Finite Group Databasebeta

← C2×#10594620 #11902473

Subgroups — C2×#10594620 #11902473

Order 1152.

4013 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×D12C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3C2×#64104C211yesmaximal, characteristic, complemented
4C2×C3×#896C211yesmaximal, characteristic, complemented
5C2×C3×#894C211yesmaximal, characteristic, complemented
6C2×#63923C211yesmaximal, characteristic, complemented
7C2×#63923C211yesmaximal, characteristic, complemented
8C2×#63921C211yesmaximal, characteristic, complemented
9C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C2×#63910C211yesmaximal, characteristic, complemented
11C2×#63907C211yesmaximal, characteristic, complemented
12C2×#63904C211yesmaximal, characteristic, complemented
13C2×#63897C211yesmaximal, characteristic, complemented
14C2×#63886C211yesmaximal, characteristic, complemented
15C2×#63881C211yesmaximal, characteristic, complemented
16#10594620C2116yesmaximal, direct product factor
17C2×#5654—31nomaximal
18C2×#5630—31nomaximal
19C23×D32C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C22×C4×C3⋊D3C2211yescharacteristic, complemented
25C22×C3×D12C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×C3×Dic6C2211yescharacteristic, complemented
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic, complemented
33C22×#626C2211yescharacteristic, complemented
34C22×#624C2211yescharacteristic, complemented
35C22×#624C2211yescharacteristic, complemented
36C22×D3×Dic3C2211yescharacteristic, complemented
37C2×D3×D12—28no—
38C2×D3×D12C2218yescomplemented
39C2×#3799—28no—
40C2×#3799C2218yescomplemented
41C2×C32×C4⋊C4C2211yescharacteristic, complemented
42C2×#3752C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic, complemented
44#64104C2218yescomplemented
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
51C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
52C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
53C3×#896C2218yescomplemented
54C3×#894C2218yescomplemented
55C2×#3722C2211yescharacteristic, complemented
56C2×#3722C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×Dic32C2211yescharacteristic, complemented
61#63923C2218yescomplemented
62#63923C2218yescomplemented
63#63921C2218yescomplemented
64D3×(C2×D3)⋊C4C2218yescomplemented
65#63910C2218yescomplemented
66#63907C2218yescomplemented
67#63904C2218yescomplemented
68#63897C2218yescomplemented
69#63886C2218yescomplemented
70#63881C2218yescomplemented
71C22×#239—31no—
72C22×D3×D4—31no—
73C22×#235—31no—
74C23×D12—31no—
75C2×C3×#123—31no—
76C2×C3×C22⋊Q8—31no—
77C2×#947—31no—
78C2×#939—31no—
79C2×C4×#67—31no—
80C22×(C2×D3)⋊C4—31no—
81#5654—316no—
82#5630—316no—
83C2×#896D311yescharacteristic, complemented
84C2×#895—31no—
85C2×#895—31no—
86C2×#895—31no—
87C2×#895—31no—
88C2×#895—61no—
89C2×#894—31no—
90C2×#894—31no—
91C2×#894D311yescharacteristic, complemented
92C2×#893—31no—
93C2×#893—31no—
94C2×#885—31no—
