Finite Group Databasebeta

← C113×#22235 #43290255

Subgroups — C113×#22235 #43290255

Order 28928.

686 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3135C211yesmaximal, characteristic
2C113×#2960C211yesmaximal, characteristic, complemented
3C113×#2931C211yesmaximal, characteristic
4C113×#1995C211yesmaximal, characteristic, complemented
5C113×#1963C211yesmaximal, characteristic
6C113×#1929C214yesmaximal, complemented
7C113×#1866C214yesmaximal, complemented
8C113×#1849C211yesmaximal, characteristic, complemented
9C113×#1746C211yesmaximal, characteristic, complemented
10C2×#131×C113C2212yes—
11#533×C113C2211yescharacteristic
12#532×C113C2211yescharacteristic
13#491×C113C412yescomplemented
14#490×C113C412yescomplemented
15#489×C113C412yescomplemented
16#489×C113C412yescomplemented
17#446×C113—21no—
18#446×C113—21no—
19C8×Q8×C113—21no—
20C8×Q8×C113—21no—
21#436×C113—21no—
22#436×C113—21no—
23C8×D4×C113—21no—
24C8×D4×C113—21no—
25C2×#108×C113C2214yes—
26#424×C113C2212yes—
27#423×C113C2211yescharacteristic
28#423×C113C2211yescharacteristic
29C2×#104×C113C2214yes—
30#416×C113C2214yes—
31#408×C113C2212yes—
32#405×C113C2212yes—
33C2×#97×C113C2211yescharacteristic
34C2×C4×C8×C113C2211yescharacteristic
35#376×C113C2211yescharacteristic
36#339×C113C2214yes—
37#336×C113C2212yes—
38#336×C113C2212yes—
39C2×#41×C113C2312yes—
40#131×C113—44no—
41C2×M16×C113—22no—
42C2×M16×C113C2312yes—
43C2×M16×C113C2312yes—
44C22×C8×C113—22no—
45C22×C8×C113C2312yes—
46C22×C8×C113C2311yescharacteristic
47C22×C8×C113C2311yescharacteristic
48C4⋊Q8×C113C2×C411yescharacteristic
49C4⋊Q8×C113C2×C411yescharacteristic
50C4⋊Q8×C113C2×C411yescharacteristic
51#127×C113C2×C411yescharacteristic
52#125×C113C2×C412yes—
53#124×C113C2×C412yes—
54C22⋊Q8×C113—21no—
55C22⋊Q8×C113—21no—
56#121×C113—21no—
57#121×C113—21no—
58C4×Q8×C113—21no—
59C4×Q8×C113—21no—
60C4×D4×C113—21no—
61C4×D4×C113—21no—
62#117×C113C2312yes—
63C2×C42×C113C2312yes—
64C2×C42×C113C2311yescharacteristic
65#108×C113—44no—
66C4⋊C8×C113—22no—
67C4⋊C8×C113—22no—
68C4⋊C8×C113—21no—
69C4⋊C8×C113—21no—
70C4⋊C8×C113—21no—
71C4⋊C8×C113—21no—
72#104×C113—44no—
73#103×C113C2×C414yes—
74#103×C113C2×C414yes—
75#102×C113C2×C414yes—
76#102×C113C2×C414yes—
77C22⋊C8×C113—22no—
78C22⋊C8×C113—22no—
79#97×C113—22no—
80#97×C113C2×C412yes—
81#97×C113C2×C412yes—
82C4×C8×C113—22no—
83C4×C8×C113D411yescharacteristic
84C4×C8×C113D411yescharacteristic
85C4×C8×C113D411yescharacteristic
86C4×C8×C113D411yescharacteristic
87#95×C113—21no—
88#95×C113—21no—
89#41×C113—24no—
90#41×C113—24no—
91C2×Q8×C113—21no—
92C2×Q8×C113—21no—
93C2×Q8×C113C22×C412yes—
94C2×D4×C113—22no—
95C2×D4×C113—21no—
96C2×D4×C113—21no—
97C2×D4×C113C22×C412yes—
98C22×C4×C113—22no—
99C22×C4×C113—22no—
100C22×C4×C113#4111yescharacteristic
101C22×C4×C113#4111yescharacteristic
102C22×C4×C113C2411yescharacteristic
103M16×C113—24no—
104M16×C113—24no—
105M16×C113—44no—
106C2×C8×C113—22no—
107C2×C8×C113—22no—
108C2×C8×C113—22no—
109C2×C8×C113—22no—
110C2×C8×C113—22no—
111C2×C8×C113—22no—
112C2×C8×C113—44no—
113C2×C8×C113C22×C414yes—
114C2×C8×C113C2×D411yescharacteristic
115C2×C8×C113C2×D411yescharacteristic
116C2×C8×C113C2×D411yescharacteristic
117C2×C8×C113C2×D411yescharacteristic
118C4⋊C4×C113—21no—
119C4⋊C4×C113—21no—
120C4⋊C4×C113—22no—
121C4⋊C4×C113—22no—
122C4⋊C4×C113—21no—
123C4⋊C4×C113—21no—
124C4⋊C4×C113C22×C412yes—
125C4⋊C4×C113C22×C412yes—
126C22⋊C4×C113—22no—
