Finite Group Databasebeta

← C113×#9093 #43277113

Subgroups — C113×#9093 #43277113

Order 28928.

536 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#2975C211yesmaximal, characteristic, complemented
2C2×#442×C113C211yesmaximal, characteristic
3C113×#1478C211yesmaximal, characteristic, complemented
4C113×#1478C211yesmaximal, characteristic, complemented
5C113×#1460C211yesmaximal, characteristic, complemented
6C113×#1281C211yesmaximal, characteristic, complemented
7C113×#1275C211yesmaximal, characteristic, complemented
8C22×D8×C113C411yescharacteristic
9C2×C4×D4×C113C2211yescharacteristic
10C2×C4×D4×C113C2211yescharacteristic
11#442×C113—22no—
12#442×C113—22no—
13#436×C113—22no—
14#436×C113—22no—
15#431×C113C2211yescharacteristic
16#431×C113C2211yescharacteristic
17#431×C113C2211yescharacteristic
18#431×C113C2211yescharacteristic
19C2×#106×C113C411yescharacteristic
20C2×#102×C113C411yescharacteristic
21C2×#102×C113C411yescharacteristic
22#407×C113—22no—
23C2×#97×C113C2211yescharacteristic
24D4⋊C8×C113—22no—
25D4⋊C8×C113—22no—
26#323×C113—22no—
27C22×D4×C113C2×C411yescharacteristic
28C22×D4×C113C2×C411yescharacteristic
29C23×C4×C113—21no—
30C23×C4×C113—21no—
31C2×D8×C113—22no—
32C2×D8×C113—22no—
33C2×D8×C113—22no—
34C2×M16×C113—24no—
35C22×C8×C113C2×C411yescharacteristic
36C22×C8×C113C2×C411yescharacteristic
37C4×D4×C113—21no—
38C4×D4×C113—21no—
39C4×D4×C113—21no—
40C4×D4×C113—21no—
41C4×D4×C113—21no—
42C4×D4×C113—21no—
43C4×D4×C113D412yes—
44C4×D4×C113D412yes—
45C2×C4⋊C4×C113C2×C411yescharacteristic
46C2×C4⋊C4×C113C2×C411yescharacteristic
47C2×C22⋊C4×C113—21no—
48C2×C22⋊C4×C113—21no—
49C2×C42×C113C2311yescharacteristic
50#106×C113—22no—
51C4⋊C8×C113—21no—
52C4⋊C8×C113—21no—
53C4⋊C8×C113—21no—
54C4⋊C8×C113—21no—
55#102×C113—22no—
56#102×C113—22no—
57C22⋊C8×C113—24no—
58C22⋊C8×C113—21no—
59C22⋊C8×C113—21no—
60C22⋊C8×C113—21no—
61C22⋊C8×C113D412yes—
62#97×C113—21no—
63#97×C113—21no—
64C4×C8×C113—21no—
65C4×C8×C113—21no—
66C4×C8×C113—21no—
67C4×C8×C113D412yes—
68C24×C113—21no—
69C24×C113—21no—
70C2×D4×C113—21no—
71C2×D4×C113—21no—
72C2×D4×C113—21no—
73C2×D4×C113—21no—
74C2×D4×C113—21no—
75C2×D4×C113—21no—
76C2×D4×C113—21no—
77C2×D4×C113—21no—
78C2×D4×C113—21no—
79C2×D4×C113—21no—
80C2×D4×C113C22⋊C412yes—
81C2×D4×C113M1612yescomplemented
82C22×C4×C113—21no—
83C22×C4×C113—22no—
84C22×C4×C113—22no—
85C22×C4×C113—21no—
86C22×C4×C113—41no—
87C22×C4×C113—41no—
88C22×C4×C113—82no—
89C22×C4×C113—82no—
90C22×C4×C113C22×C411yescharacteristic
91C22×C4×C113C2×D411yescharacteristic
92C22×C4×C113#4111yescharacteristic
93D8×C113—28no—
94M16×C113—84no—
95C2×C8×C113—21no—
96C2×C8×C113—21no—
97C2×C8×C113—21no—
98C2×C8×C113—22no—
99C2×C8×C113—22no—
100C2×C8×C113—21no—
101C2×C8×C113—21no—
102C2×C8×C113—41no—
103C2×C8×C113—41no—
104C2×C8×C113M1612yescomplemented
105C4⋊C4×C113—21no—
106C4⋊C4×C113—21no—
107C4⋊C4×C113—21no—
108C4⋊C4×C113C22⋊C412yes—
109C22⋊C4×C113—22no—
110C22⋊C4×C113—22no—
111C22⋊C4×C113—41no—
112C22⋊C4×C113—41no—
113C42×C113C2×D411yescharacteristic
114C42×C113C2×D411yescharacteristic
115C42×C113C2×D411yescharacteristic
116C42×C113#4111yescharacteristic
117C23×C113—22no—
118C23×C113—22no—
119C23×C113—41no—
120C23×C113—41no—
121C23×C113—41no—
