Finite Group Databasebeta

← #16831043

Subgroups — #16831043

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×#11745313C211yesmaximal, characteristic, complemented
2C2×#11745312C211yesmaximal, characteristic, complemented
3#14271822C211yesmaximal, characteristic, complemented
4#14271555C211yesmaximal, characteristic, complemented
5#14271411C211yesmaximal, characteristic, complemented
6#14271402C211yesmaximal, characteristic, complemented
7#14271378C211yesmaximal, characteristic, complemented
8#14271370C211yesmaximal, characteristic, complemented
9#14271325C211yesmaximal, characteristic, complemented
10#14271323C211yesmaximal, characteristic, complemented
11#14271318C211yesmaximal, characteristic, complemented
12#14271308C211yesmaximal, characteristic, complemented
13#14271263C211yesmaximal, characteristic, complemented
14#14271235C211yesmaximal, characteristic, complemented
15C29×#547C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×#41×C29C2211yescharacteristic
18C2×#90805C2211yescharacteristic
19C22×Dic58C2211yescharacteristic
20C29×C4⋊Q8C2211yescharacteristic
21C29×#123—21no—
22C29×#123—21no—
23C29×C22⋊Q8C2211yescharacteristic
24C29×C22⋊Q8C2211yescharacteristic
25C29×#121—21no—
26C4×D4×C29C2211yescharacteristic
27C4×D4×C29C2211yescharacteristic
28C2×C4⋊C4×C29—21no—
29#11745313—24no—
30#11745312—24no—
31C2×#90785C2211yescharacteristic
32C2×#90785C2211yescharacteristic
33C2×#90785C2211yescharacteristic
34C2×#90785C2211yescharacteristic
35C2×#90784C2211yescharacteristic
36C2×#90784C2211yescharacteristic
37#11745301—21no—
38C2×#90783C2211yescharacteristic
39C2×#90783C2211yescharacteristic
40C2×#90782C2211yescharacteristic
41#11745292C2211yescharacteristic
42#11745286C2211yescharacteristic
43C2×#90777C2211yescharacteristic
44C22×#6597C2211yescharacteristic
45#11745258—21no—
46#11745247—21no—
47#11745243—21no—
48#11745237C2211yescharacteristic
49C4×Dic58C2211yescharacteristic
50#11745183C2211yescharacteristic
51#11745183C2211yescharacteristic
52#11745180C2211yescharacteristic
53C22⋊#6597C2211yescharacteristic
54C22⋊#6597C2211yescharacteristic
55#11745158C2211yescharacteristic
56#11745158C2211yescharacteristic
57#11745157C2211yescharacteristic
58#11745155C2211yescharacteristic
59C4⋊#6597C2211yescharacteristic
60#11745151C2211yescharacteristic
61#41×C29—22no—
62#41×C29—22no—
63#41×C29—41no—
64#41×C29—41no—
65C2×Q8×C29C2311yescharacteristic
66C2×Q8×C29C2311yescharacteristic
67C2×D4×C29—21no—
68C2×D4×C29—21no—
69C2×D4×C29D411yescharacteristic
70C2×D4×C29C2311yescharacteristic
71C22×C4×C29—21no—
72C22×C4×C29—21no—
73C22×C4×C29—21no—
74C22×C4×C29C2311yescharacteristic
75C22×C4×C29C2311yescharacteristic
76C2×C22⋊D29—21no—
77C2×C22⋊D29—21no—
78C22×Dic29—21no—
79#90805—22no—
80#90805—41no—
81C2×D116C2311yescharacteristic
82C2×C4×D29—21no—
83C2×Dic58—22no—
84C2×Dic58—21no—
85C2×Dic58—41no—
86C2×Dic58C2311yescharacteristic
87C2×Dic58C2311yescharacteristic
88C4⋊C4×C29—21no—
89C4⋊C4×C29—21no—
90C4⋊C4×C29—21no—
91C4⋊C4×C29—21no—
92C4⋊C4×C29D411yescharacteristic
93C4⋊C4×C29C2311yescharacteristic
