Finite Group Databasebeta

← C113×#9244 #43277264

Subgroups — C113×#9244 #43277264

Order 28928.

464 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
1C2×#464×C113C211yesmaximal, characteristic
2C113×#2984C211yesmaximal, characteristic, complemented
3C113×#1527C211yesmaximal, characteristic
4C113×#1491C211yesmaximal, characteristic, complemented
5C113×#1469C211yesmaximal, characteristic
6C113×#1290C211yesmaximal, characteristic, complemented
7C113×#1283C211yesmaximal, characteristic, complemented
8C22×Q16×C113C411yescharacteristic
9C22×SD16×C113C411yescharacteristic
10C2×#124×C113C2211yescharacteristic
11C2×C4×Q8×C113C2211yescharacteristic
12#464×C113—21no—
13#464×C113—21no—
14#464×C113—21no—
15#464×C113—21no—
16#446×C113—21no—
17#446×C113—22no—
18C8×Q8×C113—21no—
19#432×C113—21no—
20#432×C113C2211yescharacteristic
21#432×C113C2211yescharacteristic
22#431×C113—21no—
23#431×C113C2211yescharacteristic
24C2×C4⋊C8×C113C2211yescharacteristic
25C2×#103×C113C411yescharacteristic
26C2×#102×C113C411yescharacteristic
27C4×M16×C113C2211yescharacteristic
28#329×C113—22no—
29Q8⋊C8×C113—21no—
30Q8⋊C8×C113—21no—
31#323×C113—21no—
32#323×C113—21no—
33C22×Q8×C113C2×C411yescharacteristic
34C22×Q8×C113C2×C411yescharacteristic
35C22×D4×C113C2×C411yescharacteristic
36C2×Q16×C113—21no—
37C2×Q16×C113—21no—
38C2×Q16×C113—42no—
39C2×SD16×C113—21no—
40C2×SD16×C113—21no—
41C2×SD16×C113—42no—
42C2×M16×C113—21no—
43C22×C8×C113C2×C411yescharacteristic
44C22×C8×C113C2×C411yescharacteristic
45#124×C113—21no—
46#124×C113—21no—
47#124×C113—21no—
48#124×C113—21no—
49C4×Q8×C113—21no—
50C4×Q8×C113—21no—
51C4×Q8×C113D411yescharacteristic
52C4×Q8×C113D411yescharacteristic
53C4×Q8×C113D411yescharacteristic
54C4×Q8×C113D411yescharacteristic
55C2×C4⋊C4×C113—21no—
56C2×C4⋊C4×C113C2×C411yescharacteristic
57C2×C22⋊C4×C113—21no—
58C2×C22⋊C4×C113—21no—
59C2×C42×C113—21no—
60C2×C42×C113C2311yescharacteristic
61C4⋊C8×C113—22no—
62C4⋊C8×C113—22no—
63C4⋊C8×C113—21no—
64C4⋊C8×C113—21no—
65C4⋊C8×C113—21no—
66C4⋊C8×C113—21no—
67C4⋊C8×C113—21no—
68#103×C113—21no—
69#103×C113—21no—
70#102×C113—21no—
71#102×C113—21no—
72C22⋊C8×C113—21no—
73C22⋊C8×C113—21no—
74C22⋊C8×C113D411yescharacteristic
75C22⋊C8×C113D411yescharacteristic
76#97×C113—22no—
77#97×C113—21no—
78#97×C113—21no—
79#97×C113D412yes—
80C4×C8×C113—22no—
81C4×C8×C113—21no—
82C4×C8×C113—21no—
83C24×C113—21no—
84C2×Q8×C113—21no—
85C2×Q8×C113—22no—
86C2×Q8×C113—21no—
87C2×Q8×C113—21no—
88C2×Q8×C113—41no—
89C2×Q8×C113—41no—
90C2×Q8×C113—41no—
91C2×Q8×C113C22⋊C411yescharacteristic
92C2×Q8×C113C22⋊C411yescharacteristic
93C2×D4×C113—21no—
94C2×D4×C113—21no—
95C2×D4×C113—41no—
96C2×D4×C113—41no—
97C22×C4×C113—21no—
98C22×C4×C113—21no—
99C22×C4×C113—21no—
100C22×C4×C113C22×C411yescharacteristic
101C22×C4×C113C2×D411yescharacteristic
102C22×C4×C113#4111yescharacteristic
103Q16×C113—42no—
104Q16×C113—42no—
105SD16×C113—42no—
106SD16×C113—42no—
107M16×C113—22no—
108M16×C113—41no—
109C2×C8×C113—21no—
110C2×C8×C113—21no—
111C2×C8×C113—21no—
112C2×C8×C113—21no—
113C2×C8×C113—22no—
114C2×C8×C113—41no—
115C2×C8×C113—41no—
116C2×C8×C113—41no—
117C2×C8×C113—41no—
118C4⋊C4×C113—21no—
119C4⋊C4×C113—21no—
120C4⋊C4×C113—21no—
121C4⋊C4×C113—21no—
122C4⋊C4×C113—21no—
123C4⋊C4×C113C22⋊C411yescharacteristic
124C4⋊C4×C113C22⋊C411yescharacteristic
