Finite Group Databasebeta

← C2×#14543656 #17951083

Subgroups — C2×#14543656 #17951083

Order 4352.

906 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763780C212yesmaximal
2#14543656C214yesmaximal, direct product factor
3C22×#10587491C211yesmaximal, characteristic
4C22×#63243—22no—
5#11763780—22no—
6#11763780—22no—
7#11763780C414yes—
8#11763780C2214yes—
9C2×#10587543C414yes—
10C2×C22⋊#3624—22no—
11C23×C4×D17C2211yescharacteristic
12C23×#3622C411yescharacteristic
13C2×#10587491—22no—
14C2×#10587491—22no—
15C2×#10587491C412yes—
16C2×#10587491C2212yes—
17C23×C8×C17C411yescharacteristic
18C24×D17Q811yescharacteristic
19C23×C4×C17C2×C411yescharacteristic
20C23×Dic17D411yescharacteristic
21C22×C4×D17—42no—
22C22×C4×D17—42no—
23C22×C4×D17C2×C411yescharacteristic
24C22×C4×D17C2×C412yes—
25C22×C4×D17C2×C412yes—
26C22×C4×D17D412yes—
27C22×C4×D17D411yescharacteristic
28C22×C4×D17D412yes—
29C22×C4×D17Q811yescharacteristic
30C22×C4×D17C2311yescharacteristic
31C22×#3624—24no—
32C2×#63243—24no—
33C2×#63243—24no—
34C2×#63243—44no—
35C2×#63243—44no—
36C22×C8×C17—21no—
37C22×C8×C17—21no—
38C22×C8×C17—42no—
39C22×C8×C17C2×C412yes—
40C22×#3622—21no—
41C22×#3622—21no—
42C22×#3622—42no—
43C22×#3622C2×C412yes—
44C22⋊#3624—24no—
45C22⋊#3624—24no—
46#10587543—24no—
47#10587543C2×C418yes—
48#10587491—24no—
49#10587491—24no—
50C24×C17C4⋊C411yescharacteristic
51C23×D17—22no—
52C23×D17—22no—
53C23×D17—42no—
54C23×D17—42no—
55C23×D17C4⋊C412yes—
56C23×D17C4⋊C411yescharacteristic
57C23×D17C4⋊C412yes—
58C23×D17C2×Q811yescharacteristic
59C22×C4×C17—22no—
60C22×C4×C17—22no—
61C22×C4×C17C4211yescharacteristic
62C22×C4×C17C4211yescharacteristic
63C22×C4×C17C22⋊C411yescharacteristic
64C22×C4×C17C22⋊C411yescharacteristic
65C22×C4×C17C4⋊C411yescharacteristic
66C22×C4×C17C22×C411yescharacteristic
67C22×Dic17—42no—
68C22×Dic17C22⋊C412yes—
69C22×Dic17C22⋊C412yes—
70C22×Dic17C4⋊C411yescharacteristic
71C22×Dic17C2×D411yescharacteristic
72C2×C4×D17—24no—
73C2×C4×D17—24no—
74C2×C4×D17—44no—
75C2×C4×D17—41no—
76C2×C4×D17—41no—
77C2×C4×D17—42no—
78C2×C4×D17—42no—
79C2×C4×D17—42no—
80C2×C4×D17—42no—
81C2×C4×D17—41no—
82C2×C4×D17—41no—
83C2×C4×D17—44no—
84C2×C4×D17C4212yes—
85C2×C4×D17C22⋊C412yes—
86C2×C4×D17C22⋊C412yes—
87C2×C4×D17C22⋊C412yes—
88C2×C4×D17C4⋊C412yes—
89C2×C4×D17C4⋊C412yes—
90C2×C4×D17C22×C412yes—
91C2×C4×D17C2×D412yes—
92C2×#3624—28no—
93C2×#3624—48no—
94#63243—48no—
95#63243—44no—
96#63243—44no—
97C2×C8×C17—22no—
98C2×C8×C17—42no—
99C2×C8×C17—42no—
100C2×C8×C17—42no—
101C2×#3622—22no—
102C2×#3622—42no—
103C2×#3622—42no—
104C2×#3622—42no—
105C2×#1293—171nomaximal, Sylow
106C23×C17—22no—
107C23×C17—22no—
108C23×C17#9511yescharacteristic
109C23×C17#9511yescharacteristic
110C23×C17#10812yes—
111C23×C17#10812yes—
112C23×C17C2×C4⋊C411yescharacteristic
113C22×D17—24no—
114C22×D17—24no—
115C22×D17—24no—
116C22×D17—24no—
117C22×D17—21no—
118C22×D17—21no—
119C22×D17—21no—
120C22×D17—21no—
121C22×D17—41no—
122C22×D17—42no—
