Finite Group Databasebeta

← C2×#10594063 #11902426

Subgroups — C2×#10594063 #11902426

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
1C23×#626C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
4C2×C3×#882C211yesmaximal, characteristic, complemented
5C2×C3×#878C211yesmaximal, characteristic, complemented
6C2×#63981C211yesmaximal, characteristic, complemented
7C2×Dic3×#67C211yesmaximal, characteristic, complemented
8C2×D3×#217C211yesmaximal, characteristic, complemented
9C2×#63916C211yesmaximal, characteristic, complemented
10C2×#63907C211yesmaximal, characteristic, complemented
11C2×#63890C211yesmaximal, characteristic, complemented
12C2×#63886C211yesmaximal, characteristic, complemented
13C2×#63886C211yesmaximal, characteristic, complemented
14C2×#63881C211yesmaximal, characteristic, complemented
15C2×#63853C211yesmaximal, characteristic, complemented
16#10594063C2116yesmaximal, direct product factor
17C2×#5630—31nomaximal
18C2×#5591—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C24×C3×D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic, complemented
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic, complemented
26C22×C3×D12C2211yescharacteristic, complemented
27C22×C3×Dic6C2211yescharacteristic, complemented
28C22×#626—28no—
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic
33C22×#626C2218yescomplemented
34C22×#626C2211yescharacteristic, complemented
35C22×#626C2211yescharacteristic, complemented
36C22×D3×Dic3C2211yescharacteristic, complemented
37C22×D3×Dic3C2211yescharacteristic, complemented
38C22×D3×Dic3C2211yescharacteristic, complemented
39C2×#3796—28no—
40C2×#3796C2218yescomplemented
41C2×C32×C22⋊C4C2211yescharacteristic
42C2×#3757C2211yescharacteristic
43C2×#3752C2211yescharacteristic, complemented
44C2×#3752C2211yescharacteristic, complemented
45C22⋊C4×C3⋊D3C2218yescomplemented
46C2×C3×#217C2211yescharacteristic
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×#882C2218yescomplemented
53C3×#878C2218yescomplemented
54#63981C2218yescomplemented
55Dic3×#67C2218yescomplemented
56D3×#217C2218yescomplemented
57C2×Dic3⋊Dic3C2211yescharacteristic, complemented
58C2×#3722C2211yescharacteristic, complemented
59C2×#3722C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63C2×Dic32C2211yescharacteristic, complemented
64#63916C2218yescomplemented
65#63907C2218yescomplemented
66#63890C2218yescomplemented
67#63886C2218yescomplemented
68#63886C2218yescomplemented
69#63881C2218yescomplemented
70#63853C2218yescomplemented
71C23×#67—31no—
72C22×#239—31no—
73C22×#237—31no—
74C23×D12—31no—
75C2×C3×C22⋊Q8—31no—
76C2×C3×#120—31no—
77C22×#217—31no—
78C2×#947—31no—
79C2×#939—31no—
80C2×#939—31no—
81C2×#938—31no—
82C2×#937—31no—
83C2×D4×Dic3—31no—
84C2×C4×#67—31no—
85#5630—316no—
86#5591—316no—
87C2×#895—31no—
88C2×#895—31no—
89C2×#895—31no—
90C2×#894—31no—
91C2×#894—31no—
92C2×#893—31no—
93C2×#886—31no—
94C2×#885—31no—
95C2×#883—31no—
96C2×#882—31no—
97C2×#882D311yescharacteristic, complemented
