Finite Group Databasebeta

← C113×#9315 #43277335

Subgroups — C113×#9315 #43277335

Order 28928.

480 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3079C211yesmaximal, characteristic
2C113×#2988C211yesmaximal, characteristic
3C113×#1987C211yesmaximal, characteristic, complemented
4C113×#1806C211yesmaximal, characteristic
5C113×#1548C211yesmaximal, characteristic, complemented
6C113×#1303C211yesmaximal, characteristic, complemented
7C113×#1292C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C113C2211yescharacteristic
9C4×#41×C113C2211yescharacteristic
10#477×C113—21no—
11#476×C113—21no—
12#475×C113C412yescomplemented
13#474×C113C412yescomplemented
14C8×Q8×C113—21no—
15C8×D4×C113—22no—
16C8×D4×C113—21no—
17#431×C113—21no—
18#431×C113C2211yescharacteristic
19#428×C113—21no—
20#423×C113C2211yescharacteristic
21#423×C113C2211yescharacteristic
22C2×C4⋊C8×C113—21no—
23C2×C4⋊C8×C113C2211yescharacteristic
24C2×#104×C113—21no—
25#417×C113—21no—
26C4×C4⋊C4×C113C2211yescharacteristic
27#340×C113—22no—
28#339×C113—21no—
29#333×C113—21no—
30#333×C113—21no—
31C2×#41×C113D411yescharacteristic
32C22×Q8×C113—21no—
33C2×M16×C113—21no—
34C2×M16×C113—21no—
35C22×C8×C113—22no—
36C22×C8×C113D412yes—
37C4⋊Q8×C113—21no—
38C4⋊Q8×C113—21no—
39C4⋊Q8×C113—21no—
40C4⋊Q8×C113C2×C412yes—
41C4×Q8×C113C2×C411yescharacteristic
42C4×Q8×C113D411yescharacteristic
43C4×D4×C113—21no—
44C4×D4×C113—21no—
45C4×D4×C113C2×C411yescharacteristic
46C4×D4×C113D411yescharacteristic
47#117×C113—21no—
48#117×C113D411yescharacteristic
49C2×C4⋊C4×C113—21no—
50C2×C4⋊C4×C113—21no—
51C2×C4⋊C4×C113—21no—
52C2×C42×C113—21no—
53C2×C42×C113—21no—
54C2×C42×C113C2311yescharacteristic
55#107×C113—22no—
56#106×C113—22no—
57C4⋊C8×C113—22no—
58C4⋊C8×C113—21no—
59C4⋊C8×C113—21no—
60C4⋊C8×C113—21no—
61C4⋊C8×C113—21no—
62C4⋊C8×C113—21no—
63C4⋊C8×C113C2×C412yes—
64C4⋊C8×C113D411yescharacteristic
65C4⋊C8×C113D411yescharacteristic
66#104×C113—42no—
67#103×C113—22no—
68#102×C113—22no—
69C22⋊C8×C113—22no—
70C22⋊C8×C113—21no—
71C4×C8×C113—22no—
72C4×C8×C113—21no—
73#95×C113—21no—
74#41×C113—21no—
75#41×C113—21no—
76#41×C113SD1612yes—
77#41×C113Q1612yes—
78C2×Q8×C113—22no—
79C2×Q8×C113—41no—
80C2×Q8×C113—82no—
81C2×Q8×C113C22⋊C411yescharacteristic
82C2×D4×C113—21no—
83C2×D4×C113C22⋊C411yescharacteristic
84C22×C4×C113—21no—
85C22×C4×C113—21no—
86C22×C4×C113—21no—
87C22×C4×C113—41no—
88C22×C4×C113—41no—
89C22×C4×C113C2×D411yescharacteristic
90C22×C4×C113C2×D411yescharacteristic
91C22×C4×C113#4111yescharacteristic
92M16×C113—41no—
93M16×C113—41no—
94M16×C113—41no—
95M16×C113—41no—
96C2×C8×C113—22no—
97C2×C8×C113—21no—
98C2×C8×C113—22no—
99C2×C8×C113—21no—
100C2×C8×C113—42no—
101C2×C8×C113—41no—
102C2×C8×C113—82no—
103C4⋊C4×C113—21no—
104C4⋊C4×C113—21no—
105C4⋊C4×C113—22no—
106C4⋊C4×C113—22no—
107C4⋊C4×C113—22no—
108C4⋊C4×C113—41no—
109C4⋊C4×C113—41no—
110C4⋊C4×C113—41no—
111C4⋊C4×C113C22⋊C411yescharacteristic
112C4⋊C4×C113C22⋊C411yescharacteristic
113C22⋊C4×C113—21no—
114C22⋊C4×C113—21no—
115C22⋊C4×C113—21no—
116C42×C113—21no—
117C42×C113—21no—
118C42×C113—21no—
119C42×C113—41no—
120C42×C113—41no—
121C42×C113C22×C411yescharacteristic
122C42×C113C2×D411yescharacteristic
123C42×C113C2×D411yescharacteristic