125C22⋊C4×C113—41no—
126C22⋊C4×C113—41no—
127C22⋊C4×C113—41no—
128C22⋊C4×C113—41no—
129C42×C113—21no—
130C42×C113—21no—
131C42×C113—21no—
132C42×C113—21no—
133C42×C113C2×D411yescharacteristic
134C42×C113C2×D411yescharacteristic
135C42×C113C2×D411yescharacteristic
136C42×C113#4111yescharacteristic
137C23×C113—41no—
138C23×C113—41no—
139C23×C113—41no—
140C23×C113—81no—
141C23×C113—81no—
142C23×C113C4×D411yescharacteristic
143Q8×C113—21no—
144Q8×C113—21no—
145Q8×C113—21no—
146Q8×C113—42no—
147Q8×C113—41no—
148Q8×C113—41no—
149Q8×C113—81no—
150Q8×C113#10012yes—
151D4×C113—41no—
152D4×C113—41no—
153D4×C113—81no—
154C2×C4×C113—21no—
155C2×C4×C113—21no—
156C2×C4×C113—21no—
157C2×C4×C113—21no—
158C2×C4×C113—21no—
159C2×C4×C113—21no—
160C2×C4×C113—21no—
161C2×C4×C113—21no—
162C2×C4×C113—41no—
163C2×C4×C113—42no—
164C2×C4×C113—41no—
165C2×C4×C113—41no—
166C2×C4×C113—41no—
167C2×C4×C113—81no—
168C2×C4×C113C2×C22⋊C411yescharacteristic
169C2×C4×C113C4×D411yescharacteristic
170C2×C4×C113#12011yescharacteristic
171C2×C4×C113#12111yescharacteristic
172C2×C4×C113#12111yescharacteristic
173C2×C4×C113#12311yescharacteristic
174C8×C113—41no—
175C8×C113—41no—
176C8×C113—42no—
177C8×C113—42no—
178C8×C113—41no—
179C8×C113—41no—
180C8×C113—81no—
181C22×C113—21no—
182C22×C113—21no—
183C22×C113—81no—
184C22×C113—81no—
185C22×C113—81no—
186C22×C113—161no—
187C22×C113—161no—
188C22×C113#38611yescharacteristic
189C22×C113#44311yescharacteristic
190C22×C113#44411yescharacteristic
191C4×C113—21no—
192C4×C113—21no—
193C4×C113—21no—
194C4×C113—22no—
195C4×C113—21no—
196C4×C113—21no—
197C4×C113—41no—
198C4×C113—41no—
199C4×C113—41no—
200C4×C113—81no—
201C4×C113C2×#10011yescharacteristic
202C4×C113#41311yescharacteristic
203#9244C11311yesmaximal, characteristic, direct product factor, Sylow
204C2×C113—21no—
205C2×C113—21no—
206C2×C113—161no—
207C2×C113#187611yescharacteristic
208C2×C113#190011yescharacteristic
209C2×C113#190511yescharacteristic
210C2×#464C2×C11311yescharacteristic
211#2984C2×C11311yescharacteristic, complemented
212#1527C2×C11311yescharacteristic
213#1491C2×C11311yescharacteristic, complemented
214#1469C2×C11311yescharacteristic
215#1290C2×C11311yescharacteristic, complemented
216#1283C2×C11311yescharacteristic, complemented
217C113#924411yescharacteristic, direct product factor, Sylow
218C22×Q16C4×C11311yescharacteristic
219C22×SD16C4×C11311yescharacteristic
220C2×#124C22×C11311yescharacteristic
221C2×C4×Q8C22×C11311yescharacteristic
222#464—21no—
223#464—21no—
224#464—21no—
225#464—21no—
226#446—21no—
227#446—22no—
228C8×Q8—21no—
229#432—21no—
230#432C22×C11311yescharacteristic
231#432C22×C11311yescharacteristic
232#431—21no—
233#431C22×C11311yescharacteristic
234C2×C4⋊C8C22×C11311yescharacteristic
235C2×#103C4×C11311yescharacteristic
236C2×#102C4×C11311yescharacteristic
237C4×M16C22×C11311yescharacteristic
238#329—22no—
239Q8⋊C8—21no—
240Q8⋊C8—21no—
241#323—21no—
242#323—21no—
243C22×Q8C2×C4×C11311yescharacteristic
244C22×Q8C2×C4×C11311yescharacteristic
245C22×D4C2×C4×C11311yescharacteristic
246C2×Q16—21no—
247C2×Q16—21no—
248C2×Q16—42no—
249C2×SD16—21no—
250C2×SD16—21no—
251C2×SD16—42no—
252C2×M16—21no—
253C22×C8C2×C4×C11311yescharacteristic
254C22×C8C2×C4×C11311yescharacteristic
255#124—21no—
256#124—21no—
257#124—21no—
