Finite Group Databasebeta

← #17958104

Subgroups — #17958104

Order 4352.

682 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 118 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
1#14545009C212yesmaximal, complemented
2#14543705C212yesmaximal, complemented
3#14543704C212yesmaximal, complemented
4C2×C22⋊C8×D17C211yesmaximal, characteristic
5C2×#10587529—22no—
6#11763704—22no—
7C22⋊#63216C2214yescomplemented
8C23×C4×D17C411yescharacteristic
9C22×C8×D17C411yescharacteristic
10C22×C8×D17C2211yescharacteristic
11C2×C22⋊#3622C2211yescharacteristic
12C2×#10587491C411yescharacteristic
13C2×#10587491C2211yescharacteristic
14C22⋊C8×D17—22no—
15C22⋊C8×D17—22no—
16C2×C17×C22⋊C8C411yescharacteristic
17C24×D17C811yescharacteristic
18C23×C4×C17C2×C411yescharacteristic
19C23×Dic17C811yescharacteristic
20C22×C4×D17—21no—
21C22×C4×D17—21no—
22C22×C4×D17—21no—
23C22×C4×D17—21no—
24C22×C4×D17—42no—
25C22×C4×D17—42no—
26C22×C4×D17C811yescharacteristic
27C22×C4×D17C811yescharacteristic
28C22×C4×D17C2×C411yescharacteristic
29C22×C4×D17C2×C411yescharacteristic
30C22×C8×C17C2×C411yescharacteristic
31C22×C8×C17C2×C411yescharacteristic
32C22×#3622C2×C411yescharacteristic
33C22×#3622C2311yescharacteristic
34C2×C8×D17—21no—
35C2×C8×D17—21no—
36C2×C8×D17—42no—
37C2×C8×D17—42no—
38C2×C8×D17D412yes—
39C2×C8×D17D412yes—
40C2×#63216—24no—
41#10587529—44no—
42C17×C22⋊C8—22no—
43C22⋊#3622—22no—
44#10587491—22no—
45#10587491—22no—
46C24×C17C2×C811yescharacteristic
47C23×D17—21no—
48C23×D17—21no—
49C23×D17—22no—
50C23×D17—42no—
51C23×D17—42no—
52C23×D17C1614yescomplemented
53C23×D17C2×C811yescharacteristic
54C23×D17C2×C811yescharacteristic
55C22×C4×C17—21no—
56C22×C4×C17—21no—
57C22×C4×C17—41no—
58C22×C4×C17—41no—
59C22×C4×C17C2×C811yescharacteristic
60C22×C4×C17C22×C411yescharacteristic
61C22×Dic17—21no—
62C22×Dic17—21no—
63C22×Dic17—42no—
64C22×Dic17C2×C811yescharacteristic
65C22×Dic17C2×C811yescharacteristic
66C2×C4×D17—22no—
67C2×C4×D17—22no—
68C2×C4×D17—21no—
69C2×C4×D17—21no—
70C2×C4×D17—21no—
71C2×C4×D17—21no—
72C2×C4×D17—21no—
73C2×C4×D17—21no—
74C2×C4×D17—44no—
75C2×C4×D17—42no—
76C2×C4×D17—42no—
77C2×C4×D17—44no—
78C2×C4×D17—42no—
79C2×C4×D17—42no—
80C2×C4×D17—42no—
81C2×C4×D17—41no—
82C2×C4×D17—41no—
83C2×C4×D17—42no—
84C2×C4×D17C22⋊C411yescharacteristic
85C2×C4×D17C22⋊C411yescharacteristic
86C2×C4×D17M1611yescharacteristic
87C2×C4×D17M1611yescharacteristic
88C2×C8×C17—21no—
89C2×C8×C17—41no—
90C2×C8×C17—41no—
91C2×C8×C17C22⋊C412yes—
92C2×#3622—21no—
93C2×#3622—41no—
94C2×#3622—41no—
95C2×#3622C2×D412yes—
96C8×D17—24no—
97C8×D17—42no—
98C8×D17—42no—
99C8×D17—42no—
100#63216—44no—
101C2×#1314—171nomaximal, Sylow
102C23×C17—21no—
103C23×C17—21no—
104C23×C17—41no—
105C23×C17—41no—
106C23×C17C2×C1612yescomplemented
107C23×C17C22×C811yescharacteristic
108C22×D17—22no—
109C22×D17—22no—
110C22×D17—21no—
111C22×D17—21no—
112C22×D17—24no—
113C22×D17—24no—
114C22×D17—42no—
115C22×D17—42no—
116C22×D17—48no—