127C22⋊C4×C113—22no—
128C22⋊C4×C113—22no—
129C42×C113—22no—
130C42×C113—22no—
131C42×C113—22no—
132C42×C113C22×C411yescharacteristic
133C42×C113C22×C411yescharacteristic
134C42×C113C2×D411yescharacteristic
135C42×C113C2×D411yescharacteristic
136C23×C113—22no—
137C23×C113C2×#4111yescharacteristic
138Q8×C113—24no—
139Q8×C113—42no—
140Q8×C113—42no—
141D4×C113—24no—
142D4×C113—42no—
143D4×C113—42no—
144D4×C113—44no—
145C2×C4×C113—22no—
146C2×C4×C113—22no—
147C2×C4×C113—22no—
148C2×C4×C113—41no—
149C2×C4×C113—41no—
150C2×C4×C113—42no—
151C2×C4×C113—42no—
152C2×C4×C113—42no—
153C2×C4×C113—42no—
154C2×C4×C113—42no—
155C2×C4×C113C4×D411yescharacteristic
156C2×C4×C113C4×D411yescharacteristic
157C2×C4×C113C4×D411yescharacteristic
158C2×C4×C113C4×D411yescharacteristic
159C2×C4×C113C23×C411yescharacteristic
160C2×C4×C113C22×D411yescharacteristic
161C2×C4×C113H(5,𝔽2)12yes—
162C2×C4×C1132−1+412yes—
163C8×C113—24no—
164C8×C113—21no—
165C8×C113—21no—
166C8×C113—21no—
167C8×C113—21no—
168C8×C113—42no—
169C8×C113—42no—
170C22×C113—21no—
171C22×C113—21no—
172C22×C113—42no—
173C22×C113—42no—
174C22×C113—42no—
175C22×C113C2×C4×D411yescharacteristic
176C22×C113#54212yes—
177C4×C113—21no—
178C4×C113—21no—
179C4×C113—21no—
180C4×C113—21no—
181C4×C113—42no—
182C4×C113—42no—
183C4×C113—42no—
184C4×C113—82no—
185C4×C113#52012yes—
186C4×C113#53511yescharacteristic
187C4×C113#53611yescharacteristic
188#22235C11311yesmaximal, characteristic, direct product factor, Sylow
189C2×C113—22no—
190C2×C113—82no—
191C2×C113#232611yescharacteristic
192C2×C113#295511yescharacteristic
193C2×C113#295511yescharacteristic
194#3135C2×C11311yescharacteristic
195#2960C2×C11311yescharacteristic, complemented
196#2931C2×C11311yescharacteristic
197#1995C2×C11311yescharacteristic, complemented
198#1963C2×C11311yescharacteristic
199#1929C2×C11314yescomplemented
200#1866C2×C11314yescomplemented
201#1849C2×C11311yescharacteristic, complemented
202#1746C2×C11311yescharacteristic, complemented
203C113#2223511yescharacteristic, direct product factor, Sylow
204C2×#131C22×C11312yes—
205#533C22×C11311yescharacteristic
206#532C22×C11311yescharacteristic
207#491C4×C11312yescomplemented
208#490C4×C11312yescomplemented
209#489C4×C11312yescomplemented
210#489C4×C11312yescomplemented
211#446—21no—
212#446—21no—
213C8×Q8—21no—
214C8×Q8—21no—
215#436—21no—
216#436—21no—
217C8×D4—21no—
218C8×D4—21no—
219C2×#108C22×C11314yes—
220#424C22×C11312yes—
221#423C22×C11311yescharacteristic
222#423C22×C11311yescharacteristic
223C2×#104C22×C11314yes—
224#416C22×C11314yes—
225#408C22×C11312yes—
226#405C22×C11312yes—
227C2×#97C22×C11311yescharacteristic
228C2×C4×C8C22×C11311yescharacteristic
229#376C22×C11311yescharacteristic
230#339C22×C11314yes—
231#336C22×C11312yes—
232#336C22×C11312yes—
233C2×#41C23×C11312yes—
234#131—44no—
235C2×M16—22no—
236C2×M16C23×C11312yes—
237C2×M16C23×C11312yes—
238C22×C8—22no—
239C22×C8C23×C11312yes—
240C22×C8C23×C11311yescharacteristic
241C22×C8C23×C11311yescharacteristic
242C4⋊Q8C2×C4×C11311yescharacteristic
243C4⋊Q8C2×C4×C11311yescharacteristic
244C4⋊Q8C2×C4×C11311yescharacteristic
245#127C2×C4×C11311yescharacteristic
246#125C2×C4×C11312yes—
247#124C2×C4×C11312yes—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250#121—21no—
251#121—21no—
252C4×Q8—21no—
253C4×Q8—21no—
254C4×D4—21no—
255C4×D4—21no—
256#117C23×C11312yes—
257C2×C42C23×C11312yes—
258C2×C42C23×C11311yescharacteristic
259#108—44no—
