Finite Group Databasebeta

← #46822440

Subgroups — #46822440

Order 34432.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575482C211yesmaximal, characteristic, complemented
2#31771262C211yesmaximal, characteristic, complemented
3#31771254C211yesmaximal, characteristic, complemented
4#31770996C211yesmaximal, characteristic, complemented
5#31770848C211yesmaximal, characteristic, complemented
6#31770846C211yesmaximal, characteristic, complemented
7#31770818C211yesmaximal, characteristic, complemented
8#31770813C211yesmaximal, characteristic, complemented
9#31770767C211yesmaximal, characteristic, complemented
10#31770767C211yesmaximal, characteristic, complemented
11#31770759C211yesmaximal, characteristic, complemented
12#31770747C211yesmaximal, characteristic, complemented
13#31770706C211yesmaximal, characteristic, complemented
14#31770676C211yesmaximal, characteristic, complemented
15C2×#135×C269C211yesmaximal, characteristic, complemented
16C2×#16864401C2211yescharacteristic
17C2×Q8×D269C2211yescharacteristic
18#22575482—24no—
19C2×Dic1076C2211yescharacteristic
20C2×#16864392C2211yescharacteristic
21C2×#16864392C2211yescharacteristic
22C2×#16864390C2211yescharacteristic
23C2×#16864390C2211yescharacteristic
24C2×#16864385C2211yescharacteristic
25#22575451C2211yescharacteristic
26#22575440—21no—
27#22575440C2211yescharacteristic
28#22575436—21no—
29#22575434—21no—
30#22575432—21no—
31#22575432C2211yescharacteristic
32#22575432C2211yescharacteristic
33#22575429C2211yescharacteristic
34#22575425—21no—
35#22575424—21no—
36#22575424C2211yescharacteristic
37Q8×Dic269C2211yescharacteristic
38D4×Dic269C2211yescharacteristic
39C4×C22⋊D269—21no—
40C4×C22⋊D269C2211yescharacteristic
41C2×#16864381—21no—
42#22575387C2211yescharacteristic
43#22575382C2211yescharacteristic
44#22575378C2211yescharacteristic
45#22575378C2211yescharacteristic
46#22575377C2211yescharacteristic
47#22575377C2211yescharacteristic
48#22575374C2211yescharacteristic
49#22575374C2211yescharacteristic
50C22⋊#14524130C2211yescharacteristic
51#22575365C2211yescharacteristic
52#22575363C2211yescharacteristic
53C2×#41×C269C2211yescharacteristic
54C2×#41×C269C2211yescharacteristic
55#135×C269—24no—
56C2×Q16×C269C2211yescharacteristic
57C2×SD16×C269C2211yescharacteristic
58C2×SD16×C269C2211yescharacteristic
59C2×D8×C269C2211yescharacteristic
60C22×C8×C269C2211yescharacteristic
61#16864401—22no—
62#16864401—41no—
63C2×Dic538—21no—
64C2×Dic538C2311yescharacteristic
65C2×Dic538C2311yescharacteristic
66Q8×D269—22no—
67Q8×D269—41no—
68C2×C22⋊D269—21no—
69C2×C22⋊D269—21no—
70C2×C22⋊D269D411yescharacteristic
71C22×Dic269—21no—
72C22×Dic269—21no—
73C2×C4×D269—21no—
74C2×C4×D269C2311yescharacteristic
75Dic1076—22no—
76#16864392—22no—
77#16864392—41no—
78#16864390—22no—
79#16864390—41no—
80#16864385—22no—
81C2×#14524130C2311yescharacteristic
82C2×#14524130C2311yescharacteristic
83C4⋊Dic269—21no—
84C4⋊Dic269C2311yescharacteristic
85C4⋊Dic269C2311yescharacteristic
86#16864381—21no—
87#16864381—21no—
88#16864381—21no—
89#16864381—21no—
90#16864381—21no—
91#16864381D411yescharacteristic
92C22⋊Dic269—21no—
93C22⋊Dic269—21no—
94C22⋊Dic269—21no—
95C22⋊Dic269—21no—
96C22⋊Dic269—21no—
97C22⋊Dic269—21no—
98C22⋊Dic269D411yescharacteristic
99#16864379—21no—
100#16864379D411yescharacteristic
101C4×Dic269—21no—
