Finite Group Databasebeta

← #16822645

Subgroups — #16822645

Order 3712.

576 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745246C211yesmaximal, characteristic
2#14271065C211yesmaximal, characteristic, complemented
3#14271063C211yesmaximal, characteristic, complemented
4#14271055C211yesmaximal, characteristic, complemented
5#14271050C211yesmaximal, characteristic, complemented
6#14271047C211yesmaximal, characteristic, complemented
7#14271041C211yesmaximal, characteristic, complemented
8#14271040C211yesmaximal, characteristic, complemented
9#14271040C211yesmaximal, characteristic, complemented
10#14271039C211yesmaximal, characteristic, complemented
11#14271038C211yesmaximal, characteristic, complemented
12#14271034C211yesmaximal, characteristic, complemented
13#14271025C211yesmaximal, characteristic, complemented
14#14271020C211yesmaximal, characteristic, complemented
15C29×#388C211yesmaximal, characteristic, complemented
16C22×C22⋊D29C2211yescharacteristic
17C22×C22⋊D29C2211yescharacteristic
18C23×Dic29C2211yescharacteristic
19C22×D116C2211yescharacteristic
20C22×C4×D29C2211yescharacteristic
21C22×C4×D29C2211yescharacteristic
22C2×C4⋊C4×C29C2211yescharacteristic
23C2×C22⋊C4×C29C2211yescharacteristic
24C2×C22⋊C4×C29C2211yescharacteristic
25C2×C22⋊C4×C29C2211yescharacteristic
26C2×C42×C29C2211yescharacteristic
27C2×C22⋊Dic29C2211yescharacteristic
28C2×#90781C2211yescharacteristic
29C2×#90781C2211yescharacteristic
30C2×#90781C2211yescharacteristic
31C2×#90781C2211yescharacteristic
32C2×#90781C2211yescharacteristic
33C2×#90781C2211yescharacteristic
34C2×#90781C2211yescharacteristic
35C2×#90781C2211yescharacteristic
36C2×C4⋊Dic29C2211yescharacteristic
37C2×C4⋊Dic29C2211yescharacteristic
38C2×#90779C2211yescharacteristic
39C2×#90779C2211yescharacteristic
40C2×C4×Dic29C2211yescharacteristic
41#11745246C418yescomplemented
42C29×#95C2211yescharacteristic
43C29×#95C2211yescharacteristic
44#11745179C2211yescharacteristic
45#11745179C2211yescharacteristic
46#11745179C2211yescharacteristic
47#11745179C2211yescharacteristic
48#11745179C2211yescharacteristic
49#11745179C2211yescharacteristic
50#11745179C2211yescharacteristic
51#11745179C2211yescharacteristic
52C24×C29C2311yescharacteristic
53C23×D29C2311yescharacteristic
54C23×D29C2311yescharacteristic
55C22×C4×C29C2311yescharacteristic
56C22×C4×C29C2311yescharacteristic
57C22×C4×C29C2311yescharacteristic
58C22×C4×C29C2311yescharacteristic
59C22×C4×C29C2311yescharacteristic
60C22×C4×C29C2311yescharacteristic
61C2×C22⋊D29—41no—
62C2×C22⋊D29—41no—
63C2×C22⋊D29—41no—
64C2×C22⋊D29—41no—
65C2×C22⋊D29C2×C414yes—
66C2×C22⋊D29C2×C414yescomplemented
67C22×Dic29—41no—
68C22×Dic29—41no—
69C22×Dic29—41no—
70C22×Dic29C2311yescharacteristic
71C22×Dic29C2311yescharacteristic
72C22×Dic29C2311yescharacteristic
73C22×Dic29C2311yescharacteristic
74C22×Dic29C2311yescharacteristic
75C22×Dic29C2311yescharacteristic
76C2×D116—41no—
77C2×D116—41no—
78C2×D116C2×C414yescomplemented
79C2×C4×D29—41no—
80C2×C4×D29—41no—
81C2×C4×D29—41no—
82C2×C4×D29—41no—
83C2×C4×D29—41no—
84C2×C4×D29C2×C414yescomplemented
85C4⋊C4×C29—41no—
86C22⋊C4×C29—41no—
87C22⋊C4×C29—41no—
88C22⋊C4×C29C2×C414yescomplemented
89C42×C29—41no—
90C22⋊Dic29—41no—
91#90781—41no—
92#90781—41no—
93#90781—41no—
94#90781—41no—
95#90781—41no—
96#90781—41no—
97#90781—41no—
98#90781C2×C414yescomplemented
99C4⋊Dic29—41no—
100C4⋊Dic29—41no—
101#90779—41no—
102#90779C2×C414yescomplemented
103C4×Dic29—41no—