122C23×C113—41no—
123C23×C113—81no—
124C23×C113—81no—
125C23×C113—81no—
126C23×C113—81no—
127C23×C113C4×D411yescharacteristic
128D4×C113—22no—
129D4×C113—22no—
130D4×C113—22no—
131D4×C113—22no—
132D4×C113—41no—
133D4×C113—41no—
134D4×C113—41no—
135D4×C113—41no—
136C2×C4×C113—22no—
137C2×C4×C113—41no—
138C2×C4×C113—41no—
139C2×C4×C113—44no—
140C2×C4×C113—41no—
141C2×C4×C113—82no—
142C2×C4×C113—82no—
143C2×C4×C113—82no—
144C2×C4×C113—81no—
145C2×C4×C113—81no—
146C2×C4×C113C2×C22⋊C411yescharacteristic
147C2×C4×C113C4×D411yescharacteristic
148C2×C4×C113#12011yescharacteristic
149C2×C4×C113#12111yescharacteristic
150C2×C4×C113#12111yescharacteristic
151C2×C4×C113#12311yescharacteristic
152C2×C4×C113C2×M1611yescharacteristic
153C2×C4×C113C2×M1611yescharacteristic
154C2×C4×C113#13111yescharacteristic
155C2×C4×C113#13111yescharacteristic
156C8×C113—22no—
157C8×C113—42no—
158C8×C113—42no—
159C8×C113—41no—
160C8×C113—81no—
161C8×C113—81no—
162C22×C113—21no—
163C22×C113—21no—
164C22×C113—42no—
165C22×C113—42no—
166C22×C113—42no—
167C22×C113—42no—
168C22×C113—82no—
169C22×C113—82no—
170C22×C113—82no—
171C22×C113—82no—
172C22×C113—81no—
173C22×C113—81no—
174C22×C113#38611yescharacteristic
175C22×C113#43511yescharacteristic
176C22×C113#43611yescharacteristic
177C4×C113—21no—
178C4×C113—21no—
179C4×C113—21no—
180C4×C113—21no—
181C4×C113—42no—
182C4×C113—81no—
183C4×C113#40711yescharacteristic
184C4×C113#40811yescharacteristic
185C4×C113#43511yescharacteristic
186C4×C113#43611yescharacteristic
187#9093C11311yesmaximal, characteristic, direct product factor, Sylow
188C2×C113—21no—
189C2×C113—21no—
190C2×C113—82no—
191C2×C113—82no—
192C2×C113#187011yescharacteristic
193C2×C113#190311yescharacteristic
194C2×C113#190411yescharacteristic
195#2975C2×C11311yescharacteristic, complemented
196C2×#442C2×C11311yescharacteristic
197#1478C2×C11311yescharacteristic, complemented
198#1478C2×C11311yescharacteristic, complemented
199#1460C2×C11311yescharacteristic, complemented
200#1281C2×C11311yescharacteristic, complemented
201#1275C2×C11311yescharacteristic, complemented
202C113#909311yescharacteristic, direct product factor, Sylow
203C22×D8C4×C11311yescharacteristic
204C2×C4×D4C22×C11311yescharacteristic
205C2×C4×D4C22×C11311yescharacteristic
206#442—22no—
207#442—22no—
208#436—22no—
209#436—22no—
210#431C22×C11311yescharacteristic
211#431C22×C11311yescharacteristic
212#431C22×C11311yescharacteristic
213#431C22×C11311yescharacteristic
214C2×#106C4×C11311yescharacteristic
215C2×#102C4×C11311yescharacteristic
216C2×#102C4×C11311yescharacteristic
217#407—22no—
218C2×#97C22×C11311yescharacteristic
219D4⋊C8—22no—
220D4⋊C8—22no—
221#323—22no—
222C22×D4C2×C4×C11311yescharacteristic
223C22×D4C2×C4×C11311yescharacteristic
224C23×C4—21no—
225C23×C4—21no—
226C2×D8—22no—
227C2×D8—22no—
228C2×D8—22no—
229C2×M16—24no—
230C22×C8C2×C4×C11311yescharacteristic
231C22×C8C2×C4×C11311yescharacteristic
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—21no—
238C4×D4D4×C11312yes—
239C4×D4D4×C11312yes—
240C2×C4⋊C4C2×C4×C11311yescharacteristic
241C2×C4⋊C4C2×C4×C11311yescharacteristic
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C42C23×C11311yescharacteristic
