Finite Group Databasebeta

← #16937540

Subgroups — #16937540

Order 4352.

438 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 75 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#14534980C211yesmaximal, characteristic, complemented
2#14529621C211yesmaximal, characteristic
3#14527300C211yesmaximal, characteristic
4#14526691C211yesmaximal, characteristic, complemented
5#14526669C211yesmaximal, characteristic, complemented
6#14526636C211yesmaximal, characteristic, complemented
7C17×#1510C211yesmaximal, characteristic
8C2×#10587505—21no—
9C2×#10587505—21no—
10#11762773C2211yescharacteristic
11#11762745—21no—
12#11762743—21no—
13#11762741—21no—
14#11762732—21no—
15#11762706—21no—
16#11762696—21no—
17#11762669C2211yescharacteristic
18C4×C22⋊Dic17C2211yescharacteristic
19C4×C22⋊Dic17C2211yescharacteristic
20#11762543—21no—
21#11762543—21no—
22C2×C17×#121C2211yescharacteristic
23C17×#407C2211yescharacteristic
24C17×#381C2211yescharacteristic
25C17×#327—21no—
26C17×#327—21no—
27C22×D4×C17—21no—
28C22×D4×C17Q811yescharacteristic
29C23×C4×C17C2311yescharacteristic
30C2×M16×C17—21no—
31C17×#121—21no—
32C17×#121—21no—
33C17×#121—21no—
34C17×#121—21no—
35C2×C4⋊C4×C17Q811yescharacteristic
36C2×C22⋊C4×C17—21no—
37C2×C22⋊C4×C17—21no—
38C2×C22⋊Dic17—21no—
39C2×C22⋊Dic17—21no—
40C2×C22⋊Dic17D411yescharacteristic
41C2×C22⋊Dic17D411yescharacteristic
42C2×C4⋊Dic17—21no—
43C2×C4⋊Dic17—21no—
44C2×C4⋊Dic17—21no—
45C2×#63225—21no—
46C2×#63225—21no—
47C2×#63225—21no—
48C2×#63225—21no—
49C2×C4×Dic17—21no—
50C2×C4×Dic17—21no—
51C2×#63223—21no—
52C17×C22⋊C8—21no—
53C17×C22⋊C8—21no—
54C17×#95—21no—
55C17×#95D411yescharacteristic
56C17×#95D411yescharacteristic
57#10587505—42no—
58#10587505—42no—
59#10587502—21no—
60#10587502—21no—
61#10587502—21no—
62#10587502—21no—
63#10587502D411yescharacteristic
64#10587502D411yescharacteristic
65C22⋊#3622—21no—
66C22⋊#3622—21no—
67C24×C17—21no—
68C24×C17C2×D411yescharacteristic
69C2×D4×C17—21no—
70C2×D4×C17—21no—
71C2×D4×C17—41no—
72C2×D4×C17—41no—
73C2×D4×C17—41no—
74C2×D4×C17—41no—
75C2×D4×C17—41no—
76C2×D4×C17—41no—
77C2×D4×C17—81no—
78C22×C4×C17—21no—
79C22×C4×C17—21no—
80C22×C4×C17—21no—
81C22×C4×C17—81no—
82C22×C4×C17C2×D411yescharacteristic
83C22×C4×C17C2×D411yescharacteristic
84C22×C4×C17C2×Q811yescharacteristic
85C22×C4×C17#4111yescharacteristic
86C22×C4×C17#4111yescharacteristic
87C22×C4×C17#4111yescharacteristic
88C22×Dic17—21no—
89C22×Dic17—21no—
90C22×Dic17—21no—
91C22×Dic17—21no—
92C22×Dic17—41no—
93M16×C17—81no—
94C2×C8×C17—41no—
95C4⋊C4×C17—21no—
96C4⋊C4×C17—21no—
97C22⋊C4×C17—41no—
98C22⋊C4×C17—41no—
99C22⋊C4×C17—81no—
100C22⋊Dic17—22no—
101C22⋊Dic17—42no—
102C22⋊Dic17—41no—
103C22⋊Dic17—41no—
104C22⋊Dic17—41no—
105C4⋊Dic17—81no—
106C4⋊Dic17—81no—
107C4⋊Dic17—81no—
108#63225—42no—
109#63225—42no—
110#63225—81no—
111#63225—81no—
112C4×Dic17—81no—
113C4×Dic17—81no—
114#63223—81no—
115C2×#3622—41no—
