Finite Group Databasebeta

← #46822398

Subgroups — #46822398

Order 34432.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575484C211yesmaximal, characteristic, complemented
2C2×SD16×D269C211yesmaximal, characteristic, complemented
3Q8×C22⋊D269C211yesmaximal, characteristic, complemented
4#31771252C211yesmaximal, characteristic
5#31770996C211yesmaximal, characteristic, complemented
6#31770849C211yesmaximal, characteristic, complemented
7#31770845C211yesmaximal, characteristic, complemented
8#31770825C211yesmaximal, characteristic, complemented
9#31770809C211yesmaximal, characteristic, complemented
10#31770769C211yesmaximal, characteristic, complemented
11#31770762C211yesmaximal, characteristic, complemented
12#31770754C211yesmaximal, characteristic, complemented
13#31770708C211yesmaximal, characteristic, complemented
14#31770679C211yesmaximal, characteristic, complemented
15#448×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C2×Q8×D269C2211yescharacteristic
18C2×D4×D269C2211yescharacteristic
19#22575484—24no—
20C2×Dic1076C2211yescharacteristic, complemented
21C2×#16864392C2211yescharacteristic, complemented
22C2×#16864392C2211yescharacteristic, complemented
23C2×#16864391C2211yescharacteristic
24C2×#16864390C2211yescharacteristic
25C2×#16864389C2211yescharacteristic
26C2×#16864389C2211yescharacteristic
27SD16×D269—24no—
28C2×#16864386C2211yescharacteristic, complemented
29C2×C8×D269C2211yescharacteristic
30#22575451—21no—
31#22575451C2211yescharacteristic, complemented
32#22575440C2211yescharacteristic
33#22575435—21no—
34#22575433C2211yescharacteristic
35#22575432—21no—
36#22575432C2211yescharacteristic, complemented
37#22575429—21no—
38#22575429C2211yescharacteristic
39#22575424—21no—
40#22575421—21no—
41Q8×Dic269C2211yescharacteristic, complemented
42#22575415C2211yescharacteristic
43C4×C22⋊D269—21no—
44C4×C22⋊D269C2211yescharacteristic
45C22⋊C4×D269—21no—
46#22575386C2211yescharacteristic, complemented
47#22575382C2211yescharacteristic, complemented
48#22575378C2211yescharacteristic, complemented
49#22575376C2211yescharacteristic, complemented
50#22575375C2211yescharacteristic
51#22575374C2211yescharacteristic
52#22575365C2211yescharacteristic
53#22575363C2211yescharacteristic, complemented
54C22×Q8×C269C2211yescharacteristic, complemented
55C2×SD16×C269C2211yescharacteristic
56C2×SD16×C269C2211yescharacteristic
57#121×C269C2211yescharacteristic
58#103×C269C2211yescharacteristic, complemented
59#103×C269C2211yescharacteristic, complemented
60C22⋊C8×C269C2211yescharacteristic, complemented
61C23×D269—21no—
62#16864402—22no—
63#16864402—41no—
64C2×Dic538—21no—
65C2×Dic538C2311yescharacteristic
66C2×Dic538C2311yescharacteristic
67Q8×D269—22no—
68Q8×D269—41no—
69C2×D1076C2311yescharacteristic
70C2×C22⋊D269—21no—
71C2×C22⋊D269—21no—
72C2×C22⋊D269D411yescharacteristic
73D4×D269—22no—
74D4×D269—41no—
75C2×C4×D269—21no—
76C2×C4×D269—21no—
77C2×C4×D269—21no—
78C2×C4×D269C2311yescharacteristic
79Dic1076—41no—
80#16864392—22no—
81#16864392—22no—
82#16864391—22no—
83#16864390—22no—
84#16864389—22no—
85#16864389D414yescomplemented
86#16864386—22no—
87C2×#14524130C2311yescharacteristic
88C2×#14524130C2311yescharacteristic
89C8×D269—22no—
90C4⋊Dic269—21no—
91C4⋊Dic269—21no—
92C4⋊Dic269C2311yescharacteristic
93#16864381—21no—
94#16864381—21no—
95#16864381—21no—
96#16864381—21no—
97#16864381D411yescharacteristic
98C22⋊Dic269—21no—
99C22⋊Dic269—21no—
100C22⋊Dic269—21no—
101C22⋊Dic269D411yescharacteristic
102#16864379—21no—
103#16864379—21no—
104#16864379—21no—
105#16864379D411yescharacteristic
106C4×Dic269—21no—
107C4×Dic269C2311yescharacteristic
108C2×Q8×C269—21no—