94C22⋊C4×C29—21no—
95C22⋊C4×C29—21no—
96C22⋊C4×C29—21no—
97C22⋊C4×C29D411yescharacteristic
98C22⋊C4×C29D411yescharacteristic
99C42×C29C2311yescharacteristic
100C22⋊Dic29—21no—
101#90785—22no—
102#90785—22no—
103#90785—22no—
104#90785—41no—
105#90784—22no—
106#90784—41no—
107#90783—22no—
108#90783D414yescomplemented
109#90782—22no—
110#90781—21no—
111#90781—21no—
112#90781—21no—
113C4⋊Dic29C2311yescharacteristic
114#90779—21no—
115#90779—21no—
116C4×Dic29—21no—
117#90777—22no—
118C2×#6597—22no—
119C2×#6597C2311yescharacteristic
120C2×#6597C2311yescharacteristic
121C2×#6597C2311yescharacteristic
122C2×#6597C2311yescharacteristic
123C23×C29—21no—
124C23×C29C2×D411yescharacteristic
125C23×C29C2×D411yescharacteristic
126C22×D29—21no—
127Q8×C29—21no—
128Q8×C29—21no—
129Q8×C29—21no—
130Q8×C29—21no—
131D4×C29—21no—
132D4×C29—41no—
133D4×C29—42no—
134D4×C29—42no—
135D4×C29C2×D412yes—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—21no—
142C2×C4×C29—21no—
143C2×C4×C29—42no—
144C2×C4×C29—42no—
145C2×C4×C29—42no—
146C2×C4×C29C2×D411yescharacteristic
147C2×C4×C29C2×D411yescharacteristic
148C2×C4×C29C2×D411yescharacteristic
149C2×C4×C29C2×D411yescharacteristic
150C2×C4×C29C2411yescharacteristic
151C22⋊D29—42no—
152C22⋊D29—42no—
153C2×Dic29—21no—
154C2×Dic29—21no—
155C2×Dic29—21no—
156C2×Dic29—42no—
157D116—21no—
158D116—21no—
159C4×D29—42no—
160Dic58—21no—
161Dic58—21no—
162Dic58—21no—
163Dic58—42no—
164Dic58C2×D412yes—
165#6597—21no—
166#6597—21no—
167#6597—21no—
168#6597C2×D412yes—
169#3269—291nomaximal, Sylow
170C22×C29—21no—
171C22×C29—21no—
172C22×C29—22no—
173C22×C29—21no—
174C22×C29—21no—
175C22×C29—21no—
176C22×C29—21no—
177C22×C29—41no—
178C22×C29—41no—
179C22×C29C22×D411yescharacteristic
180C2×D29—41no—
181C2×D29—41no—
182C2×D29—41no—
183C4×C29—21no—
184C4×C29—21no—
185C4×C29—21no—
186C4×C29—21no—
187C4×C29—41no—
188C4×C29—41no—
189C4×C29—41no—
190C4×C29C22×D411yescharacteristic
191C4×C29H(5,𝔽2)11yescharacteristic
192Dic29—22no—
193Dic29—41no—
194Dic29—41no—
195C2×#137—291no—
196C2×#135—291no—
197#548—291no—
198#547D2911yescharacteristic, complemented
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—41no—
212C2×C29—42no—
213C2×C29D4211yescharacteristic
214C2×C29#57511yescharacteristic
215C2×C29#57811yescharacteristic
216D29—81no—
217C2×#41—291no—
218C2×#41C2×D2911yescharacteristic
219C2×#41C2×D2911yescharacteristic
220C22×Q8—291no—
221#137—584no—
222#135—584no—
223C2×Q16—291no—
224C2×Q16—291no—
225C2×Q16—291no—
226C2×Q16—291no—
227C2×SD16—291no—
228C2×SD16—291no—
229C2×SD16—291no—
230C2×SD16—291no—
231C2×D8—291no—
232C2×M16—291no—
233C22×C8—291no—
234C4⋊Q8C2×D2911yescharacteristic
235#124—291no—
236#124—581no—
237#123—21no—
238#123—21no—
239C22⋊Q8—291no—
240C22⋊Q8—581no—
241C22⋊Q8C2×D2911yescharacteristic
242C22⋊Q8C2×D2911yescharacteristic
243#121—21no—
244#121—291no—
245#121—581no—
246C4×Q8—291no—
247C4×D4—581no—
248C4×D4C2×D2911yescharacteristic
249C4×D4C2×D2911yescharacteristic
250C2×C4⋊C4—21no—
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—22no—
265#41—41no—
266#41—41no—
267#41—582no—