102C4×Dic269C2311yescharacteristic
103#41×C269—22no—
104#41×C269—22no—
105#41×C269—41no—
106#41×C269—41no—
107C2×Q8×C269C2311yescharacteristic
108C2×Q8×C269C2311yescharacteristic
109C2×D4×C269—21no—
110C2×D4×C269—21no—
111C2×D4×C269C2311yescharacteristic
112C2×D4×C269C2311yescharacteristic
113C22×C4×C269—21no—
114C22×C4×C269—21no—
115C22×C4×C269C2311yescharacteristic
116Q16×C269—22no—
117SD16×C269—22no—
118SD16×C269D414yescomplemented
119D8×C269—22no—
120C2×C8×C269—22no—
121C2×C8×C269C2311yescharacteristic
122C2×C8×C269C2311yescharacteristic
123C22×D269C2×D411yescharacteristic
124Dic538—21no—
125Dic538—21no—
126Dic538—21no—
127Dic538—21no—
128Dic538—42no—
129C22⋊D269—41no—
130C22⋊D269—42no—
131C22⋊D269—42no—
132C2×Dic269—21no—
133C2×Dic269—21no—
134C2×Dic269—21no—
135C2×Dic269—21no—
136C2×Dic269—42no—
137C2×Dic269—42no—
138C2×Dic269C2×D411yescharacteristic
139C2×Dic269C2×D411yescharacteristic
140C2×Dic269C2×D411yescharacteristic
141C4×D269—21no—
142C4×D269—21no—
143C4×D269—42no—
144#14524130—21no—
145#14524130—21no—
146C23×C269—21no—
147C23×C269—21no—
148C23×C269C2×D411yescharacteristic
149Q8×C269—21no—
150Q8×C269—21no—
151Q8×C269—21no—
152Q8×C269C2×D412yes—
153D4×C269—21no—
154D4×C269—21no—
155D4×C269—21no—
156D4×C269—42no—
157D4×C269—42no—
158D4×C269C2×D412yes—
159C2×C4×C269—21no—
160C2×C4×C269—21no—
161C2×C4×C269—21no—
162C2×C4×C269—21no—
163C2×C4×C269—42no—
164C2×C4×C269—42no—
165C2×C4×C269C2×D411yescharacteristic
166C2×C4×C269C2411yescharacteristic
167C8×C269—21no—
168C8×C269C2×D412yes—
169C22×C269—21no—
170C22×C269—22no—
171C22×C269—21no—
172C22×C269—21no—
173C22×C269—41no—
174C22×C269—41no—
175C22×C269—41no—
176C22×C269—41no—
177C22×C269—41no—
178C22×C269C22×D411yescharacteristic
179C2×D269—21no—
180C2×D269—21no—
181C2×D269—21no—
182C4×C269—21no—
183C4×C269—22no—
184C4×C269—41no—
185C4×C269C22×D411yescharacteristic
186C4×C269H(5,𝔽2)11yescharacteristic
187Dic269—21no—
188Dic269—21no—
189Dic269—21no—
190Dic269—41no—
191Dic269—41no—
192Dic269—41no—
193Dic269—41no—
194C2×C269—41no—
195C2×C269—42no—
196C2×C269—81no—
197C2×C269D4211yescharacteristic
198C2×C269#57511yescharacteristic
199C2×C269#57811yescharacteristic
200D269—41no—
201C269#326911yescharacteristic, complemented, Sylow
202#3269—2691nomaximal, Sylow
203C2×#137—2691no—
204C2×#135D26911yescharacteristic, complemented
205#548—2691no—
206#547—2691no—
207#497—2691no—
208#468—2691no—
209#467—2691no—
210#463—2691no—
211#462—2691no—
212#452—2691no—
213#452—2691no—
214#451—2691no—
215#449—2691no—
216#440—2691no—
217#435—2691no—
218C2×#41—2691no—
219C2×#41C2×D26911yescharacteristic
220C2×#41C2×D26911yescharacteristic
221C22×Q8—2691no—
222#137—5384no—
223#135—24no—
224C2×Q16—2691no—
225C2×Q16—2691no—
226C2×Q16—2691no—
227C2×Q16C2×D26911yescharacteristic
228C2×SD16—2691no—
229C2×SD16—2691no—
230C2×SD16C2×D26911yescharacteristic
231C2×SD16C2×D26911yescharacteristic
232C2×D8C2×D26911yescharacteristic
233C2×M16—2691no—
234C22×C8C2×D26911yescharacteristic
235C4⋊Q8—2691no—
236#124—2691no—
237#124—5381no—
238#123—5381no—
239#123—5381no—
240C22⋊Q8—2691no—
241C22⋊Q8—2691no—
242C22⋊Q8—2691no—
243C22⋊Q8—5381no—
244#121—2691no—
245#121—5381no—
246#121—5381no—
247C4×Q8—2691no—
248C4×D4—2691no—
249C4×D4—2691no—
250C4×D4—5381no—
251C2×C4⋊C4—5381no—
252#107—2691no—
253C4⋊C8—2691no—
254#103—2691no—
255#103—2691no—
