Finite Group Databasebeta

← C2×#10594278 #11902451

Subgroups — C2×#10594278 #11902451

Order 1152.

3971 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×#67C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3C2×#64092C211yesmaximal, characteristic, complemented
4C2×C3×#884C211yesmaximal, characteristic, complemented
5C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
6C2×#63976C211yesmaximal, characteristic, complemented
7C2×#63959C211yesmaximal, characteristic, complemented
8C2×#63958C211yesmaximal, characteristic, complemented
9C2×#63922C211yesmaximal, characteristic, complemented
10C2×#63921C211yesmaximal, characteristic, complemented
11C2×#63908C211yesmaximal, characteristic, complemented
12C2×#63905C211yesmaximal, characteristic, complemented
13C2×#63904C211yesmaximal, characteristic, complemented
14C2×#63893C211yesmaximal, characteristic, complemented
15C2×#63879C211yesmaximal, characteristic, complemented
16#10594278C2116yesmaximal, direct product factor
17C2×#5612—31nomaximal
18C2×#5490—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic, complemented
25C22×C3×D12C2211yescharacteristic, complemented
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×C3×C4×D3C2211yescharacteristic, complemented
29C2×D3×#67—28no—
30C2×D3×#67C2218yescomplemented
31C22×#627C2211yescharacteristic, complemented
32C22×#626C2211yescharacteristic
33C22×#626C2211yescharacteristic, complemented
34C22×#625C2211yescharacteristic
35C22×#625C2211yescharacteristic
36C22×#625C2211yescharacteristic, complemented
37C22×#624C2211yescharacteristic, complemented
38C22×D3×Dic3C2211yescharacteristic
39C2×#3798—28no—
40C2×#3798C2218yescomplemented
41C2×C32×C22⋊C4C2211yescharacteristic, complemented
42C2×#3757C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic, complemented
44C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45C2×#3750C2211yescharacteristic, complemented
46#64092C2218yescomplemented
47C2×C3×#217C2211yescharacteristic, complemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
52C3×#884C2218yescomplemented
53C3×D3×C22⋊C4C2218yescomplemented
54#63976C2218yescomplemented
55C2×Dic3⋊Dic3C2211yescharacteristic, complemented
56C2×(C2×D3)⋊Dic3C2211yescharacteristic
57C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61#63959C2218yescomplemented
62#63958C2218yescomplemented
63C2×Dic32C2211yescharacteristic, complemented
64#63922C2218yescomplemented
65#63921C2218yescomplemented
66#63908C2218yescomplemented
67#63905C2218yescomplemented
68#63904C2218yescomplemented
69#63893C2218yescomplemented
70#63879C2218yescomplemented
71C23×#67—31no—
72C22×D3×D4—31no—
73C22×#235—31no—
74C22×#235—31no—
75C2×C3×#121—31no—
76C22×C3×C22⋊C4—31no—
77C2×#953—31no—
78C2×#938—31no—
79C2×#938—31no—
80C2×#937—31no—
81C2×#937—31no—
82C2×#936—31no—
83C2×#930—31no—
84C2×#929—31no—
85C2×C4×#67—31no—
86C2×C4×#67—31no—
87#5612—316no—
88C2×#897—31no—
89C2×#893—31no—
90C2×#885—31no—
91#5490—316no—
92C2×#884—31no—
93C2×#884D311yescharacteristic, complemented
94C2×#883—31no—
95C2×#883—31no—
96C2×#883—31no—
