Finite Group Databasebeta

← #17982971

Subgroups — #17982971

Order 4352.

764 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1(C2×#3633)⋊Q8C212yesmaximal
2#14545931C214yesmaximal
3#14545927C212yesmaximal
4#14545926C211yesmaximal, characteristic
5C4⋊C4×#3633C212yesmaximal
6C4×C4⋊#3633C211yesmaximal, characteristic
7#14545918C212yesmaximal
8C4×Q8×#595C211yesmaximal, characteristic
9C2×C4⋊#3633C2212yes—
10C2×C4⋊#3633C2212yes—
11C2×C4×#3633C2212yes—
12C2×C4×#3633C2214yes—
13(C2×#3633)⋊C4C2211yescharacteristic
14(C2×#3633)⋊C4C2211yescharacteristic
15(C2×#3633)⋊C4C2214yes—
16(C2×#3633)⋊C4C2212yes—
17(C2×#3633)⋊C4C2212yes—
18(C2×#3633)⋊C4C2214yes—
19(C2×#3633)⋊C4C2214yes—
20C2×Q8×#595C411yescharacteristic
21C2×Q8×#595C2211yescharacteristic
22C4⋊C4×#595C411yescharacteristic
23C4⋊C4×#595C412yes—
24C4⋊C4×#595C2211yescharacteristic
25C4⋊C4×#595C2212yes—
26C4×C4⋊#595C412yes—
27C4×C4⋊#595C411yescharacteristic
28C42×#595C2211yescharacteristic
29C42×#595C2212yes—
30C4×Q8×D17C411yescharacteristic
31C22×#3633C2312yes—
32C22×#3633C2314yes—
33C22×#3633C2312yes—
34C2×Q8×D17C2×C411yescharacteristic
35Q8×#595—24no—
36Q8×#595—22no—
37Q8×#595—22no—
38C2×C4⋊#595C2×C412yes—
39C2×C4⋊#595C2×C411yescharacteristic
40C2×C4⋊#595C2×C412yes—
41C2×C4⋊#595C2×C411yescharacteristic
42C2×C4×#595C2×C412yes—
43C2×C4×#595C2×C411yescharacteristic
44C2×C4×#595C2×C412yes—
45C2×C4×#595C2×C411yescharacteristic
46C2×C4×#595C2×C411yescharacteristic
47C2×C4×#595C2×C412yes—
48C2×C4×#595C2311yescharacteristic
49C2×C4×#595C2312yes—
50C2×C4×#595C2311yescharacteristic
51C2×C4×#595C2312yes—
52C2×C4×#595C2311yescharacteristic
53C4⋊#3633—24no—
54C4⋊#3633—24no—
55C4×#3633—28no—
56C4×#3633—24no—
57C4×Q8×C17C811yescharacteristic, complemented
58Q8×Dic17C811yescharacteristic, complemented
59C4⋊C4×D17C2×C412yes—
60C4⋊C4×D17C2×C411yescharacteristic
61#10587573C812yescomplemented
62#10587573C811yescharacteristic, complemented
63C42×D17C2×C412yes—
64C42×D17C2×C411yescharacteristic
65C4×Dic34C812yescomplemented
66C4×Dic34C811yescharacteristic, complemented
67(C2×#595)⋊C4C2×C412yes—
68(C2×#595)⋊C4C2×C412yes—
69(C2×#595)⋊C4C2×C412yes—
70C22×#595C22×C412yes—
71C22×#595C22×C411yescharacteristic
72C22×#595C22×C411yescharacteristic
73C22×#595C22×C412yes—
74C22×#595C22×C411yescharacteristic
75C22×#595C2411yescharacteristic
76C2×#3633—22no—
77C2×#3633—22no—
78C2×#3633—22no—
79C2×#3633—24no—
80C2×#3633—22no—
81C2×#3633—24no—
82C2×#3633—22no—
83C2×#3633—24no—
84C2×#3633#4114yes—
85C2×Q8×C17C2×C811yescharacteristic
86Q8×D17—22no—
87Q8×D17—22no—
88C2×C4×D17C22×C411yescharacteristic
89C2×C4×D17C22×C412yes—
90C2×C4×D17C22×C412yes—
91C2×C4×D17C22×C411yescharacteristic
92C2×C4×D17C22×C411yescharacteristic
93C2×Dic34C2×C811yescharacteristic
94C2×Dic34C2×C812yes—
95C4⋊#595—24no—
96C4⋊#595—24no—
97C4⋊#595—22no—
98C4⋊#595M1614yes—
99C4×#595—24no—
100C4×#595—22no—
101C4×#595—24no—
102C4×#595—24no—
103C4×#595—22no—
104C4×#595—22no—
105C4×#595—22no—
106C4×#595—22no—
107C4×#595—22no—
108C4×#595—41no—
109C4×#595—42no—
110C4×#595#4112yes—
111C4×#595#4112yes—
112C4⋊C4×C17C2×C812yes—
113C4⋊C4×C17C2×C811yescharacteristic
114C42×C17C2×C812yes—