268#41—1161no—
269C2×Q8—291no—
270C2×Q8—291no—
271C2×Q8—582no—
272C2×Q8—581no—
273C2×Q8—1161no—
274C2×Q8C22×D2911yescharacteristic
275C2×Q8C22×D2911yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—291no—
279C2×D4—581no—
280C2×D4—581no—
281C2×D4C22⋊D2911yescharacteristic
282C2×D4C22×D2911yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—581no—
287C22×C4—581no—
288C22×C4C22×D2911yescharacteristic
289C22×C4C22×D2911yescharacteristic
290Q16—582no—
291Q16—582no—
292Q16—582no—
293Q16—1161no—
294SD16—294no—
295SD16—582no—
296SD16—582no—
297SD16—1161no—
298D8—582no—
299M16—582no—
300C2×C8—291no—
301C2×C8—291no—
302C2×C8—291no—
303C2×C8—291no—
304C2×C8—582no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—291no—
310C4⋊C4—581no—
311C4⋊C4—581no—
312C4⋊C4C22⋊D2911yescharacteristic
313C4⋊C4C22×D2911yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—581no—
318C22⋊C4—581no—
319C22⋊C4—581no—
320C22⋊C4—581no—
321C22⋊C4C22⋊D2911yescharacteristic
322C22⋊C4C22⋊D2911yescharacteristic
323C42—581no—
324C42C22×D2911yescharacteristic
325C23—21no—
326C23—581no—
327C23C2×C22⋊D2911yescharacteristic
328C23C2×C22⋊D2911yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—292no—
334Q8—581no—
335Q8—581no—
336Q8—581no—
337Q8—1162no—
338D4—21no—
339D4—41no—
340D4—42no—
341D4—42no—
342D4—581no—
343D4—581no—
344D4—1162no—
345D4—1162no—
346D4D4×D2912yes—
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—581no—
358C2×C4—581no—
359C2×C4—581no—
360C2×C4—1162no—
361C2×C4—1162no—
362C2×C4C2×C22⋊D2911yescharacteristic
363C2×C4C2×C22⋊D2911yescharacteristic
364C2×C4C2×C22⋊D2911yescharacteristic
365C2×C4C2×C22⋊D2911yescharacteristic
366C2×C4C23×D2911yescharacteristic
367C8—292no—
368C8—581no—
369C8—581no—
370C8—581no—
371C22—21no—
372C22—21no—
373C22—22no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—1161no—
381C22—1161no—
382C22—1161no—
383C22C22×C22⋊D2911yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—582no—
392C4—1161no—
393C4—1161no—
394C4C2×D4×D2911yescharacteristic
395C4#1174535911yescharacteristic
396C2—41no—
397C2—41no—
398C2—42no—
399C2—2321no—
400C2D4×C22⋊D2911yescharacteristic
401C2#1427196111yescharacteristic
402C2#1427197811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#547C2
socleC22×C29C22×D4
hypercenter#547D29
hypocenterC29#3269
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C2×#11745313C2semidirect
2. C2×#11745312C2semidirect
3. #14271822C2semidirect
4. #14271555C2semidirect
5. #14271411C2semidirect
6. #14271402C2semidirect
7. #14271378C2semidirect
8. #14271370C2semidirect
9. #14271325C2semidirect
10. #14271323C2semidirect
11. #14271318C2semidirect
12. #14271308C2semidirect
13. #14271263C2semidirect
14. #14271235C2semidirect
15. C29×#547C2semidirect
108. #90783D4semidirect
198. #547D29semidirect
262. C29#3269semidirect

Maximal subgroups

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

subgroupindex
C2×#117453132
C2×#117453122
#142718222
#142715552
#142714112
#142714022
#142713782
#142713702
#142713252
#142713232
#142713182
#142713082
#142712632
#142712352
C29×#5472
#326929