Finite Group Databasebeta

← C2×#10594017 #11902911

Subgroups — C2×#10594017 #11902911

Order 1152.

2869 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C3×#876C211yesmaximal, characteristic, complemented
3C2×C3×#872C211yesmaximal, characteristic, complemented
4C2×#63923C211yesmaximal, characteristic
5C2×#63921C211yesmaximal, characteristic, complemented
6C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7C2×#63897C211yesmaximal, characteristic, complemented
8C2×#63893C211yesmaximal, characteristic, complemented
9C2×#63881C211yesmaximal, characteristic, complemented
10C2×#63865C211yesmaximal, characteristic, complemented
11C2×#63861C211yesmaximal, characteristic, complemented
12C2×#63853C211yesmaximal, characteristic, complemented
13C2×#63852C211yesmaximal, characteristic, complemented
14C2×#63850C211yesmaximal, characteristic, complemented
15C2×#63836C211yesmaximal, characteristic, complemented
16#10594017C2116yesmaximal, direct product factor
17C2×#5705—31nomaximal
18C2×#5527—31nomaximal
19C23×D32C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C22×C3×C4×D3C2211yescharacteristic
24C22×#627C2211yescharacteristic, complemented
25C22×#626C2211yescharacteristic
26C22×#626C2211yescharacteristic
27C22×#624C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C2×C32×C42C2211yescharacteristic, complemented
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic, complemented
32C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
33C4×C4⋊(C3⋊D3)C2218yescomplemented
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
40C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
41C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
42C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
43C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
44C2×C3×C4×Dic3C2211yescharacteristic, complemented
45C3×#876C2218yescomplemented
46C3×#872C2218yescomplemented
47C2×#3724C2211yescharacteristic, complemented
48C2×Dic3⋊Dic3C2211yescharacteristic, complemented
49C2×#3722C2211yescharacteristic
50C2×#3722C2211yescharacteristic
51C2×#3722C2211yescharacteristic, complemented
52C2×#3722C2211yescharacteristic, complemented
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×Dic32C2211yescharacteristic, complemented
57#63923C2218yes—
58#63921C2218yescomplemented
59D3×(C2×D3)⋊C4C2218yescomplemented
60#63897C2218yescomplemented
61#63893C2218yescomplemented
62#63881C2218yescomplemented
63#63865C2218yescomplemented
64#63861C2218yescomplemented
65#63853C2218yescomplemented
66#63852C2218yescomplemented
67#63850C2218yescomplemented
68#63836C2218yescomplemented
69C2×C3×#126—31no—
70C2×C3×#117—31no—
71C2×#929—31no—
72C22×(C2×D3)⋊C4—31no—
73#5705—316no—
74#5527—316no—
75C2×#898—31no—
76C2×#897—31no—
77C2×#896—31no—
