Finite Group Databasebeta

← C2×#10594016 #11902908

Subgroups — C2×#10594016 #11902908

Order 1152.

2821 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic, complemented
2C2×C3×#875C211yesmaximal, characteristic, complemented
3C2×C3×#872C211yesmaximal, characteristic, complemented
4C2×#63922C211yesmaximal, characteristic
5C2×#63921C211yesmaximal, characteristic, complemented
6C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7C2×#63905C211yesmaximal, characteristic, complemented
8C2×#63902C211yesmaximal, characteristic, complemented
9C2×#63888C211yesmaximal, characteristic, complemented
10C2×#63887C211yesmaximal, characteristic, complemented
11C2×#63884C211yesmaximal, characteristic, complemented
12C2×#63880C211yesmaximal, characteristic, complemented
13C2×#63862C211yesmaximal, characteristic, complemented
14C2×#63859C211yesmaximal, characteristic, complemented
15C2×#63853C211yesmaximal, characteristic, complemented
16#10594016C2116yesmaximal, direct product factor
17C2×#5679—31nomaximal
18C2×#5527—31nomaximal
19C23×D32C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×Dic6C2211yescharacteristic, complemented
24C22×#626C2211yescharacteristic
25C22×#625C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic, complemented
29C2×C32×C42C2211yescharacteristic, complemented
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×#3750C2211yescharacteristic, complemented
33C2×#3750C2211yescharacteristic, complemented
34C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
35#64081C2218yescomplemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
43C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
44C2×C3×C4×Dic3C2211yescharacteristic, complemented
45C3×#875C2218yescomplemented
46C3×#872C2218yescomplemented
47C2×#3724C2211yescharacteristic, complemented
48C2×Dic3⋊Dic3C2211yescharacteristic, complemented
49C2×Dic3⋊Dic3C2211yescharacteristic, complemented
50C2×Dic3⋊Dic3C2211yescharacteristic, complemented
51C2×#3722C2211yescharacteristic
52C2×(C2×D3)⋊Dic3C2211yescharacteristic
53C2×(C2×D3)⋊Dic3C2211yescharacteristic
54C2×(C2×D3)⋊Dic3C2211yescharacteristic
55C2×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
57#63922C2218yes—
58#63921C2218yescomplemented
59D3×(C2×D3)⋊C4C2218yescomplemented
60#63905C2218yescomplemented
61#63902C2218yescomplemented
62#63888C2218yescomplemented
63#63887C2218yescomplemented
64#63884C2218yescomplemented
65#63880C2218yescomplemented
66#63862C2218yescomplemented
67#63859C2218yescomplemented
68#63853C2218yescomplemented
69C2×C3×#124—31no—
70C2×C3×#117—31no—
71C2×#946—31no—
72C2×#946—31no—
73C2×#937—31no—
74C2×#935—31no—
75C2×#929—31no—
76C22×(C2×D3)⋊C4—31no—
77#5679—316no—
78#5527—316no—
79C2×#898—31no—
80C2×#896—31no—
81C2×#894—31no—
82C2×#894—31no—
83C2×#883—31no—
84C2×#883—31no—
85C2×#882—31no—
86C2×#67⋊C4—31no—
87C2×#67⋊C4—31no—
88C2×#67⋊C4—31no—
89C2×D3×C22⋊C4—31no—
90C2×D3×C22⋊C4—31no—
91C2×D3×C22⋊C4—31no—
92C2×#879—31no—
