Finite Group Databasebeta

← #16935519

Subgroups — #16935519

Order 4352.

634 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763212C211yesmaximal, characteristic, complemented
2C2×#11763011C211yesmaximal, characteristic
3#14533779C211yesmaximal, characteristic
4C2×#11762554C211yesmaximal, characteristic, complemented
5C2×#11762536C211yesmaximal, characteristic
6#14526625C211yesmaximal, characteristic, complemented
7C17×#1988C211yesmaximal, characteristic, complemented
8C22×#63230—21no—
9C2×#10587555C2211yescharacteristic
10C2×#10587561—21no—
11C2×C4×D68C2211yescharacteristic
12#11763212—22no—
13#11763212—22no—
14#11763011—22no—
15#11763011—22no—
16C2×#10587478—22no—
17C2×C4⋊#3622C2211yescharacteristic
18C2×#10587506—21no—
19C2×C4×#3622C2211yescharacteristic
20#11762736—22no—
21#11762715—21no—
22#11762666—22no—
23#11762554—22no—
24#11762536—22no—
25C2×C17×C4⋊Q8C2211yescharacteristic
26C2×C17×C4⋊C8C2211yescharacteristic
27C4×C4⋊C4×C17C2211yescharacteristic
28C17×#340—22no—
29C22×Q8×C17—21no—
30C22×D68D411yescharacteristic
31C22×C4×D17—21no—
32C22×Dic34—21no—
33C22×C8×C17—21no—
34C17×C4⋊Q8—21no—
35C17×C4⋊Q8—21no—
36C17×C4⋊Q8—21no—
37C17×C4⋊Q8D412yes—
38C2×C4⋊C4×C17—21no—
39C2×C4⋊C4×C17—21no—
40C2×C4⋊C4×C17D412yes—
41C2×C42×C17—21no—
42C2×C42×C17C2311yescharacteristic
43C2×#63230—24no—
44C2×#63230—42no—
45C2×#63230—42no—
46C2×#63227—24no—
47C2×#63227—21no—
48C2×C4⋊Dic17—21no—
49C2×C4⋊Dic17D411yescharacteristic
50C2×C4⋊Dic17D412yes—
51C22×#3622—21no—
52C22×#3622—21no—
53#10587561—42no—
54#10587561—42no—
55C4×D68—21no—
56C4×D68—21no—
57C4×D68—21no—
58C4×D68—21no—
59#10587555—21no—
60#10587555—21no—
61#10587555—21no—
62#10587555—21no—
63C17×C4⋊C8—21no—
64C17×C4⋊C8—21no—
65C17×#95—21no—
66#10587506—24no—
67#10587502—24no—
68#10587478—28no—
69C4⋊#3622—21no—
70C4⋊#3622D412yes—
71C4×#3622—21no—
72C4×#3622D412yes—
73C23×D17—21no—
74C2×Q8×C17—22no—
75C2×Q8×C17—41no—
76C2×Q8×C17—41no—
77C2×Q8×C17—41no—
78C2×Q8×C17—41no—
79C2×Q8×C17—41no—
80C22×C4×C17—22no—
81C22×C4×C17—41no—
82C22×C4×C17C2×D411yescharacteristic
83C22×C4×C17C2×D411yescharacteristic
84C22×C4×C17C2×D411yescharacteristic
85C22×Dic17—22no—
86C22×Dic17—21no—
87C2×D68—21no—
88C2×D68—21no—
89C2×D68—21no—
90C2×D68—21no—
91C2×D68—21no—
92C2×D68D812yes—
93C2×C4×D17—41no—
94C2×C4×D17—41no—
95C2×C4×D17—42no—
96C2×C4×D17—42no—
97C2×Dic34—41no—
98C2×Dic34—41no—
99C2×Dic34—41no—
100C2×Dic34—41no—
101C2×Dic34—41no—
102C2×Dic34—41no—
103C2×C8×C17—41no—
104C2×C8×C17—42no—
105C4⋊C4×C17—22no—
106C4⋊C4×C17—22no—
107C4⋊C4×C17—22no—
108C4⋊C4×C17—22no—
109C4⋊C4×C17—41no—
110C4⋊C4×C17—41no—
111C42×C17—41no—
112C42×C17—41no—
113C42×C17C2×D411yescharacteristic
114C42×C17C2×D411yescharacteristic
115C42×C17C2×D411yescharacteristic
116C42×C17#4111yescharacteristic
117#63230—48no—
118#63227—48no—
119#63227—41no—
120#63227—41no—
121C4⋊Dic17—22no—
122C4⋊Dic17—21no—
123C4⋊Dic17—22no—
124C4⋊Dic17—21no—
125C4⋊Dic17—41no—
126C4⋊Dic17—41no—
127C2×#3622—24no—
128C2×#3622—22no—
129C2×#3622—22no—
130C2×#3622—41no—
131C2×#3622—41no—
132#10066—171nomaximal, Sylow
133C23×C17#12011yescharacteristic