123C22×D17—41no—
124C22×D17—41no—
125C22×D17—42no—
126C22×D17—41no—
127C22×D17—48no—
128C22×D17—48no—
129C22×D17#9512yes—
130C22×D17C2×C4⋊C412yes—
131C2×C4×C17—22no—
132C2×C4×C17—22no—
133C2×C4×C17—22no—
134C2×C4×C17—21no—
135C2×C4×C17—21no—
136C2×C4×C17—21no—
137C2×C4×C17—21no—
138C2×C4×C17#9511yescharacteristic
139C2×C4×C17#9511yescharacteristic
140C2×C4×C17#9912yes—
141C2×C4×C17#9912yes—
142C2×C4×C17C2×C4211yescharacteristic
143C2×C4×C17C2×C22⋊C411yescharacteristic
144C2×Dic17—24no—
145C2×Dic17—42no—
146C2×Dic17—41no—
147C2×Dic17—41no—
148C2×Dic17#9512yes—
149C2×Dic17C2×C22⋊C412yes—
150C4×D17—24no—
151C4×D17—24no—
152C4×D17—22no—
153C4×D17—22no—
154C4×D17—22no—
155C4×D17—22no—
156C4×D17—42no—
157C4×D17—42no—
158C4×D17—42no—
159C4×D17—42no—
160#3624—48no—
161C8×C17—42no—
162#3622—42no—
163C2×#407—172no—
164C22×C22⋊C8—171no—
165#1293—174no—
166C22×C17—24no—
167C22×C17—24no—
168C22×C17—21no—
169C22×C17—21no—
170C22×C17—21no—
171C22×C17—21no—
172C22×C17#33812yes—
173C22×C17#34112yes—
174C22×C17#34112yes—
175C22×C17#34212yes—
176C22×C17C2×#9511yescharacteristic
177C22×C17C2×#10811yescharacteristic
178C22×C17C2×#10811yescharacteristic
179C2×D17—22no—
180C2×D17—22no—
181C2×D17—22no—
182C2×D17—22no—
183C2×D17—22no—
184C2×D17—22no—
185C2×D17—48no—
186C2×D17—42no—
187C2×D17—42no—
188C2×D17—42no—
189C2×D17—42no—
190C2×D17—48no—
191C4×C17—21no—
192C4×C17—21no—
193C4×C17#34212yes—
194C4×C17C2×#9911yescharacteristic
195C4×C17C2×#9911yescharacteristic
196Dic17—22no—
197Dic17—22no—
198C24×C4—171no—
199C22×M16—342no—
200C23×C8—171no—
201C23×C8#59511yescharacteristic
202#407—174no—
203#407—174no—
204#407—342no—
205#407—342no—
206C2×C22⋊C8—174no—
207C2×C22⋊C8—172no—
208C2×C22⋊C8—172no—
209C2×C22⋊C8—342no—
210C2×C22⋊C8—342no—
211C2×C22⋊C8—342no—
212C2×C17—22no—
213C2×C17—21no—
214C2×C17—21no—
215C2×C17#129314yescomplemented
216C2×C17C2×#33811yescharacteristic
217C2×C17C2×#34111yescharacteristic
218C2×C17C2×#34211yescharacteristic
219D17—42no—
220D17—42no—
221C25—171no—
222C23×C4—171no—
223C23×C4—172no—
224C23×C4—172no—
225C23×C4—172no—
226C23×C4—171no—
227C23×C4—171no—
228C23×C4—172no—
229C23×C4—171no—
230C23×C4—171no—
231C23×C4—682no—
232C23×C4—682no—
233C23×C4C2×#59511yescharacteristic
234C2×M16—344no—
235C2×M16—344no—
236C2×M16—684no—
237C2×M16—684no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—42no—
241C22×C8—172no—
242C22×C8—344no—
243C22×C8—341no—
244C22×C8—341no—
245C22×C8—682no—
246C22×C8C2×#59512yes—
247C22⋊C8—178no—
248C22⋊C8—344no—
249C22⋊C8—344no—
250C22⋊C8—344no—
251C22⋊C8—344no—
252C22⋊C8—344no—
253C17C2×#129311yescharacteristic, complemented, Sylow
254C24—172no—
255C24—171no—
256C24—171no—
257C24—172no—
258C24—342no—
259C24—342no—
260C24—682no—
261C24—682no—
262C24C4⋊#59511yescharacteristic
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—172no—
266C22×C4—171no—
267C22×C4—171no—
268C22×C4—172no—
269C22×C4—172no—
270C22×C4—172no—
271C22×C4—172no—
272C22×C4—172no—
273C22×C4—172no—