98C2×#67⋊C4—31no—
99C2×D3×C22⋊C4—31no—
100C2×D3×C22⋊C4—31no—
101C2×D3×C22⋊C4—31no—
102C2×D3×C22⋊C4—61no—
103C2×#878D311yescharacteristic, complemented
104C24×C32C2311yescharacteristic
105C23×C3⋊D3—24no—
106C23×C3⋊D3—24no—
107C23×C3⋊D3—42no—
108C23×C3⋊D3C2311yescharacteristic
109C23×C3⋊D3C2314yes—
110C23×C3⋊D3C2311yescharacteristic
111C23×C3×D3—24no—
112C23×C3×D3—24no—
113C23×C3×D3—42no—
114C23×C3×D3C2311yescharacteristic
115C23×C3×D3C2311yescharacteristic
116C23×C3×D3C2314yes—
117C23×C3×D3C2311yescharacteristic
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×#67C2314yes—
128C22×C3×Dic3—24no—
129C22×C3×Dic3C2314yes—
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C2×C3×D12—24no—
136C2×C3×D12—42no—
137C2×C3×D12C2314yescomplemented
138C2×C3×D12C2314yescomplemented
139C2×C3×Dic6—24no—
140C2×C3×Dic6C2314yescomplemented
141C2×#626—24no—
142C2×#626—24no—
143C2×#626—24no—
144C2×#626—24no—
145C2×#626—232no—
146C2×#626—42no—
147C2×#626D418yescomplemented
148C2×#626C2314yes—
149C2×#626C2314yes—
150C2×#626C2314yes—
151C2×#626C2314yes—
152C2×#626C2314yescomplemented
153C2×#626C2314yescomplemented
154C2×D3×Dic3—24no—
155C2×D3×Dic3—24no—
156C2×D3×Dic3—42no—
157C2×D3×Dic3C2314yescomplemented
158C2×D3×Dic3C2314yescomplemented
159C2×D3×Dic3C2314yescomplemented
160#3796—232no—
161C32×C22⋊C4C2314yes—
162#3757C2314yes—
163#3752C2314yescomplemented
164#3752C2314yescomplemented
165C3×#217C2314yes—
166C3×(C2×D3)⋊C4C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×C4⋊Dic3C2314yescomplemented
169C3×Dic3⋊C4C2314yescomplemented
170C3×Dic3⋊C4C2314yescomplemented
171Dic3⋊Dic3C2314yescomplemented
172#3722C2314yescomplemented
173#3722C2314yescomplemented
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×D3—61no—
183C24×D3C2×D311yescharacteristic
184C22×C3×Q8—31no—
185C22×C3×D4—31no—
186C22×C3×D4—31no—
187C22×C3×D4—31no—
188C23×C3×C4—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—38no—
195C22×#67—31no—
196C22×#67—68no—
197C22×#67C2×D311yescharacteristic
198C23×Dic3—31no—
199C23×Dic3—31no—
200C23×Dic3—31no—
201C23×Dic3C2×D311yescharacteristic
202C2×#239—38no—
203C2×#239—68no—
204C2×#237—38no—
205C2×#237—68no—
206C22×D12—31no—
207C22×D12—31no—
208C22×D12—31no—
209C22×D12—31no—
210C22×D12—38no—
211C22×D12—31no—
212C22×D12—31no—
213C22×D12—68no—
214C22×D12C2×D311yescharacteristic, complemented
215C22×D12C2×D311yescharacteristic, complemented
216C22×C4×D3—31no—
217C22×C4×D3—31no—
218C22×C4×D3—31no—
219C22×C4×D3—31no—
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3—31no—
223C22×C4×D3—61no—
224C22×C4×D3—61no—
225C22×Dic6C2×D311yescharacteristic, complemented
226C3×C22⋊Q8—38no—
227C3×#120—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
236C2×C3×C22⋊C4C2×D311yescharacteristic
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217—31no—
241C2×#217—31no—
242C2×#217—38no—
243C2×#217—61no—
244C2×#217C2×D311yescharacteristic
245#947—38no—
246#939—38no—
247#939—38no—
248#938—38no—
249#937—38no—
250D4×Dic3—38no—
