Finite Group Databasebeta

← #16831041

Subgroups — #16831041

Order 3712.

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×#11745278C211yesmaximal, characteristic, complemented
2#14271824C211yesmaximal, characteristic, complemented
3#14271812C211yesmaximal, characteristic, complemented
4#14271556C211yesmaximal, characteristic, complemented
5#14271409C211yesmaximal, characteristic, complemented
6#14271401C211yesmaximal, characteristic, complemented
7#14271380C211yesmaximal, characteristic, complemented
8#14271371C211yesmaximal, characteristic, complemented
9#14271324C211yesmaximal, characteristic, complemented
10#14271322C211yesmaximal, characteristic, complemented
11#14271319C211yesmaximal, characteristic, complemented
12#14271308C211yesmaximal, characteristic, complemented
13#14271264C211yesmaximal, characteristic, complemented
14#14271232C211yesmaximal, characteristic, complemented
15C2×C29×#137C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C22×Q8×C29C2211yescharacteristic
18C2×#90809C2211yescharacteristic
19C2×#90807C2211yescharacteristic
20C29×#137—24no—
21C2×Q16×C29C2211yescharacteristic
22C2×Q16×C29C2211yescharacteristic
23C2×SD16×C29C2211yescharacteristic
24C2×SD16×C29C2211yescharacteristic
25C2×M16×C29C2211yescharacteristic
26#11745309—21no—
27#11745309C2211yescharacteristic
28#11745308—21no—
29#11745308C2211yescharacteristic
30#11745308C2211yescharacteristic
31Q8×Dic29C2211yescharacteristic
32#11745306C2211yescharacteristic
33C2×#90785C2211yescharacteristic
34C2×#90785C2211yescharacteristic
35C2×#90784C2211yescharacteristic
36#11745301—21no—
37#11745297—21no—
38D4×Dic29C2211yescharacteristic
39C2×#90782C2211yescharacteristic
40#11745292—21no—
41#11745292C2211yescharacteristic
42#11745291—21no—
43C4×C22⋊D29—21no—
44C4×C22⋊D29C2211yescharacteristic
45#11745286C2211yescharacteristic
46C2×#90779—21no—
47#11745278—24no—
48C2×#90773C2211yescharacteristic
49C2×C8×D29C2211yescharacteristic
50#11745183C2211yescharacteristic
51#11745183C2211yescharacteristic
52#11745183C2211yescharacteristic
53#11745180C2211yescharacteristic
54C22⋊#6597C2211yescharacteristic
55#11745169C2211yescharacteristic
56#11745168C2211yescharacteristic
57#11745166C2211yescharacteristic
58#11745164C2211yescharacteristic
59#11745163C2211yescharacteristic
60#11745162C2211yescharacteristic
61#41×C29—22no—
62#41×C29—41no—
63C2×Q8×C29—21no—
64C2×Q8×C29—22no—
65C2×Q8×C29—41no—
66C2×Q8×C29C2311yescharacteristic
67C2×Q8×C29C2311yescharacteristic
68C2×Q8×C29C2311yescharacteristic
69C2×D4×C29—21no—
70C2×D4×C29C2311yescharacteristic
71C22×C4×C29—21no—
72C22×C4×C29—21no—
73C22×C4×C29C2311yescharacteristic
74C2×C22⋊D29—21no—
75C2×C22⋊D29—21no—
76C2×C22⋊D29D411yescharacteristic
77C22×Dic29—21no—
78C22×Dic29—21no—
79#90809—22no—
80#90809—41no—
81#90807—22no—
82#90807—41no—
83C2×D116—21no—
84C2×D116C2311yescharacteristic
85C2×C4×D29—21no—
86C2×C4×D29C2311yescharacteristic
87C2×Dic58C2311yescharacteristic
88Q16×C29—22no—
89Q16×C29—22no—
90SD16×C29—22no—
91SD16×C29D414yescomplemented
92M16×C29—22no—
93C2×C8×C29C2311yescharacteristic
94C2×C8×C29C2311yescharacteristic
95C22⋊Dic29—21no—
96C22⋊Dic29—21no—
97C22⋊Dic29D411yescharacteristic
98#90785—22no—