97C2×#883—61no—
98C2×#882—31no—
99C2×#67⋊C4—31no—
100C2×D3×C22⋊C4—31no—
101C2×D3×C22⋊C4—31no—
102C2×D3×C22⋊C4D311yescharacteristic, complemented
103C2×#878—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3×D3—24no—
107C23×C3×D3—24no—
108C23×C3×D3—42no—
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2314yes—
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C22×D32—24no—
115C22×D32—24no—
116C22×D32—42no—
117C22×D32C2314yes—
118C22×C32×C4C2311yescharacteristic
119C22×C32×C4C2311yescharacteristic
120C2×#638—24no—
121C2×#638C2314yes—
122C22×C3⋊Dic3C2311yescharacteristic
123C22×C3⋊Dic3C2311yescharacteristic
124C22×C3⋊Dic3C2311yescharacteristic
125C2×C4×C3⋊D3—24no—
126C2×C4×C3⋊D3C2314yescomplemented
127C2×C3×#67—24no—
128C2×C3×#67—42no—
129C2×C3×#67C2314yes—
130C2×C3×#67C2314yescomplemented
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C2×C3×D12—42no—
136C2×C3×D12C2314yescomplemented
137C2×C3×C4×D3—24no—
138C2×C3×C4×D3—24no—
139C2×C3×C4×D3—42no—
140C2×C3×C4×D3C2314yescomplemented
141C2×C3×C4×D3C2314yescomplemented
142C2×C3×C4×D3C2314yescomplemented
143D3×#67—232no—
144C2×#627—24no—
145C2×#627C2314yescomplemented
146C2×#626—24no—
147C2×#626D418yescomplemented
148C2×#626C2314yes—
149C2×#626C2314yescomplemented
150C2×#625—24no—
151C2×#625—24no—
152C2×#625—24no—
153C2×#625C2314yes—
154C2×#625C2314yes—
155C2×#625C2314yescomplemented
156C2×#624—42no—
157C2×#624C2314yescomplemented
158C2×D3×Dic3—24no—
159C2×D3×Dic3C2314yes—
160#3798—232no—
161C32×C22⋊C4C2314yescomplemented
162#3757C2314yescomplemented
163#3752C2314yescomplemented
164C4⋊(C3⋊Dic3)C2314yescomplemented
165#3750C2314yescomplemented
166C3×#217C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yes—
168C3×(C2×D3)⋊C4C2314yes—
169C3×(C2×D3)⋊C4C2314yescomplemented
170C3×Dic3⋊C4C2314yescomplemented
171Dic3⋊Dic3C2314yescomplemented
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2314yescomplemented
174(C2×D3)⋊Dic3C2314yescomplemented
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3C2×D311yescharacteristic
183C22×C3×D4—31no—
184C22×C3×D4—31no—
185C22×C3×D4—31no—
186C23×C3×C4—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—38no—
198C22×#67—31no—
199C22×#67—31no—
200C22×#67—61no—
201C22×#67—68no—
202C22×#67C2×D311yescharacteristic
203C22×#67C2×D311yescharacteristic, complemented
204C23×Dic3—31no—
205C2×D3×D4—38no—
206C2×D3×D4—68no—
207C2×#235—38no—
208C2×#235—38no—
209C2×#235—68no—
210C2×#235—68no—
211C22×D12—31no—
212C22×D12—31no—
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×C4×D3C2×D311yescharacteristic, complemented
223C22×Dic6—31no—
224C22×Dic6—31no—
225C3×#121—38no—
226C2×C3×C4⋊C4—31no—
227C2×C3×C22⋊C4—21no—
228C2×C3×C22⋊C4—31no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—38no—
233C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
234C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
235#953—38no—
236C2×#217—31no—
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217—31no—
241C2×#217—31no—
242C2×#217—31no—
243C2×#217—61no—
244C2×#217C2×D311yescharacteristic, complemented
