Finite Group Databasebeta

← C2×#14545788 #17981566

Subgroups — C2×#14545788 #17981566

Order 4352.

678 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763922C212yesmaximal
2#14545788C214yesmaximal, direct product factor
3C22×#10587532C211yesmaximal, characteristic
4#11763922—22no—
5#11763922—22no—
6#11763922C414yes—
7#11763922C2214yes—
8C2×C4⋊#3633—22no—
9C2×C22⋊#3633—22no—
10C2×C4×#3633C414yes—
11C22×#63242C411yescharacteristic
12C22×C4×#595C2211yescharacteristic
13C2×#10587532—22no—
14C2×#10587532—22no—
15C2×#10587532C412yes—
16C2×#10587532C2212yes—
17C22×C8×D17C411yescharacteristic
18C23×#595D411yescharacteristic
19C23×#595Q811yescharacteristic
20C22×#3633—24no—
21C22×C4×D17C2×C411yescharacteristic
22C22×#3624—21no—
23C2×C4×#595C2×C411yescharacteristic
24C2×C4×#595C2×C412yes—
25C2×C4×#595C2×C412yes—
26C2×C4×#595D411yescharacteristic
27C2×C4×#595D412yes—
28C2×C4×#595D412yes—
29C2×C4×#595Q811yescharacteristic
30C2×C4×#595C2311yescharacteristic
31C2×#63242—21no—
32C2×#63242—21no—
33C2×#63242—21no—
34C2×#63242C812yescomplemented
35C2×#63242C812yescomplemented
36C2×#63242C2×C412yes—
37C22⋊#3633—24no—
38C22⋊#3633—24no—
39C4⋊#3633—24no—
40C4⋊#3633—24no—
41C4×#3633—24no—
42C4×#3633C2×C418yes—
43C22×C8×C17C811yescharacteristic, complemented
44C22×#3622C811yescharacteristic, complemented
45C2×C8×D17—21no—
46C2×C8×D17—21no—
47C2×C8×D17—21no—
48C2×C8×D17—21no—
49C2×C8×D17C812yescomplemented
50C2×C8×D17C2×C412yes—
51#10587532—24no—
52#10587532—24no—
53C23×D17C4⋊C411yescharacteristic
54C22×#595—42no—
55C22×#595—42no—
56C22×#595C22⋊C412yes—
57C22×#595C22⋊C412yes—
58C22×#595C4⋊C412yes—
59C22×#595C4⋊C411yescharacteristic
60C22×#595C4⋊C411yescharacteristic
61C22×#595C4⋊C412yes—
62C22×#595C2×D411yescharacteristic
63C22×#595C2×Q811yescharacteristic
64C2×#3633—28no—
65C2×#3633—48no—
66C22×C4×C17C2×C811yescharacteristic
67C22×Dic17M1611yescharacteristic
68C2×C4×D17C4211yescharacteristic
69C2×C4×D17C4211yescharacteristic
70C2×C4×D17C22⋊C411yescharacteristic
71C2×C4×D17C22⋊C411yescharacteristic
72C2×C4×D17C4⋊C411yescharacteristic
73C2×C4×D17C2×C811yescharacteristic
74C2×C4×D17C2×C811yescharacteristic
75C2×C4×D17C2×C811yescharacteristic
76C2×C4×D17M1611yescharacteristic
77C2×C4×D17M1611yescharacteristic
78C2×C4×D17M1611yescharacteristic
79C2×C4×D17C22×C411yescharacteristic
80C2×#3624—22no—
81C2×#3624—22no—
82C2×#3624—22no—
83C4×#595C4212yes—
84C4×#595C22⋊C412yes—
85C4×#595C22⋊C412yes—
86C4×#595C22⋊C412yes—
87C4×#595C4⋊C412yes—
88C4×#595C4⋊C412yes—
89C4×#595C22×C412yes—
90C4×#595C2×D412yes—
91#63242—22no—
92#63242—22no—
93#63242—22no—
94#63242C2×C814yescomplemented
95C2×C8×C17—21no—
96C2×C8×C17—21no—
97C2×C8×C17C2×C812yescomplemented
98C2×#3622—21no—
99C2×#3622—21no—
100C2×#3622C2×C812yescomplemented
101C8×D17—22no—
102C8×D17—22no—
103C8×D17—22no—
104C8×D17—22no—
105C2×#1275—171nomaximal, Sylow
106C23×C17C4⋊C811yescharacteristic
107C22×D17—22no—
108C22×D17—22no—
109C22×D17#9511yescharacteristic
110C22×D17#9511yescharacteristic
111C22×D17C4⋊C811yescharacteristic
112C22×D17C4⋊C811yescharacteristic
113C22×D17C4⋊C811yescharacteristic
114C22×D17C2×C4⋊C411yescharacteristic
115C2×#595—24no—
116C2×#595—24no—
117C2×#595—42no—
118C2×#595—41no—
119C2×#595—41no—
120C2×#595—42no—
121C2×#595—41no—