251C4×#67—38no—
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—31no—
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#895—38no—
275#895—38no—
276#895—38no—
277#894—38no—
278#894—38no—
279#893—38no—
280#886—38no—
281#885—38no—
282#883—38no—
283#882—38no—
284#882C2×D318yescomplemented
285#67⋊C4—38no—
286D3×C22⋊C4—38no—
287D3×C22⋊C4—38no—
288D3×C22⋊C4—38no—
289D3×C22⋊C4—68no—
290#878C2×D318yescomplemented
291C23×C32—22no—
292C23×C32—22no—
293C23×C32#4114yescomplemented
294C23×C32C2412yes—
295C23×C32C2411yescharacteristic
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3—28no—
300C22×C3⋊D3—22no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3—28no—
303C22×C3⋊D3—44no—
304C22×C3⋊D3—416no—
305C22×C3⋊D3C2×D414yes—
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—28no—
315C22×C3×D3—22no—
316C22×C3×D3—22no—
317C22×C3×D3—28no—
318C22×C3×D3—44no—
319C22×C3×D3—416no—
320C22×C3×D3C2×D414yes—
321C22×C3×D3C2412yes—
322C22×C3×D3C2412yes—
323C22×C3×D3C2412yes—
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—
335C2×C3×Dic3—22no—
336C2×C3×Dic3—22no—
337C2×C3×Dic3—22no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—28no—
340C2×C3×Dic3C2×D414yes—
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C3×D12—28no—
347C3×D12—44no—
348C3×Dic6—28no—
349#626—28no—
350#626—28no—
351#626—28no—
352#626—28no—
353#626—44no—
354#626C2×D4116yescomplemented
355D3×Dic3—28no—
356D3×Dic3—28no—
357D3×Dic3—44no—
358C22×#41—91no—
359C23×D4—91no—
360#546—916no—
361C2×#124—91no—
362C2×#123—91no—
363C2×#123—91no—
364C2×C22⋊Q8—31no—
365C2×#121—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—31no—
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×C3—34no—
379C24×C3—64no—
380C24×C3—64no—
381C24×C3—122no—
382C24×C3C22×D311yescharacteristic
383C24×C3C22×D311yescharacteristic
384C23×D3—24no—
385C23×D3—24no—
386C23×D3—31no—
387C23×D3—31no—
388C23×D3—31no—
389C23×D3—31no—
390C23×D3—34no—
391C23×D3—34no—
392C23×D3—42no—
393C23×D3—61no—
394C23×D3—64no—
395C23×D3—61no—
396C23×D3—64no—
397C23×D3—64no—
398C23×D3—68no—
399C23×D3—64no—
400C23×D3—64no—
401C23×D3—124no—
402C23×D3—122no—
403C23×D3—122no—
404C23×D3—124no—
405C23×D3C22×D311yescharacteristic
406C23×D3C22×D311yescharacteristic
407C23×D3C22×D314yes—
408C23×D3C22×D311yescharacteristic
409C2×C3×Q8—34no—
410C2×C3×Q8—64no—
411C2×C3×D4—34no—
412C2×C3×D4—34no—
413C2×C3×D4—34no—
414C2×C3×D4—64no—
415C2×C3×D4—64no—
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—64no—
426C22×C3×C4C22×D311yescharacteristic
427C22×C3×C4C22×D311yescharacteristic
428C22×C3×C4C22×D311yescharacteristic
429C22×C3×C4C22×D311yescharacteristic
430C2×#67—24no—
431C2×#67—38no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—632no—
439C2×#67—64no—
440C2×#67—64no—
441C2×#67—64no—
442C2×#67—64no—
443C2×#67—122no—
444C2×#67C22×D314yes—
445C22×Dic3—24no—
446C22×Dic3—31no—
447C22×Dic3—31no—
448C22×Dic3—31no—
449C22×Dic3—31no—
450C22×Dic3—34no—
451C22×Dic3—34no—
452C22×Dic3—34no—
453C22×Dic3—61no—
