Finite Group Databasebeta

← C113×#13357 #43281377

Subgroups — C113×#13357 #43281377

Order 28928.

772 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#454×C113C212yesmaximal, complemented
2C113×#2733C211yesmaximal, characteristic, complemented
3C2×#355×C113C212yesmaximal, complemented
4C113×#1793C211yesmaximal, characteristic, complemented
5C113×#1394C211yesmaximal, characteristic, complemented
6C2×2−1+4×C113C2211yescharacteristic
7C2×AGL(1,ℤ/8)×C113—22no—
8C2×#124×C113C2212yes—
9#454×C113—24no—
10#454×C113—24no—
11C2×#104×C113—22no—
12C2×#104×C113—21no—
13#417×C113—21no—
14C2×#101×C113C2211yescharacteristic
15C2×#101×C113C2212yes—
16#394×C113—21no—
17#392×C113—22no—
18#391×C113C2211yescharacteristic
19#390×C113—21no—
20#388×C113—22no—
21#355×C113—24no—
222−1+4×C113—22no—
232−1+4×C113—21no—
242−1+4×C113—42no—
252−1+4×C113D412yescomplemented
26C2×#41×C113—22no—
27C2×#41×C113—21no—
28C2×#41×C113—41no—
29C22×Q8×C113—41no—
30C22×Q8×C113C2311yescharacteristic
31C22×D4×C113—21no—
32C22×D4×C113—21no—
33C22×D4×C113D412yes—
34AGL(1,ℤ/8)×C113—28no—
35AGL(1,ℤ/8)×C113—44no—
36C2×SD16×C113—42no—
37C2×D8×C113—42no—
38C2×M16×C113—22no—
39C2×M16×C113—21no—
40#124×C113—22no—
41#124×C113—22no—
42#124×C113—22no—
43#124×C113—22no—
44C2×C4⋊C4×C113—21no—
45C2×C4⋊C4×C113D411yescharacteristic
46C2×C22⋊C4×C113—22no—
47C2×C22⋊C4×C113—22no—
48C2×C22⋊C4×C113—22no—
49C2×C22⋊C4×C113—22no—
50C2×C42×C113D412yes—
51C2×C42×C113D411yescharacteristic
52#104×C113—28no—
53#104×C113—42no—
54#103×C113—41no—
55#102×C113—41no—
56#101×C113—22no—
57#101×C113—22no—
58#101×C113D414yescomplemented
59#95×C113—21no—
60#95×C113—22no—
61C24×C113—22no—
62#41×C113—22no—
63#41×C113—24no—
64#41×C113—24no—
65#41×C113—22no—
66#41×C113—41no—
67#41×C113—42no—
68#41×C113—42no—
69#41×C113—44no—
70#41×C113—42no—
71#41×C113—42no—
72#41×C113—41no—
73C2×Q8×C113—21no—
74C2×Q8×C113—22no—
75C2×Q8×C113—41no—
76C2×Q8×C113—41no—
77C2×Q8×C113—42no—
78C2×Q8×C113—44no—
79C2×Q8×C113—42no—
80C2×Q8×C113C2×D411yescharacteristic
81C2×Q8×C113C2×D412yes—
82C2×Q8×C113#4111yescharacteristic
83C2×D4×C113—21no—
84C2×D4×C113—22no—
85C2×D4×C113—22no—
86C2×D4×C113—22no—
87C2×D4×C113—42no—
88C2×D4×C113—42no—
89C2×D4×C113—42no—
90C2×D4×C113—41no—
91C2×D4×C113—81no—
92C2×D4×C113—81no—
93C2×D4×C113—82no—
94C2×D4×C113—81no—
95C22×C4×C113—21no—
96C22×C4×C113—21no—
97C22×C4×C113—22no—
98C22×C4×C113—41no—
99C22×C4×C113—42no—
100C22×C4×C113C2×D412yes—
101C22×C4×C113C2×D411yescharacteristic
102SD16×C113—48no—
103D8×C113—48no—
104M16×C113—24no—
105M16×C113—42no—
106M16×C113—41no—
107M16×C113—41no—
108C2×C8×C113—42no—
109C2×C8×C113—41no—
110C4⋊C4×C113—41no—
111C4⋊C4×C113—81no—
112C22⋊C4×C113—44no—
113C22⋊C4×C113—42no—
114C22⋊C4×C113—42no—
115C22⋊C4×C113—42no—
116C22⋊C4×C113—42no—
117C22⋊C4×C113—82no—
118C42×C113—22no—
119C42×C113—22no—
120C42×C113—41no—
121C23×C113—42no—
122C23×C113—42no—
123C23×C113—42no—
124C23×C113—42no—
125C23×C113—41no—
