Finite Group Databasebeta

← C103×#9213 #39914488

Subgroups — C103×#9213 #39914488

Order 26368.

450 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3106C211yesmaximal, characteristic
2C103×#2922C211yesmaximal, characteristic, complemented
3C103×#1525C211yesmaximal, characteristic, complemented
4C103×#1492C211yesmaximal, characteristic, complemented
5C103×#1489C211yesmaximal, characteristic, complemented
6C103×#1299C211yesmaximal, characteristic, complemented
7C103×#1278C211yesmaximal, characteristic, complemented
8#532×C103C2211yescharacteristic
9C4×#41×C103C2211yescharacteristic
10#482×C103—21no—
11#477×C103C411yescharacteristic
12#476×C103C411yescharacteristic
13#460×C103C411yescharacteristic
14#459×C103C411yescharacteristic
15#449×C103—21no—
16C4×SD16×C103—21no—
17C4×D8×C103—21no—
18#433×C103—22no—
19#431×C103—22no—
20#431×C103C2211yescharacteristic
21#424×C103—21no—
22#423×C103C2211yescharacteristic
23#408×C103—21no—
24C4×M16×C103C2211yescharacteristic
25C4×M16×C103C2211yescharacteristic
26C2×C4×C8×C103C2211yescharacteristic
27#329×C103—22no—
28Q8⋊C8×C103—21no—
29D4⋊C8×C103—21no—
30D4⋊C8×C103—22no—
31C2×#41×C103—21no—
32C2×#41×C103D411yescharacteristic
33C2×SD16×C103—21no—
34C2×D8×C103—21no—
35C2×M16×C103—21no—
36C2×M16×C103—21no—
37C2×M16×C103—21no—
38C22×C8×C103—21no—
39C4⋊Q8×C103C2×C411yescharacteristic
40#127×C103C2×C411yescharacteristic
41#124×C103—21no—
42#121×C103—21no—
43#121×C103—21no—
44C4×Q8×C103C2×C411yescharacteristic
45C4×Q8×C103D411yescharacteristic
46C4×D4×C103—21no—
47C4×D4×C103—21no—
48C4×D4×C103—21no—
49C4×D4×C103—21no—
50C4×D4×C103C2×C411yescharacteristic
51C4×D4×C103D411yescharacteristic
52#117×C103—21no—
53#117×C103D411yescharacteristic
54C2×C42×C103—21no—
55C2×C42×C103C2311yescharacteristic
56#107×C103—21no—
57#106×C103—21no—
58C4⋊C8×C103—24no—
59C4⋊C8×C103—21no—
60C4⋊C8×C103—21no—
61C4⋊C8×C103C2×C411yescharacteristic
62C4⋊C8×C103C2×C411yescharacteristic
63#103×C103—21no—
64#102×C103—21no—
65#102×C103—21no—
66#102×C103—21no—
67C22⋊C8×C103—24no—
68C22⋊C8×C103—21no—
69#97×C103—21no—
70#97×C103D412yes—
71C4×C8×C103—21no—
72C4×C8×C103—21no—
73C4×C8×C103—21no—
74C4×C8×C103—21no—
75C4×C8×C103D412yes—
76#41×C103—41no—
77#41×C103—41no—
78#41×C103—81no—
79#41×C103—81no—
80C2×Q8×C103—21no—
81C2×Q8×C103C22⋊C411yescharacteristic
82C2×D4×C103—21no—
83C2×D4×C103—21no—
84C2×D4×C103—21no—
85C2×D4×C103—21no—
86C2×D4×C103—41no—
87C2×D4×C103C22⋊C411yescharacteristic
88C22×C4×C103—21no—
89C22×C4×C103—21no—
90C22×C4×C103—21no—
91C22×C4×C103—41no—
92C22×C4×C103C2×D411yescharacteristic
93C22×C4×C103#4111yescharacteristic
94C22×C4×C103#4111yescharacteristic
95SD16×C103—42no—
96D8×C103—42no—
97M16×C103—22no—
98M16×C103—41no—
99M16×C103—41no—
100M16×C103—41no—
101M16×C103—81no—
102C2×C8×C103—21no—
103C2×C8×C103—21no—
104C2×C8×C103—22no—
105C2×C8×C103—22no—
106C2×C8×C103—41no—
107C2×C8×C103—41no—
108C2×C8×C103—41no—
109C2×C8×C103—41no—
110C4⋊C4×C103—21no—
111C4⋊C4×C103—21no—
112C4⋊C4×C103—21no—
113C4⋊C4×C103—21no—
114C4⋊C4×C103C22⋊C411yescharacteristic
115C4⋊C4×C103C22⋊C411yescharacteristic
116C22⋊C4×C103—21no—
117C22⋊C4×C103—21no—
118C22⋊C4×C103—21no—
119C22⋊C4×C103—41no—
120C22⋊C4×C103—41no—
