Finite Group Databasebeta

← C113×#9035 #43277055

Subgroups — C113×#9035 #43277055

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
1C113×#2905C211yesmaximal, characteristic, complemented
2C113×#2392C211yesmaximal, characteristic
3C113×#1486C212yesmaximal, complemented
4C113×#1458C211yesmaximal, characteristic, complemented
5C113×#1303C212yesmaximal, complemented
6C22×M16×C113—21no—
7C2×C4×D4×C113—21no—
8C2×C4×D4×C113C2211yescharacteristic
9C2×#117×C113C2211yescharacteristic
10#431×C113C2212yes—
11#424×C113—24no—
12#423×C113—21no—
13#423×C113C2212yes—
14#398×C113C411yescharacteristic
15#397×C113C411yescharacteristic
16#396×C113—21no—
17#394×C113—21no—
18#394×C113C411yescharacteristic
19#392×C113C411yescharacteristic
20C4×C4⋊C4×C113C2211yescharacteristic
21C4×C22⋊C4×C113—21no—
22D4⋊C8×C113—24no—
23#324×C113—21no—
24#323×C113—21no—
25C22×D4×C113—21no—
26C22×D4×C113C2×C411yescharacteristic
27C23×C4×C113—21no—
28C23×C4×C113D411yescharacteristic
29C2×M16×C113—22no—
30C2×M16×C113—22no—
31C2×M16×C113—42no—
32C2×M16×C113—42no—
33C22×C8×C113—22no—
34C4×D4×C113—22no—
35C4×D4×C113—22no—
36C4×D4×C113—42no—
37C4×D4×C113—42no—
38#117×C113—22no—
39#117×C113—22no—
40C2×C4⋊C4×C113—21no—
41C2×C4⋊C4×C113—21no—
42C2×C4⋊C4×C113C2×C411yescharacteristic
43C2×C4⋊C4×C113C2×C411yescharacteristic
44C2×C4⋊C4×C113D411yescharacteristic
45C2×C22⋊C4×C113—21no—
46C2×C22⋊C4×C113—21no—
47C2×C22⋊C4×C113—21no—
48C2×C22⋊C4×C113—21no—
49C2×C22⋊C4×C113—21no—
50C2×C22⋊C4×C113C2×C411yescharacteristic
51C2×C22⋊C4×C113D411yescharacteristic
52C2×C42×C113—21no—
53C2×C42×C113D411yescharacteristic
54C2×C42×C113C2311yescharacteristic
55C4⋊C8×C113—24no—
56C4⋊C8×C113—22no—
57C4⋊C8×C113—22no—
58C4⋊C8×C113D414yescomplemented
59C22⋊C8×C113—22no—
60C4×C8×C113—22no—
61#95×C113—21no—
62#95×C113—21no—
63#95×C113C2×C411yescharacteristic
64#95×C113C2×C411yescharacteristic
65C24×C113—21no—
66C24×C113C22⋊C411yescharacteristic
67C2×D4×C113—22no—
68C2×D4×C113—42no—
69C2×D4×C113—42no—
70C2×D4×C113—42no—
71C2×D4×C113—42no—
72C22×C4×C113—21no—
73C22×C4×C113—21no—
74C22×C4×C113—21no—
75C22×C4×C113—21no—
76C22×C4×C113—21no—
77C22×C4×C113—21no—
78C22×C4×C113—21no—
79C22×C4×C113—41no—
80C22×C4×C113—41no—
81C22×C4×C113—41no—
82C22×C4×C113—41no—
83C22×C4×C113—41no—
84C22×C4×C113—41no—
85C22×C4×C113C22⋊C411yescharacteristic
86C22×C4×C113C22⋊C411yescharacteristic
87C22×C4×C113C22⋊C411yescharacteristic
88C22×C4×C113D812yes—
89C22×C4×C113SD1612yes—
90C22×C4×C113C22×C411yescharacteristic
91C22×C4×C113C2×D411yescharacteristic
92C22×C4×C113C2×D411yescharacteristic
93M16×C113—44no—
94M16×C113—42no—
95M16×C113—42no—
96C2×C8×C113—24no—
97C2×C8×C113—44no—
98C2×C8×C113—42no—
99C4⋊C4×C113—22no—
100C4⋊C4×C113—22no—
101C4⋊C4×C113—22no—
102C4⋊C4×C113—42no—
103C4⋊C4×C113—42no—
104C22⋊C4×C113—22no—
105C22⋊C4×C113—22no—
106C22⋊C4×C113—42no—
107C22⋊C4×C113—42no—
108C22⋊C4×C113—42no—
109C22⋊C4×C113—42no—
110C22⋊C4×C113—42no—
111C42×C113—21no—
112C42×C113—21no—
113C42×C113—41no—
114C42×C113—41no—
115C42×C113C2×D412yes—
116C42×C113#4112yes—
117C23×C113—21no—
118C23×C113—21no—
119C23×C113—22no—
120C23×C113—41no—
121C23×C113—41no—