109C2×Q8×C269—22no—
110C2×Q8×C269—41no—
111C2×Q8×C269C2311yescharacteristic
112C2×Q8×C269C2311yescharacteristic
113C2×D4×C269—21no—
114C2×D4×C269C2311yescharacteristic
115C22×C4×C269—21no—
116C22×C4×C269C2311yescharacteristic
117SD16×C269—22no—
118SD16×C269—41no—
119C2×C8×C269C2311yescharacteristic
120C2×C8×C269C2311yescharacteristic
121C4⋊C4×C269C2311yescharacteristic
122C22⋊C4×C269—21no—
123C22×D269—21no—
124C22×D269—42no—
125C22×D269—42no—
126C22×D269—81no—
127C22×D269C2×D411yescharacteristic
128Dic538—21no—
129Dic538—21no—
130Dic538—21no—
131Dic538—21no—
132Dic538—42no—
133D1076—21no—
134D1076C2×D412yes—
135C22⋊D269—22no—
136C22⋊D269—42no—
137C22⋊D269—42no—
138C2×Dic269—21no—
139C2×Dic269—21no—
140C2×Dic269—21no—
141C2×Dic269C2×D411yescharacteristic
142C2×Dic269C2×D411yescharacteristic
143C2×Dic269C2×D411yescharacteristic
144C4×D269—21no—
145C4×D269—21no—
146C4×D269—42no—
147C4×D269—42no—
148C4×D269—81no—
149#14524130—21no—
150#14524130C2×D412yes—
151C23×C269—21no—
152C23×C269C2×D411yescharacteristic
153Q8×C269—21no—
154Q8×C269—21no—
155Q8×C269—21no—
156Q8×C269—42no—
157Q8×C269C2×D412yes—
158D4×C269—21no—
159D4×C269—21no—
160D4×C269—81no—
161C2×C4×C269—21no—
162C2×C4×C269—21no—
163C2×C4×C269—21no—
164C2×C4×C269—21no—
165C2×C4×C269—21no—
166C2×C4×C269—42no—
167C2×C4×C269C2×D411yescharacteristic
168C2×C4×C269C2411yescharacteristic
169C8×C269—21no—
170C8×C269—21no—
171C22×C269—21no—
172C22×C269—21no—
173C22×C269—21no—
174C22×C269—41no—
175C22×C269—41no—
176C22×C269—41no—
177C22×C269C22×D411yescharacteristic
178C2×D269—21no—
179C2×D269—21no—
180C2×D269—22no—
181C2×D269—41no—
182C2×D269—41no—
183C2×D269—84no—
184C2×D269#13712yescomplemented
185C4×C269—21no—
186C4×C269—22no—
187C4×C269—41no—
188C4×C269—41no—
189C4×C269C22×D411yescharacteristic
190C4×C269H(5,𝔽2)11yescharacteristic
191Dic269—21no—
192Dic269—21no—
193Dic269—21no—
194Dic269—41no—
195Dic269—41no—
196Dic269—41no—
197C2×C269—41no—
198C2×C269—81no—
199C2×C269D4211yescharacteristic
200C2×C269C2×#13711yescharacteristic
201C2×C269#57711yescharacteristic
202D269—22no—
203D269—42no—
204C269#326611yescharacteristic, complemented, Sylow
205#3266—2691nomaximal, Sylow
206C2×#137—2691no—
207C22×SD16—2691no—
208D4×Q8—2691no—
209#546—2691no—
210#497—2691no—
211#468—2691no—
212#467—2691no—
213#464—2691no—
214#461—2691no—
215#452—2691no—
216#451—2691no—
217#450—2691no—
218#448D26911yescharacteristic, complemented
219#440—2691no—
220#435—2691no—
221C2×#41—2691no—
222C22×Q8—2691no—
223C22×Q8C2×D26911yescharacteristic, complemented
224C22×D4—2691no—
225#137—5384no—
226C2×Q16—2691no—
227C2×Q16—2691no—
228C2×Q16—2691no—
229C2×SD16—2691no—
230C2×SD16—2691no—
231C2×SD16—2691no—
232C2×SD16—2691no—
233C2×SD16—5384no—
234C2×SD16C2×D26911yescharacteristic
235C2×SD16C2×D26911yescharacteristic
236C2×M16—2691no—
237C22×C8—2691no—
238C4⋊Q8—2691no—
239C4⋊Q8—5381no—
240#124—2691no—
241#123—5381no—
242C22⋊Q8—2691no—
243C22⋊Q8—2691no—
244C22⋊Q8—2691no—
245C22⋊Q8—5381no—
246C22⋊Q8—5381no—
247#121—5381no—
248#121C2×D26911yescharacteristic
249#120—5381no—
250C4×Q8—2691no—
251C4×D4—2691no—
252C4×D4—2691no—
253C4×D4—5381no—
254C2×C22⋊C4—5381no—
255#107—2691no—
256C4⋊C8—2691no—
257#103—2691no—
258#103—2691no—
259#103C2×D26911yescharacteristic, complemented
260#103C2×D26911yescharacteristic, complemented
261#102—2691no—
262#102—2691no—
263C22⋊C8—2691no—
264C22⋊C8C2×D26911yescharacteristic, complemented
265#97—2691no—
266C24—5381no—
267#41—5382no—
268#41—10761no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—2691no—
273C2×Q8—2691no—
274C2×Q8—5381no—
275C2×Q8—5382no—
276C2×Q8—10761no—
277C2×Q8C22×D26911yescharacteristic
278C2×Q8C22×D26911yescharacteristic
