Finite Group Databasebeta

← C2×#10594282 #11902444

Subgroups — C2×#10594282 #11902444

Order 1152.

4131 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3811C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3C2×#64091C211yesmaximal, characteristic, complemented
4C2×C3×#885C211yesmaximal, characteristic, complemented
5C2×C3×#883C211yesmaximal, characteristic, complemented
6C2×#63974C211yesmaximal, characteristic, complemented
7C2×#63971C211yesmaximal, characteristic, complemented
8C2×#63958C211yesmaximal, characteristic, complemented
9C2×#63923C211yesmaximal, characteristic, complemented
10C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#63910C211yesmaximal, characteristic, complemented
12C2×#63894C211yesmaximal, characteristic, complemented
13C2×#63888C211yesmaximal, characteristic, complemented
14C2×#63880C211yesmaximal, characteristic, complemented
15C2×#63854C211yesmaximal, characteristic, complemented
16#10594282C2116yesmaximal, direct product factor
17C2×#5676—31nomaximal
18C2×#5654—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×#638C2211yescharacteristic, complemented
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×C3×Dic6C2211yescharacteristic, complemented
28C2×#3811—28no—
29C2×#3811C2218yescomplemented
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic, complemented
33C22×#626C2211yescharacteristic, complemented
34C22×#624C2211yescharacteristic
35C22×#624C2211yescharacteristic, complemented
36C22×#624C2211yescharacteristic, complemented
37C22×#624C2211yescharacteristic, complemented
38C22×D3×Dic3C2211yescharacteristic, complemented
39C2×#3799—28no—
40C2×#3799C2218yescomplemented
41C2×C32×C22⋊C4C2211yescharacteristic, complemented
42C2×#3752C2211yescharacteristic
43C2×#3752C2211yescharacteristic, complemented
44#64091C2218yescomplemented
45C2×C3×#217C2211yescharacteristic, complemented
46C2×C3×#217C2211yescharacteristic, complemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
51C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
52C2×C3×C4×Dic3C2211yescharacteristic, complemented
53C3×#885C2218yescomplemented
54C3×#883C2218yescomplemented
55#63974C2218yescomplemented
56#63971C2218yescomplemented
57C2×#3724C2211yescharacteristic, complemented
58C2×Dic3⋊Dic3C2211yescharacteristic, complemented
59C2×#3722C2211yescharacteristic
60C2×#3722C2211yescharacteristic
61C2×#3722C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63#63958C2218yescomplemented
64#63923C2218yescomplemented
65D3×(C2×D3)⋊C4C2218yescomplemented
66#63910C2218yescomplemented
67#63894C2218yescomplemented
68#63888C2218yescomplemented
69#63880C2218yescomplemented
70#63854C2218yescomplemented
71C22×#239—31no—
72C22×D3×D4—31no—
73C22×D3×D4—31no—
74C22×#235—31no—
75C2×C3×#124—31no—
76C2×C3×#123—31no—
77C2×#946—31no—
78C2×#939—31no—
79C2×#938—31no—
80C22×(C2×D3)⋊C4—31no—
81#5676—316no—
82#5654—316no—
83C2×#896—31no—
84C2×#895—31no—
85C2×#894—31no—
86C2×#893—31no—
87C2×#885D311yescharacteristic, complemented
88C2×#884—31no—
89C2×#884—31no—
90C2×#884—31no—
91C2×#883—31no—
92C2×#883D311yescharacteristic, complemented
93C2×#882—31no—
94C2×#882—31no—
95C2×#882—31no—
96C2×#882—31no—