78C2×#896—31no—
79C2×#894—31no—
80C2×#894—31no—
81C2×#894—31no—
82C2×#894—31no—
83C2×#893—31no—
84C2×#892—31no—
85C2×#885—31no—
86C2×#883—31no—
87C2×#882—31no—
88C2×#882—31no—
89C2×#67⋊C4—31no—
90C2×D3×C22⋊C4—31no—
91C2×D3×C22⋊C4—31no—
92C2×D3×C22⋊C4—31no—
93C2×#879—31no—
94C2×#878—31no—
95C2×#876D311yescharacteristic, complemented
96C2×#875—31no—
97C2×C4×D12—31no—
98C2×C4×D12—31no—
99C2×C4×D12—61no—
100C2×#872—31no—
101C2×#872D311yescharacteristic, complemented
102C23×C3⋊D3C2311yescharacteristic
103C23×C3⋊D3C2311yescharacteristic
104C23×C3×D3C2311yescharacteristic
105C23×C3×D3C2311yescharacteristic
106C22×D32—24no—
107C22×D32—24no—
108C22×D32—42no—
109C22×D32C2314yes—
110C22×C32×C4C2311yescharacteristic
111C22×C32×C4C2311yescharacteristic
112C22×C32×C4C2311yescharacteristic
113C22×C3⋊Dic3C2311yescharacteristic
114C22×C3⋊Dic3C2311yescharacteristic
115C2×C4⋊(C3⋊D3)—24no—
116C2×C4⋊(C3⋊D3)C2314yes—
117C2×C4×C3⋊D3—42no—
118C2×C4×C3⋊D3—42no—
119C2×C4×C3⋊D3C2314yes—
120C2×C4×C3⋊D3C2314yescomplemented
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C2×C3×C4×D3—24no—
128C2×C3×C4×D3C2314yes—
129C2×#627—42no—
130C2×#627C2314yescomplemented
131C2×#626—24no—
132C2×#626—42no—
133C2×#626C2314yes—
134C2×#626C2314yes—
135C2×#624—24no—
136C2×#624C2314yes—
137C2×D3×Dic3—42no—
138C2×D3×Dic3C2314yes—
139C32×C42C2314yescomplemented
140#3752C2314yes—
141#3752C2314yescomplemented
142C4⋊(C3⋊Dic3)C2314yescomplemented
143C3×(C2×D3)⋊C4C2314yes—
144C3×(C2×D3)⋊C4C2314yes—
145C3×(C2×D3)⋊C4C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×Dic3⋊C4C2314yescomplemented
149C3×Dic3⋊C4C2314yescomplemented
150C3×Dic3⋊C4C2314yescomplemented
151C3×Dic3⋊C4C2314yescomplemented
152C3×Dic3⋊C4C2314yescomplemented
153C3×C4×Dic3C2314yescomplemented
154#3724C2314yescomplemented
155Dic3⋊Dic3C2314yescomplemented
156#3722C2314yes—
157#3722C2314yes—
158#3722C2314yescomplemented
159#3722C2314yescomplemented
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163Dic32C2314yescomplemented
164C2×#551—91noSylow
165C24×D3—31no—
166C24×D3—31no—
167C23×C3×C4—31no—
168C22×#67—31no—
169C22×#67—31no—
170C23×Dic3—31no—
171C22×D12—31no—
172C22×D12—31no—
173C22×D12—31no—
174C22×D12—31no—
175C22×D12—61no—
176C22×C4×D3—31no—
177C22×C4×D3—31no—
178C22×C4×D3—31no—
179C22×C4×D3—31no—
180C22×C4×D3—31no—
181C22×C4×D3—31no—
182C22×C4×D3—31no—
183C22×C4×D3—61no—
184C22×C4×D3—61no—
185C22×C4×D3C2×D311yescharacteristic
186C22×Dic6—31no—
187C22×Dic6—31no—
188C3×#126—38no—
189C3×#117—38no—
190C2×C3×C4⋊C4—31no—
191C2×C3×C4⋊C4—31no—
192C2×C3×C4⋊C4—31no—
193C2×C3×C4⋊C4—31no—
194C2×C3×C4⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4—31no—
200C2×C3×C42—21no—
201C2×C3×C42—31no—
202C2×C3×C42C2×D311yescharacteristic, complemented
203C2×C3×C42C2×D311yescharacteristic, complemented
