Finite Group Databasebeta

← C2×#14543616 #17950435

Subgroups — C2×#14543616 #17950435

Order 4352.

782 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763828C211yesmaximal, characteristic
2C2×C4×#63243C211yesmaximal, characteristic
3#14543616C214yesmaximal, direct product factor
4C2×C4×C8×D17C211yesmaximal, characteristic
5C22×#63243C412yes—
6#11763828—21no—
7#11763828—21no—
8#11763828C412yes—
9#11763828C2212yes—
10C2×C4⋊#3624C412yes—
11C2×#10587543—21no—
12C4×#63243—21no—
13C4×#63243—21no—
14C4×#63243C412yes—
15C4×#63243C2212yes—
16C2×#10587542—21no—
17C2×C4×#3624—21no—
18C2×C4×#3624—21no—
19C22×C8×D17—21no—
20C2×C42×D17C2211yescharacteristic
21C2×C4×#3622C411yescharacteristic
22C2×C8×Dic17—21no—
23C4×C8×D17—21no—
24C4×C8×D17—21no—
25C4×C8×D17C412yes—
26C4×C8×D17C2212yes—
27C2×C4×C8×C17C411yescharacteristic
28C22×C4×D17C2×C411yescharacteristic
29C22×C4×D17D411yescharacteristic
30C22×C4×D17Q811yescharacteristic
31C22×#3624—22no—
32C22×#3624—22no—
33C2×#63243—22no—
34C2×#63243—24no—
35C2×#63243C818yescomplemented
36C2×#63243C2×C414yes—
37C22×C8×C17—21no—
38C2×C42×C17C2×C411yescharacteristic
39C2×C4×Dic17C2×C411yescharacteristic
40C2×C4×Dic17D411yescharacteristic
41C2×C4×Dic17D411yescharacteristic
42C22×#3622—21no—
43C2×C8×D17—28no—
44C2×C8×D17—22no—
45C2×C8×D17—22no—
46C42×D17C2×C411yescharacteristic
47C42×D17C2×C411yescharacteristic
48C42×D17C2×C411yescharacteristic
49C42×D17D411yescharacteristic
50C42×D17D411yescharacteristic
51C42×D17D411yescharacteristic
52C42×D17Q811yescharacteristic
53C42×D17C2311yescharacteristic
54#10587543—22no—
55#10587543—22no—
56#10587542—22no—
57#10587542—22no—
58C4⋊#3624—22no—
59C4⋊#3624C2×C414yes—
60C4×#3624—22no—
61C4×#3624—22no—
62C4×#3624—22no—
63C4×#3624—22no—
64C4×C8×C17—21no—
65C4×C8×C17C2×C412yes—
66C8×Dic17—22no—
67C8×Dic17—22no—
68C4×#3622—21no—
69C4×#3622C2×C412yes—
70C23×D17C4⋊C411yescharacteristic
71C22×C4×C17C4211yescharacteristic
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17C4⋊C411yescharacteristic
74C22×Dic17C22⋊C411yescharacteristic
75C22×Dic17C22⋊C411yescharacteristic
76C22×Dic17C4⋊C411yescharacteristic
77C2×C4×D17—22no—
78C2×C4×D17—22no—
79C2×C4×D17—24no—
80C2×C4×D17C4211yescharacteristic
81C2×C4×D17C22⋊C411yescharacteristic
82C2×C4×D17C22⋊C411yescharacteristic
83C2×C4×D17C22⋊C411yescharacteristic
84C2×C4×D17C4⋊C411yescharacteristic
85C2×C4×D17C4⋊C411yescharacteristic
86C2×C4×D17C4⋊C411yescharacteristic
87C2×C4×D17C4⋊C411yescharacteristic
88C2×C4×D17C4⋊C411yescharacteristic
89C2×C4×D17C2×C814yes—
90C2×C4×D17M1614yes—
91C2×C4×D17C22×C411yescharacteristic
92C2×C4×D17C2×D411yescharacteristic
93C2×C4×D17C2×Q811yescharacteristic
94C2×#3624—28no—
95C2×#3624—24no—
96C2×#3624—24no—
97C2×#3624—44no—
98#63243—28no—
99#63243—24no—
100#63243C2×C818yescomplemented
101C2×C8×C17—24no—
102C2×C8×C17—22no—
103C42×C17C4211yescharacteristic
104C42×C17C22⋊C411yescharacteristic
105C42×C17C4⋊C411yescharacteristic
106C42×C17C22×C411yescharacteristic
107C4×Dic17C4211yescharacteristic
108C4×Dic17C22⋊C411yescharacteristic
109C4×Dic17C22⋊C411yescharacteristic
110C4×Dic17C22⋊C411yescharacteristic
111C4×Dic17C22⋊C411yescharacteristic
112C4×Dic17C22⋊C411yescharacteristic
113C4×Dic17C4⋊C411yescharacteristic
114C4×Dic17C4⋊C411yescharacteristic
