Finite Group Databasebeta

← C2×#10594279 #11902450

Subgroups — C2×#10594279 #11902450

Order 1152.

4137 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3811C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
4C2×C3×#884C211yesmaximal, characteristic, complemented
5C2×C3×#883C211yesmaximal, characteristic, complemented
6C2×#63981C211yesmaximal, characteristic, complemented
7C2×#63970C211yesmaximal, characteristic, complemented
8C2×#63959C211yesmaximal, characteristic, complemented
9C2×#63922C211yesmaximal, characteristic, complemented
10C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#63916C211yesmaximal, characteristic, complemented
12C2×#63904C211yesmaximal, characteristic, complemented
13C2×#63895C211yesmaximal, characteristic, complemented
14C2×#63881C211yesmaximal, characteristic, complemented
15C2×#63853C211yesmaximal, characteristic, complemented
16#10594279C2116yesmaximal, direct product factor
17C2×#5654—31nomaximal
18C2×#5612—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic, complemented
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic, complemented
26C22×C3×D12C2211yescharacteristic, complemented
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×C3×C4×D3C2211yescharacteristic, complemented
29C2×#3811—28no—
30C2×#3811C2218yescomplemented
31C22×#627C2211yescharacteristic, complemented
32C22×#626C2211yescharacteristic
33C22×#626C2211yescharacteristic
34C22×#626C2211yescharacteristic
35C22×#626C2211yescharacteristic, complemented
36C22×#625C2211yescharacteristic, complemented
37C22×#624C2211yescharacteristic
38C22×D3×Dic3C2211yescharacteristic, complemented
39C2×#3798—28no—
40C2×#3798C2218yescomplemented
41C2×C32×C22⋊C4C2211yescharacteristic, complemented
42C2×#3757C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic
44C2×#3752C2211yescharacteristic
45C22⋊C4×C3⋊D3C2218yescomplemented
46C2×C3×#217C2211yescharacteristic, complemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
50C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
51C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
52C3×#884C2218yescomplemented
53C3×#883C2218yescomplemented
54#63981C2218yescomplemented
55#63970C2218yescomplemented
56C2×Dic3⋊Dic3C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic
58C2×#3722C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62#63959C2218yescomplemented
63C2×Dic32C2211yescharacteristic, complemented
64#63922C2218yescomplemented
65D3×(C2×D3)⋊C4C2218yescomplemented
66#63916C2218yescomplemented
67#63904C2218yescomplemented
68#63895C2218yescomplemented
69#63881C2218yescomplemented
70#63853C2218yescomplemented
71C22×D3×D4—31no—
72C22×D3×D4—31no—
73C22×#235—31no—
74C22×#235—31no—
75C2×C3×#123—31no—
76C2×C3×#121—31no—
77C2×#939—31no—
78C2×#938—31no—
79C2×#938—31no—
80C2×#937—31no—
81C2×#937—31no—
82C2×#936—31no—
83C2×C4×#67—31no—
84C22×(C2×D3)⋊C4—31no—
85#5654—316no—
86#5612—316no—
87C2×#897—31no—
88C2×#896—31no—
89C2×#895—31no—
90C2×#894—31no—
91C2×#893—31no—
92C2×#893—31no—
93C2×#885—31no—