245#938—38no—
246#938—38no—
247#937—38no—
248#937—38no—
249#936—38no—
250#930—38no—
251#929—38no—
252C4×#67—38no—
253C4×#67—38no—
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—61no—
262C2×(C2×D3)⋊C4C2×D311yescharacteristic
263C2×(C2×D3)⋊C4C2×D311yescharacteristic
264C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
265C2×C4⋊Dic3—31no—
266C2×C4⋊Dic3—31no—
267C2×C4⋊Dic3—31no—
268C2×C4⋊Dic3—61no—
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4—31no—
271C2×Dic3⋊C4—31no—
272C2×Dic3⋊C4—61no—
273C2×Dic3⋊C4C2×D311yescharacteristic, complemented
274C2×C4×Dic3—31no—
275C2×C4×Dic3—31no—
276#897—38no—
277#893—38no—
278#885—38no—
279#884—38no—
280#884C2×D318yescomplemented
281#883—38no—
282#883—38no—
283#883—38no—
284#883—68no—
285#882—38no—
286#67⋊C4—38no—
287D3×C22⋊C4—38no—
288D3×C22⋊C4—38no—
289D3×C22⋊C4C2×D318yescomplemented
290#878—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32C2412yes—
295C23×C32C2411yescharacteristic
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3C2×D414yes—
299C22×C3⋊D3C2412yes—
300C22×C3×D3—22no—
301C22×C3×D3—22no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
306C22×C3×D3—22no—
307C22×C3×D3—22no—
308C22×C3×D3—22no—
309C22×C3×D3—22no—
310C22×C3×D3—28no—
311C22×C3×D3—28no—
312C22×C3×D3—44no—
313C22×C3×D3—416no—
314C22×C3×D3C2×D414yes—
315C22×C3×D3#4114yescomplemented
316C22×C3×D3C2412yes—
317C22×C3×D3C2412yes—
318C22×C3×D3C2412yes—
319C22×C3×D3C2412yes—
320C2×D32—28no—
321C2×D32—28no—
322C2×D32—44no—
323C2×D32—416no—
324C2×C32×C4—22no—
325C2×C32×C4—22no—
326C2×C32×C4C2412yes—
327C2×C32×C4C2412yes—
328#638—28no—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3—22no—
332C2×C3⋊Dic3C2412yes—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335C4×C3⋊D3—28no—
336C3×#67—28no—
337C3×#67—44no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3C2×D414yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C3×D12—44no—
347C3×C4×D3—28no—
348C3×C4×D3—28no—
349C3×C4×D3—44no—
350#627—28no—
351#626—28no—
352#626C2×D4116yescomplemented
353#625—28no—
354#625—28no—
355#625—28no—
356#624—44no—
357D3×Dic3—28no—
358C22×#41—91no—
359C23×D4—91no—
360#546—916no—
361C2×#124—91no—
362C2×#123—91no—
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—31no—
373C22×C22⋊C4—91no—
374C24×C3—21no—
375C24×C3—31no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3—31no—
379C24×C3—34no—
380C24×C3—64no—
381C24×C3—64no—
382C24×C3—122no—
383C24×C3C22×D311yescharacteristic
384C24×C3C22×D311yescharacteristic
385C23×D3—24no—
386C23×D3—24no—
387C23×D3—31no—
388C23×D3—31no—
389C23×D3—34no—
390C23×D3—34no—
391C23×D3—42no—
392C23×D3—61no—
393C23×D3—64no—
394C23×D3—64no—
395C23×D3—64no—
396C23×D3—64no—
397C23×D3—122no—
398C23×D3—122no—
399C23×D3C22×D311yescharacteristic
400C23×D3C22×D311yescharacteristic
401C23×D3C22×D314yes—
402C23×D3C22×D311yescharacteristic
403C23×D3C22×D311yescharacteristic
404C2×C3×D4—34no—
405C2×C3×D4—34no—
406C2×C3×D4—34no—
407C2×C3×D4—64no—
408C2×C3×D4—122no—
409C2×C3×D4—122no—
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—34no—