97C2×#882—61no—
98C2×#67⋊C4—31no—
99C2×D3×C22⋊C4—31no—
100C2×D3×C22⋊C4—31no—
101C2×D3×C22⋊C4—31no—
102C2×C4×D12—31no—
103C2×C4×D12—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3—24no—
106C23×C3⋊D3—24no—
107C23×C3⋊D3—42no—
108C23×C3⋊D3C2311yescharacteristic
109C23×C3⋊D3C2314yes—
110C23×C3⋊D3C2311yescharacteristic
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—42no—
121C2×#638C2314yescomplemented
122C22×C3⋊Dic3C2311yescharacteristic
123C2×C4⋊(C3⋊D3)—24no—
124C2×C4⋊(C3⋊D3)—24no—
125C2×C4⋊(C3⋊D3)C2314yes—
126C2×C4⋊(C3⋊D3)C2314yescomplemented
127C2×C3×#67—24no—
128C2×C3×#67—24no—
129C2×C3×#67C2314yes—
130C2×C3×#67C2314yes—
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C2×C3×C4×D3—24no—
138C2×C3×C4×D3C2314yescomplemented
139C2×C3×Dic6—24no—
140C2×C3×Dic6C2314yescomplemented
141#3811—232no—
142C2×#626—24no—
143C2×#626—24no—
144C2×#626—42no—
145C2×#626D418yescomplemented
146C2×#626C2314yes—
147C2×#626C2314yes—
148C2×#626C2314yescomplemented
149C2×#626C2314yescomplemented
150C2×#624—24no—
151C2×#624—24no—
152C2×#624—24no—
153C2×#624—42no—
154C2×#624C2314yes—
155C2×#624C2314yescomplemented
156C2×#624C2314yescomplemented
157C2×#624C2314yescomplemented
158C2×D3×Dic3—42no—
159C2×D3×Dic3C2314yescomplemented
160#3799—232no—
161C32×C22⋊C4C2314yescomplemented
162#3752C2314yes—
163#3752C2314yescomplemented
164C3×#217C2314yescomplemented
165C3×#217C2314yescomplemented
166C3×(C2×D3)⋊C4C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×(C2×D3)⋊C4C2314yescomplemented
169C3×C4⋊Dic3C2314yescomplemented
170C3×Dic3⋊C4C2314yescomplemented
171C3×C4×Dic3C2314yescomplemented
172#3724C2314yescomplemented
173Dic3⋊Dic3C2314yescomplemented
174#3722C2314yes—
175#3722C2314yes—
176#3722C2314yescomplemented
177(C2×D3)⋊Dic3C2314yescomplemented
178C2×#546—91noSylow
179C24×D3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3—31no—
183C24×D3—61no—
184C22×C3×Q8—31no—
185C22×C3×D4—31no—
186C22×C3×D4—31no—
187C23×C3×C4—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—61no—
195C22×#67C2×D311yescharacteristic
196C22×#67C2×D311yescharacteristic
197C23×Dic3—31no—
198C2×#239—38no—
199C2×#239—68no—
200C2×D3×D4—38no—
201C2×D3×D4—38no—
202C2×D3×D4—68no—
203C2×D3×D4—68no—
204C2×#235—38no—
205C2×#235—68no—
206C22×D12—31no—
207C22×D12—31no—
208C22×D12—31no—
209C22×D12—31no—
210C22×D12—31no—
211C22×D12—31no—
212C22×D12—31no—
213C22×D12—31no—
214C22×D12—61no—
215C22×D12—61no—
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—31no—
224C22×C4×D3—31no—
225C22×C4×D3C2×D311yescharacteristic, complemented
226C22×Dic6C2×D311yescharacteristic, complemented
227C3×#124—38no—
228C3×#123—38no—
229C2×C3×C4⋊C4—31no—
230C2×C3×C4⋊C4—31no—
231C2×C3×C22⋊C4—21no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C22⋊C4—31no—
235C2×C3×C22⋊C4—31no—
236C2×C3×C22⋊C4—31no—
237C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
238C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
239C2×C3×C42—31no—
240C2×#217—31no—
241C2×#217C2×D311yescharacteristic, complemented
242C2×#217C2×D311yescharacteristic, complemented
243#946—38no—
244#939—38no—
245#938—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—31no—
