Finite Group Databasebeta

← #15779192

Subgroups — #15779192

Order 3328.

614 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 99 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
1#13117428C211yesmaximal, characteristic
2#13114764C211yesmaximal, characteristic
3#13112962C214yesmaximal, complemented
4C13×#1785C211yesmaximal, characteristic
5C22×C13×#41C2211yescharacteristic
6C2×#88180C411yescharacteristic
7C22×C4⋊Dic13C411yescharacteristic
8C2×C13×#101C2212yes—
9C2×C13×#100—21no—
10C13×#407—21no—
11#11718891C2212yes—
12C2×#88076C2212yes—
13#11718882C412yes—
14#11718881—21no—
15#11718881—21no—
16C2×#88073—21no—
17#11718873—21no—
18#11718873—21no—
19#11718868—21no—
20C2×C13×#41—24no—
21C2×C13×#41—42no—
22C2×C13×#41—42no—
23C22×Q8×C13C2311yescharacteristic
24C22×D4×C13C2×C411yescharacteristic
25C22×D4×C13D411yescharacteristic
26C22×D4×C13D411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C23×Dic13—21no—
31C2×C13×M16—22no—
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—22no—
34C2×C22⋊Dic13—22no—
35#88180—42no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—42no—
39C2×C4⋊Dic13C2×C412yes—
40C2×C4×Dic13C2×C412yes—
41C2×#6099—22no—
42C13×#101—24no—
43C13×#100—42no—
44C13×C22⋊C8—42no—
45#88076—24no—
46#88073—42no—
47#88071—22no—
48#88071—22no—
49C22⋊#1055—42no—
50#12863—131nomaximal, Sylow
51C24×C13C22⋊C411yescharacteristic
52C24×C13C22⋊C411yescharacteristic
53C24×C13C22⋊C411yescharacteristic
54C13×#41—416no—
55C2×Q8×C13—41no—
56C2×Q8×C13—41no—
57C2×Q8×C13#4114yes—
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—22no—
62C2×D4×C13—22no—
63C2×D4×C13—41no—
64C2×D4×C13—41no—
65C2×D4×C13—41no—
66C2×D4×C13—41no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—22no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×Dic13—22no—
81C22×Dic13—22no—
82C22×Dic13—42no—
83C22×Dic13—82no—
84C13×M16—42no—
85C13×M16—42no—
86C2×C8×C13—42no—
87C22⋊Dic13—42no—
88C22⋊Dic13—82no—
89C22⋊Dic13—82no—
90C4⋊Dic13—42no—
91C4⋊Dic13—42no—
92C4⋊Dic13—42no—
93C4×Dic13—42no—
94#6099—42no—
95#6099—42no—
96C2×#1055—42no—
97#2311—131no—
98#1785—131no—
99#1785D1311yescharacteristic
100#1394—134no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13#9912yes—
116C23×C13C2×C22⋊C411yescharacteristic
117Q8×C13—44no—
118D4×C13—44no—
119D4×C13—44no—
120D4×C13—44no—
121C2×C4×C13—28no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—44no—
131C2×C4×C13—44no—
132C2×C4×C13#9912yes—
133C2×C4×C13#11712yes—
134C2×C4×C13#12312yes—
135C2×C4×C13#12312yes—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—42no—
140C2×Dic13—42no—
141C2×Dic13—42no—
142C2×Dic13—84no—
143C8×C13—82no—
144#1055—82no—
145C22×#41C2×D1311yescharacteristic
146C2×#117—131no—
147C22×C4⋊C4—131no—
148C2×#101—132no—
149C2×#101C2×D1312yes—
150C2×#100—21no—
151C2×#100—261no—
152#407—21no—
153#407—261no—
154#391—132no—
155#390—132no—
156#386—261no—
157#386—261no—
158#380—261no—
159#380—261no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—22no—
163C22×C13—42no—
164C22×C13—42no—
165C22×C13—42no—
166C22×C13—42no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—81no—
176C22×C13—81no—
177C22×C13#38111yescharacteristic