94C2×#884D311yescharacteristic, complemented
95C2×#883—31no—
96C2×#883D311yescharacteristic, complemented
97C2×#882—31no—
98C2×#882—31no—
99C2×#67⋊C4—31no—
100C2×D3×C22⋊C4—31no—
101C2×D3×C22⋊C4—31no—
102C2×D3×C22⋊C4—31no—
103C2×D3×C22⋊C4—61no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3—24no—
106C23×C3⋊D3—24no—
107C23×C3⋊D3—42no—
108C23×C3⋊D3C2314yes—
109C23×C3⋊D3C2311yescharacteristic
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
120C22×C3⋊Dic3C2311yescharacteristic
121C22×C3⋊Dic3C2311yescharacteristic
122C2×C4×C3⋊D3—24no—
123C2×C4×C3⋊D3—42no—
124C2×C4×C3⋊D3C2314yescomplemented
125C2×C4×C3⋊D3C2314yescomplemented
126C2×C3×#67—24no—
127C2×C3×#67—24no—
128C2×C3×#67—42no—
129C2×C3×#67C2314yes—
130C2×C3×#67C2314yes—
131C2×C3×#67C2314yescomplemented
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C2×C3×D12—42no—
138C2×C3×D12C2314yescomplemented
139C2×C3×C4×D3—24no—
140C2×C3×C4×D3—24no—
141C2×C3×C4×D3C2314yescomplemented
142C2×C3×C4×D3C2314yescomplemented
143#3811—232no—
144C2×#627—24no—
145C2×#627C2314yescomplemented
146C2×#626—24no—
147C2×#626—24no—
148C2×#626—24no—
149C2×#626D418yescomplemented
150C2×#626C2314yes—
151C2×#626C2314yes—
152C2×#626C2314yes—
153C2×#626C2314yescomplemented
154C2×#625—24no—
155C2×#625C2314yescomplemented
156C2×#624—24no—
157C2×#624C2314yes—
158C2×D3×Dic3—42no—
159C2×D3×Dic3C2314yescomplemented
160#3798—232no—
161C32×C22⋊C4C2314yescomplemented
162#3757C2314yescomplemented
163#3752C2314yes—
164#3752C2314yes—
165C3×#217C2314yescomplemented
166C3×(C2×D3)⋊C4C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×C4⋊Dic3C2314yescomplemented
169C3×Dic3⋊C4C2314yescomplemented
170C3×Dic3⋊C4C2314yescomplemented
171Dic3⋊Dic3C2314yescomplemented
172#3722C2314yes—
173#3722C2314yescomplemented
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—
183C24×D3—61no—
184C22×C3×D4—31no—
185C22×C3×D4—31no—
186C22×C3×D4—31no—
187C22×C3×D4—31no—
188C23×C3×C4—31no—
189C23×C3×C4—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67C2×D311yescharacteristic
197C22×#67C2×D311yescharacteristic
198C22×#67C2×D311yescharacteristic, complemented
199C23×Dic3—31no—
200C2×D3×D4—38no—
201C2×D3×D4—38no—
202C2×D3×D4—68no—
203C2×D3×D4—68no—
204C2×#235—38no—
205C2×#235—38no—
206C2×#235—68no—
207C2×#235—68no—
208C22×D12—31no—
209C22×D12—31no—
210C22×D12—31no—
211C22×D12—31no—
212C22×D12C2×D311yescharacteristic, complemented
213C22×C4×D3—31no—
214C22×C4×D3—31no—
215C22×C4×D3—31no—
216C22×C4×D3—31no—
217C22×C4×D3—31no—
218C22×C4×D3—31no—
219C22×C4×D3—31no—
220C22×C4×D3—61no—
221C22×C4×D3—61no—
222C22×C4×D3C2×D311yescharacteristic, complemented
223C22×C4×D3C2×D311yescharacteristic, complemented
224C22×Dic6—31no—
225C22×Dic6—31no—
226C3×#123—38no—
227C3×#121—38no—
228C2×C3×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic, complemented
236C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217—31no—
241C2×#217—31no—
242C2×#217—61no—
243C2×#217C2×D311yescharacteristic, complemented
244#939—38no—
245#938—38no—
246#938—38no—
247#937—38no—
