Finite Group Databasebeta

← C103×#29310 #39934585

Subgroups — C103×#29310 #39934585

Order 26368.

710 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2628C211yesmaximal, characteristic
2C103×#2317C211yesmaximal, characteristic
3C103×#2085C212yesmaximal, complemented
4C103×#2057C212yesmaximal, complemented
5C103×#1944C212yesmaximal, complemented
6C103×#1942C212yesmaximal, complemented
7C103×#1854C212yesmaximal
8C103×#1852C212yesmaximal
9C103×#1750C211yesmaximal, characteristic
10C2×C4⋊Q8×C103C2211yescharacteristic
11C2×#117×C103C2211yescharacteristic
12C2×#117×C103C2211yescharacteristic
13C22×C4⋊C4×C103C2211yescharacteristic
14C2×#107×C103C2212yes—
15C2×#107×C103C2212yes—
16C2×#107×C103C2212yes—
17C2×#106×C103C2212yes—
18C2×C22⋊C8×C103C2212yes—
19C2×#97×C103C2211yescharacteristic
20C2×C4×C8×C103C2211yescharacteristic
21#400×C103—21no—
22#399×C103—21no—
23#395×C103—21no—
24#393×C103—21no—
25#389×C103C2212yes—
26#389×C103C2212yes—
27#389×C103C2212yes—
28#385×C103—21no—
29#385×C103—21no—
30#384×C103—21no—
31#382×C103—21no—
32#382×C103C2211yescharacteristic
33#380×C103C2212yes—
34#340×C103C2212yes—
35#340×C103C2212yes—
36#340×C103C2212yes—
37#340×C103C2212yes—
38#336×C103C2212yes—
39C22×Q8×C103—21no—
40C23×C4×C103—21no—
41C23×C4×C103C2311yescharacteristic
42C22×C8×C103C2312yes—
43C22×C8×C103C2312yes—
44C4⋊Q8×C103—41no—
45C4⋊Q8×C103—41no—
46#117×C103—24no—
47#117×C103—41no—
48#117×C103—41no—
49C2×C4⋊C4×C103—21no—
50C2×C4⋊C4×C103—21no—
51C2×C4⋊C4×C103—22no—
52C2×C4⋊C4×C103—22no—
53C2×C4⋊C4×C103—22no—
54C2×C4⋊C4×C103—41no—
55C2×C4⋊C4×C103—41no—
56C2×C4⋊C4×C103D411yescharacteristic
57C2×C4⋊C4×C103D411yescharacteristic
58C2×C4⋊C4×C103C2312yes—
59C2×C4⋊C4×C103C2312yes—
60C2×C4⋊C4×C103C2312yes—
61C2×C4⋊C4×C103C2312yes—
62C2×C22⋊C4×C103—21no—
63C2×C22⋊C4×C103—22no—
64C2×C22⋊C4×C103D411yescharacteristic
65C2×C22⋊C4×C103D411yescharacteristic
66C2×C42×C103—21no—
67C2×C42×C103C2311yescharacteristic
68C2×C42×C103C2311yescharacteristic
69#107×C103—24no—
70#107×C103—42no—
71#107×C103—42no—
72#106×C103—24no—
73C22⋊C8×C103Q818yescomplemented
74#97×C103—41no—
75C4×C8×C103—41no—
76#95×C103—22no—
77#95×C103—22no—
78#95×C103—22no—
79#95×C103—21no—
80#95×C103—21no—
81#95×C103—22no—
82C24×C103C2×D411yescharacteristic
83C2×Q8×C103—42no—
84C2×Q8×C103—82no—
85C22×C4×C103—22no—
86C22×C4×C103—21no—
87C22×C4×C103—21no—
88C22×C4×C103—22no—
89C22×C4×C103—22no—
90C22×C4×C103—22no—
91C22×C4×C103—22no—
92C22×C4×C103—42no—
93C22×C4×C103—82no—
94C22×C4×C103C2×D411yescharacteristic
95C22×C4×C103C2×D411yescharacteristic
96C22×C4×C103C2×D411yescharacteristic
97C22×C4×C103C2×D411yescharacteristic
98C22×C4×C103C2×D411yescharacteristic
99C22×C4×C103C2×Q814yes—
100C22×C4×C103C2411yescharacteristic
101C2×C8×C103—22no—
102C2×C8×C103—22no—
103C2×C8×C103—22no—
104C2×C8×C103—22no—
105C2×C8×C103C2×Q814yes—
106C2×C8×C103C2×Q814yes—
107C4⋊C4×C103—22no—
108C4⋊C4×C103—22no—
109C4⋊C4×C103—22no—
110C4⋊C4×C103—22no—
111C4⋊C4×C103—22no—
112C4⋊C4×C103—22no—
113C4⋊C4×C103—22no—
114C4⋊C4×C103—41no—
115C4⋊C4×C103—41no—