260C4⋊C8—22no—
261C4⋊C8—22no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266#104—44no—
267#103C2×C4×C11314yes—
268#103C2×C4×C11314yes—
269#102C2×C4×C11314yes—
270#102C2×C4×C11314yes—
271C22⋊C8—22no—
272C22⋊C8—22no—
273#97—22no—
274#97C2×C4×C11312yes—
275#97C2×C4×C11312yes—
276C4×C8—22no—
277C4×C8D4×C11311yescharacteristic
278C4×C8D4×C11311yescharacteristic
279C4×C8D4×C11311yescharacteristic
280C4×C8D4×C11311yescharacteristic
281#95—21no—
282#95—21no—
283#41—24no—
284#41—24no—
285C2×Q8—21no—
286C2×Q8—21no—
287C2×Q8C22×C4×C11312yes—
288C2×D4—22no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4C22×C4×C11312yes—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4#41×C11311yescharacteristic
295C22×C4#41×C11311yescharacteristic
296C22×C4C24×C11311yescharacteristic
297M16—24no—
298M16—24no—
299M16—44no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—22no—
306C2×C8—44no—
307C2×C8C22×C4×C11314yes—
308C2×C8C2×D4×C11311yescharacteristic
309C2×C8C2×D4×C11311yescharacteristic
310C2×C8C2×D4×C11311yescharacteristic
311C2×C8C2×D4×C11311yescharacteristic
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4C22×C4×C11312yes—
319C4⋊C4C22×C4×C11312yes—
320C22⋊C4—22no—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C42—22no—
324C42—22no—
325C42—22no—
326C42C22×C4×C11311yescharacteristic
327C42C22×C4×C11311yescharacteristic
328C42C2×D4×C11311yescharacteristic
329C42C2×D4×C11311yescharacteristic
330C23—22no—
331C23C2×#41×C11311yescharacteristic
332Q8—24no—
333Q8—42no—
334Q8—42no—
335D4—24no—
336D4—42no—
337D4—42no—
338D4—44no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4C4×D4×C11311yescharacteristic
350C2×C4C4×D4×C11311yescharacteristic
351C2×C4C4×D4×C11311yescharacteristic
352C2×C4C4×D4×C11311yescharacteristic
353C2×C4C23×C4×C11311yescharacteristic
354C2×C4C22×D4×C11311yescharacteristic
355C2×C4H(5,𝔽2)×C11312yes—
356C2×C42−1+4×C11312yes—
357C8—24no—
358C8—21no—
359C8—21no—
360C8—21no—
361C8—21no—
362C8—42no—
363C8—42no—
364C22—21no—
365C22—21no—
366C22—42no—
367C22—42no—
368C22—42no—
369C22C2×C4×D4×C11311yescharacteristic
370C22#542×C11312yes—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—42no—
377C4—42no—
378C4—82no—
379C4#520×C11312yes—
380C4#535×C11311yescharacteristic
381C4#536×C11311yescharacteristic
382C2—22no—
383C2—82no—
384C2C113×#232611yescharacteristic
385C2C113×#295511yescharacteristic
386C2C113×#295511yescharacteristic
subgroupG/H
centerC2×C4×C113C22×D4
commutatorC2×C4C23×C4×C113
Frattini, cosocleC22×C4C24×C113
socleC22×C113C2×C4×D4
prime radical#532×C113C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C113 ◁ C2×C4×C8×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#2960C2semidirect
4. C113×#1995C2semidirect
6. C113×#1929C2semidirect
7. C113×#1866C2semidirect
8. C113×#1849C2semidirect
9. C113×#1746C2semidirect
13. #491×C113C4semidirect
14. #490×C113C4semidirect
15. #489×C113C4semidirect
16. #489×C113C4semidirect
188. #22235C113direct (N × H)
195. #2960C2×C113semidirect
197. #1995C2×C113semidirect
199. #1929C2×C113semidirect
200. #1866C2×C113semidirect
201. #1849C2×C113semidirect
202. #1746C2×C113semidirect
203. C113#22235direct (N × H)
207. #491C4×C113semidirect
208. #490C4×C113semidirect
209. #489C4×C113semidirect
210. #489C4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#31352
C113×#29602
C113×#29312
C113×#19952
C113×#19632
C113×#19292
C113×#18662
C113×#18492
C113×#17462
#22235113