248#937—38no—
249#936—38no—
250C4×#67—38no—
251C2×(C2×D3)⋊C4—31no—
252C2×(C2×D3)⋊C4—31no—
253C2×(C2×D3)⋊C4—31no—
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4—31no—
256C2×(C2×D3)⋊C4—31no—
257C2×(C2×D3)⋊C4—31no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—31no—
260C2×(C2×D3)⋊C4—31no—
261C2×(C2×D3)⋊C4—31no—
262C2×(C2×D3)⋊C4—38no—
263C2×(C2×D3)⋊C4—61no—
264C2×(C2×D3)⋊C4—61no—
265C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
266C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
267C2×C4⋊Dic3—31no—
268C2×C4⋊Dic3C2×D311yescharacteristic, complemented
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4C2×D311yescharacteristic, complemented
271C2×Dic3⋊C4C2×D311yescharacteristic, complemented
272C2×C4×Dic3—31no—
273C2×C4×Dic3—31no—
274#897—38no—
275#896—38no—
276#895—38no—
277#894—38no—
278#893—38no—
279#893—38no—
280#885—38no—
281#884C2×D318yescomplemented
282#883—38no—
283#883C2×D318yescomplemented
284#882—38no—
285#882—38no—
286#67⋊C4—38no—
287D3×C22⋊C4—38no—
288D3×C22⋊C4—38no—
289D3×C22⋊C4—38no—
290D3×C22⋊C4—68no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32C2412yes—
295C23×C32C2411yescharacteristic
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3—28no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3—22no—
301C22×C3⋊D3—28no—
302C22×C3⋊D3—44no—
303C22×C3⋊D3—416no—
304C22×C3⋊D3C2×D414yes—
305C22×C3⋊D3#4114yescomplemented
306C22×C3⋊D3C2412yes—
307C22×C3⋊D3C2412yes—
308C22×C3×D3—22no—
309C22×C3×D3—22no—
310C22×C3×D3—22no—
311C22×C3×D3—22no—
312C22×C3×D3—22no—
313C22×C3×D3—22no—
314C22×C3×D3—22no—
315C22×C3×D3—22no—
316C22×C3×D3C2×D414yes—
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—
328C2×C3⋊Dic3—22no—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3C2412yes—
331C2×C3⋊Dic3C2412yes—
332C4×C3⋊D3—28no—
333C4×C3⋊D3—44no—
334C3×#67—28no—
335C3×#67—28no—
336C3×#67—44no—
337C2×C3×Dic3—22no—
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—
346C2×C3×Dic3C2412yes—
347C3×D12—44no—
348C3×C4×D3—28no—
349C3×C4×D3—28no—
350#627—28no—
351#626—28no—
352#626—28no—
353#626—28no—
354#626C2×D4116yescomplemented
355#625—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—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—21no—
375C24×C3—31no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3C22×D311yescharacteristic
379C24×C3C22×D311yescharacteristic
380C23×D3—31no—
381C23×D3—31no—
382C23×D3—31no—
383C23×D3—31no—
384C23×D3—34no—
385C23×D3—34no—
386C23×D3—34no—
387C23×D3—34no—
388C23×D3—61no—
389C23×D3—64no—
390C23×D3—61no—
391C23×D3—64no—
392C23×D3—64no—
393C23×D3—64no—
394C23×D3—64no—
395C23×D3—64no—
396C23×D3—64no—
397C23×D3—64no—
398C23×D3—68no—
399C23×D3—64no—
400C23×D3—124no—
401C23×D3—122no—
402C23×D3—122no—
403C23×D3—122no—
404C23×D3—122no—
405C23×D3—124no—
406C23×D3C22×D311yescharacteristic
407C23×D3C22×D311yescharacteristic
408C23×D3C22×D311yescharacteristic
409C2×C3×D4—34no—
410C2×C3×D4—34no—
411C2×C3×D4—34no—
412C2×C3×D4—34no—
413C2×C3×D4—64no—
414C2×C3×D4—64no—
415C2×C3×D4—122no—