115C42×C17C2×C811yescharacteristic
116C4⋊Dic17C2×C812yes—
117C4⋊Dic17C2×C811yescharacteristic
118#63225C2×C812yes—
119#63225C2×C812yes—
120#63225C2×C812yes—
121C4×Dic17C2×C812yes—
122C4×Dic17C2×C811yescharacteristic
123C4×Dic17C2×C812yes—
124C4×Dic17C2×C811yescharacteristic
125C4×Dic17C2×C812yes—
126C4×Dic17C2×C811yescharacteristic
127#22828—171nomaximal, Sylow
128C22×D17C23×C411yescharacteristic
129C2×#595—22no—
130C2×#595—21no—
131C2×#595—21no—
132C2×#595—21no—
133C2×#595—21no—
134C2×#595—22no—
135C2×#595—22no—
136C2×#595—21no—
137C2×#595—21no—
138C2×#595—22no—
139C2×#595—22no—
140C2×#595—21no—
141C2×#595#11712yes—
142C2×#595C2×M1614yes—
143C2×#595#13112yes—
144C2×#595C2×#4111yescharacteristic
145C2×#595C2×#4112yes—
146C2×#595C2×#4111yescharacteristic
147C2×#5952−1+412yes—
148#3633—24no—
149#3633—42no—
150#3633—44no—
151Q8×C17—22no—
152C2×C4×C17C22×C811yescharacteristic
153C2×C4×C17C22×C812yes—
154C2×C4×C17C22×C811yescharacteristic
155C2×C4×C17C22×C812yes—
156C2×C4×C17C22×C811yescharacteristic
157C2×Dic17C22×C812yes—
158C2×Dic17C22×C811yescharacteristic
159C2×Dic17C22×C812yes—
160C2×Dic17C22×C811yescharacteristic
161C2×Dic17C22×C811yescharacteristic
162C4×D17—22no—
163C4×D17—22no—
164C4×D17—21no—
165C4×D17—21no—
166C4×D17—22no—
167C4×D17—21no—
168C4×D17—22no—
169C4×D17—21no—
170C4×D17#11712yes—
171C4×D17C2×M1612yes—
172Dic34—22no—
173Dic34—24no—
174C42×Q8—171no—
175#1984—172no—
176#1916—174no—
177#1839—172no—
178#1831—171no—
179C8×C4⋊C4—172no—
180C4×C4⋊C8—171no—
181#1744—172no—
182C22×C17C23×C811yescharacteristic
183C2×D17C2×#11711yescharacteristic
184C2×D17C4×#4111yescharacteristic
185C2×D17#51911yescharacteristic
186C2×D17C22×M1611yescharacteristic
187C2×D17C2×#13111yescharacteristic
188C2×D17#56811yescharacteristic
189#595—22no—
190#595—24no—
191#595—22no—
192#595—42no—
193#595—41no—
194#595#55212yes—
195#595#55612yes—
196C4×C17—22no—
197C4×C17—22no—
198C4×C17—21no—
199C4×C17—21no—
200C4×C17#43112yes—
201Dic17—22no—
202Dic17—22no—
203Dic17—21no—
204Dic17—21no—
205Dic17#43112yes—
206C2×C4×Q8—171no—
207C2×C4×Q8—171no—
208C2×C4×Q8—171no—
209C2×C4⋊C8—172no—
210C2×C4⋊C8—172no—
211C2×C4×C8—174no—
212C2×C4×C8—172no—
213C4×C4⋊C4—171no—
214C4×C4⋊C4—172no—
215C4×C4⋊C4—172no—
216C4×C4⋊C4—171no—
217C4×C4⋊C4—172no—
218C4×C4⋊C4—171no—
219C43—171no—
220C43—172no—
221#336—172no—
222#336—172no—
223#336—171no—
224#336—174no—
225#336—174no—
226#336—174no—
227#336—171no—
228C2×C17C2×#43111yescharacteristic
229C2×C17C8×#4111yescharacteristic
230C2×C17#298211yescharacteristic
231D17#235611yescharacteristic
232D17#292511yescharacteristic
233D17#297011yescharacteristic
234D17#298411yescharacteristic
235C22×Q8—171no—
236C22×C8—172no—
237C22×C8—174no—
238C22×C8—172no—
239C4×Q8—171no—
240C4×Q8—172no—
241C4×Q8—171no—
242C4×Q8—172no—
243C4×Q8—171no—
244C4×Q8—342no—
245C4×Q8—342no—
246C4×Q8—344no—
247C4×Q8#363311yescharacteristic, complemented
248C2×C4⋊C4—171no—
249C2×C4⋊C4—171no—
250C2×C4⋊C4—172no—
251C2×C4⋊C4—171no—
252C2×C4⋊C4—172no—
253C2×C4⋊C4—172no—
254C2×C42—171no—
255C2×C42—171no—
256C2×C42—172no—
257C2×C42—171no—
258C2×C42—172no—
259C2×C42—172no—
260C2×C42—171no—
261C2×C42—172no—
