Finite Group Databasebeta

← C2×#36475 #7630159

Subgroups — C2×#36475 #7630159

Order 512.

5314 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2864C213yesmaximal
2#36475C2132yesmaximal, direct product factor
3C2×#2570C213yesmaximal
4C2×#2570C213yesmaximal
5C2×#2509C213yesmaximal
6C2×#2508C213yesmaximal
7C2×#2507C213yesmaximal
8C2×#2506C213yesmaximal
9C2×#2351C211yesmaximal, characteristic
10C2×#2351C211yesmaximal, characteristic
11C2×#2351C211yesmaximal, characteristic
12C2×#2351C211yesmaximal, characteristic
13C2×Q8×C4⋊C4C211yesmaximal, characteristic
14C2×Q8×C4⋊C4C211yesmaximal, characteristic
15C2×C4×#125C213yesmaximal
16C2×C42×Q8C211yesmaximal, characteristic
17C22×#125C2213yes—
18C22×C4×Q8C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25#2864C22148yes—
26#2570C22148yes—
27#2570C22148yes—
28#2509C22148yes—
29#2508C22148yes—
30#2507C22148yes—
31#2506C22148yes—
32C2×#400C2216yes—
33C2×#400C2216yes—
34C2×#398C2216yes—
35C2×#398C2216yes—
36#2351C22116yes—
37#2351C22116yes—
38#2351C22116yes—
39#2351C22116yes—
40Q8×C4⋊C4C22116yes—
41Q8×C4⋊C4C22116yes—
42C4×#125C22148yes—
43C2×#389C2213yes—
44C2×#389C2213yes—
45C2×#389C2213yes—
46C2×#389C2213yes—
47C2×#389C2213yes—
48C2×#389C2213yes—
49C2×#389C2213yes—
50C2×#389C2213yes—
51C2×#389C2213yes—
52C2×#389C2213yes—
53C2×#389C2213yes—
54C2×#389C2213yes—
55C2×#389C2213yes—
56C2×#389C2213yes—
57C2×#387C2213yes—
58C2×#387C2216yes—
59C2×#387C2216yes—
60C2×#387C2216yes—
61C2×#387C2213yes—
62C2×#387C2213yes—
63C2×#387C2211yescharacteristic
64C2×#384C2213yes—
65C2×#384C2213yes—
66C2×#382C2213yes—
67C2×#382C2213yes—
68C2×#382C2213yes—
69C2×#382C2213yes—
70C2×#382C2213yes—
71C42×Q8C22116yes—
72C2×C4×C4⋊C4C2213yes—
73C2×C4×C4⋊C4C2213yes—
74C2×C4×C4⋊C4C2213yes—
75C2×C4×C4⋊C4C2213yes—
76C2×C4×C4⋊C4C2213yes—
77C2×C4×C4⋊C4C2213yes—
78C2×C4×C4⋊C4C2213yes—
79C2×C4×C4⋊C4C2213yes—
80C2×C4×C4⋊C4C2213yes—
81C2×C43C2213yes—
82C23×Q8C2311yescharacteristic
83C2×#125—224no—
84C2×#125C23124yes—
85C2×C4×Q8—28no—
86C2×C4×Q8—28no—
87C2×C4×Q8—28no—
88C2×C4×Q8—28no—
89C2×C4×Q8—28no—
90C2×C4×Q8—28no—
91C2×C4×Q8Q8116yes—
92C2×C4×Q8C2318yes—
93C2×C4×Q8C2318yes—
94C2×C4×Q8C2318yes—
95C2×C4×Q8C2318yes—
96C2×C4×Q8C2318yes—
97C2×C4×Q8C2318yes—
98C2×C4×Q8C2318yes—
99C22×C4⋊C4C2313yes—
100C22×C4⋊C4C2313yes—
101C22×C4⋊C4C2313yes—
102C22×C4⋊C4C2313yes—
103C22×C4⋊C4C2313yes—
104C22×C4⋊C4C2313yes—
105C22×C4⋊C4C2313yes—
106C22×C4⋊C4C2313yes—
107C22×C4⋊C4C2313yes—
108C22×C4⋊C4C2313yes—
109C22×C4⋊C4C2313yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2313yes—
112C22×C4⋊C4C2313yes—
113C22×C4⋊C4C2313yes—
