Finite Group Databasebeta

← #16930419

Subgroups — #16930419

Order 4352.

456 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#14537751C211yesmaximal, characteristic
3#14527282C211yesmaximal, characteristic, complemented
4#14527238C211yesmaximal, characteristic, complemented
5#14526679C211yesmaximal, characteristic, complemented
6#14526625C211yesmaximal, characteristic, complemented
7C17×#1806C211yesmaximal, characteristic
8#11763366C2211yescharacteristic
9#11763116—21no—
10#11763109—21no—
11#11763104C411yescharacteristic, complemented
12#11763099C411yescharacteristic, complemented
13#11763094C411yescharacteristic, complemented
14#11763089C411yescharacteristic, complemented
15#11762940—21no—
16#11762887—21no—
17#11762881—22no—
18#11762862—21no—
19#11762862C2211yescharacteristic
20#11762845—21no—
21C2×C4⋊#3622C2211yescharacteristic
22#11762805—21no—
23C4×#63223—21no—
24C2×C4×#3622C2211yescharacteristic
25#11762545—22no—
26#11762539—21no—
27#11762539—21no—
28C4×#41×C17C2211yescharacteristic
29C17×#423C2211yescharacteristic
30C2×C17×#104—21no—
31C4×C4⋊C4×C17C2211yescharacteristic
32C17×#339—21no—
33C2×#41×C17D411yescharacteristic
34C2×M16×C17—21no—
35C4×Q8×C17C2×C411yescharacteristic
36C4×Q8×C17D411yescharacteristic
37C4×D4×C17—21no—
38C4×D4×C17—21no—
39C4×D4×C17C2×C411yescharacteristic
40C4×D4×C17D411yescharacteristic
41C17×#117—21no—
42C17×#117D411yescharacteristic
43C2×C4⋊C4×C17—21no—
44C2×C42×C17—21no—
45C2×C42×C17—21no—
46C2×C42×C17C2311yescharacteristic
47#10587612—21no—
48#10587610—21no—
49#10587610—21no—
50C2×#63223—22no—
51C22×#3622—21no—
52C22×#3622—21no—
53#10587556—21no—
54#10587555C2×C411yescharacteristic
55#10587555C2×C411yescharacteristic
56C4×Dic34—21no—
57C4×Dic34—21no—
58C17×C4⋊C8—21no—
59C17×C4⋊C8—21no—
60C17×#104—42no—
61C17×#95—21no—
62#10587506—21no—
63#10587506—21no—
64#10587503—21no—
65#10587503—21no—
66C22⋊#3622—22no—
67C22⋊#3622D412yes—
68#10587479—21no—
69#10587479—21no—
70#10587478—21no—
71#10587478—21no—
72C4⋊#3622—22no—
73C4⋊#3622—21no—
74C4⋊#3622—21no—
75C4⋊#3622C2×C411yescharacteristic
76C4⋊#3622C2×C411yescharacteristic
77#10587474—22no—
78C4×#3622—21no—
79C4×#3622—21no—
80C4×#3622D411yescharacteristic
81C4×#3622D411yescharacteristic
82#41×C17—21no—
83#41×C17—21no—
84#41×C17—21no—
85#41×C17—21no—
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×C17—41no—
93C22×C4×C17C2×D411yescharacteristic
94C22×C4×C17C2×D411yescharacteristic
95C22×C4×C17#4111yescharacteristic
96C2×Dic34—21no—
97C2×Dic34—21no—
98M16×C17—41no—
99M16×C17—41no—
100C2×C8×C17—41no—
101C4⋊C4×C17—21no—
102C4⋊C4×C17—21no—
103C4⋊C4×C17—22no—
104C4⋊C4×C17—41no—
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×C17—41no—
114C42×C17—41no—
115C42×C17C22×C411yescharacteristic
116C42×C17C2×D411yescharacteristic
117C42×C17C2×D411yescharacteristic
118C42×C17#4111yescharacteristic
119C22⋊Dic17—41no—
120C4⋊Dic17—21no—
121C4⋊Dic17—21no—
122C4⋊Dic17—21no—
123C4⋊Dic17—21no—
124#63225—41no—
