Finite Group Databasebeta

← C2×#10594292 #11902418

Subgroups — C2×#10594292 #11902418

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×#3805C211yesmaximal, characteristic, complemented
3C2×#64095C211yesmaximal, characteristic, complemented
4C2×C3×#882C211yesmaximal, characteristic, complemented
5C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
6C2×#63978C211yesmaximal, characteristic, complemented
7C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8C2×#63922C211yesmaximal, characteristic, complemented
9C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C2×#63908C211yesmaximal, characteristic, complemented
11C2×#63893C211yesmaximal, characteristic, complemented
12C2×Dic3×D12C211yesmaximal, characteristic, complemented
13C2×#63891C211yesmaximal, characteristic, complemented
14C2×#63886C211yesmaximal, characteristic, complemented
15C2×#63852C211yesmaximal, characteristic, complemented
16#10594292C2116yesmaximal, direct product factor
17C2×#5591—31nomaximal
18C2×#5554—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic, complemented
25C23×C3×Dic3C2211yescharacteristic, complemented
26C22×C3×D12C2211yescharacteristic
27C22×C3×D12C2211yescharacteristic, 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, complemented
36C2×#3805—28no—
37C2×#3805C2218yescomplemented
38C22×D3×Dic3C2211yescharacteristic
39C22×D3×Dic3C2211yescharacteristic, complemented
40C22×D3×Dic3C2211yescharacteristic, complemented
41C2×C32×C22⋊C4C2211yescharacteristic, complemented
42C2×#3752C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic, complemented
44C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46#64095C2218yescomplemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
51C2×C3×C4×Dic3C2211yescharacteristic, complemented
52C3×#882C2218yescomplemented
53C3×#67⋊C4C2218yescomplemented
54#63978C2218yescomplemented
55C2×Dic3⋊Dic3C2211yescharacteristic, complemented
56C2×#3722C2211yescharacteristic, complemented
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2218yescomplemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63#63922C2218yescomplemented
64D3×(C2×D3)⋊C4C2218yescomplemented
65#63908C2218yescomplemented
66#63893C2218yescomplemented
67Dic3×D12C2218yescomplemented
68#63891C2218yescomplemented
69#63886C2218yescomplemented
70#63852C2218yescomplemented
71C23×#67—31no—
72C22×#237—31no—
73C22×#237—31no—
74C22×D3×D4—31no—
75C2×C3×#120—31no—
76C2×C3×C4×D4—31no—
77C22×#217—31no—
78C2×#939—31no—
79C2×#939—31no—
80C2×#938—31no—
81C2×#937—31no—
82C2×D4×Dic3—31no—
83C2×#930—31no—
84C2×#930—31no—
85C22×(C2×D3)⋊C4—31no—
86C22×(C2×D3)⋊C4—31no—
87#5591—316no—
88#5554—316no—
89C2×#897—31no—
90C2×#895—31no—
91C2×#886—31no—
92C2×#886—31no—
93C2×#886—31no—
94C2×#886—61no—
95C2×#885—31no—
96C2×#883—31no—
97C2×#882—31no—
98C2×#882D311yescharacteristic, complemented
99C2×#67⋊C4D311yescharacteristic, complemented
100C2×D3×C22⋊C4—31no—
101C2×#878—31no—
102C2×#875—31no—
103C2×C4×D12—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⋊Dic3—24no—
