Finite Group Databasebeta

← #16930407

Subgroups — #16930407

Order 4352.

478 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14538572C211yesmaximal, characteristic
2#14528804C211yesmaximal, characteristic
3#14527284C211yesmaximal, characteristic, complemented
4#14527240C211yesmaximal, characteristic, complemented
5#14526680C211yesmaximal, characteristic, complemented
6#14526624C211yesmaximal, characteristic, complemented
7C8×#41×C17C211yesmaximal, characteristic
8#11763366C2211yescharacteristic
9#11763116—21no—
10#11763109—21no—
11#11763104C411yescharacteristic, complemented
12#11763099C411yescharacteristic, complemented
13#11763094C411yescharacteristic, complemented
14#11763089C411yescharacteristic, complemented
15#11762845—21no—
16#11762833C2211yescharacteristic
17C2×C4⋊#3622C2211yescharacteristic
18C2×#10587508—21no—
19#11762805—21no—
20C4×C4⋊Dic17C2211yescharacteristic
21#11762568—21no—
22#11762547—22no—
23#11762541—21no—
24#11762541—21no—
25C4×#41×C17C2211yescharacteristic
26C8×Q8×C17—21no—
27C8×D4×C17—21no—
28C8×D4×C17—22no—
29C17×#431—21no—
30C17×#431C2211yescharacteristic
31C2×C4×C8×C17—21no—
32C2×C4×C8×C17C2211yescharacteristic
33C2×#41×C17D411yescharacteristic
34C22×C8×C17—22no—
35C22×C8×C17—21no—
36C4×Q8×C17C2×C411yescharacteristic
37C4×Q8×C17D411yescharacteristic
38C4×D4×C17—21no—
39C4×D4×C17—21no—
40C4×D4×C17C2×C411yescharacteristic
41C4×D4×C17D411yescharacteristic
42C17×#117—21no—
43C17×#117D411yescharacteristic
44C2×C42×C17—21no—
45C2×C42×C17C2311yescharacteristic
46#10587612—21no—
47C2×C4⋊Dic17—21no—
48#10587610—21no—
49#10587610—21no—
50C2×C4×Dic17—21no—
51C2×#63223—21no—
52C22×#3622—21no—
53#10587556—21no—
54#10587555C2×C411yescharacteristic
55#10587555C2×C411yescharacteristic
56C4×Dic34—21no—
57C4×Dic34—21no—
58C17×C4⋊C8—22no—
59C17×C4⋊C8—21no—
60C17×C22⋊C8—22no—
61C17×C22⋊C8D412yes—
62C4×C8×C17—22no—
63C4×C8×C17—21no—
64C4×C8×C17—21no—
65C4×C8×C17D411yescharacteristic
66C4×C8×C17D411yescharacteristic
67#10587508—42no—
68#10587506—21no—
69#10587506—21no—
70#10587503—21no—
71#10587503—21no—
72#10587502—21no—
73#10587479—21no—
74#10587479—21no—
75#10587478—21no—
76#10587478—21no—
77C4⋊#3622—21no—
78C4⋊#3622—21no—
79C4⋊#3622—21no—
80C4⋊#3622C2×C411yescharacteristic
81C4⋊#3622C2×C411yescharacteristic
82#41×C17—21no—
83#41×C17—21no—
84#41×C17SD1612yes—
85#41×C17Q1612yes—
86C2×Q8×C17C22⋊C411yescharacteristic
87C2×D4×C17—21no—
88C2×D4×C17C22⋊C411yescharacteristic
89C22×C4×C17—21no—
90C22×C4×C17—21no—
91C22×C4×C17—21no—
92C22×C4×C17C2×D411yescharacteristic
93C22×C4×C17C2×D411yescharacteristic
94C22×C4×C17#4111yescharacteristic
95C22×Dic17—41no—
96C2×Dic34—21no—
97C2×Dic34—21no—
98C2×C8×C17—21no—
99C2×C8×C17—22no—
100C2×C8×C17—21no—
101C2×C8×C17—42no—
102C2×C8×C17—44no—
103C4⋊C4×C17—21no—
104C4⋊C4×C17—21no—
105C4⋊C4×C17C22⋊C411yescharacteristic
106C4⋊C4×C17C22⋊C411yescharacteristic
107C22⋊C4×C17—21no—
108C22⋊C4×C17—21no—
109C22⋊C4×C17—21no—
110C42×C17—21no—
111C42×C17—21no—
112C42×C17—21no—
113C42×C17C22×C411yescharacteristic
114C42×C17C2×D411yescharacteristic
115C42×C17C2×D411yescharacteristic
116C42×C17#4111yescharacteristic
117C22⋊Dic17—41no—
118C4⋊Dic17—22no—
119C4⋊Dic17—21no—
120C4⋊Dic17—21no—
121C4⋊Dic17—21no—
122C4⋊Dic17—21no—
123C4⋊Dic17—41no—
