Finite Group Databasebeta

← C103×#19571 #39924846

Subgroups — C103×#19571 #39924846

Order 26368.

550 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×#3255C211yesmaximal, characteristic
2C103×#3230C211yesmaximal, characteristic
3C103×#3229C211yesmaximal, characteristic
4C103×#2986C211yesmaximal, characteristic
5C103×#1704C212yesmaximal, complemented
6C103×#1692C212yesmaximal, complemented
7C103×#1684C212yesmaximal, complemented
8C103×#1672C212yesmaximal, complemented
9C103×#1574C211yesmaximal, characteristic
10C103×#1548C211yesmaximal, characteristic
11C103×#1544C211yesmaximal, characteristic
12#533×C103C2211yescharacteristic
13#533×C103C2211yescharacteristic
14C2×C4⋊Q8×C103C2211yescharacteristic
15#500×C103—21no—
16#498×C103C2212yes—
17#487×C103—21no—
18#487×C103C2212yes—
19#484×C103—22no—
20#483×C103—22no—
21#477×C103C2212yes—
22#477×C103C2212yes—
23#475×C103—21no—
24#475×C103—21no—
25#475×C103—21no—
26#475×C103C2212yes—
27#470×C103—22no—
28#462×C103—21no—
29#462×C103C2212yes—
30#446×C103—21no—
31#446×C103C2212yes—
32C8×Q8×C103—21no—
33C8×Q8×C103C2212yes—
34#433×C103—22no—
35#431×C103C2211yescharacteristic
36#431×C103C2211yescharacteristic
37#431×C103C2211yescharacteristic
38#423×C103C2211yescharacteristic
39#335×C103C2212yes—
40#334×C103C2212yes—
41#333×C103C2212yes—
42#333×C103C2212yes—
43#332×C103C2211yescharacteristic
44#332×C103C2211yescharacteristic
45#332×C103C2211yescharacteristic
46#332×C103C2211yescharacteristic
47C22×Q8×C103—21no—
48C2×Q16×C103—22no—
49C2×M16×C103—21no—
50C4⋊Q8×C103—21no—
51C4⋊Q8×C103—21no—
52C4⋊Q8×C103—21no—
53C4⋊Q8×C103D411yescharacteristic
54C4⋊Q8×C103D411yescharacteristic
55C4⋊Q8×C103C2311yescharacteristic
56C4⋊Q8×C103C2311yescharacteristic
57C4⋊Q8×C103C2312yes—
58#125×C103—21no—
59#125×C103—21no—
60C22⋊Q8×C103—21no—
61C22⋊Q8×C103—21no—
62C22⋊Q8×C103—21no—
63C22⋊Q8×C103D412yes—
64C4×Q8×C103—21no—
65C4×Q8×C103—21no—
66C4×Q8×C103—21no—
67C4×Q8×C103C2312yes—
68#117×C103—21no—
69#117×C103—21no—
70C2×C4⋊C4×C103—21no—
71C2×C4⋊C4×C103—21no—
72C2×C42×C103C2311yescharacteristic
73#107×C103—22no—
74#107×C103—22no—
75#106×C103—22no—
76#106×C103—22no—
77#106×C103—22no—
78C4⋊C8×C103—22no—
79C4⋊C8×C103—22no—
80C4⋊C8×C103—21no—
81C4⋊C8×C103D411yescharacteristic
82C4⋊C8×C103D411yescharacteristic
83C4⋊C8×C103C2312yes—
84C4⋊C8×C103C2311yescharacteristic
85C4⋊C8×C103C2311yescharacteristic
86C4⋊C8×C103C2311yescharacteristic
87C4⋊C8×C103C2311yescharacteristic
88#103×C103—22no—
89#103×C103—22no—
90#103×C103—22no—
91#103×C103—22no—
92#103×C103—22no—
93#103×C103—22no—
94C22⋊C8×C103—21no—
95C22⋊C8×C103—21no—
96C22⋊C8×C103D412yes—
97#97×C103—22no—
98C4×C8×C103—22no—
99C4×C8×C103—21no—
100C4×C8×C103—21no—
101C4×C8×C103C2312yes—
102C2×Q8×C103—21no—
103C2×Q8×C103—21no—
104C2×Q8×C103—21no—
105C2×Q8×C103—22no—
106C2×Q8×C103—41no—
107C2×Q8×C103—82no—
108C2×Q8×C103C2×D412yes—
109C22×C4×C103—41no—
110C22×C4×C103C2×D411yescharacteristic
111C22×C4×C103C2×D411yescharacteristic
112C22×C4×C103#4111yescharacteristic
113Q16×C103—82no—
114M16×C103—81no—
115C2×C8×C103—21no—
116C2×C8×C103—21no—
117C2×C8×C103—21no—
118C2×C8×C103—21no—
119C2×C8×C103—22no—
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—22no—
