Finite Group Databasebeta

← C2×#10594617 #11902471

Subgroups — C2×#10594617 #11902471

Order 1152.

3961 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3802C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64105C211yesmaximal, characteristic, complemented
4C2×C3×#895C211yesmaximal, characteristic, complemented
5C2×C3×#894C211yesmaximal, characteristic, complemented
6C2×#63922C211yesmaximal, characteristic, complemented
7C2×#63922C211yesmaximal, characteristic, complemented
8C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
9C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C2×#63913C211yesmaximal, characteristic, complemented
11C2×#63885C211yesmaximal, characteristic, complemented
12C2×#63885C211yesmaximal, characteristic, complemented
13C2×#63884C211yesmaximal, characteristic, complemented
14C2×#63881C211yesmaximal, characteristic, complemented
15C2×#63879C211yesmaximal, characteristic, complemented
16#10594617C2116yesmaximal, direct product factor
17C2×#5654—31nomaximal
18C2×#5610—31nomaximal
19C23×D32C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×#634C2211yescharacteristic, complemented
23C22×C3×D12C2211yescharacteristic
24C22×C3×D12C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic, complemented
26C22×C3×D12C2211yescharacteristic, complemented
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×C3×C4×D3C2211yescharacteristic, complemented
29C22×#626C2211yescharacteristic
30C22×#625C2211yescharacteristic
31C22×#625C2211yescharacteristic
32C22×#625C2211yescharacteristic, complemented
33C22×#625C2211yescharacteristic, complemented
34C22×D3×Dic3C2211yescharacteristic, complemented
35C22×D3×Dic3C2211yescharacteristic, complemented
36C22×D3×Dic3C2211yescharacteristic, complemented
37C2×#3802—28no—
38C2×#3802C2218yescomplemented
39C2×#3795—28no—
40C2×#3795C2218yescomplemented
41C2×C32×C4⋊C4C2211yescharacteristic, complemented
42C2×#3752C2211yescharacteristic
43C2×#3752C2211yescharacteristic
44C2×#3750C2211yescharacteristic, complemented
45C2×#3750C2211yescharacteristic, complemented
46#64105C2218yescomplemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
52C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
53C3×#895C2218yescomplemented
54C3×#894C2218yescomplemented
55C2×#3722C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×Dic32C2211yescharacteristic, complemented
61#63922C2218yescomplemented
62#63922C2218yescomplemented
63D3×(C2×D3)⋊C4C2218yescomplemented
64D3×(C2×D3)⋊C4C2218yescomplemented
65#63913C2218yescomplemented
66#63885C2218yescomplemented
67#63885C2218yescomplemented
68#63884C2218yescomplemented
69#63881C2218yescomplemented
70#63879C2218yescomplemented
71C22×#237—31no—
72C22×D3×D4—31no—
73C22×D3×D4—31no—
74C22×#235—31no—
75C2×C3×#123—31no—
76C2×C3×#121—31no—
77C2×#939—31no—
78C2×#939—31no—
79C2×#937—31no—
80C2×#937—31no—
81C2×#935—31no—
82C2×C4×#67—31no—
83C22×(C2×D3)⋊C4—31no—
84C22×(C2×D3)⋊C4—31no—
85#5654—316no—
86#5610—316no—
87C2×#896—31no—
88C2×#896—31no—
89C2×#896—61no—