125#63225—41no—
126C4×Dic17—41no—
127#63223—44no—
128C2×#3622—21no—
129C2×#3622—21no—
130C2×#3622—21no—
131C2×#3622—21no—
132C2×#3622—22no—
133C2×#3622—42no—
134C2×#3622—41no—
135C2×#3622—41no—
136#9209—171nomaximal, Sylow
137C23×C17—21no—
138C23×C17#12111yescharacteristic
139Q8×C17—21no—
140Q8×C17—21no—
141D4×C17—21no—
142D4×C17—21no—
143D4×C17—41no—
144D4×C17—41no—
145C2×C4×C17—21no—
146C2×C4×C17—21no—
147C2×C4×C17—21no—
148C2×C4×C17—21no—
149C2×C4×C17—21no—
150C2×C4×C17—41no—
151C2×C4×C17—42no—
152C2×C4×C17—41no—
153C2×C4×C17—41no—
154C2×C4×C17—41no—
155C2×C4×C17—41no—
156C2×C4×C17—42no—
157C2×C4×C17—81no—
158C2×C4×C17—81no—
159C2×C4×C17C2×C22⋊C411yescharacteristic
160C2×C4×C17C4×D411yescharacteristic
161C2×C4×C17C4×D411yescharacteristic
162C2×C4×C17#12011yescharacteristic
163C2×C4×C17#12111yescharacteristic
164C2×C4×C17#12311yescharacteristic
165C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C17#13711yescharacteristic
167C2×C4×C17#13711yescharacteristic
168C2×C4×C17#13711yescharacteristic
169C2×Dic17—41no—
170C2×Dic17—41no—
171Dic34—41no—
172Dic34—41no—
173Dic34—81no—
174C8×C17—81no—
175#3622—22no—
176#3622—41no—
177#3622—42no—
178#3622—41no—
179#3622—41no—
180#3076—171no—
181#2965—171no—
182#1806D1711yescharacteristic
183#1503—171no—
184#1493—171no—
185#1301—171no—
186#1279—171no—
187C22×C17—21no—
188C22×C17—21no—
189C22×C17—41no—
190C22×C17—41no—
191C22×C17—41no—
192C22×C17#38611yescharacteristic
193C22×C17#46811yescharacteristic
194C22×C17#47011yescharacteristic
195C4×C17—21no—
196C4×C17—21no—
197C4×C17—21no—
198C4×C17—41no—
199C4×C17—41no—
200C4×C17—41no—
201C4×C17—82no—
202C4×C17#41711yescharacteristic
203C4×C17#41911yescharacteristic
204C4×C17#44311yescharacteristic
205C4×C17#44411yescharacteristic
206C4×C17#46811yescharacteristic
207C4×C17#47011yescharacteristic
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—
218#446—341no—
219#436—341no—
220#435—342no—
221#431—171no—
222#431—341no—
223#427—341no—
224#423C2×D1711yescharacteristic
225C2×C4⋊C8—171no—
226C2×#104—21no—
227#416—341no—
228C4×M16—341no—
229C2×C4×C8—171no—
230C4×C4⋊C4C2×D1711yescharacteristic
231#339—21no—
232#328—342no—
233Q8⋊C8—341no—
234Q8⋊C8—341no—
235C2×C17—21no—
236C2×C17—21no—
237C2×C17—81no—
238C2×C17#187611yescharacteristic
239C2×C17#189411yescharacteristic
240C2×C17#190611yescharacteristic
241C2×#41C22⋊D1711yescharacteristic
242C2×M16—21no—
243C2×M16—342no—
244C22×C8—341no—
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×Q8D6811yescharacteristic
255C4×D4—21no—
256C4×D4—21no—
257C4×D4C4×D1711yescharacteristic
258C4×D4D6811yescharacteristic
259#117—21no—
260#117—341no—
261#117C22⋊D1711yescharacteristic
262C2×C4⋊C4—21no—
263C2×C42—21no—
264C2×C42—21no—
265C2×C42C22×D1711yescharacteristic
266#107—341no—
267#107—341no—
268#106—341no—
269#106—341no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—171no—
273C4⋊C8—171no—
274C4⋊C8—342no—
275C4⋊C8—341no—
276C4⋊C8—341no—
