Finite Group Databasebeta

← C2×#14545908 #17982854

Subgroups — C2×#14545908 #17982854

Order 4352.

830 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763922C212yesmaximal
2#14545908C218yesmaximal, direct product factor
3C2×#11763899C212yesmaximal, complemented
4C2×#11763898C212yesmaximal, complemented
5C22×C8×#595C211yesmaximal, characteristic
6#11763922—24no—
7#11763922C2218yes—
8C2×C4⋊#3633C2214yes—
9C2×C22⋊#3633—22no—
10C2×C4×#3633—22no—
11#11763899C2218yescomplemented
12#11763898C2218yescomplemented
13C22×#63242C411yescharacteristic
14C22×C4×#595C2211yescharacteristic
15C2×C8×#595C411yescharacteristic
16C2×C8×#595C411yescharacteristic
17C2×C8×#595C414yes—
18C2×C8×#595C2211yescharacteristic
19C2×C8×#595C2211yescharacteristic
20C2×C8×#595C2214yes—
21C22×C8×D17C411yescharacteristic
22C23×#595D411yescharacteristic
23C23×#595Q811yescharacteristic
24C22×#3633—24no—
25C22×C4×D17C2×C411yescharacteristic
26C22×#3624—21no—
27C2×C4×#595C2×C412yes—
28C2×C4×#595C2×C411yescharacteristic
29C2×C4×#595D411yescharacteristic
30C2×C4×#595D412yes—
31C2×C4×#595Q811yescharacteristic
32C2×C4×#595Q812yes—
33C2×C4×#595C2311yescharacteristic
34C2×C4×#595C2312yes—
35C2×#63242—22no—
36C2×#63242—21no—
37C2×#63242C2×C411yescharacteristic
38C2×#63242C2×C411yescharacteristic
39C2×#63242C2×C414yes—
40C22⋊#3633—28no—
41C4⋊#3633—24no—
42C4⋊#3633C2318yes—
43C4×#3633—28no—
44C22×C8×C17C811yescharacteristic, complemented
45C22×#3622C811yescharacteristic, complemented
46C2×C8×D17C811yescharacteristic, complemented
47C2×C8×D17C811yescharacteristic, complemented
48C2×C8×D17C814yescomplemented
49C2×C8×D17C2×C411yescharacteristic
50C2×C8×D17C2×C411yescharacteristic
51C2×C8×D17C2×C414yes—
52C8×#595C2×C412yes—
53C8×#595C2×C412yes—
54C8×#595C2×C414yes—
55C8×#595C2×C414yes—
56C8×#595C2312yes—
57C8×#595C2312yes—
58C23×D17C4⋊C411yescharacteristic
59C22×#595—24no—
60C22×#595—24no—
61C22×#595C4⋊C412yes—
62C22×#595C4⋊C411yescharacteristic
63C22×#595C4⋊C412yes—
64C22×#595C4⋊C411yescharacteristic
65C22×#595C2×D412yes—
66C22×#595C2×D411yescharacteristic
67C22×#595C2×Q811yescharacteristic
68C22×#595C2×Q812yes—
69C2×#3633—28no—
70C2×#3633—48no—
71C22×C4×C17C2×C811yescharacteristic
72C22×Dic17M1611yescharacteristic
73C2×C4×D17C4⋊C412yes—
74C2×C4×D17C4⋊C411yescharacteristic
75C2×C4×D17C2×C812yes—
76C2×C4×D17C2×C811yescharacteristic
77C2×C4×D17M1612yes—
78C2×C4×D17M1611yescharacteristic
79C2×C4×D17C22×C411yescharacteristic
80C2×C4×D17C22×C412yes—
81C2×#3624—24no—
82C2×#3624—21no—
83C2×#3624—21no—
84C4×#595C4⋊C412yes—
85C4×#595C4⋊C412yes—
86C4×#595C4⋊C412yes—
87C4×#595C22×C411yescharacteristic
88C4×#595C22×C412yes—
89C4×#595C2×D412yes—
90C4×#595C2×D411yescharacteristic
91C4×#595C2×Q812yes—
92C4×#595C2×Q811yescharacteristic
93C4×#595C2411yescharacteristic
94#63242—24no—
95#63242—21no—
96#63242—21no—
97#63242C22×C412yes—
98#63242C22×C412yes—
99C2×C8×C17C2×C811yescharacteristic
100C2×C8×C17C2×C811yescharacteristic
101C2×C8×C17C2×C814yescomplemented
102C2×#3622C2×C811yescharacteristic
103C2×#3622C2×C811yescharacteristic
104C2×#3622C2×C814yescomplemented
105C8×D17C2×C812yes—
106C8×D17C2×C812yes—
107C8×D17C2×C814yescomplemented
