Finite Group Databasebeta

← C103×#11902 #39917177

Subgroups — C103×#11902 #39917177

Order 26368.

452 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C103×#2564C211yesmaximal, characteristic
2C103×#1799C211yesmaximal, characteristic
3C103×#1460C211yesmaximal, characteristic
4C103×#1352C212yesmaximal, complemented
5C103×#1351C212yesmaximal, complemented
6C2×C22⋊Q8×C103C411yescharacteristic, complemented
7C2×C4×D4×C103C2211yescharacteristic
8#431×C103—21no—
9C2×#99×C103—21no—
10#400×C103C411yescharacteristic, complemented
11#399×C103C2211yescharacteristic
12#395×C103C411yescharacteristic, complemented
13#393×C103C2211yescharacteristic
14#387×C103—21no—
15#386×C103—21no—
16#385×C103—21no—
17#380×C103—21no—
18#380×C103—21no—
19C2×#95×C103C411yescharacteristic, complemented
20#342×C103C2212yes—
21#323×C103—21no—
22#323×C103C2212yes—
23C22×Q8×C103C2×C411yescharacteristic
24C22×D4×C103D411yescharacteristic
25C23×C4×C103—21no—
26C23×C4×C103C2×C411yescharacteristic
27C23×C4×C103D411yescharacteristic
28C22⋊Q8×C103—41no—
29C22⋊Q8×C103—41no—
30C4×D4×C103—41no—
31C4×D4×C103—41no—
32C2×C4⋊C4×C103—21no—
33C2×C4⋊C4×C103—21no—
34C2×C4⋊C4×C103—21no—
35C2×C4⋊C4×C103—41no—
36C2×C4⋊C4×C103C2×C411yescharacteristic
37C2×C4⋊C4×C103C2×C411yescharacteristic
38C2×C22⋊C4×C103—21no—
39C2×C22⋊C4×C103—21no—
40C2×C22⋊C4×C103—22no—
41C2×C22⋊C4×C103—21no—
42C2×C22⋊C4×C103D411yescharacteristic
43C2×C22⋊C4×C103C2311yescharacteristic
44C2×C42×C103D411yescharacteristic
45C4⋊C8×C103—41no—
46#99×C103—42no—
47C22⋊C8×C103—22no—
48C4×C8×C103—41no—
49#95×C103—21no—
50#95×C103—21no—
51#95×C103—21no—
52#95×C103—21no—
53#95×C103—21no—
54#95×C103—41no—
55#95×C103C2×C411yescharacteristic
56#95×C103C2×C411yescharacteristic
57C24×C103C22⋊C411yescharacteristic
58C24×C103C2×D411yescharacteristic
59C2×Q8×C103—41no—
60C2×Q8×C103—81no—
61C2×D4×C103—41no—
62C2×D4×C103—41no—
63C2×D4×C103SD1612yes—
64C2×D4×C103Q1612yes—
65C22×C4×C103—21no—
66C22×C4×C103—21no—
67C22×C4×C103—21no—
68C22×C4×C103—21no—
69C22×C4×C103—21no—
70C22×C4×C103—21no—
71C22×C4×C103—21no—
72C22×C4×C103—21no—
73C22×C4×C103—42no—
74C22×C4×C103—42no—
75C22×C4×C103—42no—
76C22×C4×C103—81no—
77C22×C4×C103—81no—
78C22×C4×C103—81no—
79C22×C4×C103C22⋊C411yescharacteristic
80C22×C4×C103C22⋊C411yescharacteristic
81C22×C4×C103C22⋊C411yescharacteristic
82C22×C4×C103C22×C411yescharacteristic
83C22×C4×C103C2×D411yescharacteristic
84C2×C8×C103—42no—
85C4⋊C4×C103—41no—
86C4⋊C4×C103—41no—
87C4⋊C4×C103—42no—
88C4⋊C4×C103—41no—
89C4⋊C4×C103—41no—
90C4⋊C4×C103—81no—
91C4⋊C4×C103—82no—
92C22⋊C4×C103—41no—
93C22⋊C4×C103—41no—
94C22⋊C4×C103—42no—
95C22⋊C4×C103—42no—
96C22⋊C4×C103—42no—
97C22⋊C4×C103—42no—
98C22⋊C4×C103—81no—
99C42×C103—21no—
100C42×C103—21no—
101C23×C103—21no—
102C23×C103—21no—
103C23×C103—21no—
104C23×C103—21no—
105C23×C103—41no—
106C23×C103—41no—
107C23×C103—41no—
108C23×C103—41no—
109C23×C103#10312yes—
110C23×C103C2×C22⋊C411yescharacteristic
111C23×C103C2×SD1611yescharacteristic
112C23×C103C2×Q1611yescharacteristic
113Q8×C103—82no—
114D4×C103—42no—
115D4×C103—42no—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—22no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—41no—
123C2×C4×C103—42no—
124C2×C4×C103—41no—
125C2×C4×C103—41no—
126C2×C4×C103—41no—
127C2×C4×C103—41no—
128C2×C4×C103—41no—
129C2×C4×C103—41no—
130C2×C4×C103—41no—
131C2×C4×C103—41no—
132C2×C4×C103—41no—
133C2×C4×C103—41no—
134C2×C4×C103—41no—
135C2×C4×C103—41no—
136C2×C4×C103—41no—
137C2×C4×C103—41no—
138C2×C4×C103—81no—
139C2×C4×C103—81no—
140C2×C4×C103—81no—
141C2×C4×C103—84no—
142C2×C4×C103—82no—
143C2×C4×C103—82no—
144C2×C4×C103—82no—
145C2×C4×C103#9911yescharacteristic
146C2×C4×C103#9911yescharacteristic
147C2×C4×C103#10312yes—
148C8×C103—82no—
149C22×C103—21no—
150C22×C103—21no—
151C22×C103—21no—
152C22×C103—22no—
153C22×C103—21no—
154C22×C103—42no—
155C22×C103—41no—
156C22×C103—41no—
157C22×C103—42no—
158C22×C103—41no—
159C22×C103—41no—
160C22×C103—41no—
161C22×C103—41no—
162C22×C103—81no—
163C22×C103C2×#9911yescharacteristic
164C22×C103C2×#10311yescharacteristic
165C22×C103#42111yescharacteristic
166C4×C103—21no—
167C4×C103—21no—
168C4×C103—22no—
169C4×C103—42no—
170C4×C103—41no—
171C4×C103—41no—
172C4×C103—41no—
173C4×C103—81no—