454C22×Dic3—61no—
455C22×Dic3—64no—
456C22×Dic3—64no—
457C22×Dic3—122no—
458C22×Dic3C22×D314yes—
459C22×Dic3C22×D311yescharacteristic
460C22×Dic3C22×D311yescharacteristic
461C22×Dic3C22×D311yescharacteristic
462C22×Dic3C22×D311yescharacteristic
463C22×Dic3C22×D311yescharacteristic
464#239—632no—
465#237—632no—
466C2×D12—24no—
467C2×D12—38no—
468C2×D12—34no—
469C2×D12—34no—
470C2×D12—34no—
471C2×D12—34no—
472C2×D12—34no—
473C2×D12—34no—
474C2×D12—42no—
475C2×D12—632no—
476C2×D12—64no—
477C2×D12—64no—
478C2×D12—64no—
479C2×D12—64no—
480C2×D12—122no—
481C2×D12C22×D314yescomplemented
482C2×D12C22×D314yescomplemented
483C2×C4×D3—34no—
484C2×C4×D3—34no—
485C2×C4×D3—34no—
486C2×C4×D3—34no—
487C2×C4×D3—34no—
488C2×C4×D3—34no—
489C2×C4×D3—34no—
490C2×C4×D3—64no—
491C2×C4×D3—64no—
492C2×C4×D3—64no—
493C2×C4×D3—64no—
494C2×C4×D3—64no—
495C2×C4×D3—64no—
496C2×C4×D3—124no—
497C2×C4×D3—122no—
498C2×C4×D3—122no—
499C2×C4×D3—122no—
500C2×C4×D3—124no—
501C2×Dic6—24no—
502C2×Dic6C22×D314yescomplemented
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×D314yes—
511C3×C22⋊C4C22×D314yes—
512#217—34no—
513#217—34no—
514#217—34no—
515#217—34no—
516#217—34no—
517#217—64no—
518#217C22×D314yes—
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—28no—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32C22×D412yes—
545C22×C32C2×#4112yes—
546C22×C32C2×#4114yescomplemented
547C22×C32H(5,𝔽2)12yes—
548C22×C32C2511yescharacteristic
549C2×C3⋊D3—28no—
550C2×C3⋊D3—22no—
551C2×C3⋊D3—22no—
552C2×C3⋊D3—22no—
553C2×C3⋊D3—22no—
554C2×C3⋊D3—22no—
555C2×C3⋊D3—416no—
556C2×C3⋊D3—44no—
557C2×C3⋊D3C22×D414yes—
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—416no—
568C2×C3×D3—44no—
569C2×C3×D3—44no—
570C2×C3×D3C22×D414yes—
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—31no—
581C25—91no—
582C2×#41—98no—
583C2×#41—188no—
584C22×Q8—31no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—91no—
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—91no—
598C23×C4—91no—
599C23×C4—91no—
600C23×C4—91no—
601C23×C4—91no—
602#124—98no—
603#123—98no—
604#123—98no—
605C22⋊Q8—38no—
606#121—98no—
607#121—98no—
608#121—98no—
609#120—38no—
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
631C2×C42—91no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—21no—
638C23×C3—24no—
639C23×C3—34no—
640C23×C3—32no—
641C23×C3—32no—
642C23×C3—32no—
643C23×C3—42no—
644C23×C3—42no—
645C23×C3—68no—
646C23×C3—62no—
647C23×C3—62no—
648C23×C3—62no—
649C23×C3—62no—
650C23×C3—62no—
651C23×C3—62no—
652C23×C3—68no—
653C23×C3—62no—
654C23×C3—62no—
655C23×C3—124no—
656C23×C3—1216no—
657C23×C3#23714yescomplemented
658C23×C3#23914yescomplemented
659C23×C3C23×D312yes—
660C23×C3C23×D312yes—
661C23×C3C23×D311yescharacteristic
662C23×C3C23×D311yescharacteristic
663C22×D3—22no—
664C22×D3—22no—
665C22×D3—22no—
666C22×D3—22no—
667C22×D3—22no—
668C22×D3—22no—
669C22×D3—28no—
670C22×D3—22no—
671C22×D3—22no—
672C22×D3—28no—
673C22×D3—34no—
674C22×D3—34no—
675C22×D3—32no—