245#106—22no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250#102—22no—
251#102—22no—
252C22⋊C8—24no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255C22⋊C8—21no—
256C22⋊C8D4×C11312yes—
257#97—21no—
258#97—21no—
259C4×C8—21no—
260C4×C8—21no—
261C4×C8—21no—
262C4×C8D4×C11312yes—
263C24—21no—
264C24—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4C22⋊C4×C11312yes—
276C2×D4M16×C11312yescomplemented
277C22×C4—21no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—82no—
284C22×C4—82no—
285C22×C4C22×C4×C11311yescharacteristic
286C22×C4C2×D4×C11311yescharacteristic
287C22×C4#41×C11311yescharacteristic
288D8—28no—
289M16—84no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8M16×C11312yescomplemented
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4C22⋊C4×C11312yes—
304C22⋊C4—22no—
305C22⋊C4—22no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42C2×D4×C11311yescharacteristic
309C42C2×D4×C11311yescharacteristic
310C42C2×D4×C11311yescharacteristic
311C42#41×C11311yescharacteristic
312C23—22no—
313C23—22no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—81no—
322C23C4×D4×C11311yescharacteristic
323D4—22no—
324D4—22no—
325D4—22no—
326D4—22no—
327D4—41no—
328D4—41no—
329D4—41no—
330D4—41no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—44no—
335C2×C4—41no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4C2×C22⋊C4×C11311yescharacteristic
342C2×C4C4×D4×C11311yescharacteristic
343C2×C4#120×C11311yescharacteristic
344C2×C4#121×C11311yescharacteristic
345C2×C4#121×C11311yescharacteristic
346C2×C4#123×C11311yescharacteristic
347C2×C4C2×M16×C11311yescharacteristic
348C2×C4C2×M16×C11311yescharacteristic
349C2×C4#131×C11311yescharacteristic
350C2×C4#131×C11311yescharacteristic
351C8—22no—
352C8—42no—
353C8—42no—
354C8—41no—
355C8—81no—
356C8—81no—
357C22—21no—
358C22—21no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—82no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—81no—
368C22—81no—
369C22#386×C11311yescharacteristic
370C22#435×C11311yescharacteristic
371C22#436×C11311yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—42no—
377C4—81no—
378C4#407×C11311yescharacteristic
379C4#408×C11311yescharacteristic
380C4#435×C11311yescharacteristic
381C4#436×C11311yescharacteristic
382C2—21no—
383C2—21no—
384C2—82no—
385C2—82no—
386C2C113×#187011yescharacteristic
387C2C113×#190311yescharacteristic
388C2C113×#190411yescharacteristic
subgroupG/H
center, socleC22×C113#386
commutatorC22×C4C22×C4×C113
Frattini, cosocleC2×C42C23×C113
prime radicalC22×D8×C113C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#2975C2semidirect
3. C113×#1478C2semidirect
4. C113×#1478C2semidirect
5. C113×#1460C2semidirect
6. C113×#1281C2semidirect
7. C113×#1275C2semidirect
81. C2×D4×C113M16semidirect
104. C2×C8×C113M16semidirect
187. #9093C113direct (N × H)
195. #2975C2×C113semidirect
197. #1478C2×C113semidirect
198. #1478C2×C113semidirect
199. #1460C2×C113semidirect
200. #1281C2×C113semidirect
201. #1275C2×C113semidirect
202. C113#9093direct (N × H)
276. C2×D4M16×C113semidirect
299. C2×C8M16×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#29752
C2×#442×C1132
C113×#14782
C113×#14602
C113×#12812
C113×#12752
#9093113