93C2×#879—31no—
94C2×#878—31no—
95C2×#876—31no—
96C2×#875D311yescharacteristic, complemented
97C2×C4×D12—31no—
98C2×#872—31no—
99C2×#872—31no—
100C2×#872—61no—
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
115C22×C3⋊Dic3C2311yescharacteristic
116C2×C4×C3⋊D3—24no—
117C2×C4×C3⋊D3C2314yes—
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2311yescharacteristic
120C22×C3×Dic3C2311yescharacteristic
121C22×C3×Dic3C2311yescharacteristic
122C22×C3×Dic3C2311yescharacteristic
123C2×C3×D12—42no—
124C2×C3×D12C2314yes—
125C2×C3×C4×D3—24no—
126C2×C3×C4×D3C2314yes—
127C2×C3×Dic6—42no—
128C2×C3×Dic6C2314yescomplemented
129C2×#626—24no—
130C2×#626C2314yes—
131C2×#625—24no—
132C2×#625C2314yes—
133C2×#624—42no—
134C2×#624C2314yes—
135C2×D3×Dic3—42no—
136C2×D3×Dic3—42no—
137C2×D3×Dic3C2314yes—
138C2×D3×Dic3C2314yescomplemented
139C32×C42C2314yescomplemented
140#3752C2314yes—
141#3752C2314yes—
142#3750C2314yescomplemented
143#3750C2314yescomplemented
144C4×C3⋊Dic3C2314yescomplemented
145C3×(C2×D3)⋊C4C2314yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yescomplemented
150C3×(C2×D3)⋊C4C2314yescomplemented
151C3×Dic3⋊C4C2314yescomplemented
152C3×Dic3⋊C4C2314yescomplemented
153C3×C4×Dic3C2314yescomplemented
154#3724C2314yescomplemented
155Dic3⋊Dic3C2314yescomplemented
156Dic3⋊Dic3C2314yescomplemented
157Dic3⋊Dic3C2314yescomplemented
158#3722C2314yes—
159(C2×D3)⋊Dic3C2314yes—
160(C2×D3)⋊Dic3C2314yes—
161(C2×D3)⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yescomplemented
164C2×#551—91noSylow
165C24×D3—31no—
166C24×D3—31no—
167C22×C3×Q8—31no—
168C22×C3×D4—31no—
169C23×C3×C4—31no—
170C22×#67—31no—
171C22×#67—31no—
172C22×#67—31no—
173C23×Dic3—31no—
174C23×Dic3—31no—
175C22×D12—31no—
176C22×D12C2×D311yescharacteristic
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×D3C2×D311yescharacteristic
185C22×Dic6C2×D311yescharacteristic, complemented
186C3×#124—38no—
187C3×#117—38no—
188C2×C3×C4⋊C4—31no—
189C2×C3×C4⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×C3×C22⋊C4—31no—
193C2×C3×C22⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C42—21no—
197C2×C3×C42—31no—
198C2×C3×C42C2×D311yescharacteristic, complemented
199C2×C3×C42C2×D311yescharacteristic, complemented
200C2×#217—31no—
201C2×#217—31no—
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—31no—
205#946—38no—
206#946—38no—
207#937—38no—
208#935—38no—
209#929—38no—
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—38no—
222C2×(C2×D3)⋊C4—61no—
223C2×(C2×D3)⋊C4—61no—
224C2×(C2×D3)⋊C4C2×D311yescharacteristic
225C2×(C2×D3)⋊C4C2×D311yescharacteristic
226C2×(C2×D3)⋊C4C2×D311yescharacteristic
227C2×(C2×D3)⋊C4C2×D311yescharacteristic
228C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
229C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
230C2×C4⋊Dic3—31no—
231C2×C4⋊Dic3—31no—
232C2×C4⋊Dic3—31no—
233C2×Dic3⋊C4—31no—
234C2×Dic3⋊C4—31no—
235C2×Dic3⋊C4—31no—
236C2×Dic3⋊C4—31no—
237C2×Dic3⋊C4—31no—