416C2×C3×D4—122no—
417C22×C3×C4—21no—
418C22×C3×C4—21no—
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—34no—
426C22×C3×C4—64no—
427C22×C3×C4—64no—
428C22×C3×C4C22×D311yescharacteristic
429C22×C3×C4C22×D311yescharacteristic
430C22×C3×C4C22×D311yescharacteristic
431C22×C3×C4C22×D311yescharacteristic
432C2×#67—24no—
433C2×#67—24no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—38no—
437C2×#67—34no—
438C2×#67—34no—
439C2×#67—34no—
440C2×#67—34no—
441C2×#67—42no—
442C2×#67—64no—
443C2×#67—64no—
444C2×#67—64no—
445C2×#67—64no—
446C2×#67—64no—
447C2×#67C22×D314yes—
448C2×#67C22×D314yes—
449C2×#67C22×D314yescomplemented
450C22×Dic3—31no—
451C22×Dic3—31no—
452C22×Dic3—31no—
453C22×Dic3—31no—
454C22×Dic3—34no—
455C22×Dic3—61no—
456C22×Dic3—61no—
457C22×Dic3—122no—
458C22×Dic3C22×D311yescharacteristic
459C22×Dic3C22×D311yescharacteristic
460C22×Dic3C22×D311yescharacteristic
461C22×Dic3C22×D311yescharacteristic
462C22×Dic3C22×D311yescharacteristic
463D3×D4—632no—
464D3×D4—632no—
465#235—632no—
466#235—632no—
467C2×D12—38no—
468C2×D12—34no—
469C2×D12—34no—
470C2×D12—34no—
471C2×D12—34no—
472C2×D12—42no—
473C2×D12—64no—
474C2×D12—64no—
475C2×D12—64no—
476C2×D12C22×D314yescomplemented
477C2×C4×D3—24no—
478C2×C4×D3—24no—
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—64no—
487C2×C4×D3—64no—
488C2×C4×D3—64no—
489C2×C4×D3—64no—
490C2×C4×D3—64no—
491C2×C4×D3—64no—
492C2×C4×D3—124no—
493C2×C4×D3—122no—
494C2×C4×D3—122no—
495C2×C4×D3—122no—
496C2×C4×D3—124no—
497C2×C4×D3C22×D314yescomplemented
498C2×C4×D3C22×D314yescomplemented
499C2×Dic6—34no—
500C2×Dic6—34no—
501C2×Dic6—64no—
502C2×Dic6—64no—
503C3×C4⋊C4—34no—
504C3×C4⋊C4—34no—
505C3×C4⋊C4—34no—
506C3×C22⋊C4—24no—
507C3×C22⋊C4—34no—
508C3×C22⋊C4—34no—
509C3×C22⋊C4—34no—
510C3×C22⋊C4C22×D314yescomplemented
511C3×C22⋊C4C22×D314yescomplemented
512#217—34no—
513#217—34no—
514#217—34no—
515#217—34no—
516#217—34no—
517#217—64no—
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
534C4⋊Dic3—34no—
535C4⋊Dic3C22×D314yescomplemented
536Dic3⋊C4—34no—
537Dic3⋊C4C22×D314yescomplemented
538Dic3⋊C4C22×D314yescomplemented
539C4×Dic3—34no—
540C4×Dic3—34no—
541C22×C32—22no—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32—44no—
545C22×C32C22×D412yes—
546C22×C32C2×#4112yes—
547C22×C32H(5,𝔽2)12yes—
548C22×C32C2511yescharacteristic
549C2×C3⋊D3—28no—
550C2×C3⋊D3—22no—
551C2×C3⋊D3—22no—
552C2×C3⋊D3—28no—
553C2×C3⋊D3—22no—
554C2×C3⋊D3—22no—
555C2×C3⋊D3—416no—
556C2×C3⋊D3C22×D414yes—
557C2×C3⋊D3C2×#4114yescomplemented
558C2×C3×D3—28no—
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—22no—
566C2×C3×D3—22no—
567C2×C3×D3—44no—
568C2×C3×D3—44no—
569C2×C3×D3C22×D414yes—
570D32—416no—
571C32×C4—22no—
572C32×C4—22no—
573C3⋊Dic3—22no—
574C3⋊Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3—22no—
579C3×Dic3C22×D414yes—
580C25—91no—
581C25—91no—
582C2×#41—98no—
583C2×#41—188no—
584C22×Q8—91no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—31no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—91no—
