Finite Group Databasebeta

← #46845236

Subgroups — #46845236

Order 34688.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22576181C211yesmaximal, characteristic
2#31774379C211yesmaximal, characteristic, complemented
3#31774376C211yesmaximal, characteristic, complemented
4#31773999C211yesmaximal, characteristic, complemented
5#31773998C211yesmaximal, characteristic, complemented
6#31773996C211yesmaximal, characteristic, complemented
7C4×#16864644C211yesmaximal, characteristic, complemented
8#31773989C211yesmaximal, characteristic, complemented
9C4×#16864639C211yesmaximal, characteristic, complemented
10#31773977C211yesmaximal, characteristic, complemented
11#107×D271C211yesmaximal, characteristic, complemented
12#31773897C211yesmaximal, characteristic, complemented
13#31773895C211yesmaximal, characteristic, complemented
14#31773854C211yesmaximal, characteristic, complemented
15#440×C271C211yesmaximal, characteristic, complemented
16C2×#16864655C2211yescharacteristic
17C2×#16864653C2211yescharacteristic
18#22576181C418yescomplemented
19C2×#16864644C2211yescharacteristic
20C2×#16864643C2211yescharacteristic
21C2×#16864639C2211yescharacteristic
22C2×#16864637C2211yescharacteristic
23C2×C8×D271C2211yescharacteristic
24Q8×Dic271C2211yescharacteristic
25C4×Dic542C2211yescharacteristic
26#22576125C2211yescharacteristic
27C4×D1084—21no—
28C4×D1084C2211yescharacteristic
29D4×Dic271C2211yescharacteristic
30#22576122—21no—
31#22576122C2211yescharacteristic
32C4×C22⋊D271—21no—
33(C22⋊D271)⋊C4—21no—
34#22576117—21no—
35#22576117C2211yescharacteristic
36#22576116—21no—
37C2×Dic271⋊C4—21no—
38C4⋊C4×D271—21no—
39C4⋊C4×D271C2211yescharacteristic
40C4⋊C4×D271C2211yescharacteristic
41#22576094C2211yescharacteristic
42#22576093C2211yescharacteristic
43#22576093C2211yescharacteristic
44#22576085C2211yescharacteristic
45#22576084C2211yescharacteristic
46#22576083C2211yescharacteristic
47#22576082C2211yescharacteristic
48#22576081C2211yescharacteristic
49#22576080C2211yescharacteristic
50#22576070C2211yescharacteristic
51C4×C271⋊C8C2211yescharacteristic
52C8×Dic271C2211yescharacteristic
53C2×SD16×C271C2211yescharacteristic
54C4×Q8×C271C2211yescharacteristic
55C4×D4×C271C2211yescharacteristic
56#107×C271C2211yescharacteristic
57#103×C271C2211yescharacteristic
58#102×C271C2211yescharacteristic
59#97×C271C2211yescharacteristic
60#16864655—22no—
61#16864655C2×C414yescomplemented
62#16864653—22no—
63#16864653C2×C414yescomplemented
64C2×Dic542C2311yescharacteristic
65C2×D1084—21no—
66C2×D1084C2311yescharacteristic
67C2×C22⋊D271—21no—
68C22×Dic271—21no—
69C22×Dic271—21no—
70C2×C4×D271—21no—
71C2×C4×D271—21no—
72C2×C4×D271—21no—
73C2×C4×D271—21no—
74C2×C4×D271—21no—
75C2×C4×D271C2311yescharacteristic
76#16864644C2×C414yescomplemented
77#16864643C2×C414yescomplemented
78#16864639C2×C414yescomplemented
79#16864637—22no—
80C2×C271⋊C8C2311yescharacteristic
81C2×C271⋊C8C2311yescharacteristic
82C8×D271C2×C414yescomplemented
83C4⋊Dic271—21no—
84C4⋊Dic271C2311yescharacteristic
85C4⋊Dic271C2311yescharacteristic
86Dic271⋊C4—21no—
87Dic271⋊C4—21no—
88Dic271⋊C4—21no—
89Dic271⋊C4—21no—
90Dic271⋊C4D411yescharacteristic
91Dic271⋊C4D411yescharacteristic
92C22⋊Dic271—21no—
93(C2×D271)⋊C4—21no—
94(C2×D271)⋊C4—21no—
95(C2×D271)⋊C4D411yescharacteristic
96(C2×D271)⋊C4D411yescharacteristic
