Finite Group Databasebeta

← C2×#14543764 #17959040

Subgroups — C2×#14543764 #17959040

Order 4352.

668 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763687C211yesmaximal, characteristic
2C2×#11763653C211yesmaximal, characteristic
3#14543764C214yesmaximal, direct product factor
4C2×#11762735C211yesmaximal, characteristic
5C22×C22⋊#595—21no—
6C2×C22⋊#3624—21no—
7#11763687—21no—
8#11763687C2212yes—
9#11763653—21no—
10#11763653C2212yes—
11C22×#63227—21no—
12C22×#63227C2211yescharacteristic
13#11762735—21no—
14#11762735—21no—
15#11762735C412yescomplemented
16#11762735C2212yes—
17C2×#10587502—21no—
18C2×#10587502C411yescharacteristic, complemented
19C22×C4⋊C4×C17C411yescharacteristic, complemented
20C24×D17D411yescharacteristic
21C23×#595—41no—
22C23×C4×C17—21no—
23C23×C4×C17C2×C411yescharacteristic
24C23×Dic17—21no—
25C23×Dic17D411yescharacteristic
26C2×C22⋊#595—24no—
27C2×C22⋊#595—22no—
28C2×C22⋊#595—41no—
29C2×C22⋊#595—42no—
30C22×#3624—41no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—41no—
33C2×C4⋊C4×C17—41no—
34C2×C4⋊C4×C17C2×C412yescomplemented
35C2×#63227—22no—
36C2×#63227—22no—
37C2×#63227—41no—
38C2×#63227—41no—
39C2×#63227—42no—
40C2×#63227—42no—
41C2×#63227C2×C411yescharacteristic
42C2×#63227D411yescharacteristic
43C2×#63227D411yescharacteristic
44C2×#63227C2311yescharacteristic
45C22⋊#3624—22no—
46C22⋊#3624—41no—
47#10587502—21no—
48#10587502—22no—
49#10587502—22no—
50#10587502C2×C412yescomplemented
51C24×C17C22⋊C411yescharacteristic
52C23×D17—21no—
53C23×D17—21no—
54C23×D17—22no—
55C23×D17—42no—
56C23×D17—42no—
57C23×D17C22⋊C411yescharacteristic
58C23×D17D812yes—
59C23×D17SD1612yes—
60C23×D17C2×D411yescharacteristic
61C22×#595—44no—
62C22×#595—42no—
63C22×#595—82no—
64C22×#595—82no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—22no—
68C22×C4×C17—42no—
69C22×C4×C17—41no—
70C22×C4×C17—41no—
71C22×C4×C17—42no—
72C22×C4×C17—42no—
73C22×C4×C17C22⋊C411yescharacteristic
74C22×C4×C17C22×C411yescharacteristic
75C22×Dic17—21no—
76C22×Dic17—21no—
77C22×Dic17—22no—
78C22×Dic17—42no—
79C22×Dic17—42no—
80C22×Dic17—42no—
81C22×Dic17—42no—
82C22×Dic17C22⋊C411yescharacteristic
83C22×Dic17C2×D411yescharacteristic
84C22⋊#595—24no—
85C22⋊#595—44no—
86C22⋊#595—42no—
87C2×#3624—42no—
88C2×#3624—82no—
89C4⋊C4×C17—42no—
90C4⋊C4×C17—42no—
91#63227—41no—
92#63227—41no—
93#63227—41no—
94#63227—41no—
95#63227—44no—
96#63227—42no—
97#63227—42no—
98C2×#1344—171nomaximal, Sylow
99C23×C17—22no—
100C23×C17—22no—
101C23×C17#9911yescharacteristic
102C23×C17#9911yescharacteristic
103C23×C17#10212yes—
104C23×C17#10412yes—
105C23×C17C2×C22⋊C411yescharacteristic
106C22×D17—22no—
107C22×D17—22no—
108C22×D17—21no—
109C22×D17—21no—
110C22×D17—22no—
111C22×D17—22no—
112C22×D17—21no—
113C22×D17—21no—
114C22×D17—42no—
115C22×D17—42no—
116C22×D17—41no—