134C22×D17—22no—
135C22×D17—41no—
136C22×D17—41no—
137C22×D17—42no—
138C22×D17—42no—
139Q8×C17—42no—
140Q8×C17—42no—
141Q8×C17—81no—
142Q8×C17—81no—
143C2×C4×C17—22no—
144C2×C4×C17—42no—
145C2×C4×C17—42no—
146C2×C4×C17—42no—
147C2×C4×C17—42no—
148C2×C4×C17—81no—
149C2×C4×C17—81no—
150C2×C4×C17#12011yescharacteristic
151C2×C4×C17#12011yescharacteristic
152C2×C4×C17#12111yescharacteristic
153C2×C4×C17#12111yescharacteristic
154C2×C4×C17#12111yescharacteristic
155C2×C4×C17#12711yescharacteristic
156C2×C4×C17C2×D811yescharacteristic
157C2×C4×C17#13511yescharacteristic
158C2×C4×C17#13512yes—
159C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C17#13712yes—
162C2×Dic17—42no—
163C2×Dic17—41no—
164C2×Dic17—42no—
165C2×Dic17—42no—
166C2×Dic17—42no—
167D68—22no—
168D68—22no—
169D68—41no—
170D68—41no—
171C4×D17—82no—
172C4×D17—81no—
173C4×D17—81no—
174Dic34—81no—
175Dic34—81no—
176Dic34—81no—
177Dic34—81no—
178C8×C17—81no—
179#3622—24no—
180#3622—42no—
181C2×#500—171no—
182C2×#461—171no—
183#2547—171no—
184#1988D1711yescharacteristic, complemented
185C2×#332—171no—
186C2×D4⋊C8—171no—
187#1279—171no—
188C22×C17#39211yescharacteristic
189C22×C17#44711yescharacteristic
190C22×C17#44911yescharacteristic
191C22×C17#45212yes—
192C22×C17#45612yes—
193C2×D17—44no—
194C2×D17—42no—
195C2×D17—82no—
196C2×D17—81no—
197C2×D17—81no—
198C4×C17—21no—
199C4×C17—21no—
200C4×C17—82no—
201C4×C17—82no—
202C4×C17#44711yescharacteristic
203C4×C17#44911yescharacteristic
204C4×C17#46412yes—
205C4×C17#46611yescharacteristic
206C4×C17#46911yescharacteristic
207C4×C17#49511yescharacteristic
208C4×C17#49711yescharacteristic
209Dic17—82no—
210Dic17—81no—
211C22×SD16—341no—
212C2×C4⋊Q8—171no—
213C2×C4⋊Q8C2×D1711yescharacteristic
214C2×#124—341no—
215C2×C4×D4—171no—
216#500—342no—
217#500—342no—
218#461—342no—
219#461—342no—
220C2×#107—342no—
221C2×C4⋊C8—171no—
222C2×C4⋊C8C2×D1711yescharacteristic
223C2×#103—341no—
224C2×C4×C8—171no—
225#397—342no—
226#391—341no—
227#380—342no—
228C4×C4⋊C4C2×D1711yescharacteristic
229#340—22no—
230#332—342no—
231D4⋊C8—342no—
232C2×C17#164712yes—
233C2×C17#165012yes—
234C2×C17#199911yescharacteristic
235C2×C17#200511yescharacteristic
236C2×C17#201511yescharacteristic
237D17—82no—
238C22×Q8—21no—
239C22×Q8—341no—
240C22×D4—171no—
241C23×C4—341no—
242C2×SD16—344no—
243C2×SD16—682no—
244C2×SD16—682no—
245C22×C8—21no—
246C22×C8—341no—
247C22×C8—341no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8—341no—
252C4⋊Q8—341no—
253C4⋊Q8—341no—
254C4⋊Q8—341no—
255C4⋊Q8D6812yes—
256#124—682no—
257#124—682no—
258C4×D4—341no—
259C4×D4—341no—
260C4×D4—341no—
261C4×D4—341no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—171no—
265C2×C4⋊C4—172no—
266C2×C4⋊C4—341no—
267C2×C4⋊C4C22⋊D1712yes—
268C2×C22⋊C4—344no—
269C2×C22⋊C4—341no—
270C2×C42—21no—
271C2×C42C22×D1711yescharacteristic
272#107—348no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—172no—
276C4⋊C8—341no—
277#103—344no—
278C4×C8—172no—
279C4×C8—341no—
280#95—21no—
281#95—344no—
282C17#1006611yescharacteristic, complemented, Sylow
