Finite Group Databasebeta

← C2×#10594281 #11902445

Subgroups — C2×#10594281 #11902445

Order 1152.

3971 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×#3796C211yesmaximal, characteristic, complemented
3C2×#64092C211yesmaximal, characteristic, complemented
4C2×C3×#885C211yesmaximal, characteristic, complemented
5C2×C3×#882C211yesmaximal, characteristic, complemented
6C2×#63970C211yesmaximal, characteristic, complemented
7C2×D3×#217C211yesmaximal, characteristic, complemented
8C2×#63958C211yesmaximal, characteristic, complemented
9C2×#63922C211yesmaximal, characteristic, complemented
10C2×#63921C211yesmaximal, characteristic, complemented
11C2×Dic3×D12C211yesmaximal, characteristic, complemented
12C2×#63891C211yesmaximal, characteristic, complemented
13C2×#63887C211yesmaximal, characteristic, complemented
14C2×#63885C211yesmaximal, characteristic, complemented
15C2×#63880C211yesmaximal, characteristic, complemented
16#10594281C2116yesmaximal, direct product factor
17C2×#5676—31nomaximal
18C2×#5591—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic, complemented
25C22×C3×D12C2211yescharacteristic
26C22×C3×D12C2211yescharacteristic, complemented
27C22×C3×Dic6C2211yescharacteristic, complemented
28C2×D3×#67—28no—
29C2×D3×#67C2218yescomplemented
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic, complemented
32C22×#625C2211yescharacteristic
33C22×#625C2211yescharacteristic, complemented
34C22×#624C2211yescharacteristic, complemented
35C22×D3×Dic3C2211yescharacteristic
36C22×D3×Dic3C2211yescharacteristic, complemented
37C22×D3×Dic3C2211yescharacteristic, complemented
38C22×D3×Dic3C2211yescharacteristic, complemented
39C2×#3796—28no—
40C2×#3796C2218yescomplemented
41C2×C32×C22⋊C4C2211yescharacteristic, complemented
42C2×#3757C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic, complemented
44C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45C2×#3750C2211yescharacteristic, complemented
46#64092C2218yescomplemented
47C2×C3×#217C2211yescharacteristic, complemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
52C2×C3×C4×Dic3C2211yescharacteristic, complemented
53C3×#885C2218yescomplemented
54C3×#882C2218yescomplemented
55#63970C2218yescomplemented
56D3×#217C2218yescomplemented
57C2×Dic3⋊Dic3C2211yescharacteristic, complemented
58C2×Dic3⋊Dic3C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63#63958C2218yescomplemented
64#63922C2218yescomplemented
65#63921C2218yescomplemented
66Dic3×D12C2218yescomplemented
67#63891C2218yescomplemented
68#63887C2218yescomplemented
69#63885C2218yescomplemented
70#63880C2218yescomplemented
71C23×#67—31no—
72C22×#239—31no—
73C22×#237—31no—
74C22×D3×D4—31no—
75C2×C3×#124—31no—
76C2×C3×#120—31no—
77C22×#217—31no—
78C2×#946—31no—
79C2×#939—31no—
80C2×#939—31no—
81C2×#938—31no—
82C2×#938—31no—
