Finite Group Databasebeta

← #17956494

Subgroups — #17956494

Order 4352.

600 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 122 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#14544638C211yesmaximal, characteristic
2#14544510C211yesmaximal, characteristic
3#14543622C212yesmaximal
4#14543622C212yesmaximal
5C2×#11762704C211yesmaximal, characteristic
6C2×C4⋊#3624—21no—
7C2×C22⋊#3624C2212yes—
8C2×C22⋊#3624C2212yes—
9C2×#10587542—21no—
10#11763675—21no—
11#11763675—21no—
12C22×#63225C411yescharacteristic
13C22×#63225C411yescharacteristic
14C22×#63225C411yescharacteristic
15C22×C4×Dic17C2211yescharacteristic
16#11762704—21no—
17#11762704—21no—
18#11762704—21no—
19#11762704—21no—
20C2×#10587502C2211yescharacteristic
21C2×#10587502C2211yescharacteristic
22C22×C4⋊C4×C17C411yescharacteristic
23C23×C4×C17C2×C411yescharacteristic
24C23×C4×C17C2×C411yescharacteristic
25C23×C4×C17C2×C411yescharacteristic
26C23×Dic17C2×C411yescharacteristic
27C23×Dic17C2×C411yescharacteristic
28C23×Dic17C2×C411yescharacteristic
29C23×Dic17C2311yescharacteristic
30C22×#3624—22no—
31C22×#3624—22no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—42no—
35C2×#63225—21no—
36C2×#63225—21no—
37C2×#63225—22no—
38C2×#63225—21no—
39C2×#63225—21no—
40C2×#63225—21no—
41C2×#63225—21no—
42C2×#63225—22no—
43C2×#63225—42no—
44C2×#63225—42no—
45C2×C4×Dic17—42no—
46C2×C4×Dic17D411yescharacteristic
47C2×C4×Dic17D411yescharacteristic
48C2×C4×Dic17D411yescharacteristic
49C2×C4×Dic17D411yescharacteristic
50C22⋊#3624—22no—
51C22⋊#3624—24no—
52C22⋊#3624Q814yes—
53#10587542—42no—
54C4⋊#3624—42no—
55#10587502—21no—
56#10587502—21no—
57#10587502—21no—
58#10587502—21no—
59C24×C17C22×C411yescharacteristic
60C22×C4×C17—21no—
61C22×C4×C17—21no—
62C22×C4×C17—22no—
63C22×C4×C17—22no—
64C22×C4×C17—21no—
65C22×C4×C17—22no—
66C22×C4×C17—41no—
67C22×C4×C17—41no—
68C22×C4×C17—41no—
69C22×C4×C17—41no—
70C22×C4×C17—41no—
71C22×C4×C17C22⋊C411yescharacteristic
72C22×C4×C17C22⋊C411yescharacteristic
73C22×C4×C17M1612yes—
74C22×Dic17—21no—
75C22×Dic17—21no—
76C22×Dic17—22no—
77C22×Dic17—22no—
78C22×Dic17—21no—
79C22×Dic17—21no—
80C22×Dic17—21no—
81C22×Dic17—22no—
82C22×Dic17—41no—
83C22×Dic17—41no—
84C22×Dic17—41no—
85C22×Dic17—41no—
86C22×Dic17—41no—
87C22×Dic17—41no—
88C22×Dic17C22⋊C411yescharacteristic
89C22×Dic17C22⋊C411yescharacteristic
90C22×Dic17M1612yes—
91C22×Dic17C2×D411yescharacteristic
92C22×Dic17C2×D411yescharacteristic
93C22×Dic17C2×Q812yes—
94C22×Dic17#4112yes—
95C2×#3624—24no—
96C2×#3624—42no—
97C2×#3624—42no—
98C2×#3624—42no—
99C2×#3624—42no—
100C2×#3624—42no—
101C4⋊C4×C17—42no—
102C4⋊C4×C17—42no—
103#63225—24no—
104#63225—24no—
105#63225—42no—
106#63225—42no—
107#63225—42no—
108#63225—42no—
109C4×Dic17—22no—
110C4×Dic17—22no—
111C4×Dic17—41no—
112C4×Dic17—41no—
113#9883—171nomaximal, Sylow
114C23×C17—21no—
115C23×C17—21no—
116C23×C17—21no—
117C23×C17—21no—