676C22×D3—32no—
677C22×D3—32no—
678C22×D3—32no—
679C22×D3—44no—
680C22×D3—416no—
681C22×D3—64no—
682C22×D3—62no—
683C22×D3—62no—
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—64no—
693C22×D3—616no—
694C22×D3—62no—
695C22×D3—62no—
696C22×D3—62no—
697C22×D3—68no—
698C22×D3—62no—
699C22×D3—62no—
700C22×D3—68no—
701C22×D3—62no—
702C22×D3—128no—
703C22×D3—122no—
704C22×D3—122no—
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×Q8—68no—
716C3×D4—68no—
717C3×D4—68no—
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—62no—
735C2×C3×C4—62no—
736C2×C3×C4—62no—
737C2×C3×C4—62no—
738C2×C3×C4C23×D312yes—
739C2×C3×C4C23×D312yes—
740C2×C3×C4C23×D312yes—
741C2×C3×C4C23×D312yes—
742#67—28no—
743#67—316no—
744#67—68no—
745#67—68no—
746#67—68no—
747#67—68no—
748#67—124no—
749C2×Dic3—22no—
750C2×Dic3—22no—
751C2×Dic3—22no—
752C2×Dic3—22no—
753C2×Dic3—28no—
754C2×Dic3—32no—
755C2×Dic3—32no—
756C2×Dic3—32no—
757C2×Dic3—32no—
758C2×Dic3—62no—
759C2×Dic3—62no—
760C2×Dic3—68no—
761C2×Dic3—62no—
762C2×Dic3—62no—
763C2×Dic3—62no—
764C2×Dic3—62no—
765C2×Dic3—68no—
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—28no—
776D12—316no—
777D12—44no—
778D12—68no—
779D12—68no—
780D12—68no—
781D12—68no—
782D12—124no—
783C4×D3—68no—
784C4×D3—68no—
785C4×D3—68no—
786C4×D3—68no—
787C4×D3—128no—
788C4×D3—124no—
789C4×D3—124no—
790C4×D3—124no—
791C4×D3—128no—
792Dic6—28no—
793C2×C32—24no—
794C2×C32#54614yescomplemented
795C2×C32C23×D411yescharacteristic
796C2×C32C22×#4111yescharacteristic
797C2×C32C2×H(5,𝔽2)11yescharacteristic
798C3⋊D3—24no—
799C3⋊D3—42no—
800C3×D3—24no—
801C3×D3—42no—
802C3×D3—42no—
803C24—31no—
804C24—31no—
805C24—31no—
806C24—34no—
807C24—64no—
808C24—64no—
809C24—91no—
810C24—91no—
811C24—94no—
812C24—122no—
813C24—184no—
814C24—184no—
815C24—362no—
816C24C2×D3211yescharacteristic
817#41—1832no—
818C2×Q8—34no—
819C2×Q8—64no—
820C2×D4—34no—
821C2×D4—34no—
822C2×D4—34no—
823C2×D4—64no—
824C2×D4—64no—
825C2×D4—94no—
826C2×D4—98no—
827C2×D4—94no—
828C2×D4—94no—
829C2×D4—94no—
830C2×D4—94no—
831C2×D4—94no—
832C2×D4—122no—
833C2×D4—184no—
834C2×D4—1832no—
835C2×D4—184no—
836C2×D4—184no—
837C2×D4—184no—
838C2×D4—362no—
839C22×C4—31no—
840C22×C4—34no—
841C22×C4—31no—
842C22×C4—31no—
843C22×C4—31no—
844C22×C4—31no—
845C22×C4—64no—
846C22×C4—94no—
847C22×C4—94no—
848C22×C4—94no—
849C22×C4—91no—
850C22×C4—91no—
851C22×C4—94no—
852C22×C4—94no—
853C22×C4—184no—
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×D3214yes—
876C42—94no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—22no—
880C22×C3—22no—
881C22×C3—28no—
882C22×C3—28no—
883C22×C3—22no—
884C22×C3—24no—
885C22×C3—22no—
886C22×C3—22no—
887C22×C3—21no—
888C22×C3—34no—
889C22×C3—48no—
890C22×C3—42no—
891C22×C3—42no—
892C22×C3—62no—
893C22×C3—62no—
894C22×C3—68no—
895C22×C3—62no—
896C22×C3—62no—
897C22×C3—62no—
898C22×C3—62no—
899C22×C3—62no—
900C22×C3—62no—
901C22×C3—1216no—
902C22×C3—124no—
903C22×C3—124no—
904C22×C3C2×D3×D412yes—
905C22×C3C2×D3×D412yes—
