Finite Group Databasebeta

← C113×#9205 #43277225

Subgroups — C113×#9205 #43277225

Order 28928.

690 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#2617C211yesmaximal, characteristic
2C113×#2312C211yesmaximal, characteristic, complemented
3C113×#1519C212yesmaximal, complemented
4C2×#323×C113C211yesmaximal, characteristic, complemented
5C113×#1289C212yesmaximal, complemented
6C2×#121×C113C2211yescharacteristic
7C2×#120×C113—21no—
8C22×C22⋊C4×C113C2211yescharacteristic
9C2×C22⋊C8×C113C2212yes—
10#397×C113C412yescomplemented
11#394×C113—22no—
12#392×C113C412yescomplemented
13#388×C113—24no—
14#386×C113—21no—
15#380×C113C2211yescharacteristic
16#380×C113C2212yes—
17#379×C113—21no—
18C4×C22⋊C4×C113—21no—
19#327×C113—24no—
20#323×C113—22no—
21C25×C113D411yescharacteristic
22C22×D4×C113—21no—
23C22×D4×C113—22no—
24C22×D4×C113C2×C411yescharacteristic
25C23×C4×C113D411yescharacteristic
26C23×C4×C113C2311yescharacteristic
27C22×C8×C113—22no—
28#121×C113—22no—
29#121×C113—22no—
30#120×C113—44no—
31C2×C4⋊C4×C113—22no—
32C2×C4⋊C4×C113—21no—
33C2×C4⋊C4×C113C2×C411yescharacteristic
34C2×C22⋊C4×C113—22no—
35C2×C22⋊C4×C113—22no—
36C2×C22⋊C4×C113—22no—
37C2×C22⋊C4×C113—21no—
38C2×C22⋊C4×C113—22no—
39C2×C22⋊C4×C113—21no—
40C2×C22⋊C4×C113—22no—
41C2×C22⋊C4×C113—22no—
42C2×C22⋊C4×C113—22no—
43C2×C22⋊C4×C113C2×C412yes—
44C2×C22⋊C4×C113D412yes—
45C2×C42×C113—22no—
46C22⋊C8×C113—22no—
47C22⋊C8×C113—22no—
48#95×C113—22no—
49#95×C113—22no—
50#95×C113C2×C412yes—
51#95×C113D414yescomplemented
52C24×C113—21no—
53C24×C113—21no—
54C24×C113—22no—
55C24×C113—22no—
56C24×C113—21no—
57C24×C113—81no—
58C24×C113—81no—
59C24×C113C22⋊C412yes—
60C24×C113C2×D411yescharacteristic
61C2×D4×C113—22no—
62C2×D4×C113—44no—
63C2×D4×C113—41no—
64C2×D4×C113—41no—
65C2×D4×C113—42no—
66C2×D4×C113—42no—
67C2×D4×C113—82no—
68C2×D4×C113—82no—
69C2×D4×C113—81no—
70C22×C4×C113—21no—
71C22×C4×C113—21no—
72C22×C4×C113—21no—
73C22×C4×C113—22no—
74C22×C4×C113—24no—
75C22×C4×C113—81no—
76C22×C4×C113—81no—
77C22×C4×C113C22⋊C412yes—
78C22×C4×C113C22×C411yescharacteristic
79C22×C4×C113C2×D412yes—
80C22×C4×C113C2×D411yescharacteristic
81C22×C4×C113#4112yes—
82C2×C8×C113—42no—
83C2×C8×C113—82no—
84C4⋊C4×C113—22no—
85C4⋊C4×C113—82no—
86C4⋊C4×C113—81no—
87C22⋊C4×C113—24no—
88C22⋊C4×C113—24no—
89C22⋊C4×C113—44no—
90C22⋊C4×C113—42no—
91C22⋊C4×C113—42no—
92C22⋊C4×C113—42no—
93C22⋊C4×C113—42no—
94C22⋊C4×C113—82no—
95C22⋊C4×C113—82no—
96C22⋊C4×C113—82no—
97C42×C113—82no—
98C23×C113—22no—
99C23×C113—22no—
100C23×C113—22no—
101C23×C113—41no—
102C23×C113—41no—
103C23×C113—42no—
104C23×C113—42no—
105C23×C113—42no—
106C23×C113—42no—
107C23×C113—42no—
108C23×C113—42no—
109C23×C113—42no—
110C23×C113—42no—
111C23×C113—41no—
112C23×C113—41no—
113C23×C113—41no—
114C23×C113—81no—