83C2×#937—31no—
84C2×D4×Dic3—31no—
85#5676—316no—
86#5591—316no—
87C2×#886—31no—
88C2×#885D311yescharacteristic, complemented
89C2×#884—31no—
90C2×#884—31no—
91C2×#883—31no—
92C2×#883—31no—
93C2×#883—31no—
94C2×#883—61no—
95C2×#882—31no—
96C2×#882D311yescharacteristic, complemented
97C2×#67⋊C4—31no—
98C2×D3×C22⋊C4—31no—
99C2×D3×C22⋊C4—31no—
100C2×D3×C22⋊C4—31no—
101C2×#878—31no—
102C2×C4×D12—31no—
103C2×C4×D12—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3×D3—24no—
107C23×C3×D3—24no—
108C23×C3×D3—42no—
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2314yes—
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×C4×C3⋊D3—24no—
126C2×C4×C3⋊D3C2314yescomplemented
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×D12—24no—
137C2×C3×D12C2314yes—
138C2×C3×D12C2314yescomplemented
139C2×C3×Dic6—24no—
140C2×C3×Dic6C2314yescomplemented
141D3×#67—232no—
142C2×#626—24no—
143C2×#626D418yescomplemented
144C2×#626C2314yes—
145C2×#626C2314yescomplemented
146C2×#625—24no—
147C2×#625—42no—
148C2×#625C2314yes—
149C2×#625C2314yescomplemented
150C2×#624—42no—
151C2×#624C2314yescomplemented
152C2×D3×Dic3—24no—
153C2×D3×Dic3—24no—
154C2×D3×Dic3—24no—
155C2×D3×Dic3—42no—
156C2×D3×Dic3C2314yes—
157C2×D3×Dic3C2314yescomplemented
158C2×D3×Dic3C2314yescomplemented
159C2×D3×Dic3C2314yescomplemented
160#3796—232no—
161C32×C22⋊C4C2314yescomplemented
162#3757C2314yescomplemented
163#3752C2314yescomplemented
164C4⋊(C3⋊Dic3)C2314yescomplemented
165#3750C2314yescomplemented
166C3×#217C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yes—
168C3×(C2×D3)⋊C4C2314yescomplemented
169C3×(C2×D3)⋊C4C2314yescomplemented
170C3×(C2×D3)⋊C4C2314yescomplemented
171C3×C4×Dic3C2314yescomplemented
172Dic3⋊Dic3C2314yescomplemented
173Dic3⋊Dic3C2314yescomplemented
174(C2×D3)⋊Dic3C2314yes—
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×Q8—31no—
184C22×C3×D4—31no—
185C22×C3×D4—31no—
186C22×C3×D4—31no—
187C22×C3×D4—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—38no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—61no—
198C22×#67—68no—
199C22×#67C2×D311yescharacteristic
200C22×#67C2×D311yescharacteristic, complemented
201C23×Dic3—31no—
202C23×Dic3—31no—
203C23×Dic3—31no—
204C23×Dic3—31no—
205C2×#239—38no—
206C2×#239—68no—
207C2×#237—38no—
208C2×#237—68no—
209C2×D3×D4—38no—
210C2×D3×D4—68no—
211C22×D12—31no—
212C22×D12—31no—
213C22×D12C2×D311yescharacteristic
214C22×D12C2×D311yescharacteristic, complemented
215C22×C4×D3—31no—
216C22×C4×D3—31no—
217C22×C4×D3—31no—
218C22×C4×D3—31no—
219C22×C4×D3—31no—
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3—31no—
223C22×C4×D3—61no—
224C22×Dic6C2×D311yescharacteristic, complemented
225C3×#124—38no—
226C3×#120—38no—
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—31no—
233C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
