Finite Group Databasebeta

← C103×#9248 #39914523

Subgroups — C103×#9248 #39914523

Order 26368.

466 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#462×C103C211yesmaximal, characteristic
2Q8×M16×C103C211yesmaximal, characteristic
3C103×#1997C211yesmaximal, characteristic
4C103×#1548C211yesmaximal, characteristic
5C103×#1487C211yesmaximal, characteristic
6C103×#1292C211yesmaximal, characteristic
7C103×#1283C211yesmaximal, characteristic
8C22×Q16×C103C412yes—
9C2×C4⋊Q8×C103C2211yescharacteristic
10C2×C4×Q8×C103C2211yescharacteristic
11#462×C103—21no—
12#462×C103—21no—
13#462×C103—21no—
14#462×C103—21no—
15#446×C103—21no—
16#446×C103—22no—
17C8×Q8×C103—21no—
18#431×C103C2211yescharacteristic
19#423×C103—21no—
20#423×C103C2211yescharacteristic
21#423×C103C2211yescharacteristic
22C2×C4⋊C8×C103C2211yescharacteristic
23C2×#103×C103C412yes—
24C4×M16×C103—21no—
25C4×M16×C103C2211yescharacteristic
26#343×C103—21no—
27#343×C103—21no—
28#333×C103—22no—
29Q8⋊C8×C103—21no—
30Q8⋊C8×C103—21no—
31C22×Q8×C103C2×C411yescharacteristic
32C22×Q8×C103C2×C412yes—
33C2×Q16×C103—22no—
34C2×Q16×C103—22no—
35C2×Q16×C103—44no—
36C2×M16×C103—21no—
37C2×M16×C103—21no—
38C2×M16×C103D411yescharacteristic
39C2×M16×C103D411yescharacteristic
40C22×C8×C103C2×C412yes—
41C4⋊Q8×C103—21no—
42C4⋊Q8×C103—21no—
43C4⋊Q8×C103—21no—
44C4⋊Q8×C103—21no—
45C4×Q8×C103—21no—
46C4×Q8×C103—21no—
47C4×Q8×C103D411yescharacteristic
48C4×Q8×C103D411yescharacteristic
49C4×Q8×C103D411yescharacteristic
50C4×Q8×C103D411yescharacteristic
51C2×C4⋊C4×C103—21no—
52C2×C4⋊C4×C103—21no—
53C2×C4⋊C4×C103—21no—
54C2×C4⋊C4×C103C2×C411yescharacteristic
55C2×C42×C103—21no—
56C2×C42×C103C2311yescharacteristic
57C4⋊C8×C103—22no—
58C4⋊C8×C103—22no—
59C4⋊C8×C103—21no—
60C4⋊C8×C103—21no—
61C4⋊C8×C103—21no—
62C4⋊C8×C103—21no—
63C4⋊C8×C103—21no—
64C4⋊C8×C103—21no—
65C4⋊C8×C103D412yes—
66#103×C103—22no—
67#103×C103—22no—
68C22⋊C8×C103—21no—
69#97×C103—22no—
70#97×C103—21no—
71C4×C8×C103—22no—
72C4×C8×C103—21no—
73C4×C8×C103—21no—
74C2×Q8×C103—21no—
75C2×Q8×C103—22no—
76C2×Q8×C103—22no—
77C2×Q8×C103—22no—
78C2×Q8×C103—41no—
79C2×Q8×C103—42no—
80C2×Q8×C103—42no—
81C2×Q8×C103C22⋊C411yescharacteristic
82C2×Q8×C103C22⋊C411yescharacteristic
83C22×C4×C103—21no—
84C22×C4×C103—21no—
85C22×C4×C103—22no—
86C22×C4×C103C22×C411yescharacteristic
87C22×C4×C103C2×D411yescharacteristic
88C22×C4×C103#4111yescharacteristic
89Q16×C103—44no—
90Q16×C103—44no—
91M16×C103—21no—
92M16×C103—21no—
93M16×C103—21no—
94M16×C103—41no—
95M16×C103—41no—
96M16×C103—41no—
97M16×C103—41no—
98M16×C103Q1612yescomplemented
99C2×C8×C103—21no—
100C2×C8×C103—22no—
101C2×C8×C103—21no—
102C2×C8×C103—22no—
103C2×C8×C103—42no—
104C2×C8×C103—41no—
105C2×C8×C103—41no—
106C4⋊C4×C103—21no—
107C4⋊C4×C103—21no—
108C4⋊C4×C103—21no—
109C4⋊C4×C103—21no—
110C4⋊C4×C103—21no—
111C4⋊C4×C103—41no—
112C4⋊C4×C103—41no—
113C4⋊C4×C103—41no—
114C4⋊C4×C103—41no—
115C4⋊C4×C103C22⋊C411yescharacteristic
116C4⋊C4×C103C22⋊C411yescharacteristic
117C42×C103—21no—
