Finite Group Databasebeta

← C113×#8994 #43277014

Subgroups — C113×#8994 #43277014

Order 28928.

430 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3076C211yesmaximal, characteristic
2C113×#2925C211yesmaximal, characteristic
3C113×#1493C211yesmaximal, characteristic, complemented
4C113×#1481C211yesmaximal, characteristic, complemented
5C113×#1476C211yesmaximal, characteristic
6C113×#1301C211yesmaximal, characteristic, complemented
7C113×#1277C211yesmaximal, characteristic, complemented
8#533×C113C2211yescharacteristic
9C4×#41×C113C2211yescharacteristic
10#479×C113—21no—
11#478×C113—21no—
12#477×C113C411yescharacteristic
13#476×C113C411yescharacteristic
14#475×C113C411yescharacteristic
15#474×C113C411yescharacteristic
16#433×C113—22no—
17#432×C113—21no—
18#431×C113—21no—
19#431×C113C2211yescharacteristic
20#427×C113—21no—
21#423×C113C2211yescharacteristic
22C2×C4⋊C8×C113C2211yescharacteristic
23C2×C4⋊C8×C113C2211yescharacteristic
24#416×C113—21no—
25#408×C113—21no—
26#405×C113—21no—
27C2×C4×C8×C113C2211yescharacteristic
28Q8⋊C8×C113—21no—
29Q8⋊C8×C113—21no—
30Q8⋊C8×C113—21no—
31Q8⋊C8×C113—22no—
32D4⋊C8×C113—21no—
33C2×#41×C113D411yescharacteristic
34C2×M16×C113—21no—
35C22×C8×C113—21no—
36C22×C8×C113—21no—
37C22×C8×C113—21no—
38C4⋊Q8×C113C2×C411yescharacteristic
39C4⋊Q8×C113C2×C411yescharacteristic
40#125×C113—21no—
41C22⋊Q8×C113—21no—
42C22⋊Q8×C113—21no—
43C4×Q8×C113—21no—
44C4×Q8×C113—21no—
45C4×Q8×C113C2×C411yescharacteristic
46C4×Q8×C113D411yescharacteristic
47C4×D4×C113—21no—
48C4×D4×C113—21no—
49C4×D4×C113C2×C411yescharacteristic
50C4×D4×C113D411yescharacteristic
51#117×C113—21no—
52#117×C113—21no—
53#117×C113D411yescharacteristic
54C2×C42×C113—21no—
55C2×C42×C113C2311yescharacteristic
56#107×C113—21no—
57#107×C113—21no—
58#106×C113—21no—
59#106×C113—21no—
60C4⋊C8×C113—21no—
61C4⋊C8×C113—21no—
62C4⋊C8×C113—21no—
63C4⋊C8×C113—21no—
64C4⋊C8×C113C2×C411yescharacteristic
65C4⋊C8×C113C2×C411yescharacteristic
66C4⋊C8×C113D411yescharacteristic
67C4⋊C8×C113D411yescharacteristic
68C4⋊C8×C113D412yes—
69#103×C113—21no—
70#103×C113—21no—
71#102×C113—21no—
72#102×C113—21no—
73C22⋊C8×C113—22no—
74C22⋊C8×C113—22no—
75C22⋊C8×C113—21no—
76#97×C113—22no—
77C4×C8×C113—22no—
78C4×C8×C113—21no—
79C4×C8×C113—21no—
80C4×C8×C113—21no—
81#41×C113—21no—
82#41×C113—21no—
83#41×C113—21no—
84#41×C113—21no—
85C2×Q8×C113—21no—
86C2×Q8×C113—21no—
87C2×Q8×C113C22⋊C411yescharacteristic
88C2×D4×C113—21no—
89C2×D4×C113C22⋊C411yescharacteristic
90C22×C4×C113—21no—
91C22×C4×C113—21no—
92C22×C4×C113—21no—
93C22×C4×C113C2×D411yescharacteristic
94C22×C4×C113#4111yescharacteristic
95C22×C4×C113#4111yescharacteristic
96M16×C113—41no—
97M16×C113—41no—
98C2×C8×C113—22no—
99C2×C8×C113—21no—
100C2×C8×C113—21no—
101C2×C8×C113—21no—
102C2×C8×C113—22no—
103C2×C8×C113—21no—
104C2×C8×C113—41no—
105C2×C8×C113—41no—
106C2×C8×C113—41no—
107C2×C8×C113—41no—
108C2×C8×C113—41no—
109C2×C8×C113—41no—
110C2×C8×C113—41no—
111C4⋊C4×C113—21no—
112C4⋊C4×C113—21no—
113C4⋊C4×C113—21no—
114C4⋊C4×C113—21no—
115C4⋊C4×C113—21no—
116C4⋊C4×C113—21no—
117C4⋊C4×C113—41no—
118C4⋊C4×C113—41no—
119C4⋊C4×C113C22⋊C411yescharacteristic
120C4⋊C4×C113C22⋊C411yescharacteristic
121C22⋊C4×C113—21no—
122C22⋊C4×C113—21no—
123C22⋊C4×C113—21no—
