Finite Group Databasebeta

← C113×#9116 #43277136

Subgroups — C113×#9116 #43277136

Order 28928.

612 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#432×C113C211yesmaximal, characteristic
2C113×#2855C211yesmaximal, characteristic
3C2×#328×C113C212yesmaximal
4C113×#1434C211yesmaximal, characteristic
5C113×#1294C212yesmaximal
6C2×C22⋊Q8×C113C2211yescharacteristic
7C22×C42×C113C2211yescharacteristic
8#432×C113—24no—
9C2×C4⋊C8×C113—21no—
10C2×C22⋊C8×C113C2212yes—
11C2×#97×C113—21no—
12#391×C113C411yescharacteristic, complemented
13#391×C113C411yescharacteristic, complemented
14#389×C113C411yescharacteristic, complemented
15#389×C113C411yescharacteristic, complemented
16#387×C113—21no—
17#387×C113—21no—
18#385×C113—21no—
19#381×C113—21no—
20#380×C113C2211yescharacteristic
21C2×#95×C113—21no—
22C2×#95×C113—21no—
23C2×#95×C113C2212yes—
24#328×C113—24no—
25C22×Q8×C113C2×C411yescharacteristic
26C23×C4×C113—22no—
27C23×C4×C113D411yescharacteristic
28C23×C4×C113D411yescharacteristic
29C23×C4×C113C2311yescharacteristic
30C22×C8×C113—22no—
31C22⋊Q8×C113—22no—
32C22⋊Q8×C113—22no—
33C2×C4⋊C4×C113—21no—
34C2×C4⋊C4×C113—21no—
35C2×C4⋊C4×C113—21no—
36C2×C4⋊C4×C113C2×C411yescharacteristic
37C2×C4⋊C4×C113C2×C411yescharacteristic
38C2×C4⋊C4×C113C2×C411yescharacteristic
39C2×C22⋊C4×C113—21no—
40C2×C22⋊C4×C113—21no—
41C2×C42×C113—22no—
42C2×C42×C113—22no—
43C2×C42×C113C2×C411yescharacteristic
44C2×C42×C113C2×C411yescharacteristic
45C2×C42×C113D411yescharacteristic
46C2×C42×C113D411yescharacteristic
47C4⋊C8×C113—24no—
48C22⋊C8×C113—22no—
49C22⋊C8×C113D414yes—
50#97×C113—24no—
51#95×C113—24no—
52#95×C113—21no—
53#95×C113—21no—
54#95×C113—21no—
55#95×C113—21no—
56#95×C113—21no—
57#95×C113—21no—
58#95×C113—21no—
59#95×C113—22no—
60#95×C113—22no—
61#95×C113—42no—
62C24×C113C2×D411yescharacteristic
63C2×Q8×C113—22no—
64C2×Q8×C113—41no—
65C2×Q8×C113—41no—
66C22×C4×C113—22no—
67C22×C4×C113—22no—
68C22×C4×C113—21no—
69C22×C4×C113—21no—
70C22×C4×C113—22no—
71C22×C4×C113—22no—
72C22×C4×C113—24no—
73C22×C4×C113—21no—
74C22×C4×C113—21no—
75C22×C4×C113—21no—
76C22×C4×C113—21no—
77C22×C4×C113—41no—
78C22×C4×C113—41no—
79C22×C4×C113—41no—
80C22×C4×C113—42no—
81C22×C4×C113—42no—
82C22×C4×C113—42no—
83C22×C4×C113—42no—
84C22×C4×C113—42no—
85C22×C4×C113—42no—
86C22×C4×C113C22⋊C411yescharacteristic
87C22×C4×C113C22⋊C411yescharacteristic
88C22×C4×C113C22⋊C411yescharacteristic
89C22×C4×C113C22⋊C411yescharacteristic
90C22×C4×C113C22×C411yescharacteristic
91C22×C4×C113C2×D411yescharacteristic
92C22×C4×C113C2×D412yes—
93C22×C4×C113#4112yes—
94C2×C8×C113—24no—
95C2×C8×C113—42no—
96C2×C8×C113—42no—
97C4⋊C4×C113—22no—
98C4⋊C4×C113—41no—
99C4⋊C4×C113—41no—
100C4⋊C4×C113—42no—
101C4⋊C4×C113—42no—
102C4⋊C4×C113—41no—
103C4⋊C4×C113—41no—
104C22⋊C4×C113—42no—
105C22⋊C4×C113—41no—
106C22⋊C4×C113—41no—
107C42×C113—22no—
108C42×C113—22no—
109C42×C113—21no—
110C42×C113—21no—
111C42×C113—21no—
112C42×C113—21no—
