Finite Group Databasebeta

← C113×#13380 #43281400

Subgroups — C113×#13380 #43281400

Order 28928.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C113C211yesmaximal, characteristic
2C2×#366×C113C211yesmaximal, characteristic, complemented
3C2×#357×C113C211yesmaximal, characteristic, complemented
4C2×#357×C113C211yesmaximal, characteristic, complemented
5C2×C22⋊C16×C113C211yesmaximal, characteristic, complemented
6C113×#1808C211yesmaximal, characteristic, complemented
7C113×#1380C211yesmaximal, characteristic, complemented
8C22×D8×C113C2211yescharacteristic
9C23×C8×C113C2211yescharacteristic
10C2×#121×C113—21no—
11C22×C16×C113C2211yescharacteristic
12C22×C16×C113C2211yescharacteristic
13#466×C113—22no—
14#466×C113—22no—
15C2×#107×C113C2211yescharacteristic
16C2×#107×C113C2211yescharacteristic
17C2×#107×C113C2211yescharacteristic
18C2×#102×C113—21no—
19#380×C113—21no—
20#366×C113—22no—
21#357×C113—22no—
22#357×C113—22no—
23C22⋊C16×C113—22no—
24#340×C113—21no—
25C22×D4×C113—21no—
26C22×D4×C113—41no—
27C23×C4×C113D411yescharacteristic
28C2×D8×C113—21no—
29C2×D8×C113—21no—
30C2×D8×C113—21no—
31C2×D8×C113—21no—
32C2×D8×C113—21no—
33C2×D8×C113D412yes—
34C22×C8×C113—21no—
35C22×C8×C113—21no—
36C22×C8×C113—21no—
37C22×C8×C113—21no—
38C22×C8×C113—21no—
39C22×C8×C113—21no—
40C22×C8×C113D411yescharacteristic
41C22×C8×C113C2311yescharacteristic
42#121×C113—24no—
43#121×C113—42no—
44C2×C4⋊C4×C113—21no—
45C2×C4⋊C4×C113—21no—
46C2×C4⋊C4×C113—21no—
47C2×C22⋊C4×C113—41no—
48C2×C22⋊C4×C113—41no—
49C2×C16×C113—21no—
50C2×C16×C113—21no—
51C2×C16×C113—21no—
52C2×C16×C113—21no—
53C2×C16×C113—21no—
54C2×C16×C113D412yescomplemented
55#107×C113—21no—
56#107×C113—21no—
57#107×C113—21no—
58#107×C113—21no—
59#107×C113—21no—
60#107×C113D412yes—
61#102×C113—24no—
62#95×C113—41no—
63C24×C113—41no—
64C24×C113D811yescharacteristic
65C2×D4×C113—22no—
66C2×D4×C113—44no—
67C2×D4×C113—41no—
68C2×D4×C113—41no—
69C2×D4×C113—41no—
70C2×D4×C113—41no—
71C2×D4×C113—41no—
72C2×D4×C113—82no—
73C2×D4×C113—82no—
74C22×C4×C113—21no—
75C22×C4×C113—21no—
76C22×C4×C113—21no—
77C22×C4×C113—21no—
78C22×C4×C113—21no—
79C22×C4×C113—21no—
80C22×C4×C113—41no—
81C22×C4×C113—41no—
82C22×C4×C113—41no—
83C22×C4×C113D811yescharacteristic
84C22×C4×C113C2×D411yescharacteristic
85D8×C113—22no—
86D8×C113—22no—
87D8×C113—41no—
88D8×C113—41no—
89C2×C8×C113—21no—
90C2×C8×C113—21no—
91C2×C8×C113—21no—
92C2×C8×C113—41no—
93C2×C8×C113—41no—
94C2×C8×C113—41no—
95C2×C8×C113—41no—
96C2×C8×C113C2×D411yescharacteristic
97C2×C8×C113C2×D411yescharacteristic
98C2×C8×C113C2×D411yescharacteristic
99C2×C8×C113#4111yescharacteristic
100C2×C8×C113#4111yescharacteristic
101C2×C8×C113#4111yescharacteristic
102C4⋊C4×C113—22no—
103C4⋊C4×C113—41no—
104C4⋊C4×C113—41no—
105C4⋊C4×C113—41no—
106C4⋊C4×C113—41no—
107C4⋊C4×C113—41no—
108C22⋊C4×C113—44no—
109C22⋊C4×C113—82no—
110C16×C113—22no—
111C16×C113—41no—
112C23×C113—21no—
113C23×C113—21no—
114C23×C113—21no—
115C23×C113—21no—
116C23×C113—21no—
117C23×C113—21no—
118C23×C113—42no—
119C23×C113—81no—
120C23×C113—81no—
121C23×C113—81no—
122C23×C113—81no—
123C23×C113—81no—
124C23×C113—81no—
125C23×C113D1612yes—
126C23×C113C2×D811yescharacteristic