124C22⋊C4×C113—41no—
125C42×C113—21no—
126C42×C113—21no—
127C42×C113—21no—
128C42×C113—41no—
129C42×C113C22×C411yescharacteristic
130C42×C113C2×D411yescharacteristic
131C42×C113C2×D411yescharacteristic
132C42×C113C2×D411yescharacteristic
133C23×C113—21no—
134C23×C113#12311yescharacteristic
135Q8×C113—21no—
136Q8×C113—21no—
137Q8×C113—42no—
138Q8×C113—41no—
139Q8×C113—41no—
140D4×C113—21no—
141D4×C113—21no—
142D4×C113—41no—
143D4×C113—41no—
144C2×C4×C113—21no—
145C2×C4×C113—21no—
146C2×C4×C113—21no—
147C2×C4×C113—21no—
148C2×C4×C113—21no—
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—81no—
157C2×C4×C113C2×C22⋊C411yescharacteristic
158C2×C4×C113C4×D411yescharacteristic
159C2×C4×C113C4×D411yescharacteristic
160C2×C4×C113#12011yescharacteristic
161C2×C4×C113#12111yescharacteristic
162C2×C4×C113#12111yescharacteristic
163C2×C4×C113#13511yescharacteristic
164C2×C4×C113#13511yescharacteristic
165C2×C4×C113#13711yescharacteristic
166C2×C4×C113#13711yescharacteristic
167C8×C113—42no—
168C8×C113—41no—
169C8×C113—41no—
170C8×C113—41no—
171C8×C113—41no—
172C8×C113—42no—
173C8×C113—81no—
174C22×C113—21no—
175C22×C113—21no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113—41no—
179C22×C113#38611yescharacteristic
180C22×C113#48511yescharacteristic
181C22×C113#48511yescharacteristic
182C4×C113—21no—
183C4×C113—21no—
184C4×C113—21no—
185C4×C113—41no—
186C4×C113—41no—
187C4×C113—41no—
188C4×C113—81no—
189C4×C113—81no—
190C4×C113#41611yescharacteristic
191C4×C113#41911yescharacteristic
192C4×C113#44311yescharacteristic
193C4×C113#44411yescharacteristic
194C4×C113#45211yescharacteristic
195C4×C113#45211yescharacteristic
196#8994C11311yesmaximal, characteristic, direct product factor, Sylow
197C2×C113—21no—
198C2×C113—21no—
199C2×C113—81no—
200C2×C113#187311yescharacteristic
201C2×C113#187611yescharacteristic
202C2×C113#188111yescharacteristic
203#3076C2×C11311yescharacteristic
204#2925C2×C11311yescharacteristic
205#1493C2×C11311yescharacteristic, complemented
206#1481C2×C11311yescharacteristic, complemented
207#1476C2×C11311yescharacteristic
208#1301C2×C11311yescharacteristic, complemented
209#1277C2×C11311yescharacteristic, complemented
210C113#899411yescharacteristic, direct product factor, Sylow
211#533C22×C11311yescharacteristic
212C4×#41C22×C11311yescharacteristic
213#479—21no—
214#478—21no—
215#477C4×C11311yescharacteristic
216#476C4×C11311yescharacteristic
217#475C4×C11311yescharacteristic
218#474C4×C11311yescharacteristic
219#433—22no—
220#432—21no—
221#431—21no—
222#431C22×C11311yescharacteristic
223#427—21no—
224#423C22×C11311yescharacteristic
225C2×C4⋊C8C22×C11311yescharacteristic
226C2×C4⋊C8C22×C11311yescharacteristic
227#416—21no—
228#408—21no—
229#405—21no—
230C2×C4×C8C22×C11311yescharacteristic
231Q8⋊C8—21no—
232Q8⋊C8—21no—
233Q8⋊C8—21no—
234Q8⋊C8—22no—
235D4⋊C8—21no—
236C2×#41D4×C11311yescharacteristic
237C2×M16—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C4⋊Q8C2×C4×C11311yescharacteristic
242C4⋊Q8C2×C4×C11311yescharacteristic
243#125—21no—
244C22⋊Q8—21no—
245C22⋊Q8—21no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8C2×C4×C11311yescharacteristic
249C4×Q8D4×C11311yescharacteristic
250C4×D4—21no—
251C4×D4—21no—
252C4×D4C2×C4×C11311yescharacteristic