234C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
235C2×C3×C42—31no—
236C2×#217—31no—
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217—31no—
241C2×#217—31no—
242C2×#217—38no—
243C2×#217—61no—
244C2×#217C2×D311yescharacteristic, complemented
245#946—38no—
246#939—38no—
247#939—38no—
248#938—38no—
249#938—38no—
250#937—38no—
251D4×Dic3—38no—
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—61no—
259C2×(C2×D3)⋊C4C2×D311yescharacteristic
260C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
261C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
262C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
263C2×C4⋊Dic3—31no—
264C2×C4⋊Dic3—31no—
265C2×C4⋊Dic3—31no—
266C2×C4⋊Dic3—31no—
267C2×C4⋊Dic3—61no—
268C2×Dic3⋊C4—31no—
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4—31no—
271C2×Dic3⋊C4—31no—
272C2×Dic3⋊C4—61no—
273C2×C4×Dic3C2×D311yescharacteristic, complemented
274#886—38no—
275#885C2×D318yescomplemented
276#884—38no—
277#884—38no—
278#883—38no—
279#883—38no—
280#883—38no—
281#883—68no—
282#882—38no—
283#882C2×D318yescomplemented
284#67⋊C4—38no—
285D3×C22⋊C4—38no—
286D3×C22⋊C4—38no—
287D3×C22⋊C4—38no—
288#878—38no—
289C4×D12—38no—
290C4×D12—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32C2412yes—
295C23×C32C2411yescharacteristic
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3C2×D414yes—
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—22no—
310C22×C3×D3—28no—
311C22×C3×D3—28no—
312C22×C3×D3—44no—
313C22×C3×D3—416no—
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⋊Dic3—22no—
332C2×C3⋊Dic3C2412yes—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335C4×C3⋊D3—28no—
336C3×#67—28no—
337C3×#67—44no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3C2×D414yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C3×D12—28no—
347C3×D12—28no—
348C3×Dic6—28no—
349#626—28no—
350#626C2×D4116yescomplemented
351#625—28no—
352#625—44no—
353#624—44no—
354D3×Dic3—28no—
355D3×Dic3—28no—
356D3×Dic3—28no—
357D3×Dic3—44no—
358C22×#41—91no—
359C23×D4—91no—
360#546—916no—
361C2×#124—31no—
362C2×#123—91no—
363C2×#123—91no—
364C2×C22⋊Q8—91no—
365C2×#121—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—31no—
369C2×#120—91no—
370C2×C4×D4—91no—
371C2×C4×D4—91no—
372C22×C22⋊C4—91no—
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×D311yescharacteristic
401C23×D3C22×D314yes—
402C23×D3C22×D311yescharacteristic
403C23×D3C22×D311yescharacteristic
404C2×C3×Q8—34no—
405C2×C3×Q8—64no—
406C2×C3×D4—34no—
407C2×C3×D4—34no—
408C2×C3×D4—34no—
409C2×C3×D4—34no—
410C2×C3×D4—64no—
411C2×C3×D4—64no—
412C2×C3×D4—64no—
413C2×C3×D4—122no—
414C22×C3×C4—21no—
415C22×C3×C4—21no—
416C22×C3×C4—31no—
417C22×C3×C4—31no—
418C22×C3×C4—31no—
419C22×C3×C4—31no—
420C22×C3×C4C22×D311yescharacteristic
421C22×C3×C4C22×D311yescharacteristic