593C22×D4—98no—
594C22×D4—91no—
595C22×D4—188no—
596C23×C4—31no—
597C23×C4—31no—
598C23×C4—91no—
599C23×C4—91no—
600C23×C4—91no—
601C23×C4—91no—
602#124—98no—
603#123—38no—
604#123—98no—
605C22⋊Q8—98no—
606#121—38no—
607#121—98no—
608#121—98no—
609#120—98no—
610#120—98no—
611C4×D4—98no—
612C4×D4—98no—
613C2×C4⋊C4—31no—
614C2×C4⋊C4—31no—
615C2×C4⋊C4—31no—
616C2×C4⋊C4—91no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
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×C22⋊C4—91no—
629C2×C22⋊C4—98no—
630C2×C22⋊C4D3211yescharacteristic, complemented
631C2×C42—91no—
632C23×C3—24no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—22no—
639C23×C3—22no—
640C23×C3—21no—
641C23×C3—34no—
642C23×C3—32no—
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×C3—62no—
653C23×C3—62no—
654C23×C3—62no—
655C23×C3C23×D312yes—
656C23×C3C23×D312yes—
657C23×C3C23×D311yescharacteristic
658C23×C3C23×D311yescharacteristic
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—22no—
663C22×D3—22no—
664C22×D3—22no—
665C22×D3—22no—
666C22×D3—22no—
667C22×D3—34no—
668C22×D3—34no—
669C22×D3—34no—
670C22×D3—34no—
671C22×D3—32no—
672C22×D3—32no—
673C22×D3—32no—
674C22×D3—32no—
675C22×D3—64no—
676C22×D3—62no—
677C22×D3—64no—
678C22×D3—62no—
679C22×D3—68no—
680C22×D3—68no—
681C22×D3—68no—
682C22×D3—68no—
683C22×D3—68no—
684C22×D3—68no—
685C22×D3—68no—
686C22×D3—64no—
687C22×D3—64no—
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—616no—
697C22×D3—68no—
698C22×D3—128no—
699C22×D3—122no—
700C22×D3—122no—
701C22×D3—124no—
702C22×D3—124no—
703C22×D3—1216no—
704C22×D3—1216no—
705C22×D3—124no—
706C22×D3—124no—
707C22×D3—1216no—
708C22×D3—1216no—
709C22×D3—128no—
710C22×D3—1232no—
711C22×D3D3×D414yes—
712C22×D3C23×D312yes—
713C22×D3C23×D312yes—
714C22×D3C23×D312yes—
715C3×D4—68no—
716C3×D4—68no—
717C3×D4—124no—
718C3×D4—124no—
719C2×C3×C4—22no—
720C2×C3×C4—22no—
721C2×C3×C4—22no—
722C2×C3×C4—22no—
723C2×C3×C4—22no—
724C2×C3×C4—22no—
725C2×C3×C4—34no—
726C2×C3×C4—32no—
727C2×C3×C4—32no—
728C2×C3×C4—32no—
729C2×C3×C4—32no—
730C2×C3×C4—32no—
731C2×C3×C4—42no—
732C2×C3×C4—42no—
733C2×C3×C4—68no—
734C2×C3×C4—68no—
735C2×C3×C4—62no—
736C2×C3×C4—62no—
737C2×C3×C4—62no—
738C2×C3×C4—62no—
739C2×C3×C4C23×D312yes—
740C2×C3×C4C23×D312yes—
741C2×C3×C4C23×D312yes—
742C2×C3×C4C23×D312yes—
743#67—28no—
744#67—28no—
745#67—316no—
746#67—44no—
747#67—68no—
748#67—68no—
749#67—68no—
750#67—68no—
751#67—68no—
752C2×Dic3—22no—
753C2×Dic3—22no—
754C2×Dic3—22no—
755C2×Dic3—22no—
756C2×Dic3—32no—
757C2×Dic3—32no—
758C2×Dic3—32no—
759C2×Dic3—32no—
760C2×Dic3—62no—
761C2×Dic3—62no—
762C2×Dic3—62no—
763C2×Dic3—62no—
764C2×Dic3—62no—
765C2×Dic3—62no—
766C2×Dic3—122no—
767C2×Dic3—122no—
768C2×Dic3—124no—
769C2×Dic3D3×D414yes—
770C2×Dic3C23×D312yes—
771C2×Dic3C23×D312yes—
772C2×Dic3C23×D312yes—
773C2×Dic3C23×D312yes—
774C2×Dic3C23×D312yes—
775D12—316no—
776D12—44no—
777D12—68no—
778D12—68no—
779D12—68no—
780C4×D3—28no—
781C4×D3—28no—
782C4×D3—68no—
783C4×D3—68no—
784C4×D3—68no—
785C4×D3—68no—
786C4×D3—128no—