90C2×#895D311yescharacteristic, complemented
91C2×#894—31no—
92C2×#894D311yescharacteristic, complemented
93C2×#893—31no—
94C2×#885—31no—
95C2×#885—31no—
96C2×#884—31no—
97C2×#884—31no—
98C2×#882—31no—
99C2×#882—31no—
100C2×#67⋊C4—31no—
101C2×#67⋊C4—31no—
102C2×D3×C22⋊C4—31no—
103C2×D3×C22⋊C4—31no—
104C23×C3⋊D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C22×D32—24no—
111C22×D32—24no—
112C22×D32—24no—
113C22×D32—24no—
114C22×D32—42no—
115C22×D32—42no—
116C22×D32C2314yes—
117C22×D32C2314yes—
118C22×C32×C4C2311yescharacteristic
119C22×C32×C4C2311yescharacteristic
120C22×C32×C4C2311yescharacteristic
121C22×C3⋊Dic3C2311yescharacteristic
122C22×C3⋊Dic3C2311yescharacteristic
123C22×C3⋊Dic3C2311yescharacteristic
124C2×C4×C3⋊D3—24no—
125C2×C4×C3⋊D3C2314yes—
126C2×#634—24no—
127C2×#634C2314yescomplemented
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C2×C3×D12—24no—
132C2×C3×D12—24no—
133C2×C3×D12—24no—
134C2×C3×D12—42no—
135C2×C3×D12C2314yes—
136C2×C3×D12C2314yes—
137C2×C3×D12C2314yescomplemented
138C2×C3×D12C2314yescomplemented
139C2×C3×C4×D3—24no—
140C2×C3×C4×D3—42no—
141C2×C3×C4×D3C2314yescomplemented
142C2×C3×C4×D3C2314yescomplemented
143C2×#626—24no—
144C2×#626C2314yes—
145C2×#625—24no—
146C2×#625—24no—
147C2×#625—42no—
148C2×#625D418yescomplemented
149C2×#625C2314yes—
150C2×#625C2314yes—
151C2×#625C2314yescomplemented
152C2×#625C2314yescomplemented
153C2×D3×Dic3—24no—
154C2×D3×Dic3—24no—
155C2×D3×Dic3—42no—
156C2×D3×Dic3C2314yescomplemented
157C2×D3×Dic3C2314yescomplemented
158C2×D3×Dic3C2314yescomplemented
159#3802—232no—
160#3795—232no—
161C32×C4⋊C4C2314yescomplemented
162#3752C2314yes—
163#3752C2314yes—
164#3750C2314yescomplemented
165#3750C2314yescomplemented
166C3×(C2×D3)⋊C4C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×(C2×D3)⋊C4C2314yescomplemented
169C3×(C2×D3)⋊C4C2314yescomplemented
170C3×(C2×D3)⋊C4C2314yescomplemented
171C3×Dic3⋊C4C2314yescomplemented
172#3722C2314yes—
173(C2×D3)⋊Dic3C2314yescomplemented
174(C2×D3)⋊Dic3C2314yescomplemented
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C24×D3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3—31no—
183C22×C3×D4—31no—
184C22×C3×D4—31no—
185C22×C3×D4—31no—
186C22×C3×D4—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—31no—
198C23×Dic3—31no—
199C23×Dic3—31no—
200C23×Dic3—31no—
201C2×#237—38no—
202C2×#237—68no—
203C2×D3×D4—38no—
204C2×D3×D4—38no—
205C2×D3×D4—68no—
206C2×D3×D4—68no—
207C2×#235—38no—
208C2×#235—68no—
209C22×D12—31no—
210C22×D12C2×D311yescharacteristic
211C22×D12C2×D311yescharacteristic
212C22×D12C2×D311yescharacteristic, complemented
213C22×D12C2×D311yescharacteristic, complemented
214C22×C4×D3—31no—
215C22×C4×D3—31no—
216C22×C4×D3—31no—
217C22×C4×D3—31no—
218C22×C4×D3—31no—
219C22×C4×D3—61no—
220C22×C4×D3C2×D311yescharacteristic, complemented
221C22×C4×D3C2×D311yescharacteristic, complemented
222C22×Dic6—31no—
223C22×Dic6—31no—
224C22×Dic6—61no—
225C3×#123—38no—
226C3×#121—38no—
227C2×C3×C4⋊C4—21no—
228C2×C3×C4⋊C4—31no—
229C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