122C23×C113—41no—
123C23×C113—41no—
124C23×C113—41no—
125C23×C113—41no—
126C23×C113—41no—
127C23×C113—41no—
128C23×C113#10212yes—
129C23×C113C2×C22⋊C411yescharacteristic
130D4×C113—24no—
131D4×C113—42no—
132D4×C113—48no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—22no—
136C2×C4×C113—22no—
137C2×C4×C113—22no—
138C2×C4×C113—22no—
139C2×C4×C113—22no—
140C2×C4×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113—41no—
143C2×C4×C113—41no—
144C2×C4×C113—41no—
145C2×C4×C113—41no—
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—81no—
155C2×C4×C113—81no—
156C2×C4×C113—81no—
157C2×C4×C113—81no—
158C2×C4×C113#10212yes—
159C2×C4×C113C4×D412yes—
160C2×C4×C113#12011yescharacteristic
161C2×C4×C113#12112yes—
162C2×C4×C113#12311yescharacteristic
163C2×C4×C113C2×D811yescharacteristic
164C2×C4×C113C2×SD1611yescharacteristic
165C2×C4×C113AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C113#13711yescharacteristic
167C8×C113—44no—
168C8×C113—82no—
169C22×C113—21no—
170C22×C113—21no—
171C22×C113—22no—
172C22×C113—42no—
173C22×C113—42no—
174C22×C113—42no—
175C22×C113—41no—
176C22×C113—41no—
177C22×C113—42no—
178C22×C113—81no—
179C22×C113—81no—
180C22×C113—81no—
181C22×C113—81no—
182C22×C113—81no—
183C22×C113#38611yescharacteristic
184C22×C113C2×#10211yescharacteristic
185C22×C113#41711yescharacteristic
186C4×C113—22no—
187C4×C113—22no—
188C4×C113—22no—
189C4×C113—42no—
190C4×C113—41no—
191C4×C113—41no—
192C4×C113—81no—
193C4×C113—81no—
194C4×C113#44711yescharacteristic
195C4×C113#44811yescharacteristic
196C4×C113#48011yescharacteristic
197C4×C113#48111yescharacteristic
198#9035C11311yesmaximal, characteristic, direct product factor, Sylow
199C2×C113—21no—
200C2×C113—21no—
201C2×C113—42no—
202C2×C113—82no—
203C2×C113#187411yescharacteristic
204C2×C113#188411yescharacteristic
205C2×C113#189111yescharacteristic
206#2905C2×C11311yescharacteristic, complemented
207#2392C2×C11311yescharacteristic
208#1486C2×C11312yescomplemented
209#1458C2×C11311yescharacteristic, complemented
210#1303C2×C11312yescomplemented
211C113#903511yescharacteristic, direct product factor, Sylow
212C22×M16—21no—
213C2×C4×D4—21no—
214C2×C4×D4C22×C11311yescharacteristic
215C2×#117C22×C11311yescharacteristic
216#431C22×C11312yes—
217#424—24no—
218#423—21no—
219#423C22×C11312yes—
220#398C4×C11311yescharacteristic
221#397C4×C11311yescharacteristic
222#396—21no—
223#394—21no—
224#394C4×C11311yescharacteristic
225#392C4×C11311yescharacteristic
226C4×C4⋊C4C22×C11311yescharacteristic
227C4×C22⋊C4—21no—
228D4⋊C8—24no—
229#324—21no—
230#323—21no—
231C22×D4—21no—
232C22×D4C2×C4×C11311yescharacteristic
233C23×C4—21no—
234C23×C4D4×C11311yescharacteristic
235C2×M16—22no—
236C2×M16—22no—
237C2×M16—42no—
238C2×M16—42no—
239C22×C8—22no—
240C4×D4—22no—
241C4×D4—22no—
242C4×D4—42no—
243C4×D4—42no—
244#117—22no—
245#117—22no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C2×C4×C11311yescharacteristic
249C2×C4⋊C4C2×C4×C11311yescharacteristic
250C2×C4⋊C4D4×C11311yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4C2×C4×C11311yescharacteristic
257C2×C22⋊C4D4×C11311yescharacteristic