95C2×#884—31no—
96C2×#882—31no—
97C2×#882—31no—
98C2×#882—31no—
99C2×#882—31no—
100C2×#67⋊C4—31no—
101C2×D3×C22⋊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
122C2×C4⋊(C3⋊D3)—24no—
123C2×C4⋊(C3⋊D3)—24no—
124C2×C4⋊(C3⋊D3)—42no—
125C2×C4⋊(C3⋊D3)C2314yes—
126C2×C4⋊(C3⋊D3)C2314yescomplemented
127C2×C4⋊(C3⋊D3)C2314yescomplemented
128C2×C4×C3⋊D3—42no—
129C2×C4×C3⋊D3C2314yescomplemented
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C2×C3×D12—24no—
136C2×C3×D12C2314yes—
137C2×C3×C4×D3—24no—
138C2×C3×C4×D3—24no—
139C2×C3×C4×D3C2314yes—
140C2×C3×C4×D3C2314yescomplemented
141C2×C3×Dic6—24no—
142C2×C3×Dic6C2314yescomplemented
143C2×#626—24no—
144C2×#626—24no—
145C2×#626—24no—
146C2×#626—42no—
147C2×#626D418yescomplemented
148C2×#626C2314yes—
149C2×#626C2314yes—
150C2×#626C2314yes—
151C2×#626C2314yescomplemented
152C2×#626C2314yescomplemented
153C2×#624—24no—
154C2×#624—24no—
155C2×#624C2314yescomplemented
156C2×#624C2314yescomplemented
157C2×D3×Dic3—42no—
158C2×D3×Dic3C2314yescomplemented
159D3×D12—232no—
160#3799—232no—
161C32×C4⋊C4C2314yescomplemented
162#3752C2314yescomplemented
163#3752C2314yescomplemented
164C3×(C2×D3)⋊C4C2314yes—
165C3×(C2×D3)⋊C4C2314yes—
166C3×(C2×D3)⋊C4C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×(C2×D3)⋊C4C2314yescomplemented
169C3×Dic3⋊C4C2314yescomplemented
170C3×Dic3⋊C4C2314yescomplemented
171C3×Dic3⋊C4C2314yescomplemented
172#3722C2314yescomplemented
173#3722C2314yescomplemented
174#3722C2314yescomplemented
175(C2×D3)⋊Dic3C2314yes—
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C24×D3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3—31no—
183C22×C3×Q8—31no—
184C22×C3×D4—31no—
185C23×C3×C4—31no—
186C23×C3×C4—31no—
187C22×#67—31no—
188C22×#67—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C23×Dic3—31no—
193C2×#239—38no—
194C2×#239—68no—
195C2×D3×D4—38no—
196C2×D3×D4—68no—
197C2×#235—38no—
198C2×#235—68no—
199C22×D12—31no—
200C22×D12—31no—
201C22×D12—31no—
202C22×D12—31no—
203C22×D12—31no—
204C22×D12—31no—
205C22×D12—31no—
206C22×D12—31no—
207C22×D12—31no—
208C22×D12—31no—
209C22×D12—31no—
210C22×D12—38no—
211C22×D12—61no—
212C22×D12—61no—
213C22×D12—61no—
214C22×D12—68no—
215C22×D12C2×D311yescharacteristic
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×C4×D3C2×D311yescharacteristic
225C22×C4×D3C2×D311yescharacteristic, complemented
226C22×Dic6C2×D311yescharacteristic, complemented
227C3×#123—38no—
228C3×C22⋊Q8—38no—
229C2×C3×C4⋊C4—21no—
230C2×C3×C4⋊C4—31no—
231C2×C3×C4⋊C4—31no—
232C2×C3×C4⋊C4—31no—
233C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
234C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
235C2×C3×C22⋊C4—31no—
236C2×C3×C22⋊C4—31no—
237C2×C3×C22⋊C4—31no—
238C2×C3×C22⋊C4—31no—
239C2×C3×C22⋊C4—31no—
240C2×#217—31no—
241C2×#217—31no—
242#947—38no—
243#939—38no—
244C4×#67—38no—
245C2×(C2×D3)⋊C4—31no—
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
261C2×(C2×D3)⋊C4C2×D311yescharacteristic