230C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C22⋊C4—31no—
235C2×C3×C22⋊C4—31no—
236C2×#217—31no—
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—31no—
240#939—38no—
241#939—38no—
242#937—38no—
243#937—38no—
244#935—38no—
245C4×#67—38no—
246C2×(C2×D3)⋊C4—31no—
247C2×(C2×D3)⋊C4—31no—
248C2×(C2×D3)⋊C4—31no—
249C2×(C2×D3)⋊C4—31no—
250C2×(C2×D3)⋊C4—31no—
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—38no—
257C2×(C2×D3)⋊C4—38no—
258C2×(C2×D3)⋊C4—61no—
259C2×(C2×D3)⋊C4—61no—
260C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
261C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
262C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
263C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
264C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
265C2×Dic3⋊C4—31no—
266C2×Dic3⋊C4—31no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4—31no—
269C2×Dic3⋊C4—61no—
270C2×Dic3⋊C4—61no—
271C2×Dic3⋊C4C2×D311yescharacteristic, complemented
272C2×C4×Dic3—31no—
273C2×C4×Dic3—31no—
274#896—38no—
275#896—38no—
276#896—68no—
277#895C2×D318yescomplemented
278#894—38no—
279#894C2×D318yescomplemented
280#893—38no—
281#885—38no—
282#885—38no—
283#884—38no—
284#884—38no—
285#882—38no—
286#882—38no—
287#67⋊C4—38no—
288#67⋊C4—38no—
289D3×C22⋊C4—38no—
290D3×C22⋊C4—38no—
291C23×C32C2411yescharacteristic
292C22×C3⋊D3—22no—
293C22×C3⋊D3—22no—
294C22×C3⋊D3#4114yescomplemented
295C22×C3⋊D3C2412yes—
296C22×C3×D3—22no—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
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×D3C2×D414yes—
310C22×C3×D3C2×D414yes—
311C22×C3×D3C2412yes—
312C22×C3×D3C2412yes—
313C22×C3×D3C2412yes—
314C22×C3×D3C2412yes—
315C22×C3×D3C2412yes—
316C2×D32—28no—
317C2×D32—28no—
318C2×D32—28no—
319C2×D32—28no—
320C2×D32—44no—
321C2×D32—44no—
322C2×D32—416no—
323C2×D32—416no—
324C2×C32×C4—22no—
325C2×C32×C4—22no—
326C2×C32×C4—22no—
327C2×C32×C4C2412yes—
328C2×C32×C4C2412yes—
329C2×C32×C4C2412yes—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3—22no—
332C2×C3⋊Dic3C2×D414yes—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C4×C3⋊D3—28no—
337#634—28no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C3×D12—28no—
345C3×D12—28no—
346C3×D12—28no—
347C3×D12—44no—
348C3×C4×D3—28no—
349C3×C4×D3—44no—
350#626—28no—
351#625—28no—
352#625—28no—
353#625—44no—
354#625C2×D4116yescomplemented
355D3×Dic3—28no—
356D3×Dic3—28no—
357D3×Dic3—44no—
358C22×#41—91no—
359C23×D4—91no—
360#546—916no—
361C2×#124—91no—
362C2×#123—31no—
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—91no—
373C22×C22⋊C4—91no—
374C24×C3—31no—
375C24×C3—31no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3—31no—
379C23×D3—31no—
380C23×D3—31no—
381C23×D3—34no—
382C23×D3—34no—
383C23×D3—34no—
384C23×D3—34no—
385C23×D3—61no—
386C23×D3—64no—
387C23×D3—64no—
388C23×D3—64no—
389C23×D3—64no—
390C23×D3—64no—
391C23×D3—64no—
392C23×D3—64no—
393C23×D3—64no—
394C23×D3—122no—
395C23×D3—122no—
396C23×D3—122no—
397C23×D3—122no—
398C23×D3C22×D311yescharacteristic