99#90785—41no—
100#90784—41no—
101#90782—22no—
102#90781—21no—
103#90781—21no—
104#90781—21no—
105#90781—21no—
106#90781—21no—
107#90781D411yescharacteristic
108C4⋊Dic29—21no—
109C4⋊Dic29C2311yescharacteristic
110C4⋊Dic29C2311yescharacteristic
111#90779—21no—
112#90779—21no—
113#90779—21no—
114#90779—21no—
115#90779—21no—
116#90779D411yescharacteristic
117C4×Dic29—21no—
118C4×Dic29C2311yescharacteristic
119C2×#6597C2311yescharacteristic
120C2×#6597C2311yescharacteristic
121#90773—22no—
122C8×D29—22no—
123C23×C29—21no—
124C23×C29C2×D411yescharacteristic
125C22×D29—21no—
126C22×D29C2×D411yescharacteristic
127Q8×C29—21no—
128Q8×C29—21no—
129Q8×C29—21no—
130Q8×C29—21no—
131Q8×C29—21no—
132Q8×C29—42no—
133Q8×C29C2×D412yes—
134D4×C29—21no—
135D4×C29—42no—
136D4×C29C2×D412yes—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—21no—
142C2×C4×C29—42no—
143C2×C4×C29—42no—
144C2×C4×C29C2×D411yescharacteristic
145C2×C4×C29C2411yescharacteristic
146C22⋊D29—41no—
147C22⋊D29—42no—
148C22⋊D29—42no—
149C2×Dic29—21no—
150C2×Dic29—21no—
151C2×Dic29—21no—
152C2×Dic29—42no—
153C2×Dic29—42no—
154C2×Dic29C2×D411yescharacteristic
155C2×Dic29C2×D411yescharacteristic
156C2×Dic29C2×D411yescharacteristic
157D116—21no—
158D116—21no—
159D116—42no—
160C4×D29—21no—
161C4×D29—21no—
162C4×D29—42no—
163Dic58—21no—
164Dic58—21no—
165C8×C29—21no—
166C8×C29C2×D412yes—
167#6597—21no—
168#6597—21no—
169#3269—291nomaximal, Sylow
170C22×C29—22no—
171C22×C29—21no—
172C22×C29—21no—
173C22×C29—21no—
174C22×C29—41no—
175C22×C29—41no—
176C22×C29C22×D411yescharacteristic
177C2×D29—21no—
178C2×D29—21no—
179C2×D29—21no—
180C2×D29—41no—
181C2×D29—41no—
182C2×D29—41no—
183C4×C29—22no—
184C4×C29—21no—
185C4×C29—41no—
186C4×C29—41no—
187C4×C29C22×D411yescharacteristic
188C4×C29H(5,𝔽2)11yescharacteristic
189Dic29—21no—
190Dic29—21no—
191Dic29—21no—
192Dic29—41no—
193Dic29—41no—
194Dic29—41no—
195C2×#137D2911yescharacteristic, complemented
196C2×#135—291no—
197#548—291no—
198#547—291no—
199#497—291no—
200#468—291no—
201#467—291no—
202#463—291no—
203#462—291no—
204#452—291no—
205#452—291no—
206#451—291no—
207#449—291no—
208#440—291no—
209#435—291no—
210C2×C29—41no—
211C2×C29—42no—
212C2×C29D4211yescharacteristic
213C2×C29#57511yescharacteristic
214C2×C29#57811yescharacteristic
215D29—41no—
216D29—81no—
217C2×#41—291no—
218C2×#41—291no—
219C2×#41C2×D2911yescharacteristic
220C22×Q8C2×D2911yescharacteristic
221#137—24no—
222#135—584no—
223C2×Q16—291no—
224C2×Q16—291no—
225C2×Q16C2×D2911yescharacteristic
226C2×Q16C2×D2911yescharacteristic
227C2×SD16—291no—
228C2×SD16—291no—
229C2×SD16C2×D2911yescharacteristic
230C2×SD16C2×D2911yescharacteristic
231C2×D8—291no—
232C2×M16C2×D2911yescharacteristic
233C22×C8—291no—
234C4⋊Q8—291no—
235#124—291no—
236#124—581no—
237#123—581no—
238#123—581no—
239C22⋊Q8—291no—
240C22⋊Q8—291no—
241C22⋊Q8—291no—
242C22⋊Q8—581no—
243#121—291no—
244#121—581no—
245#121—581no—
246C4×Q8—291no—
247C4×D4—291no—
248C4×D4—291no—
249C4×D4—581no—
250C2×C4⋊C4—581no—
251#107—291no—
252C4⋊C8—291no—
253#103—291no—
254#103—291no—
255#103—291no—
256#103—291no—
257#102—291no—
258#102—291no—
259C22⋊C8—291no—
260C22⋊C8—291no—
261#97—291no—
262C29#326911yescharacteristic, complemented, Sylow