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×C4⋊Dic3—31no—
264C2×C4⋊Dic3C2×D311yescharacteristic, complemented
265C2×Dic3⋊C4—31no—
266C2×Dic3⋊C4—31no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4C2×D311yescharacteristic, complemented
269C2×C4×Dic3C2×D311yescharacteristic, complemented
270#896—38no—
271#895—38no—
272#894—38no—
273#893—38no—
274#885C2×D318yescomplemented
275#884—38no—
276#884—38no—
277#884—38no—
278#883—38no—
279#883C2×D318yescomplemented
280#882—38no—
281#882—38no—
282#882—38no—
283#882—38no—
284#882—68no—
285#67⋊C4—38no—
286D3×C22⋊C4—38no—
287D3×C22⋊C4—38no—
288D3×C22⋊C4—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⋊D3—22no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3—22no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3—22no—
303C22×C3⋊D3—28no—
304C22×C3⋊D3—28no—
305C22×C3⋊D3—44no—
306C22×C3⋊D3—416no—
307C22×C3⋊D3C2×D414yes—
308C22×C3⋊D3#4114yescomplemented
309C22×C3⋊D3C2412yes—
310C22×C3⋊D3C2412yes—
311C22×C3⋊D3C2412yes—
312C22×C3×D3—22no—
313C22×C3×D3—22no—
314C22×C3×D3—22no—
315C22×C3×D3—22no—
316C22×C3×D3—22no—
317C22×C3×D3C2×D414yes—
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—44no—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3C2412yes—
331C4⋊(C3⋊D3)—28no—
332C4⋊(C3⋊D3)—28no—
333C3×#67—28no—
334C3×#67—28no—
335C2×C3×Dic3—22no—
336C2×C3×Dic3—22no—
337C2×C3×Dic3—22no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3C2×D414yes—
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C3×C4×D3—28no—
348C3×Dic6—28no—
349#626—28no—
350#626—28no—
351#626—44no—
352#626C2×D4116yescomplemented
353#624—28no—
354#624—28no—
355#624—28no—
356#624—44no—
357D3×Dic3—44no—
358C22×#41—91no—
359C23×D4—91no—
360#546—916no—
361C2×#124—31no—
362C2×#123—31no—
363C2×#123—91no—
364C2×C22⋊Q8—91no—
365C2×#121—91no—
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—21no—
375C24×C3—31no—
376C24×C3—31no—
377C24×C3C22×D311yescharacteristic
378C24×C3C22×D311yescharacteristic
379C23×D3—31no—
380C23×D3—31no—
381C23×D3—31no—
382C23×D3—31no—
383C23×D3—31no—
384C23×D3—31no—
385C23×D3—34no—
386C23×D3—34no—
387C23×D3—34no—
388C23×D3—34no—
389C23×D3—61no—
390C23×D3—61no—
391C23×D3—64no—
392C23×D3—61no—
393C23×D3—64no—
394C23×D3—64no—
395C23×D3—64no—
396C23×D3—64no—
397C23×D3—64no—
398C23×D3—64no—
399C23×D3—64no—
400C23×D3—64no—
401C23×D3—124no—
402C23×D3—124no—
403C23×D3—122no—
404C23×D3—122no—
405C23×D3—122no—
406C23×D3—122no—
407C23×D3—124no—
408C23×D3C22×D311yescharacteristic
409C23×D3C22×D311yescharacteristic
410C2×C3×Q8—34no—
411C2×C3×Q8—64no—
412C2×C3×D4—34no—
413C2×C3×D4—34no—
414C2×C3×D4—64no—
415C2×C3×D4—64no—
416C22×C3×C4—21no—
417C22×C3×C4—21no—
418C22×C3×C4—31no—
419C22×C3×C4—31no—
420C22×C3×C4—31no—
421C22×C3×C4—31no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—34no—
425C22×C3×C4—64no—
426C22×C3×C4C22×D311yescharacteristic
427C22×C3×C4C22×D311yescharacteristic
428C22×C3×C4C22×D311yescharacteristic
429C22×C3×C4C22×D311yescharacteristic
430C2×#67—24no—
431C2×#67—24no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—38no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—34no—
439C2×#67—64no—
440C2×#67—64no—
441C2×#67—64no—