256#103—2691no—
257#103—2691no—
258#102—2691no—
259#102—2691no—
260C22⋊C8—2691no—
261C22⋊C8—2691no—
262#97—2691no—
263#41—22no—
264#41—22no—
265#41—41no—
266#41—41no—
267#41—5382no—
268#41—10761no—
269C2×Q8—2691no—
270C2×Q8—2691no—
271C2×Q8—5381no—
272C2×Q8—5382no—
273C2×Q8—10761no—
274C2×Q8C22×D26911yescharacteristic
275C2×Q8C22×D26911yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—2691no—
279C2×D4—5381no—
280C2×D4—5381no—
281C2×D4C22×D26911yescharacteristic
282C2×D4C22×D26911yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—2691no—
286C22×C4—5381no—
287C22×C4—5381no—
288C22×C4—5381no—
289C22×C4C22×D26911yescharacteristic
290Q16—22no—
291Q16—5382no—
292Q16—5382no—
293Q16—10761no—
294SD16—22no—
295SD16—5382no—
296SD16—10761no—
297SD16C22⋊D26914yescomplemented
298D8—22no—
299M16—5382no—
300C2×C8—22no—
301C2×C8—2691no—
302C2×C8—2691no—
303C2×C8C22×D26911yescharacteristic
304C2×C8C22×D26911yescharacteristic
305C4⋊C4—2691no—
306C4⋊C4—2691no—
307C4⋊C4—2691no—
308C4⋊C4—5381no—
309C4⋊C4—5381no—
310C4⋊C4—5381no—
311C4⋊C4—5381no—
312C4⋊C4—5381no—
313C4⋊C4—5381no—
314C22⋊C4—2691no—
315C22⋊C4—2691no—
316C22⋊C4—5381no—
317C22⋊C4—5381no—
318C22⋊C4—5381no—
319C22⋊C4—5381no—
320C22⋊C4—5381no—
321C22⋊C4—5381no—
322C22⋊C4—5381no—
323C42—2691no—
324C42—5381no—
325C23—21no—
326C23—21no—
327C23—2691no—
328C23D4×D26911yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—5381no—
333Q8—5381no—
334Q8—5381no—
335Q8—5381no—
336Q8—10762no—
337Q8C2×C22⋊D26912yes—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—10761no—
344D4—10762no—
345D4—10762no—
346D4C2×C22⋊D26912yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—2691no—
354C2×C4—2691no—
355C2×C4—2691no—
356C2×C4—5381no—
357C2×C4—5381no—
358C2×C4—5381no—
359C2×C4—5381no—
360C2×C4—5381no—
361C2×C4—5381no—
362C2×C4—10762no—
363C2×C4—10762no—
364C2×C4—10762no—
365C2×C4D4×D26911yescharacteristic
366C2×C4C23×D26911yescharacteristic
367C8—21no—
368C8—5381no—
369C8—5381no—
370C8C2×C22⋊D26912yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—5381no—
381C22—5381no—
382C22—5381no—
383C22C2×D4×D26911yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—5381no—
388C4—5381no—
389C4—5381no—
390C4—10761no—
391C4—10761no—
392C4—10761no—
393C4—10761no—
394C4C22×C22⋊D26911yescharacteristic
395C4#2257549811yescharacteristic
396C2—41no—
397C2—42no—
398C2—81no—
399C2—10761no—
400C2D4×C22⋊D26911yescharacteristic
401C2#3177140211yescharacteristic
402C2#3177141911yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC2×#135×C269C2
socleC22×C269C22×D4
hypercenterC2×#135D269
hypocenterC269#3269
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#22575482C2semidirect
2. #31771262C2semidirect
3. #31771254C2semidirect
4. #31770996C2semidirect
5. #31770848C2semidirect
6. #31770846C2semidirect
7. #31770818C2semidirect
8. #31770813C2semidirect
9. #31770767C2semidirect
10. #31770767C2semidirect
11. #31770759C2semidirect
12. #31770747C2semidirect
13. #31770706C2semidirect
14. #31770676C2semidirect
15. C2×#135×C269C2semidirect
118. SD16×C269D4semidirect
201. C269#3269semidirect
204. C2×#135D269semidirect
297. SD16C22⋊D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754822
#317712622
#317712542
#317709962
#317708482
#317708462
#317708182
#317708132
#317707672
#317707592
#317707472
#317707062
#317706762
C2×#135×C2692
#3269269