Finite Group Databasebeta

← C113×#21280 #43289300

Subgroups — C113×#21280 #43289300

Order 28928.

814 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×SD16×C113C211yesmaximal, characteristic
2C113×#2320C211yesmaximal, characteristic, complemented
3C113×#2319C211yesmaximal, characteristic
4C113×#1968C212yesmaximal
5C113×#1941C212yesmaximal, complemented
6C113×#1936C212yesmaximal
7C113×#1935C212yesmaximal, complemented
8C4×#106×C113C211yesmaximal, characteristic, complemented
9C113×#1763C211yesmaximal, characteristic, complemented
10C113×#1762C211yesmaximal, characteristic
11C113×#1726C211yesmaximal, characteristic, complemented
12C22×SD16×C113C2211yescharacteristic
13C2×C4×Q8×C113C2211yescharacteristic
14C2×C4×D4×C113C2211yescharacteristic
15C4×SD16×C113C418yescomplemented
16C2×#106×C113C2212yes—
17C2×#106×C113C2211yescharacteristic
18C2×#103×C113C2212yes—
19C2×#103×C113C2211yescharacteristic
20C2×#102×C113C2212yes—
21C2×#102×C113C2211yescharacteristic
22C2×#97×C113C2212yes—
23C2×#97×C113C2211yescharacteristic
24C2×C4×C8×C113C2212yes—
25C2×C4×C8×C113C2211yescharacteristic
26#391×C113C2212yes—
27#390×C113C2212yes—
28#389×C113C2212yes—
29#389×C113C2212yes—
30#388×C113—22no—
31#387×C113—22no—
32#383×C113—21no—
33#382×C113—21no—
34#381×C113—21no—
35#380×C113—21no—
36C4×C4⋊C4×C113C2211yescharacteristic
37C4×C4⋊C4×C113C2211yescharacteristic
38#376×C113C2211yescharacteristic
39#340×C113C2212yes—
40#340×C113C2212yes—
41#340×C113C2212yes—
42C22×Q8×C113C2311yescharacteristic
43C22×D4×C113C2311yescharacteristic
44C23×C4×C113—21no—
45C2×SD16×C113—24no—
46C2×SD16×C113C2×C414yes—
47C22×C8×C113C2311yescharacteristic
48C22×C8×C113C2312yes—
49C22×C8×C113C2311yescharacteristic
50C4×Q8×C113—22no—
51C4×Q8×C113C2×C414yes—
52C4×D4×C113—22no—
53C4×D4×C113C2×C414yes—
54C2×C4⋊C4×C113—21no—
55C2×C4⋊C4×C113—22no—
56C2×C4⋊C4×C113—22no—
57C2×C4⋊C4×C113C2312yes—
58C2×C4⋊C4×C113C2312yes—
59C2×C4⋊C4×C113C2311yescharacteristic
60C2×C4⋊C4×C113C2311yescharacteristic
61C2×C22⋊C4×C113—21no—
62C2×C22⋊C4×C113—22no—
63C2×C22⋊C4×C113—22no—
64C2×C42×C113—21no—
65C2×C42×C113—21no—
66C2×C42×C113—21no—
67C2×C42×C113C2312yes—
68C2×C42×C113C2311yescharacteristic
69#106×C113—24no—
70#106×C113C2×C414yes—
71#103×C113—24no—
72#103×C113C2×C414yes—
73#102×C113—24no—
74#102×C113C2×C414yes—
75#97×C113—24no—
76#97×C113—22no—
77C4×C8×C113—24no—
78C4×C8×C113C2×C414yes—
79#95×C113—21no—
80#95×C113—21no—
81#95×C113—22no—
82#95×C113—22no—
83#95×C113—22no—
84#95×C113—22no—
85#95×C113D411yescharacteristic
86#95×C113D411yescharacteristic
87#95×C113D412yes—
88C24×C113—21no—
89C2×Q8×C113—21no—
90C2×Q8×C113—22no—
91C2×Q8×C113—22no—
92C2×Q8×C113C22×C412yes—
93C2×D4×C113—22no—
94C2×D4×C113—22no—
95C2×D4×C113—21no—
96C2×D4×C113C22×C412yes—
97C22×C4×C113—21no—
98C22×C4×C113—21no—
99C22×C4×C113—21no—
100C22×C4×C113—24no—
101C22×C4×C113—22no—
102C22×C4×C113—22no—
103C22×C4×C113—82no—
104C22×C4×C113C2×D412yes—
105C22×C4×C113C2×D412yes—
106C22×C4×C113C2×D411yescharacteristic
107C22×C4×C113C2×D411yescharacteristic
108C22×C4×C113C2411yescharacteristic
109SD16×C113—28no—
110C2×C8×C113—22no—
111C2×C8×C113—22no—
112C2×C8×C113—22no—
113C2×C8×C113C22×C412yes—
114C2×C8×C113C22×C412yes—
115C2×C8×C113#4114yes—
116C2×C8×C113#4114yes—
117C4⋊C4×C113—24no—
118C4⋊C4×C113—21no—
119C4⋊C4×C113—21no—
120C4⋊C4×C113—22no—
121C4⋊C4×C113—22no—
122C4⋊C4×C113—22no—
123C4⋊C4×C113—22no—
124C4⋊C4×C113—82no—
125C4⋊C4×C113—82no—
126C4⋊C4×C113C22×C412yes—
127C4⋊C4×C113C22×C412yes—
128C22⋊C4×C113—24no—