124C42×C113#4111yescharacteristic
125C23×C113—21no—
126C23×C113#12111yescharacteristic
127Q8×C113—21no—
128Q8×C113—82no—
129Q8×C113—82no—
130Q8×C113#10312yes—
131D4×C113—22no—
132D4×C113—22no—
133D4×C113—21no—
134D4×C113#10312yes—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113—22no—
139C2×C4×C113—22no—
140C2×C4×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113—41no—
143C2×C4×C113—41no—
144C2×C4×C113—41no—
145C2×C4×C113—42no—
146C2×C4×C113—42no—
147C2×C4×C113—81no—
148C2×C4×C113—81no—
149C2×C4×C113—82no—
150C2×C4×C113—81no—
151C2×C4×C113C2×C22⋊C411yescharacteristic
152C2×C4×C113C4×D411yescharacteristic
153C2×C4×C113C4×D411yescharacteristic
154C2×C4×C113#12011yescharacteristic
155C2×C4×C113#12111yescharacteristic
156C2×C4×C113#12311yescharacteristic
157C2×C4×C113C2×SD1611yescharacteristic
158C2×C4×C113C2×Q1611yescharacteristic
159C2×C4×C113#13511yescharacteristic
160C2×C4×C113#13511yescharacteristic
161C8×C113—42no—
162C8×C113—42no—
163C8×C113—41no—
164C8×C113—41no—
165C8×C113—81no—
166C22×C113—21no—
167C22×C113—21no—
168C22×C113—22no—
169C22×C113—41no—
170C22×C113—41no—
171C22×C113#38611yescharacteristic
172C22×C113#46511yescharacteristic
173C22×C113#46711yescharacteristic
174C4×C113—21no—
175C4×C113—22no—
176C4×C113—21no—
177C4×C113—21no—
178C4×C113—41no—
179C4×C113—41no—
180C4×C113—82no—
181C4×C113—82no—
182C4×C113C2×#10311yescharacteristic
183C4×C113#41611yescharacteristic
184C4×C113#45511yescharacteristic
185C4×C113#45611yescharacteristic
186C4×C113#46511yescharacteristic
187C4×C113#46711yescharacteristic
188#9315C11311yesmaximal, characteristic, direct product factor, Sylow
189C2×C113—21no—
190C2×C113—21no—
191C2×C113—42no—
192C2×C113#188211yescharacteristic
193C2×C113#189211yescharacteristic
194C2×C113#190311yescharacteristic
195#3079C2×C11311yescharacteristic
196#2988C2×C11311yescharacteristic
197#1987C2×C11311yescharacteristic, complemented
198#1806C2×C11311yescharacteristic
199#1548C2×C11311yescharacteristic, complemented
200#1303C2×C11311yescharacteristic, complemented
201#1292C2×C11311yescharacteristic, complemented
202C113#931511yescharacteristic, direct product factor, Sylow
203C2×C4⋊Q8C22×C11311yescharacteristic
204C4×#41C22×C11311yescharacteristic
205#477—21no—
206#476—21no—
207#475C4×C11312yescomplemented
208#474C4×C11312yescomplemented
209C8×Q8—21no—
210C8×D4—22no—
211C8×D4—21no—
212#431—21no—
213#431C22×C11311yescharacteristic
214#428—21no—
215#423C22×C11311yescharacteristic
216#423C22×C11311yescharacteristic
217C2×C4⋊C8—21no—
218C2×C4⋊C8C22×C11311yescharacteristic
219C2×#104—21no—
220#417—21no—
221C4×C4⋊C4C22×C11311yescharacteristic
222#340—22no—
223#339—21no—
224#333—21no—
225#333—21no—
226C2×#41D4×C11311yescharacteristic
227C22×Q8—21no—
228C2×M16—21no—
229C2×M16—21no—
230C22×C8—22no—
231C22×C8D4×C11312yes—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8C2×C4×C11312yes—
236C4×Q8C2×C4×C11311yescharacteristic
237C4×Q8D4×C11311yescharacteristic
238C4×D4—21no—
239C4×D4—21no—
240C4×D4C2×C4×C11311yescharacteristic
241C4×D4D4×C11311yescharacteristic
242#117—21no—
243#117D4×C11311yescharacteristic
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42C23×C11311yescharacteristic