442C2×#67—122no—
443C2×#67—122no—
444C2×#67—122no—
445C2×#67—124no—
446C2×#67C22×D314yes—
447C2×#67C22×D314yes—
448C22×Dic3—31no—
449C22×Dic3—31no—
450C22×Dic3—34no—
451C22×Dic3—61no—
452C22×Dic3—122no—
453C22×Dic3C22×D311yescharacteristic
454C22×Dic3C22×D311yescharacteristic
455C22×Dic3C22×D311yescharacteristic
456C22×Dic3C22×D311yescharacteristic
457C22×Dic3C22×D311yescharacteristic
458C22×Dic3C22×D311yescharacteristic
459#239—632no—
460D3×D4—632no—
461D3×D4—632no—
462#235—632no—
463C2×D12—38no—
464C2×D12—34no—
465C2×D12—34no—
466C2×D12—34no—
467C2×D12—34no—
468C2×D12—34no—
469C2×D12—34no—
470C2×D12—34no—
471C2×D12—34no—
472C2×D12—64no—
473C2×D12—64no—
474C2×D12—64no—
475C2×D12—64no—
476C2×D12—64no—
477C2×D12—64no—
478C2×D12—64no—
479C2×D12—64no—
480C2×D12—124no—
481C2×D12—124no—
482C2×D12—122no—
483C2×C4×D3—24no—
484C2×C4×D3—34no—
485C2×C4×D3—34no—
486C2×C4×D3—34no—
487C2×C4×D3—34no—
488C2×C4×D3—34no—
489C2×C4×D3—34no—
490C2×C4×D3—34no—
491C2×C4×D3—34no—
492C2×C4×D3—34no—
493C2×C4×D3—64no—
494C2×C4×D3—64no—
495C2×C4×D3—64no—
496C2×C4×D3—64no—
497C2×C4×D3—64no—
498C2×C4×D3—64no—
499C2×C4×D3—122no—
500C2×C4×D3—122no—
501C2×C4×D3—122no—
502C2×C4×D3C22×D314yescomplemented
503C2×Dic6—24no—
504C2×Dic6C22×D314yescomplemented
505C3×C4⋊C4—34no—
506C3×C4⋊C4—34no—
507C3×C22⋊C4—24no—
508C3×C22⋊C4—34no—
509C3×C22⋊C4—34no—
510C3×C22⋊C4—34no—
511C3×C22⋊C4—34no—
512C3×C22⋊C4—34no—
513C3×C22⋊C4C22×D314yescomplemented
514C3×C22⋊C4C22×D314yescomplemented
515C3×C42—34no—
516#217—34no—
517#217C22×D314yescomplemented
518#217C22×D314yescomplemented
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4—34no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—34no—
524(C2×D3)⋊C4—34no—
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—34no—
528(C2×D3)⋊C4—34no—
529(C2×D3)⋊C4—34no—
530(C2×D3)⋊C4—64no—
531(C2×D3)⋊C4—64no—
532(C2×D3)⋊C4C22×D314yescomplemented
533(C2×D3)⋊C4C22×D314yescomplemented
534(C2×D3)⋊C4C22×D314yescomplemented
535C4⋊Dic3—34no—
536C4⋊Dic3C22×D314yescomplemented
537Dic3⋊C4—34no—
538Dic3⋊C4—34no—
539Dic3⋊C4—34no—
540Dic3⋊C4C22×D314yescomplemented
541C4×Dic3C22×D314yescomplemented
542C22×C32—22no—
543C22×C32—22no—
544C22×C32—22no—
545C22×C32—44no—
546C22×C32C22×D412yes—
547C22×C32C2×#4112yes—
548C22×C32H(5,𝔽2)12yes—
549C22×C32C2511yescharacteristic
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—416no—
560C2×C3⋊D3—44no—
561C2×C3⋊D3C22×D414yes—
562C2×C3⋊D3C2×#4114yescomplemented
563C2×C3×D3—28no—
564C2×C3×D3—22no—
565C2×C3×D3—22no—
566C2×C3×D3—22no—
567C2×C3×D3—22no—
568C2×C3×D3—22no—
569C2×C3×D3—44no—
570C2×C3×D3C22×D414yes—
571D32—416no—
572C32×C4—22no—
573C32×C4—22no—
574C3⋊Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3—22no—
579C3×Dic3—22no—
580C3×Dic3C22×D414yes—
581C25—91no—
582C25—91no—
583C2×#41—98no—
584C2×#41—188no—
585C22×Q8—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—91no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—98no—
593C22×D4—91no—
594C22×D4—91no—
595C22×D4—91no—
596C22×D4—188no—
597C23×C4—31no—
598C23×C4—91no—
599C23×C4—91no—
600C23×C4—91no—
601C23×C4—91no—
602C23×C4—91no—
603#124—38no—
604#123—38no—
605#123—98no—
606C22⋊Q8—98no—
607#121—98no—