417C22×C3×C4—34no—
418C22×C3×C4—34no—
419C22×C3×C4—64no—
420C22×C3×C4—64no—
421C22×C3×C4—122no—
422C22×C3×C4C22×D311yescharacteristic
423C22×C3×C4C22×D311yescharacteristic
424C22×C3×C4C22×D311yescharacteristic
425C22×C3×C4C22×D311yescharacteristic
426C2×#67—24no—
427C2×#67—34no—
428C2×#67—34no—
429C2×#67—34no—
430C2×#67—34no—
431C2×#67—34no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—38no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—42no—
439C2×#67—64no—
440C2×#67—64no—
441C2×#67—632no—
442C2×#67—64no—
443C2×#67—64no—
444C2×#67—64no—
445C2×#67—64no—
446C2×#67—64no—
447C2×#67—64no—
448C2×#67—64no—
449C2×#67—64no—
450C2×#67—124no—
451C2×#67C22×D314yes—
452C2×#67C22×D314yescomplemented
453C22×Dic3—31no—
454C22×Dic3—31no—
455C22×Dic3—31no—
456C22×Dic3—31no—
457C22×Dic3—31no—
458C22×Dic3—31no—
459C22×Dic3—34no—
460C22×Dic3—61no—
461C22×Dic3—61no—
462C22×Dic3—61no—
463C22×Dic3—64no—
464C22×Dic3C22×D311yescharacteristic
465C22×Dic3C22×D311yescharacteristic
466C22×Dic3C22×D311yescharacteristic
467C22×Dic3C22×D311yescharacteristic
468D3×D4—632no—
469#235—632no—
470#235—632no—
471C2×D12—38no—
472C2×D12—34no—
473C2×D12—34no—
474C2×D12—42no—
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—42no—
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×D3—122no—
492C2×C4×D3C22×D314yescomplemented
493C2×C4×D3C22×D314yescomplemented
494C2×C4×D3C22×D314yescomplemented
495C2×Dic6—34no—
496C2×Dic6—34no—
497C2×Dic6—64no—
498C2×Dic6—64no—
499C3×C4⋊C4—34no—
500C3×C22⋊C4—24no—
501C3×C22⋊C4—34no—
502C3×C22⋊C4—34no—
503C3×C22⋊C4—34no—
504C3×C22⋊C4—34no—
505C3×C22⋊C4C22×D314yescomplemented
506C3×C22⋊C4C22×D314yescomplemented
507#217—34no—
508#217—34no—
509#217—34no—
510#217—34no—
511#217—34no—
512#217—34no—
513#217—34no—
514#217—64no—
515#217C22×D314yescomplemented
516(C2×D3)⋊C4—34no—
517(C2×D3)⋊C4—34no—
518(C2×D3)⋊C4—34no—
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4—34no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—64no—
524(C2×D3)⋊C4C22×D314yes—
525(C2×D3)⋊C4C22×D314yes—
526(C2×D3)⋊C4C22×D314yescomplemented
527C4⋊Dic3—34no—
528C4⋊Dic3—34no—
529C4⋊Dic3—34no—
530C4⋊Dic3—64no—
531Dic3⋊C4—34no—
532Dic3⋊C4—34no—
533Dic3⋊C4—34no—
534Dic3⋊C4—64no—
535Dic3⋊C4C22×D314yescomplemented
536C4×Dic3—34no—
537C4×Dic3—34no—
538C22×C32—22no—
539C22×C32—22no—
540C22×C32—22no—
541C22×C32—44no—
542C22×C32C22×D412yes—
543C22×C32C2×#4112yes—
544C22×C32H(5,𝔽2)12yes—
545C22×C32C2511yescharacteristic
546C2×C3⋊D3—28no—
547C2×C3⋊D3—22no—
548C2×C3⋊D3—22no—
549C2×C3⋊D3C22×D414yes—
550C2×C3×D3—28no—
551C2×C3×D3—28no—
552C2×C3×D3—22no—
553C2×C3×D3—22no—
554C2×C3×D3—22no—
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—22no—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—416no—
563C2×C3×D3—44no—
564C2×C3×D3—44no—
565C2×C3×D3C22×D414yes—
566C2×C3×D3C2×#4114yescomplemented
567D32—416no—
568C32×C4—22no—
569C32×C4—22no—
570C3⋊Dic3—22no—
571C3⋊Dic3—22no—
572C3⋊Dic3—22no—
573C3×Dic3—22no—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3C22×D414yes—
577C25—31no—
578C25—91no—
