Finite Group Databasebeta

← #46822436

Subgroups — #46822436

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×#22575483C211yesmaximal, characteristic, complemented
2C2×#22575473C211yesmaximal, characteristic, complemented
3#31771264C211yesmaximal, characteristic, complemented
4#31770997C211yesmaximal, characteristic, complemented
5#31770853C211yesmaximal, characteristic, complemented
6#31770844C211yesmaximal, characteristic, complemented
7#31770820C211yesmaximal, characteristic, complemented
8#31770812C211yesmaximal, characteristic, complemented
9#31770767C211yesmaximal, characteristic, complemented
10#31770765C211yesmaximal, characteristic, complemented
11#31770760C211yesmaximal, characteristic, complemented
12#31770750C211yesmaximal, characteristic, complemented
13#31770705C211yesmaximal, characteristic, complemented
14#31770677C211yesmaximal, characteristic, complemented
15#547×C269C211yesmaximal, characteristic, complemented
16C2×#16864402C2211yescharacteristic
17C22×Dic538C2211yescharacteristic
18#22575483—24no—
19#22575473—24no—
20C2×#16864392C2211yescharacteristic
21C2×#16864392C2211yescharacteristic
22C2×#16864392C2211yescharacteristic
23C2×#16864392C2211yescharacteristic
24C2×#16864390C2211yescharacteristic
25C2×#16864390C2211yescharacteristic
26C2×#16864389C2211yescharacteristic
27C2×#16864389C2211yescharacteristic
28C2×#16864387C2211yescharacteristic
29C2×#16864386C2211yescharacteristic
30C22×#14524130C2211yescharacteristic
31#22575441C2211yescharacteristic
32#22575439—21no—
33#22575432C2211yescharacteristic
34#22575431—21no—
35#22575427C2211yescharacteristic
36#22575425—21no—
37C4×Dic538C2211yescharacteristic
38#22575413—21no—
39#22575386C2211yescharacteristic
40C4⋊#14524130C2211yescharacteristic
41#22575377C2211yescharacteristic
42#22575377C2211yescharacteristic
43#22575376C2211yescharacteristic
44#22575376C2211yescharacteristic
45#22575374C2211yescharacteristic
46#22575373C2211yescharacteristic
47C22⋊#14524130C2211yescharacteristic
48C22⋊#14524130C2211yescharacteristic
49#22575364C2211yescharacteristic
50C2×#41×C269C2211yescharacteristic
51C2×#41×C269C2211yescharacteristic
52C4⋊Q8×C269C2211yescharacteristic
53#123×C269—21no—
54#123×C269—21no—
55C22⋊Q8×C269C2211yescharacteristic
56C22⋊Q8×C269C2211yescharacteristic
57#121×C269—21no—
58C4×D4×C269C2211yescharacteristic
59C4×D4×C269C2211yescharacteristic
60C2×C4⋊C4×C269—21no—
61#16864402—22no—
62#16864402—41no—
63C2×Dic538—22no—
64C2×Dic538—21no—
65C2×Dic538—41no—
66C2×Dic538C2311yescharacteristic
67C2×Dic538C2311yescharacteristic
68C2×D1076C2311yescharacteristic
69C2×C22⋊D269—21no—
70C2×C22⋊D269—21no—
71C22×Dic269—21no—
72C2×C4×D269—21no—
73#16864392—22no—
74#16864392—22no—
75#16864392—22no—
76#16864392—41no—
77#16864390—22no—
78#16864390D414yescomplemented
79#16864389—22no—
80#16864389—41no—
81#16864387—22no—
82#16864386—22no—
83C2×#14524130—22no—
84C2×#14524130C2311yescharacteristic
85C2×#14524130C2311yescharacteristic
86C2×#14524130C2311yescharacteristic
87C2×#14524130C2311yescharacteristic
88C4⋊Dic269C2311yescharacteristic
89#16864381—21no—