104C23×C29—21no—
105C23×C29—21no—
106C23×C29—21no—
107C23×C29—21no—
108C23×C29—21no—
109C23×C29—21no—
110C23×C29C22×C412yes—
111C23×C29C2411yescharacteristic
112C22×D29—21no—
113C22×D29—21no—
114C22×D29—21no—
115C22×D29—21no—
116C22×D29—21no—
117C22×D29—21no—
118C22×D29—21no—
119C22×D29—21no—
120C22×D29—21no—
121C22×D29—21no—
122C22×D29—21no—
123C22×D29—21no—
124C22×D29C22×C412yes—
125C22×D29C22×C412yes—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29—21no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
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×C29C22×C412yes—
143C2×C4×C29C22×C412yes—
144C22⋊D29—44no—
145C22⋊D29—44no—
146C2×Dic29—21no—
147C2×Dic29—21no—
148C2×Dic29—21no—
149C2×Dic29—21no—
150C2×Dic29—21no—
151C2×Dic29—21no—
152C2×Dic29—21no—
153C2×Dic29—21no—
154C2×Dic29—21no—
155C2×Dic29—21no—
156C2×Dic29—21no—
157C2×Dic29—21no—
158C2×Dic29—21no—
159C2×Dic29—21no—
160C2×Dic29—21no—
161C2×Dic29—21no—
162C2×Dic29—44no—
163C2×Dic29C22×C412yes—
164C2×Dic29C22×C412yes—
165D116—44no—
166C4×D29—44no—
167C4×D29—44no—
168#2377—291nomaximal, Sylow
169C22×C29—22no—
170C22×C29—22no—
171C22×C29—22no—
172C22×C29—41no—
173C22×C29—41no—
174C22×C29—41no—
175C22×C29—41no—
176C22×C29C23×C411yescharacteristic
177C22×C29H(5,𝔽2)11yescharacteristic
178C22×C29H(5,𝔽2)11yescharacteristic
179C22×C29H(5,𝔽2)11yescharacteristic
180C22×C29H(5,𝔽2)11yescharacteristic
181C22×C29H(5,𝔽2)11yescharacteristic
182C22×C292−1+411yescharacteristic
183C2×D29—22no—
184C2×D29—22no—
185C2×D29—22no—
186C2×D29—22no—
187C2×D29—22no—
188C2×D29—22no—
189C2×D29—41no—
190C2×D29—41no—
191C2×D29—41no—
192C2×D29—41no—
193C2×D29—41no—
194C2×D29—41no—
195C2×D29—41no—
196C2×D29—41no—
197C4×C29—22no—
198C4×C29—22no—
199C4×C29—41no—
200C4×C29—41no—
201C4×C29—41no—
202C4×C29—41no—
203Dic29—22no—
204Dic29—22no—
205Dic29—41no—
206Dic29—41no—
207Dic29—41no—
208Dic29—41no—
209C2×#121—291no—
210#390—291no—
211#390—291no—
212#388—291no—
213#388D2911yescharacteristic, complemented
214#387—291no—
215#387—291no—
216#386—291no—
217#386—291no—
218#386—291no—
219#386—291no—
220#385—291no—
221#385—291no—
222#381—291no—
223#380—291no—
224C2×C29—42no—
225C2×C29#51811yescharacteristic
226C2×C29#51811yescharacteristic
227C2×C29#52011yescharacteristic
228C2×C29#56011yescharacteristic
229C2×C29#56011yescharacteristic
230C2×C29#56211yescharacteristic
231C2×C29#56211yescharacteristic
232D29—42no—
233D29—42no—
234C22×D4—291no—
235C22×D4—291no—
236C22×D4—291no—
237C23×C4—291no—
238C23×C4—291no—
239C23×C4—291no—
240#121—298no—
241C2×C4⋊C4—291no—
242C2×C4⋊C4—291no—
243C2×C4⋊C4—291no—
244C2×C4⋊C4—291no—
245C2×C4⋊C4C2×D2911yescharacteristic
246C2×C22⋊C4—291no—
247C2×C22⋊C4—291no—
248C2×C22⋊C4—291no—
249C2×C22⋊C4—291no—
250C2×C22⋊C4—291no—
251C2×C22⋊C4—291no—
252C2×C22⋊C4—291no—
253C2×C22⋊C4—291no—
254C2×C22⋊C4—291no—
255C2×C22⋊C4C2×D2911yescharacteristic
256C2×C22⋊C4C2×D2911yescharacteristic
257C2×C22⋊C4C2×D2911yescharacteristic
258C2×C42—291no—
259C2×C42C2×D2911yescharacteristic
260#95—291no—
261#95—291no—
262#95—291no—
263#95—291no—
264#95—291no—
265#95—291no—
266#95—291no—
267#95—291no—
268#95C2×D2911yescharacteristic
269#95C2×D2911yescharacteristic
270C29#237711yescharacteristic, complemented, Sylow
271C24—291no—
272C24—291no—
273C24C22×D2911yescharacteristic
274C2×D4—294no—
275C2×D4—294no—
276C2×D4—294no—
277C2×D4—1161no—
278C2×D4—1161no—
279C2×D4—1161no—
280C2×D4—1161no—
281C2×D4—1161no—
282C2×D4—1161no—
283C22×C4—291no—
284C22×C4—291no—