178C22×C13C2×#9911yescharacteristic
179C22×C13C2×#9911yescharacteristic
180C4×C13—22no—
181C4×C13—22no—
182C4×C13—22no—
183C4×C13—22no—
184Dic13—82no—
185Dic13—82no—
186C2×#41—24no—
187C2×#41—42no—
188C2×#41—42no—
189C22×Q8C22×D1311yescharacteristic
190C22×D4C4×D1311yescharacteristic
191C22×D4D5211yescharacteristic
192C22×D4C22⋊D1311yescharacteristic
193C23×C4—261no—
194C23×C4C4×D1311yescharacteristic
195C23×C4D5211yescharacteristic
196C23×C4C22⋊D1311yescharacteristic
197C2×M16—22no—
198C2×M16—262no—
199#117—522no—
200C2×C4⋊C4—132no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—522no—
204C2×C22⋊C4—261no—
205C2×C22⋊C4—262no—
206C2×C22⋊C4—262no—
207C2×C42—132no—
208#101—24no—
209#101—264no—
210#100—42no—
211#100—522no—
212C22⋊C8—42no—
213C22⋊C8—522no—
214#95—262no—
215#95—262no—
216C2×C13—21no—
217C2×C13—21no—
218C2×C13—42no—
219C2×C13—81no—
220C2×C13—81no—
221C2×C13#181911yescharacteristic
222C2×C13#213411yescharacteristic
223C2×C13#213511yescharacteristic
224C24#610311yescharacteristic
225C24#610311yescharacteristic
226C24#610311yescharacteristic
227#41—416no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8#612914yes—
231C2×D4—22no—
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—22no—
235C2×D4—22no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—262no—
250C22×C4—262no—
251C22×C4—522no—
252C22×C4—1042no—
253C22×C4#610311yescharacteristic
254C22×C4C2×C4×D1311yescharacteristic
255C22×C4C2×D5211yescharacteristic
256C22×C4C2×C22⋊D1311yescharacteristic
257M16—42no—
258M16—42no—
259M16—522no—
260M16—522no—
261C2×C8—42no—
262C2×C8—522no—
263C4⋊C4—522no—
264C4⋊C4—522no—
265C4⋊C4—522no—
266C22⋊C4—522no—
267C22⋊C4—1042no—
268C22⋊C4—1042no—
269C42—522no—
270C13#1286311yescharacteristic, complemented, Sylow
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23#8804612yes—
286C23C2×#610311yescharacteristic
287Q8—44no—
288D4—44no—
289D4—44no—
290D4—44no—
291C2×C4—28no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—522no—
303C2×C4—522no—
304C2×C4—522no—
305C2×C4—522no—
306C2×C4—522no—
307C2×C4—522no—
308C2×C4—1044no—
309C2×C4#8804612yes—
310C2×C4#8813112yes—
311C2×C4#8814012yes—
312C2×C4#8818912yes—
313C8—82no—
314C8—1042no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—42no—
320C22—42no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22—81no—
332C22#1171860411yescharacteristic
333C22C2×#8804611yescharacteristic
334C22C2×#8804611yescharacteristic
335C4—22no—
336C4—22no—
337C4—22no—
338C4—22no—
339C4—1042no—
340C4—1042no—
341C2—21no—
342C2—21no—
343C2—42no—
344C2—81no—
345C2—81no—
346C2#1311490811yescharacteristic
347C2#1311652711yescharacteristic
348C2#1311653011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#1785C2
socleC22×C13C2×#99
prime radicalC22×C13×#41C22
cosocleC22×Q8×C13C23
hypercenter#1785D13
hypocenterC13#12863
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #1785

Complements

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

NH ≅ G/Ntype
3. #13112962C2semidirect
270. C13#12863semidirect

Maximal subgroups

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

subgroupindex
#131174282
#131147642
#131129622
C13×#17852
#1286313