128C4⋊C4×C103—21no—
129C4⋊C4×C103—22no—
130C4⋊C4×C103—21no—
131C4⋊C4×C103—21no—
132C4⋊C4×C103—21no—
133C4⋊C4×C103—41no—
134C4⋊C4×C103—41no—
135C4⋊C4×C103—41no—
136C4⋊C4×C103—41no—
137C4⋊C4×C103C2×D412yes—
138C22⋊C4×C103—22no—
139C22⋊C4×C103—41no—
140C42×C103—22no—
141C42×C103—41no—
142C42×C103C2×D411yescharacteristic
143C42×C103C2×D411yescharacteristic
144C42×C103#4111yescharacteristic
145C42×C103C2411yescharacteristic
146C23×C103#12111yescharacteristic
147Q8×C103—22no—
148Q8×C103—22no—
149Q8×C103—42no—
150Q8×C103—41no—
151Q8×C103—41no—
152Q8×C103—41no—
153Q8×C103—41no—
154Q8×C103—82no—
155Q8×C103—82no—
156C2×C4×C103—21no—
157C2×C4×C103—21no—
158C2×C4×C103—21no—
159C2×C4×C103—21no—
160C2×C4×C103—22no—
161C2×C4×C103—22no—
162C2×C4×C103—22no—
163C2×C4×C103—41no—
164C2×C4×C103—41no—
165C2×C4×C103—42no—
166C2×C4×C103—82no—
167C2×C4×C103#12111yescharacteristic
168C2×C4×C103#12111yescharacteristic
169C2×C4×C103#12111yescharacteristic
170C2×C4×C103C22×D411yescharacteristic
171C2×C4×C103C22×D411yescharacteristic
172C2×C4×C103C2×#4111yescharacteristic
173C8×C103—22no—
174C8×C103—22no—
175C8×C103—41no—
176C8×C103—42no—
177C8×C103—41no—
178C8×C103—41no—
179C8×C103—41no—
180C22×C103—21no—
181C22×C103—21no—
182C22×C103—21no—
183C22×C103C2×#12111yescharacteristic
184C4×C103—21no—
185C4×C103—21no—
186C4×C103—21no—
187C4×C103—42no—
188C4×C103—42no—
189C4×C103—81no—
190C4×C103—81no—
191C4×C103—82no—
192C4×C103#47112yes—
193C4×C103#57711yescharacteristic
194C4×C103#57811yescharacteristic
195C4×C103#57811yescharacteristic
196C4×C103#57811yescharacteristic
197#19571C10311yesmaximal, characteristic, direct product factor, Sylow
198C2×C103—41no—
199C2×C103#304411yescharacteristic
200C2×C103#306311yescharacteristic
201C2×C103C2×#47111yescharacteristic
202#3255C2×C10311yescharacteristic
203#3230C2×C10311yescharacteristic
204#3229C2×C10311yescharacteristic
205#2986C2×C10311yescharacteristic
206#1704C2×C10312yescomplemented
207#1692C2×C10312yescomplemented
208#1684C2×C10312yescomplemented
209#1672C2×C10312yescomplemented
210#1574C2×C10311yescharacteristic
211#1548C2×C10311yescharacteristic
212#1544C2×C10311yescharacteristic
213C103#1957111yescharacteristic, direct product factor, Sylow
214#533C22×C10311yescharacteristic
215#533C22×C10311yescharacteristic
216C2×C4⋊Q8C22×C10311yescharacteristic
217#500—21no—
218#498C22×C10312yes—
219#487—21no—
220#487C22×C10312yes—
221#484—22no—
222#483—22no—
223#477C22×C10312yes—
224#477C22×C10312yes—
225#475—21no—
226#475—21no—
227#475—21no—
228#475C22×C10312yes—
229#470—22no—
230#462—21no—
231#462C22×C10312yes—
232#446—21no—
233#446C22×C10312yes—
234C8×Q8—21no—
235C8×Q8C22×C10312yes—
236#433—22no—
237#431C22×C10311yescharacteristic
238#431C22×C10311yescharacteristic
239#431C22×C10311yescharacteristic
240#423C22×C10311yescharacteristic
241#335C22×C10312yes—
242#334C22×C10312yes—
243#333C22×C10312yes—
244#333C22×C10312yes—
245#332C22×C10311yescharacteristic
246#332C22×C10311yescharacteristic
247#332C22×C10311yescharacteristic
248#332C22×C10311yescharacteristic
249C22×Q8—21no—
250C2×Q16—22no—
251C2×M16—21no—
252C4⋊Q8—21no—
253C4⋊Q8—21no—
254C4⋊Q8—21no—
255C4⋊Q8D4×C10311yescharacteristic
256C4⋊Q8D4×C10311yescharacteristic