124#63225—41no—
125#63225—41no—
126C4×Dic17—41no—
127C4×Dic17—41no—
128C4×Dic17—41no—
129#63223—41no—
130#63223—41no—
131C2×#3622—21no—
132C2×#3622—21no—
133C2×#3622—41no—
134C2×#3622—41no—
135C2×#3622—41no—
136#9207—171nomaximal, Sylow
137C23×C17—21no—
138C23×C17#12111yescharacteristic
139Q8×C17—21no—
140Q8×C17#10312yes—
141D4×C17—22no—
142D4×C17—22no—
143D4×C17—21no—
144D4×C17#10312yes—
145C2×C4×C17—21no—
146C2×C4×C17—21no—
147C2×C4×C17—21no—
148C2×C4×C17—22no—
149C2×C4×C17—22no—
150C2×C4×C17—21no—
151C2×C4×C17—21no—
152C2×C4×C17—41no—
153C2×C4×C17—42no—
154C2×C4×C17—41no—
155C2×C4×C17—41no—
156C2×C4×C17C2×C22⋊C411yescharacteristic
157C2×C4×C17C4×D411yescharacteristic
158C2×C4×C17C4×D411yescharacteristic
159C2×C4×C17#12011yescharacteristic
160C2×C4×C17#12111yescharacteristic
161C2×C4×C17#12311yescharacteristic
162C2×C4×C17C2×SD1611yescharacteristic
163C2×C4×C17C2×Q1611yescharacteristic
164C2×C4×C17#13511yescharacteristic
165C2×C4×C17#13511yescharacteristic
166C2×Dic17—42no—
167C2×Dic17—41no—
168C2×Dic17—41no—
169C2×Dic17—81no—
170C2×Dic17—81no—
171Dic34—41no—
172Dic34—41no—
173Dic34—81no—
174C8×C17—22no—
175C8×C17—42no—
176C8×C17—41no—
177#3622—41no—
178#3622—41no—
179#3622—81no—
180#3076—171no—
181C8×#41D1711yescharacteristic
182#1806—171no—
183#1503—171no—
184#1493—171no—
185#1301—171no—
186#1279—171no—
187C22×C17—21no—
188C22×C17—21no—
189C22×C17—22no—
190C22×C17—41no—
191C22×C17—41no—
192C22×C17#38611yescharacteristic
193C22×C17#46511yescharacteristic
194C22×C17#46711yescharacteristic
195C4×C17—21no—
196C4×C17—22no—
197C4×C17—21no—
198C4×C17—21no—
199C4×C17—41no—
200C4×C17—41no—
201C4×C17C2×#10311yescharacteristic
202C4×C17#41611yescharacteristic
203C4×C17#44311yescharacteristic
204C4×C17#44411yescharacteristic
205C4×C17#46511yescharacteristic
206C4×C17#46711yescharacteristic
207Dic17—82no—
208Dic17—81no—
209Dic17—81no—
210#533—171no—
211C4×#41C2×D1711yescharacteristic
212#479—341no—
213#478—341no—
214#477—171no—
215#476—171no—
216#475—171no—
217#474—171no—
218C8×Q8—21no—
219C8×D4—21no—
220C8×D4—22no—
221#431—21no—
222#431C2×D1711yescharacteristic
223#427—341no—
224#423—171no—
225C2×C4⋊C8—171no—
226C2×#104—341no—
227#416—341no—
228C2×C4×C8—21no—
229C2×C4×C8C2×D1711yescharacteristic
230C4×C4⋊C4—171no—
231#339—341no—
232#328—342no—
233Q8⋊C8—341no—
234Q8⋊C8—341no—
235C2×C17—21no—
236C2×C17—21no—
237C2×C17—42no—
238C2×C17#187611yescharacteristic
239C2×C17#189211yescharacteristic
240C2×C17#190611yescharacteristic
241C2×#41D6811yescharacteristic
242C2×M16—341no—
243C22×C8—22no—
244C22×C8—21no—
245C22×C8—341no—
246C4⋊Q8—171no—
247C4⋊Q8—171no—
248#125—341no—
249C22⋊Q8—341no—
250C22⋊Q8—341no—
251C4×Q8—341no—
252C4×Q8—341no—
253C4×Q8C4×D1711yescharacteristic
254C4×Q8C22⋊D1711yescharacteristic
255C4×D4—21no—
256C4×D4—21no—
257C4×D4C4×D1711yescharacteristic
258C4×D4C22⋊D1711yescharacteristic
259#117—21no—
260#117—341no—
261#117D6811yescharacteristic
262C2×C4⋊C4—341no—
263C2×C42—21no—
264C2×C42—341no—
265C2×C42C22×D1711yescharacteristic
266#107—341no—
267#107—341no—
268#106—341no—
269#106—341no—
270C4⋊C8—22no—
271C4⋊C8—21no—
272C4⋊C8—171no—
273C4⋊C8—171no—
274C4⋊C8—341no—
275C4⋊C8—341no—
276C4⋊C8—341no—
277#104—682no—
278#103—341no—
279#103—341no—
280#102—341no—
281#102—341no—
282C22⋊C8—22no—