123C22×C3⋊Dic3C2311yescharacteristic
124C22×C3⋊Dic3C2311yescharacteristic
125C22×C3⋊Dic3C2311yescharacteristic
126C22×C3⋊Dic3C2314yescomplemented
127C2×C3×#67—24no—
128C2×C3×#67D418yescomplemented
129C2×C3×#67C2314yes—
130C2×C3×#67C2314yescomplemented
131C22×C3×Dic3—42no—
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2314yescomplemented
137C2×C3×D12—24no—
138C2×C3×D12—42no—
139C2×C3×D12C2314yes—
140C2×C3×D12C2314yescomplemented
141C2×C3×C4×D3—42no—
142C2×C3×C4×D3C2314yescomplemented
143D3×#67—232no—
144C2×#627—24no—
145C2×#627C2314yescomplemented
146C2×#626—24no—
147C2×#626—42no—
148C2×#626C2314yes—
149C2×#626C2314yescomplemented
150C2×#625—24no—
151C2×#625—24no—
152C2×#625C2314yes—
153C2×#625C2314yescomplemented
154#3805—232no—
155C2×D3×Dic3—24no—
156C2×D3×Dic3—24no—
157C2×D3×Dic3—24no—
158C2×D3×Dic3C2314yes—
159C2×D3×Dic3C2314yescomplemented
160C2×D3×Dic3C2314yescomplemented
161C32×C22⋊C4C2314yescomplemented
162#3752C2314yescomplemented
163#3752C2314yescomplemented
164C4⋊(C3⋊Dic3)C2314yescomplemented
165C4⋊(C3⋊Dic3)C2314yescomplemented
166C3×(C2×D3)⋊C4C2314yes—
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×(C2×D3)⋊C4C2314yescomplemented
169C3×Dic3⋊C4C2314yescomplemented
170C3×C4×Dic3C2314yescomplemented
171Dic3⋊Dic3C2314yescomplemented
172#3722C2314yescomplemented
173(C2×D3)⋊Dic3C2314yes—
174(C2×D3)⋊Dic3C2314yes—
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177(C2×D3)⋊Dic3C2314yescomplemented
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—
186C22×C3×D4—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—38no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—61no—
199C22×#67—68no—
200C22×#67C2×D311yescharacteristic
201C22×#67C2×D311yescharacteristic, complemented
202C23×Dic3—31no—
203C23×Dic3—31no—
204C23×Dic3—31no—
205C23×Dic3—31no—
206C23×Dic3—31no—
207C23×Dic3—61no—
208C23×Dic3C2×D311yescharacteristic, complemented
209C2×#237—38no—
210C2×#237—38no—
211C2×#237—68no—
212C2×#237—68no—
213C2×D3×D4—38no—
214C2×D3×D4—68no—
215C22×D12—31no—
216C22×D12—31no—
217C22×D12C2×D311yescharacteristic
218C22×D12C2×D311yescharacteristic, complemented
219C22×C4×D3—31no—
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3C2×D311yescharacteristic, complemented
223C22×Dic6—31no—
224C22×Dic6—31no—
225C3×#120—38no—
226C3×C4×D4—38no—
227C2×C3×C4⋊C4—31no—
228C2×C3×C22⋊C4—21no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
233C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
234C2×C3×C42—31no—
235C2×#217—31no—
236C2×#217—31no—
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217—38no—
241#939—38no—
242#939—38no—
243#938—38no—
244#937—38no—
245D4×Dic3—38no—
246#930—38no—
247#930—38no—
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—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—38no—
261C2×(C2×D3)⋊C4—61no—
262C2×(C2×D3)⋊C4—61no—
263C2×(C2×D3)⋊C4C2×D311yescharacteristic
264C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
265C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