257C4⋊Q8C23×C10312yes—
258C4⋊Q8C23×C10311yescharacteristic
259C4⋊Q8C23×C10311yescharacteristic
260#125—21no—
261#125—21no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265C22⋊Q8D4×C10312yes—
266C4×Q8—21no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×Q8C23×C10312yes—
270#117—21no—
271#117—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C42C23×C10311yescharacteristic
275#107—22no—
276#107—22no—
277#106—22no—
278#106—22no—
279#106—22no—
280C4⋊C8—22no—
281C4⋊C8—22no—
282C4⋊C8—21no—
283C4⋊C8D4×C10311yescharacteristic
284C4⋊C8D4×C10311yescharacteristic
285C4⋊C8C23×C10311yescharacteristic
286C4⋊C8C23×C10311yescharacteristic
287C4⋊C8C23×C10311yescharacteristic
288C4⋊C8C23×C10311yescharacteristic
289C4⋊C8C23×C10312yes—
290#103—22no—
291#103—22no—
292#103—22no—
293#103—22no—
294#103—22no—
295#103—22no—
296C22⋊C8—21no—
297C22⋊C8—21no—
298C22⋊C8D4×C10312yes—
299#97—22no—
300C4×C8—22no—
301C4×C8—21no—
302C4×C8—21no—
303C4×C8C23×C10312yes—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—22no—
308C2×Q8—41no—
309C2×Q8—82no—
310C2×Q8C2×D4×C10312yes—
311C22×C4—41no—
312C22×C4C2×D4×C10311yescharacteristic
313C22×C4C2×D4×C10311yescharacteristic
314C22×C4#41×C10311yescharacteristic
315Q16—82no—
316M16—81no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—22no—
322C2×C8C2×D4×C10312yes—
323C2×C8C2×D4×C10312yes—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4C2×D4×C10312yes—
340C22⋊C4—22no—
341C22⋊C4—41no—
342C42—22no—
343C42—41no—
344C42C2×D4×C10311yescharacteristic
345C42C2×D4×C10311yescharacteristic
346C42#41×C10311yescharacteristic
347C42C24×C10311yescharacteristic
348C23#121×C10311yescharacteristic
349Q8—22no—
350Q8—22no—
351Q8—42no—
352Q8—41no—
353Q8—41no—
354Q8—41no—
355Q8—41no—
356Q8—82no—
357Q8—82no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4#121×C10311yescharacteristic
370C2×C4#121×C10311yescharacteristic
371C2×C4#121×C10311yescharacteristic
372C2×C4C22×D4×C10311yescharacteristic
373C2×C4C22×D4×C10311yescharacteristic
374C2×C4C2×#41×C10311yescharacteristic
375C8—22no—
376C8—22no—
377C8—42no—
378C8—41no—
379C8—41no—
380C8—41no—
381C8—41no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22C2×#121×C10311yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—42no—
390C4—42no—
391C4—81no—
392C4—81no—
393C4—82no—
394C4#471×C10312yes—
395C4#577×C10311yescharacteristic
396C4#578×C10311yescharacteristic
397C4#578×C10311yescharacteristic
398C4#578×C10311yescharacteristic
399C2—41no—
400C2C103×#304411yescharacteristic
401C2C103×#306311yescharacteristic
402C2C2×#471×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C2×#121
commutator, Frattini, cosocleC42C24×C103
prime radicalC23×C103#121
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
5. C103×#1704C2semidirect
6. C103×#1692C2semidirect
7. C103×#1684C2semidirect
8. C103×#1672C2semidirect
197. #19571C103direct (N × H)
206. #1704C2×C103semidirect
207. #1692C2×C103semidirect
208. #1684C2×C103semidirect
209. #1672C2×C103semidirect
213. C103#19571direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#32552
C103×#32302
C103×#32292
C103×#29862
C103×#17042
C103×#16922
C103×#16842
C103×#16722
C103×#15742
C103×#15482
C103×#15442
#19571103