116C4⋊C4×C103—42no—
117C4⋊C4×C103—42no—
118C4⋊C4×C103—82no—
119C4⋊C4×C103—82no—
120C4⋊C4×C103—82no—
121C4⋊C4×C103#4114yes—
122C22⋊C4×C103—24no—
123C22⋊C4×C103—41no—
124C22⋊C4×C103—41no—
125C22⋊C4×C103—82no—
126C42×C103—24no—
127C42×C103—21no—
128C42×C103—21no—
129C42×C103—21no—
130C42×C103—21no—
131C23×C103—21no—
132C23×C103—21no—
133C23×C103—22no—
134C23×C103—22no—
135C23×C103C4⋊Q812yes—
136C23×C103C22×D411yescharacteristic
137Q8×C103—84no—
138C2×C4×C103—21no—
139C2×C4×C103—21no—
140C2×C4×C103—24no—
141C2×C4×C103—24no—
142C2×C4×C103—24no—
143C2×C4×C103—21no—
144C2×C4×C103—21no—
145C2×C4×C103—21no—
146C2×C4×C103—21no—
147C2×C4×C103—22no—
148C2×C4×C103—22no—
149C2×C4×C103—22no—
150C2×C4×C103—22no—
151C2×C4×C103—42no—
152C2×C4×C103—42no—
153C2×C4×C103—42no—
154C2×C4×C103—42no—
155C2×C4×C103—42no—
156C2×C4×C103—42no—
157C2×C4×C103—42no—
158C2×C4×C103—42no—
159C2×C4×C103—42no—
160C2×C4×C103—42no—
161C2×C4×C103—42no—
162C2×C4×C103—84no—
163C2×C4×C103C4⋊Q812yes—
164C2×C4×C103C22×Q812yes—
165C2×C4×C103C2×#4112yes—
166C2×C4×C103H(5,𝔽2)11yescharacteristic
167C2×C4×C103H(5,𝔽2)11yescharacteristic
168C8×C103—24no—
169C8×C103—24no—
170C22×C103—22no—
171C22×C103—24no—
172C22×C103—42no—
173C22×C103—41no—
174C22×C103—41no—
175C22×C103#52511yescharacteristic
176C22×C103C2×C4⋊Q811yescharacteristic
177C22×C103#53411yescharacteristic
178C22×C103#57612yes—
179C22×C103#57812yes—
180C4×C103—22no—
181C4×C103—44no—
182C4×C103—41no—
183C4×C103—41no—
184C4×C103—41no—
185C4×C103—41no—
186C4×C103—82no—
187C4×C103—82no—
188C4×C103—82no—
189C4×C103#55412yes—
190C4×C103#55412yes—
191#29310C10311yesmaximal, characteristic, direct product factor, Sylow
192C2×C103—42no—
193C2×C103#258311yescharacteristic
194C2×C103#312412yes—
195C2×C103#316412yes—
196C2×C103#319911yescharacteristic
197C2×C103#320211yescharacteristic
198#2628C2×C10311yescharacteristic
199#2317C2×C10311yescharacteristic
200#2085C2×C10312yescomplemented
201#2057C2×C10312yescomplemented
202#1944C2×C10312yescomplemented
203#1942C2×C10312yescomplemented
204#1854C2×C10312yes—
205#1852C2×C10312yes—
206#1750C2×C10311yescharacteristic
207C103#2931011yescharacteristic, direct product factor, Sylow
208C2×C4⋊Q8C22×C10311yescharacteristic
209C2×#117C22×C10311yescharacteristic
210C2×#117C22×C10311yescharacteristic
211C22×C4⋊C4C22×C10311yescharacteristic
212C2×#107C22×C10312yes—
213C2×#107C22×C10312yes—
214C2×#107C22×C10312yes—
215C2×#106C22×C10312yes—
216C2×C22⋊C8C22×C10312yes—
217C2×#97C22×C10311yescharacteristic
218C2×C4×C8C22×C10311yescharacteristic
219#400—21no—
220#399—21no—
221#395—21no—
222#393—21no—
223#389C22×C10312yes—
224#389C22×C10312yes—
225#389C22×C10312yes—
226#385—21no—
227#385—21no—
228#384—21no—
229#382—21no—
230#382C22×C10311yescharacteristic
231#380C22×C10312yes—
232#340C22×C10312yes—
233#340C22×C10312yes—
234#340C22×C10312yes—
235#340C22×C10312yes—
236#336C22×C10312yes—
237C22×Q8—21no—
238C23×C4—21no—
239C23×C4C23×C10311yescharacteristic
240C22×C8C23×C10312yes—
241C22×C8C23×C10312yes—
242C4⋊Q8—41no—
243C4⋊Q8—41no—
244#117—24no—