266C2×C4⋊Dic3—31no—
267C2×C4⋊Dic3—31no—
268C2×C4⋊Dic3—31no—
269C2×C4⋊Dic3—31no—
270C2×C4⋊Dic3—31no—
271C2×C4⋊Dic3—61no—
272C2×C4⋊Dic3—61no—
273C2×Dic3⋊C4—31no—
274C2×Dic3⋊C4C2×D311yescharacteristic, complemented
275C2×C4×Dic3C2×D311yescharacteristic, complemented
276#897—38no—
277#895—38no—
278#886—38no—
279#886—38no—
280#886—38no—
281#886—68no—
282#885—38no—
283#883—38no—
284#882—38no—
285#882C2×D318yescomplemented
286#67⋊C4C2×D318yescomplemented
287D3×C22⋊C4—38no—
288#878—38no—
289#875—38no—
290C4×D12—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32C2×D414yes—
294C23×C32C2412yes—
295C23×C32C2411yescharacteristic
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3—22no—
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—28no—
306C22×C3×D3—22no—
307C22×C3×D3—22no—
308C22×C3×D3—22no—
309C22×C3×D3—22no—
310C22×C3×D3—22no—
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—28no—
332C2×C3⋊Dic3—22no—
333C2×C3⋊Dic3C2412yes—
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C3×#67—28no—
337C3×#67C2×D4116yescomplemented
338C2×C3×Dic3—22no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3—44no—
342C2×C3×Dic3C2×D414yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C3×D12—28no—
348C3×D12—44no—
349C3×C4×D3—44no—
350#627—28no—
351#626—28no—
352#626—44no—
353#625—28no—
354#625—28no—
355D3×Dic3—28no—
356D3×Dic3—28no—
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—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—31no—
369C2×#120—91no—
370C2×C4×D4—31no—
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×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—38no—
405C2×C3×D4—34no—
406C2×C3×D4—34no—
407C2×C3×D4—34no—
408C2×C3×D4—34no—
409C2×C3×D4—64no—
410C2×C3×D4—64no—
411C2×C3×D4—122no—
412C22×C3×C4—21no—
413C22×C3×C4—21no—
414C22×C3×C4—31no—
415C22×C3×C4—31no—
416C22×C3×C4—31no—
417C22×C3×C4—31no—
418C22×C3×C4—34no—
419C22×C3×C4—34no—
420C22×C3×C4—122no—
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—64no—
436C2×#67—64no—
437C2×#67—64no—
438C2×#67—64no—
439C2×#67—64no—
440C2×#67—64no—
441C2×#67—64no—
442C2×#67—632no—
443C2×#67—64no—
444C2×#67—124no—
445C2×#67—122no—
446C2×#67D1218yescomplemented
447C2×#67C22×D314yes—
448C2×#67C22×D314yescomplemented
449C22×Dic3—34no—
450C22×Dic3—34no—
451C22×Dic3—31no—
452C22×Dic3—31no—
453C22×Dic3—31no—
454C22×Dic3—31no—
455C22×Dic3—31no—
456C22×Dic3—31no—
457C22×Dic3—34no—
458C22×Dic3—34no—
459C22×Dic3—34no—
460C22×Dic3—42no—
461C22×Dic3—64no—
462C22×Dic3—61no—
463C22×Dic3—61no—
464C22×Dic3—61no—
465C22×Dic3—64no—
466C22×Dic3—64no—
467C22×Dic3—64no—
468C22×Dic3—64no—
469C22×Dic3—64no—
470C22×Dic3—124no—
471C22×Dic3C22×D311yescharacteristic
472C22×Dic3C22×D311yescharacteristic
473C22×Dic3C22×D311yescharacteristic
474C22×Dic3C22×D311yescharacteristic
475C22×Dic3C22×D314yescomplemented
476#237—632no—
477#237—632no—
478D3×D4—632no—
479C2×D12—24no—
480C2×D12—34no—
481C2×D12—34no—
482C2×D12—42no—
483C2×D12—64no—
484C2×D12—122no—