579C2×#41—98no—
580C2×#41—188no—
581C22×Q8—91no—
582C22×D4—31no—
583C22×D4—31no—
584C22×D4—31no—
585C22×D4—91no—
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—31no—
596C23×C4—91no—
597C23×C4—91no—
598C23×C4—91no—
599#124—98no—
600#123—98no—
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⋊C4—91no—
614C2×C22⋊C4—31no—
615C2×C22⋊C4—31no—
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—38no—
619C2×C22⋊C4—98no—
620C2×C22⋊C4—91no—
621C2×C22⋊C4—91no—
622C2×C22⋊C4—91no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4D3211yescharacteristic, complemented
628C2×C42—91no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—21no—
637C23×C3—34no—
638C23×C3—34no—
639C23×C3—32no—
640C23×C3—32no—
641C23×C3—32no—
642C23×C3—32no—
643C23×C3—42no—
644C23×C3—42no—
645C23×C3—42no—
646C23×C3—68no—
647C23×C3—68no—
648C23×C3—62no—
649C23×C3—62no—
650C23×C3—62no—
651C23×C3—62no—
652C23×C3—62no—
653C23×C3—62no—
654C23×C3—62no—
655C23×C3—62no—
656C23×C3—62no—
657C23×C3—62no—
658C23×C3—124no—
659C23×C3—1216no—
660C23×C3C23×D312yes—
661C23×C3C23×D312yes—
662C23×C3C23×D311yescharacteristic
663C23×C3C23×D311yescharacteristic
664C22×D3—22no—
665C22×D3—22no—
666C22×D3—22no—
667C22×D3—22no—
668C22×D3—22no—
669C22×D3—22no—
670C22×D3—22no—
671C22×D3—22no—
672C22×D3—22no—
673C22×D3—22no—
674C22×D3—28no—
675C22×D3—28no—
676C22×D3—34no—
677C22×D3—34no—
678C22×D3—32no—
679C22×D3—32no—
680C22×D3—44no—
681C22×D3—416no—
682C22×D3—64no—
683C22×D3—62no—
684C22×D3—68no—
685C22×D3—68no—
686C22×D3—68no—
687C22×D3—62no—
688C22×D3—62no—
689C22×D3—62no—
690C22×D3—62no—
691C22×D3—68no—
692C22×D3—122no—
693C22×D3—122no—
694C22×D3—124no—
695C22×D3—124no—
696C22×D3—1216no—
697C22×D3—1216no—
698C22×D3#23514yescomplemented
699C22×D3D3×D414yes—
700C22×D3C23×D312yes—
701C22×D3C23×D312yes—
702C22×D3C23×D312yes—
703C22×D3C23×D312yes—
704C3×D4—68no—
705C3×D4—124no—
706C3×D4—124no—
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—34no—
714C2×C3×C4—32no—
715C2×C3×C4—32no—
716C2×C3×C4—32no—
717C2×C3×C4—32no—
718C2×C3×C4—42no—
719C2×C3×C4—42no—
720C2×C3×C4—68no—
721C2×C3×C4—68no—
722C2×C3×C4—62no—
723C2×C3×C4—62no—
724C2×C3×C4—62no—
725C2×C3×C4—124no—
726C2×C3×C4C23×D312yes—
727C2×C3×C4C23×D312yes—
728C2×C3×C4C23×D312yes—
729C2×C3×C4C23×D312yes—
730#67—28no—
731#67—316no—
732#67—44no—
733#67—68no—
734#67—68no—
735#67—68no—
736#67—68no—
737#67—68no—
738#67—68no—
739#67—68no—
740#67—68no—
741#67—68no—
742#67—128no—
743C2×Dic3—22no—
744C2×Dic3—22no—
745C2×Dic3—22no—
746C2×Dic3—32no—
747C2×Dic3—32no—
748C2×Dic3—32no—
749C2×Dic3—32no—
750C2×Dic3—32no—
751C2×Dic3—32no—
752C2×Dic3—62no—
753C2×Dic3—62no—
754C2×Dic3—62no—
755C2×Dic3—62no—
756C2×Dic3—62no—
757C2×Dic3—62no—
758C2×Dic3—62no—
759C2×Dic3—62no—
760C2×Dic3—62no—
761C2×Dic3—68no—
762C2×Dic3—122no—
763C2×Dic3—122no—
764C2×Dic3—122no—
765C2×Dic3D3×D414yes—
766C2×Dic3C23×D312yes—
767C2×Dic3C23×D312yes—
768C2×Dic3C23×D312yes—
769C2×Dic3C23×D312yes—
770D12—316no—
771D12—44no—
772D12—68no—
773C4×D3—28no—
774C4×D3—28no—
775C4×D3—44no—
776C4×D3—68no—
777C4×D3—68no—
