Finite Group Databasebeta

← C113×#17655 #43285675

Subgroups — C113×#17655 #43285675

Order 28928.

1016 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3517C211yesmaximal, characteristic
2C113×#2971C211yesmaximal, characteristic, complemented
3C113×#2875C211yesmaximal, characteristic, complemented
4C113×#1530C213yesmaximal, complemented
5C113×#1529C213yesmaximal, complemented
6C113×#1525C213yesmaximal, complemented
7C113×#1524C213yesmaximal, complemented
8C2×#131×C113—21no—
9#557×C113C411yescharacteristic
10#553×C113—23no—
11#550×C113—21no—
12#550×C113C413yes—
13#550×C113C411yescharacteristic
14#547×C113C413yes—
15#540×C113—23no—
16#532×C113C2213yes—
17#529×C113C2213yes—
18#520×C113—21no—
19C4×#41×C113C2211yescharacteristic
20C8×Q8×C113—21no—
21#436×C113—23no—
22#432×C113C2213yes—
23#405×C113—23no—
24C4×M16×C113C2213yes—
25C4×M16×C113C2213yes—
26C2×#97×C113C2213yes—
27#330×C113C2211yescharacteristic
28#330×C113C2213yes—
29#329×C113C2213yes—
30#329×C113C2213yes—
31#329×C113C2216yes—
32C2×#41×C113—21no—
33C2×#41×C113C2×C416yes—
34C2×#41×C113D411yescharacteristic
35#131×C113—28no—
36C2×M16×C113—23no—
37C2×M16×C113—23no—
38C22×C8×C113—23no—
39C4⋊Q8×C113C2×C413yes—
40#127×C113—23no—
41#127×C113C2×C413yes—
42#126×C113—23no—
43#125×C113—23no—
44#125×C113C2311yescharacteristic
45#124×C113C2313yes—
46#123×C113—23no—
47#123×C113—26no—
48C22⋊Q8×C113C2×C413yes—
49#121×C113—23no—
50#121×C113—23no—
51#121×C113—23no—
52#121×C113—23no—
53#121×C113—26no—
54#121×C113C2×C413yes—
55C4×Q8×C113—21no—
56C4×Q8×C113C2×C413yes—
57C4×Q8×C113C2×C411yescharacteristic
58C4×Q8×C113D411yescharacteristic
59C4×D4×C113—23no—
60C4×D4×C113—23no—
61C4×D4×C113—23no—
62C4×D4×C113—23no—
63C4×D4×C113C2×C413yes—
64C4×D4×C113C2×C413yes—
65C4×D4×C113D413yes—
66#117×C113—23no—
67#117×C113D413yes—
68C2×C4⋊C4×C113—23no—
69C2×C42×C113C2313yes—
70C4⋊C8×C113—23no—
71C22⋊C8×C113—23no—
72#97×C113—23no—
73#97×C113C2311yescharacteristic
74#97×C113C2313yes—
75#97×C113C2311yescharacteristic
76#97×C113C2313yes—
77C4×C8×C113—23no—
78C4×C8×C113—23no—
79#41×C113—24no—
80#41×C113—44no—
81#41×C113—86no—
82C2×Q8×C113C22⋊C411yescharacteristic
83C2×Q8×C113C22×C413yes—
84C2×D4×C113—23no—
85C2×D4×C113—26no—
86C2×D4×C113—23no—
87C2×D4×C113—23no—
88C2×D4×C113C22⋊C413yes—
89C2×D4×C113C22×C413yes—
90C22×C4×C113—23no—
91C22×C4×C113—26no—
92C22×C4×C113C22×C413yes—
93C22×C4×C113C2×D413yes—
94C22×C4×C113C2×D413yes—
95M16×C113—212no—
96M16×C113—46no—
97C2×C8×C113—212no—
98C2×C8×C113—21no—
99C2×C8×C113—23no—
100C2×C8×C113—21no—
101C2×C8×C113—23no—
102C4⋊C4×C113—23no—
103C4⋊C4×C113—23no—
104C4⋊C4×C113—23no—
105C4⋊C4×C113—23no—
106C4⋊C4×C113—21no—
107C4⋊C4×C113—21no—
108C4⋊C4×C113C22⋊C413yes—
109C4⋊C4×C113C22⋊C413yes—
110C4⋊C4×C113C22×C411yescharacteristic
111C4⋊C4×C113C22×C411yescharacteristic
112C22⋊C4×C113—23no—
113C22⋊C4×C113—23no—
114C22⋊C4×C113—23no—
