Finite Group Databasebeta

← #17956506

Subgroups — #17956506

Order 4352.

598 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 106 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#14544511C211yesmaximal, characteristic
2#14543962C211yesmaximal, characteristic
3#14543657C212yesmaximal
4#14543657C212yesmaximal
5#14537093C211yesmaximal, characteristic
6C22×C4⋊#595—21no—
7C2×#10587543C2212yes—
8C2×#10587542—21no—
9C2×(C2×#595)⋊C4—21no—
10C2×(C2×#595)⋊C4C2212yes—
11#11763675—21no—
12C2×#10587576C411yescharacteristic, complemented
13C2×C42×D17C2211yescharacteristic
14#11762707C411yescharacteristic, complemented
15#11762695—21no—
16#11762691—21no—
17#11762683—21no—
18#11762680—21no—
19#11762674C411yescharacteristic, complemented
20#11762666C2211yescharacteristic
21#11762666C2211yescharacteristic
22C17×#389C411yescharacteristic, complemented
23C23×#595—22no—
24C22×C4×D17D411yescharacteristic
25C22×C4×D17D411yescharacteristic
26C22×C4×D17C2311yescharacteristic
27C22×#3624—22no—
28C2×C4⋊#595—24no—
29C2×C4⋊#595—42no—
30C2×C4⋊#595—42no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17C2×C411yescharacteristic
33C2×C4⋊C4×C17C2×C411yescharacteristic
34C2×C42×C17C2×C411yescharacteristic
35C2×#63227—21no—
36C2×#63227—21no—
37C2×C4⋊Dic17—21no—
38C2×C4⋊Dic17C2×C411yescharacteristic
39C2×C4⋊Dic17C2×C411yescharacteristic
40C2×#63225—21no—
41C2×#63225—21no—
42C2×C4×Dic17C2×C411yescharacteristic
43C2×C4×Dic17D411yescharacteristic
44C2×C4×Dic17D411yescharacteristic
45#10587576—42no—
46C42×D17—42no—
47(C2×#595)⋊C4—24no—
48(C2×#595)⋊C4—42no—
49#10587543—22no—
50#10587543Q814yes—
51#10587542—42no—
52C17×#95—21no—
53#10587502—21no—
54#10587502—21no—
55#10587502—21no—
56#10587502—21no—
57#10587502—21no—
58C23×D17C2×D411yescharacteristic
59C22×#595—24no—
60C22×#595—42no—
61C22×#595—42no—
62C22×#595—42no—
63C22×#595—42no—
64C22×#595—42no—
65C22×#595—42no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17C22⋊C411yescharacteristic
69C22×C4×C17C22⋊C411yescharacteristic
70C22×C4×C17C22×C411yescharacteristic
71C22×Dic17—21no—
72C22×Dic17—21no—
73C22×Dic17C22⋊C411yescharacteristic
74C22×Dic17C22⋊C411yescharacteristic
75C22×Dic17C2×D411yescharacteristic
76C2×C4×D17—21no—
77C2×C4×D17—21no—
78C2×C4×D17—22no—
79C2×C4×D17—22no—
80C2×C4×D17—21no—
81C2×C4×D17—21no—
82C2×C4×D17—41no—
83C2×C4×D17—41no—
84C2×C4×D17—41no—
85C2×C4×D17—41no—
86C2×C4×D17C2×Q812yes—
87C2×C4×D17#4112yes—
88C2×#3624—24no—
89C2×#3624—42no—
90C2×#3624—42no—
91C4⋊#595—48no—
92C4⋊C4×C17—41no—
93C4⋊C4×C17—41no—
94C4⋊C4×C17—42no—
95C42×C17—41no—
96#63227—41no—
97#63227—41no—
98#63227—41no—
99#63227—41no—
100C4⋊Dic17—42no—
101C4⋊Dic17—41no—
102C4⋊Dic17—41no—
103#63225—42no—
104#63225—42no—
105C4×Dic17—22no—
106C4×Dic17—22no—
107C4×Dic17—41no—
108#9887—171nomaximal, Sylow
109C23×C17C2×C22⋊C411yescharacteristic
110C22×D17—21no—
111C22×D17—21no—
112C22×D17—21no—
113C22×D17—21no—
114C22×D17#12411yescharacteristic
115C22×D17C4⋊Q811yescharacteristic
116C22×D17AGL(1,ℤ/8)11yescharacteristic
117C22×D17AGL(1,ℤ/8)11yescharacteristic
