Finite Group Databasebeta

← C2×#10594619 #11902475

Subgroups — C2×#10594619 #11902475

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×D12C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3C2×#64103C211yesmaximal, characteristic, complemented
4C2×C3×#894C211yesmaximal, characteristic, complemented
5C2×C3×#893C211yesmaximal, characteristic, complemented
6C2×#63922C211yesmaximal, characteristic, complemented
7C2×#63922C211yesmaximal, characteristic, complemented
8C2×#63921C211yesmaximal, characteristic, complemented
9C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C2×#63910C211yesmaximal, characteristic, complemented
11C2×#63906C211yesmaximal, characteristic, complemented
12C2×#63885C211yesmaximal, characteristic, complemented
13C2×#63880C211yesmaximal, characteristic, complemented
14C2×#63852C211yesmaximal, characteristic, complemented
15C2×#63851C211yesmaximal, characteristic, complemented
16#10594619C2116yesmaximal, direct product factor
17C2×#5654—31nomaximal
18C2×#5550—31nomaximal
19C23×D32C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×C4⋊(C3⋊D3)C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C22×C3×D12C2211yescharacteristic
24C22×C3×D12C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×#627C2211yescharacteristic, complemented
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic, complemented
32C22×#626C2211yescharacteristic, complemented
33C22×#625C2211yescharacteristic, complemented
34C22×#625C2211yescharacteristic, complemented
35C22×#624C2211yescharacteristic, complemented
36C22×D3×Dic3C2211yescharacteristic, complemented
37C2×D3×D12—28no—
38C2×D3×D12C2218yescomplemented
39C2×#3798—28no—
40C2×#3798C2218yescomplemented
41C2×C32×C4⋊C4C2211yescharacteristic, complemented
42C2×#3752C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic, complemented
44C2×#3752C2211yescharacteristic, complemented
45C2×#3750C2211yescharacteristic, complemented
46#64103C2218yescomplemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
52C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
53C2×C3×C4×Dic3C2211yescharacteristic, complemented
54C3×#894C2218yescomplemented
55C3×#893C2218yescomplemented
56C2×Dic3⋊Dic3C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61#63922C2218yescomplemented
62#63922C2218yescomplemented
63#63921C2218yescomplemented
64D3×(C2×D3)⋊C4C2218yescomplemented
65#63910C2218yescomplemented
66#63906C2218yescomplemented
67#63885C2218yescomplemented
68#63880C2218yescomplemented
69#63852C2218yescomplemented
70#63851C2218yescomplemented
71C22×D3×D4—31no—
72C22×#235—31no—
73C22×#235—31no—
74C23×D12—31no—
75C2×C3×#123—31no—
76C2×C3×C4×D4—31no—
77C2×#939—31no—
78C2×#937—31no—
79C2×#937—31no—
80C2×#930—31no—
81C22×(C2×D3)⋊C4—31no—
82C2×#924—31no—
83#5654—316no—
84#5550—316no—
85C2×#896—31no—
86C2×#895—31no—
87C2×#894—31no—
88C2×#894—31no—
89C2×#894—61no—
90C2×#894D311yescharacteristic, complemented
91C2×#893D311yescharacteristic, complemented
92C2×#885—31no—
93C2×#884—31no—
94C2×#884—31no—
95C2×#884—31no—