778C4×D3—68no—
779C4×D3—128no—
780C4×D3—124no—
781C4×D3—124no—
782Dic6—68no—
783Dic6—68no—
784C2×C32—42no—
785C2×C32#54614yescomplemented
786C2×C32C23×D411yescharacteristic
787C2×C32C22×#4111yescharacteristic
788C2×C32C2×H(5,𝔽2)11yescharacteristic
789C3⋊D3—24no—
790C3×D3—24no—
791C3×D3—24no—
792C3×D3—42no—
793C3×D3—42no—
794C24—31no—
795C24—31no—
796C24—31no—
797C24—31no—
798C24—34no—
799C24—64no—
800C24—64no—
801C24—94no—
802C24—91no—
803C24—122no—
804C24—184no—
805C24—184no—
806C24—362no—
807C24C2×D3211yescharacteristic
808#41—1832no—
809C2×Q8—94no—
810C2×Q8—184no—
811C2×D4—34no—
812C2×D4—34no—
813C2×D4—34no—
814C2×D4—64no—
815C2×D4—94no—
816C2×D4—98no—
817C2×D4—94no—
818C2×D4—94no—
819C2×D4—94no—
820C2×D4—94no—
821C2×D4—94no—
822C2×D4—122no—
823C2×D4—122no—
824C2×D4—184no—
825C2×D4—1832no—
826C2×D4—184no—
827C2×D4—184no—
828C2×D4—184no—
829C2×D4—184no—
830C22×C4—31no—
831C22×C4—31no—
832C22×C4—31no—
833C22×C4—31no—
834C22×C4—34no—
835C22×C4—34no—
836C22×C4—34no—
837C22×C4—64no—
838C22×C4—64no—
839C22×C4—94no—
840C22×C4—94no—
841C22×C4—91no—
842C22×C4—91no—
843C22×C4—91no—
844C22×C4—94no—
845C22×C4—122no—
846C22×C4—184no—
847C22×C4—184no—
848C22×C4—362no—
849C22×C4C2×D3211yescharacteristic
850C22×C4C2×D3211yescharacteristic
851C4⋊C4—34no—
852C4⋊C4—94no—
853C4⋊C4—94no—
854C4⋊C4—94no—
855C22⋊C4—34no—
856C22⋊C4—34no—
857C22⋊C4—34no—
858C22⋊C4—34no—
859C22⋊C4—94no—
860C22⋊C4—94no—
861C22⋊C4—94no—
862C22⋊C4—94no—
863C22⋊C4—94no—
864C22⋊C4—94no—
865C22⋊C4—94no—
866C22⋊C4C2×D3214yescomplemented
867C42—94no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—22no—
871C22×C3—22no—
872C22×C3—22no—
873C22×C3—22no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—21no—
878C22×C3—34no—
879C22×C3—34no—
880C22×C3—42no—
881C22×C3—42no—
882C22×C3—42no—
883C22×C3—44no—
884C22×C3—44no—
885C22×C3—62no—
886C22×C3—62no—
887C22×C3—62no—
888C22×C3—62no—
889C22×C3—68no—
890C22×C3—68no—
891C22×C3—62no—
892C22×C3—62no—
893C22×C3—62no—
894C22×C3—62no—
895C22×C3—62no—
896C22×C3—62no—
897C22×C3—84no—
898C22×C3—1216no—
899C22×C3—124no—
900C22×C3—124no—
901C22×C3C2×#23512yes—
902C22×C3C2×D3×D412yes—
903C22×C3C2×D3×D412yes—
904C22×C3#100412yes—
905C22×C3#100412yes—
906C22×C3D3×#4112yes—
907C22×C3C24×D311yescharacteristic
908C22×C3C24×D311yescharacteristic
909C2×D3—22no—
910C2×D3—22no—
911C2×D3—22no—
912C2×D3—22no—
913C2×D3—28no—
914C2×D3—28no—
915C2×D3—22no—
916C2×D3—22no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—34no—
922C2×D3—34no—
923C2×D3—416no—
924C2×D3—44no—
925C2×D3—44no—
926C2×D3—64no—
927C2×D3—62no—
928C2×D3—62no—
929C2×D3—62no—
930C2×D3—62no—
931C2×D3—68no—
932C2×D3—68no—
933C2×D3—122no—
934C2×D3—122no—
935C2×D3—128no—
936C2×D3—1216no—
937C2×D3—1216no—
938C2×D3C2×#23514yescomplemented
939C2×D3C2×D3×D414yes—
940C3×C4—22no—
941C3×C4—22no—
942C3×C4—22no—
943C3×C4—22no—
944C3×C4—34no—
945C3×C4—42no—
946C3×C4—42no—
947C3×C4—62no—
948C3×C4—62no—
949C3×C4—62no—
950Dic3—22no—
951Dic3—22no—
952Dic3—22no—
953Dic3—62no—
954Dic3—62no—
955Dic3—62no—
956Dic3—62no—
957Dic3—62no—
958Dic3—62no—
959Dic3—122no—