118C22×D17#13711yescharacteristic
119C22×D17#13711yescharacteristic
120C2×#595—44no—
121C2×#595—44no—
122C2×#595—44no—
123C2×#595—82no—
124C2×#595—82no—
125C2×#595—82no—
126C2×#595—82no—
127C2×C4×C17—21no—
128C2×C4×C17—21no—
129C2×C4×C17—21no—
130C2×C4×C17—21no—
131C2×C4×C17—21no—
132C2×C4×C17—21no—
133C2×C4×C17—21no—
134C2×C4×C17—41no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17#10412yes—
141C2×C4×C17C4×Q812yes—
142C2×Dic17—21no—
143C2×Dic17—21no—
144C2×Dic17—21no—
145C2×Dic17—21no—
146C2×Dic17—21no—
147C2×Dic17—21no—
148C2×Dic17—21no—
149C2×Dic17—41no—
150C2×Dic17—41no—
151C2×Dic17—41no—
152C2×Dic17—41no—
153C2×Dic17—41no—
154C2×Dic17—41no—
155C2×Dic17#9912yes—
156C2×Dic17C22⋊Q812yes—
157C4×D17—24no—
158C4×D17—24no—
159C4×D17—42no—
160C4×D17—42no—
161C4×D17—42no—
162C4×D17—42no—
163#3624—44no—
164#2851—171no—
165#1749—171no—
166C4⋊#95—171no—
167#1294—172no—
168#1294—172no—
169C22×C17#39111yescharacteristic
170C22×C17C2×#9911yescharacteristic
171C22×C17#41011yescharacteristic
172C22×C17#41711yescharacteristic
173C22×C17#41711yescharacteristic
174C22×C17C2×#10411yescharacteristic
175C22×C17#42111yescharacteristic
176C2×D17—21no—
177C2×D17—21no—
178C2×D17—21no—
179C2×D17—21no—
180C2×D17—21no—
181C2×D17—21no—
182C2×D17—21no—
183C2×D17—21no—
184C2×D17—21no—
185C2×D17—21no—
186C2×D17—21no—
187C2×D17—21no—
188C2×D17#49011yescharacteristic
189C2×D17#49111yescharacteristic
190C2×D17#50111yescharacteristic
191C2×D17#50111yescharacteristic
192#595—84no—
193C4×C17—22no—
194C4×C17—22no—
195C4×C17—41no—
196C4×C17—81no—
197C4×C17—81no—
198Dic17—22no—
199Dic17—22no—
200Dic17—41no—
201Dic17—81no—
202Dic17—81no—
203C2×#125—171no—
204C22×C4⋊C4—341no—
205C22×C42—171no—
206C2×C22⋊C8—172no—
207C2×#97—341no—
208#389—171no—
209#389#59511yescharacteristic, complemented
210#387—341no—
211#387—341no—
212#385—341no—
213#385—341no—
214#382—171no—
215#380—171no—
216#380—171no—
217C2×#95—172no—
218C2×#95—341no—
219#336—341no—
220C2×C17#150411yescharacteristic
221C2×C17#150911yescharacteristic
222C2×C17#151211yescharacteristic
223C2×C17#151311yescharacteristic
224C2×C17#198611yescharacteristic
225C2×C17#199211yescharacteristic
226C2×C17#199611yescharacteristic
227D17—21no—
228D17—21no—
229D17—21no—
230D17—21no—
231C23×C4—171no—
232C23×C4—171no—
233C23×C4—171no—
234C23×C4—342no—
235C22×C8—342no—
236#125—682no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—171no—
239C2×C4⋊C4—171no—
240C2×C4⋊C4—341no—
241C2×C4⋊C4—341no—
242C2×C4⋊C4—344no—
243C2×C4⋊C4—341no—
244C2×C4⋊C4—682no—
245C2×C4⋊C4—682no—
246C2×C4⋊C4C2×#59511yescharacteristic
247C2×C4⋊C4C2×#59511yescharacteristic
248C2×C22⋊C4—341no—
249C2×C22⋊C4—341no—
250C2×C42—171no—
251C2×C42—171no—
252C2×C42—171no—
253C2×C42—682no—
254C2×C42C2×#59511yescharacteristic
255C22⋊C8—174no—
256C22⋊C8—342no—
257#97—682no—
258#95—21no—
259#95—341no—
260#95—341no—
261#95—341no—
262#95—341no—
263#95—344no—
264#95—341no—
265#95—682no—
266C17#988711yescharacteristic, complemented, Sylow
267C24—171no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—171no—