115C23×C113—81no—
116C23×C113—84no—
117C23×C113—84no—
118C23×C113C2×C22⋊C411yescharacteristic
119C23×C113#12011yescharacteristic
120C23×C113#12311yescharacteristic
121C23×C113#13512yes—
122C23×C113AGL(1,ℤ/8)12yes—
123D4×C113—82no—
124D4×C113—88no—
125D4×C113—82no—
126D4×C113—82no—
127C2×C4×C113—22no—
128C2×C4×C113—41no—
129C2×C4×C113—42no—
130C2×C4×C113—42no—
131C2×C4×C113—41no—
132C2×C4×C113—42no—
133C2×C4×C113—42no—
134C2×C4×C113—44no—
135C2×C4×C113—44no—
136C2×C4×C113—42no—
137C2×C4×C113—42no—
138C2×C4×C113—41no—
139C2×C4×C113—41no—
140C2×C4×C113—42no—
141C2×C4×C113—41no—
142C2×C4×C113—44no—
143C2×C4×C113—81no—
144C2×C4×C113C4×D412yes—
145C2×C4×C113#12112yes—
146C8×C113—82no—
147C22×C113—21no—
148C22×C113—21no—
149C22×C113—21no—
150C22×C113—21no—
151C22×C113—21no—
152C22×C113—21no—
153C22×C113—42no—
154C22×C113—42no—
155C22×C113—44no—
156C22×C113—42no—
157C22×C113—42no—
158C22×C113—42no—
159C22×C113—82no—
160C22×C113—84no—
161C22×C113—84no—
162C22×C113—82no—
163C22×C113—82no—
164C22×C113—81no—
165C22×C113—81no—
166C22×C113—81no—
167C22×C113#38611yescharacteristic
168C22×C113#41611yescharacteristic
169C22×C113#41811yescharacteristic
170C22×C113#44912yes—
171C22×C113#48212yes—
172C4×C113—22no—
173C4×C113—22no—
174C4×C113—42no—
175C4×C113—84no—
176C4×C113—82no—
177C4×C113—81no—
178#9205C11311yesmaximal, characteristic, direct product factor, Sylow
179C2×C113—21no—
180C2×C113—22no—
181C2×C113—21no—
182C2×C113—22no—
183C2×C113—82no—
184C2×C113—161no—
185C2×C113#187511yescharacteristic
186C2×C113#191111yescharacteristic
187C2×C113#191311yescharacteristic
188#2617C2×C11311yescharacteristic
189#2312C2×C11311yescharacteristic, complemented
190#1519C2×C11312yescomplemented
191C2×#323C2×C11311yescharacteristic, complemented
192#1289C2×C11312yescomplemented
193C113#920511yescharacteristic, direct product factor, Sylow
194C2×#121C22×C11311yescharacteristic
195C2×#120—21no—
196C22×C22⋊C4C22×C11311yescharacteristic
197C2×C22⋊C8C22×C11312yes—
198#397C4×C11312yescomplemented
199#394—22no—
200#392C4×C11312yescomplemented
201#388—24no—
202#386—21no—
203#380C22×C11311yescharacteristic
204#380C22×C11312yes—
205#379—21no—
206C4×C22⋊C4—21no—
207#327—24no—
208#323—22no—
209C25D4×C11311yescharacteristic
210C22×D4—21no—
211C22×D4—22no—
212C22×D4C2×C4×C11311yescharacteristic
213C23×C4D4×C11311yescharacteristic
214C23×C4C23×C11311yescharacteristic
215C22×C8—22no—
216#121—22no—
217#121—22no—
218#120—44no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×C4×C11311yescharacteristic
222C2×C22⋊C4—22no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4C2×C4×C11312yes—
232C2×C22⋊C4D4×C11312yes—
233C2×C42—22no—
234C22⋊C8—22no—
235C22⋊C8—22no—
236#95—22no—
237#95—22no—
238#95C2×C4×C11312yes—
239#95D4×C11314yescomplemented
240C24—21no—
