Finite Group Databasebeta

← C113×#11426 #43279446

Subgroups — C113×#11426 #43279446

Order 28928.

734 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 734 conjugacy classes of subgroups — too many to draw. Only its 142 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×#2308C211yesmaximal, characteristic
2C2×#323×C113C212yesmaximal, complemented
3C113×#1317C212yesmaximal, complemented
4C113×#1316C212yesmaximal, complemented
5C23×D4×C113C411yescharacteristic
6C22×C22⋊C4×C113C411yescharacteristic
7C22×C22⋊C4×C113C2211yescharacteristic
8C2×C22⋊C8×C113—22no—
9#386×C113—22no—
10#386×C113—22no—
11#381×C113C411yescharacteristic
12#381×C113C2211yescharacteristic
13#379×C113C411yescharacteristic
14#379×C113C2211yescharacteristic
15#323×C113—22no—
16#323×C113C2214yes—
17C25×C113C2×C411yescharacteristic
18C25×C113C2×C411yescharacteristic
19C22×D4×C113—21no—
20C22×D4×C113—21no—
21C22×D4×C113—22no—
22C22×D4×C113—42no—
23C22×D4×C113—42no—
24C22×D4×C113C814yescomplemented
25C23×C4×C113—21no—
26C23×C4×C113C2×C411yescharacteristic
27C23×C4×C113D412yes—
28C22×C8×C113—42no—
29C2×C22⋊C4×C113—21no—
30C2×C22⋊C4×C113—22no—
31C2×C22⋊C4×C113—22no—
32C2×C22⋊C4×C113—42no—
33C2×C22⋊C4×C113—42no—
34C2×C22⋊C4×C113C2×C411yescharacteristic
35C2×C22⋊C4×C113C2×C411yescharacteristic
36C2×C22⋊C4×C113C2×C411yescharacteristic
37C2×C22⋊C4×C113D412yes—
38C2×C22⋊C4×C113C2311yescharacteristic
39C22⋊C8×C113—24no—
40C22⋊C8×C113—42no—
41#95×C113—22no—
42#95×C113—22no—
43C24×C113—22no—
44C24×C113—22no—
45C24×C113—21no—
46C24×C113—21no—
47C24×C113—41no—
48C24×C113—41no—
49C24×C113—82no—
50C24×C113—82no—
51C24×C113C22⋊C411yescharacteristic
52C24×C113C22⋊C411yescharacteristic
53C24×C113C2×C812yes—
54C24×C113C2×C812yescomplemented
55C24×C113M1612yes—
56C24×C113C22×C411yescharacteristic
57C2×D4×C113—24no—
58C2×D4×C113—24no—
59C2×D4×C113—48no—
60C2×D4×C113—42no—
61C2×D4×C113—42no—
62C2×D4×C113—42no—
63C2×D4×C113—42no—
64C2×D4×C113—48no—
65C22×C4×C113—22no—
66C22×C4×C113—21no—
67C22×C4×C113—21no—
68C22×C4×C113—22no—
69C22×C4×C113—21no—
70C22×C4×C113—21no—
71C22×C4×C113—41no—
72C22×C4×C113—41no—
73C22×C4×C113—42no—
74C22×C4×C113—82no—
75C22×C4×C113—82no—
76C22×C4×C113C22⋊C412yes—
77C22×C4×C113C2×C812yescomplemented
78C22×C4×C113C2×D412yes—
79C2×C8×C113—44no—
80C2×C8×C113—84no—
81C22⋊C4×C113—41no—
82C22⋊C4×C113—42no—
83C22⋊C4×C113—41no—
84C22⋊C4×C113—42no—
85C22⋊C4×C113—41no—
86C22⋊C4×C113—41no—
87C22⋊C4×C113—82no—
88C22⋊C4×C113—82no—
89C23×C113—21no—
90C23×C113—21no—
91C23×C113—21no—
92C23×C113—21no—
93C23×C113—24no—
94C23×C113—24no—
95C23×C113—22no—
96C23×C113—42no—
97C23×C113—42no—
98C23×C113—42no—
99C23×C113—42no—
100C23×C113—42no—
101C23×C113—42no—
102C23×C113—42no—
103C23×C113—41no—
104C23×C113—41no—
105C23×C113—82no—
106C23×C113—82no—
107C23×C113—82no—