422C22×C3×C4C22×D311yescharacteristic
423C22×C3×C4C22×D311yescharacteristic
424C2×#67—24no—
425C2×#67—34no—
426C2×#67—34no—
427C2×#67—34no—
428C2×#67—34no—
429C2×#67—34no—
430C2×#67—34no—
431C2×#67—38no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—42no—
435C2×#67—64no—
436C2×#67—64no—
437C2×#67—632no—
438C2×#67—64no—
439C2×#67—64no—
440C2×#67—64no—
441C2×#67—64no—
442C2×#67—124no—
443C2×#67—122no—
444C2×#67—122no—
445C2×#67C22×D314yes—
446C2×#67C22×D314yescomplemented
447C22×Dic3—31no—
448C22×Dic3—31no—
449C22×Dic3—31no—
450C22×Dic3—31no—
451C22×Dic3—31no—
452C22×Dic3—31no—
453C22×Dic3—34no—
454C22×Dic3—34no—
455C22×Dic3—34no—
456C22×Dic3—34no—
457C22×Dic3—61no—
458C22×Dic3—61no—
459C22×Dic3—61no—
460C22×Dic3—64no—
461C22×Dic3—64no—
462C22×Dic3—64no—
463C22×Dic3—122no—
464C22×Dic3C22×D311yescharacteristic
465C22×Dic3C22×D311yescharacteristic
466C22×Dic3C22×D311yescharacteristic
467C22×Dic3C22×D311yescharacteristic
468#239—632no—
469#237—632no—
470D3×D4—632no—
471C2×D12—24no—
472C2×D12—24no—
473C2×D12—38no—
474C2×D12—34no—
475C2×D12—34no—
476C2×D12—64no—
477C2×D12C22×D314yes—
478C2×D12C22×D314yescomplemented
479C2×C4×D3—34no—
480C2×C4×D3—34no—
481C2×C4×D3—34no—
482C2×C4×D3—34no—
483C2×C4×D3—34no—
484C2×C4×D3—34no—
485C2×C4×D3—34no—
486C2×C4×D3—34no—
487C2×C4×D3—64no—
488C2×C4×D3—64no—
489C2×C4×D3—64no—
490C2×C4×D3—64no—
491C2×C4×D3—64no—
492C2×C4×D3—64no—
493C2×C4×D3—124no—
494C2×C4×D3—122no—
495C2×C4×D3—122no—
496C2×C4×D3—122no—
497C2×Dic6—24no—
498C2×Dic6C22×D314yescomplemented
499C3×C22⋊C4—24no—
500C3×C22⋊C4—34no—
501C3×C22⋊C4—34no—
502C3×C22⋊C4—34no—
503C3×C22⋊C4—34no—
504C3×C22⋊C4—34no—
505C3×C22⋊C4C22×D314yescomplemented
506C3×C22⋊C4C22×D314yescomplemented
507C3×C42—34no—
508#217—34no—
509#217—34no—
510#217—34no—
511#217—34no—
512#217—34no—
513#217—34no—
514#217—64no—
515#217C22×D314yescomplemented
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—64no—
523(C2×D3)⋊C4C22×D314yes—
524(C2×D3)⋊C4C22×D314yescomplemented
525(C2×D3)⋊C4C22×D314yescomplemented
526(C2×D3)⋊C4C22×D314yescomplemented
527C4⋊Dic3—34no—
528C4⋊Dic3—34no—
529C4⋊Dic3—34no—
530C4⋊Dic3—34no—
531C4⋊Dic3—64no—
532Dic3⋊C4—34no—
533Dic3⋊C4—34no—
534Dic3⋊C4—34no—
535Dic3⋊C4—34no—
536Dic3⋊C4—64no—
537C4×Dic3C22×D314yescomplemented
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—28no—
547C2×C3⋊D3—22no—
548C2×C3⋊D3—22no—
549C2×C3⋊D3C22×D414yes—
550C2×C3×D3—28no—
551C2×C3×D3—28no—
552C2×C3×D3—22no—
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×D3—44no—
565C2×C3×D3C22×D414yes—
566C2×C3×D3C2×#4114yescomplemented
567D32—416no—
568C32×C4—22no—
569C32×C4—22no—
570C3⋊Dic3—22no—
571C3⋊Dic3—22no—
572C3⋊Dic3—22no—
573C3×Dic3—22no—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3C22×D414yes—
577C25—31no—
578C25—91no—
579C2×#41—98no—
580C2×#41—188no—
581C22×Q8—31no—