906C22×C3C2×#23712yes—
907C22×C3C2×#23714yescomplemented
908C22×C3#100412yes—
909C22×C3C2×#23912yes—
910C22×C3C2×#23914yescomplemented
911C22×C3#100912yes—
912C22×C3C24×D311yescharacteristic
913C22×C3C24×D311yescharacteristic
914C2×D3—22no—
915C2×D3—22no—
916C2×D3—28no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—22no—
923C2×D3—34no—
924C2×D3—34no—
925C2×D3—416no—
926C2×D3—44no—
927C2×D3—44no—
928C2×D3—64no—
929C2×D3—64no—
930C2×D3—64no—
931C2×D3—616no—
932C2×D3—62no—
933C2×D3—62no—
934C2×D3—62no—
935C2×D3—62no—
936C2×D3—68no—
937C2×D3—68no—
938C2×D3—64no—
939C2×D3—62no—
940C2×D3—62no—
941C2×D3—62no—
942C2×D3—62no—
943C2×D3—62no—
944C2×D3—62no—
945C2×D3—122no—
946C2×D3—122no—
947C2×D3—1216no—
948C2×D3—1216no—
949C2×D3—1232no—
950C2×D3—128no—
951C2×D3—124no—
952C2×D3—124no—
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—34no—
980C23—32no—
981C23—32no—
982C23—32no—
983C23—68no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—62no—
988C23—68no—
989C23—62no—
990C23—62no—
991C23—62no—
992C23—62no—
993C23—94no—
994C23—92no—
995C23—92no—
996C23—124no—
997C23—1216no—
998C23—188no—
999C23—182no—
1000C23—182no—
1001C23—182no—
1002C23—188no—
1003C23—182no—
1004C23—182no—
1005C23—364no—
1006C23—3616no—
1007C23#379614yescomplemented
1008C23C22×D3212yes—
1009C23C22×D3211yescharacteristic
1010Q8—68no—
1011D4—68no—
1012D4—68no—
1013D4—916no—
1014D4—124no—
1015D4—188no—
1016D4—188no—
1017D4—188no—
1018D4—188no—
1019D4—364no—
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—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—92no—
1034C2×C4—92no—
1035C2×C4—188no—
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—24no—
1045C2×C3—24no—
1046C2×C3—24no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—44no—
1051C2×C3—64no—
1052C2×C3—122no—
1053C2×C3—122no—
1054C2×C3#559114yescomplemented
1055C2×C3#563014yescomplemented
1056C2×C3C22×D3×D411yescharacteristic
1057C2×C3C22×D3×D411yescharacteristic
1058C2×C3C22×#23711yescharacteristic
1059C2×C3C2×#100411yescharacteristic
1060C2×C3C22×#23911yescharacteristic
1061C2×C3C2×#100911yescharacteristic
1062D3—24no—
1063D3—42no—
1064D3—42no—
1065D3—68no—
1066D3—64no—
1067D3—64no—
1068D3—124no—
1069D3—122no—
1070D3—122no—
1071C22—28no—
1072C22—22no—
1073C22—22no—
1074C22—34no—
1075C22—68no—
1076C22—62no—
1077C22—62no—
1078C22—62no—
1079C22—62no—
1080C22—62no—
1081C22—62no—
1082C22—62no—
1083C22—62no—
1084C22—94no—
1085C22—1216no—
1086C22—124no—
1087C22—124no—
1088C22—188no—
1089C22—182no—
1090C22—182no—
1091C22—182no—
1092C22—182no—
1093C22—182no—
1094C22—3616no—
1095C22—364no—
1096C22C2×#379612yes—
1097C22C2×#379614yescomplemented
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×#559111yescharacteristic, complemented
1112C3C2×#563011yescharacteristic, complemented
1113C2—24no—
1114C2—64no—
1115C2—122no—
1116C2—122no—
1117C2—184no—
1118C2—362no—
1119C2#1059406314yesdirect product factor
1120C2C22×#379611yescharacteristic
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. C23×#626C2semidirect