608#121—98no—
609#121—98no—
610#120—98no—
611#120—98no—
612C4×D4—98no—
613C4×D4—98no—
614C2×C4⋊C4—31no—
615C2×C4⋊C4—31no—
616C2×C4⋊C4—91no—
617C2×C4⋊C4—91no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—31no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
623C2×C22⋊C4—98no—
624C2×C22⋊C4—98no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4—91no—
628C2×C22⋊C4—91no—
629C2×C22⋊C4—91no—
630C2×C22⋊C4—91no—
631C2×C22⋊C4D3211yescharacteristic, complemented
632C2×C42—31no—
633C23×C3—24no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—22no—
639C23×C3—22no—
640C23×C3—22no—
641C23×C3—21no—
642C23×C3—34no—
643C23×C3—32no—
644C23×C3—32no—
645C23×C3—42no—
646C23×C3—42no—
647C23×C3—62no—
648C23×C3—62no—
649C23×C3—62no—
650C23×C3—62no—
651C23×C3—62no—
652C23×C3C23×D312yes—
653C23×C3C23×D312yes—
654C23×C3C23×D311yescharacteristic
655C23×C3C23×D311yescharacteristic
656C22×D3—22no—
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—34no—
662C22×D3—34no—
663C22×D3—34no—
664C22×D3—34no—
665C22×D3—32no—
666C22×D3—32no—
667C22×D3—32no—
668C22×D3—32no—
669C22×D3—32no—
670C22×D3—32no—
671C22×D3—64no—
672C22×D3—64no—
673C22×D3—62no—
674C22×D3—62no—
675C22×D3—62no—
676C22×D3—68no—
677C22×D3—68no—
678C22×D3—68no—
679C22×D3—68no—
680C22×D3—68no—
681C22×D3—68no—
682C22×D3—68no—
683C22×D3—62no—
684C22×D3—62no—
685C22×D3—62no—
686C22×D3—62no—
687C22×D3—62no—
688C22×D3—62no—
689C22×D3—62no—
690C22×D3—62no—
691C22×D3—62no—
692C22×D3—62no—
693C22×D3—62no—
694C22×D3—62no—
695C22×D3—62no—
696C22×D3—62no—
697C22×D3—68no—
698C22×D3—128no—
699C22×D3—128no—
700C22×D3—122no—
701C22×D3—122no—
702C22×D3—122no—
703C22×D3—122no—
704C22×D3—122no—
705C22×D3—122no—
706C22×D3—122no—
707C22×D3—124no—
708C22×D3—124no—
709C22×D3—1216no—
710C22×D3—1216no—
711C22×D3—124no—
712C22×D3—124no—
713C22×D3—1216no—
714C22×D3—1216no—
715C22×D3—128no—
716C22×D3—1232no—
717C22×D3D3×D414yes—
718C22×D3C23×D312yes—
719C22×D3C23×D312yes—
720C3×Q8—68no—
721C3×D4—68no—
722C3×D4—68no—
723C2×C3×C4—22no—
724C2×C3×C4—22no—
725C2×C3×C4—22no—
726C2×C3×C4—22no—
727C2×C3×C4—22no—
728C2×C3×C4—22no—
729C2×C3×C4—34no—
730C2×C3×C4—32no—
731C2×C3×C4—32no—
732C2×C3×C4—32no—
733C2×C3×C4—32no—
734C2×C3×C4—32no—
735C2×C3×C4—32no—
736C2×C3×C4—42no—
737C2×C3×C4—42no—
738C2×C3×C4—68no—
739C2×C3×C4—62no—
740C2×C3×C4—62no—
741C2×C3×C4—62no—
742C2×C3×C4—62no—
743C2×C3×C4—62no—
744C2×C3×C4C23×D312yes—
745C2×C3×C4C23×D312yes—
746C2×C3×C4C23×D312yes—
747C2×C3×C4C23×D312yes—
748#67—28no—
749#67—28no—
750#67—316no—
751#67—68no—
752#67—68no—
753#67—124no—
754#67—124no—
755#67—124no—
756#67—128no—
757C2×Dic3—22no—
758C2×Dic3—22no—
759C2×Dic3—22no—
760C2×Dic3—22no—
761C2×Dic3—22no—
762C2×Dic3—32no—
763C2×Dic3—32no—
764C2×Dic3—62no—
765C2×Dic3—62no—
766C2×Dic3—62no—
767C2×Dic3—122no—
768C2×Dic3—124no—
769C2×Dic3D3×D414yes—
770C2×Dic3C23×D312yes—
771C2×Dic3C23×D312yes—
772C2×Dic3C23×D312yes—
773C2×Dic3C23×D312yes—
774C2×Dic3C23×D312yes—
775C2×Dic3C23×D312yes—
776D12—316no—
777D12—68no—
778D12—68no—
779D12—68no—
780D12—68no—
781D12—68no—
782D12—68no—
783D12—128no—
784D12—128no—
785D12—124no—
786C4×D3—28no—
787C4×D3—68no—
788C4×D3—68no—
789C4×D3—68no—
790C4×D3—68no—