285C22×C4—294no—
286C22×C4—291no—
287C22×C4—291no—
288C22×C4—291no—
289C22×C4—291no—
290C22×C4—1161no—
291C22×C4—1161no—
292C22×C4—1161no—
293C22×C4—1161no—
294C22×C4—1161no—
295C22×C4—1161no—
296C22×C4—1161no—
297C22×C4—1161no—
298C22×C4C22×D2911yescharacteristic
299C22×C4C22×D2911yescharacteristic
300C22×C4C22×D2911yescharacteristic
301C22×C4C22×D2911yescharacteristic
302C22×C4C22×D2911yescharacteristic
303C22×C4C22×D2911yescharacteristic
304C4⋊C4—41no—
305C4⋊C4—294no—
306C4⋊C4—1161no—
307C4⋊C4—1161no—
308C4⋊C4—1161no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—294no—
312C22⋊C4—1161no—
313C22⋊C4—1161no—
314C22⋊C4—1161no—
315C22⋊C4—1161no—
316C22⋊C4—1161no—
317C22⋊C4—1161no—
318C22⋊C4—1161no—
319C22⋊C4—1161no—
320C22⋊C4C4×D2914yescomplemented
321C42—41no—
322C42—1161no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—292no—
330C23—292no—
331C23—581no—
332C23—581no—
333C23—581no—
334C23—581no—
335C23—581no—
336C23—581no—
337C23—581no—
338C23—581no—
339C23—581no—
340C23—581no—
341C23—581no—
342C23—581no—
343C23C2×C4×D2912yes—
344C23C23×D2911yescharacteristic
345D4—1164no—
346D4—1164no—
347D4—1164no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—292no—
365C2×C4—292no—
366C2×C4—581no—
367C2×C4—581no—
368C2×C4—581no—
369C2×C4—581no—
370C2×C4—581no—
371C2×C4—581no—
372C2×C4—581no—
373C2×C4—581no—
374C2×C4—581no—
375C2×C4—581no—
376C2×C4—581no—
377C2×C4—581no—
378C2×C4—581no—
379C2×C4—581no—
380C2×C4—581no—
381C2×C4—581no—
382C2×C4—1164no—
383C2×C4—1164no—
384C2×C4—1164no—
385C2×C4C2×C4×D2912yes—
386C2×C4C2×C4×D2912yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—582no—
395C22—582no—
396C22—582no—
397C22—582no—
398C22—582no—
399C22—582no—
400C22—1161no—
401C22—1161no—
402C22—1161no—
403C22—1161no—
404C22—1161no—
405C22—1161no—
406C22—1161no—
407C22—1161no—
408C22C22×C4×D2911yescharacteristic
409C22#1174535911yescharacteristic
410C22#1174535911yescharacteristic
411C22#1174536411yescharacteristic
412C22#1174536411yescharacteristic
413C22#1174536411yescharacteristic
414C22#1174536511yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—582no—
422C4—582no—
423C4—1161no—
424C4—1161no—
425C4—1161no—
426C4—1161no—
427C2—42no—
428C2—1162no—
429C2—1162no—
430C2#1427163511yescharacteristic
431C2#1427163511yescharacteristic
432C2#1427164311yescharacteristic
433C2#1427190111yescharacteristic
434C2#1427190411yescharacteristic
435C2#1427190711yescharacteristic
436C2#1427191011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC29×#388C2
socle, cosocleC23×C29C24
prime radicalC2×#11745246C2
hypercenter#388D29
hypocenterC29#2377
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #14271065C2semidirect
3. #14271063C2semidirect
4. #14271055C2semidirect
5. #14271050C2semidirect
6. #14271047C2semidirect
7. #14271041C2semidirect
8. #14271040C2semidirect
9. #14271040C2semidirect
10. #14271039C2semidirect
11. #14271038C2semidirect
12. #14271034C2semidirect
13. #14271025C2semidirect
14. #14271020C2semidirect
15. C29×#388C2semidirect
41. #11745246C4semidirect
66. C2×C22⋊D29C2×C4semidirect
78. C2×D116C2×C4semidirect
84. C2×C4×D29C2×C4semidirect
88. C22⋊C4×C29C2×C4semidirect
98. #90781C2×C4semidirect
102. #90779C2×C4semidirect
213. #388D29semidirect
270. C29#2377semidirect
320. C22⋊C4C4×D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117452462
#142710652
#142710632
#142710552
#142710502
#142710472
#142710412
#142710402
#142710392
#142710382
#142710342
#142710252
#142710202
C29×#3882
#237729