Finite Group Databasebeta

← C2×#14543687 #17951601

Subgroups — C2×#14543687 #17951601

Order 4352.

942 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763779C212yesmaximal
2#14543687C214yesmaximal, direct product factor
3C2×#11762670C211yesmaximal, characteristic
4C22×#63247—22no—
5#11763779—22no—
6#11763779—22no—
7#11763779C414yescomplemented
8#11763779C2214yes—
9C2×C22⋊#3624—22no—
10C2×C22⋊#3624C414yescomplemented
11C24×Dic17C2211yescharacteristic
12C22×C22⋊Dic17C411yescharacteristic
13#11762670—22no—
14#11762670C412yes—
15#11762670C2212yes—
16C2×#10587502—22no—
17C22×C22⋊C4×C17C411yescharacteristic
18C25×C17C2×C411yescharacteristic
19C23×C4×C17—21no—
20C23×Dic17—21no—
21C23×Dic17—42no—
22C23×Dic17—42no—
23C23×Dic17C2×C411yescharacteristic
24C23×Dic17C2×C412yes—
25C23×Dic17C2×C412yes—
26C23×Dic17D412yes—
27C23×Dic17D411yescharacteristic
28C23×Dic17D411yescharacteristic
29C23×Dic17D412yes—
30C23×Dic17Q811yescharacteristic
31C23×Dic17Q811yescharacteristic
32C23×Dic17C2311yescharacteristic
33C2×#63247—24no—
34C2×#63247—24no—
35C2×#63247—44no—
36C2×#63247—44no—
37C22×#3624—24no—
38C2×C22⋊C4×C17—21no—
39C2×C22⋊C4×C17—42no—
40C2×C22⋊C4×C17C2×C412yes—
41C2×C22⋊Dic17—21no—
42C2×C22⋊Dic17—42no—
43C2×C22⋊Dic17C2×C412yes—
44C22⋊#3624—24no—
45C22⋊#3624—24no—
46C22⋊#3624—24no—
47C22⋊#3624C2×C418yescomplemented
48#10587502—24no—
49#10587502—24no—
50C24×C17—22no—
51C24×C17—22no—
52C24×C17—44no—
53C24×C17C4211yescharacteristic
54C24×C17C4211yescharacteristic
55C24×C17C22⋊C411yescharacteristic
56C24×C17C22⋊C411yescharacteristic
57C24×C17C4⋊C411yescharacteristic
58C24×C17C4⋊C411yescharacteristic
59C24×C17C22×C411yescharacteristic
60C22×C4×C17—22no—
61C22×C4×C17—44no—
62C22×C4×C17—42no—
63C22×Dic17—24no—
64C22×Dic17—24no—
65C22×Dic17—22no—
66C22×Dic17—44no—
67C22×Dic17—44no—
68C22×Dic17—41no—
69C22×Dic17—41no—
70C22×Dic17—42no—
71C22×Dic17—42no—
72C22×Dic17—42no—
73C22×Dic17—42no—
74C22×Dic17—42no—
75C22×Dic17—42no—
76C22×Dic17—41no—
77C22×Dic17—41no—
78C22×Dic17—44no—
79C22×Dic17—42no—
80C22×Dic17C4212yes—
81C22×Dic17C22⋊C412yes—
82C22×Dic17C22⋊C412yes—
83C22×Dic17C22⋊C412yes—
84C22×Dic17C22⋊C412yes—
85C22×Dic17C22⋊C412yes—
86C22×Dic17C4⋊C412yes—
87C22×Dic17C4⋊C412yes—
88C22×Dic17C4⋊C411yescharacteristic
89C22×Dic17C4⋊C411yescharacteristic
90C22×Dic17C4⋊C412yes—
91C22×Dic17C4⋊C412yes—
92C22×Dic17C22×C412yes—
93C22×Dic17C2×D412yes—
94C22×Dic17C2×D411yescharacteristic
95C22×Dic17C2×Q811yescharacteristic
96#63247—48no—
97#63247—44no—
98#63247—44no—
99C2×#3624—28no—
100C2×#3624—48no—
101C22⋊C4×C17—42no—
102C22⋊C4×C17—42no—
103C22⋊Dic17—42no—
104C22⋊Dic17—42no—
105C2×#1306—171nomaximal, Sylow
106C23×C17—24no—
107C23×C17—22no—
108C23×C17—22no—
109C23×C17—22no—
110C23×C17—22no—
111C23×C17—24no—
112C23×C17—24no—
113C23×C17—21no—
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—21no—
117C23×C17—42no—
118C23×C17—42no—
119C23×C17—42no—
120C23×C17—42no—
121C23×C17—48no—