114C22×C4⋊C4C2313yes—
115C22×C4⋊C4C2316yes—
116C22×C4⋊C4C2316yes—
117C22×C4⋊C4C2313yes—
118C22×C4⋊C4C2313yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C42C2313yes—
121C22×C42C2313yes—
122C22×C42C2313yes—
123C22×C42C2313yes—
124C22×C42C2313yes—
125C22×C42C2313yes—
126C22×C42C2313yes—
127C22×C42C2311yescharacteristic
128C22×C42C2313yes—
129C22×C42C2313yes—
130C22×C42C2313yes—
131#400C23148yes—
132#400C23148yes—
133#398C23148yes—
134#398C23148yes—
135#389C23124yes—
136#389C23124yes—
137#389C23124yes—
138#389C23124yes—
139#389C23124yes—
140#389C23124yes—
141#389C23124yes—
142#389C23124yes—
143#389C23124yes—
144#389C23124yes—
145#389C23124yes—
146#389C23124yes—
147#389C23124yes—
148#389C23124yes—
149#387C2318yes—
150#387C23124yes—
151#387C23124yes—
152#387C23124yes—
153#387C23148yes—
154#387C23148yes—
155#387C23148yes—
156#384C23124yes—
157#384C23124yes—
158#382C23124yes—
159#382C23124yes—
160#382C23124yes—
161#382C23124yes—
162#382C23124yes—
163C4×C4⋊C4C23124yes—
164C4×C4⋊C4C23124yes—
165C4×C4⋊C4C23124yes—
166C4×C4⋊C4C23124yes—
167C4×C4⋊C4C23124yes—
168C4×C4⋊C4C23124yes—
169C4×C4⋊C4C23124yes—
170C4×C4⋊C4C23124yes—
171C4×C4⋊C4C23124yes—
172C2×#95C2316yes—
173C2×#95C2313yes—
174C2×#95C2316yes—
175C2×#95C2316yes—
176C2×#95C2316yes—
177C2×#95C2313yes—
178C2×#95C2313yes—
179C2×#95C2313yes—
180C2×#95C2316yes—
181C2×#95C2311yescharacteristic
182C2×#95C2311yescharacteristic
183C2×#95C2311yescharacteristic
184C2×#95C2311yescharacteristic
185C2×#95C2313yes—
186C2×#95C2313yes—
187C2×#95C2313yes—
188C2×#95C2313yes—
189C43C23124yes—
190C22×Q8C2×Q818yes—
191C22×Q8#4118yes—
192C22×Q8#4118yes—
193C22×Q8C2414yes—
194C23×C4C2413yes—
195C23×C4C2413yes—
196C23×C4C2413yes—
197C23×C4C2413yes—
198C23×C4C2411yescharacteristic
199C23×C4C2413yes—
200C23×C4C2413yes—
201C23×C4C2411yescharacteristic
202C23×C4C2413yes—
203C23×C4C2411yescharacteristic
204C23×C4C2411yescharacteristic
205C23×C4C2411yescharacteristic
206C23×C4C2411yescharacteristic
207C23×C4C2411yescharacteristic
208C23×C4C2413yes—
209#125—296no—
210C4×Q8—232no—
211C4×Q8—232no—
212C4×Q8—232no—
213C4×Q8—232no—
214C4×Q8—232no—
215C4×Q8—232no—
216C4×Q8C2×Q8164yes—
217C2×C4⋊C4—212no—
218C2×C4⋊C4—212no—
219C2×C4⋊C4—212no—
220C2×C4⋊C4—212no—
221C2×C4⋊C4—212no—
222C2×C4⋊C4—212no—
223C2×C4⋊C4—212no—
224C2×C4⋊C4—212no—
225C2×C4⋊C4—212no—
226C2×C4⋊C4—212no—
227C2×C4⋊C4—212no—
228C2×C4⋊C4—24no—
229C2×C4⋊C4—212no—
230C2×C4⋊C4—46no—
231C2×C4⋊C4—46no—
232C2×C4⋊C4—46no—
233C2×C4⋊C4—46no—
234C2×C4⋊C4—412no—
235C2×C4⋊C4—412no—
236C2×C4⋊C4C2×Q8124yes—
237C2×C4⋊C4#4118yes—
