Finite Group Databasebeta

← C103×#19535 #39924810

Subgroups — C103×#19535 #39924810

Order 26368.

562 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3254C211yesmaximal, characteristic
2C103×#3249C211yesmaximal, characteristic, complemented
3C103×#3228C211yesmaximal, characteristic
4C103×#2985C211yesmaximal, characteristic, complemented
5C103×#1698C212yesmaximal, complemented
6C103×#1692C212yesmaximal, complemented
7C103×#1682C212yesmaximal, complemented
8C103×#1676C212yesmaximal, complemented
9C103×#1571C211yesmaximal, characteristic, complemented
10C103×#1559C211yesmaximal, characteristic, complemented
11C103×#1551C211yesmaximal, characteristic
12#533×C103C2211yescharacteristic
13#533×C103C2211yescharacteristic
14#532×C103C2211yescharacteristic
15#500×C103C2211yescharacteristic
16#498×C103C2211yescharacteristic
17#486×C103C2211yescharacteristic
18#486×C103C2211yescharacteristic
19#482×C103—22no—
20#478×C103—22no—
21#477×C103—21no—
22#477×C103C2212yes—
23#477×C103C2212yes—
24#474×C103—21no—
25#468×C103—22no—
26#467×C103—22no—
27#462×C103—21no—
28#462×C103C2212yes—
29#461×C103—21no—
30#460×C103C2212yes—
31#446×C103—22no—
32#446×C103C2212yes—
33C8×Q8×C103C2212yes—
34#433×C103—22no—
35#432×C103C2211yescharacteristic
36#431×C103C2211yescharacteristic
37#423×C103C2211yescharacteristic
38C2×C4⋊C8×C103C2211yescharacteristic
39#335×C103C2212yes—
40#335×C103C2212yes—
41#333×C103C2212yes—
42#333×C103C2212yes—
43#332×C103C2212yes—
44#331×C103C2212yes—
45C2×#41×C103—21no—
46C2×Q16×C103—22no—
47C2×SD16×C103—22no—
48C2×M16×C103—21no—
49C22×C8×C103—21no—
50C4⋊Q8×C103D411yescharacteristic
51C4⋊Q8×C103D411yescharacteristic
52C4⋊Q8×C103C2311yescharacteristic
53C4⋊Q8×C103C2311yescharacteristic
54C4⋊Q8×C103C2311yescharacteristic
55#127×C103C2311yescharacteristic
56#125×C103—21no—
57#125×C103—21no—
58#124×C103—21no—
59C22⋊Q8×C103—21no—
60C22⋊Q8×C103—21no—
61C22⋊Q8×C103—21no—
62C22⋊Q8×C103D412yes—
63#121×C103—21no—
64#121×C103—21no—
65C4×Q8×C103—21no—
66C4×Q8×C103—21no—
67C4×Q8×C103—21no—
68C4×Q8×C103C2312yes—
69C4×D4×C103—21no—
70C4×D4×C103—21no—
71#117×C103—21no—
72#117×C103—21no—
73C2×C42×C103C2311yescharacteristic
74#107×C103—22no—
75#107×C103—22no—
76#107×C103—22no—
77#106×C103—22no—
78C4⋊C8×C103—22no—
79C4⋊C8×C103—22no—
80C4⋊C8×C103—21no—
81C4⋊C8×C103—21no—
82C4⋊C8×C103D412yes—
83C4⋊C8×C103C2312yes—
84C4⋊C8×C103C2312yes—
85C4⋊C8×C103C2312yes—
86#103×C103—22no—
87#103×C103—22no—
88#103×C103—22no—
89#102×C103—22no—
90#102×C103—22no—
91#102×C103—22no—
92C22⋊C8×C103—21no—
93C22⋊C8×C103D412yes—
94#97×C103—22no—
95#97×C103—21no—
96C4×C8×C103—22no—
97C4×C8×C103C2311yescharacteristic
98C4×C8×C103C2311yescharacteristic
99#41×C103—82no—
100C2×Q8×C103—21no—
101C2×Q8×C103—21no—
102C2×Q8×C103—21no—
103C2×Q8×C103—21no—
104C2×Q8×C103C2×D412yes—
105C2×D4×C103—21no—
106C2×D4×C103—21no—
107C2×D4×C103—21no—
108C2×D4×C103—41no—
109C22×C4×C103—41no—
110C22×C4×C103C2×D411yescharacteristic
111C22×C4×C103C2×D411yescharacteristic
112C22×C4×C103#4111yescharacteristic
113Q16×C103—82no—
114SD16×C103—82no—
115M16×C103—81no—
116C2×C8×C103—22no—
117C2×C8×C103—22no—
118C2×C8×C103—22no—
119C2×C8×C103—81no—
120C2×C8×C103C2×D412yes—
121C2×C8×C103C2×D412yes—
122C4⋊C4×C103—21no—
123C4⋊C4×C103—21no—
124C4⋊C4×C103—21no—
125C4⋊C4×C103—22no—
126C4⋊C4×C103—22no—
127C4⋊C4×C103—21no—