108C23×C113—82no—
109C23×C113—82no—
110C23×C113—84no—
111C23×C113—82no—
112C23×C113—84no—
113C23×C113—84no—
114C23×C113C22⋊C812yes—
115C23×C113C22⋊C812yes—
116C23×C113#9912yes—
117C23×C113#10012yes—
118C23×C113C2×C22⋊C411yescharacteristic
119C23×C113C22×C811yescharacteristic
120C23×C113C2×M1611yescharacteristic
121D4×C113—48no—
122D4×C113—48no—
123C2×C4×C113—22no—
124C2×C4×C113—22no—
125C2×C4×C113—22no—
126C2×C4×C113—44no—
127C2×C4×C113—42no—
128C2×C4×C113—41no—
129C2×C4×C113—41no—
130C2×C4×C113—42no—
131C2×C4×C113—42no—
132C2×C4×C113—42no—
133C2×C4×C113—42no—
134C2×C4×C113—42no—
135C2×C4×C113—41no—
136C2×C4×C113—41no—
137C2×C4×C113—82no—
138C2×C4×C113—84no—
139C8×C113—84no—
140C22×C113—22no—
141C22×C113—22no—
142C22×C113—22no—
143C22×C113—21no—
144C22×C113—21no—
145C22×C113—22no—
146C22×C113—42no—
147C22×C113—42no—
148C22×C113—41no—
149C22×C113—41no—
150C22×C113—42no—
151C22×C113—42no—
152C22×C113—42no—
153C22×C113—42no—
154C22×C113—42no—
155C22×C113—42no—
156C22×C113—42no—
157C22×C113—42no—
158C22×C113—84no—
159C22×C113—84no—
160C22×C113—82no—
161C22×C113—84no—
162C22×C113—84no—
163C22×C113—82no—
164C22×C113#32314yes—
165C22×C113C2×C22⋊C811yescharacteristic
166C22×C113C2×#9911yescharacteristic
167C22×C113C2×#10011yescharacteristic
168C4×C113—42no—
169C4×C113—42no—
170C4×C113—42no—
171C4×C113—81no—
172C4×C113—81no—
173#11426C11311yesmaximal, characteristic, direct product factor, Sylow
174C2×C113—21no—
175C2×C113—21no—
176C2×C113—24no—
177C2×C113—42no—
178C2×C113—41no—
179C2×C113—41no—
180C2×C113—82no—
181C2×C113C2×#32311yescharacteristic
182C2×C113#212112yes—
183#2308C2×C11311yescharacteristic
184C2×#323C2×C11312yescomplemented
185#1317C2×C11312yescomplemented
186#1316C2×C11312yescomplemented
187C113#1142611yescharacteristic, direct product factor, Sylow
188C23×D4C4×C11311yescharacteristic
189C22×C22⋊C4C4×C11311yescharacteristic
190C22×C22⋊C4C22×C11311yescharacteristic
191C2×C22⋊C8—22no—
192#386—22no—
193#386—22no—
194#381C4×C11311yescharacteristic
195#381C22×C11311yescharacteristic
196#379C4×C11311yescharacteristic
197#379C22×C11311yescharacteristic
198#323—22no—
199#323C22×C11314yes—
200C25C2×C4×C11311yescharacteristic
201C25C2×C4×C11311yescharacteristic
202C22×D4—21no—
203C22×D4—21no—
204C22×D4—22no—
205C22×D4—42no—
206C22×D4—42no—
207C22×D4C8×C11314yescomplemented
208C23×C4—21no—
209C23×C4C2×C4×C11311yescharacteristic
210C23×C4D4×C11312yes—
211C22×C8—42no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—22no—
214C2×C22⋊C4—22no—
215C2×C22⋊C4—42no—
216C2×C22⋊C4—42no—
217C2×C22⋊C4C2×C4×C11311yescharacteristic
218C2×C22⋊C4C2×C4×C11311yescharacteristic
219C2×C22⋊C4C2×C4×C11311yescharacteristic
220C2×C22⋊C4D4×C11312yes—
221C2×C22⋊C4C23×C11311yescharacteristic
222C22⋊C8—24no—
223C22⋊C8—42no—
224#95—22no—
225#95—22no—
226C24—22no—
