊Q8—98no—
603#121—38no—
604#121—98no—
605#121—98no—
606#120—98no—
607#120—98no—
608C4×D4—98no—
609C4×D4—98no—
610C2×C4⋊C4—31no—
611C2×C4⋊C4—91no—
612C2×C4⋊C4—91no—
613C2×C4⋊C4—91no—
614C2×C22⋊C4—31no—
615C2×C22⋊C4—31no—
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—38no—
619C2×C22⋊C4—98no—
620C2×C22⋊C4—91no—
621C2×C22⋊C4—91no—
622C2×C22⋊C4—91no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4D3211yescharacteristic, complemented
628C2×C42—91no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—21no—
637C23×C3—34no—
638C23×C3—34no—
639C23×C3—34no—
640C23×C3—32no—
641C23×C3—32no—
642C23×C3—32no—
643C23×C3—32no—
644C23×C3—42no—
645C23×C3—42no—
646C23×C3—42no—
647C23×C3—68no—
648C23×C3—68no—
649C23×C3—62no—
650C23×C3—62no—
651C23×C3—62no—
652C23×C3—62no—
653C23×C3—62no—
654C23×C3—62no—
655C23×C3—62no—
656C23×C3—62no—
657C23×C3—62no—
658C23×C3—124no—
659C23×C3—1216no—
660C23×C3C23×D312yes—
661C23×C3C23×D312yes—
662C23×C3C23×D311yescharacteristic
663C23×C3C23×D311yescharacteristic
664C22×D3—22no—
665C22×D3—22no—
666C22×D3—22no—
667C22×D3—22no—
668C22×D3—22no—
669C22×D3—22no—
670C22×D3—22no—
671C22×D3—22no—
672C22×D3—22no—
673C22×D3—28no—
674C22×D3—28no—
675C22×D3—32no—
676C22×D3—32no—
677C22×D3—44no—
678C22×D3—416no—
679C22×D3—62no—
680C22×D3—68no—
681C22×D3—68no—
682C22×D3—62no—
683C22×D3—62no—
684C22×D3—62no—
685C22×D3—62no—
686C22×D3—62no—
687C22×D3—62no—
688C22×D3—68no—
689C22×D3—68no—
690C22×D3—122no—
691C22×D3—122no—
692C22×D3—122no—
693C22×D3—124no—
694C22×D3—124no—
695C22×D3—1216no—
696C22×D3—1216no—
697C22×D3#23514yescomplemented
698C22×D3D3×D414yes—
699C22×D3D3×D414yes—
700C22×D3C23×D312yes—
701C22×D3C23×D312yes—
702C22×D3C23×D312yes—
703C22×D3C23×D312yes—
704C3×D4—68no—
705C3×D4—68no—
706C3×D4—124no—
707C2×C3×C4—22no—
708C2×C3×C4—22no—
709C2×C3×C4—22no—
710C2×C3×C4—22no—
711C2×C3×C4—22no—
712C2×C3×C4—22no—
713C2×C3×C4—32no—
714C2×C3×C4—32no—
715C2×C3×C4—32no—
716C2×C3×C4—32no—
717C2×C3×C4—42no—
718C2×C3×C4—42no—
719C2×C3×C4—68no—
720C2×C3×C4—62no—
721C2×C3×C4—62no—
722C2×C3×C4—62no—
723C2×C3×C4—62no—
724C2×C3×C4—124no—
725C2×C3×C4—124no—
726C2×C3×C4C23×D312yes—
727C2×C3×C4C23×D312yes—
728C2×C3×C4C23×D312yes—
729C2×C3×C4C23×D312yes—
730#67—28no—
731#67—316no—
732#67—316no—
733#67—44no—
734#67—68no—
735#67—68no—
736#67—68no—
737#67—68no—
738#67—68no—
739#67—68no—
740#67—68no—
741#67—128no—
742#67—124no—
743C2×Dic3—22no—
744C2×Dic3—22no—
745C2×Dic3—22no—
746C2×Dic3—22no—
747C2×Dic3—34no—
748C2×Dic3—34no—
749C2×Dic3—32no—
750C2×Dic3—32no—
751C2×Dic3—32no—
752C2×Dic3—32no—
753C2×Dic3—32no—
754C2×Dic3—32no—
755C2×Dic3—64no—
756C2×Dic3—62no—
757C2×Dic3—62no—
758C2×Dic3—62no—
759C2×Dic3—68no—
760C2×Dic3—68no—
761C2×Dic3—68no—
762C2×Dic3—62no—
763C2×Dic3—62no—
764C2×Dic3—62no—
765C2×Dic3—62no—
766C2×Dic3—122no—
767C2×Dic3—122no—
768C2×Dic3C23×D312yes—
769C2×Dic3C23×D312yes—
770C2×Dic3C23×D312yes—
771C2×Dic3C23×D312yes—
772D12—28no—
773D12—68no—
774D12—124no—
775C4×D3—28no—
776C4×D3—44no—
777C4×D3—44no—
778C4×D3—68no—
779C4×D3—68no—
780C4×D3—68no—
781Dic6—68no—