485C2×D12C22×D314yes—
486C2×D12C22×D314yescomplemented
487C2×C4×D3—34no—
488C2×C4×D3—34no—
489C2×C4×D3—34no—
490C2×C4×D3—42no—
491C2×C4×D3—64no—
492C2×C4×D3—64no—
493C2×C4×D3—64no—
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⋊C4C22×D314yescomplemented
505C3×C22⋊C4C22×D314yescomplemented
506C3×C42—34no—
507#217—34no—
508#217—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)⋊C4C22×D314yes—
526(C2×D3)⋊C4C22×D314yescomplemented
527(C2×D3)⋊C4C22×D314yescomplemented
528C4⋊Dic3—34no—
529C4⋊Dic3—34no—
530C4⋊Dic3—34no—
531C4⋊Dic3—34no—
532C4⋊Dic3—34no—
533C4⋊Dic3—64no—
534C4⋊Dic3—64no—
535Dic3⋊C4—34no—
536Dic3⋊C4C22×D314yescomplemented
537C4×Dic3C22×D314yescomplemented
538C22×C32—28no—
539C22×C32—22no—
540C22×C32—22no—
541C22×C32C22×D414yes—
542C22×C32C22×D412yes—
543C22×C32C2×#4112yes—
544C22×C32H(5,𝔽2)12yes—
545C22×C32C2511yescharacteristic
546C2×C3⋊D3—22no—
547C2×C3⋊D3—22no—
548C2×C3⋊D3—22no—
549C2×C3⋊D3—44no—
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—31no—
586C22×D4—91no—
587C22×D4—91no—
588C22×D4—98no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—188no—
593C23×C4—31no—
594C23×C4—31no—
595C23×C4—91no—
596C23×C4—91no—
597C23×C4—91no—
598C23×C4—91no—
599#124—98no—
600#123—98no—
601#123—98no—
602C22⋊Q8—98no—
603#121—98no—
604#121—98no—
605#121—98no—
606#120—38no—
607#120—98no—
608C4×D4—38no—
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—98no—
618C2×C22⋊C4—91no—
619C2×C22⋊C4—91no—
620C2×C22⋊C4—91no—
621C2×C22⋊C4—91no—
622C2×C22⋊C4—91no—
623C2×C22⋊C4—98no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4D3211yescharacteristic, complemented
628C2×C42—31no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—21no—
635C23×C3—24no—
636C23×C3—34no—
637C23×C3—34no—
638C23×C3—32no—
639C23×C3—32no—
640C23×C3—32no—
641C23×C3—32no—
642C23×C3—42no—
643C23×C3—42no—
644C23×C3—68no—
645C23×C3—62no—
646C23×C3—62no—
647C23×C3—62no—
648C23×C3—62no—
649C23×C3—62no—
650C23×C3—68no—
651C23×C3—62no—
652C23×C3—62no—
653C23×C3—62no—
654C23×C3—62no—
655C23×C3—62no—
656C23×C3—124no—
657C23×C3—1216no—
658C23×C3C2×D1214yes—
659C23×C3D3×D414yes—
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—28no—
671C22×D3—22no—
672C22×D3—22no—
673C22×D3—22no—
674C22×D3—22no—
675C22×D3—28no—
676C22×D3—32no—
677C22×D3—32no—
678C22×D3—44no—
679C22×D3—416no—
680C22×D3—62no—
681C22×D3—68no—
682C22×D3—68no—
683C22×D3—62no—
684C22×D3—62no—
685C22×D3—62no—
686C22×D3—62no—
687C22×D3—62no—
688C22×D3—62no—
689C22×D3—68no—
690C22×D3—68no—
691C22×D3—122no—
692C22×D3—122no—
693C22×D3—122no—
694C22×D3—124no—
695C22×D3—124no—
696C22×D3—1216no—
697C22×D3—1216no—
698C22×D3C2×D1214yes—
699C22×D3#23714yescomplemented
700C22×D3C23×D312yes—
701C22×D3C23×D312yes—
702C22×D3C23×D312yes—
703C22×D3C23×D312yes—
704C3×D4—316no—
705C3×D4—68no—
706C3×D4—68no—
707C3×D4—124no—
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—34no—
715C2×C3×C4—32no—
716C2×C3×C4—32no—
717C2×C3×C4—32no—
718C2×C3×C4—32no—
719C2×C3×C4—42no—
720C2×C3×C4—42no—
721C2×C3×C4—62no—