238C2×Dic3⋊C4—31no—
239C2×Dic3⋊C4—31no—
240C2×Dic3⋊C4—31no—
241C2×Dic3⋊C4—31no—
242C2×Dic3⋊C4—61no—
243C2×Dic3⋊C4—61no—
244C2×Dic3⋊C4C2×D311yescharacteristic, complemented
245C2×Dic3⋊C4C2×D311yescharacteristic, complemented
246C2×C4×Dic3—31no—
247C2×C4×Dic3—31no—
248C2×C4×Dic3—61no—
249C2×C4×Dic3C2×D311yescharacteristic, complemented
250#898—38no—
251#896—38no—
252#894—38no—
253#894—38no—
254#883—38no—
255#883—38no—
256#882—38no—
257#67⋊C4—38no—
258#67⋊C4—38no—
259#67⋊C4—38no—
260D3×C22⋊C4—38no—
261D3×C22⋊C4—38no—
262D3×C22⋊C4—38no—
263#879—38no—
264#879—38no—
265#878—38no—
266#876—38no—
267#875C2×D318yescomplemented
268C4×D12—38no—
269#872—38no—
270#872—38no—
271#872—68no—
272#872C2×D318yescomplemented
273C23×C32C2411yescharacteristic
274C22×C3⋊D3—22no—
275C22×C3⋊D3—22no—
276C22×C3⋊D3#4114yes—
277C22×C3⋊D3C2412yes—
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—22no—
285C22×C3×D3—22no—
286C22×C3×D3#4114yes—
287C22×C3×D3C2412yes—
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⋊Dic3—22no—
303C2×C3⋊Dic3C2412yes—
304C2×C3⋊Dic3C2412yes—
305C2×C3⋊Dic3C2412yes—
306C4×C3⋊D3—28no—
307C2×C3×Dic3—22no—
308C2×C3×Dic3—22no—
309C2×C3×Dic3—22no—
310C2×C3×Dic3—22no—
311C2×C3×Dic3—22no—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2412yes—
317C3×D12—44no—
318C3×C4×D3—28no—
319C3×Dic6—44no—
320#626—28no—
321#625—28no—
322#624—44no—
323D3×Dic3—44no—
324D3×Dic3—44no—
325#551—916no—
326C2×#126—91no—
327C2×#126—91no—
328C2×#124—31no—
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—
343C24×C3—31no—
344C23×D3—31no—
345C23×D3—31no—
346C23×D3—34no—
347C23×D3—34no—
348C23×D3—61no—
349C23×D3—64no—
350C23×D3—64no—
351C23×D3—64no—
352C23×D3—64no—
353C23×D3—122no—
354C23×D3—122no—
355C23×D3C22×D311yescharacteristic
356C23×D3C22×D311yescharacteristic
357C23×D3C22×D311yescharacteristic
358C2×C3×Q8—34no—
359C2×C3×Q8—122no—
360C2×C3×D4—34no—
361C2×C3×D4—122no—
362C22×C3×C4—21no—
363C22×C3×C4—21no—
364C22×C3×C4—21no—
365C22×C3×C4—31no—
366C22×C3×C4—31no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—34no—
371C22×C3×C4—64no—
372C22×C3×C4C22×D311yescharacteristic
373C22×C3×C4C22×D311yescharacteristic
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C22×D311yescharacteristic
376C22×C3×C4C22×D311yescharacteristic
377C22×C3×C4C22×D311yescharacteristic
378C2×#67—34no—
379C2×#67—34no—
380C2×#67—34no—
381C2×#67—64no—
382C2×#67—64no—
383C2×#67—64no—
384C22×Dic3—31no—
385C22×Dic3—31no—
386C22×Dic3—31no—
387C22×Dic3—31no—
388C22×Dic3—31no—
389C22×Dic3—31no—
390C22×Dic3—34no—
391C22×Dic3—34no—
392C22×Dic3—61no—
393C22×Dic3—61no—
394C22×Dic3—61no—
395C22×Dic3—122no—
396C22×Dic3—122no—
397C22×Dic3C22×D311yescharacteristic
398C22×Dic3C22×D311yescharacteristic
399C22×Dic3C22×D311yescharacteristic
400C22×Dic3C22×D311yescharacteristic
401C22×Dic3C22×D311yescharacteristic
402C2×D12—34no—
403C2×D12—42no—
404C2×D12—64no—
405C2×D12C22×D314yes—
406C2×C4×D3—24no—
407C2×C4×D3—34no—
408C2×C4×D3—34no—