96C2×#882—31no—
97C2×#882—31no—
98C2×#67⋊C4—31no—
99C2×D3×C22⋊C4—31no—
100C2×D3×C22⋊C4—31no—
101C2×D3×C22⋊C4—31no—
102C2×#875—31no—
103C2×C4×D12—31no—
104C23×C3⋊D3C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C22×D32—24no—
111C22×D32—24no—
112C22×D32—24no—
113C22×D32—24no—
114C22×D32—42no—
115C22×D32—42no—
116C22×D32C2314yes—
117C22×D32C2314yes—
118C22×C32×C4C2311yescharacteristic
119C22×C32×C4C2311yescharacteristic
120C22×C32×C4C2311yescharacteristic
121C22×C3⋊Dic3C2311yescharacteristic
122C22×C3⋊Dic3C2311yescharacteristic
123C2×C4⋊(C3⋊D3)—24no—
124C2×C4⋊(C3⋊D3)C2314yes—
125C2×C4×C3⋊D3—24no—
126C2×C4×C3⋊D3C2314yescomplemented
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C22×C3×Dic3C2311yescharacteristic
130C22×C3×Dic3C2311yescharacteristic
131C2×C3×D12—24no—
132C2×C3×D12—24no—
133C2×C3×D12C2314yes—
134C2×C3×D12C2314yes—
135C2×C3×C4×D3—24no—
136C2×C3×C4×D3—24no—
137C2×C3×C4×D3—24no—
138C2×C3×C4×D3C2314yes—
139C2×C3×C4×D3C2314yescomplemented
140C2×C3×C4×D3C2314yescomplemented
141C2×#627—24no—
142C2×#627C2314yescomplemented
143C2×#626—24no—
144C2×#626—24no—
145C2×#626—42no—
146C2×#626D418yescomplemented
147C2×#626C2314yes—
148C2×#626C2314yes—
149C2×#626C2314yescomplemented
150C2×#626C2314yescomplemented
151C2×#625—24no—
152C2×#625—42no—
153C2×#625C2314yescomplemented
154C2×#625C2314yescomplemented
155C2×#624—42no—
156C2×#624C2314yescomplemented
157C2×D3×Dic3—42no—
158C2×D3×Dic3C2314yescomplemented
159D3×D12—232no—
160#3798—232no—
161C32×C4⋊C4C2314yescomplemented
162#3752C2314yescomplemented
163#3752C2314yescomplemented
164#3752C2314yescomplemented
165#3750C2314yescomplemented
166C3×(C2×D3)⋊C4C2314yes—
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×(C2×D3)⋊C4C2314yescomplemented
169C3×(C2×D3)⋊C4C2314yescomplemented
170C3×(C2×D3)⋊C4C2314yescomplemented
171C3×Dic3⋊C4C2314yescomplemented
172C3×C4×Dic3C2314yescomplemented
173Dic3⋊Dic3C2314yescomplemented
174#3722C2314yescomplemented
175(C2×D3)⋊Dic3C2314yes—
176(C2×D3)⋊Dic3C2314yes—
177(C2×D3)⋊Dic3C2314yescomplemented
178C2×#546—91noSylow
179C24×D3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3—31no—
183C22×C3×D4—31no—
184C22×C3×D4—31no—
185C23×C3×C4—31no—
186C23×C3×C4—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—31no—
195C22×#67—31no—
196C23×Dic3—31no—
197C2×D3×D4—38no—
198C2×D3×D4—68no—
199C2×#235—38no—
200C2×#235—38no—
201C2×#235—68no—
202C2×#235—68no—
203C22×D12—31no—
204C22×D12—31no—
205C22×D12—31no—
206C22×D12—31no—
207C22×D12—31no—
208C22×D12—31no—
209C22×D12—38no—
210C22×D12—61no—
211C22×D12—68no—
212C22×D12C2×D311yescharacteristic
213C22×D12C2×D311yescharacteristic
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
221C22×C4×D3C2×D311yescharacteristic, complemented
222C22×C4×D3C2×D311yescharacteristic, complemented
223C22×Dic6—31no—
224C22×Dic6—31no—
225C3×#123—38no—
226C3×C4×D4—38no—
227C2×C3×C4⋊C4—21no—
228C2×C3×C4⋊C4—31no—
229C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
230C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C22⋊C4—31no—