97C4×Dic271—21no—
98C4×Dic271—21no—
99C4×Dic271—21no—
100C4×Dic271C2311yescharacteristic
101C2×Q8×C271C2311yescharacteristic
102C2×D4×C271C2311yescharacteristic
103C22×C4×C271—21no—
104SD16×C271C2×C414yescomplemented
105C2×C8×C271C2311yescharacteristic
106C2×C8×C271C2311yescharacteristic
107C4⋊C4×C271—21no—
108C4⋊C4×C271C2311yescharacteristic
109C4⋊C4×C271C2311yescharacteristic
110C22⋊C4×C271—21no—
111C42×C271—21no—
112C42×C271C2311yescharacteristic
113C22×D271—21no—
114C22×D271C2×D411yescharacteristic
115Dic542—21no—
116Dic542C22×C412yes—
117D1084—24no—
118D1084—21no—
119D1084C22×C412yes—
120C22⋊D271—24no—
121C2×Dic271—21no—
122C2×Dic271—24no—
123C2×Dic271—21no—
124C2×Dic271—21no—
125C2×Dic271—81no—
126C2×Dic271C2×D411yescharacteristic
127C2×Dic271C2×D411yescharacteristic
128C2×Dic271C2×D411yescharacteristic
129C4×D271—24no—
130C4×D271—81no—
131C4×D271—81no—
132C4×D271—81no—
133C4×D271—81no—
134C4×D271C22×C412yes—
135C4×D271#4112yes—
136C271⋊C8—21no—
137C271⋊C8C22×C412yes—
138C23×C271—21no—
139Q8×C271—21no—
140Q8×C271C22×C412yes—
141D4×C271—21no—
142D4×C271C22×C412yes—
143C2×C4×C271—21no—
144C2×C4×C271—21no—
145C2×C4×C271—21no—
146C2×C4×C271—81no—
147C2×C4×C271C2×D411yescharacteristic
148C2×C4×C271C2×D411yescharacteristic
149C2×C4×C271C2411yescharacteristic
150C8×C271—21no—
151C8×C271C22×C412yes—
152C22×C271—22no—
153C22×C271—41no—
154C22×C271—41no—
155C22×C271C22×D411yescharacteristic
156C2×D271—21no—
157C2×D271—21no—
158C2×D271—22no—
159C2×D271—41no—
160C2×D271—41no—
161C2×D271C4×D412yes—
162C4×C271—22no—
163C4×C271—21no—
164C4×C271—21no—
165C4×C271—41no—
166C4×C271—41no—
167C4×C271C23×C411yescharacteristic
168C4×C271C2×#4111yescharacteristic
169Dic271—22no—
170Dic271—21no—
171Dic271—21no—
172Dic271—41no—
173Dic271—41no—
174Dic271C4×D412yes—
175C2×C271—42no—
176C2×C271C2×C4×D411yescharacteristic
177C2×C271#57611yescharacteristic
178C2×C271#57811yescharacteristic
179D271—22no—
180D271—42no—
181C271#295111yescharacteristic, complemented, Sylow
182#2951—2711nomaximal, Sylow
183C2×#135—2711no—
184#520—2711no—
185#520—2711no—
186#440—2711no—
187#440—2711no—
188#440—2711no—
189#440D27111yescharacteristic, complemented
190C4×Q16—2711no—
191C4×Q16—2711no—
192C4×D8—2711no—
193C4×D8—2711no—
194C2×#107—2711no—
195#417—2711no—
196#417—2711no—
197#405—2711no—
198C2×#41—2711no—
199C2×#41—2711no—
200#135—2718no—
201C2×Q16—2711no—
202C2×SD16—2711no—
203C2×SD16C2×D27111yescharacteristic
204C2×D8—2711no—
205C2×M16—2711no—
206C22×C8—2711no—
207C4×Q8—2711no—
208C4×Q8—2711no—
209C4×Q8—2711no—
210C4×Q8C2×D27111yescharacteristic
211C4×D4—2711no—
212C4×D4—2711no—
213C4×D4—2711no—
214C4×D4—5421no—
215C4×D4—5421no—
216C4×D4—5421no—
217C4×D4—5421no—
218C4×D4C2×D27111yescharacteristic
219#117—2711no—
220#117—5421no—
221#117—5421no—
222C2×C4⋊C4—2711no—
223C2×C4⋊C4—2711no—
224C2×C4⋊C4—5421no—
225C2×C4⋊C4—5421no—
226#107—2711no—
227#107—2711no—
228#107—2711no—
229#107C2×D27111yescharacteristic
230#103—2711no—
231#103—2711no—
232#103—2711no—
233#103C2×D27111yescharacteristic
234#102—2711no—
235#102—2711no—
236#102—2711no—
237#102C2×D27111yescharacteristic
238#97—2711no—
239#97C2×D27111yescharacteristic
240C4×C8—2711no—
241C4×C8—2711no—
242#41—2714no—
243#41—2714no—
244#41—5422no—
245#41—5422no—
246C2×Q8—2711no—
247C2×Q8C22×D27111yescharacteristic
248C2×D4—2711no—
249C2×D4—5421no—