262C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
263C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
264C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
265C2×Dic3⋊C4C2×D311yescharacteristic, complemented
266C2×Dic3⋊C4C2×D311yescharacteristic, complemented
267C2×Dic3⋊C4C2×D311yescharacteristic, complemented
268C2×C4×Dic3—31no—
269C2×C4×Dic3—31no—
270#896C2×D318yescomplemented
271#895—38no—
272#895—38no—
273#895—38no—
274#895—38no—
275#895—68no—
276#894—38no—
277#894—38no—
278#894C2×D318yescomplemented
279#893—38no—
280#893—38no—
281#885—38no—
282#884—38no—
283#882—38no—
284#882—38no—
285#882—38no—
286#882—38no—
287#67⋊C4—38no—
288D3×C22⋊C4—38no—
289D3×C22⋊C4—38no—
290D3×C22⋊C4—38no—
291C23×C32C2411yescharacteristic
292C22×C3⋊D3—22no—
293C22×C3⋊D3—22no—
294C22×C3⋊D3—22no—
295C22×C3⋊D3—22no—
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3C2×D414yes—
301C22×C3⋊D3C2412yes—
302C22×C3⋊D3C2412yes—
303C22×C3⋊D3C2412yes—
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—22no—
311C22×C3×D3C2×D414yes—
312C22×C3×D3#4114yescomplemented
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⋊Dic3C2412yes—
332C4⋊(C3⋊D3)—28no—
333C4⋊(C3⋊D3)—28no—
334C4⋊(C3⋊D3)—44no—
335C4×C3⋊D3—44no—
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—
346C3×D12—28no—
347C3×C4×D3—28no—
348C3×C4×D3—28no—
349C3×Dic6—28no—
350#626—28no—
351#626—28no—
352#626—28no—
353#626—44no—
354#626C2×D4116yescomplemented
355#624—28no—
356#624—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—31no—
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—31no—
375C24×C3—31no—
376C24×C3—31no—
377C23×D3—31no—
378C23×D3—31no—
379C23×D3—31no—
380C23×D3—31no—
381C23×D3—31no—
382C23×D3—31no—
383C23×D3—34no—
384C23×D3—34no—
385C23×D3—34no—
386C23×D3—34no—
387C23×D3—61no—
388C23×D3—61no—
389C23×D3—61no—
390C23×D3—64no—
391C23×D3—64no—
392C23×D3—64no—
393C23×D3—64no—
394C23×D3—64no—
395C23×D3—64no—
396C23×D3—64no—
397C23×D3—64no—
398C23×D3—122no—
399C23×D3—122no—
400C23×D3—122no—
401C23×D3—122no—
402C23×D3C22×D311yescharacteristic
403C23×D3C22×D311yescharacteristic
404C23×D3C22×D311yescharacteristic
405C2×C3×Q8—34no—
406C2×C3×Q8—64no—
407C2×C3×D4—34no—
408C2×C3×D4—64no—
409C22×C3×C4—21no—
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—31no—
417C22×C3×C4—34no—
418C22×C3×C4—34no—
419C22×C3×C4—64no—
420C22×C3×C4—64no—
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—34no—
429C2×#67—34no—
430C2×#67—34no—
431C2×#67—34no—
432C2×#67—34no—
433C2×#67—64no—
434C2×#67—64no—
435C2×#67—64no—
436C2×#67—122no—
437C22×Dic3—31no—
438C22×Dic3—31no—
439C22×Dic3—34no—
440C22×Dic3—61no—
441C22×Dic3—122no—
442C22×Dic3C22×D311yescharacteristic
443C22×Dic3C22×D311yescharacteristic
444C22×Dic3C22×D311yescharacteristic
445C22×Dic3C22×D311yescharacteristic
446C22×Dic3C22×D311yescharacteristic
447#239—632no—
448D3×D4—632no—
449#235—632no—
450C2×D12—24no—
451C2×D12—38no—
452C2×D12—34no—