245#117—41no—
246#117—41no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—41no—
253C2×C4⋊C4—41no—
254C2×C4⋊C4D4×C10311yescharacteristic
255C2×C4⋊C4D4×C10311yescharacteristic
256C2×C4⋊C4C23×C10312yes—
257C2×C4⋊C4C23×C10312yes—
258C2×C4⋊C4C23×C10312yes—
259C2×C4⋊C4C23×C10312yes—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4D4×C10311yescharacteristic
263C2×C22⋊C4D4×C10311yescharacteristic
264C2×C42—21no—
265C2×C42C23×C10311yescharacteristic
266C2×C42C23×C10311yescharacteristic
267#107—24no—
268#107—42no—
269#107—42no—
270#106—24no—
271C22⋊C8Q8×C10318yescomplemented
272#97—41no—
273C4×C8—41no—
274#95—22no—
275#95—22no—
276#95—22no—
277#95—21no—
278#95—21no—
279#95—22no—
280C24C2×D4×C10311yescharacteristic
281C2×Q8—42no—
282C2×Q8—82no—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—42no—
291C22×C4—82no—
292C22×C4C2×D4×C10311yescharacteristic
293C22×C4C2×D4×C10311yescharacteristic
294C22×C4C2×D4×C10311yescharacteristic
295C22×C4C2×D4×C10311yescharacteristic
296C22×C4C2×D4×C10311yescharacteristic
297C22×C4C2×Q8×C10314yes—
298C22×C4C24×C10311yescharacteristic
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8C2×Q8×C10314yes—
304C2×C8C2×Q8×C10314yes—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—22no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4—82no—
317C4⋊C4—82no—
318C4⋊C4—82no—
319C4⋊C4#41×C10314yes—
320C22⋊C4—24no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—82no—
324C42—24no—
325C42—21no—
326C42—21no—
327C42—21no—
328C42—21no—
329C23—21no—
330C23—21no—
331C23—22no—
332C23—22no—
333C23C4⋊Q8×C10312yes—
334C23C22×D4×C10311yescharacteristic
335Q8—84no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—84no—
361C2×C4C4⋊Q8×C10312yes—
362C2×C4C22×Q8×C10312yes—
363C2×C4C2×#41×C10312yes—
364C2×C4H(5,𝔽2)×C10311yescharacteristic
365C2×C4H(5,𝔽2)×C10311yescharacteristic
366C8—24no—
367C8—24no—
368C22—22no—
369C22—24no—
370C22—42no—
371C22—41no—
372C22—41no—
373C22#525×C10311yescharacteristic
374C22C2×C4⋊Q8×C10311yescharacteristic
375C22#534×C10311yescharacteristic
376C22#576×C10312yes—
377C22#578×C10312yes—
378C4—22no—
379C4—44no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—82no—
385C4—82no—
386C4—82no—
387C4#554×C10312yes—
388C4#554×C10312yes—
389C2—42no—
390C2C103×#258311yescharacteristic
391C2C103×#312412yes—
392C2C103×#316412yes—
393C2C103×#319911yescharacteristic
394C2C103×#320211yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC24×C103C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C2×#117×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C103×#2085C2semidirect
4. C103×#2057C2semidirect
5. C103×#1944C2semidirect
6. C103×#1942C2semidirect
73. C22⋊C8×C103Q8semidirect
191. #29310C103direct (N × H)
200. #2085C2×C103semidirect
201. #2057C2×C103semidirect
202. #1944C2×C103semidirect
203. #1942C2×C103semidirect
207. C103#29310direct (N × H)
271. C22⋊C8Q8×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#26282
C103×#23172
C103×#20852
C103×#20572
C103×#19442
C103×#19422
C103×#18542
C103×#18522
C103×#17502
#29310103