235C2×C3×C22⋊C4—31no—
236C2×C3×C42—31no—
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—31no—
240#939—38no—
241#937—38no—
242#937—38no—
243#930—38no—
244C2×(C2×D3)⋊C4—31no—
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—38no—
256C2×(C2×D3)⋊C4—61no—
257C2×(C2×D3)⋊C4—61no—
258C2×(C2×D3)⋊C4—61no—
259C2×(C2×D3)⋊C4C2×D311yescharacteristic
260C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
261C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
262C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
263C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
264C2×C4⋊Dic3—31no—
265#924—38no—
266C2×Dic3⋊C4—31no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4—31no—
269C2×Dic3⋊C4—61no—
270C2×Dic3⋊C4C2×D311yescharacteristic, complemented
271C2×C4×Dic3C2×D311yescharacteristic, complemented
272#896—38no—
273#895—38no—
274#894—38no—
275#894—38no—
276#894—68no—
277#894C2×D318yescomplemented
278#893C2×D318yescomplemented
279#885—38no—
280#884—38no—
281#884—38no—
282#884—38no—
283#882—38no—
284#882—38no—
285#67⋊C4—38no—
286D3×C22⋊C4—38no—
287D3×C22⋊C4—38no—
288D3×C22⋊C4—38no—
289#875—38no—
290C4×D12—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⋊D3C2×D414yes—
298C22×C3⋊D3C2412yes—
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×D3C2×D414yes—
311C22×C3×D3#4114yescomplemented
312C22×C3×D3C2412yes—
313C22×C3×D3C2412yes—
314C22×C3×D3C2412yes—
315C22×C3×D3C2412yes—
316C2×D32—28no—
317C2×D32—28no—
318C2×D32—28no—
319C2×D32—28no—
320C2×D32—44no—
321C2×D32—44no—
322C2×D32—416no—
323C2×D32—416no—
324C2×C32×C4—22no—
325C2×C32×C4—22no—
326C2×C32×C4—22no—
327C2×C32×C4C2412yes—
328C2×C32×C4C2412yes—
329C2×C32×C4C2412yes—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3—22no—
332C2×C3⋊Dic3C2412yes—
333C2×C3⋊Dic3C2412yes—
334C4⋊(C3⋊D3)—28no—
335C4×C3⋊D3—28no—
336C2×C3×Dic3—22no—
337C2×C3×Dic3—22no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3C2×D414yes—
340C2×C3×Dic3C2412yes—
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C3×D12—28no—
345C3×D12—28no—
346C3×C4×D3—28no—
347C3×C4×D3—28no—
348C3×C4×D3—28no—
349#627—28no—
350#626—28no—
351#626—28no—
352#626—44no—
353#626C2×D4116yescomplemented
354#625—28no—
355#625—44no—
356#624—44no—
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—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—91no—
369C2×#120—91no—
370C2×C4×D4—31no—
371C2×C4×D4—91no—
372C22×C22⋊C4—91no—
373C22×C22⋊C4—91no—
374C24×C3—31no—
375C24×C3—31no—
376C24×C3—31no—
377C24×C3—31no—
378C23×D3—31no—
379C23×D3—31no—
380C23×D3—31no—
381C23×D3—31no—
382C23×D3—34no—
383C23×D3—34no—
384C23×D3—34no—
385C23×D3—34no—
386C23×D3—61no—
387C23×D3—61no—
388C23×D3—64no—
389C23×D3—64no—
390C23×D3—64no—
391C23×D3—64no—
392C23×D3—64no—
393C23×D3—64no—
394C23×D3—64no—
395C23×D3—64no—
396C23×D3—122no—
397C23×D3—122no—
398C23×D3—122no—
399C23×D3—122no—
400C23×D3C22×D311yescharacteristic
401C23×D3C22×D311yescharacteristic
402C23×D3C22×D311yescharacteristic
403C23×D3C22×D311yescharacteristic
404C2×C3×D4—34no—
405C2×C3×D4—34no—
406C2×C3×D4—64no—