117C22×D17—41no—
118C22×D17—44no—
119C22×D17—44no—
120C22×D17—41no—
121C22×D17—41no—
122C22×D17—84no—
123C22×D17—81no—
124C22×D17—81no—
125C22×D17#10212yes—
126C22×D17C2×D811yescharacteristic
127C22×D17C2×SD1611yescharacteristic
128C2×#595—44no—
129C2×#595—88no—
130C2×#595—82no—
131C2×#595—82no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17—42no—
135C2×C4×C17—42no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—42no—
139C2×C4×C17—42no—
140C2×C4×C17—42no—
141C2×C4×C17—82no—
142C2×C4×C17—82no—
143C2×Dic17—21no—
144C2×Dic17—21no—
145C2×Dic17—42no—
146C2×Dic17—41no—
147C2×Dic17—41no—
148C2×Dic17—42no—
149C2×Dic17—42no—
150C2×Dic17—42no—
151C2×Dic17—81no—
152C2×Dic17—84no—
153#3624—82no—
154C2×#397—171no—
155C2×#342—171no—
156C2×#323—171no—
157#1344—174no—
158C22×C17—24no—
159C22×C17—24no—
160C22×C17—21no—
161C22×C17—21no—
162C22×C17—21no—
163C22×C17—21no—
164C22×C17#32712yes—
165C22×C17#32712yes—
166C22×C17#35212yes—
167C22×C17#35412yes—
168C22×C17C2×#9911yescharacteristic
169C22×C17C2×#10211yescharacteristic
170C22×C17C2×#10411yescharacteristic
171C2×D17—21no—
172C2×D17—22no—
173C2×D17—21no—
174C2×D17—44no—
175C2×D17—44no—
176C2×D17—41no—
177C2×D17—41no—
178C2×D17—41no—
179C2×D17—41no—
180C2×D17—42no—
181C2×D17—41no—
182C2×D17—41no—
183C2×D17—82no—
184C2×D17—81no—
185C2×D17—82no—
186C2×D17—81no—
187#595—84no—
188C4×C17—41no—
189C4×C17—41no—
190C4×C17—82no—
191Dic17—41no—
192Dic17—41no—
193Dic17—82no—
194C22×C4⋊C4#59511yescharacteristic, complemented
195C22×C22⋊C4—171no—
196C22×C22⋊C4—341no—
197C22×C22⋊C4—341no—
198C2×C22⋊C8—341no—
199#397—172no—
200#397—172no—
201#397—341no—
202#397—341no—
203C2×#95—171no—
204C2×#95—341no—
205#342—172no—
206#342—341no—
207#323—172no—
208#323—341no—
209C2×C17—21no—
210C2×C17—22no—
211C2×C17—21no—
212C2×C17#134414yescomplemented
213C2×C17C2×#32711yescharacteristic
214C2×C17C2×#35211yescharacteristic
215C2×C17C2×#35411yescharacteristic
216D17—41no—
217D17—42no—
218D17—41no—
219C25—171no—
220C23×C4—21no—
221C23×C4—171no—
222C23×C4—341no—
223C23×C4—681no—
224C23×C4C2×#59511yescharacteristic
225C22×C8—681no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—41no—
228C2×C4⋊C4—41no—
229C2×C4⋊C4C2×#59512yescomplemented
230C2×C22⋊C4—171no—
231C2×C22⋊C4—171no—
232C2×C22⋊C4—171no—
233C2×C22⋊C4—171no—
234C2×C22⋊C4—342no—
235C2×C22⋊C4—344no—
236C2×C22⋊C4—342no—
237C2×C22⋊C4—342no—
238C2×C22⋊C4—681no—
239C2×C22⋊C4—681no—
240C2×C22⋊C4—682no—
241C2×C22⋊C4—682no—
242C2×C22⋊C4—682no—
243C2×C22⋊C4—681no—
244C22⋊C8—342no—
245C22⋊C8—681no—
246#95—172no—
247#95—342no—
248#95—342no—
249#95—341no—
250C17C2×#134411yescharacteristic, complemented, Sylow
251C24—171no—
252C24—171no—
253C24—172no—
254C24—172no—
255C24—341no—
256C24—342no—
257C24—341no—
258C24—682no—
259C24—682no—
260C24C22⋊#59511yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—171no—