118C42×C103—21no—
119C42×C103—21no—
120C42×C103—21no—
121C42×C103C2×D411yescharacteristic
122C42×C103C2×D411yescharacteristic
123C42×C103C2×D411yescharacteristic
124C42×C103#4111yescharacteristic
125C23×C103C4×D411yescharacteristic
126Q8×C103—21no—
127Q8×C103—21no—
128Q8×C103—21no—
129Q8×C103—42no—
130Q8×C103—42no—
131Q8×C103—42no—
132Q8×C103—82no—
133Q8×C103#10012yes—
134C2×C4×C103—21no—
135C2×C4×C103—21no—
136C2×C4×C103—21no—
137C2×C4×C103—21no—
138C2×C4×C103—21no—
139C2×C4×C103—21no—
140C2×C4×C103—41no—
141C2×C4×C103—42no—
142C2×C4×C103—42no—
143C2×C4×C103—81no—
144C2×C4×C103—82no—
145C2×C4×C103C2×C22⋊C411yescharacteristic
146C2×C4×C103C4×D411yescharacteristic
147C2×C4×C103#12011yescharacteristic
148C2×C4×C103#12111yescharacteristic
149C2×C4×C103#12111yescharacteristic
150C2×C4×C103#12311yescharacteristic
151C2×C4×C103C2×Q1611yescharacteristic
152C2×C4×C103#13511yescharacteristic
153C2×C4×C103#13711yescharacteristic
154C2×C4×C103#13711yescharacteristic
155C8×C103—22no—
156C8×C103—42no—
157C8×C103—41no—
158C8×C103—42no—
159C8×C103—81no—
160C8×C103—81no—
161C22×C103—21no—
162C22×C103—21no—
163C22×C103#38611yescharacteristic
164C22×C103C4×Q1611yescharacteristic
165C22×C103#44111yescharacteristic
166C4×C103—21no—
167C4×C103—22no—
168C4×C103—21no—
169C4×C103—21no—
170C4×C103—41no—
171C4×C103—41no—
172C4×C103—41no—
173C4×C103—82no—
174C4×C103C2×#10011yescharacteristic
175C4×C103#41311yescharacteristic
176C4×C103#45111yescharacteristic
177C4×C103#45211yescharacteristic
178C4×C103#46211yescharacteristic
179C4×C103#46411yescharacteristic
180#9248C10311yesmaximal, characteristic, direct product factor, Sylow
181C2×C103—21no—
182C2×C103—21no—
183C2×C103#187811yescharacteristic
184C2×C103#190011yescharacteristic
185C2×C103#190211yescharacteristic
186C2×#462C2×C10311yescharacteristic
187Q8×M16C2×C10311yescharacteristic
188#1997C2×C10311yescharacteristic
189#1548C2×C10311yescharacteristic
190#1487C2×C10311yescharacteristic
191#1292C2×C10311yescharacteristic
192#1283C2×C10311yescharacteristic
193C103#924811yescharacteristic, direct product factor, Sylow
194C22×Q16C4×C10312yes—
195C2×C4⋊Q8C22×C10311yescharacteristic
196C2×C4×Q8C22×C10311yescharacteristic
197#462—21no—
198#462—21no—
199#462—21no—
200#462—21no—
201#446—21no—
202#446—22no—
203C8×Q8—21no—
204#431C22×C10311yescharacteristic
205#423—21no—
206#423C22×C10311yescharacteristic
207#423C22×C10311yescharacteristic
208C2×C4⋊C8C22×C10311yescharacteristic
209C2×#103C4×C10312yes—
210C4×M16—21no—
211C4×M16C22×C10311yescharacteristic
212#343—21no—
213#343—21no—
214#333—22no—
215Q8⋊C8—21no—
216Q8⋊C8—21no—
217C22×Q8C2×C4×C10311yescharacteristic
218C22×Q8C2×C4×C10312yes—
219C2×Q16—22no—
220C2×Q16—22no—
221C2×Q16—44no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16D4×C10311yescharacteristic
225C2×M16D4×C10311yescharacteristic
226C22×C8C2×C4×C10312yes—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4×Q8—21no—
232C4×Q8—21no—
233C4×Q8D4×C10311yescharacteristic
234C4×Q8D4×C10311yescharacteristic