277#104—42no—
278#103—341no—
279#103—341no—
280#102—341no—
281#102—341no—
282C22⋊C8—172no—
283C22⋊C8—342no—
284#97—342no—
285C4×C8—171no—
286C4×C8—171no—
287C4×C8—341no—
288C4×C8—341no—
289#95—21no—
290C17#920911yescharacteristic, complemented, Sylow
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
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—41no—
304C22×C4D4×D1711yescharacteristic
305C22×C4#6325411yescharacteristic
306C22×C4C2×C22⋊D1711yescharacteristic
307M16—41no—
308M16—41no—
309M16—684no—
310C2×C8—41no—
311C2×C8—341no—
312C2×C8—341no—
313C2×C8—342no—
314C2×C8—341no—
315C2×C8—341no—
316C2×C8—682no—
317C2×C8—681no—
318C2×C8—681no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—22no—
322C4⋊C4—41no—
323C4⋊C4—341no—
324C4⋊C4—341no—
325C4⋊C4—341no—
326C4⋊C4—341no—
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—41no—
339C42—41no—
340C42—681no—
341C42C2×C4×D1711yescharacteristic
342C42C2×D6811yescharacteristic
343C42D4×D1711yescharacteristic
344C42#6325411yescharacteristic
345C23—21no—
346C23#1058762511yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—681no—
350Q8—681no—
351Q8—1361no—
352D4—21no—
353D4—21no—
354D4—41no—
355D4—41no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—681no—
371C2×C4—681no—
372C2×C4#1058756711yescharacteristic
373C2×C4#1058756711yescharacteristic
374C2×C4#1058756811yescharacteristic
375C2×C4#1058757211yescharacteristic
376C2×C4C2×#6322711yescharacteristic
377C2×C4#1058761811yescharacteristic
378C2×C4#1058762511yescharacteristic
379C2×C4#1058762811yescharacteristic
380C2×C4#1058763711yescharacteristic
381C2×C4#1058763711yescharacteristic
382C8—81no—
383C8—342no—
384C8—681no—
385C8—682no—
386C8—681no—
387C8—681no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22#1176268611yescharacteristic
394C22#1176305311yescharacteristic
395C22#1176306511yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—82no—
403C4—1361no—
404C4—1361no—
405C4#1176280811yescharacteristic
406C4#1176281711yescharacteristic
407C4#1176292311yescharacteristic
408C4#1176292811yescharacteristic
409C4#1176305311yescharacteristic
410C4#1176306511yescharacteristic
411C2—21no—
412C2—21no—
413C2—81no—
414C2#1452910911yescharacteristic
415C2#1452921511yescharacteristic
416C2#1452928311yescharacteristic
subgroupG/H
centerC2×C4#10587625
commutatorC42×C17C22×C4
FrattiniC2×C42C22×D17
FittingC17×#1806C2
socleC22×C17#386
prime radicalC2×#41×C17D4
cosocleC2×C42×C17C23
hypercenter#1806D17
hypocenterC17#9209
LCSG ▷ C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
3. #14527282C2semidirect
4. #14527238C2semidirect
5. #14526679C2semidirect
6. #14526625C2semidirect
11. #11763104C4semidirect
12. #11763099C4semidirect
13. #11763094C4semidirect
14. #11763089C4semidirect
290. C17#9209semidirect

Maximal subgroups

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

subgroupindex
#145385722
#145377512
#145272822
#145272382
#145266792
#145266252
C17×#18062
#920917