128C4⋊C4×C103—21no—
129C4⋊C4×C103—21no—
130C4⋊C4×C103—21no—
131C4⋊C4×C103—21no—
132C4⋊C4×C103—21no—
133C4⋊C4×C103—41no—
134C4⋊C4×C103—41no—
135C4⋊C4×C103C2×D412yes—
136C22⋊C4×C103—22no—
137C22⋊C4×C103—41no—
138C22⋊C4×C103—41no—
139C22⋊C4×C103—41no—
140C42×C103—22no—
141C42×C103—41no—
142C42×C103C2×D411yescharacteristic
143C42×C103C2×D411yescharacteristic
144C42×C103#4111yescharacteristic
145C42×C103C2411yescharacteristic
146C23×C103—41no—
147C23×C103#12111yescharacteristic
148Q8×C103—22no—
149Q8×C103—22no—
150Q8×C103—41no—
151Q8×C103—41no—
152Q8×C103—81no—
153Q8×C103—81no—
154Q8×C103—81no—
155D4×C103—41no—
156D4×C103—42no—
157D4×C103—41no—
158D4×C103—81no—
159D4×C103—82no—
160C2×C4×C103—21no—
161C2×C4×C103—22no—
162C2×C4×C103—21no—
163C2×C4×C103—22no—
164C2×C4×C103—22no—
165C2×C4×C103—41no—
166C2×C4×C103—41no—
167C2×C4×C103—41no—
168C2×C4×C103—41no—
169C2×C4×C103—82no—
170C2×C4×C103#12111yescharacteristic
171C2×C4×C103#12111yescharacteristic
172C2×C4×C103#12111yescharacteristic
173C2×C4×C103C22×D411yescharacteristic
174C2×C4×C103C22×D411yescharacteristic
175C2×C4×C103C2×#4111yescharacteristic
176C8×C103—22no—
177C8×C103—22no—
178C8×C103—42no—
179C8×C103—42no—
180C8×C103—42no—
181C22×C103—21no—
182C22×C103—21no—
183C22×C103—21no—
184C22×C103—81no—
185C22×C103—81no—
186C22×C103—81no—
187C22×C103C2×#12111yescharacteristic
188C4×C103—21no—
189C4×C103—21no—
190C4×C103—21no—
191C4×C103—21no—
192C4×C103—42no—
193C4×C103—42no—
194C4×C103—81no—
195C4×C103—81no—
196C4×C103—81no—
197C4×C103#57611yescharacteristic
198C4×C103#57812yes—
199C4×C103#57811yescharacteristic
200#19535C10311yesmaximal, characteristic, direct product factor, Sylow
201C2×C103—41no—
202C2×C103—161no—
203C2×C103#304411yescharacteristic
204C2×C103#306111yescharacteristic
205C2×C103#306811yescharacteristic
206#3254C2×C10311yescharacteristic
207#3249C2×C10311yescharacteristic, complemented
208#3228C2×C10311yescharacteristic
209#2985C2×C10311yescharacteristic, complemented
210#1698C2×C10312yescomplemented
211#1692C2×C10312yescomplemented
212#1682C2×C10312yescomplemented
213#1676C2×C10312yescomplemented
214#1571C2×C10311yescharacteristic, complemented
215#1559C2×C10311yescharacteristic, complemented
216#1551C2×C10311yescharacteristic
217C103#1953511yescharacteristic, direct product factor, Sylow
218#533C22×C10311yescharacteristic
219#533C22×C10311yescharacteristic
220#532C22×C10311yescharacteristic
221#500C22×C10311yescharacteristic
222#498C22×C10311yescharacteristic
223#486C22×C10311yescharacteristic
224#486C22×C10311yescharacteristic
225#482—22no—
226#478—22no—
227#477—21no—
228#477C22×C10312yes—
229#477C22×C10312yes—
230#474—21no—
231#468—22no—
232#467—22no—
233#462—21no—
234#462C22×C10312yes—
235#461—21no—
236#460C22×C10312yes—
237#446—22no—
238#446C22×C10312yes—
239C8×Q8C22×C10312yes—
240#433—22no—
241#432C22×C10311yescharacteristic
242#431C22×C10311yescharacteristic
243#423C22×C10311yescharacteristic
244C2×C4⋊C8C22×C10311yescharacteristic
245#335C22×C10312yes—
246#335C22×C10312yes—
247#333C22×C10312yes—
248#333C22×C10312yes—
249#332C22×C10312yes—
250#331C22×C10312yes—
251C2×#41—21no—
252C2×Q16—22no—
253C2×SD16—22no—
254C2×M16—21no—
255C22×C8—21no—
256C4⋊Q8D4×C10311yescharacteristic
257C4⋊Q8D4×C10311yescharacteristic
258C4⋊Q8C23×C10311yescharacteristic