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—31no—
207#929—38no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4—31no—
215C2×(C2×D3)⋊C4—31no—
216C2×(C2×D3)⋊C4—31no—
217C2×(C2×D3)⋊C4—31no—
218C2×(C2×D3)⋊C4—31no—
219C2×(C2×D3)⋊C4—31no—
220C2×(C2×D3)⋊C4—31no—
221C2×(C2×D3)⋊C4—31no—
222C2×(C2×D3)⋊C4—31no—
223C2×(C2×D3)⋊C4—38no—
224C2×(C2×D3)⋊C4—61no—
225C2×(C2×D3)⋊C4—61no—
226C2×(C2×D3)⋊C4C2×D311yescharacteristic
227C2×(C2×D3)⋊C4C2×D311yescharacteristic
228C2×(C2×D3)⋊C4C2×D311yescharacteristic
229C2×(C2×D3)⋊C4C2×D311yescharacteristic
230C2×(C2×D3)⋊C4C2×D311yescharacteristic
231C2×C4⋊Dic3—31no—
232C2×C4⋊Dic3—31no—
233C2×C4⋊Dic3—31no—
234C2×C4⋊Dic3—61no—
235C2×Dic3⋊C4—31no—
236C2×Dic3⋊C4—31no—
237C2×Dic3⋊C4—31no—
238C2×Dic3⋊C4C2×D311yescharacteristic, complemented
239C2×Dic3⋊C4C2×D311yescharacteristic, complemented
240C2×Dic3⋊C4C2×D311yescharacteristic, complemented
241C2×Dic3⋊C4C2×D311yescharacteristic, complemented
242C2×Dic3⋊C4C2×D311yescharacteristic, complemented
243C2×C4×Dic3—31no—
244C2×C4×Dic3—31no—
245C2×C4×Dic3C2×D311yescharacteristic, complemented
246#898—38no—
247#897—38no—
248#896—38no—
249#896—38no—
250#894—38no—
251#894—38no—
252#894—38no—
253#894—38no—
254#893—38no—
255#892—38no—
256#885—38no—
257#883—38no—
258#882—38no—
259#882—38no—
260#67⋊C4—38no—
261D3×C22⋊C4—38no—
262D3×C22⋊C4—38no—
263D3×C22⋊C4—38no—
264#879—38no—
265#878—38no—
266#876C2×D318yescomplemented
267#875—38no—
268C4×D12—38no—
269C4×D12—38no—
270C4×D12—68no—
271#872—38no—
272#872C2×D318yescomplemented
273C23×C32C2411yescharacteristic
274C22×C3⋊D3—22no—
275C22×C3⋊D3—22no—
276C22×C3⋊D3—22no—
277C22×C3⋊D3—22no—
278C22×C3⋊D3—22no—
279C22×C3⋊D3#4114yes—
280C22×C3⋊D3C2412yes—
281C22×C3⋊D3C2412yes—
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3#4114yes—
288C22×C3×D3C2412yes—
289C22×C3×D3C2412yes—
290C2×D32—28no—
291C2×D32—28no—
292C2×D32—44no—
293C2×D32—416no—
294C2×C32×C4—22no—
295C2×C32×C4—22no—
296C2×C32×C4—22no—
297C2×C32×C4C2412yes—
298C2×C32×C4C2412yes—
299C2×C32×C4C2412yes—
300C2×C3⋊Dic3—22no—
301C2×C3⋊Dic3—22no—
302C2×C3⋊Dic3C2412yes—
303C2×C3⋊Dic3C2412yes—
304C4⋊(C3⋊D3)—28no—
305C4×C3⋊D3—44no—
306C4×C3⋊D3—44no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3—22no—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C3×C4×D3—28no—
320#627—44no—
321#626—28no—
322#626—44no—
323#624—28no—
324D3×Dic3—44no—
325#551—916no—
326C2×#126—31no—
327C2×#126—91no—
328C2×#124—91no—
329C2×#123—91no—
330C2×#123—91no—
331C2×#123—91no—
332C2×C22⋊Q8—91no—
333C2×C22⋊Q8—91no—
334C2×#120—91no—
335C2×C4×D4—91no—
336C2×C4×D4—91no—
337C2×#117—31no—
338C2×#117—91no—
339C22×C22⋊C4—91no—
340C22×C22⋊C4—91no—
341C24×C3—31no—
342C24×C3—31no—
343C23×D3—31no—
344C23×D3—31no—
345C23×D3—31no—
346C23×D3—31no—
347C23×D3—34no—