90#16864381—21no—
91C22⋊Dic269—21no—
92#16864379—21no—
93#16864379—21no—
94#16864379—21no—
95C4×Dic269—21no—
96#41×C269—22no—
97#41×C269—22no—
98#41×C269—41no—
99#41×C269—41no—
100C2×Q8×C269C2311yescharacteristic
101C2×Q8×C269C2311yescharacteristic
102C2×D4×C269—21no—
103C2×D4×C269—21no—
104C2×D4×C269D411yescharacteristic
105C2×D4×C269C2311yescharacteristic
106C22×C4×C269—21no—
107C22×C4×C269—21no—
108C22×C4×C269—21no—
109C22×C4×C269C2311yescharacteristic
110C22×C4×C269C2311yescharacteristic
111C4⋊C4×C269—21no—
112C4⋊C4×C269—21no—
113C4⋊C4×C269—21no—
114C4⋊C4×C269—21no—
115C4⋊C4×C269D411yescharacteristic
116C4⋊C4×C269C2311yescharacteristic
117C22⋊C4×C269—21no—
118C22⋊C4×C269—21no—
119C22⋊C4×C269—21no—
120C22⋊C4×C269D411yescharacteristic
121C22⋊C4×C269D411yescharacteristic
122C42×C269C2311yescharacteristic
123C22×D269—21no—
124Dic538—21no—
125Dic538—21no—
126Dic538—21no—
127Dic538—42no—
128Dic538C2×D412yes—
129D1076—21no—
130D1076—21no—
131C22⋊D269—42no—
132C22⋊D269—42no—
133C2×Dic269—21no—
134C2×Dic269—21no—
135C2×Dic269—21no—
136C2×Dic269—42no—
137C4×D269—42no—
138#14524130—21no—
139#14524130—21no—
140#14524130—21no—
141#14524130C2×D412yes—
142C23×C269—21no—
143C23×C269C2×D411yescharacteristic
144C23×C269C2×D411yescharacteristic
145Q8×C269—21no—
146Q8×C269—21no—
147Q8×C269—21no—
148Q8×C269—21no—
149D4×C269—21no—
150D4×C269—41no—
151D4×C269—42no—
152D4×C269—42no—
153D4×C269C2×D412yes—
154C2×C4×C269—21no—
155C2×C4×C269—21no—
156C2×C4×C269—21no—
157C2×C4×C269—21no—
158C2×C4×C269—21no—
159C2×C4×C269—21no—
160C2×C4×C269—21no—
161C2×C4×C269—42no—
162C2×C4×C269—42no—
163C2×C4×C269—42no—
164C2×C4×C269C2×D411yescharacteristic
165C2×C4×C269C2×D411yescharacteristic
166C2×C4×C269C2×D411yescharacteristic
167C2×C4×C269C2×D411yescharacteristic
168C2×C4×C269C2411yescharacteristic
169C22×C269—21no—
170C22×C269—21no—
171C22×C269—22no—
172C22×C269—21no—
173C22×C269—21no—
174C22×C269—21no—
175C22×C269—21no—
176C22×C269—41no—
177C22×C269—41no—
178C22×C269C22×D411yescharacteristic
179C2×D269—41no—
180C2×D269—41no—
181C2×D269—41no—
182C4×C269—21no—
183C4×C269—21no—
184C4×C269—21no—
185C4×C269—21no—
186C4×C269—41no—
187C4×C269—41no—
188C4×C269—41no—
189C4×C269C22×D411yescharacteristic
190C4×C269H(5,𝔽2)11yescharacteristic
191Dic269—22no—
192Dic269—41no—
193Dic269—41no—
194C2×C269—41no—
195C2×C269—41no—
196C2×C269—42no—
197C2×C269D4211yescharacteristic
198C2×C269#57511yescharacteristic
199C2×C269#57811yescharacteristic
200D269—81no—
201C269#326911yescharacteristic, complemented, Sylow
202#3269—2691nomaximal, Sylow
203C2×#137—2691no—
204C2×#135—2691no—
205#548—2691no—
206#547D26911yescharacteristic, complemented
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—5384no—
224C2×Q16—2691no—
225C2×Q16—2691no—
226C2×Q16—2691no—
227C2×Q16—2691no—
228C2×SD16—2691no—
229C2×SD16—2691no—
230C2×SD16—2691no—
231C2×SD16—2691no—
232C2×D8—2691no—
233C2×M16—2691no—
234C22×C8—2691no—
235C4⋊Q8C2×D26911yescharacteristic
236#124—2691no—
237#124—5381no—
238#123—21no—
239#123—21no—
240C22⋊Q8—2691no—
241C22⋊Q8—5381no—
242C22⋊Q8C2×D26911yescharacteristic