407C2×C3×D4—64no—
408C22×C3×C4—21no—
409C22×C3×C4—21no—
410C22×C3×C4—21no—
411C22×C3×C4—31no—
412C22×C3×C4—31no—
413C22×C3×C4—31no—
414C22×C3×C4—31no—
415C22×C3×C4—34no—
416C22×C3×C4—34no—
417C22×C3×C4—34no—
418C22×C3×C4—64no—
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—34no—
428C2×#67—34no—
429C2×#67—34no—
430C2×#67—34no—
431C2×#67—38no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—64no—
437C2×#67—64no—
438C2×#67—64no—
439C2×#67—64no—
440C2×#67—122no—
441C2×#67—122no—
442C2×#67—122no—
443C22×Dic3—31no—
444C22×Dic3—31no—
445C22×Dic3—31no—
446C22×Dic3—31no—
447C22×Dic3—34no—
448C22×Dic3—61no—
449C22×Dic3—61no—
450C22×Dic3—122no—
451C22×Dic3C22×D311yescharacteristic
452C22×Dic3C22×D311yescharacteristic
453C22×Dic3C22×D311yescharacteristic
454C22×Dic3C22×D311yescharacteristic
455D3×D4—632no—
456#235—632no—
457#235—632no—
458C2×D12—24no—
459C2×D12—24no—
460C2×D12—38no—
461C2×D12—34no—
462C2×D12—34no—
463C2×D12—34no—
464C2×D12—34no—
465C2×D12—34no—
466C2×D12—34no—
467C2×D12—64no—
468C2×D12—632no—
469C2×D12—64no—
470C2×D12—64no—
471C2×D12—64no—
472C2×D12—64no—
473C2×D12—124no—
474C2×D12—122no—
475C2×D12C22×D314yes—
476C2×D12C22×D314yes—
477C2×C4×D3—24no—
478C2×C4×D3—24no—
479C2×C4×D3—24no—
480C2×C4×D3—34no—
481C2×C4×D3—34no—
482C2×C4×D3—34no—
483C2×C4×D3—34no—
484C2×C4×D3—34no—
485C2×C4×D3—64no—
486C2×C4×D3—64no—
487C2×C4×D3—64no—
488C2×C4×D3—124no—
489C2×C4×D3—122no—
490C2×C4×D3—122no—
491C2×C4×D3—122no—
492C2×C4×D3C22×D314yes—
493C2×C4×D3C22×D314yescomplemented
494C2×C4×D3C22×D314yescomplemented
495C2×Dic6—34no—
496C2×Dic6—34no—
497C2×Dic6—64no—
498C2×Dic6—64no—
499C3×C4⋊C4—24no—
500C3×C4⋊C4—34no—
501C3×C4⋊C4C22×D314yescomplemented
502C3×C4⋊C4C22×D314yescomplemented
503C3×C22⋊C4—34no—
504C3×C22⋊C4—34no—
505C3×C22⋊C4—34no—
506C3×C22⋊C4—34no—
507C3×C22⋊C4—34no—
508C3×C42—34no—
509#217—34no—
510#217—34no—
511#217—34no—
512(C2×D3)⋊C4—34no—
513(C2×D3)⋊C4—34no—
514(C2×D3)⋊C4—34no—
515(C2×D3)⋊C4—34no—
516(C2×D3)⋊C4—34no—
517(C2×D3)⋊C4—34no—
518(C2×D3)⋊C4—34no—
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4—34no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—64no—
524(C2×D3)⋊C4—64no—
525(C2×D3)⋊C4—64no—
526(C2×D3)⋊C4C22×D314yes—
527(C2×D3)⋊C4C22×D314yescomplemented
528(C2×D3)⋊C4C22×D314yescomplemented
529(C2×D3)⋊C4C22×D314yescomplemented
530(C2×D3)⋊C4C22×D314yescomplemented
531C4⋊Dic3—34no—
532Dic3⋊C4—34no—
533Dic3⋊C4—34no—
534Dic3⋊C4—34no—
535Dic3⋊C4—64no—
536Dic3⋊C4C22×D314yescomplemented
537C4×Dic3C22×D314yescomplemented
538C22×C32C22×D412yes—
539C22×C32C2×#4112yes—
540C22×C32H(5,𝔽2)12yes—
541C22×C32C2511yescharacteristic
542C2×C3⋊D3—28no—
543C2×C3⋊D3—22no—
544C2×C3⋊D3—22no—
545C2×C3⋊D3—22no—
546C2×C3⋊D3—22no—
547C2×C3⋊D3—22no—
548C2×C3⋊D3—44no—
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—44no—
563C2×C3×D3—44no—
564C2×C3×D3C22×D414yes—
565C2×C3×D3C2×#4114yescomplemented
566D32—416no—
567D32—416no—
568C32×C4—22no—
569C32×C4—22no—
570C32×C4—22no—
571C3⋊Dic3—22no—
572C3⋊Dic3—22no—
