Finite Group Databasebeta

← #15778927

Subgroups — #15778927

Order 3328.

432 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 103 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#13117552C211yesmaximal, characteristic
2C2×#11718070C212yesmaximal
3#13114832C211yesmaximal, characteristic
4#13112962C212yesmaximal
5C13×#1801C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88198C2211yescharacteristic
8C2×C4×Dic26C411yescharacteristic
9C13×#423—21no—
10C2×C13×#101C2212yes—
11#11718891C2211yescharacteristic
12C2×#88076C2212yes—
13#11718639—21no—
14#11718639—21no—
15#11718638C411yescharacteristic
16#11718635C411yescharacteristic
17#11718594—21no—
18#11718594—21no—
19#11718593C411yescharacteristic
20#11718585—21no—
21C13×#343—21no—
22#11718122—21no—
23#11718070—24no—
24C22×Q8×C13C2311yescharacteristic
25C22×Dic26C2×C411yescharacteristic
26C2×C13×M16—22no—
27C4×Q8×C13—42no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34#88198—21no—
35#88198—21no—
36#88198D412yes—
37#88198Q812yes—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×#6101—21no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×C4×Dic13—21no—
43C2×C4×Dic13C2×C411yescharacteristic
44C2×C4×Dic13C2×C411yescharacteristic
45C2×#6099—22no—
46C4×Dic26—42no—
47C13×C4⋊C8—42no—
48C13×#101—22no—
49C13×#101—22no—
50#88076—22no—
51#88076—22no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60C4⋊#1055—42no—
61#12804—131nomaximal, Sylow
62C2×Q8×C13—41no—
63C2×Q8×C13—41no—
64C2×Q8×C13C2×D411yescharacteristic
65C2×Q8×C13C2×Q811yescharacteristic
66C2×Q8×C13#4111yescharacteristic
67C2×Q8×C13#4111yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C2×Dic26—21no—
80C2×Dic26—41no—
81C2×Dic26—41no—
82C2×Dic26C4⋊C412yes—
83C13×M16—42no—
84C13×M16—42no—
85C2×C8×C13—42no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C42×C13—22no—
90C42×C13—22no—
91C42×C13—22no—
92C4⋊Dic13—41no—
93#6101—22no—
94#6101—22no—
95#6101—22no—
96#6101—22no—
97#6101—42no—
98C4×Dic13—21no—
99C4×Dic13—42no—
100C4×Dic13—41no—
101C4×Dic13C4⋊C412yes—
102#6099—42no—
103#6099—42no—
104C2×#1055—42no—
105#2327—131no—
106C2×#356—132no—
107#1801—131no—
108#1801D1311yescharacteristic
109#1394—132no—
110C23×C13C2×C22⋊C411yescharacteristic
111Q8×C13—41no—
112Q8×C13—41no—
113Q8×C13—41no—
114Q8×C13—41no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13#9912yes—
129C2×C4×C13C2×C4⋊C411yescharacteristic
130C2×C4×C13#11711yescharacteristic
131C2×C4×C13#12111yescharacteristic
132C2×C4×C13#12111yescharacteristic
133C2×C4×C13C22⋊Q811yescharacteristic
134C2×C4×C13C22⋊Q811yescharacteristic
135C2×Dic13—22no—
136C2×Dic13—22no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—42no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146Dic26—42no—
147Dic26—42no—
148C8×C13—82no—
149#1055—82no—
150C2×C4⋊Q8—131no—
151C2×C4×Q8—131no—
152C2×C4×Q8C2×D1311yescharacteristic
153#423—21no—
154#423—261no—
155C2×#101—132no—
156C2×#101C2×D1312yes—
157#391—131no—
158#391—131no—
159#387—261no—
160#387—261no—
161#387—261no—
162#387—261no—
163#382—131no—
164#376—131no—
165#356—264no—
166#343—21no—
167#343—261no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13#38011yescharacteristic
171C22×C13C2×#9911yescharacteristic
172C22×C13#41011yescharacteristic