127D4×C113—42no—
128D4×C113—42no—
129D4×C113—88no—
130D4×C113—81no—
131D4×C113—81no—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—41no—
136C2×C4×C113—41no—
137C2×C4×C113—41no—
138C2×C4×C113—41no—
139C2×C4×C113—42no—
140C2×C4×C113—81no—
141C2×C4×C113—81no—
142C2×C4×C113—81no—
143C2×C4×C113—81no—
144C2×C4×C113—81no—
145C2×C4×C113—81no—
146C2×C4×C113—81no—
147C2×C4×C113—81no—
148C2×C4×C113#12011yescharacteristic
149C2×C4×C113#12111yescharacteristic
150C2×C4×C113#12311yescharacteristic
151C2×C4×C113#13511yescharacteristic
152C2×C4×C113AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C113#13711yescharacteristic
154C8×C113—41no—
155C8×C113#12111yescharacteristic
156C8×C113#12111yescharacteristic
157C8×C113#12311yescharacteristic
158C8×C113#12411yescharacteristic
159C22×C113—22no—
160C22×C113—22no—
161C22×C113—22no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—82no—
167C22×C113—82no—
168C22×C113—82no—
169C22×C113—161no—
170C22×C113—161no—
171C22×C113—161no—
172C22×C113—161no—
173C22×C113#44711yescharacteristic
174C22×C113#46611yescharacteristic
175C22×C113#48011yescharacteristic
176C22×C113C2×D1611yescharacteristic
177C22×C113#50811yescharacteristic
178C22×C113#50911yescharacteristic
179C22×C113#51011yescharacteristic
180C4×C113—41no—
181C4×C113—82no—
182C4×C113—161no—
183C4×C113—161no—
184C4×C113#39411yescharacteristic
185C4×C113#45211yescharacteristic
186C4×C113#46811yescharacteristic
187C4×C113#48211yescharacteristic
188#13380C11311yesmaximal, characteristic, direct product factor, Sylow
189C2×C113—42no—
190C2×C113—162no—
191C2×C113#203311yescharacteristic
192C2×C113#218411yescharacteristic
193C2×C113#218911yescharacteristic
194C2×C113#221511yescharacteristic
195C2×C113#222011yescharacteristic
196C2×C113#223211yescharacteristic
197C2×C113#223411yescharacteristic
198C2×#466C2×C11311yescharacteristic
199C2×#366C2×C11311yescharacteristic, complemented
200C2×#357C2×C11311yescharacteristic, complemented
201C2×#357C2×C11311yescharacteristic, complemented
202C2×C22⋊C16C2×C11311yescharacteristic, complemented
203#1808C2×C11311yescharacteristic, complemented
204#1380C2×C11311yescharacteristic, complemented
205C113#1338011yescharacteristic, direct product factor, Sylow
206C22×D8C22×C11311yescharacteristic
207C23×C8C22×C11311yescharacteristic
208C2×#121—21no—
209C22×C16C22×C11311yescharacteristic
210C22×C16C22×C11311yescharacteristic
211#466—22no—
212#466—22no—
213C2×#107C22×C11311yescharacteristic
214C2×#107C22×C11311yescharacteristic
215C2×#107C22×C11311yescharacteristic
216C2×#102—21no—
217#380—21no—
218#366—22no—
219#357—22no—
220#357—22no—
221C22⋊C16—22no—
222#340—21no—
223C22×D4—21no—
224C22×D4—41no—
225C23×C4D4×C11311yescharacteristic
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—21no—
229C2×D8—21no—
230C2×D8—21no—
231C2×D8D4×C11312yes—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8D4×C11311yescharacteristic
239C22×C8C23×C11311yescharacteristic
240#121—24no—
241#121—42no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C22⋊C4—41no—
246C2×C22⋊C4—41no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—21no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16D4×C11312yescomplemented