573C3×Dic3—22no—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3C22×D414yes—
577C25—91no—
578C25—91no—
579C2×#41—98no—
580C2×#41—188no—
581C22×Q8—91no—
582C22×D4—31no—
583C22×D4—31no—
584C22×D4—98no—
585C22×D4—91no—
586C22×D4—91no—
587C22×D4—91no—
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—38no—
601#123—98no—
602C22⋊Q8—98no—
603#121—98no—
604#121—98no—
605#121—98no—
606#120—98no—
607#120—98no—
608C4×D4—38no—
609C4×D4—98no—
610C2×C4⋊C4—31no—
611C2×C4⋊C4—91no—
612C2×C4⋊C4—91no—
613C2×C4⋊C4D3211yescharacteristic, complemented
614C2×C22⋊C4—31no—
615C2×C22⋊C4—31no—
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—98no—
620C2×C22⋊C4—98no—
621C2×C22⋊C4—91no—
622C2×C22⋊C4—91no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4—91no—
628C2×C42—31no—
629C23×C3—21no—
630C23×C3—34no—
631C23×C3—34no—
632C23×C3—32no—
633C23×C3—32no—
634C23×C3—32no—
635C23×C3—32no—
636C23×C3—62no—
637C23×C3—62no—
638C23×C3—62no—
639C23×C3—62no—
640C23×C3—62no—
641C23×C3—62no—
642C23×C3—62no—
643C23×C3—62no—
644C23×C3—62no—
645C23×C3—62no—
646C23×C3C23×D311yescharacteristic
647C23×C3C23×D311yescharacteristic
648C22×D3—22no—
649C22×D3—22no—
650C22×D3—22no—
651C22×D3—22no—
652C22×D3—22no—
653C22×D3—22no—
654C22×D3—22no—
655C22×D3—22no—
656C22×D3—22no—
657C22×D3—22no—
658C22×D3—34no—
659C22×D3—34no—
660C22×D3—32no—
661C22×D3—32no—
662C22×D3—32no—
663C22×D3—32no—
664C22×D3—64no—
665C22×D3—62no—
666C22×D3—62no—
667C22×D3—68no—
668C22×D3—68no—
669C22×D3—68no—
670C22×D3—68no—
671C22×D3—68no—
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—68no—
683C22×D3—68no—
684C22×D3—68no—
685C22×D3—122no—
686C22×D3—122no—
687C22×D3—122no—
688C22×D3—122no—
689C22×D3—122no—
690C22×D3—124no—
691C22×D3—124no—
692C22×D3—124no—
693C22×D3—124no—
694C22×D3—1216no—
695C22×D3—1216no—
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—68no—
706C2×C3×C4—22no—
707C2×C3×C4—22no—
708C2×C3×C4—22no—
709C2×C3×C4—22no—
710C2×C3×C4—22no—
711C2×C3×C4—22no—
712C2×C3×C4—22no—
713C2×C3×C4—22no—
714C2×C3×C4—22no—
715C2×C3×C4—34no—
716C2×C3×C4—32no—
717C2×C3×C4—32no—
718C2×C3×C4—32no—
719C2×C3×C4—32no—
720C2×C3×C4—42no—
721C2×C3×C4—42no—
722C2×C3×C4—42no—
723C2×C3×C4—68no—
724C2×C3×C4—68no—
725C2×C3×C4—68no—
726C2×C3×C4—62no—
727C2×C3×C4—62no—
728C2×C3×C4—62no—
729C2×C3×C4C23×D312yes—
730C2×C3×C4C23×D312yes—
731C2×C3×C4C23×D312yes—
732C2×C3×C4C23×D312yes—
733C2×C3×C4C23×D312yes—
734C2×C3×C4C23×D312yes—
735#67—316no—
736#67—68no—
737#67—68no—
738#67—68no—
739#67—68no—
740#67—124no—
741#67—124no—
742#67—124no—
743C2×Dic3—22no—
744C2×Dic3—22no—
745C2×Dic3—22no—
746C2×Dic3—32no—
747C2×Dic3—32no—
748C2×Dic3—32no—
749C2×Dic3—32no—
750C2×Dic3—62no—
751C2×Dic3—62no—
752C2×Dic3—62no—
753C2×Dic3—62no—
754C2×Dic3—62no—
755C2×Dic3—62no—
756C2×Dic3—122no—
757C2×Dic3—122no—
758C2×Dic3—124no—
759C2×Dic3D3×D414yes—
760C2×Dic3C23×D312yes—
761C2×Dic3C23×D312yes—
762C2×Dic3C23×D312yes—
763C2×Dic3C23×D312yes—
764D12—28no—
765D12—28no—
766D12—316no—
767D12—68no—
768D12—68no—
769D12—68no—
770D12—68no—
771D12—128no—
772D12—124no—
773C4×D3—28no—
774C4×D3—28no—