115C4×Dic17C4⋊C411yescharacteristic
116C4×Dic17C22×C411yescharacteristic
117C4×Dic17C2×D411yescharacteristic
118C4×Dic17C2×D411yescharacteristic
119C2×#3622—24no—
120C2×#3622—22no—
121C8×D17—28no—
122C8×D17—28no—
123C2×#1278—171nomaximal, Sylow
124C23×C17#9511yescharacteristic
125C22×D17—22no—
126C22×D17—22no—
127C22×D17#9511yescharacteristic
128C22×D17C4⋊C814yes—
129C22×D17C2×C4⋊C411yescharacteristic
130C2×C4×C17—22no—
131C2×C4×C17#9511yescharacteristic
132C2×C4×C17#9511yescharacteristic
133C2×C4×C17#9511yescharacteristic
134C2×C4×C17C4×C812yes—
135C2×C4×C17#9712yes—
136C2×C4×C17#10812yes—
137C2×C4×C17#10812yes—
138C2×C4×C17C2×C4211yescharacteristic
139C2×C4×C17C2×C22⋊C411yescharacteristic
140C2×C4×C17C2×C4⋊C411yescharacteristic
141C2×Dic17—22no—
142C2×Dic17#9511yescharacteristic
143C2×Dic17#9511yescharacteristic
144C2×Dic17#9511yescharacteristic
145C2×Dic17C22⋊C814yes—
146C2×Dic17#10414yes—
147C2×Dic17C2×C22⋊C411yescharacteristic
148C2×Dic17C2×C22⋊C411yescharacteristic
149C2×Dic17C2×C4⋊C411yescharacteristic
150C4×D17—22no—
151C4×D17—22no—
152C4×D17—21no—
153C4×D17—21no—
154C4×D17—21no—
155C4×D17—21no—
156C4×D17—22no—
157C4×D17—22no—
158C4×D17—22no—
159C4×D17—22no—
160C4×D17C4×C812yes—
161C4×D17#9712yes—
162C4×D17C22⋊C814yes—
163C4×D17C4⋊C814yes—
164C4×D17C22×C812yes—
165C4×D17C2×M1612yes—
166#3624—28no—
167#3624—44no—
168C8×C17—24no—
169#3622—24no—
170C2×#431—171no—
171C2×C4×M16—171no—
172C22×C4×C8—171no—
173#1278—174no—
174C22×C17#33612yes—
175C22×C17#33912yes—
176C22×C17#34112yes—
177C22×C17C2×#9511yescharacteristic
178C2×D17—21no—
179C2×D17—21no—
180C2×D17—21no—
181C2×D17—21no—
182C2×D17—28no—
183C2×D17#33612yes—
184C2×D17C2×C4⋊C812yes—
185C4×C17—21no—
186C4×C17—21no—
187C4×C17#33612yes—
188C4×C17#34112yes—
189C4×C17C2×C4×C811yescharacteristic
190C4×C17C2×#9711yescharacteristic
191C4×C17C2×#10811yescharacteristic
192C4×C17C2×#10811yescharacteristic
193Dic17—21no—
194Dic17—21no—
195Dic17#33612yes—
196Dic17#33912yes—
197Dic17C2×C22⋊C812yes—
198Dic17C2×#10412yes—
199C22×M16—172no—
200C23×C8—341no—
201C22×C42—171no—
202#431—172no—
203#431—172no—
204#431—341no—
205#431—341no—
206C2×C4⋊C8—172no—
207C2×C22⋊C8—341no—
208C4×M16—172no—
209C4×M16—172no—
210C4×M16—341no—
211C4×M16—341no—
212C2×#97—341no—
213C2×C4×C8—171no—
214C2×C4×C8—172no—
215C2×C4×C8—172no—
216C2×C4×C8—341no—
217C2×C4×C8—341no—
218C2×C4×C8—341no—
219C2×C4×C8—341no—
220C2×C4×C8—341no—
221C2×C4×C8#59511yescharacteristic
222C2×C17#127814yescomplemented
223C2×C17C2×#33611yescharacteristic
224C2×C17C2×#33911yescharacteristic
225C2×C17C2×#34111yescharacteristic
226D17—22no—
227D17—22no—
228C23×C4—171no—
229C23×C4—171no—
230C23×C4—171no—
231C2×M16—178no—
232C2×M16—174no—
233C2×M16—344no—
234C2×M16—342no—
235C22×C8—21no—
236C22×C8—342no—
237C22×C8—342no—
238C22×C8—348no—
239C22×C8—342no—
240C22×C8—341no—
241C22×C8—342no—
242C2×C42—171no—
243C2×C42—171no—
244C2×C42—171no—
245C2×C42—171no—
246C2×C42—171no—
247C2×C42—171no—
248C2×C42—171no—
249C2×C42—171no—
250C2×C42—171no—
251C2×C42—171no—
252C2×C42—171no—
253C2×C42C2×#59511yescharacteristic
254C4⋊C8—174no—
255C4⋊C8—342no—
256C22⋊C8—342no—
257C22⋊C8—342no—
258#97—342no—
259#97—342no—
260C4×C8—21no—
261C4×C8—172no—
262C4×C8—342no—
263C4×C8—342no—
