Finite Group Databasebeta

← C113×#9273 #43277293

Subgroups — C113×#9273 #43277293

Order 28928.

560 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
1C113×#3205C211yesmaximal, characteristic
2C113×#2935C211yesmaximal, characteristic, complemented
3C113×#1965C211yesmaximal, characteristic, complemented
4C113×#1547C211yesmaximal, characteristic, complemented
5C2×#331×C113C211yesmaximal, characteristic, complemented
6C113×#1301C211yesmaximal, characteristic, complemented
7C113×#1283C211yesmaximal, characteristic, complemented
8C2×#131×C113—21no—
9#532×C113C2211yescharacteristic
10C2×#127×C113C2211yescharacteristic
11#493×C113—21no—
12#486×C113—21no—
13#459×C113—22no—
14#447×C113C414yes—
15#436×C113—21no—
16#435×C113—22no—
17C8×D4×C113—21no—
18#431×C113C2211yescharacteristic
19#423×C113C2211yescharacteristic
20C2×C4⋊C8×C113C2211yescharacteristic
21C2×C4⋊C8×C113C2211yescharacteristic
22C2×#100×C113—21no—
23C2×#100×C113—21no—
24#408×C113—21no—
25C4×M16×C113C2211yescharacteristic
26#332×C113—21no—
27#331×C113—21no—
28#331×C113—21no—
29#331×C113—21no—
30C2×#41×C113—21no—
31C22×D4×C113—21no—
32C22×D4×C113—21no—
33C22×D4×C113C2×C412yes—
34C2×D8×C113—24no—
35#131×C113—42no—
36#131×C113—42no—
37C2×M16×C113—22no—
38C2×M16×C113—21no—
39C2×M16×C113D411yescharacteristic
40C2×M16×C113D411yescharacteristic
41C22×C8×C113—22no—
42C22×C8×C113—21no—
43C22×C8×C113—21no—
44C4⋊Q8×C113D411yescharacteristic
45#127×C113—21no—
46#127×C113—21no—
47#127×C113—21no—
48#127×C113—21no—
49#127×C113D411yescharacteristic
50#124×C113—21no—
51#121×C113—21no—
52#121×C113C2×C412yes—
53C4×D4×C113—21no—
54C4×D4×C113D412yes—
55C2×C42×C113C2311yescharacteristic
56C4⋊C8×C113—21no—
57C4⋊C8×C113—21no—
58C4⋊C8×C113—21no—
59C4⋊C8×C113—21no—
60C4⋊C8×C113—21no—
61C4⋊C8×C113—21no—
62C4⋊C8×C113D411yescharacteristic
63C4⋊C8×C113D411yescharacteristic
64#102×C113—24no—
65#100×C113—42no—
66#100×C113—42no—
67C22⋊C8×C113—22no—
68C22⋊C8×C113—22no—
69C22⋊C8×C113C2×C412yes—
70#97×C113—21no—
71C4×C8×C113—21no—
72C4×C8×C113—21no—
73C24×C113—22no—
74#41×C113—41no—
75#41×C113—41no—
76#41×C113—41no—
77#41×C113—41no—
78C2×Q8×C113—21no—
79C2×D4×C113—22no—
80C2×D4×C113—22no—
81C2×D4×C113—22no—
82C2×D4×C113—21no—
83C2×D4×C113—21no—
84C2×D4×C113—41no—
85C2×D4×C113—41no—
86C2×D4×C113—41no—
87C2×D4×C113—41no—
88C2×D4×C113—41no—
89C2×D4×C113—41no—
90C2×D4×C113—41no—
91C2×D4×C113—41no—
92C2×D4×C113—81no—
93C2×D4×C113—81no—
94C2×D4×C113—82no—
95C2×D4×C113C22⋊C412yes—
96C22×C4×C113—22no—
97C22×C4×C113C22×C411yescharacteristic
98C22×C4×C113C2×D411yescharacteristic
99C22×C4×C113#4111yescharacteristic
100D8×C113—84no—
101M16×C113—21no—
102M16×C113—21no—
103M16×C113—21no—
104M16×C113—44no—
105M16×C113—41no—
106M16×C113—41no—
107M16×C113D812yescomplemented
108C2×C8×C113—21no—
109C2×C8×C113—22no—
110C2×C8×C113—21no—
111C2×C8×C113—21no—
112C2×C8×C113—21no—
113C2×C8×C113—44no—
114C2×C8×C113—41no—
115C2×C8×C113—41no—
116C2×C8×C113—41no—
117C2×C8×C113—41no—
118C2×C8×C113—81no—
119C4⋊C4×C113—21no—
120C4⋊C4×C113C22⋊C412yes—
121C22⋊C4×C113—22no—
122C22⋊C4×C113—22no—
123C42×C113C2×D411yescharacteristic
124C42×C113C2×D411yescharacteristic
125C42×C113C2×D411yescharacteristic
126C42×C113#4111yescharacteristic
127C23×C113—22no—
128C23×C113—42no—
129C23×C113—42no—
130C23×C113—42no—