791C4×D3—68no—
792C4×D3—68no—
793C4×D3—124no—
794C4×D3—124no—
795C4×D3—124no—
796Dic6—28no—
797C2×C32—42no—
798C2×C32#54614yescomplemented
799C2×C32C23×D411yescharacteristic
800C2×C32C22×#4111yescharacteristic
801C2×C32C2×H(5,𝔽2)11yescharacteristic
802C3⋊D3—24no—
803C3⋊D3—24no—
804C3⋊D3—42no—
805C3×D3—24no—
806C3×D3—42no—
807C24—31no—
808C24—31no—
809C24—94no—
810C24—91no—
811C24—91no—
812C24—91no—
813C24—94no—
814C24—184no—
815C24—184no—
816C24—184no—
817C24—184no—
818C24—362no—
819C24—362no—
820C24C2×D3211yescharacteristic
821#41—1832no—
822C2×Q8—34no—
823C2×Q8—64no—
824C2×D4—34no—
825C2×D4—34no—
826C2×D4—64no—
827C2×D4—64no—
828C2×D4—94no—
829C2×D4—98no—
830C2×D4—94no—
831C2×D4—94no—
832C2×D4—94no—
833C2×D4—94no—
834C2×D4—94no—
835C2×D4—94no—
836C2×D4—184no—
837C2×D4—184no—
838C2×D4—184no—
839C2×D4—184no—
840C2×D4—1832no—
841C2×D4—362no—
842C2×D4—362no—
843C22×C4—31no—
844C22×C4—31no—
845C22×C4—31no—
846C22×C4—31no—
847C22×C4—31no—
848C22×C4—31no—
849C22×C4—34no—
850C22×C4—64no—
851C22×C4—94no—
852C22×C4—94no—
853C22×C4—94no—
854C22×C4—94no—
855C22×C4—94no—
856C22×C4—91no—
857C22×C4—184no—
858C22×C4—184no—
859C22×C4—184no—
860C22×C4—362no—
861C22×C4—362no—
862C22×C4C2×D3211yescharacteristic
863C22×C4C2×D3211yescharacteristic
864C4⋊C4—34no—
865C4⋊C4—34no—
866C4⋊C4—94no—
867C4⋊C4—94no—
868C22⋊C4—34no—
869C22⋊C4—34no—
870C22⋊C4—34no—
871C22⋊C4—34no—
872C22⋊C4—34no—
873C22⋊C4—94no—
874C22⋊C4—94no—
875C22⋊C4—94no—
876C22⋊C4—94no—
877C22⋊C4—94no—
878C22⋊C4—94no—
879C22⋊C4C2×D3214yescomplemented
880C42—34no—
881C22×C3—24no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—22no—
886C22×C3—22no—
887C22×C3—22no—
888C22×C3—22no—
889C22×C3—22no—
890C22×C3—22no—
891C22×C3—21no—
892C22×C3—34no—
893C22×C3—42no—
894C22×C3—42no—
895C22×C3—48no—
896C22×C3—44no—
897C22×C3—44no—
898C22×C3—68no—
899C22×C3—62no—
900C22×C3—62no—
901C22×C3—62no—
902C22×C3—62no—
903C22×C3—62no—
904C22×C3—124no—
905C22×C3C2×D3×D412yes—
906C22×C3C2×D3×D412yes—
907C22×C3D3×#4112yes—
908C22×C3D3×#4112yes—
909C22×C3#100912yes—
910C22×C3#100912yes—
911C22×C3C24×D311yescharacteristic
912C22×C3C24×D311yescharacteristic
913C2×D3—28no—
914C2×D3—22no—
915C2×D3—22no—
916C2×D3—22no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—34no—
920C2×D3—34no—
921C2×D3—34no—
922C2×D3—34no—
923C2×D3—44no—
924C2×D3—64no—
925C2×D3—64no—
926C2×D3—68no—
927C2×D3—68no—
928C2×D3—68no—
929C2×D3—68no—
930C2×D3—62no—
931C2×D3—62no—
932C2×D3—62no—
933C2×D3—62no—
934C2×D3—62no—
935C2×D3—62no—
936C2×D3—62no—
937C2×D3—62no—
938C2×D3—62no—
939C2×D3—62no—
940C2×D3—62no—
941C2×D3—62no—
942C2×D3—62no—
943C2×D3—62no—
944C2×D3—122no—
945C2×D3—122no—
946C2×D3—122no—
947C2×D3—122no—
948C2×D3—128no—
949C2×D3—128no—
950C2×D3—122no—
951C2×D3—122no—
952C2×D3—122no—
953C2×D3—1216no—
954C2×D3—1216no—
955C2×D3—1216no—
956C2×D3—1216no—
957C2×D3—1232no—
958C2×D3—124no—
959C2×D3—124no—
960C2×D3—244no—
961C2×D3C2×D3×D414yes—
962C3×C4—22no—
963C3×C4—22no—
964C3×C4—22no—
965C3×C4—22no—
966C3×C4—34no—
967C3×C4—42no—
968C3×C4—42no—
969C3×C4—62no—
970C3×C4—62no—
971C3×C4—62no—
972C3×C4—62no—
973C3×C4—62no—
974Dic3—22no—
975Dic3—22no—
976Dic3—22no—
977Dic3—22no—
978Dic3—22no—