117C22×D17—48no—
118C22×D17—42no—
119C22×D17—42no—
120C22×D17—41no—
121C22×D17—41no—
122C22×D17C22⋊C811yescharacteristic
123C22×D17C22⋊C811yescharacteristic
124C22×D17C2×C1612yes—
125C22×D17C2×C1612yescomplemented
126C22×D17M3212yes—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—42no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17—41no—
134C2×C4×C17C2×C22⋊C411yescharacteristic
135C2×C4×C17C2×M1611yescharacteristic
136C2×Dic17—22no—
137C2×Dic17—21no—
138C2×Dic17—42no—
139C2×Dic17—42no—
140C2×Dic17—41no—
141C2×Dic17C22⋊C811yescharacteristic
142C2×Dic17C22⋊C811yescharacteristic
143C4×D17—22no—
144C4×D17—21no—
145C4×D17—21no—
146C4×D17—22no—
147C4×D17—42no—
148C4×D17—42no—
149C4×D17—42no—
150C4×D17—42no—
151C4×D17—41no—
152C4×D17—41no—
153C4×D17—42no—
154C4×D17#9912yes—
155C4×D17#10012yes—
156C8×C17—22no—
157C8×C17—41no—
158#3622—22no—
159#3622—41no—
160C22×C22⋊C8—171no—
161C2×C22⋊C16—172no—
162#1314—172no—
163#1314—172no—
164C22×C17—21no—
165C22×C17—21no—
166C22×C17—22no—
167C22×C17—42no—
168C22×C17—42no—
169C22×C17—41no—
170C22×C17—41no—
171C22×C17C2×C22⋊C811yescharacteristic
172C22×C17C22×C1611yescharacteristic
173C22×C17C2×M3211yescharacteristic
174C2×D17—21no—
175C2×D17—21no—
176C2×D17—24no—
177C2×D17—24no—
178C2×D17—22no—
179C2×D17—48no—
180C2×D17—42no—
181C2×D17—41no—
182C2×D17—41no—
183C2×D17—48no—
184C2×D17—42no—
185C2×D17#32312yes—
186C2×D17C22⋊C1612yes—
187C2×D17C22⋊C1612yes—
188C2×D17#34912yes—
189C4×C17—21no—
190C4×C17—41no—
191C4×C17C2×#9911yescharacteristic
192C4×C17C2×#10011yescharacteristic
193Dic17—21no—
194Dic17—41no—
195Dic17#32312yes—
196C24×C4—171no—
197C23×C8—171no—
198C23×C8—171no—
199C22×C16—342no—
200C2×C22⋊C8—171no—
201C2×C22⋊C8—171no—
202C2×C22⋊C8—171no—
203C2×C22⋊C8—342no—
204C2×C22⋊C8—342no—
205C2×C22⋊C8#59511yescharacteristic
206C22⋊C16—174no—
207C22⋊C16—342no—
208C2×C17—21no—
209C2×C17—21no—
210C2×C17—42no—
211C2×C17C2×#32311yescharacteristic
212C2×C17C2×C22⋊C1611yescharacteristic
213C2×C17C2×#34911yescharacteristic
214D17—22no—
215D17—42no—
216D17#131414yescomplemented
217C25—171no—
218C23×C4—171no—
219C23×C4—171no—
220C23×C4—171no—
221C23×C4—171no—
222C23×C4—171no—
223C23×C4—341no—
224C23×C4—341no—
225C23×C4—341no—
226C23×C4—341no—
227C23×C4—682no—
228C23×C4—682no—
229C23×C4C2×#59511yescharacteristic
230C22×C8—171no—
231C22×C8—172no—
232C22×C8—172no—
233C22×C8—171no—
234C22×C8—341no—
235C22×C8—341no—
236C22×C8—682no—
237C22×C8—682no—
238C22×C8C2×#59511yescharacteristic
239C22×C8C2×#59511yescharacteristic
240C2×C16—344no—
241C2×C16—684no—
242C22⋊C8—22no—
243C22⋊C8—342no—
244C22⋊C8—342no—
245C22⋊C8—342no—
246C17C2×#131411yescharacteristic, complemented, Sylow
247C24—171no—
248C24—171no—
249C24—174no—
250C24—341no—
251C24—341no—
252C24—342no—
253C24—682no—
254C24—682no—
255C24#6324211yescharacteristic
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—171no—
261C22×C4—171no—
262C22×C4—171no—
263C22×C4—171no—
264C22×C4—171no—