264C4×C8—342no—
265C4×C8—342no—
266C4×C8—342no—
267C4×C8—342no—
268C4×C8—341no—
269C4×C8C2×#59512yes—
270C17C2×#127811yescharacteristic, complemented, Sylow
271C24—171no—
272C22×C4—171no—
273C22×C4—171no—
274C22×C4—171no—
275C22×C4—171no—
276C22×C4—174no—
277C22×C4—174no—
278C22×C4—171no—
279C22×C4—171no—
280C22×C4—171no—
281C22×C4—171no—
282C22×C4—171no—
283C22×C4—171no—
284C22×C4—171no—
285C22×C4—171no—
286C22×C4—171no—
287C22×C4—171no—
288C22×C4—171no—
289C22×C4—344no—
290C22×C4—342no—
291C22×C4—342no—
292C22×C4C4×#59511yescharacteristic
293C22×C4C4⋊#59511yescharacteristic
294C22×C4C22⋊#59511yescharacteristic
295M16—178no—
296M16—344no—
297M16—348no—
298C2×C8—24no—
299C2×C8—22no—
300C2×C8—348no—
301C2×C8—348no—
302C2×C8—344no—
303C2×C8—344no—
304C2×C8—348no—
305C2×C8—342no—
306C2×C8—344no—
307C2×C8—684no—
308C42—171no—
309C42—171no—
310C42—171no—
311C42—171no—
312C42—171no—
313C42—171no—
314C42—171no—
315C42—171no—
316C42—171no—
317C42—171no—
318C42—171no—
319C42—171no—
320C42C4×#59511yescharacteristic
321C42C4⋊#59511yescharacteristic
322C42C22⋊#59511yescharacteristic
323C42C22×#59511yescharacteristic
324C23—171no—
325C23—171no—
326C23—174no—
327C23—342no—
328C23—342no—
329C23(C2×#595)⋊C411yescharacteristic
330C2×C4—22no—
331C2×C4—171no—
332C2×C4—171no—
333C2×C4—171no—
334C2×C4—171no—
335C2×C4—174no—
336C2×C4—174no—
337C2×C4—172no—
338C2×C4—172no—
339C2×C4—172no—
340C2×C4—172no—
341C2×C4—174no—
342C2×C4—174no—
343C2×C4—171no—
344C2×C4—171no—
345C2×C4—342no—
346C2×C4—342no—
347C2×C4—342no—
348C2×C4—342no—
349C2×C4—342no—
350C2×C4—341no—
351C2×C4—341no—
352C2×C4—341no—
353C2×C4—341no—
354C2×C4—342no—
355C2×C4—342no—
356C2×C4C8×#59512yes—
357C2×C4#1058753212yes—
358C2×C4#1058753512yes—
359C2×C4#1058753612yes—
360C2×C4(C2×#595)⋊C411yescharacteristic
361C2×C4(C2×#595)⋊C411yescharacteristic
362C2×C4(C2×#595)⋊C411yescharacteristic
363C2×C4C2×C4×#59511yescharacteristic
364C2×C4C2×C4⋊#59511yescharacteristic
365C2×C4C2×C22⋊#59511yescharacteristic
366C8—24no—
367C8—344no—
368C8—348no—
369C8—684no—
370C22—172no—
371C22—172no—
372C22—348no—
373C22—341no—
374C22—341no—
375C22—341no—
376C22—341no—
377C22#1176367412yes—
378C22#1176368012yes—
379C22#1176368512yes—
380C22C2×(C2×#595)⋊C411yescharacteristic
381C4—21no—
382C4—21no—
383C4—172no—
384C4—172no—
385C4—172no—
386C4—172no—
387C4—341no—
388C4—341no—
389C4#1176367412yes—
390C4#1176368512yes—
391C4C2×C8×#59511yescharacteristic
392C4C2×#1058753211yescharacteristic
393C4C2×#1058753511yescharacteristic
394C4C2×#1058753611yescharacteristic
395C2—342no—
396C2—342no—
397C2#1454361614yesdirect product factor
398C2C2×#1176367411yescharacteristic
399C2C2×#1176368011yescharacteristic
400C2C2×#1176368511yescharacteristic
subgroupG/H
centerC22×C4C4⋊#595
commutatorC4×C17C2×C4×C8
FrattiniC42C22×#595
FittingC2×C4×C8×C17C4
socleC23×C17#95
prime radicalC23×D17C4⋊C4
cosocleC42×D17C23
hypercenterC2×C4×C8#595
hypocenterC17C2×#1278
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
3. #14543616C2direct (N × H)
35. C2×#63243C8semidirect
100. #63243C2×C8semidirect
222. C2×C17#1278semidirect
270. C17C2×#1278semidirect
397. C2#14543616direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117638282
C2×C4×#632432
#145436162
C2×C4×C8×D172
C2×#127817