270C22×C4—171no—
271C22×C4—341no—
272C22×C4—341no—
273C22×C4—342no—
274C22×C4—682no—
275C22×C4—682no—
276C22×C4—682no—
277C22×C4—682no—
278C22×C4—684no—
279C22×C4—682no—
280C22×C4—1362no—
281C22×C4—1362no—
282C22×C4C22⋊#59511yescharacteristic
283C22×C4C22×#59511yescharacteristic
284C2×C8—682no—
285C2×C8—1362no—
286C4⋊C4—42no—
287C4⋊C4—42no—
288C22⋊C4—344no—
289C22⋊C4—681no—
290C22⋊C4—681no—
291C22⋊C4—681no—
292C22⋊C4—681no—
293C22⋊C4—682no—
294C22⋊C4—684no—
295C22⋊C4—682no—
296C22⋊C4—682no—
297C22⋊C4—684no—
298C23—22no—
299C23—22no—
300C23—171no—
301C23—172no—
302C23—171no—
303C23—341no—
304C23—341no—
305C23—342no—
306C23—342no—
307C23—341no—
308C23—341no—
309C23—342no—
310C23—342no—
311C23—681no—
312C23—681no—
313C23—684no—
314C23—684no—
315C23—681no—
316C23—681no—
317C23—682no—
318C23—682no—
319C23—1361no—
320C23—1364no—
321C23—1361no—
322C23#1058754712yes—
323C23#1058754812yes—
324C23#1058755111yescharacteristic
325C23#1058755111yescharacteristic
326C23C2×C22⋊#59511yescharacteristic
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—341no—
339C2×C4—341no—
340C2×C4—682no—
341C2×C4—681no—
342C2×C4—681no—
343C2×C4—682no—
344C2×C4—682no—
345C2×C4—684no—
346C2×C4—682no—
347C2×C4—1361no—
348C2×C4—1364no—
349C2×C4—1362no—
350C2×C4—1368no—
351C2×C4—1362no—
352C8—1362no—
353C22—21no—
354C22—21no—
355C22—24no—
356C22—24no—
357C22—21no—
358C22—21no—
359C22—341no—
360C22—342no—
361C22—341no—
362C22—681no—
363C22—682no—
364C22—681no—
365C22—681no—
366C22—681no—
367C22—684no—
368C22—684no—
369C22—681no—
370C22—681no—
371C22—1361no—
372C22—1361no—
373C22—1362no—
374C22—1362no—
375C22#1176366012yes—
376C22#1176366012yes—
377C22#1176371112yes—
378C22#1176371512yes—
379C22C2×#1058755111yescharacteristic
380C22C2×#1058754711yescharacteristic
381C22C2×#1058754811yescharacteristic
382C4—41no—
383C4—41no—
384C4—82no—
385C4—681no—
386C4—681no—
387C4—1362no—
388C4—1364no—
389C2—21no—
390C2—21no—
391C2—22no—
392C2—681no—
393C2—681no—
394C2—682no—
395C2#1454376414yesdirect product factor
396C2C2×#1176366011yescharacteristic
397C2C2×#1176371111yescharacteristic
398C2C2×#1176371511yescharacteristic
subgroupG/H
centerC23#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17#99
prime radicalC24×D17D4
cosocleC2×#63227C23
hypercenterC22×C4⋊C4#595
hypocenterC17C2×#1344
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14543764C2direct (N × H)
15. #11762735C4semidirect
18. C2×#10587502C4semidirect
19. C22×C4⋊C4×C17C4semidirect
34. C2×C4⋊C4×C17C2×C4semidirect
50. #10587502C2×C4semidirect
194. C22×C4⋊C4#595semidirect
212. C2×C17#1344semidirect
229. C2×C4⋊C4C2×#595semidirect
250. C17C2×#1344semidirect
395. C2#14543764direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117636872
C2×#117636532
#145437642
C2×#117627352
C2×#134417