116#10384—171nomaximal, Sylow
117C23×C17—21no—
118C23×C17—21no—
119C23×C17—41no—
120C23×C17—41no—
121C23×C17—41no—
122C23×C17—41no—
123C23×C17—41no—
124C23×C17—81no—
125C23×C17—81no—
126C23×C17#12011yescharacteristic
127C23×C17C22⋊Q811yescharacteristic
128C23×C17#12411yescharacteristic
129D4×C17—81no—
130D4×C17—81no—
131D4×C17—81no—
132D4×C17—81no—
133D4×C17—81no—
134D4×C17—81no—
135C2×C4×C17—41no—
136C2×C4×C17—41no—
137C2×C4×C17—41no—
138C2×C4×C17—41no—
139C2×C4×C17—41no—
140C2×C4×C17—41no—
141C2×C4×C17—41no—
142C2×C4×C17—41no—
143C2×C4×C17—41no—
144C2×C4×C17—41no—
145C2×C4×C17—41no—
146C2×C4×C17—41no—
147C2×C4×C17—41no—
148C2×C4×C17—41no—
149C2×C4×C17—41no—
150C2×C4×C17C22⋊Q811yescharacteristic
151C2×C4×C17C22⋊Q811yescharacteristic
152C2×C4×C17#12411yescharacteristic
153C2×C4×C17#12411yescharacteristic
154C2×Dic17—22no—
155C2×Dic17—41no—
156C2×Dic17—41no—
157C2×Dic17—42no—
158C2×Dic17—41no—
159C2×Dic17—41no—
160C2×Dic17—41no—
161C2×Dic17—41no—
162C2×Dic17—41no—
163C2×Dic17—41no—
164C2×Dic17—41no—
165C2×Dic17—41no—
166C2×Dic17—41no—
167C2×Dic17—81no—
168C2×Dic17—81no—
169C8×C17—81no—
170#3622—81no—
171#2667—171no—
172#1964—171no—
173#1510D1711yescharacteristic
174#1507—171no—
175#1305—171no—
176#1297—171no—
177#1284—171no—
178C22×C17—21no—
179C22×C17—21no—
180C22×C17—21no—
181C22×C17—21no—
182C22×C17—21no—
183C22×C17—21no—
184C22×C17—21no—
185C22×C17—21no—
186C22×C17—81no—
187C22×C17—81no—
188C22×C17—81no—
189C22×C17—81no—
190C22×C17—81no—
191C22×C17—161no—
192C22×C17—161no—
193C22×C17#39311yescharacteristic
194C22×C17#45311yescharacteristic
195C22×C17#45411yescharacteristic
196C4×C17—21no—
197C4×C17—21no—
198C4×C17—21no—
199C4×C17—21no—
200C4×C17—81no—
201C4×C17—81no—
202C4×C17—81no—
203Dic17—42no—
204Dic17—81no—
205Dic17—81no—
206Dic17—81no—
207Dic17—82no—
208C2×#121C2×D1711yescharacteristic
209C2×#99—341no—
210C2×#99—341no—
211#407—171no—
212#407C2×D1711yescharacteristic
213#399—341no—
214#398—341no—
215#398—341no—
216#396—341no—
217#389—341no—
218#387—341no—
219#381C2×D1711yescharacteristic
220#380—171no—
221C4×C22⋊C4—171no—
222C4×C22⋊C4—171no—
223#327—21no—
224#327—21no—
225#327—341no—
226#327—341no—
227C2×C17—21no—
228C2×C17—21no—
229C2×C17—41no—
230C2×C17—41no—
231C2×C17—161no—
232C2×C17#202711yescharacteristic
233C2×C17#203111yescharacteristic
234C2×C17#203211yescharacteristic
235C22×D4—21no—
236C22×D4Dic3411yescharacteristic
237C23×C4C22×D1711yescharacteristic
238C2×M16—21no—
239C2×M16—341no—
240#121—21no—
241#121—21no—
242#121—21no—
243#121—21no—
244C2×C4⋊C4—341no—
245C2×C4⋊C4—341no—
246C2×C4⋊C4—341no—
247C2×C4⋊C4—341no—
248C2×C4⋊C4—341no—
249C2×C4⋊C4—341no—
250C2×C4⋊C4—341no—
251C2×C4⋊C4Dic3411yescharacteristic
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—171no—
255C2×C22⋊C4—171no—
256C2×C22⋊C4—341no—
257C2×C22⋊C4—341no—
258C2×C42—341no—
259C2×C42—341no—
260#99—682no—
261#99—682no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264C22⋊C8—341no—
