Finite Group Databasebeta

← #15778919

Subgroups — #15778919

Order 3328.

468 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C4×#88198C211yesmaximal, 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#11718637C411yescharacteristic
14#11718635C411yescharacteristic
15#11718633—21no—
16#11718633—21no—
17C4×#6101—21no—
18C4×#6101—21no—
19C42×Dic13C411yescharacteristic
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—41no—
28C4×Q8×C13—41no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35#88198—21no—
36#88198—21no—
37#88198D412yes—
38#88198Q812yes—
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×C4×Dic13—21no—
46C2×C4×Dic13—21no—
47C2×C4×Dic13—21no—
48C2×C4×Dic13C2×C411yescharacteristic
49C2×C4×Dic13C2×C411yescharacteristic
50C2×#6099—22no—
51C4×Dic26—41no—
52C4×Dic26—41no—
53C13×C4⋊C8—41no—
54C13×C4⋊C8—41no—
55C13×#101—22no—
56C13×#101—22no—
57#88076—22no—
58#88076—22no—
59#88071—21no—
60#88071—21no—
61#88071—21no—
62#88071—21no—
63C4⋊#1055—41no—
64C4⋊#1055—41no—
65#12802—131nomaximal, Sylow
66C2×Q8×C13—41no—
67C2×Q8×C13—41no—
68C2×Q8×C13C2×D411yescharacteristic
69C2×Q8×C13C2×Q811yescharacteristic
70C2×Q8×C13#4111yescharacteristic
71C2×Q8×C13#4111yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—21no—
83C2×Dic26—21no—
84C2×Dic26—41no—
85C2×Dic26—41no—
86C2×Dic26C4⋊C412yes—
87C13×M16—42no—
88C13×M16—42no—
89C2×C8×C13—42no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C42×C13—21no—
94C42×C13—21no—
95C42×C13—21no—
96C42×C13—21no—
97C42×C13—21no—
98C42×C13—21no—
99C4⋊Dic13—41no—
100#6101—22no—
101#6101—22no—
102#6101—22no—
103#6101—22no—
104#6101—42no—
105#6101—42no—
106#6101—42no—
107C4×Dic13—24no—
108C4×Dic13—21no—
109C4×Dic13—42no—
110C4×Dic13—41no—
111C4×Dic13—41no—
112C4×Dic13—41no—
113C4×Dic13C4⋊C412yes—
114#6099—42no—
115#6099—42no—
116C2×#1055—42no—
117C4×C4⋊Q8—131no—
118C2×#356—132no—
119#1801—131no—
120#1801D1311yescharacteristic
121#1394—132no—
122C23×C13C2×C22⋊C411yescharacteristic
123Q8×C13—41no—
124Q8×C13—41no—
125Q8×C13—41no—
126Q8×C13—41no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—22no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13#9911yescharacteristic
141C2×C4×C13#9911yescharacteristic
142C2×C4×C13C2×C4⋊C411yescharacteristic
143C2×C4×C13#11711yescharacteristic
144C2×C4×C13#12111yescharacteristic
145C2×C4×C13#12111yescharacteristic
146C2×C4×C13C22⋊Q811yescharacteristic
147C2×C4×C13C22⋊Q811yescharacteristic
148C2×Dic13—22no—
149C2×Dic13—22no—
150C2×Dic13—22no—
151C2×Dic13—22no—
152C2×Dic13—22no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160Dic26—42no—
161Dic26—42no—
162C8×C13—82no—
163#1055—82no—
164C2×C4⋊Q8—131no—
165C2×C4×Q8—131no—
166C2×C4×Q8C2×D1311yescharacteristic
167#423—21no—
168#423—261no—
169C2×#101—132no—
170C2×#101C2×D1312yes—
171#391—131no—
172#391—131no—
173#389—261no—
174#389—261no—
175#384—131no—
176C4×C4⋊C4—261no—
177C4×C4⋊C4—261no—
178C43—131no—
179#356—264no—
180#343—21no—
181#343—261no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13#38011yescharacteristic
185C22×C13C2×#9911yescharacteristic
186C22×C13#41011yescharacteristic
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—41no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13#35612yescomplemented
198Dic13—24no—
199Dic13—42no—