348C23×D3—34no—
349C23×D3—61no—
350C23×D3—61no—
351C23×D3—64no—
352C23×D3—64no—
353C23×D3—64no—
354C23×D3—64no—
355C23×D3—122no—
356C23×D3—122no—
357C23×D3C22×D311yescharacteristic
358C23×D3C22×D311yescharacteristic
359C22×C3×C4—21no—
360C22×C3×C4—21no—
361C22×C3×C4—21no—
362C22×C3×C4—31no—
363C22×C3×C4—31no—
364C22×C3×C4—31no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—34no—
369C22×C3×C4—64no—
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C22×D311yescharacteristic
376C2×#67—34no—
377C2×#67—34no—
378C2×#67—64no—
379C2×#67—122no—
380C22×Dic3—31no—
381C22×Dic3—31no—
382C22×Dic3—31no—
383C22×Dic3—31no—
384C22×Dic3—34no—
385C22×Dic3—61no—
386C22×Dic3—61no—
387C22×Dic3—122no—
388C22×Dic3C22×D311yescharacteristic
389C22×Dic3C22×D311yescharacteristic
390C22×Dic3C22×D311yescharacteristic
391C22×Dic3C22×D311yescharacteristic
392C22×Dic3C22×D311yescharacteristic
393C22×Dic3C22×D311yescharacteristic
394C2×D12—34no—
395C2×D12—34no—
396C2×D12—34no—
397C2×D12—34no—
398C2×D12—64no—
399C2×D12—64no—
400C2×D12—64no—
401C2×D12—68no—
402C2×D12—64no—
403C2×D12—122no—
404C2×C4×D3—24no—
405C2×C4×D3—34no—
406C2×C4×D3—34no—
407C2×C4×D3—34no—
408C2×C4×D3—34no—
409C2×C4×D3—34no—
410C2×C4×D3—34no—
411C2×C4×D3—34no—
412C2×C4×D3—64no—
413C2×C4×D3—64no—
414C2×C4×D3—64no—
415C2×C4×D3—64no—
416C2×C4×D3—122no—
417C2×C4×D3—122no—
418C2×C4×D3—122no—
419C2×C4×D3—122no—
420C2×C4×D3—122no—
421C2×C4×D3—124no—
422C2×C4×D3—124no—
423C2×C4×D3C22×D314yes—
424C2×Dic6—34no—
425C2×Dic6—34no—
426C2×Dic6—122no—
427C2×Dic6—122no—
428C3×C4⋊C4—34no—
429C3×C4⋊C4—34no—
430C3×C4⋊C4—34no—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—34no—
433C3×C22⋊C4—34no—
434C3×C22⋊C4—34no—
435C3×C22⋊C4—34no—
436C3×C22⋊C4—34no—
437C3×C22⋊C4—34no—
438C3×C42—24no—
439C3×C42—34no—
440C3×C42C22×D314yescomplemented
441C3×C42C22×D314yescomplemented
442#217—34no—
443#217—34no—
444#217—34no—
445(C2×D3)⋊C4—34no—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4—34no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4—34no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—34no—
457(C2×D3)⋊C4—34no—
458(C2×D3)⋊C4—34no—
459(C2×D3)⋊C4—34no—
460(C2×D3)⋊C4—64no—
461(C2×D3)⋊C4—64no—
462(C2×D3)⋊C4C22×D314yes—
463(C2×D3)⋊C4C22×D314yes—
464(C2×D3)⋊C4C22×D314yes—
465(C2×D3)⋊C4C22×D314yes—
466(C2×D3)⋊C4C22×D314yes—
467C4⋊Dic3—34no—
468C4⋊Dic3—34no—
469C4⋊Dic3—34no—
470C4⋊Dic3—64no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—34no—
474Dic3⋊C4C22×D314yescomplemented
475Dic3⋊C4C22×D314yescomplemented
476Dic3⋊C4C22×D314yescomplemented
477Dic3⋊C4C22×D314yescomplemented
478Dic3⋊C4C22×D314yescomplemented
479C4×Dic3—34no—
480C4×Dic3—34no—
481C4×Dic3C22×D314yescomplemented
482C22×C32C2×#4112yes—
483C22×C32C2×#4112yes—
484C22×C32H(5,𝔽2)12yes—
485C22×C32C2511yescharacteristic