960Dic3—122no—
961Dic3—122no—
962Dic3C2×D3×D414yes—
963C32C2×#54611yescharacteristic, complemented, Sylow
964C23—22no—
965C23—22no—
966C23—22no—
967C23—34no—
968C23—34no—
969C23—32no—
970C23—32no—
971C23—32no—
972C23—32no—
973C23—68no—
974C23—68no—
975C23—62no—
976C23—62no—
977C23—62no—
978C23—62no—
979C23—62no—
980C23—62no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—62no—
985C23—94no—
986C23—92no—
987C23—124no—
988C23—1216no—
989C23—188no—
990C23—188no—
991C23—182no—
992C23—182no—
993C23—364no—
994C23—3616no—
995C23C22×D3212yes—
996C23C22×D3211yescharacteristic
997Q8—188no—
998D4—68no—
999D4—916no—
1000D4—124no—
1001D4—124no—
1002D4—188no—
1003D4—188no—
1004D4—188no—
1005D4—188no—
1006D4—188no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—34no—
1010C2×C4—32no—
1011C2×C4—32no—
1012C2×C4—32no—
1013C2×C4—32no—
1014C2×C4—68no—
1015C2×C4—68no—
1016C2×C4—62no—
1017C2×C4—62no—
1018C2×C4—62no—
1019C2×C4—92no—
1020C2×C4—92no—
1021C2×C4—92no—
1022C2×C4—124no—
1023C2×C4—188no—
1024C2×C4—188no—
1025C2×C4—182no—
1026C2×C4—182no—
1027C2×C4—182no—
1028C2×C4—364no—
1029C2×C4C22×D3212yes—
1030C2×C4C22×D3212yes—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—24no—
1035C2×C3—42no—
1036C2×C3—42no—
1037C2×C3—64no—
1038C2×C3—64no—
1039C2×C3—82no—
1040C2×C3—122no—
1041C2×C3—122no—
1042C2×C3#549014yescomplemented
1043C2×C3#561214yescomplemented
1044C2×C3C22×#23511yescharacteristic
1045C2×C3C22×D3×D411yescharacteristic
1046C2×C3C22×D3×D411yescharacteristic
1047C2×C3C2×#100411yescharacteristic
1048C2×C3C2×#100411yescharacteristic
1049C2×C3C2×D3×#4111yescharacteristic
1050D3—24no—
1051D3—24no—
1052D3—42no—
1053D3—42no—
1054D3—64no—
1055D3—64no—
1056D3—124no—
1057C22—22no—
1058C22—22no—
1059C22—22no—
1060C22—34no—
1061C22—34no—
1062C22—44no—
1063C22—62no—
1064C22—62no—
1065C22—62no—
1066C22—62no—
1067C22—68no—
1068C22—68no—
1069C22—62no—
1070C22—62no—
1071C22—62no—
1072C22—62no—
1073C22—62no—
1074C22—62no—
1075C22—94no—
1076C22—1216no—
1077C22—124no—
1078C22—124no—
1079C22—182no—
1080C22—182no—
1081C22—188no—
1082C22—3616no—
1083C22D3×#23512yes—
1084C22D32×D412yes—
1085C22#6431312yes—
1086C22C23×D3211yescharacteristic
1087C4—22no—
1088C4—22no—
1089C4—34no—
1090C4—62no—
1091C4—62no—
1092C4—62no—
1093C4—182no—
1094C4—182no—
1095C4—182no—
1096C3—21no—
1097C3C2×#549011yescharacteristic, complemented
1098C3C2×#561211yescharacteristic, complemented
1099C2—42no—
1100C2—64no—
1101C2—64no—
1102C2—122no—
1103C2—122no—
1104C2—184no—
1105C2#1059427814yesdirect product factor
1106C2C2×D3×#23511yescharacteristic
1107C2C2×D32×D411yescharacteristic
1108C2C2×#6431311yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×#67C2semidirect
2. C22×#3798C2semidirect
3. C2×#64092C2semidirect
4. C2×C3×#884C2semidirect
5. C2×C3×D3×C22⋊C4C2semidirect
6. C2×#63976C2semidirect
7. C2×#63959C2semidirect
8. C2×#63958C2semidirect
9. C2×#63922C2semidirect
10. C2×#63921C2semidirect
11. C2×#63908C2semidirect
12. C2×#63905C2semidirect
13. C2×#63904C2semidirect
14. C2×#63893C2semidirect
15. C2×#63879C2semidirect