399C23×D3C22×D311yescharacteristic
400C23×D3C22×D311yescharacteristic
401C23×D3C22×D311yescharacteristic
402C23×D3C22×D311yescharacteristic
403C2×C3×D4—34no—
404C2×C3×D4—34no—
405C2×C3×D4—34no—
406C2×C3×D4—34no—
407C2×C3×D4—64no—
408C2×C3×D4—64no—
409C2×C3×D4—64no—
410C2×C3×D4—122no—
411C22×C3×C4—21no—
412C22×C3×C4—21no—
413C22×C3×C4—21no—
414C22×C3×C4—31no—
415C22×C3×C4—31no—
416C22×C3×C4—31no—
417C22×C3×C4—34no—
418C22×C3×C4—34no—
419C22×C3×C4—64no—
420C22×C3×C4—122no—
421C22×C3×C4C22×D311yescharacteristic
422C22×C3×C4C22×D311yescharacteristic
423C22×C3×C4C22×D311yescharacteristic
424C22×C3×C4C22×D311yescharacteristic
425C22×C3×C4C22×D311yescharacteristic
426C22×C3×C4C22×D311yescharacteristic
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—64no—
439C2×#67—64no—
440C2×#67—64no—
441C2×#67—64no—
442C2×#67—64no—
443C2×#67—122no—
444C2×#67—122no—
445C22×Dic3—31no—
446C22×Dic3—31no—
447C22×Dic3—31no—
448C22×Dic3—31no—
449C22×Dic3—31no—
450C22×Dic3—31no—
451C22×Dic3—34no—
452C22×Dic3—34no—
453C22×Dic3—34no—
454C22×Dic3—61no—
455C22×Dic3—61no—
456C22×Dic3—61no—
457C22×Dic3—64no—
458C22×Dic3—64no—
459C22×Dic3—122no—
460C22×Dic3C22×D311yescharacteristic
461C22×Dic3C22×D311yescharacteristic
462C22×Dic3C22×D311yescharacteristic
463#237—632no—
464D3×D4—632no—
465D3×D4—632no—
466#235—632no—
467C2×D12—24no—
468C2×D12—24no—
469C2×D12—24no—
470C2×D12—34no—
471C2×D12—42no—
472C2×D12—64no—
473C2×D12C22×D314yes—
474C2×D12C22×D314yes—
475C2×D12C22×D314yescomplemented
476C2×D12C22×D314yescomplemented
477C2×C4×D3—24no—
478C2×C4×D3—34no—
479C2×C4×D3—34no—
480C2×C4×D3—34no—
481C2×C4×D3—34no—
482C2×C4×D3—34no—
483C2×C4×D3—42no—
484C2×C4×D3—64no—
485C2×C4×D3—64no—
486C2×C4×D3—64no—
487C2×C4×D3—64no—
488C2×C4×D3—64no—
489C2×C4×D3—124no—
490C2×C4×D3—122no—
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—24no—
500C3×C4⋊C4—34no—
501C3×C4⋊C4C22×D314yescomplemented
502C3×C4⋊C4C22×D314yescomplemented
503C3×C22⋊C4—34no—
504C3×C22⋊C4—34no—
505C3×C22⋊C4—34no—
506C3×C22⋊C4—34no—
507C3×C22⋊C4—34no—
508#217—34no—
509#217—34no—
510#217—34no—
511#217—34no—
512(C2×D3)⋊C4—34no—
513(C2×D3)⋊C4—34no—
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—64no—
523(C2×D3)⋊C4—64no—
524(C2×D3)⋊C4C22×D314yescomplemented
525(C2×D3)⋊C4C22×D314yescomplemented
526(C2×D3)⋊C4C22×D314yescomplemented
527(C2×D3)⋊C4C22×D314yescomplemented
528(C2×D3)⋊C4C22×D314yescomplemented
529Dic3⋊C4—34no—
530Dic3⋊C4—34no—
531Dic3⋊C4—34no—
532Dic3⋊C4—34no—
533Dic3⋊C4—64no—
534Dic3⋊C4—64no—
535Dic3⋊C4C22×D314yescomplemented
536C4×Dic3—34no—
537C4×Dic3—34no—
538C22×C32C22×D412yes—
539C22×C32C2×#4112yes—
540C22×C32H(5,𝔽2)12yes—
541C22×C32C2511yescharacteristic
542C2×C3⋊D3—28no—
543C2×C3⋊D3—22no—
544C2×C3⋊D3—22no—
545C2×C3⋊D3C2×#4114yescomplemented
546C2×C3×D3—28no—
547C2×C3×D3—28no—
548C2×C3×D3—22no—
549C2×C3×D3—22no—
550C2×C3×D3—22no—
551C2×C3×D3—22no—
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—44no—
562C2×C3×D3—44no—
563C2×C3×D3—44no—
564C2×C3×D3C22×D414yes—
565C2×C3×D3C22×D414yes—
566D32—416no—
