Finite Group Databasebeta

← C113×#19054 #43287074

Subgroups — C113×#19054 #43287074

Order 28928.

926 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×#3550C211yesmaximal, characteristic, complemented
2C113×#3235C212yesmaximal, complemented
3C113×#3150C211yesmaximal, characteristic
4C113×#1660C214yesmaximal, complemented
5C113×#1657C214yesmaximal, complemented
6C113×#1536C211yesmaximal, characteristic, complemented
7C113×#1531C212yesmaximal, complemented
8C2×#135×C113—22no—
9#563×C113C2214yes—
10#559×C113—21no—
11Q82×C113—21no—
12#556×C113—22no—
13D4×Q8×C113—22no—
14#542×C113—24no—
15#536×C113—22no—
16#533×C113C2212yes—
17#532×C113C2211yescharacteristic
18#532×C113C2211yescharacteristic
19#501×C113C2214yes—
20#497×C113—21no—
21#497×C113C2212yes—
22#496×C113—21no—
23#496×C113C2212yes—
24#490×C113C2214yes—
25#482×C113—24no—
26#476×C113—22no—
27#474×C113—22no—
28#432×C113C2212yes—
29C2×#97×C113C2211yescharacteristic
30#330×C113C2218yes—
31#329×C113C2214yes—
32C2×#41×C113—21no—
33C2×#41×C113D412yes—
34C22×Q8×C113—22no—
35#135×C113—48no—
36C2×Q16×C113—22no—
37C2×SD16×C113—22no—
38C2×SD16×C113—22no—
39C2×D8×C113—22no—
40C22×C8×C113—21no—
41C4⋊Q8×C113—24no—
42C4⋊Q8×C113—24no—
43C4⋊Q8×C113D411yescharacteristic
44C4⋊Q8×C113D412yes—
45C4⋊Q8×C113D412yes—
46C4⋊Q8×C113C2311yescharacteristic
47#127×C113D411yescharacteristic
48#127×C113C2311yescharacteristic
49#126×C113—28no—
50#125×C113C2314yes—
51#124×C113—24no—
52#124×C113—24no—
53#124×C113—21no—
54#124×C113C2312yes—
55#123×C113—24no—
56#123×C113—24no—
57C22⋊Q8×C113—24no—
58C22⋊Q8×C113—22no—
59C22⋊Q8×C113—22no—
60C22⋊Q8×C113—28no—
61#121×C113—22no—
62#121×C113—22no—
63C4×Q8×C113—24no—
64C4×Q8×C113—22no—
65C4×Q8×C113—22no—
66C4×D4×C113—24no—
67C4×D4×C113—22no—
68C4×D4×C113—22no—
69#117×C113—22no—
70#117×C113D414yes—
71C2×C42×C113C2311yescharacteristic
72#107×C113—24no—
73#106×C113—24no—
74C4⋊C8×C113—22no—
75#102×C113—24no—
76#102×C113—24no—
77C22⋊C8×C113—22no—
78#97×C113—21no—
79#97×C113C2314yes—
80#97×C113C2312yes—
81#41×C113—44no—
82#41×C113—44no—
83C2×Q8×C113—24no—
84C2×Q8×C113—22no—
85C2×Q8×C113—22no—
86C2×Q8×C113—21no—
87C2×Q8×C113—84no—
88C2×Q8×C113C2×D412yes—
89C2×D4×C113—22no—
90C2×D4×C113—22no—
91C2×D4×C113—22no—
92C2×D4×C113—21no—
93C2×D4×C113—41no—
94C2×D4×C113C2×D412yes—
95C22×C4×C113—24no—
96C22×C4×C113—22no—
97C22×C4×C113—41no—
98C22×C4×C113C2×D411yescharacteristic
99C22×C4×C113C2×D412yes—
100Q16×C113—44no—
101SD16×C113—44no—
102SD16×C113—44no—
103D8×C113—44no—
104C2×C8×C113—24no—
105C2×C8×C113—22no—
106C2×C8×C113—24no—
107C4⋊C4×C113—28no—
108C4⋊C4×C113—22no—
109C4⋊C4×C113—22no—
110C4⋊C4×C113—22no—
111C4⋊C4×C113—24no—
112C4⋊C4×C113—24no—