258#124—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8D4×C11311yescharacteristic
262C4×Q8D4×C11311yescharacteristic
263C4×Q8D4×C11311yescharacteristic
264C4×Q8D4×C11311yescharacteristic
265C2×C4⋊C4—21no—
266C2×C4⋊C4C2×C4×C11311yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C42—21no—
270C2×C42C23×C11311yescharacteristic
271C4⋊C8—22no—
272C4⋊C8—22no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278#103—21no—
279#103—21no—
280#102—21no—
281#102—21no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8D4×C11311yescharacteristic
285C22⋊C8D4×C11311yescharacteristic
286#97—22no—
287#97—21no—
288#97—21no—
289#97D4×C11312yes—
290C4×C8—22no—
291C4×C8—21no—
292C4×C8—21no—
293C24—21no—
294C2×Q8—21no—
295C2×Q8—22no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8C22⋊C4×C11311yescharacteristic
302C2×Q8C22⋊C4×C11311yescharacteristic
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—41no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4C22×C4×C11311yescharacteristic
311C22×C4C2×D4×C11311yescharacteristic
312C22×C4#41×C11311yescharacteristic
313Q16—42no—
314Q16—42no—
315SD16—42no—
316SD16—42no—
317M16—22no—
318M16—41no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—21no—
323C2×C8—22no—
324C2×C8—41no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4C22⋊C4×C11311yescharacteristic
334C4⋊C4C22⋊C4×C11311yescharacteristic
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C42—21no—
340C42—21no—
341C42—21no—
342C42—21no—
343C42C2×D4×C11311yescharacteristic
344C42C2×D4×C11311yescharacteristic
345C42C2×D4×C11311yescharacteristic
346C42#41×C11311yescharacteristic
347C23—41no—
348C23—41no—
349C23—41no—
350C23—81no—
351C23—81no—
352C23C4×D4×C11311yescharacteristic
353Q8—21no—
354Q8—21no—
355Q8—21no—
356Q8—42no—
357Q8—41no—
358Q8—41no—
359Q8—81no—
360Q8#100×C11312yes—
361D4—41no—
362D4—41no—
363D4—81no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—81no—
378C2×C4C2×C22⋊C4×C11311yescharacteristic
379C2×C4C4×D4×C11311yescharacteristic
380C2×C4#120×C11311yescharacteristic
381C2×C4#121×C11311yescharacteristic
382C2×C4#121×C11311yescharacteristic
383C2×C4#123×C11311yescharacteristic
384C8—41no—
385C8—41no—
386C8—42no—
387C8—42no—
388C8—41no—
389C8—41no—
390C8—81no—
391C22—21no—
392C22—21no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—161no—
397C22—161no—
398C22#386×C11311yescharacteristic
399C22#443×C11311yescharacteristic
400C22#444×C11311yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—22no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—81no—
411C4C2×#100×C11311yescharacteristic
412C4#413×C11311yescharacteristic
413C2—21no—
414C2—21no—
415C2—161no—
416C2C113×#187611yescharacteristic
417C2C113×#190011yescharacteristic
418C2C113×#190511yescharacteristic
subgroupG/H
center, socleC22×C113#386
commutatorC22×C4C22×C4×C113
Frattini, cosocleC2×C42C23×C113
prime radicalC22×D4×C113C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#2984C2semidirect
4. C113×#1491C2semidirect
6. C113×#1290C2semidirect
7. C113×#1283C2semidirect
203. #9244C113direct (N × H)
211. #2984C2×C113semidirect
213. #1491C2×C113semidirect
215. #1290C2×C113semidirect
216. #1283C2×C113semidirect
217. C113#9244direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#464×C1132
C113×#29842
C113×#15272
C113×#14912
C113×#14692
C113×#12902
C113×#12832
#9244113