121C42×C103—21no—
122C42×C103—21no—
123C42×C103—21no—
124C42×C103C22×C411yescharacteristic
125C42×C103C2×D411yescharacteristic
126C42×C103C2×D411yescharacteristic
127C42×C103C2×D411yescharacteristic
128C23×C103—21no—
129C23×C103—41no—
130C23×C103#12311yescharacteristic
131Q8×C103—21no—
132Q8×C103—21no—
133Q8×C103—81no—
134D4×C103—21no—
135D4×C103—21no—
136D4×C103—42no—
137D4×C103—41no—
138D4×C103—41no—
139D4×C103—41no—
140D4×C103—41no—
141D4×C103—81no—
142D4×C103—82no—
143C2×C4×C103—21no—
144C2×C4×C103—21no—
145C2×C4×C103—21no—
146C2×C4×C103—21no—
147C2×C4×C103—21no—
148C2×C4×C103—21no—
149C2×C4×C103—21no—
150C2×C4×C103—21no—
151C2×C4×C103—21no—
152C2×C4×C103—42no—
153C2×C4×C103—41no—
154C2×C4×C103—41no—
155C2×C4×C103—41no—
156C2×C4×C103—41no—
157C2×C4×C103—41no—
158C2×C4×C103—81no—
159C2×C4×C103—81no—
160C2×C4×C103C2×C22⋊C411yescharacteristic
161C2×C4×C103C4×D411yescharacteristic
162C2×C4×C103C4×D411yescharacteristic
163C2×C4×C103#12011yescharacteristic
164C2×C4×C103#12111yescharacteristic
165C2×C4×C103#12111yescharacteristic
166C8×C103—42no—
167C8×C103—42no—
168C8×C103—42no—
169C8×C103—41no—
170C8×C103—41no—
171C8×C103—81no—
172C22×C103—21no—
173C22×C103—21no—
174C22×C103—21no—
175C22×C103—41no—
176C22×C103—41no—
177C22×C103—41no—
178C22×C103—81no—
179C22×C103—81no—
180C22×C103—81no—
181C22×C103#38611yescharacteristic
182C4×C103—21no—
183C4×C103—21no—
184C4×C103—21no—
185C4×C103—41no—
186C4×C103—41no—
187C4×C103—41no—
188C4×C103—81no—
189C4×C103#42111yescharacteristic
190C4×C103#42111yescharacteristic
191C4×C103#44311yescharacteristic
192C4×C103#44411yescharacteristic
193C4×C103#47111yescharacteristic
194C4×C103#47211yescharacteristic
195#9213C10311yesmaximal, characteristic, direct product factor, Sylow
196C2×C103—41no—
197C2×C103—81no—
198C2×C103—161no—
199C2×C103#187611yescharacteristic
200C2×C103#189711yescharacteristic
201C2×C103#190711yescharacteristic
202#3106C2×C10311yescharacteristic
203#2922C2×C10311yescharacteristic, complemented
204#1525C2×C10311yescharacteristic, complemented
205#1492C2×C10311yescharacteristic, complemented
206#1489C2×C10311yescharacteristic, complemented
207#1299C2×C10311yescharacteristic, complemented
208#1278C2×C10311yescharacteristic, complemented
209C103#921311yescharacteristic, direct product factor, Sylow
210#532C22×C10311yescharacteristic
211C4×#41C22×C10311yescharacteristic
212#482—21no—
213#477C4×C10311yescharacteristic
214#476C4×C10311yescharacteristic
215#460C4×C10311yescharacteristic
216#459C4×C10311yescharacteristic
217#449—21no—
218C4×SD16—21no—
219C4×D8—21no—
220#433—22no—
221#431—22no—
222#431C22×C10311yescharacteristic
223#424—21no—
224#423C22×C10311yescharacteristic
225#408—21no—
226C4×M16C22×C10311yescharacteristic
227C4×M16C22×C10311yescharacteristic
228C2×C4×C8C22×C10311yescharacteristic
229#329—22no—
230Q8⋊C8—21no—
231D4⋊C8—21no—
232D4⋊C8—22no—
233C2×#41—21no—
234C2×#41D4×C10311yescharacteristic
235C2×SD16—21no—
236C2×D8—21no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C22×C8—21no—
241C4⋊Q8C2×C4×C10311yescharacteristic
242#127C2×C4×C10311yescharacteristic
243#124—21no—
244#121—21no—
245#121—21no—
246C4×Q8C2×C4×C10311yescharacteristic