775C4×D3—28no—
776C4×D3—68no—
777C4×D3—68no—
778C4×D3—128no—
779C4×D3—124no—
780C4×D3—124no—
781C4×D3—124no—
782Dic6—68no—
783Dic6—68no—
784C2×C32#54614yescomplemented
785C2×C32C23×D411yescharacteristic
786C2×C32C22×#4111yescharacteristic
787C2×C32C2×H(5,𝔽2)11yescharacteristic
788C3⋊D3—24no—
789C3⋊D3—42no—
790C3×D3—24no—
791C3×D3—24no—
792C3×D3—42no—
793C3×D3—42no—
794C24—31no—
795C24—31no—
796C24—31no—
797C24—31no—
798C24—94no—
799C24—94no—
800C24—91no—
801C24—91no—
802C24—184no—
803C24—184no—
804C24—184no—
805C24—184no—
806C24—362no—
807C24—362no—
808#41—1832no—
809C2×Q8—94no—
810C2×Q8—184no—
811C2×D4—34no—
812C2×D4—34no—
813C2×D4—64no—
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—94no—
823C2×D4—184no—
824C2×D4—184no—
825C2×D4—1832no—
826C2×D4—184no—
827C2×D4—184no—
828C2×D4—362no—
829C2×D4—362no—
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—64no—
840C22×C4—94no—
841C22×C4—94no—
842C22×C4—91no—
843C22×C4—91no—
844C22×C4—94no—
845C22×C4—184no—
846C22×C4—362no—
847C22×C4—362no—
848C22×C4C2×D3211yescharacteristic
849C22×C4C2×D3211yescharacteristic
850C22×C4C2×D3211yescharacteristic
851C4⋊C4—34no—
852C4⋊C4—94no—
853C4⋊C4—94no—
854C4⋊C4C2×D3214yescomplemented
855C22⋊C4—34no—
856C22⋊C4—34no—
857C22⋊C4—34no—
858C22⋊C4—34no—
859C22⋊C4—34no—
860C22⋊C4—94no—
861C22⋊C4—94no—
862C22⋊C4—94no—
863C22⋊C4—94no—
864C22⋊C4—94no—
865C22⋊C4—94no—
866C22⋊C4—94no—
867C42—34no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—22no—
871C22×C3—21no—
872C22×C3—34no—
873C22×C3—34no—
874C22×C3—68no—
875C22×C3—62no—
876C22×C3—62no—
877C22×C3—62no—
878C22×C3—62no—
879C22×C3—68no—
880C22×C3—62no—
881C22×C3—62no—
882C22×C3—62no—
883C22×C3—62no—
884C22×C3—62no—
885C22×C3—62no—
886C22×C3—124no—
887C22×C3—124no—
888C22×C3C2×#23512yes—
889C22×C3C2×D3×D412yes—
890C22×C3C2×D3×D412yes—
891C22×C3D3×#4112yes—
892C22×C3#100912yes—
893C22×C3#100912yes—
894C22×C3C24×D311yescharacteristic
895C22×C3C24×D311yescharacteristic
896C2×D3—28no—
897C2×D3—22no—
898C2×D3—22no—
899C2×D3—22no—
900C2×D3—22no—
901C2×D3—28no—
902C2×D3—22no—
903C2×D3—22no—
904C2×D3—22no—
905C2×D3—22no—
906C2×D3—22no—
907C2×D3—22no—
908C2×D3—34no—
909C2×D3—34no—
910C2×D3—44no—
911C2×D3—44no—
912C2×D3—64no—
913C2×D3—68no—
914C2×D3—62no—
915C2×D3—62no—
916C2×D3—62no—
917C2×D3—62no—
918C2×D3—68no—
919C2×D3—62no—
920C2×D3—62no—
921C2×D3—62no—
922C2×D3—62no—
923C2×D3—62no—
924C2×D3—62no—
925C2×D3—122no—
926C2×D3—128no—
927C2×D3—122no—
928C2×D3—122no—
929C2×D3—122no—
930C2×D3—122no—
931C2×D3—1216no—
932C2×D3—1216no—
933C2×D3—1216no—
934C2×D3—1216no—
935C2×D3—124no—
936C2×D3—124no—
937C2×D3—244no—
938C2×D3C2×#23514yescomplemented
939C2×D3C2×D3×D414yes—
940C3×C4—22no—
941C3×C4—22no—
942C3×C4—22no—
943C3×C4—22no—
944C3×C4—22no—
945C3×C4—22no—
946C3×C4—34no—
947C3×C4—42no—
948C3×C4—42no—
949C3×C4—42no—
950C3×C4—62no—
951C3×C4—62no—
952C3×C4—62no—
953Dic3—22no—
954Dic3—22no—
955Dic3—22no—
956Dic3—62no—
957Dic3—62no—
958Dic3—62no—
959Dic3—62no—
960Dic3—122no—
961Dic3—122no—
962Dic3C2×D3×D414yes—