409C2×C4×D3—34no—
410C2×C4×D3—34no—
411C2×C4×D3—34no—
412C2×C4×D3—34no—
413C2×C4×D3—64no—
414C2×C4×D3—64no—
415C2×C4×D3—64no—
416C2×C4×D3—68no—
417C2×C4×D3—122no—
418C2×C4×D3—122no—
419C2×C4×D3—122no—
420C2×C4×D3—122no—
421C2×C4×D3C22×D314yes—
422C2×Dic6—42no—
423C2×Dic6C22×D314yescomplemented
424C3×C4⋊C4—34no—
425C3×C4⋊C4—34no—
426C3×C22⋊C4—34no—
427C3×C22⋊C4—34no—
428C3×C22⋊C4—34no—
429C3×C22⋊C4—34no—
430C3×C22⋊C4—34no—
431C3×C22⋊C4—34no—
432C3×C42—24no—
433C3×C42—34no—
434C3×C42C22×D314yescomplemented
435C3×C42C22×D314yescomplemented
436#217—34no—
437#217—34no—
438#217—34no—
439#217—34no—
440#217—34no—
441(C2×D3)⋊C4—34no—
442(C2×D3)⋊C4—34no—
443(C2×D3)⋊C4—34no—
444(C2×D3)⋊C4—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—64no—
453(C2×D3)⋊C4—64no—
454(C2×D3)⋊C4C22×D314yes—
455(C2×D3)⋊C4C22×D314yes—
456(C2×D3)⋊C4C22×D314yes—
457(C2×D3)⋊C4C22×D314yes—
458(C2×D3)⋊C4C22×D314yescomplemented
459(C2×D3)⋊C4C22×D314yescomplemented
460C4⋊Dic3—34no—
461C4⋊Dic3—34no—
462C4⋊Dic3—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—64no—
473Dic3⋊C4—64no—
474Dic3⋊C4C22×D314yescomplemented
475Dic3⋊C4C22×D314yescomplemented
476C4×Dic3—34no—
477C4×Dic3—34no—
478C4×Dic3—64no—
479C4×Dic3C22×D314yescomplemented
480C22×C32C2×#4112yes—
481C22×C32C2×#4112yes—
482C22×C32H(5,𝔽2)12yes—
483C22×C32C2511yescharacteristic
484C2×C3⋊D3—28no—
485C2×C3⋊D3—22no—
486C2×C3⋊D3—22no—
487C2×C3⋊D3C2×#4114yes—
488C2×C3×D3—28no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3—22no—
492C2×C3×D3—22no—
493C2×C3×D3—22no—
494C2×C3×D3—22no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—44no—
498C2×C3×D3—44no—
499C2×C3×D3C2×#4114yes—
500D32—416no—
501C32×C4—22no—
502C32×C4—22no—
503C32×C4—22no—
504C3⋊Dic3—22no—
505C3⋊Dic3—22no—
506C3⋊Dic3—22no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C25—91no—
513C22×Q8—31no—
514C22×D4—31no—
515C22×D4—91no—
516C22×D4—91no—
517C23×C4—31no—
518C23×C4—91no—
519C23×C4—91no—
520C23×C4—91no—
521C23×C4—91no—
522#126—98no—
523#126—98no—
524#124—38no—
525#123—98no—
526#123—98no—
527#123—98no—
528C22⋊Q8—98no—
529C22⋊Q8—98no—
530#120—98no—
531C4×D4—98no—
532C4×D4—98no—
533#117—38no—
534#117—98no—
535C2×C4⋊C4—31no—
536C2×C4⋊C4—31no—
537C2×C4⋊C4—91no—
538C2×C4⋊C4—91no—
539C2×C4⋊C4—91no—
540C2×C4⋊C4—91no—
541C2×C4⋊C4—91no—
542C2×C4⋊C4—91no—
543C2×C22⋊C4—31no—
544C2×C22⋊C4—31no—
545C2×C22⋊C4—31no—
546C2×C22⋊C4—31no—
547C2×C22⋊C4—31no—
548C2×C22⋊C4—31no—
549C2×C22⋊C4—98no—
550C2×C22⋊C4—98no—
551C2×C22⋊C4—91no—
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×C42—31no—
560C2×C42—91no—
561C2×C42D3211yescharacteristic, complemented
562C23×C3—21no—
563C23×C3—34no—
564C23×C3—32no—
565C23×C3—32no—
566C23×C3—32no—
567C23×C3—62no—
568C23×C3—62no—
569C23×C3—62no—
570C23×C3—62no—
571C23×C3—62no—
572C23×C3—62no—
573C23×C3—62no—
574C23×C3—62no—
575C23×C3C23×D311yescharacteristic
576C23×C3C23×D311yescharacteristic
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—22no—