259C4⋊Q8C23×C10311yescharacteristic
260C4⋊Q8C23×C10311yescharacteristic
261#127C23×C10311yescharacteristic
262#125—21no—
263#125—21no—
264#124—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8—21no—
268C22⋊Q8D4×C10312yes—
269#121—21no—
270#121—21no—
271C4×Q8—21no—
272C4×Q8—21no—
273C4×Q8—21no—
274C4×Q8C23×C10312yes—
275C4×D4—21no—
276C4×D4—21no—
277#117—21no—
278#117—21no—
279C2×C42C23×C10311yescharacteristic
280#107—22no—
281#107—22no—
282#107—22no—
283#106—22no—
284C4⋊C8—22no—
285C4⋊C8—22no—
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8D4×C10312yes—
289C4⋊C8C23×C10312yes—
290C4⋊C8C23×C10312yes—
291C4⋊C8C23×C10312yes—
292#103—22no—
293#103—22no—
294#103—22no—
295#102—22no—
296#102—22no—
297#102—22no—
298C22⋊C8—21no—
299C22⋊C8D4×C10312yes—
300#97—22no—
301#97—21no—
302C4×C8—22no—
303C4×C8C23×C10311yescharacteristic
304C4×C8C23×C10311yescharacteristic
305#41—82no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8C2×D4×C10312yes—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—41no—
315C22×C4—41no—
316C22×C4C2×D4×C10311yescharacteristic
317C22×C4C2×D4×C10311yescharacteristic
318C22×C4#41×C10311yescharacteristic
319Q16—82no—
320SD16—82no—
321M16—81no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—81no—
326C2×C8C2×D4×C10312yes—
327C2×C8C2×D4×C10312yes—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4C2×D4×C10312yes—
342C22⋊C4—22no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C42—22no—
347C42—41no—
348C42C2×D4×C10311yescharacteristic
349C42C2×D4×C10311yescharacteristic
350C42#41×C10311yescharacteristic
351C42C24×C10311yescharacteristic
352C23—41no—
353C23#121×C10311yescharacteristic
354Q8—22no—
355Q8—22no—
356Q8—41no—
357Q8—41no—
358Q8—81no—
359Q8—81no—
360Q8—81no—
361D4—41no—
362D4—42no—
363D4—41no—
364D4—81no—
365D4—82no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—82no—
376C2×C4#121×C10311yescharacteristic
377C2×C4#121×C10311yescharacteristic
378C2×C4#121×C10311yescharacteristic
379C2×C4C22×D4×C10311yescharacteristic
380C2×C4C22×D4×C10311yescharacteristic
381C2×C4C2×#41×C10311yescharacteristic
382C8—22no—
383C8—22no—
384C8—42no—
385C8—42no—
386C8—42no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22C2×#121×C10311yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—42no—
399C4—42no—
400C4—81no—
401C4—81no—
402C4—81no—
403C4#576×C10311yescharacteristic
404C4#578×C10312yes—
405C4#578×C10311yescharacteristic
406C2—41no—
407C2—161no—
408C2C103×#304411yescharacteristic
409C2C103×#306111yescharacteristic
410C2C103×#306811yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
prime radical#532×C103C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#3249C2semidirect
4. C103×#2985C2semidirect
5. C103×#1698C2semidirect
6. C103×#1692C2semidirect
7. C103×#1682C2semidirect
8. C103×#1676C2semidirect
9. C103×#1571C2semidirect
10. C103×#1559C2semidirect
200. #19535C103direct (N × H)
207. #3249C2×C103semidirect
209. #2985C2×C103semidirect
210. #1698C2×C103semidirect
211. #1692C2×C103semidirect
212. #1682C2×C103semidirect
213. #1676C2×C103semidirect
214. #1571C2×C103semidirect
215. #1559C2×C103semidirect
217. C103#19535direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#32542
C103×#32492
C103×#32282
C103×#29852
C103×#16982
C103×#16922
C103×#16822
C103×#16762
C103×#15712
C103×#15592
C103×#15512
#19535103