253#107—21no—
254#107—21no—
255#107—21no—
256#107—21no—
257#107—21no—
258#107D4×C11312yes—
259#102—24no—
260#95—41no—
261C24—41no—
262C24D8×C11311yescharacteristic
263C2×D4—22no—
264C2×D4—44no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—82no—
271C2×D4—82no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4D8×C11311yescharacteristic
282C22×C4C2×D4×C11311yescharacteristic
283D8—22no—
284D8—22no—
285D8—41no—
286D8—41no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8C2×D4×C11311yescharacteristic
295C2×C8C2×D4×C11311yescharacteristic
296C2×C8C2×D4×C11311yescharacteristic
297C2×C8#41×C11311yescharacteristic
298C2×C8#41×C11311yescharacteristic
299C2×C8#41×C11311yescharacteristic
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C22⋊C4—44no—
307C22⋊C4—82no—
308C16—22no—
309C16—41no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—42no—
317C23—81no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—81no—
322C23—81no—
323C23D16×C11312yes—
324C23C2×D8×C11311yescharacteristic
325D4—42no—
326D4—42no—
327D4—88no—
328D4—81no—
329D4—81no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4#120×C11311yescharacteristic
347C2×C4#121×C11311yescharacteristic
348C2×C4#123×C11311yescharacteristic
349C2×C4#135×C11311yescharacteristic
350C2×C4AGL(1,ℤ/8)×C11311yescharacteristic
351C2×C4#137×C11311yescharacteristic
352C8—41no—
353C8#121×C11311yescharacteristic
354C8#121×C11311yescharacteristic
355C8#123×C11311yescharacteristic
356C8#124×C11311yescharacteristic
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—161no—
368C22—161no—
369C22—161no—
370C22—161no—
371C22#447×C11311yescharacteristic
372C22#466×C11311yescharacteristic
373C22#480×C11311yescharacteristic
374C22C2×D16×C11311yescharacteristic
375C22#508×C11311yescharacteristic
376C22#509×C11311yescharacteristic
377C22#510×C11311yescharacteristic
378C4—41no—
379C4—82no—
380C4—161no—
381C4—161no—
382C4#394×C11311yescharacteristic
383C4#452×C11311yescharacteristic
384C4#468×C11311yescharacteristic
385C4#482×C11311yescharacteristic
386C2—42no—
387C2—162no—
388C2C113×#203311yescharacteristic
389C2C113×#218411yescharacteristic
390C2C113×#218911yescharacteristic
391C2C113×#221511yescharacteristic
392C2C113×#222011yescharacteristic
393C2C113×#223211yescharacteristic
394C2C113×#223411yescharacteristic
subgroupG/H
center, socleC23×C113C2×D8
commutator, Frattini, cosocleC22×C8C23×C113
prime radicalC2×#466×C113C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C23×C4×C113 ◁ C23×C8×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#366×C113C2semidirect
3. C2×#357×C113C2semidirect
4. C2×#357×C113C2semidirect
5. C2×C22⋊C16×C113C2semidirect
6. C113×#1808C2semidirect
7. C113×#1380C2semidirect
54. C2×C16×C113D4semidirect
188. #13380C113direct (N × H)
199. C2×#366C2×C113semidirect
200. C2×#357C2×C113semidirect
201. C2×#357C2×C113semidirect
202. C2×C22⋊C16C2×C113semidirect
203. #1808C2×C113semidirect
204. #1380C2×C113semidirect
205. C113#13380direct (N × H)
252. C2×C16D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1132
C2×#366×C1132
C2×#357×C1132
C2×C22⋊C16×C1132
C113×#18082
C113×#13802
#13380113