585C22×D3—34no—
586C22×D3—34no—
587C22×D3—32no—
588C22×D3—32no—
589C22×D3—64no—
590C22×D3—62no—
591C22×D3—68no—
592C22×D3—68no—
593C22×D3—68no—
594C22×D3—62no—
595C22×D3—62no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3—68no—
599C22×D3—122no—
600C22×D3—122no—
601C22×D3—124no—
602C22×D3—124no—
603C22×D3—1216no—
604C22×D3—1216no—
605C22×D3#23514yes—
606C22×D3C23×D312yes—
607C22×D3C23×D312yes—
608C22×D3C23×D312yes—
609C3×Q8—124no—
610C3×D4—124no—
611C2×C3×C4—24no—
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—22no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—32no—
622C2×C3×C4—32no—
623C2×C3×C4—32no—
624C2×C3×C4—32no—
625C2×C3×C4—32no—
626C2×C3×C4—42no—
627C2×C3×C4—42no—
628C2×C3×C4—68no—
629C2×C3×C4—62no—
630C2×C3×C4—62no—
631C2×C3×C4—62no—
632C2×C3×C4—62no—
633C2×C3×C4—62no—
634C2×C3×C4C23×D312yes—
635C2×C3×C4C23×D312yes—
636C2×C3×C4C23×D312yes—
637C2×C3×C4C23×D312yes—
638C2×C3×C4C23×D312yes—
639C2×C3×C4C23×D312yes—
640#67—68no—
641#67—68no—
642#67—68no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—22no—
646C2×Dic3—22no—
647C2×Dic3—22no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—32no—
654C2×Dic3—62no—
655C2×Dic3—62no—
656C2×Dic3—62no—
657C2×Dic3—64no—
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×Dic3—124no—
668C2×Dic3C23×D312yes—
669C2×Dic3C23×D312yes—
670C2×Dic3C23×D312yes—
671C2×Dic3C23×D312yes—
672C2×Dic3C23×D312yes—
673D12—44no—
674D12—68no—
675C4×D3—28no—
676C4×D3—68no—
677C4×D3—68no—
678C4×D3—616no—
679C4×D3—124no—
680C4×D3—124no—
681C4×D3—124no—
682C4×D3—124no—
683Dic6—44no—
684C2×C32#55114yescomplemented
685C2×C32C22×#4111yescharacteristic
686C2×C32C22×#4111yescharacteristic
687C2×C32C2×H(5,𝔽2)11yescharacteristic
688C3⋊D3—24no—
689C3×D3—24no—
690C3×D3—42no—
691C3×D3—42no—
692C24—31no—
693C24—31no—
694C24—31no—
695C24—94no—
696C24—91no—
697C24—184no—
698C24—184no—
699C24—362no—
700C2×Q8—34no—
701C2×Q8—122no—
702C2×D4—34no—
703C2×D4—94no—
704C2×D4—94no—
705C2×D4—122no—
706C2×D4—184no—
707C2×D4—184no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—34no—
714C22×C4—64no—
715C22×C4—94no—
716C22×C4—94no—
717C22×C4—94no—
718C22×C4—91no—
719C22×C4—91no—
720C22×C4—91no—
721C22×C4—94no—
722C22×C4—184no—
723C22×C4—362no—
724C22×C4—362no—
725C22×C4—362no—
726C22×C4C2×D3211yescharacteristic
727C22×C4C2×D3211yescharacteristic
728C22×C4C2×D3211yescharacteristic
729C4⋊C4—34no—
730C4⋊C4—34no—
731C4⋊C4—94no—
732C4⋊C4—94no—
733C4⋊C4—94no—
734C4⋊C4—94no—
735C4⋊C4—94no—
736C4⋊C4—94no—
737C22⋊C4—34no—
738C22⋊C4—34no—
739C22⋊C4—34no—
740C22⋊C4—34no—
741C22⋊C4—34no—
742C22⋊C4—34no—
743C22⋊C4—94no—
744C22⋊C4—94no—
745C22⋊C4—94no—
746C22⋊C4—94no—
747C22⋊C4—94no—
748C22⋊C4—94no—
749C22⋊C4—94no—
750C22⋊C4—94no—
751C42—34no—
752C42—94no—
753C42C2×D3214yescomplemented
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—21no—
758C22×C3—34no—
759C22×C3—68no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3—62no—
765C22×C3—62no—
766C22×C3—62no—