227C24—22no—
228C24—21no—
229C24—21no—
230C24—41no—
231C24—41no—
232C24—82no—
233C24—82no—
234C24C22⋊C4×C11311yescharacteristic
235C24C22⋊C4×C11311yescharacteristic
236C24C2×C8×C11312yes—
237C24C2×C8×C11312yescomplemented
238C24M16×C11312yes—
239C24C22×C4×C11311yescharacteristic
240C2×D4—24no—
241C2×D4—24no—
242C2×D4—48no—
243C2×D4—42no—
244C2×D4—42no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—48no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—42no—
257C22×C4—82no—
258C22×C4—82no—
259C22×C4C22⋊C4×C11312yes—
260C22×C4C2×C8×C11312yescomplemented
261C22×C4C2×D4×C11312yes—
262C2×C8—44no—
263C2×C8—84no—
264C22⋊C4—41no—
265C22⋊C4—42no—
266C22⋊C4—41no—
267C22⋊C4—42no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—82no—
271C22⋊C4—82no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—24no—
277C23—24no—
278C23—22no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—42no—
283C23—42no—
284C23—42no—
285C23—42no—
286C23—41no—
287C23—41no—
288C23—82no—
289C23—82no—
290C23—82no—
291C23—82no—
292C23—82no—
293C23—84no—
294C23—82no—
295C23—84no—
296C23—84no—
297C23C22⋊C8×C11312yes—
298C23C22⋊C8×C11312yes—
299C23#99×C11312yes—
300C23#100×C11312yes—
301C23C2×C22⋊C4×C11311yescharacteristic
302C23C22×C8×C11311yescharacteristic
303C23C2×M16×C11311yescharacteristic
304D4—48no—
305D4—48no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—44no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—82no—
321C2×C4—84no—
322C8—84no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—42no—
330C22—42no—
331C22—41no—
332C22—41no—
333C22—42no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22—84no—
342C22—84no—
343C22—82no—
344C22—84no—
345C22—84no—
346C22—82no—
347C22#323×C11314yes—
348C22C2×C22⋊C8×C11311yescharacteristic
349C22C2×#99×C11311yescharacteristic
350C22C2×#100×C11311yescharacteristic
351C4—42no—
352C4—42no—
353C4—42no—
354C4—81no—
355C4—81no—
356C2—21no—
357C2—21no—
358C2—24no—
359C2—41no—
360C2—41no—
361C2—42no—
362C2—82no—
363C2C2×#323×C11311yescharacteristic
364C2C113×#212112yes—
subgroupG/H
center, socleC22×C113C2×#99
commutatorC23C22×C8×C113
Frattini, cosocleC2×C22⋊C4C23×C113
prime radicalC23×D4×C113C4
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C24×C113 ◁ C22×C22⋊C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#323×C113C2semidirect
3. C113×#1317C2semidirect
4. C113×#1316C2semidirect
24. C22×D4×C113C8semidirect
54. C24×C113C2×C8semidirect
77. C22×C4×C113C2×C8semidirect
173. #11426C113direct (N × H)
184. C2×#323C2×C113semidirect
185. #1317C2×C113semidirect
186. #1316C2×C113semidirect
187. C113#11426direct (N × H)
207. C22×D4C8×C113semidirect
237. C24C2×C8×C113semidirect
260. C22×C4C2×C8×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#23082
C2×#323×C1132
C113×#13172
C113×#13162
#11426113