979Dic3—62no—
980Dic3—62no—
981Dic3—122no—
982Dic3C2×D3×D414yes—
983C32C2×#54611yescharacteristic, complemented, Sylow
984C23—22no—
985C23—22no—
986C23—22no—
987C23—34no—
988C23—32no—
989C23—32no—
990C23—62no—
991C23—62no—
992C23—62no—
993C23—62no—
994C23—62no—
995C23—94no—
996C23—94no—
997C23—92no—
998C23—92no—
999C23—92no—
1000C23—188no—
1001C23—188no—
1002C23—188no—
1003C23—188no—
1004C23—182no—
1005C23—182no—
1006C23—182no—
1007C23—182no—
1008C23—182no—
1009C23—182no—
1010C23—182no—
1011C23—364no—
1012C23—3616no—
1013C23—364no—
1014C23—3616no—
1015C23C22×D3212yes—
1016C23C22×D3211yescharacteristic
1017Q8—68no—
1018D4—68no—
1019D4—68no—
1020D4—916no—
1021D4—188no—
1022D4—188no—
1023D4—188no—
1024D4—188no—
1025D4—364no—
1026D4—364no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—34no—
1030C2×C4—32no—
1031C2×C4—32no—
1032C2×C4—32no—
1033C2×C4—32no—
1034C2×C4—32no—
1035C2×C4—32no—
1036C2×C4—68no—
1037C2×C4—62no—
1038C2×C4—62no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—62no—
1042C2×C4—92no—
1043C2×C4—188no—
1044C2×C4—188no—
1045C2×C4—188no—
1046C2×C4—182no—
1047C2×C4—364no—
1048C2×C4—364no—
1049C2×C4C22×D3212yes—
1050C2×C4C22×D3212yes—
1051C2×C3—21no—
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—24no—
1055C2×C3—44no—
1056C2×C3—42no—
1057C2×C3—42no—
1058C2×C3—64no—
1059C2×C3—122no—
1060C2×C3#565414yescomplemented
1061C2×C3#567614yescomplemented
1062C2×C3C22×D3×D411yescharacteristic
1063C2×C3C22×D3×D411yescharacteristic
1064C2×C3C2×D3×#4111yescharacteristic
1065C2×C3C2×D3×#4111yescharacteristic
1066C2×C3C2×#100911yescharacteristic
1067C2×C3C2×#100911yescharacteristic
1068D3—24no—
1069D3—42no—
1070D3—64no—
1071D3—64no—
1072D3—64no—
1073D3—64no—
1074D3—124no—
1075D3—124no—
1076D3—122no—
1077D3—122no—
1078D3—242no—
1079C22—22no—
1080C22—22no—
1081C22—22no—
1082C22—34no—
1083C22—44no—
1084C22—62no—
1085C22—62no—
1086C22—68no—
1087C22—62no—
1088C22—62no—
1089C22—62no—
1090C22—94no—
1091C22—94no—
1092C22—124no—
1093C22—182no—
1094C22—182no—
1095C22—182no—
1096C22—182no—
1097C22—188no—
1098C22—188no—
1099C22—182no—
1100C22—182no—
1101C22—182no—
1102C22—3616no—
1103C22—3616no—
1104C22—364no—
1105C22#6430812yes—
1106C22D32×D412yes—
1107C22#6431212yes—
1108C22C23×D3211yescharacteristic
1109C4—22no—
1110C4—22no—
1111C4—34no—
1112C4—62no—
1113C4—62no—
1114C4—62no—
1115C4—62no—
1116C4—62no—
1117C4—182no—
1118C3—21no—
1119C3C2×#565411yescharacteristic, complemented
1120C3C2×#567611yescharacteristic, complemented
1121C2—42no—
1122C2—64no—
1123C2—122no—
1124C2—184no—
1125C2—184no—
1126C2—362no—
1127C2#1059428214yesdirect product factor
1128C2C2×#6430811yescharacteristic
1129C2C2×D32×D411yescharacteristic
1130C2C2×#6431211yescharacteristic
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×#3811C2semidirect
2. C22×#3799C2semidirect
3. C2×#64091C2semidirect
4. C2×C3×#885C2semidirect
5. C2×C3×#883C2semidirect
6. C2×#63974C2semidirect
7. C2×#63971C2semidirect
8. C2×#63958C2semidirect
9. C2×#63923C2semidirect
10. C2×D3×(C2×D3)⋊C4C2semidirect
11. C2×#63910C2semidirect
12. C2×#63894C2semidirect
13. C2×#63888C2semidirect
14. C2×#63880C2semidirect
15. C2×#63854C2semidirect