963C32C2×#54611yescharacteristic, complemented, Sylow
964C23—34no—
965C23—34no—
966C23—32no—
967C23—32no—
968C23—32no—
969C23—32no—
970C23—62no—
971C23—62no—
972C23—62no—
973C23—62no—
974C23—62no—
975C23—62no—
976C23—62no—
977C23—62no—
978C23—62no—
979C23—62no—
980C23—94no—
981C23—92no—
982C23—92no—
983C23—188no—
984C23—188no—
985C23—188no—
986C23—188no—
987C23—182no—
988C23—182no—
989C23—182no—
990C23—182no—
991C23—182no—
992C23—364no—
993C23—364no—
994C23—3616no—
995C23—3616no—
996C23C22×D3211yescharacteristic
997Q8—188no—
998D4—68no—
999D4—68no—
1000D4—916no—
1001D4—188no—
1002D4—188no—
1003D4—188no—
1004D4—188no—
1005D4—364no—
1006D4—364no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—34no—
1011C2×C4—32no—
1012C2×C4—32no—
1013C2×C4—32no—
1014C2×C4—32no—
1015C2×C4—68no—
1016C2×C4—68no—
1017C2×C4—68no—
1018C2×C4—62no—
1019C2×C4—62no—
1020C2×C4—62no—
1021C2×C4—92no—
1022C2×C4—92no—
1023C2×C4—188no—
1024C2×C4—182no—
1025C2×C4—182no—
1026C2×C4—364no—
1027C2×C4—364no—
1028C2×C4C22×D3212yes—
1029C2×C4C22×D3212yes—
1030C2×C4C22×D3212yes—
1031C2×C3—21no—
1032C2×C3—24no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—64no—
1036C2×C3—64no—
1037C2×C3—122no—
1038C2×C3—122no—
1039C2×C3#555014yescomplemented
1040C2×C3#565414yescomplemented
1041C2×C3C22×#23511yescharacteristic
1042C2×C3C22×D3×D411yescharacteristic
1043C2×C3C22×D3×D411yescharacteristic
1044C2×C3C2×D3×#4111yescharacteristic
1045C2×C3C2×#100911yescharacteristic
1046C2×C3C2×#100911yescharacteristic
1047D3—24no—
1048D3—24no—
1049D3—42no—
1050D3—42no—
1051D3—64no—
1052D3—64no—
1053D3—124no—
1054D3—122no—
1055D3—122no—
1056D3—242no—
1057C22—34no—
1058C22—34no—
1059C22—62no—
1060C22—68no—
1061C22—68no—
1062C22—62no—
1063C22—62no—
1064C22—62no—
1065C22—62no—
1066C22—62no—
1067C22—62no—
1068C22—62no—
1069C22—62no—
1070C22—62no—
1071C22—94no—
1072C22—124no—
1073C22—124no—
1074C22—182no—
1075C22—188no—
1076C22—182no—
1077C22—182no—
1078C22—182no—
1079C22—182no—
1080C22—3616no—
1081C22—3616no—
1082C22—364no—
1083C22D3×#23512yes—
1084C22D32×D412yes—
1085C22#6432012yes—
1086C22C23×D3211yescharacteristic
1087C4—22no—
1088C4—22no—
1089C4—22no—
1090C4—34no—
1091C4—62no—
1092C4—62no—
1093C4—62no—
1094C4—182no—
1095C4—182no—
1096C3—21no—
1097C3C2×#555011yescharacteristic, complemented
1098C3C2×#565411yescharacteristic, complemented
1099C2—64no—
1100C2—64no—
1101C2—122no—
1102C2—122no—
1103C2—184no—
1104C2—362no—
1105C2#1059461914yesdirect product factor
1106C2C2×D3×#23511yescharacteristic
1107C2C2×D32×D411yescharacteristic
1108C2C2×#6432011yescharacteristic
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×#3798C2semidirect
3. C2×#64103C2semidirect
4. C2×C3×#894C2semidirect
5. C2×C3×#893C2semidirect
6. C2×#63922C2semidirect
7. C2×#63922C2semidirect
8. C2×#63921C2semidirect
9. C2×D3×(C2×D3)⋊C4C2semidirect
10. C2×#63910C2semidirect
11. C2×#63906C2semidirect
12. C2×#63885C2semidirect
13. C2×#63880C2semidirect
14. C2×#63852C2semidirect
15. C2×#63851C2semidirect
16. #10594619C2direct (N × H)
22. C22×C4×C3⋊D3C22semidirect