243C22⋊Q8C2×D26911yescharacteristic
244#121—21no—
245#121—2691no—
246#121—5381no—
247C4×Q8—2691no—
248C4×D4—5381no—
249C4×D4C2×D26911yescharacteristic
250C4×D4C2×D26911yescharacteristic
251C2×C4⋊C4—21no—
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—5382no—
272C2×Q8—5381no—
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—21no—
286C22×C4—5381no—
287C22×C4—5381no—
288C22×C4C22×D26911yescharacteristic
289C22×C4C22×D26911yescharacteristic
290Q16—5382no—
291Q16—5382no—
292Q16—5382no—
293Q16—10761no—
294SD16—2694no—
295SD16—5382no—
296SD16—5382no—
297SD16—10761no—
298D8—5382no—
299M16—5382no—
300C2×C8—2691no—
301C2×C8—2691no—
302C2×C8—2691no—
303C2×C8—2691no—
304C2×C8—5382no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—2691no—
310C4⋊C4—5381no—
311C4⋊C4—5381no—
312C4⋊C4C22⋊D26911yescharacteristic
313C4⋊C4C22×D26911yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—5381no—
318C22⋊C4—5381no—
319C22⋊C4—5381no—
320C22⋊C4—5381no—
321C22⋊C4C22⋊D26911yescharacteristic
322C22⋊C4C22⋊D26911yescharacteristic
323C42—5381no—
324C42C22×D26911yescharacteristic
325C23—21no—
326C23—5381no—
327C23C2×C22⋊D26911yescharacteristic
328C23C2×C22⋊D26911yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—2692no—
334Q8—5381no—
335Q8—5381no—
336Q8—5381no—
337Q8—10762no—
338D4—21no—
339D4—41no—
340D4—42no—
341D4—42no—
342D4—5381no—
343D4—5381no—
344D4—10762no—
345D4—10762no—
346D4D4×D26912yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—5381no—
358C2×C4—5381no—
359C2×C4—5381no—
360C2×C4—10762no—
361C2×C4—10762no—
362C2×C4C2×C22⋊D26911yescharacteristic
363C2×C4C2×C22⋊D26911yescharacteristic
364C2×C4C2×C22⋊D26911yescharacteristic
365C2×C4C2×C22⋊D26911yescharacteristic
366C2×C4C23×D26911yescharacteristic
367C8—2692no—
368C8—5381no—
369C8—5381no—
370C8—5381no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—22no—
378C22—41no—
379C22—41no—
380C22—10761no—
381C22—10761no—
382C22—10761no—
383C22C22×C22⋊D26911yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—5382no—
392C4—10761no—
393C4—10761no—
394C4C2×D4×D26911yescharacteristic
395C4#2257549811yescharacteristic
396C2—41no—
397C2—41no—
398C2—42no—
399C2—21521no—
400C2D4×C22⋊D26911yescharacteristic
401C2#3177140311yescharacteristic
402C2#3177142011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#547×C269C2
socleC22×C269C22×D4
hypercenter#547D269
hypocenterC269#3269
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C2×#22575483C2semidirect
2. C2×#22575473C2semidirect
3. #31771264C2semidirect
4. #31770997C2semidirect
5. #31770853C2semidirect
6. #31770844C2semidirect
7. #31770820C2semidirect
8. #31770812C2semidirect
9. #31770767C2semidirect
10. #31770765C2semidirect
11. #31770760C2semidirect
12. #31770750C2semidirect
13. #31770705C2semidirect
14. #31770677C2semidirect
15. #547×C269C2semidirect
78. #16864390D4semidirect
201. C269#3269semidirect
206. #547D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754832
C2×#225754732
#317712642
#317709972
#317708532
#317708442
#317708202
#317708122
#317707672
#317707652
#317707602
#317707502
#317707052
#317706772
#547×C2692
#3269269