129C22⋊C4×C113—82no—
130C22⋊C4×C113—82no—
131C42×C113—24no—
132C42×C113—22no—
133C42×C113—22no—
134C42×C113—81no—
135C42×C113—81no—
136C42×C113C22×C412yes—
137C42×C113#4112yes—
138C23×C113—22no—
139C23×C113—42no—
140C23×C113—41no—
141C23×C113—42no—
142C23×C113—41no—
143C23×C113C22×D411yescharacteristic
144Q8×C113—22no—
145Q8×C113—22no—
146Q8×C113—42no—
147D4×C113—22no—
148D4×C113—22no—
149D4×C113—42no—
150C2×C4×C113—21no—
151C2×C4×C113—21no—
152C2×C4×C113—22no—
153C2×C4×C113—22no—
154C2×C4×C113—22no—
155C2×C4×C113—22no—
156C2×C4×C113—22no—
157C2×C4×C113—22no—
158C2×C4×C113—22no—
159C2×C4×C113—22no—
160C2×C4×C113—22no—
161C2×C4×C113—22no—
162C2×C4×C113—42no—
163C2×C4×C113—41no—
164C2×C4×C113—42no—
165C2×C4×C113—41no—
166C2×C4×C113—42no—
167C2×C4×C113—42no—
168C2×C4×C113—42no—
169C2×C4×C113—42no—
170C2×C4×C113—42no—
171C2×C4×C113—42no—
172C2×C4×C113—84no—
173C2×C4×C113C4×D412yes—
174C2×C4×C113C4×D412yes—
175C2×C4×C113C23×C411yescharacteristic
176C2×C4×C113C2×#4112yes—
177C2×C4×C113C2×#4112yes—
178C2×C4×C113C2×#4111yescharacteristic
179C8×C113—22no—
180C8×C113—24no—
181C8×C113#11714yes—
182C22×C113—42no—
183C22×C113—42no—
184C22×C113—42no—
185C22×C113—82no—
186C22×C113—82no—
187C22×C113C2×C4×D411yescharacteristic
188C22×C113#53212yes—
189C22×C113#57711yescharacteristic
190C22×C113#57712yes—
191C22×C113#57711yescharacteristic
192C4×C113—22no—
193C4×C113—22no—
194C4×C113—42no—
195C4×C113—42no—
196C4×C113—42no—
197C4×C113—42no—
198C4×C113—42no—
199C4×C113—82no—
200C4×C113—82no—
201C4×C113C2×#11711yescharacteristic
202C4×C113C4×#4111yescharacteristic
203C4×C113#52912yes—
204#21280C11311yesmaximal, characteristic, direct product factor, Sylow
205C2×C113—82no—
206C2×C113#229311yescharacteristic
207C2×C113#294911yescharacteristic
208C2×C113#295211yescharacteristic
209C2×C113#317312yes—
210C2×C113#317412yes—
211C2×C4×SD16C2×C11311yescharacteristic
212#2320C2×C11311yescharacteristic, complemented
213#2319C2×C11311yescharacteristic
214#1968C2×C11312yes—
215#1941C2×C11312yescomplemented
216#1936C2×C11312yes—
217#1935C2×C11312yescomplemented
218C4×#106C2×C11311yescharacteristic, complemented
219#1763C2×C11311yescharacteristic, complemented
220#1762C2×C11311yescharacteristic
221#1726C2×C11311yescharacteristic, complemented
222C113#2128011yescharacteristic, direct product factor, Sylow
223C22×SD16C22×C11311yescharacteristic
224C2×C4×Q8C22×C11311yescharacteristic
225C2×C4×D4C22×C11311yescharacteristic
226C4×SD16C4×C11318yescomplemented
227C2×#106C22×C11312yes—
228C2×#106C22×C11311yescharacteristic
229C2×#103C22×C11312yes—
230C2×#103C22×C11311yescharacteristic
231C2×#102C22×C11312yes—
232C2×#102C22×C11311yescharacteristic
233C2×#97C22×C11312yes—
234C2×#97C22×C11311yescharacteristic
235C2×C4×C8C22×C11312yes—
236C2×C4×C8C22×C11311yescharacteristic
237#391C22×C11312yes—
238#390C22×C11312yes—
239#389C22×C11312yes—
240#389C22×C11312yes—
241#388—22no—
242#387—22no—
243#383—21no—
244#382—21no—
245#381—21no—
246#380—21no—
247C4×C4⋊C4C22×C11311yescharacteristic
248C4×C4⋊C4C22×C11311yescharacteristic
249#376C22×C11311yescharacteristic
250#340C22×C11312yes—
251#340C22×C11312yes—
252#340C22×C11312yes—
253C22×Q8C23×C11311yescharacteristic
254C22×D4C23×C11311yescharacteristic
255C23×C4—21no—
256C2×SD16—24no—
257C2×SD16C2×C4×C11314yes—
258C22×C8C23×C11311yescharacteristic
259C22×C8C23×C11312yes—
260C22×C8C23×C11311yescharacteristic
261C4×Q8—22no—
262C4×Q8C2×C4×C11314yes—
263C4×D4—22no—
264C4×D4C2×C4×C11314yes—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4C23×C11312yes—