567D32—416no—
568C32×C4—22no—
569C32×C4—22no—
570C32×C4—22no—
571C3⋊Dic3—22no—
572C3⋊Dic3—22no—
573C3⋊Dic3C22×D414yes—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C25—91no—
578C25—91no—
579C2×#41—98no—
580C2×#41—188no—
581C22×Q8—91no—
582C22×D4—31no—
583C22×D4—31no—
584C22×D4—31no—
585C22×D4—31no—
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—91no—
596C23×C4—91no—
597C23×C4—91no—
598C23×C4—91no—
599#124—98no—
600#123—38no—
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⋊C4D3211yescharacteristic, complemented
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⋊C4—91no—
628C2×C42—91no—
629C23×C3—21no—
630C23×C3—34no—
631C23×C3—34no—
632C23×C3—32no—
633C23×C3—32no—
634C23×C3—32no—
635C23×C3—32no—
636C23×C3—32no—
637C23×C3—62no—
638C23×C3—62no—
639C23×C3—62no—
640C23×C3—62no—
641C23×C3—62no—
642C23×C3—62no—
643C23×C3—62no—
644C23×C3—62no—
645C23×C3—62no—
646C23×C3—62no—
647C23×C3—62no—
648C23×C3—62no—
649C23×C3—62no—
650C23×C3C23×D311yescharacteristic
651C23×C3C23×D311yescharacteristic
652C22×D3—22no—
653C22×D3—22no—
654C22×D3—22no—
655C22×D3—22no—
656C22×D3—22no—
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—22no—
663C22×D3—22no—
664C22×D3—22no—
665C22×D3—34no—
666C22×D3—34no—
667C22×D3—32no—
668C22×D3—32no—
669C22×D3—64no—
670C22×D3—62no—
671C22×D3—68no—
672C22×D3—68no—
673C22×D3—68no—
674C22×D3—68no—
675C22×D3—68no—
676C22×D3—68no—
677C22×D3—62no—
678C22×D3—62no—
679C22×D3—62no—
680C22×D3—62no—
681C22×D3—68no—
682C22×D3—68no—
683C22×D3—122no—
684C22×D3—122no—
685C22×D3—124no—
686C22×D3—124no—
687C22×D3—124no—
688C22×D3—124no—
689C22×D3—1216no—
690C22×D3—1216no—
691C22×D3—1216no—
692C22×D3—1216no—
693C22×D3D3×D414yes—
694C22×D3D3×D414yes—
695C22×D3C23×D312yes—
696C22×D3C23×D312yes—
697C22×D3C23×D312yes—
698C22×D3C23×D312yes—
699C22×D3C23×D312yes—
700C3×D4—68no—
701C3×D4—68no—
702C3×D4—68no—
703C3×D4—124no—
704C2×C3×C4—22no—
705C2×C3×C4—22no—
706C2×C3×C4—22no—
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—42no—
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—124no—
724C2×C3×C4C23×D312yes—
725C2×C3×C4C23×D312yes—
726C2×C3×C4C23×D312yes—
727C2×C3×C4C23×D312yes—
728C2×C3×C4C23×D312yes—
729C2×C3×C4C23×D312yes—
730#67—316no—
731#67—316no—
732#67—68no—
733#67—68no—
734#67—68no—
735#67—68no—
736#67—68no—
737#67—124no—
738#67—124no—
739C2×Dic3—22no—
740C2×Dic3—22no—
741C2×Dic3—22no—
742C2×Dic3—34no—
743C2×Dic3—34no—
744C2×Dic3—32no—
745C2×Dic3—32no—
746C2×Dic3—32no—
747C2×Dic3—32no—
748C2×Dic3—32no—
749C2×Dic3—32no—
750C2×Dic3—64no—
751C2×Dic3—62no—
752C2×Dic3—62no—
753C2×Dic3—62no—
754C2×Dic3—68no—
755C2×Dic3—68no—
756C2×Dic3—62no—
757C2×Dic3—62no—
758C2×Dic3—62no—
759C2×Dic3—62no—
760C2×Dic3—122no—
761C2×Dic3—122no—
762C2×Dic3—124no—
763C2×Dic3C23×D312yes—
764C2×Dic3C23×D312yes—
765C2×Dic3C23×D312yes—
766D12—28no—
767D12—28no—
768D12—28no—
769D12—44no—
770D12—68no—
771C4×D3—28no—
772C4×D3—44no—
773C4×D3—68no—
774C4×D3—68no—
775C4×D3—68no—
776C4×D3—68no—
777C4×D3—128no—
778C4×D3—124no—
779Dic6—68no—
780Dic6—68no—