235C4×Q8D4×C10311yescharacteristic
236C4×Q8D4×C10311yescharacteristic
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4C2×C4×C10311yescharacteristic
241C2×C42—21no—
242C2×C42C23×C10311yescharacteristic
243C4⋊C8—22no—
244C4⋊C8—22no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8D4×C10312yes—
252#103—22no—
253#103—22no—
254C22⋊C8—21no—
255#97—22no—
256#97—21no—
257C4×C8—22no—
258C4×C8—21no—
259C4×C8—21no—
260C2×Q8—21no—
261C2×Q8—22no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—41no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8C22⋊C4×C10311yescharacteristic
268C2×Q8C22⋊C4×C10311yescharacteristic
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4C22×C4×C10311yescharacteristic
273C22×C4C2×D4×C10311yescharacteristic
274C22×C4#41×C10311yescharacteristic
275Q16—44no—
276Q16—44no—
277M16—21no—
278M16—21no—
279M16—21no—
280M16—41no—
281M16—41no—
282M16—41no—
283M16—41no—
284M16Q16×C10312yescomplemented
285C2×C8—21no—
286C2×C8—22no—
287C2×C8—21no—
288C2×C8—22no—
289C2×C8—42no—
290C2×C8—41no—
291C2×C8—41no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4C22⋊C4×C10311yescharacteristic
302C4⋊C4C22⋊C4×C10311yescharacteristic
303C42—21no—
304C42—21no—
305C42—21no—
306C42—21no—
307C42C2×D4×C10311yescharacteristic
308C42C2×D4×C10311yescharacteristic
309C42C2×D4×C10311yescharacteristic
310C42#41×C10311yescharacteristic
311C23C4×D4×C10311yescharacteristic
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—42no—
316Q8—42no—
317Q8—42no—
318Q8—82no—
319Q8#100×C10312yes—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4C2×C22⋊C4×C10311yescharacteristic
332C2×C4C4×D4×C10311yescharacteristic
333C2×C4#120×C10311yescharacteristic
334C2×C4#121×C10311yescharacteristic
335C2×C4#121×C10311yescharacteristic
336C2×C4#123×C10311yescharacteristic
337C2×C4C2×Q16×C10311yescharacteristic
338C2×C4#135×C10311yescharacteristic
339C2×C4#137×C10311yescharacteristic
340C2×C4#137×C10311yescharacteristic
341C8—22no—
342C8—42no—
343C8—41no—
344C8—42no—
345C8—81no—
346C8—81no—
347C22—21no—
348C22—21no—
349C22#386×C10311yescharacteristic
350C22C4×Q16×C10311yescharacteristic
351C22#441×C10311yescharacteristic
352C4—21no—
353C4—22no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—82no—
360C4C2×#100×C10311yescharacteristic
361C4#413×C10311yescharacteristic
362C4#451×C10311yescharacteristic
363C4#452×C10311yescharacteristic
364C4#462×C10311yescharacteristic
365C4#464×C10311yescharacteristic
366C2—21no—
367C2—21no—
368C2C103×#187811yescharacteristic
369C2C103×#190011yescharacteristic
370C2C103×#190211yescharacteristic
subgroupG/H
center, socleC22×C103#386
commutatorC22×C4C22×C4×C103
Frattini, cosocleC2×C42C23×C103
prime radicalC23×C103C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
98. M16×C103Q16semidirect
180. #9248C103direct (N × H)
193. C103#9248direct (N × H)
284. M16Q16×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#462×C1032
Q8×M16×C1032
C103×#19972
C103×#15482
C103×#14872
C103×#12922
C103×#12832
#9248103