Finite Group Databasebeta

← C113×#8840 #43276860

Subgroups — C113×#8840 #43276860

Order 28928.

446 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#2988C211yesmaximal, characteristic
2C113×#1831C211yesmaximal, characteristic, complemented
3C4×#104×C113C211yesmaximal, characteristic
4C113×#1565C211yesmaximal, characteristic, complemented
5C113×#1477C211yesmaximal, characteristic
6C113×#1283C211yesmaximal, characteristic, complemented
7C113×#1276C211yesmaximal, characteristic, complemented
8C4×#41×C113C2211yescharacteristic
9C8×Q8×C113—21no—
10C8×D4×C113—22no—
11C8×D4×C113—21no—
12#431×C113—21no—
13#431×C113C2211yescharacteristic
14#431×C113C2211yescharacteristic
15C2×C4⋊C8×C113—21no—
16C2×C4⋊C8×C113C2211yescharacteristic
17C2×C4⋊C8×C113C2211yescharacteristic
18C2×#104×C113C411yescharacteristic
19C2×#104×C113C411yescharacteristic
20C4×M16×C113C2211yescharacteristic
21C43×C113C2211yescharacteristic
22#339×C113C411yescharacteristic
23#339×C113C411yescharacteristic
24#336×C113—22no—
25#335×C113—21no—
26#334×C113—21no—
27Q8⋊C8×C113—21no—
28D4⋊C8×C113—21no—
29C2×#41×C113C2×C411yescharacteristic
30C2×M16×C113C2×C411yescharacteristic
31C2×M16×C113C2×C411yescharacteristic
32C22×C8×C113—22no—
33C22×C8×C113—21no—
34C22×C8×C113D412yes—
35C4×Q8×C113D411yescharacteristic
36C4×Q8×C113Q811yescharacteristic
37C4×D4×C113—21no—
38C4×D4×C113—21no—
39C4×D4×C113D411yescharacteristic
40C4×D4×C113Q811yescharacteristic
41#117×C113—21no—
42#117×C113C2×C411yescharacteristic
43C2×C42×C113—21no—
44C2×C42×C113—21no—
45C2×C42×C113—21no—
46C2×C42×C113C2×C411yescharacteristic
47C2×C42×C113C2×C411yescharacteristic
48C2×C42×C113C2311yescharacteristic
49C4⋊C8×C113—22no—
50C4⋊C8×C113—21no—
51C4⋊C8×C113—21no—
52C4⋊C8×C113—21no—
53C4⋊C8×C113—21no—
54C4⋊C8×C113—21no—
55C4⋊C8×C113D411yescharacteristic
56C4⋊C8×C113D411yescharacteristic
57#104×C113—22no—
58#104×C113C814yescomplemented
59C22⋊C8×C113—22no—
60C22⋊C8×C113—21no—
61C22⋊C8×C113—21no—
62#97×C113—21no—
63C4×C8×C113—22no—
64C4×C8×C113—21no—
65C4×C8×C113—21no—
66C4×C8×C113—21no—
67#41×C113—21no—
68#41×C113—21no—
69#41×C113C2×C812yes—
70#41×C113M1612yes—
71C2×Q8×C113C4⋊C411yescharacteristic
72C2×D4×C113—21no—
73C2×D4×C113C4⋊C411yescharacteristic
74C22×C4×C113—21no—
75C22×C4×C113—21no—
76C22×C4×C113—21no—
77C22×C4×C113—21no—
78C22×C4×C113—21no—
79C22×C4×C113C22×C411yescharacteristic
80C22×C4×C113C2×D411yescharacteristic
81C22×C4×C113#4111yescharacteristic
82M16×C113—21no—
83M16×C113—21no—
84M16×C113—21no—
85M16×C113C2×C812yescomplemented
86C2×C8×C113—21no—
87C2×C8×C113—21no—
88C2×C8×C113—21no—
89C2×C8×C113—22no—
90C2×C8×C113—21no—
91C2×C8×C113—42no—
92C2×C8×C113—42no—
93C2×C8×C113—41no—
94C2×C8×C113—41no—
95C2×C8×C113—82no—
96C4⋊C4×C113—21no—
97C4⋊C4×C113—21no—
98C4⋊C4×C113C4⋊C411yescharacteristic
99C4⋊C4×C113C4⋊C411yescharacteristic
100C22⋊C4×C113—21no—
101C22⋊C4×C113—21no—
102C22⋊C4×C113—21no—
103C42×C113—21no—
104C42×C113—21no—
105C42×C113—21no—
106C42×C113—21no—
107C42×C113—21no—
108C42×C113—21no—
109C42×C113—41no—
110C42×C113—41no—
111C42×C113—42no—
112C42×C113C2×C812yescomplemented
113C42×C113C2×D411yescharacteristic
114C42×C113C2×D411yescharacteristic
115C42×C113C2×Q811yescharacteristic
116C42×C113#4111yescharacteristic
117C23×C113—21no—
118C23×C113C4×D411yescharacteristic
119Q8×C113—21no—