781Dic6—128no—
782C2×C32#54614yescomplemented
783C2×C32C23×D411yescharacteristic
784C2×C32C22×#4111yescharacteristic
785C2×C32C2×H(5,𝔽2)11yescharacteristic
786C3⋊D3—24no—
787C3×D3—24no—
788C3×D3—24no—
789C3×D3—42no—
790C3×D3—42no—
791C3×D3—42no—
792C24—31no—
793C24—31no—
794C24—31no—
795C24—31no—
796C24—31no—
797C24—94no—
798C24—94no—
799C24—91no—
800C24—184no—
801C24—184no—
802C24—184no—
803C24—184no—
804C24—362no—
805C24—362no—
806#41—1832no—
807C2×Q8—94no—
808C2×Q8—184no—
809C2×D4—34no—
810C2×D4—34no—
811C2×D4—34no—
812C2×D4—34no—
813C2×D4—64no—
814C2×D4—64no—
815C2×D4—64no—
816C2×D4—94no—
817C2×D4—94no—
818C2×D4—98no—
819C2×D4—94no—
820C2×D4—94no—
821C2×D4—94no—
822C2×D4—122no—
823C2×D4—184no—
824C2×D4—184no—
825C2×D4—1832no—
826C2×D4—184no—
827C2×D4—362no—
828C22×C4—31no—
829C22×C4—31no—
830C22×C4—31no—
831C22×C4—34no—
832C22×C4—34no—
833C22×C4—64no—
834C22×C4—94no—
835C22×C4—94no—
836C22×C4—94no—
837C22×C4—91no—
838C22×C4—91no—
839C22×C4—91no—
840C22×C4—94no—
841C22×C4—122no—
842C22×C4—184no—
843C22×C4—184no—
844C22×C4—184no—
845C22×C4—362no—
846C22×C4C2×D3211yescharacteristic
847C22×C4C2×D3211yescharacteristic
848C22×C4C2×D3211yescharacteristic
849C4⋊C4—34no—
850C4⋊C4—94no—
851C4⋊C4—94no—
852C4⋊C4C2×D3214yescomplemented
853C22⋊C4—34no—
854C22⋊C4—34no—
855C22⋊C4—34no—
856C22⋊C4—34no—
857C22⋊C4—34no—
858C22⋊C4—94no—
859C22⋊C4—94no—
860C22⋊C4—94no—
861C22⋊C4—94no—
862C22⋊C4—94no—
863C22⋊C4—94no—
864C22⋊C4—94no—
865C42—94no—
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—22no—
869C22×C3—21no—
870C22×C3—34no—
871C22×C3—34no—
872C22×C3—68no—
873C22×C3—62no—
874C22×C3—62no—
875C22×C3—62no—
876C22×C3—62no—
877C22×C3—68no—
878C22×C3—62no—
879C22×C3—62no—
880C22×C3—62no—
881C22×C3—62no—
882C22×C3—62no—
883C22×C3—62no—
884C22×C3—62no—
885C22×C3—62no—
886C22×C3—62no—
887C22×C3—124no—
888C22×C3—124no—
889C22×C3—124no—
890C22×C3C2×D3×D412yes—
891C22×C3C2×D3×D412yes—
892C22×C3#100412yes—
893C22×C3D3×#4112yes—
894C22×C3D3×#4112yes—
895C22×C3#100912yes—
896C22×C3C24×D311yescharacteristic
897C22×C3C24×D311yescharacteristic
898C2×D3—28no—
899C2×D3—22no—
900C2×D3—22no—
901C2×D3—22no—
902C2×D3—22no—
903C2×D3—28no—
904C2×D3—22no—
905C2×D3—22no—
906C2×D3—22no—
907C2×D3—22no—
908C2×D3—22no—
909C2×D3—22no—
910C2×D3—22no—
911C2×D3—22no—
912C2×D3—22no—
913C2×D3—34no—
914C2×D3—34no—
915C2×D3—44no—
916C2×D3—44no—
917C2×D3—44no—
918C2×D3—64no—
919C2×D3—68no—
920C2×D3—62no—
921C2×D3—62no—
922C2×D3—62no—
923C2×D3—62no—
924C2×D3—68no—
925C2×D3—122no—
926C2×D3—128no—
927C2×D3—122no—
928C2×D3—1216no—
929C2×D3—1216no—
930C2×D3—1216no—
931C2×D3—1216no—
932C2×D3C2×D3×D414yes—
933C2×D3C2×D3×D414yes—
934C3×C4—22no—
935C3×C4—22no—
936C3×C4—22no—
937C3×C4—22no—
938C3×C4—22no—
939C3×C4—22no—
940C3×C4—42no—
941C3×C4—42no—
942C3×C4—42no—
943C3×C4—62no—
944C3×C4—62no—
945C3×C4—62no—
946Dic3—22no—
947Dic3—22no—
948Dic3—22no—
949Dic3—34no—
950Dic3—34no—
951Dic3—64no—
952Dic3—62no—
953Dic3—62no—
954Dic3—62no—
955Dic3—62no—
956Dic3—122no—
957Dic3—122no—
958C32C2×#54611yescharacteristic, complemented, Sylow