722C2×C3×C4—62no—
723C2×C3×C4—62no—
724C2×C3×C4—124no—
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—68no—
732#67—68no—
733#67—68no—
734#67—68no—
735#67—68no—
736#67—68no—
737#67—68no—
738#67—128no—
739#67—124no—
740#67C2×D12116yescomplemented
741C2×Dic3—22no—
742C2×Dic3—22no—
743C2×Dic3—22no—
744C2×Dic3—32no—
745C2×Dic3—32no—
746C2×Dic3—32no—
747C2×Dic3—32no—
748C2×Dic3—32no—
749C2×Dic3—32no—
750C2×Dic3—44no—
751C2×Dic3—62no—
752C2×Dic3—62no—
753C2×Dic3—62no—
754C2×Dic3—68no—
755C2×Dic3—62no—
756C2×Dic3—62no—
757C2×Dic3—68no—
758C2×Dic3—62no—
759C2×Dic3—62no—
760C2×Dic3—62no—
761C2×Dic3—62no—
762C2×Dic3—68no—
763C2×Dic3—68no—
764C2×Dic3—68no—
765C2×Dic3—122no—
766C2×Dic3—122no—
767C2×Dic3—128no—
768C2×Dic3—122no—
769C2×Dic3C2×D1214yes—
770C2×Dic3C23×D312yes—
771C2×Dic3C23×D312yes—
772C2×Dic3C23×D312yes—
773C2×Dic3C23×D312yes—
774D12—28no—
775D12—44no—
776D12—68no—
777D12—124no—
778C4×D3—44no—
779C4×D3—68no—
780C4×D3—68no—
781C4×D3—68no—
782Dic6—68no—
783Dic6—68no—
784C2×C32—24no—
785C2×C32#54614yescomplemented
786C2×C32C23×D411yescharacteristic
787C2×C32C22×#4111yescharacteristic
788C2×C32C2×H(5,𝔽2)11yescharacteristic
789C3⋊D3—42no—
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—38no—
813C2×D4—34no—
814C2×D4—34no—
815C2×D4—34no—
816C2×D4—64no—
817C2×D4—64no—
818C2×D4—94no—
819C2×D4—94no—
820C2×D4—94no—
821C2×D4—94no—
822C2×D4—94no—
823C2×D4—122no—
824C2×D4—184no—
825C2×D4—1832no—
826C2×D4—184no—
827C2×D4—184no—
828C2×D4—184no—
829C2×D4—362no—
830C22×C4—31no—
831C22×C4—31no—
832C22×C4—31no—
833C22×C4—31no—
834C22×C4—34no—
835C22×C4—34no—
836C22×C4—94no—
837C22×C4—94no—
838C22×C4—94no—
839C22×C4—94no—
840C22×C4—91no—
841C22×C4—91no—
842C22×C4—91no—
843C22×C4—122no—
844C22×C4—122no—
845C22×C4—184no—
846C22×C4—184no—
847C22×C4—184no—
848C22×C4—184no—
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—94no—
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—34no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—22no—
871C22×C3—22no—
872C22×C3—28no—
873C22×C3—28no—
874C22×C3—22no—
875C22×C3—24no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—21no—
879C22×C3—34no—
880C22×C3—34no—
881C22×C3—42no—
882C22×C3—42no—
883C22×C3—48no—
884C22×C3—62no—
885C22×C3—62no—
886C22×C3—62no—
887C22×C3—62no—
888C22×C3—68no—
889C22×C3—68no—
890C22×C3—62no—
891C22×C3—62no—
892C22×C3—62no—
893C22×C3—62no—
894C22×C3—62no—
895C22×C3—62no—
896C22×C3—1216no—
897C22×C3—124no—
898C22×C3—124no—
899C22×C3C22×D1214yes—
900C22×C3C22×D1212yes—
901C22×C3C2×D3×D414yes—
902C22×C3C2×D3×D412yes—
903C22×C3C2×#23712yes—
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—416no—
922C2×D3—44no—
923C2×D3—44no—
924C2×D3—62no—
925C2×D3—62no—
926C2×D3—62no—
927C2×D3—62no—
928C2×D3—62no—
929C2×D3—62no—
930C2×D3—122no—
931C2×D3—122no—
932C2×D3—122no—
933C2×D3—1216no—
934C2×D3—1216no—
935C2×D3—124no—
936C2×D3—124no—
937C2×D3—244no—
938C2×D3C22×D1214yes—
939C2×D3C2×#23714yescomplemented
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—