120Q8×C113C4⋊C812yes—
121D4×C113—22no—
122D4×C113—22no—
123D4×C113—21no—
124D4×C113C4⋊C812yes—
125C2×C4×C113—21no—
126C2×C4×C113—22no—
127C2×C4×C113—22no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—22no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113—22no—
134C2×C4×C113—41no—
135C2×C4×C113—41no—
136C2×C4×C113—41no—
137C2×C4×C113—41no—
138C2×C4×C113—41no—
139C2×C4×C113—41no—
140C2×C4×C113—41no—
141C2×C4×C113—81no—
142C2×C4×C113C2×C4⋊C411yescharacteristic
143C2×C4×C113C4×D411yescharacteristic
144C2×C4×C113#12011yescharacteristic
145C2×C4×C113C22⋊Q811yescharacteristic
146C2×C4×C113C22⋊Q811yescharacteristic
147C2×C4×C113#12311yescharacteristic
148C2×C4×C113C22×C811yescharacteristic
149C2×C4×C113C2×M1611yescharacteristic
150C2×C4×C113#13111yescharacteristic
151C2×C4×C113#13111yescharacteristic
152C8×C113—22no—
153C8×C113—41no—
154C8×C113—41no—
155C8×C113—42no—
156C8×C113—41no—
157C8×C113—81no—
158C8×C113—81no—
159C22×C113—21no—
160C22×C113—21no—
161C22×C113—22no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113#38511yescharacteristic
165C22×C113C8×D411yescharacteristic
166C22×C113#43511yescharacteristic
167C4×C113—22no—
168C4×C113—21no—
169C4×C113—21no—
170C4×C113—21no—
171C4×C113—42no—
172C4×C113—42no—
173C4×C113—41no—
174C4×C113—41no—
175C4×C113C2×C4⋊C811yescharacteristic
176C4×C113#42411yescharacteristic
177C4×C113C8×D411yescharacteristic
178C4×C113#43511yescharacteristic
179C4×C113#45411yescharacteristic
180C4×C113#45511yescharacteristic
181#8840C11311yesmaximal, characteristic, direct product factor, Sylow
182C2×C113—21no—
183C2×C113—21no—
184C2×C113—42no—
185C2×C113#185011yescharacteristic
186C2×C113#186011yescharacteristic
187C2×C113#186111yescharacteristic
188#2988C2×C11311yescharacteristic
189#1831C2×C11311yescharacteristic, complemented
190C4×#104C2×C11311yescharacteristic
191#1565C2×C11311yescharacteristic, complemented
192#1477C2×C11311yescharacteristic
193#1283C2×C11311yescharacteristic, complemented
194#1276C2×C11311yescharacteristic, complemented
195C113#884011yescharacteristic, direct product factor, Sylow
196C4×#41C22×C11311yescharacteristic
197C8×Q8—21no—
198C8×D4—22no—
199C8×D4—21no—
200#431—21no—
201#431C22×C11311yescharacteristic
202#431C22×C11311yescharacteristic
203C2×C4⋊C8—21no—
204C2×C4⋊C8C22×C11311yescharacteristic
205C2×C4⋊C8C22×C11311yescharacteristic
206C2×#104C4×C11311yescharacteristic
207C2×#104C4×C11311yescharacteristic
208C4×M16C22×C11311yescharacteristic
209C43C22×C11311yescharacteristic
210#339C4×C11311yescharacteristic
211#339C4×C11311yescharacteristic
212#336—22no—
213#335—21no—
214#334—21no—
215Q8⋊C8—21no—
216D4⋊C8—21no—
217C2×#41C2×C4×C11311yescharacteristic
218C2×M16C2×C4×C11311yescharacteristic
219C2×M16C2×C4×C11311yescharacteristic
220C22×C8—22no—
221C22×C8—21no—
222C22×C8D4×C11312yes—
223C4×Q8D4×C11311yescharacteristic
224C4×Q8Q8×C11311yescharacteristic
225C4×D4—21no—
226C4×D4—21no—
227C4×D4D4×C11311yescharacteristic
228C4×D4Q8×C11311yescharacteristic
229#117—21no—
230#117C2×C4×C11311yescharacteristic
231C2×C42—21no—
232C2×C42—21no—
233C2×C42—21no—
234C2×C42C2×C4×C11311yescharacteristic
235C2×C42C2×C4×C11311yescharacteristic
236C2×C42C23×C11311yescharacteristic
237C4⋊C8—22no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8D4×C11311yescharacteristic
244C4⋊C8D4×C11311yescharacteristic