767C22×C3—62no—
768C22×C3—124no—
769C22×C3—124no—
770C22×C3C2×#23512yes—
771C22×C3#100412yes—
772C22×C3D3×#4112yes—
773C22×C3D3×#4112yes—
774C22×C3D3×#4112yes—
775C22×C3#100912yes—
776C22×C3C24×D311yescharacteristic
777C22×C3C24×D311yescharacteristic
778C2×D3—22no—
779C2×D3—22no—
780C2×D3—28no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—34no—
788C2×D3—34no—
789C2×D3—44no—
790C2×D3—44no—
791C2×D3—64no—
792C2×D3—68no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—68no—
798C2×D3—122no—
799C2×D3—122no—
800C2×D3—128no—
801C2×D3—1216no—
802C2×D3—1216no—
803C2×D3C2×#23514yes—
804C3×C4—24no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—22no—
811C3×C4—42no—
812C3×C4—42no—
813C3×C4—62no—
814C3×C4—62no—
815C3×C4—62no—
816C3×C4—62no—
817C3×C4—62no—
818Dic3—22no—
819Dic3—22no—
820Dic3—22no—
821Dic3—22no—
822Dic3—22no—
823Dic3—64no—
824Dic3—62no—
825Dic3—62no—
826Dic3—62no—
827Dic3—62no—
828Dic3—62no—
829Dic3—62no—
830Dic3—122no—
831Dic3—122no—
832C32C2×#55111yescharacteristic, complemented, Sylow
833C23—34no—
834C23—32no—
835C23—32no—
836C23—32no—
837C23—62no—
838C23—62no—
839C23—62no—
840C23—62no—
841C23—62no—
842C23—62no—
843C23—62no—
844C23—62no—
845C23—94no—
846C23—92no—
847C23—188no—
848C23—188no—
849C23—182no—
850C23—182no—
851C23—364no—
852C23—3616no—
853C23C22×D3211yescharacteristic
854Q8—124no—
855D4—124no—
856D4—188no—
857D4—188no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—32no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—68no—
867C2×C4—62no—
868C2×C4—62no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—62no—
872C2×C4—92no—
873C2×C4—92no—
874C2×C4—92no—
875C2×C4—188no—
876C2×C4—182no—
877C2×C4—182no—
878C2×C4—182no—
879C2×C4—364no—
880C2×C4—364no—
881C2×C4—364no—
882C2×C4C22×D3212yes—
883C2×C4C22×D3212yes—
884C2×C4C22×D3212yes—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—21no—
888C2×C3—24no—
889C2×C3—64no—
890C2×C3—122no—
891C2×C3—122no—
892C2×C3#552714yescomplemented
893C2×C3#567914yescomplemented
894C2×C3C22×#23511yescharacteristic
895C2×C3C2×#100411yescharacteristic
896C2×C3C2×D3×#4111yescharacteristic
897C2×C3C2×D3×#4111yescharacteristic
898C2×C3C2×D3×#4111yescharacteristic
899C2×C3C2×#100911yescharacteristic
900D3—24no—
901D3—42no—
902D3—42no—
903D3—64no—
904D3—64no—
905D3—124no—
906C22—34no—
907C22—62no—
908C22—62no—
909C22—68no—
910C22—62no—
911C22—62no—
912C22—62no—
913C22—62no—
914C22—62no—
915C22—62no—
916C22—94no—
917C22—124no—
918C22—124no—
919C22—182no—
920C22—182no—
921C22—188no—
922C22—3616no—
923C22D3×#23512yes—
924C22#6430612yes—
925C22#6430712yes—
926C22C23×D3211yescharacteristic
927C4—22no—
928C4—22no—
929C4—22no—
930C4—62no—
931C4—62no—
932C4—62no—
933C4—62no—
934C4—62no—
935C4—182no—
936C4—182no—
937C4—182no—
938C3—21no—
939C3C2×#552711yescharacteristic, complemented
940C3C2×#567911yescharacteristic, complemented
941C2—64no—
942C2—122no—
943C2—122no—
944C2—184no—
945C2#1059401614yesdirect product factor