959C23—34no—
960C23—34no—
961C23—32no—
962C23—32no—
963C23—32no—
964C23—32no—
965C23—32no—
966C23—62no—
967C23—62no—
968C23—62no—
969C23—62no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—62no—
974C23—62no—
975C23—62no—
976C23—62no—
977C23—62no—
978C23—62no—
979C23—94no—
980C23—92no—
981C23—188no—
982C23—188no—
983C23—188no—
984C23—188no—
985C23—182no—
986C23—182no—
987C23—364no—
988C23—364no—
989C23—3616no—
990C23—3616no—
991C23C22×D3211yescharacteristic
992Q8—188no—
993D4—68no—
994D4—68no—
995D4—68no—
996D4—916no—
997D4—124no—
998D4—188no—
999D4—188no—
1000D4—188no—
1001D4—364no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—32no—
1006C2×C4—32no—
1007C2×C4—32no—
1008C2×C4—68no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—62no—
1012C2×C4—94no—
1013C2×C4—92no—
1014C2×C4—92no—
1015C2×C4—92no—
1016C2×C4—124no—
1017C2×C4—188no—
1018C2×C4—188no—
1019C2×C4—188no—
1020C2×C4—182no—
1021C2×C4—182no—
1022C2×C4—364no—
1023C2×C4C22×D3212yes—
1024C2×C4C22×D3212yes—
1025C2×C4C22×D3212yes—
1026C2×C3—24no—
1027C2×C3—21no—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—64no—
1031C2×C3—64no—
1032C2×C3—122no—
1033C2×C3—122no—
1034C2×C3—122no—
1035C2×C3#561014yescomplemented
1036C2×C3#565414yescomplemented
1037C2×C3C22×D3×D411yescharacteristic
1038C2×C3C22×D3×D411yescharacteristic
1039C2×C3C2×#100411yescharacteristic
1040C2×C3C2×D3×#4111yescharacteristic
1041C2×C3C2×D3×#4111yescharacteristic
1042C2×C3C2×#100911yescharacteristic
1043D3—24no—
1044D3—24no—
1045D3—42no—
1046D3—42no—
1047D3—42no—
1048D3—64no—
1049D3—64no—
1050D3—124no—
1051C22—34no—
1052C22—34no—
1053C22—68no—
1054C22—68no—
1055C22—62no—
1056C22—62no—
1057C22—62no—
1058C22—62no—
1059C22—62no—
1060C22—62no—
1061C22—62no—
1062C22—62no—
1063C22—62no—
1064C22—62no—
1065C22—62no—
1066C22—62no—
1067C22—62no—
1068C22—94no—
1069C22—124no—
1070C22—124no—
1071C22—124no—
1072C22—188no—
1073C22—182no—
1074C22—182no—
1075C22—3616no—
1076C22—3616no—
1077C22#6430712yes—
1078C22D32×D412yes—
1079C22#6431912yes—
1080C22C23×D3211yescharacteristic
1081C4—22no—
1082C4—22no—
1083C4—22no—
1084C4—62no—
1085C4—62no—
1086C4—62no—
1087C4—94no—
1088C4—182no—
1089C4—182no—
1090C3—21no—
1091C3C2×#561011yescharacteristic, complemented
1092C3C2×#565411yescharacteristic, complemented
1093C2—64no—
1094C2—64no—
1095C2—122no—
1096C2—122no—
1097C2—122no—
1098C2—184no—
1099C2#1059461714yesdirect product factor
1100C2C2×#6430711yescharacteristic
1101C2C2×D32×D411yescharacteristic
1102C2C2×#6431911yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3802C2semidirect
2. C22×#3795C2semidirect
3. C2×#64105C2semidirect
4. C2×C3×#895C2semidirect
5. C2×C3×#894C2semidirect
6. C2×#63922C2semidirect
7. C2×#63922C2semidirect
8. C2×D3×(C2×D3)⋊C4C2semidirect
9. C2×D3×(C2×D3)⋊C4C2semidirect
10. C2×#63913C2semidirect
11. C2×#63885C2semidirect
12. C2×#63885C2semidirect
13. C2×#63884C2semidirect
14. C2×#63881C2semidirect
15. C2×#63879C2semidirect
16. #10594617C2direct (N × H)
22. C22×#634C22semidirect