486C2×C3⋊D3—22no—
487C2×C3⋊D3—28no—
488C2×C3⋊D3—22no—
489C2×C3⋊D3—22no—
490C2×C3⋊D3—22no—
491C2×C3⋊D3—22no—
492C2×C3⋊D3—44no—
493C2×C3⋊D3C2×#4114yes—
494C2×C3×D3—28no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—22no—
499C2×C3×D3—22no—
500C2×C3×D3—44no—
501C2×C3×D3C2×#4114yes—
502D32—416no—
503C32×C4—22no—
504C32×C4—22no—
505C32×C4—22no—
506C3⋊Dic3—22no—
507C3⋊Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C3×Dic3—22no—
514C25—91no—
515C22×Q8—91no—
516C22×D4—91no—
517C22×D4—91no—
518C22×D4—91no—
519C23×C4—31no—
520C23×C4—91no—
521C23×C4—91no—
522C23×C4—91no—
523C23×C4—91no—
524#126—38no—
525#126—98no—
526#124—98no—
527#123—98no—
528#123—98no—
529#123—98no—
530C22⋊Q8—98no—
531C22⋊Q8—98no—
532#120—98no—
533C4×D4—98no—
534C4×D4—98no—
535#117—38no—
536#117—98no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—31no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—31no—
542C2×C4⋊C4—91no—
543C2×C4⋊C4—91no—
544C2×C4⋊C4—91no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—98no—
551C2×C22⋊C4—98no—
552C2×C22⋊C4—91no—
553C2×C22⋊C4—91no—
554C2×C22⋊C4—91no—
555C2×C22⋊C4—91no—
556C2×C22⋊C4—91no—
557C2×C22⋊C4—91no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—91no—
560C2×C22⋊C4—91no—
561C2×C42—31no—
562C2×C42—91no—
563C2×C42D3211yescharacteristic, complemented
564C23×C3—21no—
565C23×C3—34no—
566C23×C3—32no—
567C23×C3—32no—
568C23×C3—62no—
569C23×C3—62no—
570C23×C3—62no—
571C23×C3—62no—
572C23×C3—62no—
573C23×C3C23×D311yescharacteristic
574C23×C3C23×D311yescharacteristic
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—34no—
581C22×D3—34no—
582C22×D3—32no—
583C22×D3—32no—
584C22×D3—32no—
585C22×D3—32no—
586C22×D3—64no—
587C22×D3—62no—
588C22×D3—62no—
589C22×D3—68no—
590C22×D3—68no—
591C22×D3—68no—
592C22×D3—62no—
593C22×D3—62no—
594C22×D3—62no—
595C22×D3—62no—
596C22×D3—64no—
597C22×D3—62no—
598C22×D3—62no—
599C22×D3—62no—
600C22×D3—62no—
601C22×D3—62no—
602C22×D3—62no—
603C22×D3—68no—
604C22×D3—122no—
605C22×D3—122no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3—124no—
609C22×D3—124no—
610C22×D3—1216no—
611C22×D3—1216no—
612C22×D3#23514yes—
613C22×D3C23×D312yes—
614C22×D3C23×D312yes—
615C2×C3×C4—24no—
616C2×C3×C4—24no—
617C2×C3×C4—22no—
618C2×C3×C4—22no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—22no—
622C2×C3×C4—22no—
623C2×C3×C4—22no—
624C2×C3×C4—22no—
625C2×C3×C4—22no—
626C2×C3×C4—32no—
627C2×C3×C4—32no—
628C2×C3×C4—32no—
629C2×C3×C4—32no—
630C2×C3×C4—32no—
631C2×C3×C4—32no—
632C2×C3×C4—42no—
633C2×C3×C4—68no—
634C2×C3×C4—62no—
635C2×C3×C4—62no—
636C2×C3×C4—62no—
637C2×C3×C4—62no—
638C2×C3×C4—62no—
639C2×C3×C4—62no—
640C2×C3×C4C23×D312yes—
641C2×C3×C4C23×D312yes—
642C2×C3×C4C23×D312yes—
643C2×C3×C4C23×D312yes—
644C2×C3×C4C23×D312yes—