453C2×D12—34no—
454C2×D12—34no—
455C2×D12—34no—
456C2×D12—34no—
457C2×D12—34no—
458C2×D12—34no—
459C2×D12—34no—
460C2×D12—34no—
461C2×D12—34no—
462C2×D12—34no—
463C2×D12—64no—
464C2×D12—64no—
465C2×D12—64no—
466C2×D12—632no—
467C2×D12—64no—
468C2×D12—64no—
469C2×D12—64no—
470C2×D12—64no—
471C2×D12—64no—
472C2×D12—64no—
473C2×D12—64no—
474C2×D12—124no—
475C2×D12—124no—
476C2×D12—122no—
477C2×D12—122no—
478C2×D12—124no—
479C2×D12—122no—
480C2×D12C22×D314yes—
481C2×C4×D3—24no—
482C2×C4×D3—24no—
483C2×C4×D3—34no—
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—64no—
491C2×C4×D3—64no—
492C2×C4×D3—64no—
493C2×C4×D3—64no—
494C2×C4×D3—64no—
495C2×C4×D3—122no—
496C2×C4×D3—122no—
497C2×C4×D3—122no—
498C2×C4×D3—124no—
499C2×C4×D3C22×D314yes—
500C2×C4×D3C22×D314yescomplemented
501C2×Dic6—24no—
502C2×Dic6C22×D314yescomplemented
503C3×C4⋊C4—24no—
504C3×C4⋊C4—34no—
505C3×C4⋊C4—34no—
506C3×C4⋊C4—34no—
507C3×C4⋊C4C22×D314yescomplemented
508C3×C4⋊C4C22×D314yescomplemented
509C3×C22⋊C4—34no—
510C3×C22⋊C4—34no—
511C3×C22⋊C4—34no—
512C3×C22⋊C4—34no—
513C3×C22⋊C4—34no—
514#217—34no—
515#217—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—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—64no—
529(C2×D3)⋊C4—64no—
530(C2×D3)⋊C4C22×D314yes—
531(C2×D3)⋊C4C22×D314yes—
532(C2×D3)⋊C4C22×D314yescomplemented
533(C2×D3)⋊C4C22×D314yescomplemented
534(C2×D3)⋊C4C22×D314yescomplemented
535Dic3⋊C4C22×D314yescomplemented
536Dic3⋊C4C22×D314yescomplemented
537Dic3⋊C4C22×D314yescomplemented
538C4×Dic3—34no—
539C4×Dic3—34no—
540C22×C32C22×D412yes—
541C22×C32C2×#4112yes—
542C22×C32H(5,𝔽2)12yes—
543C22×C32C2511yescharacteristic
544C2×C3⋊D3—28no—
545C2×C3⋊D3—22no—
546C2×C3⋊D3—22no—
547C2×C3⋊D3—22no—
548C2×C3⋊D3—22no—
549C2×C3⋊D3—22no—
550C2×C3⋊D3—22no—
551C2×C3⋊D3—22no—
552C2×C3⋊D3—22no—
553C2×C3⋊D3—44no—
554C2×C3⋊D3—44no—
555C2×C3⋊D3C22×D414yes—
556C2×C3×D3—28no—
557C2×C3×D3—28no—
558C2×C3×D3—22no—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—22no—
563C2×C3×D3—22no—
564C2×C3×D3—22no—
565C2×C3×D3—44no—
566C2×C3×D3C22×D414yes—
567C2×C3×D3C2×#4114yescomplemented
568D32—416no—
569D32—416no—
570C32×C4—22no—
571C32×C4—22no—
572C32×C4—22no—
573C3⋊Dic3—22no—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3C22×D414yes—
579C25—91no—
580C25—91no—
581C2×#41—98no—
582C2×#41—188no—
583C22×Q8—31no—
584C22×D4—31no—
585C22×D4—98no—
586C22×D4—91no—
587C22×D4—91no—
588C22×D4—91no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—91no—
593C22×D4—91no—
594C22×D4—188no—
595C23×C4—31no—
596C23×C4—31no—
597C23×C4—91no—
598C23×C4—91no—
599C23×C4—91no—
600C23×C4—91no—
601#124—98no—
602#123—38no—
603#123—98no—
604C22⋊Q8—38no—
605#121—98no—
606#121—98no—
607#121—98no—
608#120—98no—
609#120—98no—
610C4×D4—98no—
611C4×D4—98no—
612C2×C4⋊C4—31no—
613C2×C4⋊C4—31no—
614C2×C4⋊C4—31no—
615C2×C4⋊C4D3211yescharacteristic, complemented
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—31no—
621C2×C22⋊C4—98no—