25. C22×C3×D12C22semidirect
26. C22×C3×D12C22semidirect
27. C22×C3×C4×D3C22semidirect
28. C22×C3×C4×D3C22semidirect
32. C22×#625C22semidirect
33. C22×#625C22semidirect
34. C22×D3×Dic3C22semidirect
35. C22×D3×Dic3C22semidirect
36. C22×D3×Dic3C22semidirect
38. C2×#3802C22semidirect
40. C2×#3795C22semidirect
41. C2×C32×C4⋊C4C22semidirect
44. C2×#3750C22semidirect
45. C2×#3750C22semidirect
46. #64105C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×(C2×D3)⋊C4C22semidirect
52. C2×C3×Dic3⋊C4C22semidirect
53. C3×#895C22semidirect
54. C3×#894C22semidirect
56. C2×(C2×D3)⋊Dic3C22semidirect
57. C2×(C2×D3)⋊Dic3C22semidirect
58. C2×(C2×D3)⋊Dic3C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×Dic32C22semidirect
61. #63922C22semidirect
62. #63922C22semidirect
63. D3×(C2×D3)⋊C4C22semidirect
64. D3×(C2×D3)⋊C4C22semidirect
65. #63913C22semidirect
66. #63885C22semidirect
67. #63885C22semidirect
68. #63884C22semidirect
69. #63881C22semidirect
70. #63879C22semidirect
90. C2×#895D3semidirect
92. C2×#894D3semidirect
127. C2×#634C23semidirect
137. C2×C3×D12C23semidirect
138. C2×C3×D12C23semidirect
141. C2×C3×C4×D3C23semidirect
142. C2×C3×C4×D3C23semidirect
148. C2×#625D4semidirect
151. C2×#625C23semidirect
152. C2×#625C23semidirect
156. C2×D3×Dic3C23semidirect
157. C2×D3×Dic3C23semidirect
158. C2×D3×Dic3C23semidirect
161. C32×C4⋊C4C23semidirect
164. #3750C23semidirect
165. #3750C23semidirect
166. C3×(C2×D3)⋊C4C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×(C2×D3)⋊C4C23semidirect
169. C3×(C2×D3)⋊C4C23semidirect
170. C3×(C2×D3)⋊C4C23semidirect
171. C3×Dic3⋊C4C23semidirect
173. (C2×D3)⋊Dic3C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
212. C22×D12C2×D3semidirect
213. C22×D12C2×D3semidirect
220. C22×C4×D3C2×D3semidirect
221. C22×C4×D3C2×D3semidirect
229. C2×C3×C4⋊C4C2×D3semidirect
230. C2×C3×C4⋊C4C2×D3semidirect
260. C2×(C2×D3)⋊C4C2×D3semidirect
261. C2×(C2×D3)⋊C4C2×D3semidirect
262. C2×(C2×D3)⋊C4C2×D3semidirect
263. C2×(C2×D3)⋊C4C2×D3semidirect
264. C2×(C2×D3)⋊C4C2×D3semidirect
271. C2×Dic3⋊C4C2×D3semidirect
277. #895C2×D3semidirect
279. #894C2×D3semidirect
294. C22×C3⋊D3#41semidirect
354. #625C2×D4semidirect
475. C2×D12C22×D3semidirect
476. C2×D12C22×D3semidirect
491. C2×C4×D3C22×D3semidirect
492. C2×C4×D3C22×D3semidirect
501. C3×C4⋊C4C22×D3semidirect
502. C3×C4⋊C4C22×D3semidirect
524. (C2×D3)⋊C4C22×D3semidirect
525. (C2×D3)⋊C4C22×D3semidirect
526. (C2×D3)⋊C4C22×D3semidirect
527. (C2×D3)⋊C4C22×D3semidirect
528. (C2×D3)⋊C4C22×D3semidirect
535. Dic3⋊C4C22×D3semidirect
545. C2×C3⋊D3C2×#41semidirect
613. C2×C4⋊C4D32semidirect
782. C2×C32#546semidirect
852. C4⋊C4C2×D32semidirect
958. C32C2×#546semidirect
1035. C2×C3#5610semidirect
1036. C2×C3#5654semidirect
1091. C3C2×#5610semidirect
1092. C3C2×#5654semidirect
1099. C2#10594617direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38022
C22×#37952
C2×#641052
C2×C3×#8952
C2×C3×#8942
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639132
C2×#638852
C2×#638842
C2×#638812
C2×#638792
#105946172
C2×#56543
C2×#56103