Finite Group Databasebeta

← C113×#10194 #43278214

Subgroups — C113×#10194 #43278214

Order 28928.

640 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3246C211yesmaximal, characteristic, complemented
2C113×#3208C211yesmaximal, characteristic, complemented
3C113×#3151C211yesmaximal, characteristic
4C113×#1986C211yesmaximal, characteristic, complemented
5C113×#1982C211yesmaximal, characteristic, complemented
6C113×#1502C211yesmaximal, characteristic, complemented
7C113×#1283C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C113—22no—
9#533×C113C2211yescharacteristic
10#532×C113C2211yescharacteristic
11C2×#127×C113C2211yescharacteristic
12#496×C113—22no—
13#493×C113—21no—
14#492×C113—21no—
15#492×C113—21no—
16#486×C113—21no—
17#476×C113—21no—
18#475×C113—21no—
19#465×C113—22no—
20#461×C113—21no—
21#460×C113—22no—
22#460×C113—21no—
23#450×C113—22no—
24#431×C113C2211yescharacteristic
25C2×C4⋊C8×C113C2211yescharacteristic
26C2×#102×C113—22no—
27C4×M16×C113C2211yescharacteristic
28C4×C4⋊C4×C113C2211yescharacteristic
29#339×C113—22no—
30#327×C113—22no—
31C2×#41×C113—21no—
32C22×D4×C113—21no—
33C22×D4×C113—21no—
34C22×D4×C113—21no—
35AGL(1,ℤ/8)×C113—44no—
36AGL(1,ℤ/8)×C113—44no—
37C2×SD16×C113—24no—
38C2×SD16×C113—24no—
39C2×SD16×C113—22no—
40C2×D8×C113—24no—
41C2×M16×C113D412yes—
42C22×C8×C113D412yes—
43C4⋊Q8×C113D411yescharacteristic
44C4⋊Q8×C113D411yescharacteristic
45C4⋊Q8×C113D411yescharacteristic
46#127×C113—21no—
47#127×C113—21no—
48#127×C113—21no—
49#127×C113D412yes—
50#127×C113D411yescharacteristic
51#125×C113—21no—
52#124×C113—21no—
53C22⋊Q8×C113—21no—
54C22⋊Q8×C113—21no—
55#121×C113—21no—
56#121×C113—21no—
57C4×Q8×C113—21no—
58C4×Q8×C113—21no—
59C4×D4×C113—21no—
60C4×D4×C113—21no—
61#117×C113—21no—
62C2×C4⋊C4×C113—21no—
63C2×C42×C113—21no—
64C2×C42×C113C2311yescharacteristic
65#106×C113—22no—
66C4⋊C8×C113—21no—
67C4⋊C8×C113—21no—
68C4⋊C8×C113—21no—
69#103×C113—22no—
70#102×C113—24no—
71#102×C113—22no—
72#102×C113—44no—
73C22⋊C8×C113D412yes—
74#97×C113—21no—
75C4×C8×C113—21no—
76C4×C8×C113—21no—
77#95×C113—21no—
78C24×C113—41no—
79#41×C113—42no—
80#41×C113—42no—
81C2×Q8×C113—21no—
82C2×Q8×C113—21no—
83C2×Q8×C113—21no—
84C2×D4×C113—21no—
85C2×D4×C113—22no—
86C2×D4×C113—21no—
87C2×D4×C113—22no—
88C2×D4×C113—22no—
89C2×D4×C113—21no—
90C2×D4×C113—42no—
91C2×D4×C113—42no—
92C2×D4×C113—41no—
93C2×D4×C113—41no—
94C2×D4×C113—41no—
95C2×D4×C113—41no—
96C2×D4×C113—42no—
97C2×D4×C113—42no—
98C2×D4×C113—82no—
99C22×C4×C113—41no—
100C22×C4×C113—41no—
101C22×C4×C113C2×D411yescharacteristic
102C22×C4×C113C2×D411yescharacteristic
103C22×C4×C113C2×D411yescharacteristic
104SD16×C113—48no—
105SD16×C113—84no—
106SD16×C113—82no—
107D8×C113—48no—
108M16×C113—22no—
109M16×C113SD1614yescomplemented
110C2×C8×C113—22no—
111C2×C8×C113—22no—
112C2×C8×C113—22no—
113C2×C8×C113—42no—
114C4⋊C4×C113—22no—
115C4⋊C4×C113—21no—
116C4⋊C4×C113—21no—
117C4⋊C4×C113—21no—
118C4⋊C4×C113—21no—
119C4⋊C4×C113—21no—
120C4⋊C4×C113—21no—
121C4⋊C4×C113—41no—
122C4⋊C4×C113—41no—
123C4⋊C4×C113—41no—
124C22⋊C4×C113—41no—
125C22⋊C4×C113—41no—
126C22⋊C4×C113—41no—
127C42×C113—41no—
128C42×C113—42no—
129C42×C113C2×D411yescharacteristic
130C42×C113C2×D411yescharacteristic