782Dic6—68no—
783Dic6—128no—
784C2×C32—42no—
785C2×C32#54614yescomplemented
786C2×C32C23×D411yescharacteristic
787C2×C32C22×#4111yescharacteristic
788C2×C32C2×H(5,𝔽2)11yescharacteristic
789C3⋊D3—42no—
790C3×D3—24no—
791C3×D3—24no—
792C3×D3—24no—
793C3×D3—42no—
794C24—31no—
795C24—31no—
796C24—31no—
797C24—31no—
798C24—34no—
799C24—64no—
800C24—64no—
801C24—94no—
802C24—91no—
803C24—122no—
804C24—184no—
805C24—184no—
806C24—362no—
807C24C2×D3211yescharacteristic
808#41—1832no—
809C2×Q8—94no—
810C2×Q8—184no—
811C2×D4—34no—
812C2×D4—34no—
813C2×D4—34no—
814C2×D4—64no—
815C2×D4—64no—
816C2×D4—94no—
817C2×D4—94no—
818C2×D4—94no—
819C2×D4—98no—
820C2×D4—94no—
821C2×D4—94no—
822C2×D4—94no—
823C2×D4—122no—
824C2×D4—184no—
825C2×D4—184no—
826C2×D4—1832no—
827C2×D4—184no—
828C2×D4—184no—
829C2×D4—362no—
830C22×C4—31no—
831C22×C4—31no—
832C22×C4—31no—
833C22×C4—31no—
834C22×C4—34no—
835C22×C4—34no—
836C22×C4—34no—
837C22×C4—64no—
838C22×C4—94no—
839C22×C4—94no—
840C22×C4—94no—
841C22×C4—91no—
842C22×C4—91no—
843C22×C4—91no—
844C22×C4—122no—
845C22×C4—122no—
846C22×C4—184no—
847C22×C4—184no—
848C22×C4—184no—
849C22×C4C2×D3211yescharacteristic
850C22×C4C2×D3211yescharacteristic
851C4⋊C4—34no—
852C4⋊C4—94no—
853C4⋊C4—94no—
854C4⋊C4—94no—
855C22⋊C4—34no—
856C22⋊C4—34no—
857C22⋊C4—34no—
858C22⋊C4—34no—
859C22⋊C4—94no—
860C22⋊C4—94no—
861C22⋊C4—94no—
862C22⋊C4—94no—
863C22⋊C4—94no—
864C22⋊C4—94no—
865C22⋊C4—94no—
866C22⋊C4C2×D3214yescomplemented
867C42—94no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—22no—
871C22×C3—22no—
872C22×C3—22no—
873C22×C3—22no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—21no—
878C22×C3—34no—
879C22×C3—34no—
880C22×C3—34no—
881C22×C3—42no—
882C22×C3—42no—
883C22×C3—42no—
884C22×C3—44no—
885C22×C3—44no—
886C22×C3—62no—
887C22×C3—62no—
888C22×C3—62no—
889C22×C3—62no—
890C22×C3—62no—
891C22×C3—62no—
892C22×C3—68no—
893C22×C3—68no—
894C22×C3—68no—
895C22×C3—62no—
896C22×C3—62no—
897C22×C3—62no—
898C22×C3—84no—
899C22×C3—1216no—
900C22×C3—124no—
901C22×C3C2×#23512yes—
902C22×C3C2×D3×D412yes—
903C22×C3C2×D3×D412yes—
904C22×C3#100412yes—
905C22×C3#100412yes—
906C22×C3D3×#4112yes—
907C22×C3C24×D311yescharacteristic
908C22×C3C24×D311yescharacteristic
909C2×D3—22no—
910C2×D3—22no—
911C2×D3—22no—
912C2×D3—22no—
913C2×D3—22no—
914C2×D3—22no—
915C2×D3—28no—
916C2×D3—28no—
917C2×D3—28no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—416no—
922C2×D3—44no—
923C2×D3—62no—
924C2×D3—62no—
925C2×D3—62no—
926C2×D3—62no—
927C2×D3—62no—
928C2×D3—62no—
929C2×D3—122no—
930C2×D3—122no—
931C2×D3—122no—
932C2×D3—1216no—
933C2×D3—1216no—
934C2×D3—124no—
935C2×D3—124no—
936C2×D3—244no—
937C2×D3C2×#23514yescomplemented
938C2×D3C2×D3×D414yes—
939C2×D3C2×D3×D414yes—
940C3×C4—22no—
941C3×C4—22no—
942C3×C4—22no—
943C3×C4—22no—
944C3×C4—42no—
945C3×C4—42no—
946C3×C4—62no—
947C3×C4—62no—
948C3×C4—62no—
949C3×C4—62no—
950Dic3—22no—
951Dic3—22no—
952Dic3—22no—
953Dic3—22no—
954Dic3—34no—
955Dic3—34no—
956Dic3—64no—
957Dic3—62no—
958Dic3—62no—
959Dic3—62no—
960Dic3—62no—
961Dic3—122no—