787C4×D3—124no—
788C4×D3—124no—
789C4×D3—124no—
790C4×D3—128no—
791Dic6—68no—
792Dic6—68no—
793C2×C32—42no—
794C2×C32#54614yescomplemented
795C2×C32C23×D411yescharacteristic
796C2×C32C22×#4111yescharacteristic
797C2×C32C2×H(5,𝔽2)11yescharacteristic
798C3⋊D3—24no—
799C3⋊D3—24no—
800C3×D3—24no—
801C3×D3—42no—
802C3×D3—42no—
803C24—31no—
804C24—31no—
805C24—31no—
806C24—94no—
807C24—91no—
808C24—91no—
809C24—94no—
810C24—184no—
811C24—184no—
812C24—184no—
813C24—184no—
814C24—362no—
815C24—362no—
816C24C2×D3211yescharacteristic
817#41—1832no—
818C2×Q8—94no—
819C2×Q8—184no—
820C2×D4—34no—
821C2×D4—34no—
822C2×D4—34no—
823C2×D4—34no—
824C2×D4—64no—
825C2×D4—64no—
826C2×D4—94no—
827C2×D4—98no—
828C2×D4—94no—
829C2×D4—94no—
830C2×D4—94no—
831C2×D4—94no—
832C2×D4—122no—
833C2×D4—122no—
834C2×D4—184no—
835C2×D4—184no—
836C2×D4—184no—
837C2×D4—1832no—
838C2×D4—184no—
839C22×C4—31no—
840C22×C4—31no—
841C22×C4—31no—
842C22×C4—31no—
843C22×C4—31no—
844C22×C4—34no—
845C22×C4—34no—
846C22×C4—64no—
847C22×C4—64no—
848C22×C4—94no—
849C22×C4—94no—
850C22×C4—91no—
851C22×C4—91no—
852C22×C4—94no—
853C22×C4—94no—
854C22×C4—184no—
855C22×C4—184no—
856C22×C4—362no—
857C22×C4—362no—
858C22×C4C2×D3211yescharacteristic
859C22×C4C2×D3211yescharacteristic
860C4⋊C4—34no—
861C4⋊C4—34no—
862C4⋊C4—34no—
863C4⋊C4—94no—
864C22⋊C4—34no—
865C22⋊C4—34no—
866C22⋊C4—34no—
867C22⋊C4—94no—
868C22⋊C4—94no—
869C22⋊C4—94no—
870C22⋊C4—94no—
871C22⋊C4—94no—
872C22⋊C4—94no—
873C22⋊C4—94no—
874C22⋊C4—94no—
875C22⋊C4C2×D3214yescomplemented
876C42—94no—
877C22×C3—24no—
878C22×C3—22no—
879C22×C3—22no—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—22no—
886C22×C3—22no—
887C22×C3—21no—
888C22×C3—34no—
889C22×C3—42no—
890C22×C3—42no—
891C22×C3—48no—
892C22×C3—44no—
893C22×C3—44no—
894C22×C3—62no—
895C22×C3—62no—
896C22×C3—68no—
897C22×C3—62no—
898C22×C3—62no—
899C22×C3—62no—
900C22×C3—62no—
901C22×C3—62no—
902C22×C3—62no—
903C22×C3—124no—
904C22×C3—124no—
905C22×C3C2×D3×D412yes—
906C22×C3C2×D3×D412yes—
907C22×C3#100412yes—
908C22×C3D3×#4112yes—
909C22×C3D3×#4112yes—
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—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—34no—
923C2×D3—34no—
924C2×D3—34no—
925C2×D3—34no—
926C2×D3—44no—
927C2×D3—44no—
928C2×D3—64no—
929C2×D3—64no—
930C2×D3—64no—
931C2×D3—64no—
932C2×D3—616no—
933C2×D3—68no—
934C2×D3—68no—
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—68no—
944C2×D3—68no—
945C2×D3—122no—
946C2×D3—122no—
947C2×D3—128no—
948C2×D3—1216no—
949C2×D3—1216no—
950C2×D3—1216no—
951C2×D3—1216no—
952C2×D3—1232no—
953C2×D3C2×D3×D414yes—
954C3×C4—22no—
955C3×C4—22no—
956C3×C4—22no—
957C3×C4—22no—
958C3×C4—34no—
959C3×C4—42no—
960C3×C4—42no—
961C3×C4—62no—
962C3×C4—62no—
963C3×C4—62no—
964C3×C4—62no—
965Dic3—22no—
966Dic3—22no—
967Dic3—22no—
968Dic3—22no—
969Dic3—62no—
970Dic3—62no—
971Dic3—62no—
972Dic3—62no—
973Dic3—122no—
974Dic3—122no—
975Dic3C2×D3×D414yes—
976C32C2×#54611yescharacteristic, complemented, Sylow
977C23—22no—
978C23—22no—