131C42×C113C2×D411yescharacteristic
132C42×C113#4111yescharacteristic
133C23×C113—41no—
134C23×C113—42no—
135C23×C113—82no—
136C23×C113—82no—
137C23×C113—81no—
138C23×C113—81no—
139C23×C113#12711yescharacteristic
140Q8×C113—42no—
141Q8×C113—42no—
142Q8×C113—41no—
143Q8×C113—41no—
144D4×C113—44no—
145D4×C113—44no—
146D4×C113—42no—
147D4×C113—44no—
148D4×C113—41no—
149D4×C113—41no—
150D4×C113—81no—
151D4×C113—82no—
152D4×C113—81no—
153D4×C113—81no—
154D4×C113—81no—
155D4×C113—81no—
156D4×C113—82no—
157C2×C4×C113—21no—
158C2×C4×C113—21no—
159C2×C4×C113—41no—
160C2×C4×C113—42no—
161C2×C4×C113—41no—
162C2×C4×C113—41no—
163C2×C4×C113—41no—
164C2×C4×C113—81no—
165C2×C4×C113—81no—
166C2×C4×C113—82no—
167C2×C4×C113#12011yescharacteristic
168C2×C4×C113#12011yescharacteristic
169C2×C4×C113#12011yescharacteristic
170C2×C4×C113#12111yescharacteristic
171C2×C4×C113#12111yescharacteristic
172C2×C4×C113#12111yescharacteristic
173C2×C4×C113C2×SD1612yes—
174C2×C4×C113AGL(1,ℤ/8)12yes—
175C8×C113—24no—
176C8×C113—42no—
177C8×C113—42no—
178C22×C113—21no—
179C22×C113—21no—
180C22×C113—82no—
181C22×C113—81no—
182C22×C113—82no—
183C22×C113—81no—
184C22×C113—81no—
185C22×C113—82no—
186C22×C113—162no—
187C22×C113—162no—
188C22×C113#39211yescharacteristic
189C22×C113#49211yescharacteristic
190C22×C113#49611yescharacteristic
191C4×C113—21no—
192C4×C113—21no—
193C4×C113—21no—
194C4×C113—82no—
195C4×C113—81no—
196C4×C113—81no—
197C4×C113—81no—
198C4×C113#45012yes—
199C4×C113#45311yescharacteristic
200C4×C113#45411yescharacteristic
201C4×C113#46012yes—
202#10194C11311yesmaximal, characteristic, direct product factor, Sylow
203C2×C113—21no—
204C2×C113—21no—
205C2×C113—161no—
206C2×C113—162no—
207C2×C113#200611yescharacteristic
208C2×C113#200811yescharacteristic
209C2×C113#201411yescharacteristic
210#3246C2×C11311yescharacteristic, complemented
211#3208C2×C11311yescharacteristic, complemented
212#3151C2×C11311yescharacteristic
213#1986C2×C11311yescharacteristic, complemented
214#1982C2×C11311yescharacteristic, complemented
215#1502C2×C11311yescharacteristic, complemented
216#1283C2×C11311yescharacteristic, complemented
217C113#1019411yescharacteristic, direct product factor, Sylow
218C2×AGL(1,ℤ/8)—22no—
219#533C22×C11311yescharacteristic
220#532C22×C11311yescharacteristic
221C2×#127C22×C11311yescharacteristic
222#496—22no—
223#493—21no—
224#492—21no—
225#492—21no—
226#486—21no—
227#476—21no—
228#475—21no—
229#465—22no—
230#461—21no—
231#460—22no—
232#460—21no—
233#450—22no—
234#431C22×C11311yescharacteristic
235C2×C4⋊C8C22×C11311yescharacteristic
236C2×#102—22no—
237C4×M16C22×C11311yescharacteristic
238C4×C4⋊C4C22×C11311yescharacteristic
239#339—22no—
240#327—22no—
241C2×#41—21no—
242C22×D4—21no—
243C22×D4—21no—
244C22×D4—21no—
245AGL(1,ℤ/8)—44no—
246AGL(1,ℤ/8)—44no—
247C2×SD16—24no—
248C2×SD16—24no—
249C2×SD16—22no—
250C2×D8—24no—
251C2×M16D4×C11312yes—
252C22×C8D4×C11312yes—
253C4⋊Q8D4×C11311yescharacteristic
254C4⋊Q8D4×C11311yescharacteristic
255C4⋊Q8D4×C11311yescharacteristic
256#127—21no—
257#127—21no—
258#127—21no—
259#127D4×C11312yes—
260#127D4×C11311yescharacteristic
261#125—21no—
262#124—21no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265#121—21no—