113C4⋊C4×C113—22no—
114C4⋊C4×C113C2×D414yes—
115C4⋊C4×C113C2×D414yes—
116C22⋊C4×C113—24no—
117C22⋊C4×C113—28no—
118C22⋊C4×C113—24no—
119C22⋊C4×C113—24no—
120C22⋊C4×C113—42no—
121C42×C113—24no—
122C42×C113—24no—
123C42×C113C2×D411yescharacteristic
124C42×C113C2×D412yes—
125C42×C113C2411yescharacteristic
126C23×C113—22no—
127C23×C113—41no—
128C23×C113#12011yescharacteristic
129Q8×C113—42no—
130Q8×C113—44no—
131Q8×C113—42no—
132Q8×C113—44no—
133Q8×C113—84no—
134D4×C113—42no—
135D4×C113—44no—
136D4×C113—42no—
137D4×C113—44no—
138D4×C113—82no—
139D4×C113—82no—
140C2×C4×C113—22no—
141C2×C4×C113—24no—
142C2×C4×C113—22no—
143C2×C4×C113—24no—
144C2×C4×C113—42no—
145C2×C4×C113—44no—
146C2×C4×C113—41no—
147C2×C4×C113—84no—
148C2×C4×C113—82no—
149C2×C4×C113#12012yes—
150C2×C4×C113#12011yescharacteristic
151C2×C4×C113C22×D412yes—
152C2×C4×C113C22×D411yescharacteristic
153C8×C113—24no—
154C8×C113—44no—
155C22×C113—21no—
156C22×C113—22no—
157C22×C113—42no—
158C22×C113—44no—
159C22×C113—81no—
160C22×C113—82no—
161C22×C113C2×#12011yescharacteristic
162C4×C113—21no—
163C4×C113—22no—
164C4×C113—22no—
165C4×C113—42no—
166C4×C113—44no—
167C4×C113—44no—
168C4×C113—81no—
169C4×C113#45312yes—
170#19054C11311yesmaximal, characteristic, direct product factor, Sylow
171C2×C113—41no—
172C2×C113—82no—
173C2×C113—161no—
174C2×C113C2×#45311yescharacteristic
175C2×C113#302012yes—
176#3550C2×C11311yescharacteristic, complemented
177#3235C2×C11312yescomplemented
178#3150C2×C11311yescharacteristic
179#1660C2×C11314yescomplemented
180#1657C2×C11314yescomplemented
181#1536C2×C11311yescharacteristic, complemented
182#1531C2×C11312yescomplemented
183C113#1905411yescharacteristic, direct product factor, Sylow
184C2×#135—22no—
185#563C22×C11314yes—
186#559—21no—
187Q82—21no—
188#556—22no—
189D4×Q8—22no—
190#542—24no—
191#536—22no—
192#533C22×C11312yes—
193#532C22×C11311yescharacteristic
194#532C22×C11311yescharacteristic
195#501C22×C11314yes—
196#497—21no—
197#497C22×C11312yes—
198#496—21no—
199#496C22×C11312yes—
200#490C22×C11314yes—
201#482—24no—
202#476—22no—
203#474—22no—
204#432C22×C11312yes—
205C2×#97C22×C11311yescharacteristic
206#330C22×C11318yes—
207#329C22×C11314yes—
208C2×#41—21no—
209C2×#41D4×C11312yes—
210C22×Q8—22no—
211#135—48no—
212C2×Q16—22no—
213C2×SD16—22no—
214C2×SD16—22no—
215C2×D8—22no—
216C22×C8—21no—
217C4⋊Q8—24no—
218C4⋊Q8—24no—
219C4⋊Q8D4×C11311yescharacteristic
220C4⋊Q8D4×C11312yes—
221C4⋊Q8D4×C11312yes—
222C4⋊Q8C23×C11311yescharacteristic
223#127D4×C11311yescharacteristic
224#127C23×C11311yescharacteristic
225#126—28no—
226#125C23×C11314yes—
227#124—24no—
228#124—24no—
229#124—21no—
230#124C23×C11312yes—
