Finite Group Databasebeta

← #15764237

Subgroups — #15764237

Order 3328.

484 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718726C211yesmaximal, characteristic
2C2×#11718730C211yesmaximal, characteristic
3#13115808C211yesmaximal, characteristic
4C2×#11718135C211yesmaximal, characteristic
5C2×#11718135C211yesmaximal, characteristic
6#13112717C211yesmaximal, characteristic
7C13×#2822C211yesmaximal, characteristic
8C2×C13×#125C2211yescharacteristic
9C2×C13×#125C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C13×#400—21no—
12C13×#400—21no—
13C13×#398—22no—
14C13×#398—21no—
15C13×#398—21no—
16C13×#382C2211yescharacteristic
17#11718730—22no—
18#11718730—22no—
19#11718726—22no—
20#11718726—22no—
21C2×#88050—21no—
22C2×#88050—21no—
23C2×#88048—21no—
24C2×#88047—21no—
25C2×#88043C2211yescharacteristic
26C2×#88043C2211yescharacteristic
27C2×#88043C2211yescharacteristic
28#11718135—22no—
29#11718135—22no—
30#11718121—22no—
31C22×Dic26—21no—
32C13×#125—21no—
33C13×#125—21no—
34C13×#125—21no—
35C13×#125—21no—
36C13×#125—21no—
37C13×#125—21no—
38C13×#125—21no—
39C13×#125—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—22no—
45C2×C13×C4⋊C4D411yescharacteristic
46C2×C13×C4⋊C4D411yescharacteristic
47C2×C13×C4⋊C4D411yescharacteristic
48C2×C13×C4⋊C4D411yescharacteristic
49C2×C13×C4⋊C4D412yes—
50C2×C42×C13C2311yescharacteristic
51C2×C4⋊Dic13—21no—
52C2×C4⋊Dic13—21no—
53C22×#1055—21no—
54C22×#1055—21no—
55C22×#1055—21no—
56#88123—21no—
57#88123—21no—
58#88123—21no—
59#88123D412yes—
60C13×#95—22no—
61C13×#95—22no—
62C13×#95—22no—
63C13×#95—21no—
64C13×#95—21no—
65#88050—24no—
66#88050—24no—
67#88048—24no—
68#88047—24no—
69#88043—21no—
70#88043—21no—
71#88043—21no—
72#88043—21no—
73#88043D412yes—
74#88043D412yes—
75#10084—131nomaximal, Sylow
76C22×C4×C13—22no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×Dic13—41no—
85C2×Dic26—22no—
86C2×Dic26—44no—
87C2×Dic26—41no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4—21no—
96C13×C4⋊C4—42no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—41no—
103C13×C4⋊C4—41no—
104C13×C4⋊C4—41no—
105C13×C4⋊C4—82no—
106C42×C13C2×D411yescharacteristic
107C42×C13C2×D411yescharacteristic
108C42×C13C2×D411yescharacteristic
109C42×C13#4111yescharacteristic
110C4⋊Dic13—22no—
111C4⋊Dic13—22no—
112C4⋊Dic13—41no—
113C4⋊Dic13—41no—
114C2×#1055—24no—
115C2×#1055—22no—
116C2×#1055—22no—
117C2×#1055—22no—
118C2×#1055—42no—
119C2×#1055—41no—
120C2×#1055—41no—
121C2×#501—131no—
122C2×#491—131no—
123#2822D1311yescharacteristic
124#1993—131no—
125C2×#330—131no—
126C2×#330—131no—
127#1295—131no—
128C23×C13#12011yescharacteristic
129C2×C4×C13—22no—
130C2×C4×C13—21no—
131C2×C4×C13—22no—
132C2×C4×C13—21no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13#12011yescharacteristic
147C2×C4×C13#12011yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#12111yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×C4×C13#12711yescharacteristic
152C2×Dic13—42no—
153C2×Dic13—82no—
154Dic26—44no—
155Dic26—82no—
156#1055—24no—
157#1055—42no—
158#1055—42no—
159C2×C4⋊Q8—131no—
160C2×#125C2×D1311yescharacteristic
161C2×#125C2×D1311yescharacteristic
162#501—262no—
163#501—262no—
164#491—262no—
165#491—262no—
166C2×#107—261no—
167C2×#106—261no—