16. #10594278C2direct (N × H)
22. C22×C4×C3⋊D3C22semidirect
24. C22×C3×#67C22semidirect
25. C22×C3×D12C22semidirect
26. C22×C3×C4×D3C22semidirect
27. C22×C3×C4×D3C22semidirect
28. C22×C3×C4×D3C22semidirect
30. C2×D3×#67C22semidirect
31. C22×#627C22semidirect
33. C22×#626C22semidirect
36. C22×#625C22semidirect
37. C22×#624C22semidirect
40. C2×#3798C22semidirect
41. C2×C32×C22⋊C4C22semidirect
42. C2×#3757C22semidirect
43. C2×#3752C22semidirect
44. C2×C4⋊(C3⋊Dic3)C22semidirect
45. C2×#3750C22semidirect
46. #64092C22semidirect
47. C2×C3×#217C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×Dic3⋊C4C22semidirect
52. C3×#884C22semidirect
53. C3×D3×C22⋊C4C22semidirect
54. #63976C22semidirect
55. C2×Dic3⋊Dic3C22semidirect
57. C2×(C2×D3)⋊Dic3C22semidirect
58. C2×(C2×D3)⋊Dic3C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. #63959C22semidirect
62. #63958C22semidirect
63. C2×Dic32C22semidirect
64. #63922C22semidirect
65. #63921C22semidirect
66. #63908C22semidirect
67. #63905C22semidirect
68. #63904C22semidirect
69. #63893C22semidirect
70. #63879C22semidirect
93. C2×#884D3semidirect
102. C2×D3×C22⋊C4D3semidirect
126. C2×C4×C3⋊D3C23semidirect
130. C2×C3×#67C23semidirect
136. C2×C3×D12C23semidirect
140. C2×C3×C4×D3C23semidirect
141. C2×C3×C4×D3C23semidirect
142. C2×C3×C4×D3C23semidirect
145. C2×#627C23semidirect
147. C2×#626D4semidirect
149. C2×#626C23semidirect
155. C2×#625C23semidirect
157. C2×#624C23semidirect
161. C32×C22⋊C4C23semidirect
162. #3757C23semidirect
163. #3752C23semidirect
164. C4⋊(C3⋊Dic3)C23semidirect
165. #3750C23semidirect
166. C3×#217C23semidirect
169. C3×(C2×D3)⋊C4C23semidirect
170. C3×Dic3⋊C4C23semidirect
171. Dic3⋊Dic3C23semidirect
173. (C2×D3)⋊Dic3C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
203. C22×#67C2×D3semidirect
213. C22×D12C2×D3semidirect
220. C22×C4×D3C2×D3semidirect
221. C22×C4×D3C2×D3semidirect
222. C22×C4×D3C2×D3semidirect
233. C2×C3×C22⋊C4C2×D3semidirect
234. C2×C3×C22⋊C4C2×D3semidirect
244. C2×#217C2×D3semidirect
264. C2×(C2×D3)⋊C4C2×D3semidirect
273. C2×Dic3⋊C4C2×D3semidirect
280. #884C2×D3semidirect
289. D3×C22⋊C4C2×D3semidirect
315. C22×C3×D3#41semidirect
352. #626C2×D4semidirect
452. C2×#67C22×D3semidirect
476. C2×D12C22×D3semidirect
492. C2×C4×D3C22×D3semidirect
493. C2×C4×D3C22×D3semidirect
494. C2×C4×D3C22×D3semidirect
505. C3×C22⋊C4C22×D3semidirect
506. C3×C22⋊C4C22×D3semidirect
515. #217C22×D3semidirect
526. (C2×D3)⋊C4C22×D3semidirect
535. Dic3⋊C4C22×D3semidirect
566. C2×C3×D3C2×#41semidirect
627. C2×C22⋊C4D32semidirect
698. C22×D3#235semidirect
785. C2×C32#546semidirect
866. C22⋊C4C2×D32semidirect
938. C2×D3C2×#235semidirect
963. C32C2×#546semidirect
1042. C2×C3#5490semidirect
1043. C2×C3#5612semidirect
1097. C3C2×#5490semidirect
1098. C3C2×#5612semidirect
1105. C2#10594278direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×#672
C22×#37982
C2×#640922
C2×C3×#8842
C2×C3×D3×C22⋊C42
C2×#639762
C2×#639592
C2×#639582
C2×#639222
C2×#639212
C2×#639082
C2×#639052
C2×#639042
C2×#638932
C2×#638792
#105942782
C2×#56123
C2×#54903