113C23×C113—21no—
114C23×C113—21no—
115C23×C113—21no—
116C23×C113—21no—
117C23×C113C2×C22⋊C411yescharacteristic
118C23×C113#12112yes—
119C23×C113AGL(1,ℤ/8)11yescharacteristic
120C23×C113#13711yescharacteristic
121C23×C113#13712yes—
122Q8×C113—82no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113—42no—
139C2×C4×C113—42no—
140C2×C4×C113—44no—
141C2×C4×C113—42no—
142C2×C4×C113—42no—
143C2×C4×C113—44no—
144C2×C4×C113—44no—
145C2×C4×C113—44no—
146C2×C4×C113—41no—
147C2×C4×C113—41no—
148C2×C4×C113—41no—
149C2×C4×C113—41no—
150C2×C4×C113—41no—
151C2×C4×C113—41no—
152C2×C4×C113—41no—
153C2×C4×C113—41no—
154C2×C4×C113—41no—
155C2×C4×C113—41no—
156C2×C4×C113—41no—
157C2×C4×C113—41no—
158C2×C4×C113—82no—
159C2×C4×C113—82no—
160C2×C4×C113—82no—
161C2×C4×C113—82no—
162C2×C4×C113#10412yes—
163C2×C4×C113C4×D412yes—
164C2×C4×C113#12011yescharacteristic
165C2×C4×C113#12311yescharacteristic
166C8×C113—44no—
167C22×C113—22no—
168C22×C113—22no—
169C22×C113—22no—
170C22×C113—21no—
171C22×C113—21no—
172C22×C113—21no—
173C22×C113—21no—
174C22×C113—22no—
175C22×C113#38611yescharacteristic
176C22×C113#41011yescharacteristic
177C22×C113#41011yescharacteristic
178C22×C113#41711yescharacteristic
179C22×C113#41911yescharacteristic
180C22×C113C2×#10411yescharacteristic
181C22×C113#42111yescharacteristic
182C22×C113#46812yes—
183C22×C113#47012yes—
184C4×C113—22no—
185C4×C113—21no—
186C4×C113—22no—
187C4×C113—21no—
188C4×C113—41no—
189C4×C113—41no—
190C4×C113—41no—
191C4×C113—84no—
192C4×C113—81no—
193C4×C113—81no—
194C4×C113—81no—
195C4×C113—81no—
196#9116C11311yesmaximal, characteristic, direct product factor, Sylow
197C2×C113—22no—
198C2×C113—22no—
199C2×C113#150611yescharacteristic
200C2×C113#150911yescharacteristic
201C2×C113#151211yescharacteristic
202C2×C113#151511yescharacteristic
203C2×C113#187111yescharacteristic
204C2×C113#189411yescharacteristic
205C2×C113#189911yescharacteristic
206C2×#432C2×C11311yescharacteristic
207#2855C2×C11311yescharacteristic
208C2×#328C2×C11312yes—
209#1434C2×C11311yescharacteristic
210#1294C2×C11312yes—
211C113#911611yescharacteristic, direct product factor, Sylow
212C2×C22⋊Q8C22×C11311yescharacteristic
213C22×C42C22×C11311yescharacteristic
214#432—24no—
215C2×C4⋊C8—21no—
216C2×C22⋊C8C22×C11312yes—
217C2×#97—21no—
218#391C4×C11311yescharacteristic, complemented
219#391C4×C11311yescharacteristic, complemented
220#389C4×C11311yescharacteristic, complemented
221#389C4×C11311yescharacteristic, complemented
222#387—21no—
223#387—21no—
224#385—21no—
225#381—21no—
226#380C22×C11311yescharacteristic
227C2×#95—21no—
228C2×#95—21no—
229C2×#95C22×C11312yes—
230#328—24no—
231C22×Q8C2×C4×C11311yescharacteristic
232C23×C4—22no—
233C23×C4D4×C11311yescharacteristic
234C23×C4D4×C11311yescharacteristic
235C23×C4C23×C11311yescharacteristic
236C22×C8—22no—
237C22⋊Q8—22no—
238C22⋊Q8—22no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4C2×C4×C11311yescharacteristic