168C2×#103—261no—
169C2×#103—261no—
170C2×#97—131no—
171C2×#97—131no—
172C2×#97—131no—
173#400—21no—
174#400—21no—
175#398—22no—
176#398—21no—
177#398—21no—
178#382C2×D1311yescharacteristic
179#340—262no—
180#330—262no—
181#330—262no—
182C22×C13#39211yescharacteristic
183C22×C13#45412yes—
184C22×C13#45511yescharacteristic
185C22×C13#45611yescharacteristic
186C22×C13#45612yes—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—82no—
194C4×C13—81no—
195C4×C13—81no—
196C4×C13—81no—
197C4×C13—81no—
198Dic13—82no—
199C22×Q8—261no—
200C22×C8—261no—
201C22×C8—261no—
202C22×C8—261no—
203C4⋊Q8—132no—
204C4⋊Q8—261no—
205C4⋊Q8—261no—
206C4⋊Q8—261no—
207#125—21no—
208#125—21no—
209#125—21no—
210#125—21no—
211#125—21no—
212#125—21no—
213#125—21no—
214#125—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4—261no—
222C2×C4⋊C4C22⋊D1311yescharacteristic
223C2×C4⋊C4C22⋊D1311yescharacteristic
224C2×C4⋊C4C22⋊D1311yescharacteristic
225C2×C4⋊C4C22⋊D1311yescharacteristic
226C2×C4⋊C4C22⋊D1312yes—
227C2×C42C22×D1311yescharacteristic
228#107—264no—
229#106—264no—
230#103—264no—
231#103—264no—
232#97—132no—
233#97—132no—
234#97—261no—
235#97—261no—
236#97—261no—
237#97—261no—
238#95—22no—
239#95—22no—
240#95—22no—
241#95—21no—
242#95—21no—
243C2×C13#166312yes—
244C2×C13#166412yes—
245C2×C13#200311yescharacteristic
246C2×C13#200511yescharacteristic
247C2×C13#200711yescharacteristic
248C2×Q8—262no—
249C2×Q8—524no—
250C2×Q8—521no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—521no—
257C22×C4C2×C22⋊D1311yescharacteristic
258C22×C4C2×C22⋊D1311yescharacteristic
259C22×C4C2×C22⋊D1311yescharacteristic
260C2×C8—264no—
261C2×C8—262no—
262C2×C8—262no—
263C2×C8—262no—
264C2×C8—521no—
265C2×C8—522no—
266C2×C8—521no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—82no—
285C4⋊C4—262no—
286C4⋊C4—262no—
287C4⋊C4—521no—
288C4⋊C4—521no—
289C42D4×D1311yescharacteristic
290C42D4×D1311yescharacteristic
291C42D4×D1311yescharacteristic
292C42#612911yescharacteristic
293C13#1008411yescharacteristic, complemented, Sylow
294C23#8820711yescharacteristic
295Q8—524no—
296Q8—1042no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—522no—
315C2×C4—1042no—
316C2×C4#8819111yescharacteristic
317C2×C4#8819111yescharacteristic
318C2×C4#8819211yescharacteristic
319C2×C4#8819311yescharacteristic
320C2×C4#8819311yescharacteristic
321C2×C4#8819411yescharacteristic
322C8—264no—
323C8—522no—
324C8—522no—
325C22#1171888411yescharacteristic
326C22#1171890311yescharacteristic
327C22#1171890612yes—
328C22#1171890711yescharacteristic
329C22#1171890712yes—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4—81no—
341C4—1042no—
342C2#1311416412yes—
343C2#1311417012yes—
344C2#1311585611yescharacteristic
345C2#1311587011yescharacteristic
346C2#1311588311yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2822C2
socle, prime radicalC23×C13#120
hypercenter#2822D13
hypocenterC13#10084
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

Complements

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

NH ≅ G/Ntype
293. C13#10084semidirect

Maximal subgroups

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

subgroupindex
C2×#117187262
C2×#117187302
#131158082
C2×#117181352
#131127172
C13×#28222
#1008413