622C2×C22⋊C4—98no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4—91no—
628C2×C22⋊C4—91no—
629C2×C22⋊C4—91no—
630C2×C42—91no—
631C23×C3—21no—
632C23×C3—34no—
633C23×C3—34no—
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×C3C23×D311yescharacteristic
645C23×C3C23×D311yescharacteristic
646C22×D3—22no—
647C22×D3—22no—
648C22×D3—22no—
649C22×D3—22no—
650C22×D3—22no—
651C22×D3—22no—
652C22×D3—22no—
653C22×D3—34no—
654C22×D3—34no—
655C22×D3—32no—
656C22×D3—32no—
657C22×D3—32no—
658C22×D3—32no—
659C22×D3—32no—
660C22×D3—32no—
661C22×D3—64no—
662C22×D3—62no—
663C22×D3—62no—
664C22×D3—62no—
665C22×D3—68no—
666C22×D3—68no—
667C22×D3—68no—
668C22×D3—68no—
669C22×D3—68no—
670C22×D3—62no—
671C22×D3—62no—
672C22×D3—62no—
673C22×D3—62no—
674C22×D3—62no—
675C22×D3—62no—
676C22×D3—62no—
677C22×D3—62no—
678C22×D3—62no—
679C22×D3—62no—
680C22×D3—62no—
681C22×D3—62no—
682C22×D3—62no—
683C22×D3—62no—
684C22×D3—62no—
685C22×D3—62no—
686C22×D3—68no—
687C22×D3—68no—
688C22×D3—68no—
689C22×D3—122no—
690C22×D3—122no—
691C22×D3—122no—
692C22×D3—122no—
693C22×D3—122no—
694C22×D3—122no—
695C22×D3—122no—
696C22×D3—122no—
697C22×D3—124no—
698C22×D3—124no—
699C22×D3—124no—
700C22×D3—124no—
701C22×D3—1216no—
702C22×D3—1216no—
703C22×D3—1216no—
704C22×D3—1216no—
705C22×D3D3×D414yes—
706C22×D3#23914yescomplemented
707C22×D3C23×D312yes—
708C22×D3C23×D312yes—
709C22×D3C23×D312yes—
710C3×Q8—68no—
711C3×D4—68no—
712C2×C3×C4—24no—
713C2×C3×C4—22no—
714C2×C3×C4—22no—
715C2×C3×C4—22no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—22no—
719C2×C3×C4—22no—
720C2×C3×C4—22no—
721C2×C3×C4—22no—
722C2×C3×C4—34no—
723C2×C3×C4—32no—
724C2×C3×C4—32no—
725C2×C3×C4—32no—
726C2×C3×C4—32no—
727C2×C3×C4—32no—
728C2×C3×C4—42no—
729C2×C3×C4—42no—
730C2×C3×C4—68no—
731C2×C3×C4—68no—
732C2×C3×C4—62no—
733C2×C3×C4—62no—
734C2×C3×C4—62no—
735C2×C3×C4—62no—
736C2×C3×C4C23×D312yes—
737C2×C3×C4C23×D312yes—
738C2×C3×C4C23×D312yes—
739C2×C3×C4C23×D312yes—
740C2×C3×C4C23×D312yes—
741C2×C3×C4C23×D312yes—
742#67—316no—
743#67—68no—
744#67—68no—
745#67—68no—
746#67—124no—
747C2×Dic3—22no—
748C2×Dic3—22no—
749C2×Dic3—22no—
750C2×Dic3—22no—
751C2×Dic3—32no—
752C2×Dic3—32no—
753C2×Dic3—62no—
754C2×Dic3—62no—
755C2×Dic3—62no—
756C2×Dic3—122no—
757C2×Dic3—124no—
758C2×Dic3D3×D414yes—
759C2×Dic3C23×D312yes—
760C2×Dic3C23×D312yes—
761C2×Dic3C23×D312yes—
762C2×Dic3C23×D312yes—
763C2×Dic3C23×D312yes—
764D12—28no—
765D12—316no—
766D12—68no—
767D12—68no—
768D12—68no—
769D12—68no—
770D12—68no—
771D12—68no—
772D12—68no—
773D12—128no—
774D12—128no—
775D12—124no—
776D12—124no—
777D12—128no—
778D12—124no—
779C4×D3—28no—
780C4×D3—28no—
781C4×D3—68no—
782C4×D3—68no—
783C4×D3—68no—
784C4×D3—68no—
785C4×D3—124no—
786C4×D3—124no—
787C4×D3—124no—
788C4×D3—128no—
789Dic6—28no—
790C2×C32#54614yescomplemented
791C2×C32C23×D411yescharacteristic
792C2×C32C22×#4111yescharacteristic
793C2×C32C2×H(5,𝔽2)11yescharacteristic
794C3⋊D3—24no—