582C22×D4—31no—
583C22×D4—31no—
584C22×D4—31no—
585C22×D4—31no—
586C22×D4—91no—
587C22×D4—91no—
588C22×D4—98no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—188no—
593C23×C4—91no—
594C23×C4—91no—
595C23×C4—91no—
596C23×C4—91no—
597C23×C4—91no—
598C23×C4—91no—
599#124—38no—
600#123—98no—
601#123—98no—
602C22⋊Q8—98no—
603#121—98no—
604#121—98no—
605#121—98no—
606#120—38no—
607#120—98no—
608C4×D4—98no—
609C4×D4—98no—
610C2×C4⋊C4—91no—
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—31no—
619C2×C22⋊C4—98no—
620C2×C22⋊C4—98no—
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—31no—
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—32no—
640C23×C3—32no—
641C23×C3—32no—
642C23×C3—32no—
643C23×C3—42no—
644C23×C3—42no—
645C23×C3—42no—
646C23×C3—68no—
647C23×C3—68no—
648C23×C3—62no—
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—22no—
674C22×D3—28no—
675C22×D3—28no—
676C22×D3—34no—
677C22×D3—34no—
678C22×D3—32no—
679C22×D3—32no—
680C22×D3—44no—
681C22×D3—416no—
682C22×D3—64no—
683C22×D3—62no—
684C22×D3—68no—
685C22×D3—68no—
686C22×D3—68no—
687C22×D3—62no—
688C22×D3—62no—
689C22×D3—62no—
690C22×D3—62no—
691C22×D3—68no—
692C22×D3—122no—
693C22×D3—122no—
694C22×D3—124no—
695C22×D3—124no—
696C22×D3—1216no—
697C22×D3—1216no—
698C22×D3D3×D414yes—
699C22×D3#23714yescomplemented
700C22×D3C23×D312yes—
701C22×D3C23×D312yes—
702C22×D3C23×D312yes—
703C22×D3C23×D312yes—
704C3×Q8—68no—
705C3×D4—68no—
706C3×D4—68no—
707C3×D4—68no—
708C3×D4—124no—
709C2×C3×C4—22no—
710C2×C3×C4—22no—
711C2×C3×C4—22no—
712C2×C3×C4—22no—
713C2×C3×C4—22no—
714C2×C3×C4—22no—
715C2×C3×C4—34no—
716C2×C3×C4—32no—
717C2×C3×C4—32no—
718C2×C3×C4—32no—
719C2×C3×C4—32no—
720C2×C3×C4—42no—
721C2×C3×C4—42no—
722C2×C3×C4—62no—
723C2×C3×C4—62no—
724C2×C3×C4—62no—
725C2×C3×C4C23×D312yes—
726C2×C3×C4C23×D312yes—
727C2×C3×C4C23×D312yes—
728C2×C3×C4C23×D312yes—
729#67—28no—
730#67—316no—
731#67—44no—
732#67—68no—
733#67—68no—
734#67—68no—
735#67—68no—
736#67—68no—
737#67—128no—
738#67—124no—
739#67—124no—
740C2×Dic3—22no—
741C2×Dic3—22no—
742C2×Dic3—22no—
743C2×Dic3—32no—
744C2×Dic3—32no—
745C2×Dic3—32no—
746C2×Dic3—32no—
747C2×Dic3—32no—
748C2×Dic3—32no—
749C2×Dic3—62no—
750C2×Dic3—62no—
751C2×Dic3—62no—
752C2×Dic3—68no—
753C2×Dic3—62no—
754C2×Dic3—62no—
755C2×Dic3—62no—
756C2×Dic3—62no—
757C2×Dic3—62no—
758C2×Dic3—62no—
759C2×Dic3—68no—
760C2×Dic3—68no—
761C2×Dic3—122no—
762C2×Dic3—122no—
763C2×Dic3—122no—
764C2×Dic3—124no—
765C2×Dic3D3×D414yes—
766C2×Dic3C23×D312yes—
767C2×Dic3C23×D312yes—
768C2×Dic3C23×D312yes—
769C2×Dic3C23×D312yes—
770D12—28no—
771D12—28no—
772D12—316no—
773D12—68no—
774C4×D3—68no—
775C4×D3—68no—
776C4×D3—68no—
777C4×D3—68no—
778C4×D3—68no—
779C4×D3—128no—
780C4×D3—124no—
781C4×D3—124no—
782C4×D3—124no—
783Dic6—28no—
784C2×C32—42no—
785C2×C32#54614yescomplemented