122C2×#595—41no—
123C2×#595#9512yes—
124C2×#595#9512yes—
125C2×#595C2×C22⋊C412yes—
126C2×#595C2×C4⋊C412yes—
127#3633—48no—
128C2×C4×C17C4×C811yescharacteristic
129C2×C4×C17C4×C811yescharacteristic
130C2×C4×C17C22⋊C811yescharacteristic
131C2×C4×C17C22⋊C811yescharacteristic
132C2×C4×C17C4⋊C811yescharacteristic
133C2×C4×C17C22×C811yescharacteristic
134C2×Dic17#9711yescharacteristic
135C2×Dic17#9711yescharacteristic
136C2×Dic17C22⋊C811yescharacteristic
137C2×Dic17C22⋊C811yescharacteristic
138C2×Dic17C4⋊C811yescharacteristic
139C2×Dic17C2×M1611yescharacteristic
140C4×D17#9511yescharacteristic
141C4×D17#9511yescharacteristic
142C4×D17C4×C811yescharacteristic
143C4×D17C4×C811yescharacteristic
144C4×D17#9711yescharacteristic
145C4×D17#9711yescharacteristic
146C4×D17C22⋊C811yescharacteristic
147C4×D17C22⋊C811yescharacteristic
148C4×D17C22⋊C811yescharacteristic
149C4×D17C22⋊C811yescharacteristic
150C4×D17C4⋊C811yescharacteristic
151C4×D17C4⋊C811yescharacteristic
152C4×D17C2×C4211yescharacteristic
153C4×D17C2×C22⋊C411yescharacteristic
154C4×D17C22×C811yescharacteristic
155C4×D17C2×M1611yescharacteristic
156#3624—24no—
157C8×C17—22no—
158#3622—22no—
159C2×#431—172no—
160C22×#97—171no—
161#1275—174no—
162C22×C17—22no—
163C22×C17#33611yescharacteristic
164C22×C17#33611yescharacteristic
165C22×C17C2×C4⋊C811yescharacteristic
166C2×D17—22no—
167C2×D17—21no—
168C2×D17—21no—
169C2×D17—21no—
170C2×D17—21no—
171C2×D17—22no—
172C2×D17—22no—
173C2×D17#33611yescharacteristic
174C2×D17#33611yescharacteristic
175C2×D17H(3,ℤ/4)12yes—
176C2×D17#33812yes—
177C2×D17C2×#9511yescharacteristic
178C2×D17C2×C4⋊C811yescharacteristic
179#595—22no—
180#595—22no—
181#595—22no—
182#595—22no—
183C4×C17#33611yescharacteristic
184C4×C17#33611yescharacteristic
185C4×C17C2×C4×C811yescharacteristic
186C4×C17C2×C22⋊C811yescharacteristic
187Dic17#33611yescharacteristic
188Dic17#33611yescharacteristic
189Dic17C2×#9711yescharacteristic
190Dic17C2×C22⋊C811yescharacteristic
191C23×C8—171no—
192C23×C8—171no—
193C22×C42—171no—
194#431—174no—
195#431—174no—
196#431—342no—
197#431—342no—
198C2×C4⋊C8—342no—
199C2×C22⋊C8—342no—
200C2×#97—172no—
201C2×#97—172no—
202C2×#97—342no—
203C2×#97—342no—
204C2×C4×C8—174no—
205C2×C17—21no—
206C2×C17—21no—
207C2×C17#127512yescomplemented
208C2×C17C2×#33611yescharacteristic
209D17—21no—
210D17—21no—
211D17#127512yescomplemented
212D17C2×H(3,ℤ/4)11yescharacteristic
213D17C2×#33811yescharacteristic
214C23×C4—171no—
215C23×C4—171no—
216C23×C4—171no—
217C22×C8—172no—
218C22×C8—172no—
219C22×C8—172no—
220C22×C8—171no—
221C22×C8—172no—
222C22×C8—172no—
223C22×C8—341no—
224C22×C8—341no—
225C22×C8—341no—
226C22×C8—341no—
227C22×C8—341no—
228C22×C8—341no—
229C22×C8—341no—
230C22×C8—341no—
231C22×C8—344no—
232C22×C8#363311yescharacteristic, complemented
233C2×C42—172no—
234C2×C42—171no—
235C2×C42—172no—
236C2×C42—172no—
237C2×C42—172no—
238C2×C42—171no—
239C2×C42—171no—
240C2×C42—171no—
241C4⋊C8—344no—
242C4⋊C8—344no—
243C22⋊C8—344no—
244C22⋊C8—344no—
245#97—344no—
246#97—344no—
247C4×C8—178no—
248C4×C8—344no—
249C17C2×#127511yescharacteristic, complemented, Sylow
250C24—171no—
251C22×C4—171no—
252C22×C4—171no—
253C22×C4—171no—
254C22×C4—171no—
255C22×C4—171no—
256C22×C4—171no—
257C22×C4—171no—