962Dic3—122no—
963C32C2×#54611yescharacteristic, complemented, Sylow
964C23—22no—
965C23—22no—
966C23—22no—
967C23—34no—
968C23—34no—
969C23—34no—
970C23—32no—
971C23—32no—
972C23—32no—
973C23—32no—
974C23—68no—
975C23—68no—
976C23—62no—
977C23—62no—
978C23—62no—
979C23—62no—
980C23—62no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—62no—
985C23—92no—
986C23—124no—
987C23—1216no—
988C23—188no—
989C23—188no—
990C23—182no—
991C23—182no—
992C23—182no—
993C23—364no—
994C23—3616no—
995C23C22×D3212yes—
996C23C22×D3211yescharacteristic
997Q8—188no—
998D4—68no—
999D4—68no—
1000D4—916no—
1001D4—124no—
1002D4—188no—
1003D4—188no—
1004D4—188no—
1005D4—188no—
1006D4—364no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—32no—
1010C2×C4—32no—
1011C2×C4—32no—
1012C2×C4—32no—
1013C2×C4—68no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—94no—
1019C2×C4—92no—
1020C2×C4—92no—
1021C2×C4—92no—
1022C2×C4—124no—
1023C2×C4—124no—
1024C2×C4—188no—
1025C2×C4—188no—
1026C2×C4—188no—
1027C2×C4—182no—
1028C2×C4—182no—
1029C2×C4C22×D3212yes—
1030C2×C4C22×D3212yes—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—24no—
1035C2×C3—42no—
1036C2×C3—42no—
1037C2×C3—64no—
1038C2×C3—64no—
1039C2×C3—64no—
1040C2×C3—82no—
1041C2×C3—122no—
1042C2×C3#549014yescomplemented
1043C2×C3#561014yescomplemented
1044C2×C3C22×#23511yescharacteristic
1045C2×C3C22×D3×D411yescharacteristic
1046C2×C3C22×D3×D411yescharacteristic
1047C2×C3C2×#100411yescharacteristic
1048C2×C3C2×#100411yescharacteristic
1049C2×C3C2×D3×#4111yescharacteristic
1050D3—24no—
1051D3—24no—
1052D3—24no—
1053D3—42no—
1054D3—122no—
1055D3—122no—
1056D3—242no—
1057C22—22no—
1058C22—22no—
1059C22—22no—
1060C22—34no—
1061C22—34no—
1062C22—34no—
1063C22—44no—
1064C22—62no—
1065C22—62no—
1066C22—62no—
1067C22—62no—
1068C22—62no—
1069C22—62no—
1070C22—68no—
1071C22—68no—
1072C22—68no—
1073C22—62no—
1074C22—62no—
1075C22—62no—
1076C22—1216no—
1077C22—124no—
1078C22—182no—
1079C22—182no—
1080C22—182no—
1081C22—3616no—
1082C22—364no—
1083C22D3×#23512yes—
1084C22D32×D412yes—
1085C22#6431312yes—
1086C22C23×D3211yescharacteristic
1087C4—22no—
1088C4—22no—
1089C4—62no—
1090C4—62no—
1091C4—62no—
1092C4—62no—
1093C4—94no—
1094C4—182no—
1095C4—182no—
1096C3—21no—
1097C3C2×#549011yescharacteristic, complemented
1098C3C2×#561011yescharacteristic, complemented
1099C2—42no—
1100C2—64no—
1101C2—64no—
1102C2—64no—
1103C2—122no—
1104C2—362no—
1105C2#1059427314yesdirect product factor
1106C2C2×D3×#23511yescharacteristic
1107C2C2×D32×D411yescharacteristic
1108C2C2×#6431311yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×#67C2semidirect
2. C22×#3795C2semidirect
3. C2×#64094C2semidirect
4. C2×C3×#884C2semidirect
5. C2×C3×D3×C22⋊C4C2semidirect
6. C2×#63976C2semidirect
7. C2×#63971C2semidirect
8. C2×#63969C2semidirect
9. C2×#63922C2semidirect
10. C2×D3×(C2×D3)⋊C4C2semidirect
11. C2×#63906C2semidirect
12. C2×#63902C2semidirect
13. C2×C4×#625C2semidirect
14. C2×#63896C2semidirect
15. C2×#63850C2semidirect
16. #10594273C2direct (N × H)
22. C22×#634C22semidirect