122C23×C17—48no—
123C23×C17#9511yescharacteristic
124C23×C17#9511yescharacteristic
125C23×C17#9511yescharacteristic
126C23×C17#9511yescharacteristic
127C23×C17#9912yes—
128C23×C17#9912yes—
129C23×C17C2×C4211yescharacteristic
130C23×C17C2×C22⋊C411yescharacteristic
131C23×C17C2×C4⋊C411yescharacteristic
132C2×C4×C17—44no—
133C2×C4×C17—42no—
134C2×C4×C17—84no—
135C2×Dic17—24no—
136C2×Dic17—24no—
137C2×Dic17—24no—
138C2×Dic17—24no—
139C2×Dic17—22no—
140C2×Dic17—22no—
141C2×Dic17—22no—
142C2×Dic17—22no—
143C2×Dic17—42no—
144C2×Dic17—42no—
145C2×Dic17—42no—
146C2×Dic17—41no—
147C2×Dic17—41no—
148C2×Dic17—42no—
149C2×Dic17—42no—
150C2×Dic17—42no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17—44no—
154C2×Dic17—42no—
155C2×Dic17—84no—
156C2×Dic17#9512yes—
157C2×Dic17#9512yes—
158C2×Dic17C2×C22⋊C412yes—
159C2×Dic17C2×C4⋊C412yes—
160#3624—48no—
161C2×#407—172no—
162C2×#381—171no—
163#1306—174no—
164C22×C17—24no—
165C22×C17—24no—
166C22×C17—22no—
167C22×C17—22no—
168C22×C17—21no—
169C22×C17—21no—
170C22×C17—21no—
171C22×C17—21no—
172C22×C17—22no—
173C22×C17—22no—
174C22×C17—22no—
175C22×C17—22no—
176C22×C17—42no—
177C22×C17—42no—
178C22×C17—42no—
179C22×C17—42no—
180C22×C17—44no—
181C22×C17—44no—
182C22×C17—44no—
183C22×C17—44no—
184C22×C17#34212yes—
185C22×C17#34212yes—
186C22×C17#34414yes—
187C22×C17C2×#9511yescharacteristic
188C22×C17C2×#9911yescharacteristic
189C22×C17C2×#9911yescharacteristic
190C4×C17—82no—
191Dic17—22no—
192Dic17—22no—
193Dic17—22no—
194Dic17—22no—
195Dic17—82no—
196C24×C4—171no—
197C22×M16—342no—
198C22×C22⋊C4—171no—
199C22×C22⋊C4#59511yescharacteristic
200#407—174no—
201#407—174no—
202#407—342no—
203#407—342no—
204C2×C22⋊C8—174no—
205C2×C22⋊C8—342no—
206#381—172no—
207#381—172no—
208#381—342no—
209C2×#95—342no—
210C2×C17—21no—
211C2×C17—21no—
212C2×C17—22no—
213C2×C17—41no—
214C2×C17—41no—
215C2×C17—41no—
216C2×C17—41no—
217C2×C17#130614yescomplemented
218C2×C17C2×#34211yescharacteristic
219C2×C17C2×#34412yes—
220C25C2×#59511yescharacteristic
221C23×C4—21no—
222C23×C4—172no—
223C23×C4—172no—
224C23×C4—172no—
225C23×C4—171no—
226C23×C4—171no—
227C23×C4—171no—
228C23×C4—171no—
229C23×C4—172no—
230C23×C4—171no—
231C23×C4—171no—
232C23×C4—341no—
233C23×C4—682no—
234C23×C4—682no—
235C2×M16—344no—
236C2×M16—344no—
237C2×M16—684no—
238C2×M16—684no—
239C22×C8—344no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—42no—
242C2×C22⋊C4—172no—
243C2×C22⋊C4—341no—
244C2×C22⋊C4—682no—
245C2×C22⋊C4C2×#59512yes—
246C22⋊C8—178no—
247C22⋊C8—344no—
248C22⋊C8—344no—
249C22⋊C8—344no—
250#95—344no—
251#95—344no—
252C17C2×#130611yescharacteristic, complemented, Sylow
253C24—22no—
254C24—22no—
255C24—44no—
256C24C4×#59511yescharacteristic
257C24C4×#59511yescharacteristic
258C24C4⋊#59511yescharacteristic
259C24C4⋊#59511yescharacteristic
260C24C22⋊#59511yescharacteristic
261C24C22⋊#59511yescharacteristic
262C24C22×#59511yescharacteristic
263C22×C4—22no—
264C22×C4—44no—