118C23×C17C2×C22⋊C411yescharacteristic
119C23×C17C4×Q812yes—
120C23×C17C2×M1611yescharacteristic
121C23×C17C2×M1611yescharacteristic
122C23×C17#13112yes—
123C2×C4×C17—21no—
124C2×C4×C17—21no—
125C2×C4×C17—22no—
126C2×C4×C17—21no—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—44no—
130C2×C4×C17—42no—
131C2×C4×C17—41no—
132C2×C4×C17—41no—
133C2×C4×C17—42no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—82no—
138C2×C4×C17#10012yes—
139C2×Dic17—24no—
140C2×Dic17—24no—
141C2×Dic17—21no—
142C2×Dic17—21no—
143C2×Dic17—21no—
144C2×Dic17—21no—
145C2×Dic17—21no—
146C2×Dic17—21no—
147C2×Dic17—21no—
148C2×Dic17—21no—
149C2×Dic17—22no—
150C2×Dic17—42no—
151C2×Dic17—42no—
152C2×Dic17—42no—
153C2×Dic17—41no—
154C2×Dic17—41no—
155C2×Dic17—42no—
156C2×Dic17—41no—
157C2×Dic17—41no—
158C2×Dic17—41no—
159C2×Dic17—82no—
160C2×Dic17#9912yes—
161C2×Dic17#10112yes—
162C2×Dic17C22⋊Q812yes—
163C2×Dic17#12411yescharacteristic
164C2×Dic17C4⋊Q811yescharacteristic
165#3624—44no—
166#3624—82no—
167C2×#389—171no—
168#1797—171no—
169#1749—171no—
170#1280—172no—
171#1280—172no—
172C22×C17—21no—
173C22×C17—21no—
174C22×C17—21no—
175C22×C17—21no—
176C22×C17—22no—
177C22×C17—22no—
178C22×C17—22no—
179C22×C17—22no—
180C22×C17#39111yescharacteristic
181C22×C17#40711yescharacteristic
182C22×C17#40811yescharacteristic
183C22×C17C2×#9911yescharacteristic
184C22×C17#41011yescharacteristic
185C22×C17C2×#10011yescharacteristic
186C22×C17C2×#10111yescharacteristic
187C22×C17#44612yes—
188C22×C17#44612yes—
189C4×C17—22no—
190C4×C17—42no—
191C4×C17—41no—
192C4×C17—81no—
193Dic17—22no—
194Dic17—22no—
195Dic17—22no—
196Dic17—21no—
197Dic17—21no—
198Dic17—42no—
199Dic17—81no—
200C22×C4⋊C4—171no—
201C22×C4⋊C4—171no—
202C22×C4⋊C4—171no—
203C22×C4⋊C4#59511yescharacteristic
204C22×C42—171no—
205C2×C4⋊C8—341no—
206C2×C22⋊C8—172no—
207C2×C22⋊C8—172no—
208C2×#97—341no—
209#389—341no—
210#389—341no—
211#389—341no—
212#389—341no—
213C2×#95—171no—
214C2×#95—171no—
215#336—341no—
216#336—341no—
217C2×C17—22no—
218C2×C17—22no—
219C2×C17#146311yescharacteristic
220C2×C17#146611yescharacteristic
221C2×C17#147011yescharacteristic
222C2×C17#147111yescharacteristic
223C2×C17#198511yescharacteristic
224C2×C17#199611yescharacteristic
225C2×C17#199711yescharacteristic
226C23×C4—171no—
227C23×C4—171no—
228C23×C4—171no—
229C23×C4—171no—
230C23×C4C2×#59511yescharacteristic
231C23×C4C2×#59511yescharacteristic
232C23×C4C2×#59511yescharacteristic
233C22×C8—342no—
234C22×C8—342no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—42no—
238C2×C4⋊C4—341no—
239C2×C4⋊C4—341no—
240C2×C4⋊C4—342no—
241C2×C4⋊C4—342no—
242C2×C4⋊C4—341no—
243C2×C4⋊C4—341no—
244C2×C4⋊C4—341no—
245C2×C4⋊C4—341no—
246C2×C4⋊C4—682no—
247C2×C4⋊C4—682no—
248C2×C42—171no—
249C2×C42—171no—
250C2×C42—171no—
251C2×C42—171no—
252C2×C42—682no—
253C4⋊C8—682no—
254C22⋊C8—174no—
255C22⋊C8—342no—
256C22⋊C8—344no—
257#97—682no—
258#95—341no—