200Dic13—42no—
201Dic13—81no—
202C22×Q8—131no—
203C22×Q8C22×D1311yescharacteristic
204C2×M16—22no—
205C2×M16—262no—
206C4⋊Q8—132no—
207C4⋊Q8—132no—
208C4⋊Q8—261no—
209C4⋊Q8—261no—
210C4×Q8—41no—
211C4×Q8—41no—
212C4×Q8—521no—
213C4×Q8—521no—
214C2×C4⋊C4—131no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4C4×D1311yescharacteristic
221C2×C4⋊C4D5211yescharacteristic
222C2×C4⋊C4C22⋊D1311yescharacteristic
223C2×C42—131no—
224C2×C42—131no—
225C2×C42—261no—
226C2×C42—261no—
227C2×C42—261no—
228C2×C42C4×D1311yescharacteristic
229C2×C42D5211yescharacteristic
230C2×C42C22⋊D1311yescharacteristic
231C4⋊C8—41no—
232C4⋊C8—41no—
233C4⋊C8—521no—
234C4⋊C8—521no—
235#101—22no—
236#101—22no—
237#101—262no—
238#101—262no—
239#95—261no—
240#95—261no—
241#95—261no—
242#95—261no—
243C2×C13—21no—
244C2×C13—21no—
245C2×C13#179911yescharacteristic
246C2×C13C2×#35611yescharacteristic
247C2×C13#213211yescharacteristic
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—132no—
251C2×Q8—261no—
252C2×Q8—521no—
253C2×Q8—521no—
254C2×Q8D4×D1311yescharacteristic
255C2×Q8#612911yescharacteristic
256C2×Q8Q8×D1311yescharacteristic
257C2×Q8#613111yescharacteristic
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4#610311yescharacteristic
263C22×C4#610311yescharacteristic
264C22×C4#610311yescharacteristic
265C22×C4#610311yescharacteristic
266C22×C4C2×C4×D1311yescharacteristic
267C22×C4C2×D5211yescharacteristic
268C22×C4C2×C22⋊D1311yescharacteristic
269M16—42no—
270M16—42no—
271M16—522no—
272M16—522no—
273C2×C8—42no—
274C2×C8—522no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—262no—
279C4⋊C4—262no—
280C4⋊C4—262no—
281C4⋊C4—262no—
282C4⋊C4—521no—
283C4⋊C4—522no—
284C4⋊C4—522no—
285C4⋊C4—522no—
286C42—21no—
287C42—21no—
288C42—21no—
289C42—21no—
290C42—21no—
291C42—21no—
292C42—132no—
293C42—264no—
294C42—261no—
295C42—521no—
296C42—522no—
297C42—521no—
298C42—521no—
299C13#1280211yescharacteristic, complemented, Sylow
300C23C2×#610311yescharacteristic
301Q8—41no—
302Q8—41no—
303Q8—41no—
304Q8—41no—
305Q8—522no—
306Q8—522no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—262no—
321C2×C4—262no—
322C2×C4—262no—
323C2×C4—262no—
324C2×C4—262no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4#8804611yescharacteristic
333C2×C4#8804611yescharacteristic
334C2×C4C4⋊C4×D1311yescharacteristic
335C2×C4#8814611yescharacteristic
336C2×C4#8814911yescharacteristic
337C2×C4#8815111yescharacteristic
338C2×C4#8819211yescharacteristic
339C2×C4#8820011yescharacteristic
340C8—82no—
341C8—1042no—
342C22—21no—
343C22—21no—
344C22C2×#8804611yescharacteristic
345C22#1171864811yescharacteristic
346C22#1171866711yescharacteristic
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—264no—
358C4—522no—
359C4—522no—
360C4—1041no—
361C4#1171807012yescomplemented
362C2—21no—
363C2—21no—
364C2#1311482111yescharacteristic
365C2C2×#1171807011yescharacteristic
366C2#1311651911yescharacteristic
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#12802
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
197. C4×C13#356semidirect
299. C13#12802semidirect
361. C4#11718070semidirect

Maximal subgroups

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

subgroupindex
C4×#881982
C2×#117180702
#131148322
#131129622
C13×#18012
#1280213