247C4×Q8D4×C10311yescharacteristic
248C4×D4—21no—
249C4×D4—21no—
250C4×D4—21no—
251C4×D4—21no—
252C4×D4C2×C4×C10311yescharacteristic
253C4×D4D4×C10311yescharacteristic
254#117—21no—
255#117D4×C10311yescharacteristic
256C2×C42—21no—
257C2×C42C23×C10311yescharacteristic
258#107—21no—
259#106—21no—
260C4⋊C8—24no—
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8C2×C4×C10311yescharacteristic
264C4⋊C8C2×C4×C10311yescharacteristic
265#103—21no—
266#102—21no—
267#102—21no—
268#102—21no—
269C22⋊C8—24no—
270C22⋊C8—21no—
271#97—21no—
272#97D4×C10312yes—
273C4×C8—21no—
274C4×C8—21no—
275C4×C8—21no—
276C4×C8—21no—
277C4×C8D4×C10312yes—
278#41—41no—
279#41—41no—
280#41—81no—
281#41—81no—
282C2×Q8—21no—
283C2×Q8C22⋊C4×C10311yescharacteristic
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4C22⋊C4×C10311yescharacteristic
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—41no—
294C22×C4C2×D4×C10311yescharacteristic
295C22×C4#41×C10311yescharacteristic
296C22×C4#41×C10311yescharacteristic
297SD16—42no—
298D8—42no—
299M16—22no—
300M16—41no—
301M16—41no—
302M16—41no—
303M16—81no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4C22⋊C4×C10311yescharacteristic
317C4⋊C4C22⋊C4×C10311yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C42—21no—
324C42—21no—
325C42—21no—
326C42C22×C4×C10311yescharacteristic
327C42C2×D4×C10311yescharacteristic
328C42C2×D4×C10311yescharacteristic
329C42C2×D4×C10311yescharacteristic
330C23—21no—
331C23—41no—
332C23#123×C10311yescharacteristic
333Q8—21no—
334Q8—21no—
335Q8—81no—
336D4—21no—
337D4—21no—
338D4—42no—
339D4—41no—
340D4—41no—
341D4—41no—
342D4—41no—
343D4—81no—
344D4—82no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4—81no—
362C2×C4C2×C22⋊C4×C10311yescharacteristic
363C2×C4C4×D4×C10311yescharacteristic
364C2×C4C4×D4×C10311yescharacteristic
365C2×C4#120×C10311yescharacteristic
366C2×C4#121×C10311yescharacteristic
367C2×C4#121×C10311yescharacteristic
368C8—42no—
369C8—42no—
370C8—42no—
371C8—41no—
372C8—41no—
373C8—81no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22#386×C10311yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—81no—
391C4#421×C10311yescharacteristic
392C4#421×C10311yescharacteristic
393C4#443×C10311yescharacteristic
394C4#444×C10311yescharacteristic
395C4#471×C10311yescharacteristic
396C4#472×C10311yescharacteristic
397C2—41no—
398C2—81no—
399C2—161no—
400C2C103×#187611yescharacteristic
401C2C103×#189711yescharacteristic
402C2C103×#190711yescharacteristic
subgroupG/H
centerC2×C4×C103#121
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
socleC22×C103#386
prime radicalC103×#3106C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2922C2semidirect
3. C103×#1525C2semidirect
4. C103×#1492C2semidirect
5. C103×#1489C2semidirect
6. C103×#1299C2semidirect
7. C103×#1278C2semidirect
195. #9213C103direct (N × H)
203. #2922C2×C103semidirect
204. #1525C2×C103semidirect
205. #1492C2×C103semidirect
206. #1489C2×C103semidirect
207. #1299C2×C103semidirect
208. #1278C2×C103semidirect
209. C103#9213direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#31062
C103×#29222
C103×#15252
C103×#14922
C103×#14892
C103×#12992
C103×#12782
#9213103