266#121—21no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×D4—21no—
270C4×D4—21no—
271#117—21no—
272C2×C4⋊C4—21no—
273C2×C42—21no—
274C2×C42C23×C11311yescharacteristic
275#106—22no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279#103—22no—
280#102—24no—
281#102—22no—
282#102—44no—
283C22⋊C8D4×C11312yes—
284#97—21no—
285C4×C8—21no—
286C4×C8—21no—
287#95—21no—
288C24—41no—
289#41—42no—
290#41—42no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×D4—21no—
295C2×D4—22no—
296C2×D4—21no—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—21no—
300C2×D4—42no—
301C2×D4—42no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—42no—
307C2×D4—42no—
308C2×D4—82no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4C2×D4×C11311yescharacteristic
312C22×C4C2×D4×C11311yescharacteristic
313C22×C4C2×D4×C11311yescharacteristic
314SD16—48no—
315SD16—84no—
316SD16—82no—
317D8—48no—
318M16—22no—
319M16SD16×C11314yescomplemented
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—42no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C42—41no—
338C42—42no—
339C42C2×D4×C11311yescharacteristic
340C42C2×D4×C11311yescharacteristic
341C42C2×D4×C11311yescharacteristic
342C42#41×C11311yescharacteristic
343C23—41no—
344C23—42no—
345C23—82no—
346C23—82no—
347C23—81no—
348C23—81no—
349C23#127×C11311yescharacteristic
350Q8—42no—
351Q8—42no—
352Q8—41no—
353Q8—41no—
354D4—44no—
355D4—44no—
356D4—42no—
357D4—44no—
358D4—41no—
359D4—41no—
360D4—81no—
361D4—82no—
362D4—81no—
363D4—81no—
364D4—81no—
365D4—81no—
366D4—82no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—82no—
377C2×C4#120×C11311yescharacteristic
378C2×C4#120×C11311yescharacteristic
379C2×C4#120×C11311yescharacteristic
380C2×C4#121×C11311yescharacteristic
381C2×C4#121×C11311yescharacteristic
382C2×C4#121×C11311yescharacteristic
383C2×C4C2×SD16×C11312yes—
384C2×C4AGL(1,ℤ/8)×C11312yes—
385C8—24no—
386C8—42no—
387C8—42no—
388C22—21no—
389C22—21no—
390C22—82no—
391C22—81no—
392C22—82no—
393C22—81no—
394C22—81no—
395C22—82no—
396C22—162no—
397C22—162no—
398C22#392×C11311yescharacteristic
399C22#492×C11311yescharacteristic
400C22#496×C11311yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—82no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4#450×C11312yes—
409C4#453×C11311yescharacteristic
410C4#454×C11311yescharacteristic
411C4#460×C11312yes—
412C2—21no—
413C2—21no—
414C2—162no—
415C2—161no—
416C2C113×#200611yescharacteristic
417C2C113×#200811yescharacteristic
418C2C113×#201411yescharacteristic
subgroupG/H
center, socleC22×C113#392
commutator, Frattini, cosocleC2×C42C23×C113
prime radicalC113×#3151C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3246C2semidirect
2. C113×#3208C2semidirect
4. C113×#1986C2semidirect
5. C113×#1982C2semidirect
6. C113×#1502C2semidirect
7. C113×#1283C2semidirect
109. M16×C113SD16semidirect
202. #10194C113direct (N × H)
210. #3246C2×C113semidirect
211. #3208C2×C113semidirect
213. #1986C2×C113semidirect
214. #1982C2×C113semidirect
215. #1502C2×C113semidirect
216. #1283C2×C113semidirect
217. C113#10194direct (N × H)
319. M16SD16×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#32462
C113×#32082
C113×#31512
C113×#19862
C113×#19822
C113×#15022
C113×#12832
#10194113