126C23×C113—42no—
127C23×C113—42no—
128C23×C113—42no—
129C23×C113#12011yescharacteristic
130Q8×C113—24no—
131Q8×C113—22no—
132Q8×C113—41no—
133Q8×C113—42no—
134Q8×C113—41no—
135Q8×C113—41no—
136Q8×C113—42no—
137D4×C113—24no—
138D4×C113—22no—
139D4×C113—41no—
140D4×C113—42no—
141D4×C113—44no—
142D4×C113—42no—
143D4×C113—42no—
144D4×C113—82no—
145D4×C113—84no—
146D4×C113—84no—
147C2×C4×C113—21no—
148C2×C4×C113—22no—
149C2×C4×C113—21no—
150C2×C4×C113—22no—
151C2×C4×C113—22no—
152C2×C4×C113—44no—
153C2×C4×C113—42no—
154C2×C4×C113—42no—
155C2×C4×C113—44no—
156C2×C4×C113—41no—
157C2×C4×C113—41no—
158C2×C4×C113—41no—
159C2×C4×C113—42no—
160C2×C4×C113—42no—
161C2×C4×C113—42no—
162C2×C4×C113—42no—
163C2×C4×C113—41no—
164C2×C4×C113#12012yes—
165C2×C4×C113#12112yes—
166C2×C4×C113#12111yescharacteristic
167C2×C4×C113#12711yescharacteristic
168C8×C113—44no—
169C8×C113—81no—
170C22×C113—21no—
171C22×C113—21no—
172C22×C113—42no—
173C22×C113—82no—
174C22×C113—82no—
175C22×C113—82no—
176C22×C113—82no—
177C22×C113—81no—
178C22×C113—81no—
179C22×C113—82no—
180C22×C113—82no—
181C22×C113—82no—
182C22×C113#39211yescharacteristic
183C22×C113B(4,𝔽2)11yescharacteristic
184C22×C113B(4,𝔽2)11yescharacteristic
185C4×C113—22no—
186C4×C113—21no—
187C4×C113—21no—
188C4×C113—22no—
189C4×C113—42no—
190C4×C113—42no—
191C4×C113—82no—
192C4×C113—81no—
193#13357C11311yesmaximal, characteristic, direct product factor, Sylow
194C2×C113—21no—
195C2×C113—21no—
196C2×C113—82no—
197C2×C113—162no—
198C2×C113#202111yescharacteristic
199C2×C113#220211yescharacteristic
200C2×C113#220411yescharacteristic
201C2×#454C2×C11312yescomplemented
202#2733C2×C11311yescharacteristic, complemented
203C2×#355C2×C11312yescomplemented
204#1793C2×C11311yescharacteristic, complemented
205#1394C2×C11311yescharacteristic, complemented
206C113#1335711yescharacteristic, direct product factor, Sylow
207C2×2−1+4C22×C11311yescharacteristic
208C2×AGL(1,ℤ/8)—22no—
209C2×#124C22×C11312yes—
210#454—24no—
211#454—24no—
212C2×#104—22no—
213C2×#104—21no—
214#417—21no—
215C2×#101C22×C11311yescharacteristic
216C2×#101C22×C11312yes—
217#394—21no—
218#392—22no—
219#391C22×C11311yescharacteristic
220#390—21no—
221#388—22no—
222#355—24no—
2232−1+4—22no—
2242−1+4—21no—
2252−1+4—42no—
2262−1+4D4×C11312yescomplemented
227C2×#41—22no—
228C2×#41—21no—
229C2×#41—41no—
230C22×Q8—41no—
231C22×Q8C23×C11311yescharacteristic
232C22×D4—21no—
233C22×D4—21no—
234C22×D4D4×C11312yes—
235AGL(1,ℤ/8)—28no—
236AGL(1,ℤ/8)—44no—
237C2×SD16—42no—
238C2×D8—42no—
239C2×M16—22no—
240C2×M16—21no—
241#124—22no—
242#124—22no—
243#124—22no—
244#124—22no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4D4×C11311yescharacteristic
247C2×C22⋊C4—22no—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C22⋊C4—22no—
251C2×C42D4×C11312yes—
252C2×C42D4×C11311yescharacteristic
253#104—28no—
254#104—42no—
255#103—41no—
256#102—41no—
257#101—22no—
258#101—22no—
