Finite Group Databasebeta

← C113×#19264 #43287284

Subgroups — C113×#19264 #43287284

Order 28928.

650 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3169C211yesmaximal, characteristic
2C113×#3112C212yesmaximal, complemented
3C2×C8×Q8×C113C211yesmaximal, characteristic, complemented
4C113×#1678C214yesmaximal, complemented
5C113×#1676C212yesmaximal, complemented
6C113×#1668C212yesmaximal, complemented
7C113×#1568C211yesmaximal, characteristic, complemented
8C113×#1551C212yesmaximal, complemented
9#532×C113C2212yes—
10C2×C4×Q8×C113C2211yescharacteristic
11#500×C113C2211yescharacteristic
12#493×C113C2211yescharacteristic
13#486×C113C2212yes—
14#480×C113—22no—
15#477×C113C2214yes—
16#466×C113—21no—
17#466×C113—21no—
18#460×C113C2214yes—
19#448×C113—22no—
20C8×Q8×C113—21no—
21C8×Q8×C113—21no—
22C8×Q8×C113C2212yes—
23C8×Q8×C113C2212yes—
24#440×C113—24no—
25C4×D8×C113—21no—
26C4×D8×C113—21no—
27#432×C113C2212yes—
28C2×C4⋊C8×C113—21no—
29C2×C4⋊C8×C113C2211yescharacteristic
30C2×C4×C8×C113—21no—
31C2×C4×C8×C113C2211yescharacteristic
32#335×C113C2212yes—
33#334×C113C2212yes—
34#333×C113C2214yes—
35#331×C113C2214yes—
36C2×#41×C113—22no—
37C22×Q8×C113D411yescharacteristic
38C2×SD16×C113—24no—
39C2×D8×C113—21no—
40C2×D8×C113—21no—
41C22×C8×C113—21no—
42C22×C8×C113D411yescharacteristic
43C22×C8×C113D411yescharacteristic
44C4⋊Q8×C113C2312yes—
45#127×C113C2312yes—
46#124×C113—22no—
47#121×C113—22no—
48#121×C113—22no—
49C4×Q8×C113—21no—
50C4×Q8×C113—21no—
51C4×Q8×C113D412yes—
52C4×Q8×C113C2312yes—
53C4×D4×C113—22no—
54C4×D4×C113—22no—
55C2×C4⋊C4×C113—21no—
56C2×C4⋊C4×C113D411yescharacteristic
57C2×C42×C113—21no—
58C2×C42×C113C2311yescharacteristic
59#107×C113—21no—
60#107×C113—21no—
61#107×C113—24no—
62C4⋊C8×C113—22no—
63C4⋊C8×C113—22no—
64C4⋊C8×C113—21no—
65C4⋊C8×C113C2312yes—
66C4⋊C8×C113C2314yes—
67#103×C113—24no—
68#102×C113—22no—
69#102×C113—22no—
70#102×C113—24no—
71C22⋊C8×C113—22no—
72#97×C113—22no—
73C4×C8×C113—22no—
74C4×C8×C113—22no—
75C4×C8×C113D411yescharacteristic
76C4×C8×C113D411yescharacteristic
77C4×C8×C113C2311yescharacteristic
78C4×C8×C113C2311yescharacteristic
79#41×C113—84no—
80C2×Q8×C113—24no—
81C2×Q8×C113—21no—
82C2×Q8×C113—22no—
83C2×Q8×C113C2×D412yes—
84C2×D4×C113—22no—
85C2×D4×C113—22no—
86C2×D4×C113—22no—
87C2×D4×C113—42no—
88C22×C4×C113—21no—
89C22×C4×C113—21no—
90C22×C4×C113—42no—
91C22×C4×C113C2×D411yescharacteristic
92C22×C4×C113C2×D411yescharacteristic
93C22×C4×C113#4111yescharacteristic
94SD16×C113—48no—
95D8×C113—42no—
96D8×C113—42no—
97C2×C8×C113—22no—
98C2×C8×C113—22no—
99C2×C8×C113—24no—
100C2×C8×C113—41no—
101C2×C8×C113—42no—
102C2×C8×C113C2×D411yescharacteristic
103C2×C8×C113C2×D411yescharacteristic
104C2×C8×C113C2×D411yescharacteristic
105C2×C8×C113C2×D411yescharacteristic
106C4⋊C4×C113—22no—
107C4⋊C4×C113—21no—
108C4⋊C4×C113—22no—
109C4⋊C4×C113—22no—
110C4⋊C4×C113—22no—
111C4⋊C4×C113C2×D412yes—
112C22⋊C4×C113—42no—
113C22⋊C4×C113—42no—
114C42×C113—22no—
115C42×C113—22no—