795C3⋊D3—42no—
796C3⋊D3—42no—
797C3×D3—24no—
798C3×D3—24no—
799C3×D3—42no—
800C24—31no—
801C24—31no—
802C24—31no—
803C24—94no—
804C24—94no—
805C24—91no—
806C24—91no—
807C24—91no—
808C24—184no—
809C24—184no—
810C24—184no—
811C24—184no—
812C24—362no—
813C24—362no—
814#41—1832no—
815C2×Q8—34no—
816C2×Q8—64no—
817C2×D4—34no—
818C2×D4—64no—
819C2×D4—94no—
820C2×D4—98no—
821C2×D4—94no—
822C2×D4—94no—
823C2×D4—94no—
824C2×D4—94no—
825C2×D4—94no—
826C2×D4—94no—
827C2×D4—94no—
828C2×D4—184no—
829C2×D4—184no—
830C2×D4—184no—
831C2×D4—1832no—
832C2×D4—184no—
833C2×D4—184no—
834C2×D4—362no—
835C2×D4—362no—
836C22×C4—31no—
837C22×C4—31no—
838C22×C4—31no—
839C22×C4—31no—
840C22×C4—31no—
841C22×C4—34no—
842C22×C4—34no—
843C22×C4—64no—
844C22×C4—64no—
845C22×C4—94no—
846C22×C4—94no—
847C22×C4—94no—
848C22×C4—91no—
849C22×C4—94no—
850C22×C4—184no—
851C22×C4—184no—
852C22×C4—362no—
853C22×C4—362no—
854C22×C4C2×D3211yescharacteristic
855C22×C4C2×D3211yescharacteristic
856C22×C4C2×D3211yescharacteristic
857C4⋊C4—34no—
858C4⋊C4—34no—
859C4⋊C4—34no—
860C4⋊C4C2×D3214yescomplemented
861C22⋊C4—34no—
862C22⋊C4—34no—
863C22⋊C4—34no—
864C22⋊C4—34no—
865C22⋊C4—34no—
866C22⋊C4—94no—
867C22⋊C4—94no—
868C22⋊C4—94no—
869C22⋊C4—94no—
870C22⋊C4—94no—
871C22⋊C4—94no—
872C22⋊C4—94no—
873C42—94no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—21no—
878C22×C3—34no—
879C22×C3—34no—
880C22×C3—68no—
881C22×C3—62no—
882C22×C3—62no—
883C22×C3—62no—
884C22×C3—62no—
885C22×C3—68no—
886C22×C3—62no—
887C22×C3—62no—
888C22×C3—62no—
889C22×C3—124no—
890C22×C3C2×D3×D412yes—
891C22×C3C2×D3×D412yes—
892C22×C3C2×#23912yes—
893C22×C3D3×#4112yes—
894C22×C3#100912yes—
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—34no—
908C2×D3—34no—
909C2×D3—44no—
910C2×D3—64no—
911C2×D3—68no—
912C2×D3—62no—
913C2×D3—62no—
914C2×D3—62no—
915C2×D3—62no—
916C2×D3—68no—
917C2×D3—62no—
918C2×D3—62no—
919C2×D3—62no—
920C2×D3—62no—
921C2×D3—62no—
922C2×D3—62no—
923C2×D3—62no—
924C2×D3—62no—
925C2×D3—62no—
926C2×D3—62no—
927C2×D3—62no—
928C2×D3—62no—
929C2×D3—122no—
930C2×D3—128no—
931C2×D3—122no—
932C2×D3—122no—
933C2×D3—122no—
934C2×D3—122no—
935C2×D3—122no—
936C2×D3—122no—
937C2×D3—122no—
938C2×D3—1216no—
939C2×D3—1216no—
940C2×D3—1216no—
941C2×D3—1216no—
942C2×D3—124no—
943C2×D3—124no—
944C2×D3—124no—
945C2×D3—124no—
946C2×D3—244no—
947C2×D3—244no—
948C2×D3C2×D3×D414yes—
949C2×D3C2×#23914yescomplemented
950C3×C4—24no—
951C3×C4—22no—
952C3×C4—22no—
953C3×C4—22no—
954C3×C4—22no—
955C3×C4—22no—
956C3×C4—22no—
957C3×C4—34no—
958C3×C4—42no—
959C3×C4—42no—
960C3×C4—62no—
961C3×C4—62no—
962C3×C4—62no—
963C3×C4—62no—
964Dic3—22no—
965Dic3—22no—
966Dic3—22no—
967Dic3—22no—
968Dic3—62no—
969Dic3—62no—
970Dic3—122no—
971Dic3C2×D3×D414yes—
972C32C2×#54611yescharacteristic, complemented, Sylow
973C23—34no—
974C23—34no—
975C23—32no—
976C23—32no—
977C23—32no—
978C23—62no—
979C23—62no—
980C23—62no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—62no—