645C2×C3×C4C23×D312yes—
646#67—68no—
647#67—124no—
648C2×Dic3—22no—
649C2×Dic3—22no—
650C2×Dic3—22no—
651C2×Dic3—22no—
652C2×Dic3—22no—
653C2×Dic3—22no—
654C2×Dic3—32no—
655C2×Dic3—32no—
656C2×Dic3—32no—
657C2×Dic3—32no—
658C2×Dic3—62no—
659C2×Dic3—62no—
660C2×Dic3—62no—
661C2×Dic3—62no—
662C2×Dic3—62no—
663C2×Dic3—62no—
664C2×Dic3—122no—
665C2×Dic3—122no—
666C2×Dic3—124no—
667C2×Dic3C23×D312yes—
668C2×Dic3C23×D312yes—
669C2×Dic3C23×D312yes—
670C2×Dic3C23×D312yes—
671C2×Dic3C23×D312yes—
672C2×Dic3C23×D312yes—
673D12—68no—
674D12—68no—
675D12—616no—
676D12—68no—
677D12—124no—
678C4×D3—28no—
679C4×D3—68no—
680C4×D3—68no—
681C4×D3—124no—
682C4×D3—124no—
683C4×D3—124no—
684C4×D3—124no—
685C4×D3—124no—
686C4×D3—128no—
687C4×D3—128no—
688Dic6—124no—
689Dic6—124no—
690C2×C32#55114yescomplemented
691C2×C32C22×#4111yescharacteristic
692C2×C32C22×#4111yescharacteristic
693C2×C32C2×H(5,𝔽2)11yescharacteristic
694C3⋊D3—24no—
695C3⋊D3—42no—
696C3×D3—24no—
697C3×D3—42no—
698C24—31no—
699C24—31no—
700C24—94no—
701C24—91no—
702C24—91no—
703C24—184no—
704C24—184no—
705C24—362no—
706C2×Q8—94no—
707C2×Q8—362no—
708C2×D4—94no—
709C2×D4—94no—
710C2×D4—94no—
711C2×D4—184no—
712C2×D4—184no—
713C2×D4—362no—
714C22×C4—31no—
715C22×C4—31no—
716C22×C4—31no—
717C22×C4—31no—
718C22×C4—31no—
719C22×C4—31no—
720C22×C4—34no—
721C22×C4—64no—
722C22×C4—94no—
723C22×C4—94no—
724C22×C4—91no—
725C22×C4—91no—
726C22×C4—94no—
727C22×C4—94no—
728C22×C4—184no—
729C22×C4—362no—
730C22×C4—362no—
731C22×C4—362no—
732C22×C4C2×D3211yescharacteristic
733C22×C4C2×D3211yescharacteristic
734C22×C4C2×D3211yescharacteristic
735C4⋊C4—34no—
736C4⋊C4—34no—
737C4⋊C4—34no—
738C4⋊C4—34no—
739C4⋊C4—34no—
740C4⋊C4—94no—
741C4⋊C4—94no—
742C4⋊C4—94no—
743C22⋊C4—34no—
744C22⋊C4—34no—
745C22⋊C4—34no—
746C22⋊C4—34no—
747C22⋊C4—34no—
748C22⋊C4—94no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C22⋊C4—94no—
752C22⋊C4—94no—
753C22⋊C4—94no—
754C22⋊C4—94no—
755C22⋊C4—94no—
756C22⋊C4—94no—
757C42—34no—
758C42—94no—
759C42C2×D3214yescomplemented
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—22no—
763C22×C3—21no—
764C22×C3—34no—
765C22×C3—68no—
766C22×C3—62no—
767C22×C3—62no—
768C22×C3—62no—
769C22×C3—62no—
770C22×C3—62no—
771C22×C3—124no—
772C22×C3C2×#23512yes—
773C22×C3D3×#4112yes—
774C22×C3D3×#4112yes—
775C22×C3D3×#4112yes—
776C22×C3#100912yes—
777C22×C3#100912yes—
778C22×C3C24×D311yescharacteristic
779C22×C3C24×D311yescharacteristic
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—28no—
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—34no—
787C2×D3—34no—
788C2×D3—44no—
789C2×D3—64no—
790C2×D3—62no—
791C2×D3—68no—
792C2×D3—62no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—68no—
796C2×D3—64no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—62no—