243C2×C4⋊C4C2×C4×C11311yescharacteristic
244C2×C4⋊C4C2×C4×C11311yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C42—22no—
248C2×C42—22no—
249C2×C42C2×C4×C11311yescharacteristic
250C2×C42C2×C4×C11311yescharacteristic
251C2×C42D4×C11311yescharacteristic
252C2×C42D4×C11311yescharacteristic
253C4⋊C8—24no—
254C22⋊C8—22no—
255C22⋊C8D4×C11314yes—
256#97—24no—
257#95—24no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—22no—
266#95—22no—
267#95—42no—
268C24C2×D4×C11311yescharacteristic
269C2×Q8—22no—
270C2×Q8—41no—
271C2×Q8—41no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—24no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4C22⋊C4×C11311yescharacteristic
293C22×C4C22⋊C4×C11311yescharacteristic
294C22×C4C22⋊C4×C11311yescharacteristic
295C22×C4C22⋊C4×C11311yescharacteristic
296C22×C4C22×C4×C11311yescharacteristic
297C22×C4C2×D4×C11311yescharacteristic
298C22×C4C2×D4×C11312yes—
299C22×C4#41×C11312yes—
300C2×C8—24no—
301C2×C8—42no—
302C2×C8—42no—
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C42—22no—
314C42—22no—
315C42—21no—
316C42—21no—
317C42—21no—
318C42—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23C2×C22⋊C4×C11311yescharacteristic
324C23#121×C11312yes—
325C23AGL(1,ℤ/8)×C11311yescharacteristic
326C23#137×C11311yescharacteristic
327C23#137×C11312yes—
328Q8—82no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—44no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4#104×C11312yes—
369C2×C4C4×D4×C11312yes—
370C2×C4#120×C11311yescharacteristic
371C2×C4#123×C11311yescharacteristic
372C8—44no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22#386×C11311yescharacteristic
382C22#410×C11311yescharacteristic
383C22#410×C11311yescharacteristic
384C22#417×C11311yescharacteristic
385C22#419×C11311yescharacteristic
386C22C2×#104×C11311yescharacteristic
387C22#421×C11311yescharacteristic
388C22#468×C11312yes—
389C22#470×C11312yes—
390C4—22no—
391C4—21no—
392C4—22no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—84no—
398C4—81no—
399C4—81no—
400C4—81no—
401C4—81no—
402C2—22no—
403C2—22no—
404C2C113×#150611yescharacteristic
405C2C113×#150911yescharacteristic
406C2C113×#151211yescharacteristic
407C2C113×#151511yescharacteristic
408C2C113×#187111yescharacteristic
409C2C113×#189411yescharacteristic
410C2C113×#189911yescharacteristic
subgroupG/H
center, socleC23×C113C2×C22⋊C4
commutatorC22×C4C22×C4×C113
Frattini, cosocleC23×C4C23×C113
prime radicalC24×C113C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C113 ◁ C22×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
12. #391×C113C4semidirect
13. #391×C113C4semidirect
14. #389×C113C4semidirect
15. #389×C113C4semidirect
196. #9116C113direct (N × H)
211. C113#9116direct (N × H)
218. #391C4×C113semidirect
219. #391C4×C113semidirect
220. #389C4×C113semidirect
221. #389C4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#432×C1132
C113×#28552
C2×#328×C1132
C113×#14342
C113×#12942
#9116113