108C8×D17C2×C814yescomplemented
109C8×D17C22×C412yes—
110C8×D17C22×C412yes—
111C2×#1564—171nomaximal, Sylow
112C23×C17C4⋊C811yescharacteristic
113C22×D17—22no—
114C22×D17—22no—
115C22×D17C4⋊C811yescharacteristic
116C22×D17C4⋊C812yes—
117C22×D17C2×C4⋊C412yes—
118C22×D17C2×C4⋊C411yescharacteristic
119C2×#595—22no—
120C2×#595—22no—
121C2×#595—24no—
122C2×#595—24no—
123C2×#595—24no—
124C2×#595—24no—
125C2×#595#10814yes—
126C2×#595C2×C4⋊C411yescharacteristic
127C2×#595C2×C4⋊C412yes—
128C2×#595C2×C4⋊C411yescharacteristic
129C2×#595C2×C4⋊C412yes—
130C2×#595#13514yes—
131C2×#595C22×D411yescharacteristic
132C2×#595C22×Q811yescharacteristic
133#3633—48no—
134C2×C4×C17C4⋊C812yes—
135C2×C4×C17C4⋊C811yescharacteristic
136C2×C4×C17C22×C811yescharacteristic
137C2×C4×C17C22×C812yes—
138C2×Dic17C4⋊C812yes—
139C2×Dic17C4⋊C811yescharacteristic
140C2×Dic17C2×M1612yes—
141C2×Dic17C2×M1611yescharacteristic
142C4×D17C4⋊C812yes—
143C4×D17C4⋊C812yes—
144C4×D17C4⋊C812yes—
145C4×D17C2×C4⋊C412yes—
146C4×D17C2×C4⋊C411yescharacteristic
147C4×D17C22×C811yescharacteristic
148C4×D17C22×C812yes—
149C4×D17C2×M1612yes—
150C4×D17C2×M1611yescharacteristic
151C4×D17C23×C411yescharacteristic
152#3624—22no—
153#3624—22no—
154C8×C17C22×C812yes—
155C8×C17C22×C812yes—
156#3622C22×C812yes—
157#3622C22×C812yes—
158C2×#431—172no—
159C22×C4×C8—171no—
160#1564—178no—
161C2×#335—172no—
162C2×#334—172no—
163C22×C17—22no—
164C22×C17C2×C4⋊C812yes—
165C22×C17C2×C4⋊C811yescharacteristic
166C2×D17—22no—
167C2×D17—24no—
168C2×D17—22no—
169C2×D17—22no—
170C2×D17C2×C4⋊C812yes—
171C2×D17C2×C4⋊C811yescharacteristic
172C2×D17#42712yes—
173C2×D17C2×#10812yes—
174C2×D17C22×C4⋊C411yescharacteristic
175#595—22no—
176#595—21no—
177#595—21no—
178#595#42712yes—
179#595C2×#10814yes—
180#595C2×#13512yes—
181C4×C17C2×C4⋊C811yescharacteristic
182C4×C17C2×C4⋊C812yes—
183C4×C17C23×C811yescharacteristic
184Dic17C2×C4⋊C811yescharacteristic
185Dic17C2×C4⋊C812yes—
186Dic17C22×M1611yescharacteristic
187C23×C8—171no—
188C23×C8—171no—
189C22×C42—171no—
190#431—178no—
191#431—344no—
192C2×C4⋊C8—174no—
193C2×C22⋊C8—342no—
194C2×C4×C8—171no—
195C2×C4×C8—171no—
196C2×C4×C8—174no—
197C2×C4×C8—171no—
198C2×C4×C8—171no—
199C2×C4×C8—174no—
200C2×C4×C8—342no—
201#335—178no—
202#334—178no—
203C2×C17—22no—
204C2×C17#156412yescomplemented
205C2×C17C22×C4⋊C811yescharacteristic
206D17—22no—
207D17#156412yescomplemented
208D17C2×#42711yescharacteristic
209D17C22×#10811yescharacteristic
210C23×C4—171no—
211C23×C4—171no—
212C23×C4—171no—
213C22×C8—171no—
214C22×C8—171no—
215C22×C8—171no—
216C22×C8—171no—
217C22×C8—171no—
218C22×C8—174no—
219C22×C8—174no—
220C22×C8—171no—
221C22×C8—171no—
222C22×C8—174no—
223C22×C8—342no—
224C22×C8—341no—
225C22×C8—341no—
226C22×C8—344no—
227C22×C8#363311yescharacteristic, complemented
228C2×C42—171no—
229C2×C42—172no—
230C2×C42—171no—
231C2×C42—172no—
232C2×C42—172no—
233C2×C42—171no—
234C2×C42—171no—
235C2×C42—172no—
236C4⋊C8—178no—
237C4⋊C8—344no—
238C22⋊C8—348no—
239C4×C8—172no—
240C4×C8—172no—
241C4×C8—172no—
242C4×C8—172no—
243C4×C8—174no—
244C4×C8—174no—
245C4×C8—348no—
246C17C2×#156411yescharacteristic, complemented, Sylow
247C24—171no—
248C22×C4—171no—