238C2×C4⋊C4C24112yes—
239C2×C4⋊C4C24112yes—
240C2×C4⋊C4C24112yes—
241C2×C4⋊C4C24112yes—
242C2×C4⋊C4C24112yes—
243C2×C4⋊C4C24112yes—
244C2×C4⋊C4C24112yes—
245C2×C4⋊C4C24112yes—
246C2×C4⋊C4C24112yes—
247C2×C4⋊C4C24112yes—
248C2×C4⋊C4C24112yes—
249C2×C4⋊C4C2414yes—
250C2×C4⋊C4C24112yes—
251C2×C4⋊C4C24112yes—
252C2×C4⋊C4C24112yes—
253C2×C4⋊C4C24112yes—
254C2×C4⋊C4C24112yes—
255C2×C4⋊C4C24124yes—
256C2×C4⋊C4C24124yes—
257C2×C4⋊C4C24112yes—
258C2×C4⋊C4C2414yes—
259C2×C42—212no—
260C2×C42—212no—
261C2×C42—212no—
262C2×C42—212no—
263C2×C42—212no—
264C2×C42—212no—
265C2×C42—212no—
266C2×C42—24no—
267C2×C42—46no—
268C2×C42—46no—
269C2×C42C2×Q8124yes—
270C2×C42C24112yes—
271C2×C42C24112yes—
272C2×C42C24112yes—
273C2×C42C24112yes—
274C2×C42C24112yes—
275C2×C42C24112yes—
276C2×C42C24112yes—
277C2×C42C2414yes—
278C2×C42C24112yes—
279C2×C42C24112yes—
280C2×C42C24112yes—
281#95C2414yes—
282#95C2414yes—
283#95C2414yes—
284#95C2414yes—
285#95C24124yes—
286#95C24112yes—
287#95C24112yes—
288#95C24112yes—
289#95C24112yes—
290#95C24112yes—
291#95C24112yes—
292#95C24112yes—
293#95C24112yes—
294#95C24124yes—
295#95C24124yes—
296#95C24124yes—
297#95C24124yes—
298C24C2511yescharacteristic
299C2×Q8#125164yescomplemented
300C2×Q8C22×Q8116yes—
301C2×Q8C2×#41116yes—
302C2×Q8C2×#41116yes—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—26no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—26no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—26no—
318C22×C4—26no—
319C22×C4—26no—
320C22×C4—26no—
321C22×C4—26no—
322C22×C4—26no—
323C22×C4—26no—
324C22×C4—26no—
325C22×C4—26no—
326C22×C4—26no—
327C22×C4—26no—
328C22×C4—22no—
329C22×C4—26no—
330C22×C4—26no—
331C22×C4—26no—
332C22×C4—26no—
333C22×C4—26no—
334C22×C4—22no—
335C22×C4—26no—
336C22×C4—22no—
337C22×C4—26no—
338C22×C4—22no—
339C22×C4C22×Q814yes—
340C22×C4C22×Q8112yes—
341C22×C4C22×Q8112yes—
342C22×C4C2×#4114yes—
343C22×C4C2×#4114yes—
344C22×C4C2×#4114yes—
345C22×C4C2×#41112yes—
346C22×C4C2×#41112yes—
347C22×C42−1+414yes—
348C22×C4C2512yes—
349C22×C4C2516yes—
350C22×C4C2516yes—
351C22×C4C2512yes—
352C22×C4C2516yes—
353C22×C4C2516yes—
354C22×C4C2516yes—
355C22×C4C2516yes—
356C22×C4C2512yes—
357C22×C4C2516yes—
358C22×C4C2512yes—
359C22×C4C2512yes—
360C22×C4C2512yes—
361C22×C4C2512yes—
362C22×C4C2516yes—
363C4⋊C4—224no—
364C4⋊C4—224no—
365C4⋊C4—224no—
366C4⋊C4—224no—
367C4⋊C4—224no—
368C4⋊C4—224no—
369C4⋊C4—224no—
370C4⋊C4—224no—
371C4⋊C4—224no—
372C4⋊C4—224no—
373C4⋊C4—224no—
374C4⋊C4—28no—
375C4⋊C4—224no—
376C4⋊C4—412no—
377C4⋊C4—412no—
378C4⋊C4—412no—
379C4⋊C4—412no—
380C4⋊C4—424no—