279C2×D4—21no—
280C2×D4—2691no—
281C2×D4—2691no—
282C2×D4—5381no—
283C2×D4—5382no—
284C2×D4—5381no—
285C2×D4—10761no—
286C2×D4C22×D26911yescharacteristic
287C22×C4—21no—
288C22×C4—2691no—
289C22×C4—5381no—
290C22×C4—5381no—
291C22×C4—5381no—
292C22×C4C22×D26911yescharacteristic
293Q16—5382no—
294Q16—5382no—
295Q16—10761no—
296SD16—22no—
297SD16—41no—
298SD16—2694no—
299SD16—5382no—
300SD16—5382no—
301SD16—5382no—
302M16—5382no—
303C2×C8—2691no—
304C2×C8—2691no—
305C2×C8—5382no—
306C2×C8C22×D26911yescharacteristic
307C2×C8C22×D26911yescharacteristic
308C4⋊C4—2691no—
309C4⋊C4—2691no—
310C4⋊C4—5381no—
311C4⋊C4—5381no—
312C4⋊C4—5381no—
313C4⋊C4—5381no—
314C4⋊C4—5381no—
315C4⋊C4—5381no—
316C4⋊C4C22×D26911yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—2691no—
319C22⋊C4—2691no—
320C22⋊C4—5381no—
321C22⋊C4—5381no—
322C22⋊C4—5381no—
323C22⋊C4—5381no—
324C22⋊C4—5381no—
325C22⋊C4—5381no—
326C42—2691no—
327C42—5381no—
328C23—21no—
329C23—2691no—
330C23—5381no—
331C23—10762no—
332C23—10762no—
333C23—21521no—
334C23D4×D26911yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—42no—
339Q8—5381no—
340Q8—5381no—
341Q8—5381no—
342Q8—5381no—
343Q8—10762no—
344Q8D4×D26912yes—
345D4—21no—
346D4—21no—
347D4—81no—
348D4—2692no—
349D4—5382no—
350D4—5381no—
351D4—10762no—
352D4—10762no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—42no—
359C2×C4—2691no—
360C2×C4—2691no—
361C2×C4—2691no—
362C2×C4—5381no—
363C2×C4—5381no—
364C2×C4—5381no—
365C2×C4—5381no—
366C2×C4—5381no—
367C2×C4—10762no—
368C2×C4—10762no—
369C2×C4—21521no—
370C2×C4D4×D26911yescharacteristic
371C2×C4C23×D26911yescharacteristic
372C8—21no—
373C8—21no—
374C8—2692no—
375C8—5381no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—2692no—
383C22—5381no—
384C22—5381no—
385C22—5382no—
386C22—10761no—
387C22—10761no—
388C22—21524no—
389C22C2×D4×D26911yescharacteristic
390C4—21no—
391C4—22no—
392C4—41no—
393C4—41no—
394C4—5381no—
395C4—5381no—
396C4—5381no—
397C4—10761no—
398C4—10761no—
399C4—10761no—
400C4C2×D4×D26911yescharacteristic
401C4#2257549811yescharacteristic
402C2—41no—
403C2—81no—
404C2—5382no—
405C2—10762no—
406C2#3177123711yescharacteristic
407C2#137×D26911yescharacteristic
408C2#3177141111yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#448×C269C2
socleC22×C269C22×D4
prime radical#31771252C2
hypercenter#448D269
hypocenterC269#3266
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#22575484C2semidirect
2. C2×SD16×D269C2semidirect
3. Q8×C22⋊D269C2semidirect
5. #31770996C2semidirect
6. #31770849C2semidirect
7. #31770845C2semidirect
8. #31770825C2semidirect
9. #31770809C2semidirect
10. #31770769C2semidirect
11. #31770762C2semidirect
12. #31770754C2semidirect
13. #31770708C2semidirect
14. #31770679C2semidirect
15. #448×C269C2semidirect
20. C2×Dic1076C22semidirect
21. C2×#16864392C22semidirect
22. C2×#16864392C22semidirect
28. C2×#16864386C22semidirect
31. #22575451C22semidirect
36. #22575432C22semidirect
41. Q8×Dic269C22semidirect
46. #22575386C22semidirect
47. #22575382C22semidirect
48. #22575378C22semidirect
49. #22575376C22semidirect
53. #22575363C22semidirect
54. C22×Q8×C269C22semidirect
58. #103×C269C22semidirect
59. #103×C269C22semidirect
60. C22⋊C8×C269C22semidirect
85. #16864389D4semidirect
184. C2×D269#137semidirect
204. C269#3266semidirect
218. #448D269semidirect
223. C22×Q8C2×D269semidirect
259. #103C2×D269semidirect
260. #103C2×D269semidirect
264. C22⋊C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754842
C2×SD16×D2692
Q8×C22⋊D2692
#317712522
#317709962
#317708492
#317708452
#317708252
#317708092
#317707692
#317707622
#317707542
#317707082
#317706792
#448×C2692
#3266269