253C4×D4D4×C11311yescharacteristic
254#117—21no—
255#117—21no—
256#117D4×C11311yescharacteristic
257C2×C42—21no—
258C2×C42C23×C11311yescharacteristic
259#107—21no—
260#107—21no—
261#106—21no—
262#106—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8C2×C4×C11311yescharacteristic
268C4⋊C8C2×C4×C11311yescharacteristic
269C4⋊C8D4×C11311yescharacteristic
270C4⋊C8D4×C11311yescharacteristic
271C4⋊C8D4×C11312yes—
272#103—21no—
273#103—21no—
274#102—21no—
275#102—21no—
276C22⋊C8—22no—
277C22⋊C8—22no—
278C22⋊C8—21no—
279#97—22no—
280C4×C8—22no—
281C4×C8—21no—
282C4×C8—21no—
283C4×C8—21no—
284#41—21no—
285#41—21no—
286#41—21no—
287#41—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8C22⋊C4×C11311yescharacteristic
291C2×D4—21no—
292C2×D4C22⋊C4×C11311yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4C2×D4×C11311yescharacteristic
297C22×C4#41×C11311yescharacteristic
298C22×C4#41×C11311yescharacteristic
299M16—41no—
300M16—41no—
301C2×C8—22no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—22no—
306C2×C8—21no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4C22⋊C4×C11311yescharacteristic
323C4⋊C4C22⋊C4×C11311yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—41no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—41no—
332C42C22×C4×C11311yescharacteristic
333C42C2×D4×C11311yescharacteristic
334C42C2×D4×C11311yescharacteristic
335C42C2×D4×C11311yescharacteristic
336C23—21no—
337C23#123×C11311yescharacteristic
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—41no—
342Q8—41no—
343D4—21no—
344D4—21no—
345D4—41no—
346D4—41no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4C2×C22⋊C4×C11311yescharacteristic
361C2×C4C4×D4×C11311yescharacteristic
362C2×C4C4×D4×C11311yescharacteristic
363C2×C4#120×C11311yescharacteristic
364C2×C4#121×C11311yescharacteristic
365C2×C4#121×C11311yescharacteristic
366C2×C4#135×C11311yescharacteristic
367C2×C4#135×C11311yescharacteristic
368C2×C4#137×C11311yescharacteristic
369C2×C4#137×C11311yescharacteristic
370C8—42no—
371C8—41no—
372C8—41no—
373C8—41no—
374C8—41no—
375C8—42no—
376C8—81no—
377C22—21no—
378C22—21no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22#386×C11311yescharacteristic
383C22#485×C11311yescharacteristic
384C22#485×C11311yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—81no—
392C4—81no—
393C4#416×C11311yescharacteristic
394C4#419×C11311yescharacteristic
395C4#443×C11311yescharacteristic
396C4#444×C11311yescharacteristic
397C4#452×C11311yescharacteristic
398C4#452×C11311yescharacteristic
399C2—21no—
400C2—21no—
401C2—81no—
402C2C113×#187311yescharacteristic
403C2C113×#187611yescharacteristic
404C2C113×#188111yescharacteristic
subgroupG/H
centerC2×C4×C113#120
commutatorC42C22×C4×C113
Frattini, cosocleC2×C42C23×C113
socleC22×C113#386
prime radicalC2×#41×C113D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
3. C113×#1493C2semidirect
4. C113×#1481C2semidirect
6. C113×#1301C2semidirect
7. C113×#1277C2semidirect
196. #8994C113direct (N × H)
205. #1493C2×C113semidirect
206. #1481C2×C113semidirect
208. #1301C2×C113semidirect
209. #1277C2×C113semidirect
210. C113#8994direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#30762
C113×#29252
C113×#14932
C113×#14812
C113×#14762
C113×#13012
C113×#12772
#8994113