985C23—94no—
986C23—92no—
987C23—92no—
988C23—92no—
989C23—188no—
990C23—188no—
991C23—188no—
992C23—188no—
993C23—182no—
994C23—182no—
995C23—182no—
996C23—182no—
997C23—182no—
998C23—182no—
999C23—182no—
1000C23—182no—
1001C23—364no—
1002C23—364no—
1003C23—3616no—
1004C23—3616no—
1005C23C22×D3211yescharacteristic
1006Q8—68no—
1007D4—68no—
1008D4—916no—
1009D4—188no—
1010D4—188no—
1011D4—188no—
1012D4—188no—
1013D4—188no—
1014D4—364no—
1015D4—364no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—34no—
1020C2×C4—32no—
1021C2×C4—32no—
1022C2×C4—32no—
1023C2×C4—32no—
1024C2×C4—32no—
1025C2×C4—68no—
1026C2×C4—68no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—92no—
1032C2×C4—188no—
1033C2×C4—188no—
1034C2×C4—182no—
1035C2×C4—364no—
1036C2×C4—364no—
1037C2×C4C22×D3212yes—
1038C2×C4C22×D3212yes—
1039C2×C4C22×D3212yes—
1040C2×C3—24no—
1041C2×C3—21no—
1042C2×C3—21no—
1043C2×C3—21no—
1044C2×C3—64no—
1045C2×C3—64no—
1046C2×C3—122no—
1047C2×C3#563014yescomplemented
1048C2×C3#565414yescomplemented
1049C2×C3C22×D3×D411yescharacteristic
1050C2×C3C22×D3×D411yescharacteristic
1051C2×C3C22×#23911yescharacteristic
1052C2×C3C2×D3×#4111yescharacteristic
1053C2×C3C2×#100911yescharacteristic
1054C2×C3C2×#100911yescharacteristic
1055D3—24no—
1056D3—24no—
1057D3—42no—
1058D3—64no—
1059D3—64no—
1060D3—124no—
1061D3—122no—
1062D3—122no—
1063D3—122no—
1064D3—122no—
1065D3—242no—
1066D3—242no—
1067C22—34no—
1068C22—34no—
1069C22—68no—
1070C22—68no—
1071C22—62no—
1072C22—62no—
1073C22—62no—
1074C22—62no—
1075C22—62no—
1076C22—62no—
1077C22—62no—
1078C22—94no—
1079C22—124no—
1080C22—188no—
1081C22—182no—
1082C22—182no—
1083C22—182no—
1084C22—182no—
1085C22—182no—
1086C22—182no—
1087C22—182no—
1088C22—182no—
1089C22—3616no—
1090C22—3616no—
1091C22—364no—
1092C22—364no—
1093C22#6430812yes—
1094C22D32×D412yes—
1095C22D3×#23912yes—
1096C22C23×D3211yescharacteristic
1097C4—22no—
1098C4—22no—
1099C4—22no—
1100C4—34no—
1101C4—62no—
1102C4—62no—
1103C4—62no—
1104C4—62no—
1105C4—182no—
1106C3—21no—
1107C3C2×#563011yescharacteristic, complemented
1108C3C2×#565411yescharacteristic, complemented
1109C2—64no—
1110C2—64no—
1111C2—122no—
1112C2—184no—
1113C2—362no—
1114C2—362no—
1115C2#1059462014yesdirect product factor
1116C2C2×#6430811yescharacteristic
1117C2C2×D32×D411yescharacteristic
1118C2C2×D3×#23911yescharacteristic
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×D3×D12C2semidirect
2. C22×#3799C2semidirect
3. C2×#64104C2semidirect
4. C2×C3×#896C2semidirect
5. C2×C3×#894C2semidirect
6. C2×#63923C2semidirect
7. C2×#63923C2semidirect
8. C2×#63921C2semidirect
9. C2×D3×(C2×D3)⋊C4C2semidirect
10. C2×#63910C2semidirect
11. C2×#63907C2semidirect
12. C2×#63904C2semidirect
13. C2×#63897C2semidirect
14. C2×#63886C2semidirect
15. C2×#63881C2semidirect
16. #10594620C2direct (N × H)
22. C22×C4⋊(C3⋊D3)C22semidirect
23. C22×C4⋊(C3⋊D3)C22semidirect
24. C22×C4×C3⋊D3C22semidirect