263#41—22no—
264#41—41no—
265#41—582no—
266#41—582no—
267#41—1161no—
268#41—1161no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—291no—
273C2×Q8C22×D2911yescharacteristic
274C2×Q8C22×D2911yescharacteristic
275C2×Q8C22×D2911yescharacteristic
276C2×D4—21no—
277C2×D4—291no—
278C2×D4—291no—
279C2×D4—581no—
280C2×D4—581no—
281C2×D4—581no—
282C2×D4C22×D2911yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—291no—
286C22×C4—581no—
287C22×C4—581no—
288C22×C4—581no—
289C22×C4C22×D2911yescharacteristic
290Q16—22no—
291Q16—22no—
292Q16—582no—
293Q16—1161no—
294SD16—22no—
295SD16—582no—
296SD16—1161no—
297SD16C22⋊D2914yescomplemented
298D8—582no—
299M16—22no—
300C2×C8—291no—
301C2×C8—291no—
302C2×C8—582no—
303C2×C8C22×D2911yescharacteristic
304C2×C8C22×D2911yescharacteristic
305C4⋊C4—291no—
306C4⋊C4—291no—
307C4⋊C4—291no—
308C4⋊C4—581no—
309C4⋊C4—581no—
310C4⋊C4—581no—
311C4⋊C4—581no—
312C4⋊C4—581no—
313C4⋊C4—581no—
314C22⋊C4—291no—
315C22⋊C4—291no—
316C22⋊C4—581no—
317C22⋊C4—581no—
318C22⋊C4—581no—
319C22⋊C4—581no—
320C22⋊C4—581no—
321C22⋊C4—581no—
322C22⋊C4—581no—
323C42—291no—
324C42—581no—
325C23—21no—
326C23—291no—
327C23—581no—
328C23D4×D2911yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—42no—
335Q8—581no—
336Q8—581no—
337Q8C2×C22⋊D2912yes—
338D4—21no—
339D4—42no—
340D4—581no—
341D4—581no—
342D4—1162no—
343D4—1161no—
344D4—1162no—
345D4—1162no—
346D4C2×C22⋊D2912yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—291no—
355C2×C4—291no—
356C2×C4—291no—
357C2×C4—581no—
358C2×C4—581no—
359C2×C4—581no—
360C2×C4—581no—
361C2×C4—581no—
362C2×C4—1162no—
363C2×C4—1162no—
364C2×C4—1162no—
365C2×C4D4×D2911yescharacteristic
366C2×C4C23×D2911yescharacteristic
367C8—21no—
368C8—581no—
369C8—581no—
370C8C2×C22⋊D2912yes—
371C22—21no—
372C22—22no—
373C22—21no—
374C22—21no—
375C22—41no—
376C22—41no—
377C22—581no—
378C22—581no—
379C22—581no—
380C22—1161no—
381C22—1161no—
382C22—1161no—
383C22C2×D4×D2911yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—41no—
388C4—581no—
389C4—581no—
390C4—581no—
391C4—1161no—
392C4—1161no—
393C4—1161no—
394C4#1174535911yescharacteristic
395C4C22×C22⋊D2911yescharacteristic
396C2—41no—
397C2—42no—
398C2—1161no—
399C2—2321no—
400C2D4×C22⋊D2911yescharacteristic
401C2#1427196211yescharacteristic
402C2#1427197911yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#137C2
socleC22×C29C22×D4
hypercenterC2×#137D29
hypocenterC29#3269
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#11745278C2semidirect
2. #14271824C2semidirect
3. #14271812C2semidirect
4. #14271556C2semidirect
5. #14271409C2semidirect
6. #14271401C2semidirect
7. #14271380C2semidirect
8. #14271371C2semidirect
9. #14271324C2semidirect
10. #14271322C2semidirect
11. #14271319C2semidirect
12. #14271308C2semidirect
13. #14271264C2semidirect
14. #14271232C2semidirect
15. C2×C29×#137C2semidirect
91. SD16×C29D4semidirect
195. C2×#137D29semidirect
262. C29#3269semidirect
297. SD16C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117452782
#142718242
#142718122
#142715562
#142714092
#142714012
#142713802
#142713712
#142713242
#142713222
#142713192
#142713082
#142712642
#142712322
C2×C29×#1372
#326929