131C23×C113—82no—
132C23×C113—82no—
133C23×C113C4×D411yescharacteristic
134Q8×C113—41no—
135Q8×C113—41no—
136D4×C113—42no—
137D4×C113—44no—
138D4×C113—42no—
139D4×C113—42no—
140D4×C113—41no—
141D4×C113—41no—
142D4×C113—41no—
143D4×C113—41no—
144D4×C113—82no—
145D4×C113—82no—
146D4×C113—81no—
147D4×C113—81no—
148D4×C113—81no—
149D4×C113—81no—
150D4×C113—81no—
151D4×C113—81no—
152C2×C4×C113—21no—
153C2×C4×C113—21no—
154C2×C4×C113—22no—
155C2×C4×C113—41no—
156C2×C4×C113—42no—
157C2×C4×C113—42no—
158C2×C4×C113C2×C22⋊C411yescharacteristic
159C2×C4×C113C4×D411yescharacteristic
160C2×C4×C113#12011yescharacteristic
161C2×C4×C113#12111yescharacteristic
162C2×C4×C113#12111yescharacteristic
163C2×C4×C113#12311yescharacteristic
164C2×C4×C113C2×D811yescharacteristic
165C2×C4×C113#13511yescharacteristic
166C2×C4×C113AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C113AGL(1,ℤ/8)11yescharacteristic
168C8×C113—22no—
169C8×C113—42no—
170C8×C113—41no—
171C8×C113—41no—
172C8×C113—41no—
173C8×C113—81no—
174C8×C113—81no—
175C22×C113—21no—
176C22×C113—21no—
177C22×C113—42no—
178C22×C113—42no—
179C22×C113—42no—
180C22×C113—82no—
181C22×C113—82no—
182C22×C113—82no—
183C22×C113—162no—
184C22×C113—162no—
185C22×C113#38611yescharacteristic
186C22×C113C4×D811yescharacteristic
187C22×C113#44211yescharacteristic
188C4×C113—21no—
189C4×C113—21no—
190C4×C113—21no—
191C4×C113—42no—
192C4×C113#44711yescharacteristic
193C4×C113#44911yescharacteristic
194C4×C113#45911yescharacteristic
195C4×C113#46311yescharacteristic
196C4×C113#47111yescharacteristic
197C4×C113#47211yescharacteristic
198#9273C11311yesmaximal, characteristic, direct product factor, Sylow
199C2×C113—21no—
200C2×C113—21no—
201C2×C113—82no—
202C2×C113—162no—
203C2×C113#187911yescharacteristic
204C2×C113#190711yescharacteristic
205C2×C113#191411yescharacteristic
206#3205C2×C11311yescharacteristic
207#2935C2×C11311yescharacteristic, complemented
208#1965C2×C11311yescharacteristic, complemented
209#1547C2×C11311yescharacteristic, complemented
210C2×#331C2×C11311yescharacteristic, complemented
211#1301C2×C11311yescharacteristic, complemented
212#1283C2×C11311yescharacteristic, complemented
213C113#927311yescharacteristic, direct product factor, Sylow
214C2×#131—21no—
215#532C22×C11311yescharacteristic
216C2×#127C22×C11311yescharacteristic
217#493—21no—
218#486—21no—
219#459—22no—
220#447C4×C11314yes—
221#436—21no—
222#435—22no—
223C8×D4—21no—
224#431C22×C11311yescharacteristic
225#423C22×C11311yescharacteristic
226C2×C4⋊C8C22×C11311yescharacteristic
227C2×C4⋊C8C22×C11311yescharacteristic
228C2×#100—21no—
229C2×#100—21no—
230#408—21no—
231C4×M16C22×C11311yescharacteristic
232#332—21no—
233#331—21no—
234#331—21no—
235#331—21no—
236C2×#41—21no—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4C2×C4×C11312yes—
240C2×D8—24no—
241#131—42no—
242#131—42no—
243C2×M16—22no—
244C2×M16—21no—
245C2×M16D4×C11311yescharacteristic
246C2×M16D4×C11311yescharacteristic
247C22×C8—22no—
248C22×C8—21no—
249C22×C8—21no—
250C4⋊Q8D4×C11311yescharacteristic
251#127—21no—
252#127—21no—
253#127—21no—
254#127—21no—
255#127D4×C11311yescharacteristic
256#124—21no—
257#121—21no—
258#121C2×C4×C11312yes—
259C4×D4—21no—
260C4×D4D4×C11312yes—
261C2×C42C23×C11311yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8D4×C11311yescharacteristic