265C22×C4—171no—
266C22×C4—342no—
267C22×C4—342no—
268C22×C4—341no—
269C22×C4—341no—
270C22×C4—341no—
271C22×C4—341no—
272C22×C4—341no—
273C22×C4—341no—
274C22×C4—341no—
275C22×C4—341no—
276C22×C4—681no—
277C22×C4—681no—
278C22×C4—682no—
279C22×C4—682no—
280C22×C4—684no—
281C22×C4—684no—
282C22×C4—682no—
283C22×C4—682no—
284C22×C4—682no—
285C22×C4—682no—
286C22×C4—682no—
287C22×C4#6324211yescharacteristic
288C22×C4C22×#59511yescharacteristic
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—172no—
293C2×C8—344no—
294C2×C8—341no—
295C2×C8—682no—
296C2×C8—682no—
297C2×C8—682no—
298C2×C8—681no—
299C2×C8—681no—
300C2×C8C22⋊#59512yes—
301C16—684no—
302C23—21no—
303C23—21no—
304C23—41no—
305C23—41no—
306C23—171no—
307C23—171no—
308C23—172no—
309C23—172no—
310C23—172no—
311C23—342no—
312C23—342no—
313C23—344no—
314C23—344no—
315C23—341no—
316C23—341no—
317C23—681no—
318C23—681no—
319C23—682no—
320C23—682no—
321C23—688no—
322C23—682no—
323C23—688no—
324C23—682no—
325C23#1058752912yescomplemented
326C23C2×#6324211yescharacteristic
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—171no—
335C2×C4—172no—
336C2×C4—172no—
337C2×C4—171no—
338C2×C4—342no—
339C2×C4—342no—
340C2×C4—342no—
341C2×C4—341no—
342C2×C4—341no—
343C2×C4—341no—
344C2×C4—682no—
345C2×C4—682no—
346C2×C4—682no—
347C2×C4—682no—
348C2×C4—682no—
349C2×C4—682no—
350C2×C4—682no—
351C2×C4—681no—
352C2×C4—681no—
353C2×C4—681no—
354C2×C4D17⋊M1611yescharacteristic
355C2×C4C2×C22⋊#59511yescharacteristic
356C8—22no—
357C8—41no—
358C8—342no—
359C8—681no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—42no—
364C22—42no—
365C22—41no—
366C22—41no—
367C22—172no—
368C22—172no—
369C22—172no—
370C22—172no—
371C22—344no—
372C22—344no—
373C22—341no—
374C22—341no—
375C22—342no—
376C22—682no—
377C22—682no—
378C22—688no—
379C22—688no—
380C22—681no—
381C22—681no—
382C22#1176377711yescharacteristic
383C22C2×#1058752911yescharacteristic
384C22#1176386511yescharacteristic
385C4—21no—
386C4—41no—
387C4—172no—
388C4—341no—
389C4—681no—
390C4D17⋊#9911yescharacteristic
391C4D17⋊#10011yescharacteristic
392C2—21no—
393C2—21no—
394C2—42no—
395C2—174no—
396C2—342no—
397C2—682no—
398C2#1454401011yescharacteristic
399C2#1454500911yescharacteristic
400C2#1454501811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#595
commutatorC22×C17C22×C16
FrattiniC22×C4C22×#595
FittingC2×C17×C22⋊C8C4
socleC22×C17C2×C22⋊C8
prime radicalC24×D17C8
cosocleC22×#3622C23
hypercenterC2×C22⋊C8#595
hypocenterC17C2×#1314
LCSG ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #14545009C2semidirect
2. #14543705C2semidirect
3. #14543704C2semidirect
7. C22⋊#63216C22semidirect
52. C23×D17C16semidirect
106. C23×C17C2×C16semidirect
125. C22×D17C2×C16semidirect
216. D17#1314semidirect
246. C17C2×#1314semidirect
325. C23#10587529semidirect

Maximal subgroups

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

subgroupindex
#145450092
#145437052
#145437042
C2×C22⋊C8×D172
C2×#131417