269C2×C4⋊C4C23×C11312yes—
270C2×C4⋊C4C23×C11311yescharacteristic
271C2×C4⋊C4C23×C11311yescharacteristic
272C2×C22⋊C4—21no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C42—21no—
276C2×C42—21no—
277C2×C42—21no—
278C2×C42C23×C11312yes—
279C2×C42C23×C11311yescharacteristic
280#106—24no—
281#106C2×C4×C11314yes—
282#103—24no—
283#103C2×C4×C11314yes—
284#102—24no—
285#102C2×C4×C11314yes—
286#97—24no—
287#97—22no—
288C4×C8—24no—
289C4×C8C2×C4×C11314yes—
290#95—21no—
291#95—21no—
292#95—22no—
293#95—22no—
294#95—22no—
295#95—22no—
296#95D4×C11311yescharacteristic
297#95D4×C11311yescharacteristic
298#95D4×C11312yes—
299C24—21no—
300C2×Q8—21no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8C22×C4×C11312yes—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—21no—
307C2×D4C22×C4×C11312yes—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—24no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—82no—
315C22×C4C2×D4×C11312yes—
316C22×C4C2×D4×C11312yes—
317C22×C4C2×D4×C11311yescharacteristic
318C22×C4C2×D4×C11311yescharacteristic
319C22×C4C24×C11311yescharacteristic
320SD16—28no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8C22×C4×C11312yes—
325C2×C8C22×C4×C11312yes—
326C2×C8#41×C11314yes—
327C2×C8#41×C11314yes—
328C4⋊C4—24no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—82no—
336C4⋊C4—82no—
337C4⋊C4C22×C4×C11312yes—
338C4⋊C4C22×C4×C11312yes—
339C22⋊C4—24no—
340C22⋊C4—82no—
341C22⋊C4—82no—
342C42—24no—
343C42—22no—
344C42—22no—
345C42—81no—
346C42—81no—
347C42C22×C4×C11312yes—
348C42#41×C11312yes—
349C23—22no—
350C23—42no—
351C23—41no—
352C23—42no—
353C23—41no—
354C23C22×D4×C11311yescharacteristic
355Q8—22no—
356Q8—22no—
357Q8—42no—
358D4—22no—
359D4—22no—
360D4—42no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—84no—
384C2×C4C4×D4×C11312yes—
385C2×C4C4×D4×C11312yes—
386C2×C4C23×C4×C11311yescharacteristic
387C2×C4C2×#41×C11312yes—
388C2×C4C2×#41×C11312yes—
389C2×C4C2×#41×C11311yescharacteristic
390C8—22no—
391C8—24no—
392C8#117×C11314yes—
393C22—42no—
394C22—42no—
395C22—42no—
396C22—82no—
397C22—82no—
398C22C2×C4×D4×C11311yescharacteristic
399C22#532×C11312yes—
400C22#577×C11311yescharacteristic
401C22#577×C11312yes—
402C22#577×C11311yescharacteristic
403C4—22no—
404C4—22no—
405C4—42no—
406C4—42no—
407C4—42no—
408C4—42no—
409C4—42no—
410C4—82no—
411C4—82no—
412C4C2×#117×C11311yescharacteristic
413C4C4×#41×C11311yescharacteristic
414C4#529×C11312yes—
415C2—82no—
416C2C113×#229311yescharacteristic
417C2C113×#294911yescharacteristic
418C2C113×#295211yescharacteristic
419C2C113×#317312yes—
420C2C113×#317412yes—
subgroupG/H
center, socleC23×C113C22×D4
commutatorC2×C4C23×C4×C113
Frattini, cosocleC22×C4C24×C113
prime radicalC22×D4×C113C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ #376×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#2320C2semidirect
5. C113×#1941C2semidirect
7. C113×#1935C2semidirect
8. C4×#106×C113C2semidirect
9. C113×#1763C2semidirect
11. C113×#1726C2semidirect
15. C4×SD16×C113C4semidirect
204. #21280C113direct (N × H)
212. #2320C2×C113semidirect
215. #1941C2×C113semidirect
217. #1935C2×C113semidirect
218. C4×#106C2×C113semidirect
219. #1763C2×C113semidirect
221. #1726C2×C113semidirect
222. C113#21280direct (N × H)
226. C4×SD16C4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×C4×SD16×C1132
C113×#23202
C113×#23192
C113×#19682
C113×#19412
C113×#19362
C113×#19352
C4×#106×C1132
C113×#17632
C113×#17622
C113×#17262
#21280113