259#95—341no—
260#95—341no—
261#95—341no—
262C17#988311yescharacteristic, complemented, Sylow
263C24C22×#59511yescharacteristic
264C22×C4—21no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—171no—
276C22×C4—171no—
277C22×C4—171no—
278C22×C4—171no—
279C22×C4—172no—
280C22×C4—172no—
281C22×C4—172no—
282C22×C4—342no—
283C22×C4—342no—
284C22×C4—341no—
285C22×C4—341no—
286C22×C4—341no—
287C22×C4—341no—
288C22×C4—341no—
289C22×C4—342no—
290C22×C4—681no—
291C22×C4—681no—
292C22×C4—681no—
293C22×C4—681no—
294C22×C4—681no—
295C22×C4—681no—
296C22×C4#6324312yes—
297C22×C4C22⋊#59511yescharacteristic
298C22×C4C22⋊#59511yescharacteristic
299C2×C8—344no—
300C2×C8—682no—
301C2×C8—682no—
302C2×C8—682no—
303C2×C8—682no—
304C2×C8—682no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—344no—
308C4⋊C4—344no—
309C4⋊C4—682no—
310C4⋊C4—682no—
311C4⋊C4—682no—
312C4⋊C4—682no—
313C42—342no—
314C42—342no—
315C42—681no—
316C42—681no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23C2×#6324311yescharacteristic
322C23D17⋊M1611yescharacteristic
323C23#1058767812yes—
324C23Q8×#59512yes—
325C23C2×C22⋊#59511yescharacteristic
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—82no—
341C2×C4—172no—
342C2×C4—171no—
343C2×C4—171no—
344C2×C4—172no—
345C2×C4—172no—
346C2×C4—344no—
347C2×C4—344no—
348C2×C4—341no—
349C2×C4—341no—
350C2×C4—341no—
351C2×C4—341no—
352C2×C4—341no—
353C2×C4—341no—
354C2×C4—341no—
355C2×C4—341no—
356C2×C4—342no—
357C2×C4—682no—
358C2×C4—682no—
359C2×C4—682no—
360C2×C4—681no—
361C2×C4—681no—
362C2×C4—682no—
363C2×C4—681no—
364C2×C4—681no—
365C2×C4—681no—
366C2×C4—1362no—
367C2×C4#1058755312yes—
368C8—684no—
369C8—1362no—
370C22—22no—
371C22—22no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—22no—
377C22—22no—
378C22(C2×#595)⋊Q811yescharacteristic
379C22#1176378011yescharacteristic
380C22#1176378211yescharacteristic
381C22D17⋊#9911yescharacteristic
382C22#1176378811yescharacteristic
383C22C2×#1058755311yescharacteristic
384C22D17⋊#10111yescharacteristic
385C22#1176385912yes—
386C22#1176386112yes—
387C4—22no—
388C4—42no—
389C4—41no—
390C4—81no—
391C4—342no—
392C4—341no—
393C4—341no—
394C4—342no—
395C4—342no—
396C4—682no—
397C4—1361no—
398C2—22no—
399C2—22no—
400C2#1454403311yescharacteristic
401C2#1454404311yescharacteristic
402C2#1454405611yescharacteristic
403C2#1454406011yescharacteristic
404C2#1454495711yescharacteristic
405C2#1454497511yescharacteristic
406C2#1454497611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutator, prime radicalC24×C17C22×C4
FrattiniC24C22×#595
FittingC22×C4⋊C4×C17C4
socleC23×C17C2×C22⋊C4
cosocleC23×Dic17C23
hypercenterC22×C4⋊C4#595
hypocenterC17#9883
LCSG ▷ C24×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
262. C17#9883semidirect

Maximal subgroups

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

subgroupindex
#145446382
#145445102
#145436222
C2×#117627042
#988317