786C2×C32C23×D411yescharacteristic
787C2×C32C22×#4111yescharacteristic
788C2×C32C2×H(5,𝔽2)11yescharacteristic
789C3⋊D3—24no—
790C3×D3—24no—
791C3×D3—24no—
792C3×D3—42no—
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—34no—
810C2×Q8—64no—
811C2×D4—34no—
812C2×D4—34no—
813C2×D4—34no—
814C2×D4—34no—
815C2×D4—64no—
816C2×D4—64no—
817C2×D4—64no—
818C2×D4—94no—
819C2×D4—98no—
820C2×D4—94no—
821C2×D4—94no—
822C2×D4—94no—
823C2×D4—94no—
824C2×D4—122no—
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—94no—
835C22×C4—94no—
836C22×C4—94no—
837C22×C4—94no—
838C22×C4—94no—
839C22×C4—91no—
840C22×C4—91no—
841C22×C4—91no—
842C22×C4—94no—
843C22×C4—184no—
844C22×C4—184no—
845C22×C4—184no—
846C22×C4—184no—
847C22×C4—362no—
848C22×C4—362no—
849C22×C4C2×D3211yescharacteristic
850C22×C4C2×D3211yescharacteristic
851C4⋊C4—94no—
852C4⋊C4—94no—
853C4⋊C4—94no—
854C4⋊C4—94no—
855C22⋊C4—34no—
856C22⋊C4—34no—
857C22⋊C4—34no—
858C22⋊C4—34no—
859C22⋊C4—34no—
860C22⋊C4—94no—
861C22⋊C4—94no—
862C22⋊C4—94no—
863C22⋊C4—94no—
864C22⋊C4—94no—
865C22⋊C4—94no—
866C22⋊C4C2×D3214yescomplemented
867C42—34no—
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—42no—
881C22×C3—42no—
882C22×C3—42no—
883C22×C3—44no—
884C22×C3—44no—
885C22×C3—68no—
886C22×C3—68no—
887C22×C3—62no—
888C22×C3—62no—
889C22×C3—62no—
890C22×C3—62no—
891C22×C3—62no—
892C22×C3—62no—
893C22×C3—62no—
894C22×C3—62no—
895C22×C3—62no—
896C22×C3—62no—
897C22×C3—84no—
898C22×C3—1216no—
899C22×C3—124no—
900C22×C3—124no—
901C22×C3C2×D3×D412yes—
902C22×C3C2×D3×D412yes—
903C22×C3C2×#23712yes—
904C22×C3#100412yes—
905C22×C3D3×#4112yes—
906C22×C3#100912yes—
907C22×C3C24×D311yescharacteristic
908C22×C3C24×D311yescharacteristic
909C2×D3—22no—
910C2×D3—22no—
911C2×D3—22no—
912C2×D3—22no—
913C2×D3—28no—
914C2×D3—28no—
915C2×D3—22no—
916C2×D3—22no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—34no—
922C2×D3—34no—
923C2×D3—416no—
924C2×D3—44no—
925C2×D3—44no—
926C2×D3—64no—
927C2×D3—68no—
928C2×D3—62no—
929C2×D3—62no—
930C2×D3—62no—
931C2×D3—62no—
932C2×D3—68no—
933C2×D3—122no—
934C2×D3—122no—
935C2×D3—128no—
936C2×D3—1216no—
937C2×D3—1216no—
938C2×D3C2×D3×D414yes—
939C2×D3C2×#23714yescomplemented
940C3×C4—22no—
941C3×C4—22no—
942C3×C4—22no—
943C3×C4—22no—
944C3×C4—34no—
945C3×C4—42no—
946C3×C4—42no—
947C3×C4—62no—
948C3×C4—62no—
949C3×C4—62no—
950Dic3—22no—
951Dic3—22no—
952Dic3—22no—
953Dic3—62no—
954Dic3—62no—
955Dic3—62no—
956Dic3—62no—
957Dic3—62no—
958Dic3—62no—
959Dic3—122no—
960Dic3—122no—
961Dic3—122no—
962Dic3C2×D3×D414yes—
963C32C2×#54611yescharacteristic, complemented, Sylow
964C23—22no—
965C23—22no—
966C23—22no—
967C23—34no—
968C23—34no—
969C23—32no—
970C23—32no—
971C23—32no—
972C23—32no—
973C23—68no—
974C23—68no—
975C23—62no—
976C23—62no—
977C23—62no—
978C23—62no—
979C23—62no—