271C22×C4—171no—
272C22×C4—172no—
273C22×C4—172no—
274C22×C4—171no—
275C22×C4—342no—
276C22×C4—341no—
277C22×C4—341no—
278C22×C4—341no—
279C22×C4—341no—
280C22×C4—342no—
281C22×C4—344no—
282C22×C4—341no—
283C22×C4—341no—
284C22×C4—681no—
285C22×C4—681no—
286C22×C4—681no—
287C22×C4—681no—
288C22×C4—682no—
289C22×C4—682no—
290C22×C4—682no—
291C22×C4—682no—
292C22×C4—682no—
293C22×C4—682no—
294C22×C4C22⋊#59511yescharacteristic
295C22×C4C22⋊#59511yescharacteristic
296C22×C4C22×#59511yescharacteristic
297C2×C8—344no—
298C2×C8—682no—
299C2×C8—682no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—42no—
303C4⋊C4—681no—
304C4⋊C4—681no—
305C4⋊C4—682no—
306C4⋊C4—682no—
307C4⋊C4—688no—
308C4⋊C4—682no—
309C22⋊C4—681no—
310C22⋊C4—681no—
311C22⋊C4—681no—
312C22⋊C4—681no—
313C42—41no—
314C42—342no—
315C42—342no—
316C42—681no—
317C23—171no—
318C23—171no—
319C23—171no—
320C23—171no—
321C23—171no—
322C23—171no—
323C23—341no—
324C23—341no—
325C23—341no—
326C23—341no—
327C23C2×C22⋊#59511yescharacteristic
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—172no—
342C2×C4—172no—
343C2×C4—344no—
344C2×C4—344no—
345C2×C4—341no—
346C2×C4—341no—
347C2×C4—341no—
348C2×C4—341no—
349C2×C4—341no—
350C2×C4—341no—
351C2×C4—341no—
352C2×C4—682no—
353C2×C4—682no—
354C2×C4—682no—
355C2×C4—682no—
356C2×C4—684no—
357C2×C4—684no—
358C2×C4—684no—
359C2×C4—681no—
360C2×C4—681no—
361C2×C4—681no—
362C2×C4—681no—
363C2×C4—681no—
364C2×C4—681no—
365C2×C4—1362no—
366C2×C4—1362no—
367C2×C4—1362no—
368C2×C4—1362no—
369C2×C4#1058755012yes—
370C2×C4Q8×#59512yes—
371C8—684no—
372C22—171no—
373C22—171no—
374C22—171no—
375C22—171no—
376C22—341no—
377C22—341no—
378C22—341no—
379C22—341no—
380C22—341no—
381C22—341no—
382C22—341no—
383C22—341no—
384C22—341no—
385C22—341no—
386C22—341no—
387C22—341no—
388C22(C2×#595)⋊Q811yescharacteristic
389C22D17⋊#9911yescharacteristic
390C22#1176378811yescharacteristic
391C22#1176380011yescharacteristic
392C22#1176380011yescharacteristic
393C22C2×#1058755011yescharacteristic
394C22#1176380711yescharacteristic
395C4—22no—
396C4—22no—
397C4—41no—
398C4—81no—
399C4—81no—
400C4—342no—
401C4—342no—
402C4—681no—
403C4—1364no—
404C4—1361no—
405C4—1361no—
406C2—341no—
407C2—341no—
408C2—341no—
409C2—341no—
410C2#1454417111yescharacteristic
411C2#1454418811yescharacteristic
412C2#1454419511yescharacteristic
413C2#1454420011yescharacteristic
414C2#1454495911yescharacteristic
415C2#1454496711yescharacteristic
416C2#1454497511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#595
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC17×#389C4
socleC23×C17C2×C22⋊C4
prime radicalC23×D17C2×D4
cosocleC22×C4×D17C23
hypercenter#389#595
hypocenterC17#9887
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
12. C2×#10587576C4semidirect
14. #11762707C4semidirect
19. #11762674C4semidirect
22. C17×#389C4semidirect
209. #389#595semidirect
266. C17#9887semidirect

Maximal subgroups

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

subgroupindex
#145445112
#145439622
#145436572
#145370932
#988717