250C2×D4—5421no—
251C2×D4C22×D27111yescharacteristic
252C22×C4—21no—
253C22×C4—2711no—
254C22×C4—5421no—
255C22×C4—5421no—
256C22×C4—5421no—
257C22×C4—5421no—
258C22×C4—5421no—
259C22×C4—5421no—
260C22×C4—5421no—
261Q16—2714no—
262SD16—2714no—
263SD16C4×D27114yescomplemented
264D8—2714no—
265M16—5422no—
266C2×C8—2711no—
267C2×C8—2714no—
268C2×C8—2711no—
269C2×C8C22×D27111yescharacteristic
270C2×C8C22×D27111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—2711no—
273C4⋊C4—2711no—
274C4⋊C4—2711no—
275C4⋊C4—2711no—
276C4⋊C4—5421no—
277C4⋊C4—5421no—
278C4⋊C4—5421no—
279C4⋊C4—5421no—
280C4⋊C4—5421no—
281C4⋊C4C22×D27111yescharacteristic
282C4⋊C4C22×D27111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—2711no—
285C22⋊C4—2711no—
286C22⋊C4—5421no—
287C22⋊C4—5421no—
288C22⋊C4—5421no—
289C42—21no—
290C42—2711no—
291C42—5421no—
292C42—5421no—
293C42—5421no—
294C42C22×D27111yescharacteristic
295C23—21no—
296C23—2711no—
297C23—5421no—
298Q8—21no—
299Q8—2712no—
300Q8—5421no—
301Q8C2×C4×D27112yes—
302D4—21no—
303D4—2712no—
304D4—5424no—
305D4—5424no—
306D4—5421no—
307D4C2×C4×D27112yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—2711no—
313C2×C4—2712no—
314C2×C4—2712no—
315C2×C4—2711no—
316C2×C4—2711no—
317C2×C4—5424no—
318C2×C4—5424no—
319C2×C4—5421no—
320C2×C4—5421no—
321C2×C4—5421no—
322C2×C4—21681no—
323C2×C4—21681no—
324C2×C4—21681no—
325C2×C4—21681no—
326C2×C4—21681no—
327C2×C4D4×D27111yescharacteristic
328C2×C4D4×D27111yescharacteristic
329C2×C4C23×D27111yescharacteristic
330C8—21no—
331C8—2712no—
332C8—5421no—
333C8C2×C4×D27112yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—2712no—
338C22—5421no—
339C22—5421no—
340C22—5422no—
341C22—10841no—
342C22—10841no—
343C22C2×D4×D27111yescharacteristic
344C4—22no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—2712no—
350C4—5422no—
351C4—5421no—
352C4—5421no—
353C4—10841no—
354C4—10841no—
355C4C22×C4×D27111yescharacteristic
356C4#41×D27111yescharacteristic
357C2—42no—
358C2—5422no—
359C2—10842no—
360C2C4×D4×D27111yescharacteristic
361C2#3177470111yescharacteristic
362C2#3177471311yescharacteristic
subgroupG/H
centerC22C2×D4×D271
commutatorC4×C271C23×C4
FrattiniC2×C4C23×D271
Fitting#440×C271C2
socleC22×C271C22×D4
prime radicalC2×#22576181C2
cosocleC2×C4×C271C24
hypercenter#440D271
hypocenterC271#2951
LCSG ▷ C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #31774379C2semidirect
3. #31774376C2semidirect
4. #31773999C2semidirect
5. #31773998C2semidirect
6. #31773996C2semidirect
7. C4×#16864644C2semidirect
8. #31773989C2semidirect
9. C4×#16864639C2semidirect
10. #31773977C2semidirect
11. #107×D271C2semidirect
12. #31773897C2semidirect
13. #31773895C2semidirect
14. #31773854C2semidirect
15. #440×C271C2semidirect
18. #22576181C4semidirect
61. #16864655C2×C4semidirect
63. #16864653C2×C4semidirect
76. #16864644C2×C4semidirect
77. #16864643C2×C4semidirect
78. #16864639C2×C4semidirect
82. C8×D271C2×C4semidirect
104. SD16×C271C2×C4semidirect
181. C271#2951semidirect
189. #440D271semidirect
263. SD16C4×D271semidirect

Maximal subgroups

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

subgroupindex
C2×#225761812
#317743792
#317743762
#317739992
#317739982
#317739962
C4×#168646442
#317739892
C4×#168646392
#317739772
#107×D2712
#317738972
#317738952
#317738542
#440×C2712
#2951271