16. #10594282C2direct (N × H)
21. C22×#638C22semidirect
23. C22×C4⋊(C3⋊D3)C22semidirect
26. C22×C3×C4×D3C22semidirect
27. C22×C3×Dic6C22semidirect
29. C2×#3811C22semidirect
32. C22×#626C22semidirect
33. C22×#626C22semidirect
35. C22×#624C22semidirect
36. C22×#624C22semidirect
37. C22×#624C22semidirect
38. C22×D3×Dic3C22semidirect
40. C2×#3799C22semidirect
41. C2×C32×C22⋊C4C22semidirect
43. C2×#3752C22semidirect
44. #64091C22semidirect
45. C2×C3×#217C22semidirect
46. C2×C3×#217C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×C4⋊Dic3C22semidirect
51. C2×C3×Dic3⋊C4C22semidirect
52. C2×C3×C4×Dic3C22semidirect
53. C3×#885C22semidirect
54. C3×#883C22semidirect
55. #63974C22semidirect
56. #63971C22semidirect
57. C2×#3724C22semidirect
58. C2×Dic3⋊Dic3C22semidirect
61. C2×#3722C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. #63958C22semidirect
64. #63923C22semidirect
65. D3×(C2×D3)⋊C4C22semidirect
66. #63910C22semidirect
67. #63894C22semidirect
68. #63888C22semidirect
69. #63880C22semidirect
70. #63854C22semidirect
87. C2×#885D3semidirect
92. C2×#883D3semidirect
121. C2×#638C23semidirect
126. C2×C4⋊(C3⋊D3)C23semidirect
138. C2×C3×C4×D3C23semidirect
140. C2×C3×Dic6C23semidirect
145. C2×#626D4semidirect
148. C2×#626C23semidirect
149. C2×#626C23semidirect
155. C2×#624C23semidirect
156. C2×#624C23semidirect
157. C2×#624C23semidirect
159. C2×D3×Dic3C23semidirect
161. C32×C22⋊C4C23semidirect
163. #3752C23semidirect
164. C3×#217C23semidirect
165. C3×#217C23semidirect
166. C3×(C2×D3)⋊C4C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×(C2×D3)⋊C4C23semidirect
169. C3×C4⋊Dic3C23semidirect
170. C3×Dic3⋊C4C23semidirect
171. C3×C4×Dic3C23semidirect
172. #3724C23semidirect
173. Dic3⋊Dic3C23semidirect
176. #3722C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
225. C22×C4×D3C2×D3semidirect
226. C22×Dic6C2×D3semidirect
237. C2×C3×C22⋊C4C2×D3semidirect
238. C2×C3×C22⋊C4C2×D3semidirect
241. C2×#217C2×D3semidirect
242. C2×#217C2×D3semidirect
260. C2×(C2×D3)⋊C4C2×D3semidirect
261. C2×(C2×D3)⋊C4C2×D3semidirect
262. C2×(C2×D3)⋊C4C2×D3semidirect
264. C2×C4⋊Dic3C2×D3semidirect
268. C2×Dic3⋊C4C2×D3semidirect
269. C2×C4×Dic3C2×D3semidirect
274. #885C2×D3semidirect
279. #883C2×D3semidirect
308. C22×C3⋊D3#41semidirect
352. #626C2×D4semidirect
502. C2×C4×D3C22×D3semidirect
504. C2×Dic6C22×D3semidirect
513. C3×C22⋊C4C22×D3semidirect
514. C3×C22⋊C4C22×D3semidirect
517. #217C22×D3semidirect
518. #217C22×D3semidirect
532. (C2×D3)⋊C4C22×D3semidirect
533. (C2×D3)⋊C4C22×D3semidirect
534. (C2×D3)⋊C4C22×D3semidirect
536. C4⋊Dic3C22×D3semidirect
540. Dic3⋊C4C22×D3semidirect
541. C4×Dic3C22×D3semidirect
562. C2×C3⋊D3C2×#41semidirect
631. C2×C22⋊C4D32semidirect
798. C2×C32#546semidirect
879. C22⋊C4C2×D32semidirect
983. C32C2×#546semidirect
1060. C2×C3#5654semidirect
1061. C2×C3#5676semidirect
1119. C3C2×#5654semidirect
1120. C3C2×#5676semidirect
1127. C2#10594282direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38112
C22×#37992
C2×#640912
C2×C3×#8852
C2×C3×#8832
C2×#639742
C2×#639712
C2×#639582
C2×#639232
C2×D3×(C2×D3)⋊C42
C2×#639102
C2×#638942
C2×#638882
C2×#638802
C2×#638542
#105942822
C2×#56763
C2×#56543