274C22×C4—172no—
275C22×C4—172no—
276C22×C4—172no—
277C22×C4—344no—
278C22×C4—344no—
279C22×C4—682no—
280C22×C4—681no—
281C22×C4—681no—
282C22×C4—682no—
283C22×C4—681no—
284C22×C4—681no—
285C22×C4—684no—
286C22×C4—682no—
287C22×C4—682no—
288C22×C4—684no—
289C22×C4—682no—
290C22×C4C4×#59511yescharacteristic
291C22×C4C4×#59511yescharacteristic
292C22×C4C4⋊#59511yescharacteristic
293C22×C4C22⋊#59511yescharacteristic
294C22×C4C22⋊#59511yescharacteristic
295C22×C4C22×#59511yescharacteristic
296M16—684no—
297M16—684no—
298M16—688no—
299C2×C8—22no—
300C2×C8—42no—
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—348no—
304C2×C8—342no—
305C2×C8—682no—
306C2×C8—688no—
307C2×C8—682no—
308C2×C8—682no—
309C23—22no—
310C23—22no—
311C23—172no—
312C23—172no—
313C23—341no—
314C23—341no—
315C23—341no—
316C23—341no—
317C23—344no—
318C23—344no—
319C23—344no—
320C23—344no—
321C23—681no—
322C23—681no—
323C23—682no—
324C23—681no—
325C23—681no—
326C23—682no—
327C23—688no—
328C23—688no—
329C23#1058753512yes—
330C23#1058753612yes—
331C23(C2×#595)⋊C411yescharacteristic
332C23(C2×#595)⋊C411yescharacteristic
333C23C2×C4⋊#59511yescharacteristic
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—172no—
342C2×C4—172no—
343C2×C4—344no—
344C2×C4—342no—
345C2×C4—342no—
346C2×C4—342no—
347C2×C4—342no—
348C2×C4—344no—
349C2×C4—344no—
350C2×C4—682no—
351C2×C4—682no—
352C2×C4—682no—
353C2×C4—682no—
354C2×C4—681no—
355C2×C4—682no—
356C2×C4—681no—
357C2×C4#1058753912yes—
358C2×C4(C2×#595)⋊C411yescharacteristic
359C2×C4(C2×#595)⋊C411yescharacteristic
360C2×C4#1058755112yes—
361C2×C4C2×C4×#59511yescharacteristic
362C2×C4C2×C22⋊#59511yescharacteristic
363C8—42no—
364C8—688no—
365C8—682no—
366C22—24no—
367C22—24no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—342no—
373C22—342no—
374C22—342no—
375C22—342no—
376C22—342no—
377C22—342no—
378C22—682no—
379C22—682no—
380C22—682no—
381C22—682no—
382C22—688no—
383C22—688no—
384C22#1176367812yes—
385C22#1176368512yes—
386C22#1176368512yes—
387C22#1176368712yes—
388C22C2×(C2×#595)⋊C411yescharacteristic
389C22C2×#1058753511yescharacteristic
390C22C2×#1058753611yescharacteristic
391C4—21no—
392C4—21no—
393C4—342no—
394C4—342no—
395C4#1176368712yes—
396C4C2×#1058755111yescharacteristic
397C4C2×#1058753911yescharacteristic
398C2—21no—
399C2—21no—
400C2—22no—
401C2—682no—
402C2—682no—
403C2#1454365614yesdirect product factor
404C2C2×#1176367811yescharacteristic
405C2C2×#1176368511yescharacteristic
406C2C2×#1176368711yescharacteristic
subgroupG/H
centerC23(C2×#595)⋊C4
commutatorC2×C4×C17C2×C42
FrattiniC22×C4C22×#595
FittingC23×C8×C17C4
socleC23×C17#95
prime radicalC24×D17Q8
cosocleC22×C4×D17C23
hypercenterC23×C8#595
hypocenterC17C2×#1293
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
2. #14543656C2direct (N × H)
215. C2×C17#1293semidirect
253. C17C2×#1293semidirect
403. C2#14543656direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117637802
#145436562
C22×#105874912
C2×#129317