231#123—24no—
232#123—24no—
233C22⋊Q8—24no—
234C22⋊Q8—22no—
235C22⋊Q8—22no—
236C22⋊Q8—28no—
237#121—22no—
238#121—22no—
239C4×Q8—24no—
240C4×Q8—22no—
241C4×Q8—22no—
242C4×D4—24no—
243C4×D4—22no—
244C4×D4—22no—
245#117—22no—
246#117D4×C11314yes—
247C2×C42C23×C11311yescharacteristic
248#107—24no—
249#106—24no—
250C4⋊C8—22no—
251#102—24no—
252#102—24no—
253C22⋊C8—22no—
254#97—21no—
255#97C23×C11314yes—
256#97C23×C11312yes—
257#41—44no—
258#41—44no—
259C2×Q8—24no—
260C2×Q8—22no—
261C2×Q8—22no—
262C2×Q8—21no—
263C2×Q8—84no—
264C2×Q8C2×D4×C11312yes—
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—22no—
268C2×D4—21no—
269C2×D4—41no—
270C2×D4C2×D4×C11312yes—
271C22×C4—24no—
272C22×C4—22no—
273C22×C4—41no—
274C22×C4C2×D4×C11311yescharacteristic
275C22×C4C2×D4×C11312yes—
276Q16—44no—
277SD16—44no—
278SD16—44no—
279D8—44no—
280C2×C8—24no—
281C2×C8—22no—
282C2×C8—24no—
283C4⋊C4—28no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—24no—
288C4⋊C4—24no—
289C4⋊C4—22no—
290C4⋊C4C2×D4×C11314yes—
291C4⋊C4C2×D4×C11314yes—
292C22⋊C4—24no—
293C22⋊C4—28no—
294C22⋊C4—24no—
295C22⋊C4—24no—
296C22⋊C4—42no—
297C42—24no—
298C42—24no—
299C42C2×D4×C11311yescharacteristic
300C42C2×D4×C11312yes—
301C42C24×C11311yescharacteristic
302C23—22no—
303C23—41no—
304C23#120×C11311yescharacteristic
305Q8—42no—
306Q8—44no—
307Q8—42no—
308Q8—44no—
309Q8—84no—
310D4—42no—
311D4—44no—
312D4—42no—
313D4—44no—
314D4—82no—
315D4—82no—
316C2×C4—22no—
317C2×C4—24no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—41no—
323C2×C4—84no—
324C2×C4—82no—
325C2×C4#120×C11312yes—
326C2×C4#120×C11311yescharacteristic
327C2×C4C22×D4×C11312yes—
328C2×C4C22×D4×C11311yescharacteristic
329C8—24no—
330C8—44no—
331C22—21no—
332C22—22no—
333C22—42no—
334C22—44no—
335C22—81no—
336C22—82no—
337C22C2×#120×C11311yescharacteristic
338C4—21no—
339C4—22no—
340C4—22no—
341C4—42no—
342C4—44no—
343C4—44no—
344C4—81no—
345C4#453×C11312yes—
346C2—41no—
347C2—82no—
348C2—161no—
349C2C2×#453×C11311yescharacteristic
350C2C113×#302012yes—
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC113×#3150C2
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
1. C113×#3550C2semidirect
2. C113×#3235C2semidirect
4. C113×#1660C2semidirect
5. C113×#1657C2semidirect
6. C113×#1536C2semidirect
7. C113×#1531C2semidirect
170. #19054C113direct (N × H)
176. #3550C2×C113semidirect
177. #3235C2×C113semidirect
179. #1660C2×C113semidirect
180. #1657C2×C113semidirect
181. #1536C2×C113semidirect
182. #1531C2×C113semidirect
183. C113#19054direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#35502
C113×#32352
C113×#31502
C113×#16602
C113×#16572
C113×#15362
C113×#15312
#19054113