381C4⋊C4—424no—
382C4⋊C4C22×Q8148yes—
383C4⋊C4C2×#41116yes—
384C42—224no—
385C42—224no—
386C42—224no—
387C42—224no—
388C42—224no—
389C42—224no—
390C42—224no—
391C42—28no—
392C42—412no—
393C42—412no—
394C42C22×Q8148yes—
395C23C23×Q812yes—
396C23C22×#4112yes—
397C23C22×#4112yes—
398C23C22×#4112yes—
399C23C2×2−1+412yes—
400C23#58512yes—
401C23#58512yes—
402C23C2611yescharacteristic
403Q8C2×#125164yescomplemented
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—26no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—26no—
415C2×C4—22no—
416C2×C4—224no—
417C2×C4—28no—
418C2×C4—28no—
419C2×C4—28no—
420C2×C4—28no—
421C2×C4—28no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—26no—
425C2×C4—26no—
426C2×C4—26no—
427C2×C4—26no—
428C2×C4—26no—
429C2×C4—26no—
430C2×C4—26no—
431C2×C4—26no—
432C2×C4—26no—
433C2×C4—22no—
434C2×C4—26no—
435C2×C4—26no—
436C2×C4—26no—
437C2×C4—26no—
438C2×C4—26no—
439C2×C4—22no—
440C2×C4—26no—
441C2×C4—22no—
442C2×C4—26no—
443C2×C4—22no—
444C2×C4—26no—
445C2×C4—26no—
446C2×C4—412no—
447C2×C4—412no—
448C2×C4—412no—
449C2×C4—44no—
450C2×C4—412no—
451C2×C4—44no—
452C2×C4—412no—
453C2×C4—412no—
454C2×C4C2×#125148yes—
455C2×C4C23×Q814yes—
456C2×C4C23×Q8112yes—
457C2×C4C23×Q8112yes—
458C2×C4C22×#4114yes—
459C2×C4C22×#4114yes—
460C2×C4C22×#4114yes—
461C2×C4C22×#41112yes—
462C2×C4C22×#41112yes—
463C2×C4C2×2−1+414yes—
464C22C22×#12514yes—
465C22Q8×#4114yes—
466C22#348014yes—
467C22#348214yes—
468C22#350214yes—
469C22#351614yes—
470C22#352414yes—
471C22C24×Q811yescharacteristic
472C22C23×#4111yescharacteristic
473C22C23×#4111yescharacteristic
474C22C23×#4111yescharacteristic
475C22C22×2−1+411yescharacteristic
476C22C2×#58511yescharacteristic
477C22C2×#58511yescharacteristic
478C4—24no—
479C4—24no—
480C4—24no—
481C4—212no—
482C4—24no—
483C4—24no—
484C4—42no—
485C4—46no—
486C4—42no—
487C4—46no—
488C4—46no—
489C4—46no—
490C4—46no—
491C4—46no—
492C4C22×#125124yes—
493C2#3647518yesdirect product factor
494C2C23×#12511yescharacteristic
495C2C2×#348011yescharacteristic
496C2C2×Q8×#4111yescharacteristic
497C2C2×#348211yescharacteristic
498C2C2×#350211yescharacteristic
499C2C2×#351611yescharacteristic
500C2C2×#352411yescharacteristic
subgroupG/H
center, socle, prime radicalC24C25
commutator, Frattini, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36475C2direct (N × H)
299. C2×Q8#125semidirect
403. Q8C2×#125semidirect
493. C2#36475direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28642
#364752
C2×#25702
C2×#25092
C2×#25082
C2×#25072
C2×#25062
C2×#23512
C2×Q8×C4⋊C42
C2×C4×#1252
C2×C42×Q82