249C22×C4—171no—
250C22×C4—171no—
251C22×C4—172no—
252C22×C4—172no—
253C22×C4—171no—
254C22×C4—171no—
255C22×C4—171no—
256C22×C4—172no—
257C22×C4—171no—
258C22×C4—172no—
259C22×C4—172no—
260C22×C4—172no—
261C22×C4—171no—
262C22×C4—172no—
263C22×C4—172no—
264C22×C4—171no—
265C22×C4—344no—
266C22×C4—344no—
267C22×C4C2×#363311yescharacteristic
268C2×C8—171no—
269C2×C8—171no—
270C2×C8—174no—
271C2×C8—172no—
272C2×C8—172no—
273C2×C8—172no—
274C2×C8—172no—
275C2×C8—174no—
276C2×C8—174no—
277C2×C8—172no—
278C2×C8—172no—
279C2×C8—341no—
280C2×C8—341no—
281C2×C8—344no—
282C2×C8—344no—
283C2×C8—341no—
284C2×C8—341no—
285C2×C8—348no—
286C2×C8—688no—
287C2×C8C2×#363311yescharacteristic
288C2×C8C2×#363311yescharacteristic
289C2×C8C2×#363314yescomplemented
290C42—172no—
291C42—172no—
292C42—172no—
293C42—171no—
294C42—172no—
295C42—172no—
296C42—171no—
297C42—171no—
298C42—172no—
299C42—171no—
300C23—171no—
301C23—172no—
302C23—172no—
303C23—171no—
304C23—342no—
305C23—342no—
306C23C4⋊#363311yescharacteristic
307C2×C4—171no—
308C2×C4—171no—
309C2×C4—172no—
310C2×C4—174no—
311C2×C4—174no—
312C2×C4—172no—
313C2×C4—171no—
314C2×C4—172no—
315C2×C4—171no—
316C2×C4—171no—
317C2×C4—172no—
318C2×C4—171no—
319C2×C4—172no—
320C2×C4—172no—
321C2×C4—172no—
322C2×C4—172no—
323C2×C4—171no—
324C2×C4—171no—
325C2×C4—172no—
326C2×C4—171no—
327C2×C4—172no—
328C2×C4—171no—
329C2×C4—344no—
330C2×C4—344no—
331C2×C4—344no—
332C2×C4—344no—
333C2×C4—342no—
334C2×C4—342no—
335C2×C4C4⋊#363312yes—
336C2×C4C4⋊#363311yescharacteristic
337C2×C4C22×#363311yescharacteristic
338C2×C4C22×#363312yes—
339C8—172no—
340C8—172no—
341C8—342no—
342C8—342no—
343C8—688no—
344C8C22×#363312yes—
345C8C22×#363312yes—
346C22—22no—
347C22—171no—
348C22—171no—
349C22—172no—
350C22—172no—
351C22—172no—
352C22—342no—
353C22—342no—
354C22—344no—
355C22—342no—
356C22C2×C4⋊#363312yes—
357C22C2×C4⋊#363311yescharacteristic
358C4—172no—
359C4—172no—
360C4—174no—
361C4—171no—
362C4—172no—
363C4—171no—
364C4—342no—
365C4—341no—
366C4—341no—
367C4C2×C4⋊#363311yescharacteristic
368C4C2×C4⋊#363312yes—
369C4C23×#363311yescharacteristic
370C2—22no—
371C2—171no—
372C2—171no—
373C2—172no—
374C2—342no—
375C2#1454590812yesdirect product factor
376C2C22×C4⋊#363311yescharacteristic
subgroupG/H
centerC2×C4C4⋊#3633
commutatorC4×C17C23×C8
FrattiniC4C23×#3633
FittingC22×C8×C17C8
socleC22×C17C2×C4⋊C8
prime radicalC23×D17C4⋊C4
cosocleC4×#595C24
hypercenterC22×C8#3633
hypocenterC17C2×#1564
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #14545908C2direct (N × H)
3. C2×#11763899C2semidirect
4. C2×#11763898C2semidirect
11. #11763899C22semidirect
12. #11763898C22semidirect
44. C22×C8×C17C8semidirect
45. C22×#3622C8semidirect
46. C2×C8×D17C8semidirect
47. C2×C8×D17C8semidirect
48. C2×C8×D17C8semidirect
101. C2×C8×C17C2×C8semidirect
104. C2×#3622C2×C8semidirect
107. C8×D17C2×C8semidirect
108. C8×D17C2×C8semidirect
204. C2×C17#1564semidirect
207. D17#1564semidirect
227. C22×C8#3633semidirect
246. C17C2×#1564semidirect
289. C2×C8C2×#3633semidirect
375. C2#14545908direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117639222
#145459082
C2×#117638992
C2×#117638982
C22×C8×#5952
C2×#156417