962Dic3C22×D1214yes—
963C32C2×#54611yescharacteristic, complemented, Sylow
964C23—22no—
965C23—22no—
966C23—34no—
967C23—34no—
968C23—32no—
969C23—32no—
970C23—32no—
971C23—32no—
972C23—68no—
973C23—62no—
974C23—62no—
975C23—62no—
976C23—62no—
977C23—62no—
978C23—68no—
979C23—62no—
980C23—62no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—92no—
985C23—124no—
986C23—1216no—
987C23—188no—
988C23—188no—
989C23—182no—
990C23—182no—
991C23—182no—
992C23—364no—
993C23—3616no—
994C23D3×D1214yes—
995C23C22×D3212yes—
996C23C22×D3211yescharacteristic
997Q8—188no—
998D4—316no—
999D4—68no—
1000D4—68no—
1001D4—124no—
1002D4—188no—
1003D4—188no—
1004D4—188no—
1005D4—188no—
1006D4—364no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—34no—
1010C2×C4—32no—
1011C2×C4—32no—
1012C2×C4—32no—
1013C2×C4—32no—
1014C2×C4—62no—
1015C2×C4—62no—
1016C2×C4—62no—
1017C2×C4—92no—
1018C2×C4—92no—
1019C2×C4—92no—
1020C2×C4—124no—
1021C2×C4—124no—
1022C2×C4—188no—
1023C2×C4—188no—
1024C2×C4—188no—
1025C2×C4—182no—
1026C2×C4—182no—
1027C2×C4—182no—
1028C2×C4—188no—
1029C2×C4C22×D3212yes—
1030C2×C4C22×D3212yes—
1031C2×C3—24no—
1032C2×C3—24no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—21no—
1036C2×C3—24no—
1037C2×C3—44no—
1038C2×C3—64no—
1039C2×C3—64no—
1040C2×C3—122no—
1041C2×C3—122no—
1042C2×C3#555414yescomplemented
1043C2×C3#559114yescomplemented
1044C2×C3C23×D1211yescharacteristic
1045C2×C3C22×D3×D411yescharacteristic
1046C2×C3C22×#23711yescharacteristic
1047C2×C3C2×#100411yescharacteristic
1048C2×C3C2×#100411yescharacteristic
1049C2×C3C2×D3×#4111yescharacteristic
1050D3—24no—
1051D3—24no—
1052D3—42no—
1053D3—42no—
1054D3—122no—
1055D3—122no—
1056D3—242no—
1057C22—22no—
1058C22—22no—
1059C22—28no—
1060C22—34no—
1061C22—34no—
1062C22—62no—
1063C22—62no—
1064C22—62no—
1065C22—62no—
1066C22—68no—
1067C22—68no—
1068C22—62no—
1069C22—62no—
1070C22—62no—
1071C22—62no—
1072C22—62no—
1073C22—62no—
1074C22—1216no—
1075C22—124no—
1076C22—124no—
1077C22—182no—
1078C22—182no—
1079C22—182no—
1080C22—3616no—
1081C22—364no—
1082C22C2×D3×D1214yes—
1083C22C2×D3×D1212yes—
1084C22D3×#23712yes—
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×#555411yescharacteristic, complemented
1098C3C2×#559111yescharacteristic, complemented
1099C2—24no—
1100C2—64no—
1101C2—64no—
1102C2—122no—
1103C2—122no—
1104C2—362no—
1105C2#1059429214yesdirect product factor
1106C2C22×D3×D1211yescharacteristic
1107C2C2×D3×#23711yescharacteristic
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×#3805C2semidirect
3. C2×#64095C2semidirect
4. C2×C3×#882C2semidirect
5. C2×C3×#67⋊C4C2semidirect
6. C2×#63978C2semidirect
7. C22×(C2×D3)⋊Dic3C2semidirect
8. C2×#63922C2semidirect
9. C2×D3×(C2×D3)⋊C4C2semidirect
10. C2×#63908C2semidirect
11. C2×#63893C2semidirect
12. C2×Dic3×D12C2semidirect
13. C2×#63891C2semidirect
14. C2×#63886C2semidirect
15. C2×#63852C2semidirect
16. #10594292C2direct (N × H)
22. C23×C3⋊Dic3C22semidirect
24. C22×C3×#67C22semidirect
25. C23×C3×Dic3C22semidirect