801C2×D3—62no—
802C2×D3—62no—
803C2×D3—122no—
804C2×D3—122no—
805C2×D3—122no—
806C2×D3—128no—
807C2×D3—122no—
808C2×D3—1216no—
809C2×D3—1216no—
810C2×D3—128no—
811C2×D3—124no—
812C2×D3—124no—
813C2×D3C2×#23514yes—
814C3×C4—24no—
815C3×C4—24no—
816C3×C4—22no—
817C3×C4—22no—
818C3×C4—22no—
819C3×C4—22no—
820C3×C4—22no—
821C3×C4—22no—
822C3×C4—42no—
823C3×C4—62no—
824C3×C4—62no—
825C3×C4—62no—
826C3×C4—62no—
827C3×C4—62no—
828C3×C4—62no—
829Dic3—22no—
830Dic3—22no—
831Dic3—22no—
832Dic3—22no—
833Dic3—22no—
834Dic3—22no—
835Dic3—62no—
836Dic3—62no—
837Dic3—62no—
838Dic3—62no—
839Dic3—122no—
840Dic3—122no—
841C32C2×#55111yescharacteristic, complemented, Sylow
842C23—34no—
843C23—32no—
844C23—32no—
845C23—62no—
846C23—62no—
847C23—62no—
848C23—62no—
849C23—62no—
850C23—94no—
851C23—92no—
852C23—92no—
853C23—188no—
854C23—188no—
855C23—182no—
856C23—182no—
857C23—182no—
858C23—182no—
859C23—182no—
860C23—364no—
861C23—3616no—
862C23C22×D3211yescharacteristic
863Q8—364no—
864D4—188no—
865D4—188no—
866D4—364no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—32no—
871C2×C4—32no—
872C2×C4—32no—
873C2×C4—32no—
874C2×C4—32no—
875C2×C4—32no—
876C2×C4—68no—
877C2×C4—62no—
878C2×C4—62no—
879C2×C4—62no—
880C2×C4—62no—
881C2×C4—62no—
882C2×C4—62no—
883C2×C4—92no—
884C2×C4—92no—
885C2×C4—188no—
886C2×C4—182no—
887C2×C4—182no—
888C2×C4—364no—
889C2×C4—364no—
890C2×C4—364no—
891C2×C4C22×D3212yes—
892C2×C4C22×D3212yes—
893C2×C4C22×D3212yes—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—24no—
898C2×C3—64no—
899C2×C3—122no—
900C2×C3#552714yescomplemented
901C2×C3#570514yescomplemented
902C2×C3C22×#23511yescharacteristic
903C2×C3C2×D3×#4111yescharacteristic
904C2×C3C2×D3×#4111yescharacteristic
905C2×C3C2×D3×#4111yescharacteristic
906C2×C3C2×#100911yescharacteristic
907C2×C3C2×#100911yescharacteristic
908D3—24no—
909D3—42no—
910D3—64no—
911D3—64no—
912D3—124no—
913D3—124no—
914D3—122no—
915D3—122no—
916C22—34no—
917C22—62no—
918C22—62no—
919C22—68no—
920C22—62no—
921C22—62no—
922C22—62no—
923C22—94no—
924C22—124no—
925C22—182no—
926C22—182no—
927C22—188no—
928C22—182no—
929C22—182no—
930C22—182no—
931C22—3616no—
932C22—364no—
933C22D3×#23512yes—
934C22#6430612yes—
935C22#6430812yes—
936C22C23×D3211yescharacteristic
937C4—22no—
938C4—22no—
939C4—22no—
940C4—62no—
941C4—62no—
942C4—62no—
943C4—62no—
944C4—62no—
945C4—62no—
946C4—182no—
947C4—182no—
948C3—21no—
949C3C2×#552711yescharacteristic, complemented
950C3C2×#570511yescharacteristic, complemented
951C2—64no—
952C2—122no—
953C2—184no—
954C2—362no—
955C2#1059401714yesdirect product factor
956C2C2×D3×#23511yescharacteristic
957C2C2×#6430611yescharacteristic
958C2C2×#6430811yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC2×#63923C2
hypercenterC2×C42D32