946C2C2×D3×#23511yescharacteristic
947C2C2×#6430611yescharacteristic
948C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC2×#63922C2
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×#64081C2semidirect
2. C2×C3×#875C2semidirect
3. C2×C3×#872C2semidirect
5. C2×#63921C2semidirect
6. C2×D3×(C2×D3)⋊C4C2semidirect
7. C2×#63905C2semidirect
8. C2×#63902C2semidirect
9. C2×#63888C2semidirect
10. C2×#63887C2semidirect
11. C2×#63884C2semidirect
12. C2×#63880C2semidirect
13. C2×#63862C2semidirect
14. C2×#63859C2semidirect
15. C2×#63853C2semidirect
16. #10594016C2direct (N × H)
23. C22×C3×Dic6C22semidirect
28. C22×D3×Dic3C22semidirect
29. C2×C32×C42C22semidirect
32. C2×#3750C22semidirect
33. C2×#3750C22semidirect
34. C2×C4×C3⋊Dic3C22semidirect
35. #64081C22semidirect
40. C2×C3×(C2×D3)⋊C4C22semidirect
41. C2×C3×(C2×D3)⋊C4C22semidirect
42. C2×C3×Dic3⋊C4C22semidirect
43. C2×C3×Dic3⋊C4C22semidirect
44. C2×C3×C4×Dic3C22semidirect
45. C3×#875C22semidirect
46. C3×#872C22semidirect
47. C2×#3724C22semidirect
48. C2×Dic3⋊Dic3C22semidirect
49. C2×Dic3⋊Dic3C22semidirect
50. C2×Dic3⋊Dic3C22semidirect
56. C2×(C2×D3)⋊Dic3C22semidirect
58. #63921C22semidirect
59. D3×(C2×D3)⋊C4C22semidirect
60. #63905C22semidirect
61. #63902C22semidirect
62. #63888C22semidirect
63. #63887C22semidirect
64. #63884C22semidirect
65. #63880C22semidirect
66. #63862C22semidirect
67. #63859C22semidirect
68. #63853C22semidirect
96. C2×#875D3semidirect
101. C2×#872D3semidirect
128. C2×C3×Dic6C23semidirect
138. C2×D3×Dic3C23semidirect
139. C32×C42C23semidirect
142. #3750C23semidirect
143. #3750C23semidirect
144. C4×C3⋊Dic3C23semidirect
149. C3×(C2×D3)⋊C4C23semidirect
150. C3×(C2×D3)⋊C4C23semidirect
151. C3×Dic3⋊C4C23semidirect
152. C3×Dic3⋊C4C23semidirect
153. C3×C4×Dic3C23semidirect
154. #3724C23semidirect
155. Dic3⋊Dic3C23semidirect
156. Dic3⋊Dic3C23semidirect
157. Dic3⋊Dic3C23semidirect
163. (C2×D3)⋊Dic3C23semidirect
185. C22×Dic6C2×D3semidirect
198. C2×C3×C42C2×D3semidirect
199. C2×C3×C42C2×D3semidirect
228. C2×(C2×D3)⋊C4C2×D3semidirect
229. C2×(C2×D3)⋊C4C2×D3semidirect
244. C2×Dic3⋊C4C2×D3semidirect
245. C2×Dic3⋊C4C2×D3semidirect
249. C2×C4×Dic3C2×D3semidirect
267. #875C2×D3semidirect
272. #872C2×D3semidirect
423. C2×Dic6C22×D3semidirect
434. C3×C42C22×D3semidirect
435. C3×C42C22×D3semidirect
458. (C2×D3)⋊C4C22×D3semidirect
459. (C2×D3)⋊C4C22×D3semidirect
474. Dic3⋊C4C22×D3semidirect
475. Dic3⋊C4C22×D3semidirect
479. C4×Dic3C22×D3semidirect
561. C2×C42D32semidirect
684. C2×C32#551semidirect
753. C42C2×D32semidirect
832. C32C2×#551semidirect
892. C2×C3#5527semidirect
893. C2×C3#5679semidirect
939. C3C2×#5527semidirect
940. C3C2×#5679semidirect
945. C2#10594016direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640812
C2×C3×#8752
C2×C3×#8722
C2×#639222
C2×#639212
C2×D3×(C2×D3)⋊C42
C2×#639052
C2×#639022
C2×#638882
C2×#638872
C2×#638842
C2×#638802
C2×#638622
C2×#638592
C2×#638532
#105940162
C2×#56793
C2×#55273