2. C22×#3796C2semidirect
3. C2×C22⋊C4×C3⋊D3C2semidirect
4. C2×C3×#882C2semidirect
5. C2×C3×#878C2semidirect
6. C2×#63981C2semidirect
7. C2×Dic3×#67C2semidirect
8. C2×D3×#217C2semidirect
9. C2×#63916C2semidirect
10. C2×#63907C2semidirect
11. C2×#63890C2semidirect
12. C2×#63886C2semidirect
13. C2×#63886C2semidirect
14. C2×#63881C2semidirect
15. C2×#63853C2semidirect
16. #10594063C2direct (N × H)
21. C22×C4×C3⋊D3C22semidirect
22. C22×C4×C3⋊D3C22semidirect
25. C22×C3×D12C22semidirect
26. C22×C3×D12C22semidirect
27. C22×C3×Dic6C22semidirect
33. C22×#626C22semidirect
34. C22×#626C22semidirect
35. C22×#626C22semidirect
36. C22×D3×Dic3C22semidirect
37. C22×D3×Dic3C22semidirect
38. C22×D3×Dic3C22semidirect
40. C2×#3796C22semidirect
43. C2×#3752C22semidirect
44. C2×#3752C22semidirect
45. C22⋊C4×C3⋊D3C22semidirect
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×#882C22semidirect
53. C3×#878C22semidirect
54. #63981C22semidirect
55. Dic3×#67C22semidirect
56. D3×#217C22semidirect
57. C2×Dic3⋊Dic3C22semidirect
58. C2×#3722C22semidirect
59. C2×#3722C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. C2×Dic32C22semidirect
64. #63916C22semidirect
65. #63907C22semidirect
66. #63890C22semidirect
67. #63886C22semidirect
68. #63886C22semidirect
69. #63881C22semidirect
70. #63853C22semidirect
97. C2×#882D3semidirect
103. C2×#878D3semidirect
124. C2×C4×C3⋊D3C23semidirect
125. C2×C4×C3⋊D3C23semidirect
137. C2×C3×D12C23semidirect
138. C2×C3×D12C23semidirect
140. C2×C3×Dic6C23semidirect
147. C2×#626D4semidirect
152. C2×#626C23semidirect
153. C2×#626C23semidirect
157. C2×D3×Dic3C23semidirect
158. C2×D3×Dic3C23semidirect
159. C2×D3×Dic3C23semidirect
163. #3752C23semidirect
164. #3752C23semidirect
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
172. #3722C23semidirect
173. #3722C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
214. C22×D12C2×D3semidirect
215. C22×D12C2×D3semidirect
225. C22×Dic6C2×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
284. #882C2×D3semidirect
290. #878C2×D3semidirect
293. C23×C32#41semidirect
354. #626C2×D4semidirect
481. C2×D12C22×D3semidirect
482. C2×D12C22×D3semidirect
502. C2×Dic6C22×D3semidirect
532. (C2×D3)⋊C4C22×D3semidirect
533. (C2×D3)⋊C4C22×D3semidirect
535. C4⋊Dic3C22×D3semidirect
537. Dic3⋊C4C22×D3semidirect
538. Dic3⋊C4C22×D3semidirect
546. C22×C32C2×#41semidirect
657. C23×C3#237semidirect
658. C23×C3#239semidirect
794. C2×C32#546semidirect
907. C22×C3C2×#237semidirect
910. C22×C3C2×#239semidirect
976. C32C2×#546semidirect
1007. C23#3796semidirect
1054. C2×C3#5591semidirect
1055. C2×C3#5630semidirect
1097. C22C2×#3796semidirect
1111. C3C2×#5591semidirect
1112. C3C2×#5630semidirect
1119. C2#10594063direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6262
C22×#37962
C2×C22⋊C4×C3⋊D32
C2×C3×#8822
C2×C3×#8782
C2×#639812
C2×Dic3×#672
C2×D3×#2172
C2×#639162
C2×#639072
C2×#638902
C2×#638862
C2×#638812
C2×#638532
#105940632
C2×#56303
C2×#55913