24. C22×C3×#67C22semidirect
25. C22×C3×D12C22semidirect
26. C22×C3×C4×D3C22semidirect
27. C22×C3×C4×D3C22semidirect
28. C22×C3×C4×D3C22semidirect
30. C2×D3×#67C22semidirect
32. C22×#626C22semidirect
35. C22×#625C22semidirect
37. C22×D3×Dic3C22semidirect
38. C22×D3×Dic3C22semidirect
40. C2×#3795C22semidirect
41. C2×C32×C22⋊C4C22semidirect
42. C2×#3757C22semidirect
43. C2×#3752C22semidirect
44. C2×#3752C22semidirect
45. C2×C4×C3⋊Dic3C22semidirect
46. #64094C22semidirect
47. C2×C3×#217C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×Dic3⋊C4C22semidirect
52. C3×#884C22semidirect
53. C3×D3×C22⋊C4C22semidirect
54. #63976C22semidirect
55. #63971C22semidirect
56. #63969C22semidirect
57. C2×#3724C22semidirect
58. C2×#3724C22semidirect
59. C2×Dic3⋊Dic3C22semidirect
60. C2×#3722C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. #63922C22semidirect
65. D3×(C2×D3)⋊C4C22semidirect
66. #63906C22semidirect
67. #63902C22semidirect
68. C4×#625C22semidirect
69. #63896C22semidirect
70. #63850C22semidirect
96. C2×#884D3semidirect
102. C2×D3×C22⋊C4D3semidirect
126. C2×#634C23semidirect
130. C2×C3×#67C23semidirect
136. C2×C3×D12C23semidirect
140. C2×C3×C4×D3C23semidirect
141. C2×C3×C4×D3C23semidirect
142. C2×C3×C4×D3C23semidirect
147. C2×#626C23semidirect
150. C2×#625D4semidirect
153. C2×#625C23semidirect
158. C2×D3×Dic3C23semidirect
159. C2×D3×Dic3C23semidirect
161. C32×C22⋊C4C23semidirect
162. #3757C23semidirect
163. #3752C23semidirect
164. #3752C23semidirect
165. C4×C3⋊Dic3C23semidirect
166. C3×#217C23semidirect
169. C3×(C2×D3)⋊C4C23semidirect
170. C3×Dic3⋊C4C23semidirect
171. #3724C23semidirect
172. #3724C23semidirect
173. Dic3⋊Dic3C23semidirect
174. #3722C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
203. C22×#67C2×D3semidirect
215. C22×D12C2×D3semidirect
219. C22×C4×D3C2×D3semidirect
220. C22×C4×D3C2×D3semidirect
221. C22×C4×D3C2×D3semidirect
233. C2×C3×C22⋊C4C2×D3semidirect
234. C2×C3×C22⋊C4C2×D3semidirect
242. C2×#217C2×D3semidirect
265. C2×(C2×D3)⋊C4C2×D3semidirect
272. C2×Dic3⋊C4C2×D3semidirect
283. #884C2×D3semidirect
289. D3×C22⋊C4C2×D3semidirect
315. C22×C3×D3#41semidirect
354. #625C2×D4semidirect
452. C2×#67C22×D3semidirect
480. C2×D12C22×D3semidirect
490. C2×C4×D3C22×D3semidirect
491. C2×C4×D3C22×D3semidirect
492. C2×C4×D3C22×D3semidirect
505. C3×C22⋊C4C22×D3semidirect
506. C3×C22⋊C4C22×D3semidirect
513. #217C22×D3semidirect
527. (C2×D3)⋊C4C22×D3semidirect
534. Dic3⋊C4C22×D3semidirect
566. C2×C3×D3C2×#41semidirect
627. C2×C22⋊C4D32semidirect
697. C22×D3#235semidirect
785. C2×C32#546semidirect
866. C22⋊C4C2×D32semidirect
937. C2×D3C2×#235semidirect
963. C32C2×#546semidirect
1042. C2×C3#5490semidirect
1043. C2×C3#5610semidirect
1097. C3C2×#5490semidirect
1098. C3C2×#5610semidirect
1105. C2#10594273direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×#672
C22×#37952
C2×#640942
C2×C3×#8842
C2×C3×D3×C22⋊C42
C2×#639762
C2×#639712
C2×#639692
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639062
C2×#639022
C2×C4×#6252
C2×#638962
C2×#638502
#105942732
C2×#56103
C2×#54903