115C22⋊C4×C113—23no—
116C22⋊C4×C113—23no—
117C22⋊C4×C113C22⋊C416yes—
118C42×C113—23no—
119C42×C113C22×C413yes—
120C42×C113C2×D413yes—
121C42×C113C2×D413yes—
122C42×C113C2411yescharacteristic
123C23×C113—23no—
124C23×C113C2×C22⋊C413yes—
125Q8×C113—43no—
126Q8×C113#10414yes—
127D4×C113—26no—
128D4×C113—43no—
129D4×C113—46no—
130D4×C113—83no—
131D4×C113—83no—
132D4×C113—86no—
133C2×C4×C113—26no—
134C2×C4×C113—21no—
135C2×C4×C113—23no—
136C2×C4×C113—21no—
137C2×C4×C113—43no—
138C2×C4×C113—43no—
139C2×C4×C113—46no—
140C2×C4×C113—86no—
141C2×C4×C113C2×C22⋊C413yes—
142C2×C4×C113C2×C22⋊C413yes—
143C2×C4×C113C2×C22⋊C413yes—
144C2×C4×C113C23×C411yescharacteristic
145C2×C4×C113C22×D411yescharacteristic
146C2×C4×C113C22×D411yescharacteristic
147C8×C113—22no—
148C8×C113—26no—
149C8×C113—22no—
150C8×C113—43no—
151C22×C113—23no—
152C22×C113—23no—
153C22×C113—23no—
154C22×C113—43no—
155C22×C113—43no—
156C22×C113—43no—
157C22×C113C22×C22⋊C411yescharacteristic
158C4×C113—21no—
159C4×C113—23no—
160C4×C113—21no—
161C4×C113—21no—
162C4×C113—23no—
163C4×C113—43no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113C2×#10416yes—
167#17655C11311yesmaximal, characteristic, direct product factor, Sylow
168C2×C113—43no—
169C2×C113—83no—
170C2×C113#288811yescharacteristic
171C2×C113C22×#10411yescharacteristic
172C2×C113#290111yescharacteristic
173#3517C2×C11311yescharacteristic
174#2971C2×C11311yescharacteristic, complemented
175#2875C2×C11311yescharacteristic, complemented
176#1530C2×C11313yescomplemented
177#1529C2×C11313yescomplemented
178#1525C2×C11313yescomplemented
179#1524C2×C11313yescomplemented
180C113#1765511yescharacteristic, direct product factor, Sylow
181C2×#131—21no—
182#557C4×C11311yescharacteristic
183#553—23no—
184#550—21no—
185#550C4×C11313yes—
186#550C4×C11311yescharacteristic
187#547C4×C11313yes—
188#540—23no—
189#532C22×C11313yes—
190#529C22×C11313yes—
191#520—21no—
192C4×#41C22×C11311yescharacteristic
193C8×Q8—21no—
194#436—23no—
195#432C22×C11313yes—
196#405—23no—
197C4×M16C22×C11313yes—
198C4×M16C22×C11313yes—
199C2×#97C22×C11313yes—
200#330C22×C11311yescharacteristic
201#330C22×C11313yes—
202#329C22×C11313yes—
203#329C22×C11313yes—
204#329C22×C11316yes—
205C2×#41—21no—
206C2×#41C2×C4×C11316yes—
207C2×#41D4×C11311yescharacteristic
208#131—28no—
209C2×M16—23no—
210C2×M16—23no—
211C22×C8—23no—
212C4⋊Q8C2×C4×C11313yes—
213#127—23no—
214#127C2×C4×C11313yes—
215#126—23no—
216#125—23no—
217#125C23×C11311yescharacteristic
218#124C23×C11313yes—
219#123—23no—
220#123—26no—
221C22⋊Q8C2×C4×C11313yes—
222#121—23no—
223#121—23no—
224#121—23no—
225#121—23no—
226#121—26no—
227#121C2×C4×C11313yes—
228C4×Q8—21no—
229C4×Q8C2×C4×C11313yes—
230C4×Q8C2×C4×C11311yescharacteristic
231C4×Q8D4×C11311yescharacteristic
232C4×D4—23no—
233C4×D4—23no—
234C4×D4—23no—
235C4×D4—23no—
236C4×D4C2×C4×C11313yes—