269C4⋊C8D4×C11311yescharacteristic
270#102—24no—
271#100—42no—
272#100—42no—
273C22⋊C8—22no—
274C22⋊C8—22no—
275C22⋊C8C2×C4×C11312yes—
276#97—21no—
277C4×C8—21no—
278C4×C8—21no—
279C24—22no—
280#41—41no—
281#41—41no—
282#41—41no—
283#41—41no—
284C2×Q8—21no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—81no—
299C2×D4—81no—
300C2×D4—82no—
301C2×D4C22⋊C4×C11312yes—
302C22×C4—22no—
303C22×C4C22×C4×C11311yescharacteristic
304C22×C4C2×D4×C11311yescharacteristic
305C22×C4#41×C11311yescharacteristic
306D8—84no—
307M16—21no—
308M16—21no—
309M16—21no—
310M16—44no—
311M16—41no—
312M16—41no—
313M16D8×C11312yescomplemented
314C2×C8—21no—
315C2×C8—22no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—44no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—81no—
325C4⋊C4—21no—
326C4⋊C4C22⋊C4×C11312yes—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C42C2×D4×C11311yescharacteristic
330C42C2×D4×C11311yescharacteristic
331C42C2×D4×C11311yescharacteristic
332C42#41×C11311yescharacteristic
333C23—22no—
334C23—42no—
335C23—42no—
336C23—42no—
337C23—82no—
338C23—82no—
339C23C4×D4×C11311yescharacteristic
340Q8—41no—
341Q8—41no—
342D4—42no—
343D4—44no—
344D4—42no—
345D4—42no—
346D4—41no—
347D4—41no—
348D4—41no—
349D4—41no—
350D4—82no—
351D4—82no—
352D4—81no—
353D4—81no—
354D4—81no—
355D4—81no—
356D4—81no—
357D4—81no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4C2×C22⋊C4×C11311yescharacteristic
365C2×C4C4×D4×C11311yescharacteristic
366C2×C4#120×C11311yescharacteristic
367C2×C4#121×C11311yescharacteristic
368C2×C4#121×C11311yescharacteristic
369C2×C4#123×C11311yescharacteristic
370C2×C4C2×D8×C11311yescharacteristic
371C2×C4#135×C11311yescharacteristic
372C2×C4AGL(1,ℤ/8)×C11311yescharacteristic
373C2×C4AGL(1,ℤ/8)×C11311yescharacteristic
374C8—22no—
375C8—42no—
376C8—41no—
377C8—41no—
378C8—41no—
379C8—81no—
380C8—81no—
381C22—21no—
382C22—21no—
383C22—42no—
384C22—42no—
385C22—42no—
386C22—82no—
387C22—82no—
388C22—82no—
389C22—162no—
390C22—162no—
391C22#386×C11311yescharacteristic
392C22C4×D8×C11311yescharacteristic
393C22#442×C11311yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—42no—
398C4#447×C11311yescharacteristic
399C4#449×C11311yescharacteristic
400C4#459×C11311yescharacteristic
401C4#463×C11311yescharacteristic
402C4#471×C11311yescharacteristic
403C4#472×C11311yescharacteristic
404C2—21no—
405C2—21no—
406C2—82no—
407C2—162no—
408C2C113×#187911yescharacteristic
409C2C113×#190711yescharacteristic
410C2C113×#191411yescharacteristic
subgroupG/H
center, socleC22×C113#386
commutatorC22×C4C22×C4×C113
Frattini, cosocleC2×C42C23×C113
prime radicalC113×#3205C2
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×#2935C2semidirect
3. C113×#1965C2semidirect
4. C113×#1547C2semidirect
5. C2×#331×C113C2semidirect
6. C113×#1301C2semidirect
7. C113×#1283C2semidirect
107. M16×C113D8semidirect
198. #9273C113direct (N × H)
207. #2935C2×C113semidirect
208. #1965C2×C113semidirect
209. #1547C2×C113semidirect
210. C2×#331C2×C113semidirect
211. #1301C2×C113semidirect
212. #1283C2×C113semidirect
213. C113#9273direct (N × H)
313. M16D8×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#32052
C113×#29352
C113×#19652
C113×#15472
C2×#331×C1132
C113×#13012
C113×#12832
#9273113