116C42×C113C2×D411yescharacteristic
117C42×C113C2×D411yescharacteristic
118C42×C113#4111yescharacteristic
119C42×C113C2411yescharacteristic
120C23×C113—42no—
121C23×C113#12111yescharacteristic
122Q8×C113—24no—
123Q8×C113—22no—
124Q8×C113—82no—
125Q8×C113#13514yes—
126D4×C113—44no—
127D4×C113—42no—
128D4×C113—42no—
129D4×C113—82no—
130D4×C113—84no—
131C2×C4×C113—24no—
132C2×C4×C113—22no—
133C2×C4×C113—22no—
134C2×C4×C113—22no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—22no—
138C2×C4×C113—42no—
139C2×C4×C113—42no—
140C2×C4×C113—84no—
141C2×C4×C113#12111yescharacteristic
142C2×C4×C113#12111yescharacteristic
143C2×C4×C113#12111yescharacteristic
144C2×C4×C113C22×D411yescharacteristic
145C2×C4×C113C22×D411yescharacteristic
146C2×C4×C113C2×#4111yescharacteristic
147C8×C113—21no—
148C8×C113—21no—
149C8×C113—21no—
150C8×C113—44no—
151C8×C113—42no—
152C8×C113#13712yes—
153C22×C113—21no—
154C22×C113—21no—
155C22×C113—82no—
156C22×C113—82no—
157C22×C113—82no—
158C22×C113#47212yes—
159C22×C113C2×#12111yescharacteristic
160C4×C113—21no—
161C4×C113—24no—
162C4×C113—21no—
163C4×C113—21no—
164C4×C113—21no—
165C4×C113—42no—
166C4×C113—82no—
167C4×C113C2×#13512yes—
168C4×C113C2×#13711yescharacteristic
169C4×C113#57511yescharacteristic
170#19264C11311yesmaximal, characteristic, direct product factor, Sylow
171C2×C113—22no—
172C2×C113—162no—
173C2×C113#303711yescharacteristic
174C2×C113#305011yescharacteristic
175C2×C113C2×#47211yescharacteristic
176#3169C2×C11311yescharacteristic
177#3112C2×C11312yescomplemented
178C2×C8×Q8C2×C11311yescharacteristic, complemented
179#1678C2×C11314yescomplemented
180#1676C2×C11312yescomplemented
181#1668C2×C11312yescomplemented
182#1568C2×C11311yescharacteristic, complemented
183#1551C2×C11312yescomplemented
184C113#1926411yescharacteristic, direct product factor, Sylow
185#532C22×C11312yes—
186C2×C4×Q8C22×C11311yescharacteristic
187#500C22×C11311yescharacteristic
188#493C22×C11311yescharacteristic
189#486C22×C11312yes—
190#480—22no—
191#477C22×C11314yes—
192#466—21no—
193#466—21no—
194#460C22×C11314yes—
195#448—22no—
196C8×Q8—21no—
197C8×Q8—21no—
198C8×Q8C22×C11312yes—
199C8×Q8C22×C11312yes—
200#440—24no—
201C4×D8—21no—
202C4×D8—21no—
203#432C22×C11312yes—
204C2×C4⋊C8—21no—
205C2×C4⋊C8C22×C11311yescharacteristic
206C2×C4×C8—21no—
207C2×C4×C8C22×C11311yescharacteristic
208#335C22×C11312yes—
209#334C22×C11312yes—
210#333C22×C11314yes—
211#331C22×C11314yes—
212C2×#41—22no—
213C22×Q8D4×C11311yescharacteristic
214C2×SD16—24no—
215C2×D8—21no—
216C2×D8—21no—
217C22×C8—21no—
218C22×C8D4×C11311yescharacteristic
219C22×C8D4×C11311yescharacteristic
220C4⋊Q8C23×C11312yes—
221#127C23×C11312yes—
222#124—22no—
223#121—22no—
224#121—22no—
225C4×Q8—21no—
226C4×Q8—21no—
227C4×Q8D4×C11312yes—
228C4×Q8C23×C11312yes—
229C4×D4—22no—
230C4×D4—22no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4D4×C11311yescharacteristic
233C2×C42—21no—
234C2×C42C23×C11311yescharacteristic
235#107—21no—
236#107—21no—