258C2×C42—21no—
259C2×C42D4×C11311yescharacteristic
260C2×C42C23×C11311yescharacteristic
261C4⋊C8—24no—
262C4⋊C8—22no—
263C4⋊C8—22no—
264C4⋊C8D4×C11314yescomplemented
265C22⋊C8—22no—
266C4×C8—22no—
267#95—21no—
268#95—21no—
269#95C2×C4×C11311yescharacteristic
270#95C2×C4×C11311yescharacteristic
271C24—21no—
272C24C22⋊C4×C11311yescharacteristic
273C2×D4—22no—
274C2×D4—42no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—42no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4C22⋊C4×C11311yescharacteristic
292C22×C4C22⋊C4×C11311yescharacteristic
293C22×C4C22⋊C4×C11311yescharacteristic
294C22×C4D8×C11312yes—
295C22×C4SD16×C11312yes—
296C22×C4C22×C4×C11311yescharacteristic
297C22×C4C2×D4×C11311yescharacteristic
298C22×C4C2×D4×C11311yescharacteristic
299M16—44no—
300M16—42no—
301M16—42no—
302C2×C8—24no—
303C2×C8—44no—
304C2×C8—42no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—42no—
309C4⋊C4—42no—
310C22⋊C4—22no—
311C22⋊C4—22no—
312C22⋊C4—42no—
313C22⋊C4—42no—
314C22⋊C4—42no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C42—21no—
318C42—21no—
319C42—41no—
320C42—41no—
321C42C2×D4×C11312yes—
322C42#41×C11312yes—
323C23—21no—
324C23—21no—
325C23—22no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23#102×C11312yes—
335C23C2×C22⋊C4×C11311yescharacteristic
336D4—24no—
337D4—42no—
338D4—48no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
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—81no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4#102×C11312yes—
365C2×C4C4×D4×C11312yes—
366C2×C4#120×C11311yescharacteristic
367C2×C4#121×C11312yes—
368C2×C4#123×C11311yescharacteristic
369C2×C4C2×D8×C11311yescharacteristic
370C2×C4C2×SD16×C11311yescharacteristic
371C2×C4AGL(1,ℤ/8)×C11311yescharacteristic
372C2×C4#137×C11311yescharacteristic
373C8—44no—
374C8—82no—
375C22—21no—
376C22—21no—
377C22—22no—
378C22—42no—
379C22—42no—
380C22—42no—
381C22—41no—
382C22—41no—
383C22—42no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—81no—
388C22—81no—
389C22#386×C11311yescharacteristic
390C22C2×#102×C11311yescharacteristic
391C22#417×C11311yescharacteristic
392C4—22no—
393C4—22no—
394C4—22no—
395C4—42no—
396C4—41no—
397C4—41no—
398C4—81no—
399C4—81no—
400C4#447×C11311yescharacteristic
401C4#448×C11311yescharacteristic
402C4#480×C11311yescharacteristic
403C4#481×C11311yescharacteristic
404C2—21no—
405C2—21no—
406C2—42no—
407C2—82no—
408C2C113×#187411yescharacteristic
409C2C113×#188411yescharacteristic
410C2C113×#189111yescharacteristic
subgroupG/H
centerC2×C4×C113#120
commutatorC22×C4C22×C4×C113
Frattini, cosocleC2×C42C23×C113
socleC22×C113#386
prime radical#392×C113C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#2905C2semidirect
3. C113×#1486C2semidirect
4. C113×#1458C2semidirect
5. C113×#1303C2semidirect
58. C4⋊C8×C113D4semidirect
198. #9035C113direct (N × H)
206. #2905C2×C113semidirect
208. #1486C2×C113semidirect
209. #1458C2×C113semidirect
210. #1303C2×C113semidirect
211. C113#9035direct (N × H)
264. C4⋊C8D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#29052
C113×#23922
C113×#14862
C113×#14582
C113×#13032
#9035113