979C23—22no—
980C23—34no—
981C23—32no—
982C23—32no—
983C23—32no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—62no—
988C23—62no—
989C23—62no—
990C23—62no—
991C23—62no—
992C23—94no—
993C23—94no—
994C23—92no—
995C23—92no—
996C23—188no—
997C23—188no—
998C23—188no—
999C23—188no—
1000C23—182no—
1001C23—182no—
1002C23—182no—
1003C23—182no—
1004C23—364no—
1005C23—3616no—
1006C23—364no—
1007C23—3616no—
1008C23C22×D3212yes—
1009C23C22×D3211yescharacteristic
1010Q8—188no—
1011D4—68no—
1012D4—68no—
1013D4—916no—
1014D4—124no—
1015D4—124no—
1016D4—188no—
1017D4—188no—
1018D4—188no—
1019D4—188no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—34no—
1023C2×C4—32no—
1024C2×C4—32no—
1025C2×C4—32no—
1026C2×C4—32no—
1027C2×C4—32no—
1028C2×C4—68no—
1029C2×C4—68no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—62no—
1034C2×C4—92no—
1035C2×C4—92no—
1036C2×C4—188no—
1037C2×C4—188no—
1038C2×C4—182no—
1039C2×C4—182no—
1040C2×C4—364no—
1041C2×C4—364no—
1042C2×C4C22×D3212yes—
1043C2×C4C22×D3212yes—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—21no—
1047C2×C3—24no—
1048C2×C3—44no—
1049C2×C3—42no—
1050C2×C3—42no—
1051C2×C3—64no—
1052C2×C3—122no—
1053C2×C3—122no—
1054C2×C3#561214yescomplemented
1055C2×C3#565414yescomplemented
1056C2×C3C22×D3×D411yescharacteristic
1057C2×C3C22×D3×D411yescharacteristic
1058C2×C3C2×#100411yescharacteristic
1059C2×C3C2×D3×#4111yescharacteristic
1060C2×C3C2×D3×#4111yescharacteristic
1061C2×C3C2×#100911yescharacteristic
1062D3—24no—
1063D3—42no—
1064D3—42no—
1065D3—68no—
1066D3—64no—
1067D3—64no—
1068D3—64no—
1069D3—64no—
1070D3—124no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—34no—
1075C22—44no—
1076C22—62no—
1077C22—62no—
1078C22—68no—
1079C22—62no—
1080C22—62no—
1081C22—62no—
1082C22—62no—
1083C22—62no—
1084C22—62no—
1085C22—94no—
1086C22—94no—
1087C22—124no—
1088C22—124no—
1089C22—182no—
1090C22—182no—
1091C22—182no—
1092C22—182no—
1093C22—188no—
1094C22—188no—
1095C22—3616no—
1096C22—3616no—
1097C22#6430612yes—
1098C22D32×D412yes—
1099C22#6431412yes—
1100C22C23×D3211yescharacteristic
1101C4—22no—
1102C4—22no—
1103C4—34no—
1104C4—62no—
1105C4—62no—
1106C4—62no—
1107C4—62no—
1108C4—182no—
1109C4—182no—
1110C3—21no—
1111C3C2×#561211yescharacteristic, complemented
1112C3C2×#565411yescharacteristic, complemented
1113C2—42no—
1114C2—64no—
1115C2—122no—
1116C2—122no—
1117C2—184no—
1118C2—184no—
1119C2#1059427914yesdirect product factor
1120C2C2×#6430611yescharacteristic
1121C2C2×D32×D411yescharacteristic
1122C2C2×#6431411yescharacteristic
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×#3798C2semidirect
3. C2×C22⋊C4×C3⋊D3C2semidirect
4. C2×C3×#884C2semidirect
5. C2×C3×#883C2semidirect
6. C2×#63981C2semidirect
7. C2×#63970C2semidirect
8. C2×#63959C2semidirect
9. C2×#63922C2semidirect
10. C2×D3×(C2×D3)⋊C4C2semidirect
11. C2×#63916C2semidirect
12. C2×#63904C2semidirect
13. C2×#63895C2semidirect
14. C2×#63881C2semidirect
15. C2×#63853C2semidirect
16. #10594279C2direct (N × H)
21. C22×C4×C3⋊D3C22semidirect