241C24—21no—
242C24—22no—
243C24—22no—
244C24—21no—
245C24—81no—
246C24—81no—
247C24C22⋊C4×C11312yes—
248C24C2×D4×C11311yescharacteristic
249C2×D4—22no—
250C2×D4—44no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—42no—
254C2×D4—42no—
255C2×D4—82no—
256C2×D4—82no—
257C2×D4—81no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—22no—
262C22×C4—24no—
263C22×C4—81no—
264C22×C4—81no—
265C22×C4C22⋊C4×C11312yes—
266C22×C4C22×C4×C11311yescharacteristic
267C22×C4C2×D4×C11312yes—
268C22×C4C2×D4×C11311yescharacteristic
269C22×C4#41×C11312yes—
270C2×C8—42no—
271C2×C8—82no—
272C4⋊C4—22no—
273C4⋊C4—82no—
274C4⋊C4—81no—
275C22⋊C4—24no—
276C22⋊C4—24no—
277C22⋊C4—44no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—82no—
283C22⋊C4—82no—
284C22⋊C4—82no—
285C42—82no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—41no—
290C23—41no—
291C23—42no—
292C23—42no—
293C23—42no—
294C23—42no—
295C23—42no—
296C23—42no—
297C23—42no—
298C23—42no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—81no—
303C23—81no—
304C23—84no—
305C23—84no—
306C23C2×C22⋊C4×C11311yescharacteristic
307C23#120×C11311yescharacteristic
308C23#123×C11311yescharacteristic
309C23#135×C11312yes—
310C23AGL(1,ℤ/8)×C11312yes—
311D4—82no—
312D4—88no—
313D4—82no—
314D4—82no—
315C2×C4—22no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—44no—
331C2×C4—81no—
332C2×C4C4×D4×C11312yes—
333C2×C4#121×C11312yes—
334C8—82no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—42no—
342C22—42no—
343C22—44no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—82no—
348C22—84no—
349C22—84no—
350C22—82no—
351C22—82no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22#386×C11311yescharacteristic
356C22#416×C11311yescharacteristic
357C22#418×C11311yescharacteristic
358C22#449×C11312yes—
359C22#482×C11312yes—
360C4—22no—
361C4—22no—
362C4—42no—
363C4—82no—
364C4—84no—
365C4—81no—
366C2—21no—
367C2—22no—
368C2—21no—
369C2—22no—
370C2—82no—
371C2—161no—
372C2C113×#187511yescharacteristic
373C2C113×#191111yescharacteristic
374C2C113×#191311yescharacteristic
subgroupG/H
center, socleC22×C113#386
commutatorC22×C4C22×C4×C113
Frattini, cosocleC23×C4C23×C113
prime radicalC113×#2617C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#2312C2semidirect
3. C113×#1519C2semidirect
4. C2×#323×C113C2semidirect
5. C113×#1289C2semidirect
10. #397×C113C4semidirect
12. #392×C113C4semidirect
51. #95×C113D4semidirect
178. #9205C113direct (N × H)
189. #2312C2×C113semidirect
190. #1519C2×C113semidirect
191. C2×#323C2×C113semidirect
192. #1289C2×C113semidirect
193. C113#9205direct (N × H)
198. #397C4×C113semidirect
200. #392C4×C113semidirect
239. #95D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#26172
C113×#23122
C113×#15192
C2×#323×C1132
C113×#12892
#9205113