980C23—62no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—62no—
985C23—94no—
986C23—92no—
987C23—124no—
988C23—1216no—
989C23—188no—
990C23—188no—
991C23—182no—
992C23—182no—
993C23—364no—
994C23—3616no—
995C23C22×D3212yes—
996C23C22×D3211yescharacteristic
997Q8—68no—
998D4—68no—
999D4—68no—
1000D4—68no—
1001D4—916no—
1002D4—124no—
1003D4—188no—
1004D4—188no—
1005D4—188no—
1006D4—364no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—34no—
1010C2×C4—32no—
1011C2×C4—32no—
1012C2×C4—32no—
1013C2×C4—32no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—92no—
1018C2×C4—92no—
1019C2×C4—92no—
1020C2×C4—188no—
1021C2×C4—188no—
1022C2×C4—188no—
1023C2×C4—188no—
1024C2×C4—182no—
1025C2×C4—182no—
1026C2×C4—182no—
1027C2×C4—364no—
1028C2×C4—364no—
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—82no—
1040C2×C3—122no—
1041C2×C3—122no—
1042C2×C3#559114yescomplemented
1043C2×C3#567614yescomplemented
1044C2×C3C22×D3×D411yescharacteristic
1045C2×C3C22×D3×D411yescharacteristic
1046C2×C3C22×#23711yescharacteristic
1047C2×C3C2×#100411yescharacteristic
1048C2×C3C2×D3×#4111yescharacteristic
1049C2×C3C2×#100911yescharacteristic
1050D3—24no—
1051D3—24no—
1052D3—42no—
1053D3—42no—
1054D3—64no—
1055D3—64no—
1056D3—124no—
1057C22—22no—
1058C22—22no—
1059C22—22no—
1060C22—34no—
1061C22—34no—
1062C22—44no—
1063C22—62no—
1064C22—62no—
1065C22—62no—
1066C22—62no—
1067C22—68no—
1068C22—68no—
1069C22—62no—
1070C22—62no—
1071C22—62no—
1072C22—62no—
1073C22—62no—
1074C22—62no—
1075C22—94no—
1076C22—1216no—
1077C22—124no—
1078C22—124no—
1079C22—182no—
1080C22—182no—
1081C22—188no—
1082C22—3616no—
1083C22#6430712yes—
1084C22D32×D412yes—
1085C22D3×#23712yes—
1086C22C23×D3211yescharacteristic
1087C4—22no—
1088C4—22no—
1089C4—34no—
1090C4—62no—
1091C4—62no—
1092C4—62no—
1093C4—182no—
1094C4—182no—
1095C4—182no—
1096C3—21no—
1097C3C2×#559111yescharacteristic, complemented
1098C3C2×#567611yescharacteristic, complemented
1099C2—42no—
1100C2—64no—
1101C2—64no—
1102C2—122no—
1103C2—122no—
1104C2—184no—
1105C2#1059428114yesdirect product factor
1106C2C2×#6430711yescharacteristic
1107C2C2×D32×D411yescharacteristic
1108C2C2×D3×#23711yescharacteristic
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×#3796C2semidirect
3. C2×#64092C2semidirect
4. C2×C3×#885C2semidirect
5. C2×C3×#882C2semidirect
6. C2×#63970C2semidirect
7. C2×D3×#217C2semidirect
8. C2×#63958C2semidirect
9. C2×#63922C2semidirect
10. C2×#63921C2semidirect
11. C2×Dic3×D12C2semidirect
12. C2×#63891C2semidirect
13. C2×#63887C2semidirect
14. C2×#63885C2semidirect
15. C2×#63880C2semidirect
16. #10594281C2direct (N × H)
22. C22×C4×C3⋊D3C22semidirect
24. C22×C3×#67C22semidirect
26. C22×C3×D12C22semidirect
27. C22×C3×Dic6C22semidirect
29. C2×D3×#67C22semidirect
31. C22×#626C22semidirect
33. C22×#625C22semidirect
34. C22×#624C22semidirect