258C22×C4—171no—
259C22×C4—171no—
260C22×C4—171no—
261C22×C4—171no—
262C22×C4—171no—
263C22×C4—171no—
264C22×C4—172no—
265C22×C4—172no—
266C22×C4—172no—
267C22×C4—171no—
268C22×C4—171no—
269C22×C4—172no—
270C22×C4—171no—
271C22×C4—171no—
272C22×C4—682no—
273C22×C4—682no—
274C22×C4C2×#363311yescharacteristic
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—174no—
278C2×C8—172no—
279C2×C8—342no—
280C2×C8—342no—
281C2×C8—342no—
282C2×C8—342no—
283C2×C8—342no—
284C2×C8—342no—
285C2×C8—342no—
286C2×C8—342no—
287C2×C8—342no—
288C2×C8—342no—
289C2×C8—341no—
290C2×C8—341no—
291C2×C8—348no—
292C2×C8—688no—
293C2×C8C2×#363312yescomplemented
294C42—172no—
295C42—172no—
296C42—172no—
297C42—172no—
298C42—172no—
299C42—172no—
300C42—172no—
301C42—172no—
302C23—171no—
303C23—171no—
304C23—171no—
305C23—171no—
306C23—171no—
307C23—171no—
308C23—342no—
309C23—342no—
310C23C4⋊#363311yescharacteristic
311C2×C4—171no—
312C2×C4—171no—
313C2×C4—171no—
314C2×C4—171no—
315C2×C4—171no—
316C2×C4—171no—
317C2×C4—171no—
318C2×C4—171no—
319C2×C4—171no—
320C2×C4—171no—
321C2×C4—171no—
322C2×C4—171no—
323C2×C4—171no—
324C2×C4—171no—
325C2×C4—171no—
326C2×C4—171no—
327C2×C4—171no—
328C2×C4—171no—
329C2×C4—171no—
330C2×C4—171no—
331C2×C4—171no—
332C2×C4—171no—
333C2×C4—172no—
334C2×C4—172no—
335C2×C4—172no—
336C2×C4—172no—
337C2×C4—344no—
338C2×C4—344no—
339C2×C4—681no—
340C2×C4—682no—
341C2×C4—681no—
342C2×C4—681no—
343C2×C4—682no—
344C2×C4—681no—
345C2×C4C4×#363311yescharacteristic
346C2×C4C4×#363311yescharacteristic
347C2×C4C4⋊#363311yescharacteristic
348C2×C4C22⋊#363311yescharacteristic
349C2×C4C22⋊#363311yescharacteristic
350C2×C4C22×#363311yescharacteristic
351C8—22no—
352C8—344no—
353C8—342no—
354C8—688no—
355C22—22no—
356C22—172no—
357C22—172no—
358C22—171no—
359C22—171no—
360C22—171no—
361C22—171no—
362C22—341no—
363C22—341no—
364C22—341no—
365C22—341no—
366C22—342no—
367C22—342no—
368C22—342no—
369C22(C2×#3633)⋊C411yescharacteristic
370C22(C2×#3633)⋊C411yescharacteristic
371C22C2×C4⋊#363311yescharacteristic
372C4—171no—
373C4—171no—
374C4—171no—
375C4—171no—
376C4—342no—
377C4—342no—
378C4—342no—
379C4—342no—
380C4(C2×#3633)⋊C411yescharacteristic
381C4(C2×#3633)⋊C411yescharacteristic
382C4C2×C4×#363311yescharacteristic
383C4C2×C22⋊#363311yescharacteristic
384C2—21no—
385C2—21no—
386C2—171no—
387C2—171no—
388C2—172no—
389C2—341no—
390C2—341no—
391C2#1454578812yesdirect product factor
392C2C2×(C2×#3633)⋊C411yescharacteristic
subgroupG/H
centerC2×C4C4×#3633
commutatorC4×C17C2×C4×C8
FrattiniC2×C4C22×#3633
FittingC22×C8×C17C8
socleC22×C17#336
prime radicalC23×D17C4⋊C4
cosocleC2×C4×#595C23
hypercenterC22×C8#3633
hypocenterC17C2×#1275
LCSG ▷ C4×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #14545788C2direct (N × H)
34. C2×#63242C8semidirect
35. C2×#63242C8semidirect
43. C22×C8×C17C8semidirect
44. C22×#3622C8semidirect
49. C2×C8×D17C8semidirect
94. #63242C2×C8semidirect
97. C2×C8×C17C2×C8semidirect
100. C2×#3622C2×C8semidirect
207. C2×C17#1275semidirect
211. D17#1275semidirect
232. C22×C8#3633semidirect
249. C17C2×#1275semidirect
293. C2×C8C2×#3633semidirect
391. C2#14545788direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117639222
#145457882
C22×#105875322
C2×#127517