237#107—24no—
238C4⋊C8—22no—
239C4⋊C8—22no—
240C4⋊C8—21no—
241C4⋊C8C23×C11312yes—
242C4⋊C8C23×C11314yes—
243#103—24no—
244#102—22no—
245#102—22no—
246#102—24no—
247C22⋊C8—22no—
248#97—22no—
249C4×C8—22no—
250C4×C8—22no—
251C4×C8D4×C11311yescharacteristic
252C4×C8D4×C11311yescharacteristic
253C4×C8C23×C11311yescharacteristic
254C4×C8C23×C11311yescharacteristic
255#41—84no—
256C2×Q8—24no—
257C2×Q8—21no—
258C2×Q8—22no—
259C2×Q8C2×D4×C11312yes—
260C2×D4—22no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—42no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—42no—
267C22×C4C2×D4×C11311yescharacteristic
268C22×C4C2×D4×C11311yescharacteristic
269C22×C4#41×C11311yescharacteristic
270SD16—48no—
271D8—42no—
272D8—42no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—24no—
276C2×C8—41no—
277C2×C8—42no—
278C2×C8C2×D4×C11311yescharacteristic
279C2×C8C2×D4×C11311yescharacteristic
280C2×C8C2×D4×C11311yescharacteristic
281C2×C8C2×D4×C11311yescharacteristic
282C4⋊C4—22no—
283C4⋊C4—21no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4C2×D4×C11312yes—
288C22⋊C4—42no—
289C22⋊C4—42no—
290C42—22no—
291C42—22no—
292C42C2×D4×C11311yescharacteristic
293C42C2×D4×C11311yescharacteristic
294C42#41×C11311yescharacteristic
295C42C24×C11311yescharacteristic
296C23—42no—
297C23#121×C11311yescharacteristic
298Q8—24no—
299Q8—22no—
300Q8—82no—
301Q8#135×C11314yes—
302D4—44no—
303D4—42no—
304D4—42no—
305D4—82no—
306D4—84no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—84no—
317C2×C4#121×C11311yescharacteristic
318C2×C4#121×C11311yescharacteristic
319C2×C4#121×C11311yescharacteristic
320C2×C4C22×D4×C11311yescharacteristic
321C2×C4C22×D4×C11311yescharacteristic
322C2×C4C2×#41×C11311yescharacteristic
323C8—21no—
324C8—21no—
325C8—21no—
326C8—44no—
327C8—42no—
328C8#137×C11312yes—
329C22—21no—
330C22—21no—
331C22—82no—
332C22—82no—
333C22—82no—
334C22#472×C11312yes—
335C22C2×#121×C11311yescharacteristic
336C4—24no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—82no—
343C4C2×#135×C11312yes—
344C4C2×#137×C11311yescharacteristic
345C4#575×C11311yescharacteristic
346C2—22no—
347C2—162no—
348C2C113×#303711yescharacteristic
349C2C113×#305011yescharacteristic
350C2C2×#472×C11311yescharacteristic
subgroupG/H
center, socleC22×C113C2×#121
commutator, Frattini, cosocleC42C24×C113
prime radicalC113×#3169C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#3112C2semidirect
3. C2×C8×Q8×C113C2semidirect
4. C113×#1678C2semidirect
5. C113×#1676C2semidirect
6. C113×#1668C2semidirect
7. C113×#1568C2semidirect
8. C113×#1551C2semidirect
170. #19264C113direct (N × H)
177. #3112C2×C113semidirect
178. C2×C8×Q8C2×C113semidirect
179. #1678C2×C113semidirect
180. #1676C2×C113semidirect
181. #1668C2×C113semidirect
182. #1568C2×C113semidirect
183. #1551C2×C113semidirect
184. C113#19264direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#31692
C113×#31122
C2×C8×Q8×C1132
C113×#16782
C113×#16762
C113×#16682
C113×#15682
C113×#15512
#19264113