22. C22×C4×C3⋊D3C22semidirect
25. C22×C3×#67C22semidirect
26. C22×C3×D12C22semidirect
27. C22×C3×C4×D3C22semidirect
28. C22×C3×C4×D3C22semidirect
30. C2×#3811C22semidirect
31. C22×#627C22semidirect
35. C22×#626C22semidirect
36. C22×#625C22semidirect
38. C22×D3×Dic3C22semidirect
40. C2×#3798C22semidirect
41. C2×C32×C22⋊C4C22semidirect
42. C2×#3757C22semidirect
45. C22⋊C4×C3⋊D3C22semidirect
46. C2×C3×#217C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×C4⋊Dic3C22semidirect
50. C2×C3×Dic3⋊C4C22semidirect
51. C2×C3×Dic3⋊C4C22semidirect
52. C3×#884C22semidirect
53. C3×#883C22semidirect
54. #63981C22semidirect
55. #63970C22semidirect
56. C2×Dic3⋊Dic3C22semidirect
58. C2×#3722C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. #63959C22semidirect
63. C2×Dic32C22semidirect
64. #63922C22semidirect
65. D3×(C2×D3)⋊C4C22semidirect
66. #63916C22semidirect
67. #63904C22semidirect
68. #63895C22semidirect
69. #63881C22semidirect
70. #63853C22semidirect
94. C2×#884D3semidirect
96. C2×#883D3semidirect
124. C2×C4×C3⋊D3C23semidirect
125. C2×C4×C3⋊D3C23semidirect
131. C2×C3×#67C23semidirect
138. C2×C3×D12C23semidirect
141. C2×C3×C4×D3C23semidirect
142. C2×C3×C4×D3C23semidirect
145. C2×#627C23semidirect
149. C2×#626D4semidirect
153. C2×#626C23semidirect
155. C2×#625C23semidirect
159. C2×D3×Dic3C23semidirect
161. C32×C22⋊C4C23semidirect
162. #3757C23semidirect
165. C3×#217C23semidirect
166. C3×(C2×D3)⋊C4C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×C4⋊Dic3C23semidirect
169. C3×Dic3⋊C4C23semidirect
170. C3×Dic3⋊C4C23semidirect
171. Dic3⋊Dic3C23semidirect
173. #3722C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
198. C22×#67C2×D3semidirect
212. C22×D12C2×D3semidirect
222. C22×C4×D3C2×D3semidirect
223. C22×C4×D3C2×D3semidirect
235. C2×C3×C22⋊C4C2×D3semidirect
236. C2×C3×C22⋊C4C2×D3semidirect
243. C2×#217C2×D3semidirect
265. C2×(C2×D3)⋊C4C2×D3semidirect
266. C2×(C2×D3)⋊C4C2×D3semidirect
268. C2×C4⋊Dic3C2×D3semidirect
270. C2×Dic3⋊C4C2×D3semidirect
271. C2×Dic3⋊C4C2×D3semidirect
281. #884C2×D3semidirect
283. #883C2×D3semidirect
305. C22×C3⋊D3#41semidirect
354. #626C2×D4semidirect
449. C2×#67C22×D3semidirect
476. C2×D12C22×D3semidirect
497. C2×C4×D3C22×D3semidirect
498. C2×C4×D3C22×D3semidirect
510. C3×C22⋊C4C22×D3semidirect
511. C3×C22⋊C4C22×D3semidirect
518. #217C22×D3semidirect
532. (C2×D3)⋊C4C22×D3semidirect
533. (C2×D3)⋊C4C22×D3semidirect
535. C4⋊Dic3C22×D3semidirect
537. Dic3⋊C4C22×D3semidirect
538. Dic3⋊C4C22×D3semidirect
557. C2×C3⋊D3C2×#41semidirect
630. C2×C22⋊C4D32semidirect
794. C2×C32#546semidirect
875. C22⋊C4C2×D32semidirect
976. C32C2×#546semidirect
1054. C2×C3#5612semidirect
1055. C2×C3#5654semidirect
1111. C3C2×#5612semidirect
1112. C3C2×#5654semidirect
1119. C2#10594279direct (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×#37982
C2×C22⋊C4×C3⋊D32
C2×C3×#8842
C2×C3×#8832
C2×#639812
C2×#639702
C2×#639592
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639162
C2×#639042
C2×#638952
C2×#638812
C2×#638532
#105942792
C2×#56543
C2×#56123