262C2×C42—171no—
263C2×C42—172no—
264C2×C42—171no—
265C2×C42—171no—
266C2×C42—172no—
267C4⋊C8—344no—
268C4⋊C8—344no—
269C4×C8—344no—
270C4×C8—348no—
271#95—172no—
272#95—172no—
273#95—172no—
274C17#2282811yescharacteristic, complemented, Sylow
275C2×Q8—172no—
276C2×Q8—171no—
277C2×Q8—342no—
278C2×Q8—342no—
279C2×Q8C2×#363311yescharacteristic
280C22×C4—171no—
281C22×C4—171no—
282C22×C4—171no—
283C22×C4—172no—
284C22×C4—171no—
285C22×C4—172no—
286C22×C4—171no—
287C22×C4—171no—
288C22×C4—172no—
289C22×C4—171no—
290C22×C4—172no—
291C2×C8—174no—
292C2×C8—342no—
293C2×C8—342no—
294C2×C8—342no—
295C2×C8—344no—
296C2×C8—344no—
297C2×C8—342no—
298C2×C8—342no—
299C2×C8—344no—
300C4⋊C4—174no—
301C4⋊C4—172no—
302C4⋊C4—172no—
303C4⋊C4—172no—
304C4⋊C4—172no—
305C4⋊C4—171no—
306C4⋊C4—342no—
307C4⋊C4—344no—
308C4⋊C4—344no—
309C4⋊C4C2×#363312yes—
310C4⋊C4C2×#363311yescharacteristic
311C42—172no—
312C42—172no—
313C42—171no—
314C42—171no—
315C42—172no—
316C42—171no—
317C42—172no—
318C42—172no—
319C42—344no—
320C42—342no—
321C42—342no—
322C42—342no—
323C42—344no—
324C42—342no—
325C42—342no—
326C42—342no—
327C42—344no—
328C42—681no—
329C42—682no—
330C42C2×#363312yes—
331C42C2×#363311yescharacteristic
332C23—171no—
333Q8—22no—
334Q8—344no—
335Q8—342no—
336C2×C4—171no—
337C2×C4—171no—
338C2×C4—172no—
339C2×C4—172no—
340C2×C4—171no—
341C2×C4—172no—
342C2×C4—172no—
343C2×C4—172no—
344C2×C4—172no—
345C2×C4—174no—
346C2×C4—171no—
347C2×C4—171no—
348C2×C4—172no—
349C2×C4—172no—
350C2×C4—342no—
351C2×C4—342no—
352C2×C4—342no—
353C2×C4—341no—
354C2×C4—341no—
355C2×C4—342no—
356C2×C4—341no—
357C2×C4—341no—
358C2×C4—341no—
359C2×C4—342no—
360C2×C4—341no—
361C2×C4—341no—
362C2×C4—342no—
363C2×C4—341no—
364C2×C4—342no—
365C2×C4—341no—
366C2×C4—341no—
367C2×C4—342no—
368C2×C4—341no—
369C2×C4—342no—
370C2×C4C22×#363311yescharacteristic
371C2×C4C22×#363311yescharacteristic
372C2×C4C22×#363312yes—
373C2×C4C22×#363312yes—
374C2×C4C22×#363311yescharacteristic
375C8—344no—
376C8—682no—
377C8—684no—
378C22—171no—
379C22—171no—
380C22—171no—
381C22—171no—
382C22—171no—
383C22—171no—
384C22C23×#363311yescharacteristic
385C4—22no—
386C4—22no—
387C4—21no—
388C4—21no—
389C4—172no—
390C4—172no—
391C4—172no—
392C4—344no—
393C4—342no—
394C4—342no—
395C4—342no—
396C4—342no—
397C4—341no—
398C4—341no—
399C4—681no—
400C4—682no—
401C4#1176392212yes—
402C2—171no—
403C2—171no—
404C2—171no—
405C2—171no—
406C2C2×#1176392211yescharacteristic
407C2#41×#363311yescharacteristic
408C2#1454602711yescharacteristic
subgroupG/H
center, FrattiniC22C23×#3633
commutator, socleC22×C17C23×C8
FittingC4×Q8×C17C8
prime radicalC22×D17C23×C4
cosocleC22×#595C24
hypercenterC4×Q8#3633
hypocenterC17#22828
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
57. C4×Q8×C17C8semidirect
58. Q8×Dic17C8semidirect
61. #10587573C8semidirect
62. #10587573C8semidirect
65. C4×Dic34C8semidirect
66. C4×Dic34C8semidirect
247. C4×Q8#3633semidirect
274. C17#22828semidirect

Maximal subgroups

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

subgroupindex
(C2×#3633)⋊Q82
#145459312
#145459272
#145459262
C4⋊C4×#36332
C4×C4⋊#36332
#145459182
C4×Q8×#5952
#2282817