27. C22×C3×D12C22semidirect
28. C22×C3×C4×D3C22semidirect
30. C2×D3×#67C22semidirect
31. C22×#627C22semidirect
33. C22×#626C22semidirect
35. C22×#625C22semidirect
37. C2×#3805C22semidirect
39. C22×D3×Dic3C22semidirect
40. C22×D3×Dic3C22semidirect
41. C2×C32×C22⋊C4C22semidirect
42. C2×#3752C22semidirect
43. C2×#3752C22semidirect
44. C2×C4⋊(C3⋊Dic3)C22semidirect
45. C2×C4⋊(C3⋊Dic3)C22semidirect
46. #64095C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×Dic3⋊C4C22semidirect
51. C2×C3×C4×Dic3C22semidirect
52. C3×#882C22semidirect
53. C3×#67⋊C4C22semidirect
54. #63978C22semidirect
55. C2×Dic3⋊Dic3C22semidirect
56. C2×#3722C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. #63922C22semidirect
64. D3×(C2×D3)⋊C4C22semidirect
65. #63908C22semidirect
66. #63893C22semidirect
67. Dic3×D12C22semidirect
68. #63891C22semidirect
69. #63886C22semidirect
70. #63852C22semidirect
98. C2×#882D3semidirect
99. C2×#67⋊C4D3semidirect
126. C22×C3⋊Dic3C23semidirect
128. C2×C3×#67D4semidirect
130. C2×C3×#67C23semidirect
136. C22×C3×Dic3C23semidirect
140. C2×C3×D12C23semidirect
142. C2×C3×C4×D3C23semidirect
145. C2×#627C23semidirect
149. C2×#626C23semidirect
153. C2×#625C23semidirect
159. C2×D3×Dic3C23semidirect
160. C2×D3×Dic3C23semidirect
161. C32×C22⋊C4C23semidirect
162. #3752C23semidirect
163. #3752C23semidirect
164. C4⋊(C3⋊Dic3)C23semidirect
165. C4⋊(C3⋊Dic3)C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×(C2×D3)⋊C4C23semidirect
169. C3×Dic3⋊C4C23semidirect
170. C3×C4×Dic3C23semidirect
171. Dic3⋊Dic3C23semidirect
172. #3722C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
201. C22×#67C2×D3semidirect
208. C23×Dic3C2×D3semidirect
218. C22×D12C2×D3semidirect
222. C22×C4×D3C2×D3semidirect
232. C2×C3×C22⋊C4C2×D3semidirect
233. C2×C3×C22⋊C4C2×D3semidirect
264. C2×(C2×D3)⋊C4C2×D3semidirect
265. C2×(C2×D3)⋊C4C2×D3semidirect
274. C2×Dic3⋊C4C2×D3semidirect
275. C2×C4×Dic3C2×D3semidirect
285. #882C2×D3semidirect
286. #67⋊C4C2×D3semidirect
315. C22×C3×D3#41semidirect
337. C3×#67C2×D4semidirect
446. C2×#67D12semidirect
448. C2×#67C22×D3semidirect
475. C22×Dic3C22×D3semidirect
486. C2×D12C22×D3semidirect
494. C2×C4×D3C22×D3semidirect
504. C3×C22⋊C4C22×D3semidirect
505. C3×C22⋊C4C22×D3semidirect
526. (C2×D3)⋊C4C22×D3semidirect
527. (C2×D3)⋊C4C22×D3semidirect
536. Dic3⋊C4C22×D3semidirect
537. C4×Dic3C22×D3semidirect
566. C2×C3×D3C2×#41semidirect
627. C2×C22⋊C4D32semidirect
699. C22×D3#237semidirect
740. #67C2×D12semidirect
785. C2×C32#546semidirect
866. C22⋊C4C2×D32semidirect
939. C2×D3C2×#237semidirect
963. C32C2×#546semidirect
1042. C2×C3#5554semidirect
1043. C2×C3#5591semidirect
1097. C3C2×#5554semidirect
1098. C3C2×#5591semidirect
1105. C2#10594292direct (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×#38052
C2×#640952
C2×C3×#8822
C2×C3×#67⋊C42
C2×#639782
C22×(C2×D3)⋊Dic32
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639082
C2×#638932
C2×Dic3×D122
C2×#638912
C2×#638862
C2×#638522
#105942922
C2×#55913
C2×#55543