283C22⋊C8C22⋊D1712yes—
284C4×C8—22no—
285C4×C8—21no—
286C4×C8—21no—
287C4×C8C22⋊D1711yescharacteristic
288C4×C8C22⋊D1711yescharacteristic
289#95—341no—
290C17#920711yescharacteristic, complemented, Sylow
291#41—21no—
292#41—21no—
293#41#6321912yes—
294#41Dic6812yes—
295C2×Q8—341no—
296C2×Q8—341no—
297C2×Q8#6322711yescharacteristic
298C2×D4—21no—
299C2×D4#6322711yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—681no—
304C22×C4C2×D6811yescharacteristic
305C22×C4#6325211yescharacteristic
306C22×C4C2×C22⋊D1711yescharacteristic
307M16—681no—
308M16—681no—
309C2×C8—21no—
310C2×C8—22no—
311C2×C8—21no—
312C2×C8—42no—
313C2×C8—44no—
314C2×C8—341no—
315C2×C8—341no—
316C2×C8—681no—
317C2×C8—681no—
318C2×C8—681no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—342no—
322C4⋊C4—341no—
323C4⋊C4—341no—
324C4⋊C4—341no—
325C4⋊C4—341no—
326C4⋊C4—681no—
327C4⋊C4—681no—
328C4⋊C4—681no—
329C4⋊C4#6322711yescharacteristic
330C4⋊C4#6322711yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—681no—
335C42—21no—
336C42—21no—
337C42—21no—
338C42—681no—
339C42—681no—
340C42—681no—
341C42C2×C4×D1711yescharacteristic
342C42#6325211yescharacteristic
343C42C2×C22⋊D1711yescharacteristic
344C42C2×C22⋊D1711yescharacteristic
345C23—21no—
346C23#1058761611yescharacteristic
347Q8—21no—
348Q8—681no—
349Q8—681no—
350Q8—1361no—
351Q8#1058748712yes—
352D4—22no—
353D4—22no—
354D4—21no—
355D4#1058748712yes—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—682no—
368C2×C4—681no—
369C2×C4—681no—
370C2×C4—1361no—
371C2×C4—1361no—
372C2×C4C2×#6321911yescharacteristic
373C2×C4#1058759011yescharacteristic
374C2×C4#1058759011yescharacteristic
375C2×C4C2×Dic6811yescharacteristic
376C2×C4C2×#6322711yescharacteristic
377C2×C4C4×C22⋊D1711yescharacteristic
378C2×C4C4×C22⋊D1711yescharacteristic
379C2×C4#1058761511yescharacteristic
380C2×C4#1058761611yescharacteristic
381C2×C4#1058763911yescharacteristic
382C8—22no—
383C8—42no—
384C8—41no—
385C8—681no—
386C8—681no—
387C8—1361no—
388C22—21no—
389C22—21no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22#1176268811yescharacteristic
394C22#1176303811yescharacteristic
395C22#1176305011yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—1362no—
403C4—1361no—
404C4—1361no—
405C4C2×#1058748711yescharacteristic
406C4#1176280611yescharacteristic
407C4#1176292411yescharacteristic
408C4#1176292911yescharacteristic
409C4#1176303811yescharacteristic
410C4#1176305011yescharacteristic
411C2—21no—
412C2—21no—
413C2—42no—
414C2#1452911111yescharacteristic
415C2#1452920711yescharacteristic
416C2#1452928511yescharacteristic
subgroupG/H
centerC2×C4#10587616
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC8×#41×C17C2
socleC22×C17#386
prime radicalC2×#41×C17D4
cosocleC2×C42×C17C23
hypercenterC8×#41D17
hypocenterC17#9207
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
3. #14527284C2semidirect
4. #14527240C2semidirect
5. #14526680C2semidirect
6. #14526624C2semidirect
11. #11763104C4semidirect
12. #11763099C4semidirect
13. #11763094C4semidirect
14. #11763089C4semidirect
290. C17#9207semidirect

Maximal subgroups

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

subgroupindex
#145385722
#145288042
#145272842
#145272402
#145266802
#145266242
C8×#41×C172
#920717