237C4×D4C2×C4×C11313yes—
238C4×D4D4×C11313yes—
239#117—23no—
240#117D4×C11313yes—
241C2×C4⋊C4—23no—
242C2×C42C23×C11313yes—
243C4⋊C8—23no—
244C22⋊C8—23no—
245#97—23no—
246#97C23×C11311yescharacteristic
247#97C23×C11313yes—
248#97C23×C11311yescharacteristic
249#97C23×C11313yes—
250C4×C8—23no—
251C4×C8—23no—
252#41—24no—
253#41—44no—
254#41—86no—
255C2×Q8C22⋊C4×C11311yescharacteristic
256C2×Q8C22×C4×C11313yes—
257C2×D4—23no—
258C2×D4—26no—
259C2×D4—23no—
260C2×D4—23no—
261C2×D4C22⋊C4×C11313yes—
262C2×D4C22×C4×C11313yes—
263C22×C4—23no—
264C22×C4—26no—
265C22×C4C22×C4×C11313yes—
266C22×C4C2×D4×C11313yes—
267C22×C4C2×D4×C11313yes—
268M16—212no—
269M16—46no—
270C2×C8—212no—
271C2×C8—21no—
272C2×C8—23no—
273C2×C8—21no—
274C2×C8—23no—
275C4⋊C4—23no—
276C4⋊C4—23no—
277C4⋊C4—23no—
278C4⋊C4—23no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4C22⋊C4×C11313yes—
282C4⋊C4C22⋊C4×C11313yes—
283C4⋊C4C22×C4×C11311yescharacteristic
284C4⋊C4C22×C4×C11311yescharacteristic
285C22⋊C4—23no—
286C22⋊C4—23no—
287C22⋊C4—23no—
288C22⋊C4—23no—
289C22⋊C4—23no—
290C22⋊C4C22⋊C4×C11316yes—
291C42—23no—
292C42C22×C4×C11313yes—
293C42C2×D4×C11313yes—
294C42C2×D4×C11313yes—
295C42C24×C11311yescharacteristic
296C23—23no—
297C23C2×C22⋊C4×C11313yes—
298Q8—43no—
299Q8#104×C11314yes—
300D4—26no—
301D4—43no—
302D4—46no—
303D4—83no—
304D4—86no—
305D4—83no—
306C2×C4—26no—
307C2×C4—21no—
308C2×C4—23no—
309C2×C4—21no—
310C2×C4—43no—
311C2×C4—43no—
312C2×C4—46no—
313C2×C4—86no—
314C2×C4C2×C22⋊C4×C11313yes—
315C2×C4C2×C22⋊C4×C11313yes—
316C2×C4C2×C22⋊C4×C11313yes—
317C2×C4C23×C4×C11311yescharacteristic
318C2×C4C22×D4×C11311yescharacteristic
319C2×C4C22×D4×C11311yescharacteristic
320C8—22no—
321C8—26no—
322C8—22no—
323C8—43no—
324C22—23no—
325C22—23no—
326C22—23no—
327C22—43no—
328C22—43no—
329C22—43no—
330C22C22×C22⋊C4×C11311yescharacteristic
331C4—21no—
332C4—23no—
333C4—21no—
334C4—21no—
335C4—23no—
336C4—43no—
337C4—41no—
338C4—41no—
339C4C2×#104×C11316yes—
340C2—43no—
341C2—83no—
342C2C113×#288811yescharacteristic
343C2C22×#104×C11311yescharacteristic
344C2C113×#290111yescharacteristic
subgroupG/H
center, socleC22×C113C22×C22⋊C4
commutatorC2×C4C23×C4×C113
Frattini, cosocleC42C24×C113
prime radicalC113×#3517C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C4×#41×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#2971C2semidirect
3. C113×#2875C2semidirect
4. C113×#1530C2semidirect
5. C113×#1529C2semidirect
6. C113×#1525C2semidirect
7. C113×#1524C2semidirect
167. #17655C113direct (N × H)
174. #2971C2×C113semidirect
175. #2875C2×C113semidirect
176. #1530C2×C113semidirect
177. #1529C2×C113semidirect
178. #1525C2×C113semidirect
179. #1524C2×C113semidirect
180. C113#17655direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#35172
C113×#29712
C113×#28752
C113×#15302
C113×#15292
C113×#15252
C113×#15242
#17655113