hypocenterC32C2×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C4⋊(C3⋊D3)C2semidirect
2. C2×C3×#876C2semidirect
3. C2×C3×#872C2semidirect
5. C2×#63921C2semidirect
6. C2×D3×(C2×D3)⋊C4C2semidirect
7. C2×#63897C2semidirect
8. C2×#63893C2semidirect
9. C2×#63881C2semidirect
10. C2×#63865C2semidirect
11. C2×#63861C2semidirect
12. C2×#63853C2semidirect
13. C2×#63852C2semidirect
14. C2×#63850C2semidirect
15. C2×#63836C2semidirect
16. #10594017C2direct (N × H)
22. C22×C4×C3⋊D3C22semidirect
24. C22×#627C22semidirect
29. C2×C32×C42C22semidirect
31. C2×#3752C22semidirect
32. C2×C4⋊(C3⋊Dic3)C22semidirect
33. C4×C4⋊(C3⋊D3)C22semidirect
39. C2×C3×Dic3⋊C4C22semidirect
40. C2×C3×Dic3⋊C4C22semidirect
41. C2×C3×Dic3⋊C4C22semidirect
42. C2×C3×Dic3⋊C4C22semidirect
43. C2×C3×Dic3⋊C4C22semidirect
44. C2×C3×C4×Dic3C22semidirect
45. C3×#876C22semidirect
46. C3×#872C22semidirect
47. C2×#3724C22semidirect
48. C2×Dic3⋊Dic3C22semidirect
51. C2×#3722C22semidirect
52. C2×#3722C22semidirect
56. C2×Dic32C22semidirect
58. #63921C22semidirect
59. D3×(C2×D3)⋊C4C22semidirect
60. #63897C22semidirect
61. #63893C22semidirect
62. #63881C22semidirect
63. #63865C22semidirect
64. #63861C22semidirect
65. #63853C22semidirect
66. #63852C22semidirect
67. #63850C22semidirect
68. #63836C22semidirect
95. C2×#876D3semidirect
101. C2×#872D3semidirect
120. C2×C4×C3⋊D3C23semidirect
130. C2×#627C23semidirect
139. C32×C42C23semidirect
141. #3752C23semidirect
142. C4⋊(C3⋊Dic3)C23semidirect
148. C3×Dic3⋊C4C23semidirect
149. C3×Dic3⋊C4C23semidirect
150. C3×Dic3⋊C4C23semidirect
151. C3×Dic3⋊C4C23semidirect
152. C3×Dic3⋊C4C23semidirect
153. C3×C4×Dic3C23semidirect
154. #3724C23semidirect
155. Dic3⋊Dic3C23semidirect
158. #3722C23semidirect
159. #3722C23semidirect
163. Dic32C23semidirect
202. C2×C3×C42C2×D3semidirect
203. C2×C3×C42C2×D3semidirect
238. C2×Dic3⋊C4C2×D3semidirect
239. C2×Dic3⋊C4C2×D3semidirect
240. C2×Dic3⋊C4C2×D3semidirect
241. C2×Dic3⋊C4C2×D3semidirect
242. C2×Dic3⋊C4C2×D3semidirect
245. C2×C4×Dic3C2×D3semidirect
266. #876C2×D3semidirect
272. #872C2×D3semidirect
440. C3×C42C22×D3semidirect
441. C3×C42C22×D3semidirect
474. Dic3⋊C4C22×D3semidirect
475. Dic3⋊C4C22×D3semidirect
476. Dic3⋊C4C22×D3semidirect
477. Dic3⋊C4C22×D3semidirect
478. Dic3⋊C4C22×D3semidirect
481. C4×Dic3C22×D3semidirect
563. C2×C42D32semidirect
690. C2×C32#551semidirect
759. C42C2×D32semidirect
841. C32C2×#551semidirect
900. C2×C3#5527semidirect
901. C2×C3#5705semidirect
949. C3C2×#5527semidirect
950. C3C2×#5705semidirect
955. C2#10594017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C2×C3×#8762
C2×C3×#8722
C2×#639232
C2×#639212
C2×D3×(C2×D3)⋊C42
C2×#638972
C2×#638932
C2×#638812
C2×#638652
C2×#638612
C2×#638532
C2×#638522
C2×#638502
C2×#638362
#105940172
C2×#57053
C2×#55273