27. C22×C3×C4×D3C22semidirect
28. C22×C3×Dic6C22semidirect
32. C22×#626C22semidirect
33. C22×#626C22semidirect
34. C22×#624C22semidirect
35. C22×#624C22semidirect
36. C22×D3×Dic3C22semidirect
38. C2×D3×D12C22semidirect
40. C2×#3799C22semidirect
41. C2×C32×C4⋊C4C22semidirect
42. C2×#3752C22semidirect
43. C2×#3752C22semidirect
44. #64104C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×Dic3⋊C4C22semidirect
51. C2×C3×Dic3⋊C4C22semidirect
52. C2×C3×Dic3⋊C4C22semidirect
53. C3×#896C22semidirect
54. C3×#894C22semidirect
55. C2×#3722C22semidirect
56. C2×#3722C22semidirect
57. C2×#3722C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×Dic32C22semidirect
61. #63923C22semidirect
62. #63923C22semidirect
63. #63921C22semidirect
64. D3×(C2×D3)⋊C4C22semidirect
65. #63910C22semidirect
66. #63907C22semidirect
67. #63904C22semidirect
68. #63897C22semidirect
69. #63886C22semidirect
70. #63881C22semidirect
83. C2×#896D3semidirect
91. C2×#894D3semidirect
126. C2×C4⋊(C3⋊D3)C23semidirect
127. C2×C4⋊(C3⋊D3)C23semidirect
129. C2×C4×C3⋊D3C23semidirect
140. C2×C3×C4×D3C23semidirect
142. C2×C3×Dic6C23semidirect
147. C2×#626D4semidirect
151. C2×#626C23semidirect
152. C2×#626C23semidirect
155. C2×#624C23semidirect
156. C2×#624C23semidirect
158. C2×D3×Dic3C23semidirect
161. C32×C4⋊C4C23semidirect
162. #3752C23semidirect
163. #3752C23semidirect
166. C3×(C2×D3)⋊C4C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×(C2×D3)⋊C4C23semidirect
169. C3×Dic3⋊C4C23semidirect
170. C3×Dic3⋊C4C23semidirect
171. C3×Dic3⋊C4C23semidirect
172. #3722C23semidirect
173. #3722C23semidirect
174. #3722C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
225. C22×C4×D3C2×D3semidirect
226. C22×Dic6C2×D3semidirect
233. C2×C3×C4⋊C4C2×D3semidirect
234. C2×C3×C4⋊C4C2×D3semidirect
262. C2×(C2×D3)⋊C4C2×D3semidirect
263. C2×(C2×D3)⋊C4C2×D3semidirect
264. C2×(C2×D3)⋊C4C2×D3semidirect
265. C2×Dic3⋊C4C2×D3semidirect
266. C2×Dic3⋊C4C2×D3semidirect
267. C2×Dic3⋊C4C2×D3semidirect
270. #896C2×D3semidirect
278. #894C2×D3semidirect
312. C22×C3×D3#41semidirect
354. #626C2×D4semidirect
500. C2×C4×D3C22×D3semidirect
502. C2×Dic6C22×D3semidirect
507. C3×C4⋊C4C22×D3semidirect
508. C3×C4⋊C4C22×D3semidirect
532. (C2×D3)⋊C4C22×D3semidirect
533. (C2×D3)⋊C4C22×D3semidirect
534. (C2×D3)⋊C4C22×D3semidirect
535. Dic3⋊C4C22×D3semidirect
536. Dic3⋊C4C22×D3semidirect
537. Dic3⋊C4C22×D3semidirect
567. C2×C3×D3C2×#41semidirect
615. C2×C4⋊C4D32semidirect
706. C22×D3#239semidirect
790. C2×C32#546semidirect
860. C4⋊C4C2×D32semidirect
949. C2×D3C2×#239semidirect
972. C32C2×#546semidirect
1047. C2×C3#5630semidirect
1048. C2×C3#5654semidirect
1107. C3C2×#5630semidirect
1108. C3C2×#5654semidirect
1115. C2#10594620direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D122
C22×#37992
C2×#641042
C2×C3×#8962
C2×C3×#8942
C2×#639232
C2×#639212
C2×D3×(C2×D3)⋊C42
C2×#639102
C2×#639072
C2×#639042
C2×#638972
C2×#638862
C2×#638812
#105946202
C2×#56543
C2×#56303