265C22⋊C8—341no—
266#95—21no—
267#95—171no—
268#95—171no—
269#95—341no—
270#95—341no—
271#95—341no—
272#95—341no—
273#95C22⋊D1711yescharacteristic
274#95C22⋊D1711yescharacteristic
275C17#1038411yescharacteristic, complemented, Sylow
276C24—21no—
277C24D4×D1711yescharacteristic
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—81no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—81no—
291C22×C4—341no—
292C22×C4—341no—
293C22×C4—341no—
294C22×C4—341no—
295C22×C4—681no—
296C22×C4C2×Dic3411yescharacteristic
297C22×C4#6325211yescharacteristic
298C22×C4D4×D1711yescharacteristic
299C22×C4#6325411yescharacteristic
300C22×C4#6325411yescharacteristic
301C22×C4C2×C22⋊D1711yescharacteristic
302M16—81no—
303M16—1361no—
304C2×C8—41no—
305C2×C8—681no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—682no—
309C4⋊C4—682no—
310C4⋊C4—1361no—
311C4⋊C4—1361no—
312C4⋊C4—1361no—
313C4⋊C4—1361no—
314C4⋊C4—1361no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—81no—
318C22⋊C4—342no—
319C22⋊C4—682no—
320C22⋊C4—681no—
321C22⋊C4—681no—
322C22⋊C4—681no—
323C42—1361no—
324C42—1361no—
325C23—21no—
326C23—21no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—81no—
333C23—81no—
334C23#1058756411yescharacteristic
335C23#1058757111yescharacteristic
336C23#1058762311yescharacteristic
337D4—81no—
338D4—81no—
339D4—81no—
340D4—81no—
341D4—81no—
342D4—81no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—342no—
359C2×C4—681no—
360C2×C4—681no—
361C2×C4—681no—
362C2×C4—682no—
363C2×C4—681no—
364C2×C4—681no—
365C2×C4—681no—
366C2×C4—681no—
367C2×C4—681no—
368C2×C4—681no—
369C2×C4—681no—
370C2×C4—681no—
371C2×C4—1361no—
372C2×C4—1361no—
373C2×C4#1058756411yescharacteristic
374C2×C4#1058757111yescharacteristic
375C2×C4#1058761011yescharacteristic
376C2×C4#1058762211yescharacteristic
377C8—81no—
378C8—1361no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—161no—
393C22—161no—
394C22#1176272111yescharacteristic
395C22#1176297511yescharacteristic
396C22#1176298011yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—81no—
402C4—81no—
403C4—81no—
404C4—682no—
405C4—1361no—
406C4—1361no—
407C4—1361no—
408C4—1362no—
409C2—21no—
410C2—21no—
411C2—41no—
412C2—41no—
413C2—161no—
414C2#1452993811yescharacteristic
415C2#1452995411yescharacteristic
416C2#1452996111yescharacteristic
subgroupG/H
centerC22#11762721
commutator, cosocleC23×C4×C17C23
FrattiniC23×C4C22×D17
FittingC17×#1510C2
socleC22×C17#393
prime radicalC2×C17×#121C22
hypercenter#1510D17
hypocenterC17#10384
LCSG ▷ C23×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
1. #14534980C2semidirect
4. #14526691C2semidirect
5. #14526669C2semidirect
6. #14526636C2semidirect
275. C17#10384semidirect

Maximal subgroups

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

subgroupindex
#145349802
#145296212
#145273002
#145266912
#145266692
#145266362
C17×#15102
#1038417