174C4×C103—81no—
175C4×C103—81no—
176C4×C103—162no—
177#11902C10311yesmaximal, characteristic, direct product factor, Sylow
178C2×C103—21no—
179C2×C103—21no—
180C2×C103—41no—
181C2×C103—42no—
182C2×C103—41no—
183C2×C103#152011yescharacteristic
184C2×C103#212111yescharacteristic
185C2×C103#212611yescharacteristic
186#2564C2×C10311yescharacteristic
187#1799C2×C10311yescharacteristic
188#1460C2×C10311yescharacteristic
189#1352C2×C10312yescomplemented
190#1351C2×C10312yescomplemented
191C103#1190211yescharacteristic, direct product factor, Sylow
192C2×C22⋊Q8C4×C10311yescharacteristic, complemented
193C2×C4×D4C22×C10311yescharacteristic
194#431—21no—
195C2×#99—21no—
196#400C4×C10311yescharacteristic, complemented
197#399C22×C10311yescharacteristic
198#395C4×C10311yescharacteristic, complemented
199#393C22×C10311yescharacteristic
200#387—21no—
201#386—21no—
202#385—21no—
203#380—21no—
204#380—21no—
205C2×#95C4×C10311yescharacteristic, complemented
206#342C22×C10312yes—
207#323—21no—
208#323C22×C10312yes—
209C22×Q8C2×C4×C10311yescharacteristic
210C22×D4D4×C10311yescharacteristic
211C23×C4—21no—
212C23×C4C2×C4×C10311yescharacteristic
213C23×C4D4×C10311yescharacteristic
214C22⋊Q8—41no—
215C22⋊Q8—41no—
216C4×D4—41no—
217C4×D4—41no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—41no—
222C2×C4⋊C4C2×C4×C10311yescharacteristic
223C2×C4⋊C4C2×C4×C10311yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4D4×C10311yescharacteristic
229C2×C22⋊C4C23×C10311yescharacteristic
230C2×C42D4×C10311yescharacteristic
231C4⋊C8—41no—
232#99—42no—
233C22⋊C8—22no—
234C4×C8—41no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—41no—
241#95C2×C4×C10311yescharacteristic
242#95C2×C4×C10311yescharacteristic
243C24C22⋊C4×C10311yescharacteristic
244C24C2×D4×C10311yescharacteristic
245C2×Q8—41no—
246C2×Q8—81no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4SD16×C10312yes—
250C2×D4Q16×C10312yes—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—81no—
263C22×C4—81no—
264C22×C4—81no—
265C22×C4C22⋊C4×C10311yescharacteristic
266C22×C4C22⋊C4×C10311yescharacteristic
267C22×C4C22⋊C4×C10311yescharacteristic
268C22×C4C22×C4×C10311yescharacteristic
269C22×C4C2×D4×C10311yescharacteristic
270C2×C8—42no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—42no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—81no—
277C4⋊C4—82no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—42no—
284C22⋊C4—81no—
285C42—21no—
286C42—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23#103×C10312yes—
296C23C2×C22⋊C4×C10311yescharacteristic
297C23C2×SD16×C10311yescharacteristic
298C23C2×Q16×C10311yescharacteristic
299Q8—82no—
300D4—42no—
301D4—42no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—84no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4#99×C10311yescharacteristic
332C2×C4#99×C10311yescharacteristic
333C2×C4#103×C10312yes—
334C8—82no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—21no—
340C22—42no—
341C22—41no—
342C22—41no—
343C22—42no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—81no—
349C22C2×#99×C10311yescharacteristic
350C22C2×#103×C10311yescharacteristic
351C22#421×C10311yescharacteristic
352C4—22no—
353C4—21no—
354C4—21no—
355C4—42no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—81no—
360C4—81no—
361C4—81no—
362C4—162no—
363C2—21no—
364C2—21no—
365C2—41no—
366C2—42no—
367C2—41no—
368C2C103×#152011yescharacteristic
369C2C103×#212111yescharacteristic
370C2C103×#212611yescharacteristic
subgroupG/H
center, socleC22×C103C2×#99
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×C22⋊C4C23×C103
prime radicalC22×D4×C103D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C22×C4×C103 ◁ C2×C4×D4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
4. C103×#1352C2semidirect
5. C103×#1351C2semidirect
6. C2×C22⋊Q8×C103C4semidirect
10. #400×C103C4semidirect
12. #395×C103C4semidirect
19. C2×#95×C103C4semidirect
177. #11902C103direct (N × H)
189. #1352C2×C103semidirect
190. #1351C2×C103semidirect
191. C103#11902direct (N × H)
192. C2×C22⋊Q8C4×C103semidirect
196. #400C4×C103semidirect
198. #395C4×C103semidirect
205. C2×#95C4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#25642
C103×#17992
C103×#14602
C103×#13522
C103×#13512
#11902103