283C24—341no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—681no—
291C2×Q8—681no—
292C2×Q8—681no—
293C2×Q8—681no—
294C2×Q8—681no—
295C2×Q8—681no—
296C2×D4—172no—
297C2×D4—341no—
298C2×D4—341no—
299C2×D4—341no—
300C2×D4—341no—
301C2×D4—341no—
302C22×C4—22no—
303C22×C4—41no—
304C22×C4—341no—
305C22×C4—342no—
306C22×C4—681no—
307C22×C4—681no—
308C22×C4—682no—
309C22×C4—682no—
310C22×C4D4×D1711yescharacteristic
311C22×C4D4×D1711yescharacteristic
312C22×C4C2×C22⋊D1711yescharacteristic
313SD16—688no—
314C2×C8—41no—
315C2×C8—42no—
316C2×C8—344no—
317C2×C8—342no—
318C2×C8—342no—
319C2×C8—681no—
320C2×C8—681no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—341no—
328C4⋊C4—342no—
329C4⋊C4—341no—
330C4⋊C4—342no—
331C4⋊C4—681no—
332C4⋊C4—681no—
333C22⋊C4—688no—
334C22⋊C4—681no—
335C22⋊C4—681no—
336C42—41no—
337C42—41no—
338C42C2×D6811yescharacteristic
339C42#6325211yescharacteristic
340C42D4×D1711yescharacteristic
341C42D4×D1711yescharacteristic
342C23—342no—
343C23—681no—
344C23—682no—
345C23—681no—
346C23—682no—
347C23#1058762311yescharacteristic
348Q8—42no—
349Q8—42no—
350Q8—81no—
351Q8—81no—
352Q8—1361no—
353Q8—1361no—
354Q8—1361no—
355Q8—1361no—
356D4—342no—
357D4—342no—
358D4—681no—
359D4—681no—
360C2×C4—22no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—682no—
368C2×C4—682no—
369C2×C4—681no—
370C2×C4—682no—
371C2×C4—682no—
372C2×C4—1361no—
373C2×C4—1362no—
374C2×C4—1361no—
375C2×C4#1058756811yescharacteristic
376C2×C4#1058756811yescharacteristic
377C2×C4#1058757011yescharacteristic
378C2×C4#1058757011yescharacteristic
379C2×C4D8×D1711yescharacteristic
380C2×C4#1058759711yescharacteristic
381C2×C4#1058760011yescharacteristic
382C2×C4#1058760211yescharacteristic
383C2×C4#1058761611yescharacteristic
384C2×C4#1058762611yescharacteristic
385C2×C4#1058762812yes—
386C2×C4#1058763612yes—
387C8—81no—
388C8—344no—
389C8—682no—
390C22—684no—
391C22—682no—
392C22—1361no—
393C22—1362no—
394C22—1361no—
395C22#1176271811yescharacteristic
396C22#1176294111yescharacteristic
397C22#1176295311yescharacteristic
398C22#1176296912yes—
399C22#1176299012yes—
400C4—21no—
401C4—21no—
402C4—82no—
403C4—82no—
404C4—1361no—
405C4—1362no—
406C4#1176294411yescharacteristic
407C4#1176295511yescharacteristic
408C4#1176303112yes—
409C4#1176304411yescharacteristic
410C4#1176306111yescharacteristic
411C4#1176319111yescharacteristic
412C4#1176320111yescharacteristic
413C2—1362no—
414C2#1452801812yes—
415C2#1452803912yes—
416C2#1452978111yescharacteristic
417C2#1452982111yescharacteristic
418C2#1452987711yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1988C2
socleC23×C17#120
prime radicalC22×D68D4
hypercenter#1988D17
hypocenterC17#10066
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
1. C2×#11763212C2semidirect
4. C2×#11762554C2semidirect
6. #14526625C2semidirect
7. C17×#1988C2semidirect
184. #1988D17semidirect
282. C17#10066semidirect

Maximal subgroups

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

subgroupindex
C2×#117632122
C2×#117630112
#145337792
C2×#117625542
C2×#117625362
#145266252
C17×#19882
#1006617