36. C22×D3×Dic3C22semidirect
37. C22×D3×Dic3C22semidirect
38. C22×D3×Dic3C22semidirect
40. C2×#3796C22semidirect
41. C2×C32×C22⋊C4C22semidirect
42. C2×#3757C22semidirect
43. C2×#3752C22semidirect
44. C2×C4⋊(C3⋊Dic3)C22semidirect
45. C2×#3750C22semidirect
46. #64092C22semidirect
47. C2×C3×#217C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×(C2×D3)⋊C4C22semidirect
52. C2×C3×C4×Dic3C22semidirect
53. C3×#885C22semidirect
54. C3×#882C22semidirect
55. #63970C22semidirect
56. D3×#217C22semidirect
57. C2×Dic3⋊Dic3C22semidirect
58. C2×Dic3⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. #63958C22semidirect
64. #63922C22semidirect
65. #63921C22semidirect
66. Dic3×D12C22semidirect
67. #63891C22semidirect
68. #63887C22semidirect
69. #63885C22semidirect
70. #63880C22semidirect
88. C2×#885D3semidirect
96. C2×#882D3semidirect
126. C2×C4×C3⋊D3C23semidirect
130. C2×C3×#67C23semidirect
138. C2×C3×D12C23semidirect
140. C2×C3×Dic6C23semidirect
143. C2×#626D4semidirect
145. C2×#626C23semidirect
149. C2×#625C23semidirect
151. C2×#624C23semidirect
157. C2×D3×Dic3C23semidirect
158. C2×D3×Dic3C23semidirect
159. C2×D3×Dic3C23semidirect
161. C32×C22⋊C4C23semidirect
162. #3757C23semidirect
163. #3752C23semidirect
164. C4⋊(C3⋊Dic3)C23semidirect
165. #3750C23semidirect
166. C3×#217C23semidirect
168. C3×(C2×D3)⋊C4C23semidirect
169. C3×(C2×D3)⋊C4C23semidirect
170. C3×(C2×D3)⋊C4C23semidirect
171. C3×C4×Dic3C23semidirect
172. Dic3⋊Dic3C23semidirect
173. Dic3⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
200. C22×#67C2×D3semidirect
214. C22×D12C2×D3semidirect
224. C22×Dic6C2×D3semidirect
233. C2×C3×C22⋊C4C2×D3semidirect
234. C2×C3×C22⋊C4C2×D3semidirect
244. C2×#217C2×D3semidirect
260. C2×(C2×D3)⋊C4C2×D3semidirect
261. C2×(C2×D3)⋊C4C2×D3semidirect
262. C2×(C2×D3)⋊C4C2×D3semidirect
273. C2×C4×Dic3C2×D3semidirect
275. #885C2×D3semidirect
283. #882C2×D3semidirect
315. C22×C3×D3#41semidirect
350. #626C2×D4semidirect
446. C2×#67C22×D3semidirect
478. C2×D12C22×D3semidirect
498. C2×Dic6C22×D3semidirect
505. C3×C22⋊C4C22×D3semidirect
506. C3×C22⋊C4C22×D3semidirect
515. #217C22×D3semidirect
524. (C2×D3)⋊C4C22×D3semidirect
525. (C2×D3)⋊C4C22×D3semidirect
526. (C2×D3)⋊C4C22×D3semidirect
537. C4×Dic3C22×D3semidirect
566. C2×C3×D3C2×#41semidirect
627. C2×C22⋊C4D32semidirect
699. C22×D3#237semidirect
785. C2×C32#546semidirect
866. C22⋊C4C2×D32semidirect
939. C2×D3C2×#237semidirect
963. C32C2×#546semidirect
1042. C2×C3#5591semidirect
1043. C2×C3#5676semidirect
1097. C3C2×#5591semidirect
1098. C3C2×#5676semidirect
1105. C2#10594281direct (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×#37962
C2×#640922
C2×C3×#8852
C2×C3×#8822
C2×#639702
C2×D3×#2172
C2×#639582
C2×#639222
C2×#639212
C2×Dic3×D122
C2×#638912
C2×#638872
C2×#638852
C2×#638802
#105942812
C2×#56763
C2×#55913