265C22×C4—42no—
266C22×C4—172no—
267C22×C4—172no—
268C22×C4—172no—
269C22×C4—172no—
270C22×C4—172no—
271C22×C4—172no—
272C22×C4—172no—
273C22×C4—172no—
274C22×C4—171no—
275C22×C4—171no—
276C22×C4—171no—
277C22×C4—171no—
278C22×C4—172no—
279C22×C4—172no—
280C22×C4—172no—
281C22×C4—172no—
282C22×C4—344no—
283C22×C4—344no—
284C22×C4—342no—
285C22×C4—681no—
286C22×C4—682no—
287C22×C4—681no—
288C22×C4—681no—
289C22×C4—682no—
290C22×C4—681no—
291C22×C4—682no—
292C22×C4—684no—
293C22×C4—682no—
294C22×C4—684no—
295C22×C4—682no—
296C22×C4—682no—
297C22×C4—684no—
298C22×C4—682no—
299M16—684no—
300M16—684no—
301M16—688no—
302C2×C8—348no—
303C2×C8—688no—
304C22⋊C4—42no—
305C22⋊C4—42no—
306C22⋊C4—682no—
307C22⋊C4—682no—
308C23—24no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—22no—
314C23—22no—
315C23—22no—
316C23—22no—
317C23—24no—
318C23—24no—
319C23—42no—
320C23—42no—
321C23—42no—
322C23—42no—
323C23—48no—
324C23—48no—
325C23#1058753912yes—
326C23(C2×#595)⋊C411yescharacteristic
327C23(C2×#595)⋊C411yescharacteristic
328C23(C2×#595)⋊C411yescharacteristic
329C23(C2×#595)⋊C411yescharacteristic
330C23#1058755112yes—
331C23C2×C4×#59511yescharacteristic
332C23C2×C4⋊#59511yescharacteristic
333C23C2×C22⋊#59511yescharacteristic
334C2×C4—44no—
335C2×C4—42no—
336C2×C4—84no—
337C2×C4—172no—
338C2×C4—172no—
339C2×C4—172no—
340C2×C4—172no—
341C2×C4—342no—
342C2×C4—342no—
343C2×C4—342no—
344C2×C4—342no—
345C2×C4—344no—
346C2×C4—344no—
347C2×C4—344no—
348C2×C4—344no—
349C2×C4—681no—
350C2×C4—682no—
351C2×C4—682no—
352C2×C4—682no—
353C2×C4—682no—
354C2×C4—681no—
355C2×C4—681no—
356C2×C4—681no—
357C2×C4—682no—
358C2×C4—682no—
359C2×C4—684no—
360C2×C4—682no—
361C2×C4—1364no—
362C8—688no—
363C22—24no—
364C22—24no—
365C22—22no—
366C22—22no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—42no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—44no—
380C22—44no—
381C22—44no—
382C22—44no—
383C22#1176368712yes—
384C22#1176368712yes—
385C22#1176369014yes—
386C22C2×(C2×#595)⋊C411yescharacteristic
387C22C2×#1058755111yescharacteristic
388C22C2×#1058753911yescharacteristic
389C4—82no—
390C4—342no—
391C4—342no—
392C4—342no—
393C4—342no—
394C4—1362no—
395C2—21no—
396C2—21no—
397C2—22no—
398C2—41no—
399C2—41no—
400C2—41no—
401C2—41no—
402C2#1454368714yesdirect product factor
403C2C2×#1176368711yescharacteristic
404C2C2×#1176369012yes—
subgroupG/H
centerC23(C2×#595)⋊C4
commutatorC23×C17C2×C42
FrattiniC24C22×#595
FittingC22×C22⋊C4×C17C4
socleC23×C17#95
prime radicalC25×C17C2×C4
cosocleC23×Dic17C23
hypercenterC22×C22⋊C4#595
hypocenterC17C2×#1306
LCSG ▷ C23×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #14543687C2direct (N × H)
7. #11763779C4semidirect
10. C2×C22⋊#3624C4semidirect
47. C22⋊#3624C2×C4semidirect
217. C2×C17#1306semidirect
252. C17C2×#1306semidirect
402. C2#14543687direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637792
#145436872
C2×#117626702
C2×#130617