259#101D4×C11314yescomplemented
260#95—21no—
261#95—22no—
262C24—22no—
263#41—22no—
264#41—24no—
265#41—24no—
266#41—22no—
267#41—41no—
268#41—42no—
269#41—42no—
270#41—44no—
271#41—42no—
272#41—42no—
273#41—41no—
274C2×Q8—21no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—42no—
279C2×Q8—44no—
280C2×Q8—42no—
281C2×Q8C2×D4×C11311yescharacteristic
282C2×Q8C2×D4×C11312yes—
283C2×Q8#41×C11311yescharacteristic
284C2×D4—21no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—41no—
292C2×D4—81no—
293C2×D4—81no—
294C2×D4—82no—
295C2×D4—81no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—22no—
299C22×C4—41no—
300C22×C4—42no—
301C22×C4C2×D4×C11312yes—
302C22×C4C2×D4×C11311yescharacteristic
303SD16—48no—
304D8—48no—
305M16—24no—
306M16—42no—
307M16—41no—
308M16—41no—
309C2×C8—42no—
310C2×C8—41no—
311C4⋊C4—41no—
312C4⋊C4—81no—
313C22⋊C4—44no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—42no—
318C22⋊C4—82no—
319C42—22no—
320C42—22no—
321C42—41no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—41no—
327C23—42no—
328C23—42no—
329C23—42no—
330C23#120×C11311yescharacteristic
331Q8—24no—
332Q8—22no—
333Q8—41no—
334Q8—42no—
335Q8—41no—
336Q8—41no—
337Q8—42no—
338D4—24no—
339D4—22no—
340D4—41no—
341D4—42no—
342D4—44no—
343D4—42no—
344D4—42no—
345D4—82no—
346D4—84no—
347D4—84no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—44no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—44no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4#120×C11312yes—
366C2×C4#121×C11312yes—
367C2×C4#121×C11311yescharacteristic
368C2×C4#127×C11311yescharacteristic
369C8—44no—
370C8—81no—
371C22—21no—
372C22—21no—
373C22—42no—
374C22—82no—
375C22—82no—
376C22—82no—
377C22—82no—
378C22—81no—
379C22—81no—
380C22—82no—
381C22—82no—
382C22—82no—
383C22#392×C11311yescharacteristic
384C22B(4,𝔽2)×C11311yescharacteristic
385C22B(4,𝔽2)×C11311yescharacteristic
386C4—22no—
387C4—21no—
388C4—21no—
389C4—22no—
390C4—42no—
391C4—42no—
392C4—82no—
393C4—81no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2—162no—
398C2C113×#202111yescharacteristic
399C2C113×#220211yescharacteristic
400C2C113×#220411yescharacteristic
subgroupG/H
center, socleC22×C113B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C23×C113
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C113 ◁ C22×Q8×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#454×C113C2semidirect
2. C113×#2733C2semidirect
3. C2×#355×C113C2semidirect
4. C113×#1793C2semidirect
5. C113×#1394C2semidirect
25. 2−1+4×C113D4semidirect
58. #101×C113D4semidirect
193. #13357C113direct (N × H)
201. C2×#454C2×C113semidirect
202. #2733C2×C113semidirect
203. C2×#355C2×C113semidirect
204. #1793C2×C113semidirect
205. #1394C2×C113semidirect
206. C113#13357direct (N × H)
226. 2−1+4D4×C113semidirect
259. #101D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#454×C1132
C113×#27332
C2×#355×C1132
C113×#17932
C113×#13942
#13357113