250#107—22no—
251#106—22no—
252C4⋊C8—22no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8C2×C4×C11312yes—
259C4⋊C8D4×C11311yescharacteristic
260C4⋊C8D4×C11311yescharacteristic
261#104—42no—
262#103—22no—
263#102—22no—
264C22⋊C8—22no—
265C22⋊C8—21no—
266C4×C8—22no—
267C4×C8—21no—
268#95—21no—
269#41—21no—
270#41—21no—
271#41SD16×C11312yes—
272#41Q16×C11312yes—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—82no—
276C2×Q8C22⋊C4×C11311yescharacteristic
277C2×D4—21no—
278C2×D4C22⋊C4×C11311yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4C2×D4×C11311yescharacteristic
285C22×C4C2×D4×C11311yescharacteristic
286C22×C4#41×C11311yescharacteristic
287M16—41no—
288M16—41no—
289M16—41no—
290M16—41no—
291C2×C8—22no—
292C2×C8—21no—
293C2×C8—22no—
294C2×C8—21no—
295C2×C8—42no—
296C2×C8—41no—
297C2×C8—82no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4C22⋊C4×C11311yescharacteristic
307C4⋊C4C22⋊C4×C11311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C42—21no—
312C42—21no—
313C42—21no—
314C42—41no—
315C42—41no—
316C42C22×C4×C11311yescharacteristic
317C42C2×D4×C11311yescharacteristic
318C42C2×D4×C11311yescharacteristic
319C42#41×C11311yescharacteristic
320C23—21no—
321C23#121×C11311yescharacteristic
322Q8—21no—
323Q8—82no—
324Q8—82no—
325Q8#103×C11312yes—
326D4—22no—
327D4—22no—
328D4—21no—
329D4#103×C11312yes—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—82no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4C2×C22⋊C4×C11311yescharacteristic
347C2×C4C4×D4×C11311yescharacteristic
348C2×C4C4×D4×C11311yescharacteristic
349C2×C4#120×C11311yescharacteristic
350C2×C4#121×C11311yescharacteristic
351C2×C4#123×C11311yescharacteristic
352C2×C4C2×SD16×C11311yescharacteristic
353C2×C4C2×Q16×C11311yescharacteristic
354C2×C4#135×C11311yescharacteristic
355C2×C4#135×C11311yescharacteristic
356C8—42no—
357C8—42no—
358C8—41no—
359C8—41no—
360C8—81no—
361C22—21no—
362C22—21no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22#386×C11311yescharacteristic
367C22#465×C11311yescharacteristic
368C22#467×C11311yescharacteristic
369C4—21no—
370C4—22no—
371C4—21no—
372C4—21no—
373C4—41no—
374C4—41no—
375C4—82no—
376C4—82no—
377C4C2×#103×C11311yescharacteristic
378C4#416×C11311yescharacteristic
379C4#455×C11311yescharacteristic
380C4#456×C11311yescharacteristic
381C4#465×C11311yescharacteristic
382C4#467×C11311yescharacteristic
383C2—21no—
384C2—21no—
385C2—42no—
386C2C113×#188211yescharacteristic
387C2C113×#189211yescharacteristic
388C2C113×#190311yescharacteristic
subgroupG/H
center, socleC22×C113#386
commutatorC42C22×C4×C113
Frattini, cosocleC2×C42C23×C113
prime radicalC2×#41×C113D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
3. C113×#1987C2semidirect
5. C113×#1548C2semidirect
6. C113×#1303C2semidirect
7. C113×#1292C2semidirect
12. #475×C113C4semidirect
13. #474×C113C4semidirect
188. #9315C113direct (N × H)
197. #1987C2×C113semidirect
199. #1548C2×C113semidirect
200. #1303C2×C113semidirect
201. #1292C2×C113semidirect
202. C113#9315direct (N × H)
207. #475C4×C113semidirect
208. #474C4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#30792
C113×#29882
C113×#19872
C113×#18062
C113×#15482
C113×#13032
C113×#12922
#9315113