245#104—22no—
246#104C8×C11314yescomplemented
247C22⋊C8—22no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250#97—21no—
251C4×C8—22no—
252C4×C8—21no—
253C4×C8—21no—
254C4×C8—21no—
255#41—21no—
256#41—21no—
257#41C2×C8×C11312yes—
258#41M16×C11312yes—
259C2×Q8C4⋊C4×C11311yescharacteristic
260C2×D4—21no—
261C2×D4C4⋊C4×C11311yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4C22×C4×C11311yescharacteristic
268C22×C4C2×D4×C11311yescharacteristic
269C22×C4#41×C11311yescharacteristic
270M16—21no—
271M16—21no—
272M16—21no—
273M16C2×C8×C11312yescomplemented
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—22no—
278C2×C8—21no—
279C2×C8—42no—
280C2×C8—42no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—82no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4C4⋊C4×C11311yescharacteristic
287C4⋊C4C4⋊C4×C11311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C42—21no—
292C42—21no—
293C42—21no—
294C42—21no—
295C42—21no—
296C42—21no—
297C42—41no—
298C42—41no—
299C42—42no—
300C42C2×C8×C11312yescomplemented
301C42C2×D4×C11311yescharacteristic
302C42C2×D4×C11311yescharacteristic
303C42C2×Q8×C11311yescharacteristic
304C42#41×C11311yescharacteristic
305C23—21no—
306C23C4×D4×C11311yescharacteristic
307Q8—21no—
308Q8C4⋊C8×C11312yes—
309D4—22no—
310D4—22no—
311D4—21no—
312D4C4⋊C8×C11312yes—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—22no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—81no—
330C2×C4C2×C4⋊C4×C11311yescharacteristic
331C2×C4C4×D4×C11311yescharacteristic
332C2×C4#120×C11311yescharacteristic
333C2×C4C22⋊Q8×C11311yescharacteristic
334C2×C4C22⋊Q8×C11311yescharacteristic
335C2×C4#123×C11311yescharacteristic
336C2×C4C22×C8×C11311yescharacteristic
337C2×C4C2×M16×C11311yescharacteristic
338C2×C4#131×C11311yescharacteristic
339C2×C4#131×C11311yescharacteristic
340C8—22no—
341C8—41no—
342C8—41no—
343C8—42no—
344C8—41no—
345C8—81no—
346C8—81no—
347C22—21no—
348C22—21no—
349C22—22no—
350C22—41no—
351C22—41no—
352C22#385×C11311yescharacteristic
353C22C8×D4×C11311yescharacteristic
354C22#435×C11311yescharacteristic
355C4—22no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—42no—
360C4—42no—
361C4—41no—
362C4—41no—
363C4C2×C4⋊C8×C11311yescharacteristic
364C4#424×C11311yescharacteristic
365C4C8×D4×C11311yescharacteristic
366C4#435×C11311yescharacteristic
367C4#454×C11311yescharacteristic
368C4#455×C11311yescharacteristic
369C2—21no—
370C2—21no—
371C2—42no—
372C2C113×#185011yescharacteristic
373C2C113×#186011yescharacteristic
374C2C113×#186111yescharacteristic
subgroupG/H
centerC2×C4×C113#120
commutatorC2×C4C22×C8×C113
Frattini, cosocleC2×C42C23×C113
socleC22×C113#385
prime radicalC2×#41×C113C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#1831C2semidirect
4. C113×#1565C2semidirect
6. C113×#1283C2semidirect
7. C113×#1276C2semidirect
58. #104×C113C8semidirect
85. M16×C113C2×C8semidirect
112. C42×C113C2×C8semidirect
181. #8840C113direct (N × H)
189. #1831C2×C113semidirect
191. #1565C2×C113semidirect
193. #1283C2×C113semidirect
194. #1276C2×C113semidirect
195. C113#8840direct (N × H)
246. #104C8×C113semidirect
273. M16C2×C8×C113semidirect
300. C42C2×C8×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#29882
C113×#18312
C4×#104×C1132
C113×#15652
C113×#14772
C113×#12832
C113×#12762
#8840113