26. C22×C3×C4×D3C22semidirect
27. C22×C3×C4×D3C22semidirect
28. C22×#627C22semidirect
31. C22×#626C22semidirect
32. C22×#626C22semidirect
33. C22×#625C22semidirect
34. C22×#625C22semidirect
35. C22×#624C22semidirect
36. C22×D3×Dic3C22semidirect
38. C2×D3×D12C22semidirect
40. C2×#3798C22semidirect
41. C2×C32×C4⋊C4C22semidirect
42. C2×#3752C22semidirect
43. C2×#3752C22semidirect
44. C2×#3752C22semidirect
45. C2×#3750C22semidirect
46. #64103C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×(C2×D3)⋊C4C22semidirect
52. C2×C3×Dic3⋊C4C22semidirect
53. C2×C3×C4×Dic3C22semidirect
54. C3×#894C22semidirect
55. C3×#893C22semidirect
56. C2×Dic3⋊Dic3C22semidirect
57. C2×#3722C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. #63922C22semidirect
62. #63922C22semidirect
63. #63921C22semidirect
64. D3×(C2×D3)⋊C4C22semidirect
65. #63910C22semidirect
66. #63906C22semidirect
67. #63885C22semidirect
68. #63880C22semidirect
69. #63852C22semidirect
70. #63851C22semidirect
90. C2×#894D3semidirect
91. C2×#893D3semidirect
126. C2×C4×C3⋊D3C23semidirect
139. C2×C3×C4×D3C23semidirect
140. C2×C3×C4×D3C23semidirect
142. C2×#627C23semidirect
146. C2×#626D4semidirect
149. C2×#626C23semidirect
150. C2×#626C23semidirect
153. C2×#625C23semidirect
154. C2×#625C23semidirect
156. C2×#624C23semidirect
158. C2×D3×Dic3C23semidirect
161. C32×C4⋊C4C23semidirect
162. #3752C23semidirect
163. #3752C23semidirect
164. #3752C23semidirect
165. #3750C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×(C2×D3)⋊C4C23semidirect
169. C3×(C2×D3)⋊C4C23semidirect
170. C3×(C2×D3)⋊C4C23semidirect
171. C3×Dic3⋊C4C23semidirect
172. C3×C4×Dic3C23semidirect
173. Dic3⋊Dic3C23semidirect
174. #3722C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
221. C22×C4×D3C2×D3semidirect
222. C22×C4×D3C2×D3semidirect
229. C2×C3×C4⋊C4C2×D3semidirect
230. C2×C3×C4⋊C4C2×D3semidirect
260. C2×(C2×D3)⋊C4C2×D3semidirect
261. C2×(C2×D3)⋊C4C2×D3semidirect
262. C2×(C2×D3)⋊C4C2×D3semidirect
263. C2×(C2×D3)⋊C4C2×D3semidirect
270. C2×Dic3⋊C4C2×D3semidirect
271. C2×C4×Dic3C2×D3semidirect
277. #894C2×D3semidirect
278. #893C2×D3semidirect
311. C22×C3×D3#41semidirect
353. #626C2×D4semidirect
493. C2×C4×D3C22×D3semidirect
494. C2×C4×D3C22×D3semidirect
501. C3×C4⋊C4C22×D3semidirect
502. C3×C4⋊C4C22×D3semidirect
527. (C2×D3)⋊C4C22×D3semidirect
528. (C2×D3)⋊C4C22×D3semidirect
529. (C2×D3)⋊C4C22×D3semidirect
530. (C2×D3)⋊C4C22×D3semidirect
536. Dic3⋊C4C22×D3semidirect
537. C4×Dic3C22×D3semidirect
565. C2×C3×D3C2×#41semidirect
613. C2×C4⋊C4D32semidirect
698. C22×D3#235semidirect
784. C2×C32#546semidirect
854. C4⋊C4C2×D32semidirect
938. C2×D3C2×#235semidirect
963. C32C2×#546semidirect
1039. C2×C3#5550semidirect
1040. C2×C3#5654semidirect
1097. C3C2×#5550semidirect
1098. C3C2×#5654semidirect
1105. C2#10594619direct (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×#37982
C2×#641032
C2×C3×#8942
C2×C3×#8932
C2×#639222
C2×#639212
C2×D3×(C2×D3)⋊C42
C2×#639102
C2×#639062
C2×#638852
C2×#638802
C2×#638522
C2×#638512
#105946192
C2×#56543
C2×#55503