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—22no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—41no—
183Dic13—42no—
184Dic13—42no—
185Dic13—81no—
186Dic13—81no—
187C22×Q8—131no—
188C22×Q8C22×D1311yescharacteristic
189C2×M16—22no—
190C2×M16—262no—
191C4⋊Q8—132no—
192C4⋊Q8—132no—
193C4⋊Q8—261no—
194C4⋊Q8—261no—
195C4×Q8—42no—
196C4×Q8—522no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4C4×D1311yescharacteristic
202C2×C4⋊C4D5211yescharacteristic
203C2×C4⋊C4C22⋊D1311yescharacteristic
204C2×C42—131no—
205C2×C42—131no—
206C2×C42—261no—
207C2×C42C4×D1311yescharacteristic
208C2×C42D5211yescharacteristic
209C2×C42C22⋊D1311yescharacteristic
210C4⋊C8—42no—
211C4⋊C8—522no—
212#101—22no—
213#101—22no—
214#101—262no—
215#101—262no—
216#95—261no—
217#95—261no—
218#95—261no—
219#95—261no—
220#95—261no—
221#95—261no—
222#95—261no—
223#95—261no—
224C2×C13—21no—
225C2×C13—21no—
226C2×C13#179911yescharacteristic
227C2×C13#213311yescharacteristic
228C2×C13#213511yescharacteristic
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—132no—
232C2×Q8—261no—
233C2×Q8—521no—
234C2×Q8—521no—
235C2×Q8D4×D1311yescharacteristic
236C2×Q8#612911yescharacteristic
237C2×Q8Q8×D1311yescharacteristic
238C2×Q8#613111yescharacteristic
239C22×C4—261no—
240C22×C4—261no—
241C22×C4—261no—
242C22×C4—261no—
243C22×C4#610311yescharacteristic
244C22×C4#610311yescharacteristic
245C22×C4#610311yescharacteristic
246C22×C4#610311yescharacteristic
247C22×C4C2×C4×D1311yescharacteristic
248C22×C4C2×D5211yescharacteristic
249C22×C4C2×C22⋊D1311yescharacteristic
250M16—42no—
251M16—42no—
252M16—522no—
253M16—522no—
254C2×C8—42no—
255C2×C8—522no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—262no—
260C4⋊C4—262no—
261C4⋊C4—262no—
262C4⋊C4—262no—
263C4⋊C4—521no—
264C4⋊C4—522no—
265C42—22no—
266C42—22no—
267C42—22no—
268C42—132no—
269C42—261no—
270C42—521no—
271C42—522no—
272C13#1280411yescharacteristic, complemented, Sylow
273C23C2×#610311yescharacteristic
274Q8—41no—
275Q8—41no—
276Q8—41no—
277Q8—41no—
278Q8—522no—
279Q8—522no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—262no—
294C2×C4—262no—
295C2×C4—521no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—522no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4#8804612yes—
305C2×C4C4⋊C4×D1311yescharacteristic
306C2×C4#8814611yescharacteristic
307C2×C4#8814911yescharacteristic
308C2×C4#8815111yescharacteristic
309C2×C4#8819211yescharacteristic
310C2×C4#8820011yescharacteristic
311C8—82no—
312C8—1042no—
313C22—21no—
314C22—21no—
315C22C2×#8804611yescharacteristic
316C22#1171864811yescharacteristic
317C22#1171866711yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—522no—
329C4—522no—
330C4—1041no—
331C4—1041no—
332C2—21no—
333C2—21no—
334C2#1311482111yescharacteristic
335C2#1311652311yescharacteristic
336C2#1311653011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#1801C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC22×Q8×C13C23
hypercenter#1801D13
hypocenterC13#12804
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
272. C13#12804semidirect

Maximal subgroups

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

subgroupindex
#131175522
C2×#117180702
#131148322
#131129622
C13×#18012
#1280413