Finite Group Databasebeta

← C113×#22812 #43290832

Subgroups — C113×#22812 #43290832

Order 28928.

802 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×SD16×C113C211yesmaximal, characteristic
2C113×#2357C211yesmaximal, characteristic
3C113×#2356C211yesmaximal, characteristic, complemented
4C113×#1973C212yesmaximal
5C113×#1927C212yesmaximal, complemented
6C113×#1926C212yesmaximal
7C113×#1846C211yesmaximal, characteristic, complemented
8C113×#1805C211yesmaximal, characteristic, complemented
9C113×#1804C211yesmaximal, characteristic
10C113×#1776C212yesmaximal, complemented
11C113×#1770C211yesmaximal, characteristic, complemented
12C22×SD16×C113C2211yescharacteristic
13C2×C4×Q8×C113C2211yescharacteristic
14C2×C4×D4×C113C2211yescharacteristic
15C4×SD16×C113C418yescomplemented
16C2×#107×C113C2212yes—
17C2×#106×C113C2212yes—
18C2×#106×C113C2211yescharacteristic
19C2×C4⋊C8×C113C2211yescharacteristic
20C2×#103×C113C2212yes—
21C2×#103×C113C2211yescharacteristic
22C2×#102×C113C2212yes—
23C2×#102×C113C2211yescharacteristic
24C2×#97×C113C2212yes—
25C2×C4×C8×C113C2211yescharacteristic
26#391×C113C2212yes—
27#390×C113C2212yes—
28#388×C113—22no—
29#387×C113—22no—
30#383×C113—21no—
31#382×C113C2211yescharacteristic
32#382×C113C2211yescharacteristic
33#381×C113—21no—
34C4×C4⋊C4×C113C2212yes—
35C4×C4⋊C4×C113C2212yes—
36C4×C4⋊C4×C113C2211yescharacteristic
37C4×C22⋊C4×C113—21no—
38#376×C113—21no—
39#340×C113C2212yes—
40#340×C113C2212yes—
41#336×C113C2212yes—
42C22×Q8×C113C2311yescharacteristic
43C22×D4×C113C2311yescharacteristic
44C23×C4×C113—21no—
45C2×SD16×C113—22no—
46C2×SD16×C113—22no—
47C2×SD16×C113C2×C414yes—
48C22×C8×C113C2312yes—
49C22×C8×C113C2311yescharacteristic
50C22×C8×C113C2311yescharacteristic
51C4×Q8×C113—22no—
52C4×Q8×C113C2×C414yes—
53C4×D4×C113—22no—
54C4×D4×C113C2×C414yes—
55C2×C4⋊C4×C113—21no—
56C2×C4⋊C4×C113D412yes—
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—22no—
66C2×C42×C113—22no—
67C2×C42×C113C2312yes—
68C2×C42×C113C2311yescharacteristic
69#107×C113—24no—
70#106×C113—42no—
71#106×C113C2×C414yes—
72C4⋊C8×C113—22no—
73#103×C113—42no—
74#103×C113C2×C414yes—
75#102×C113—42no—
76#102×C113C2×C414yes—
77#97×C113—24no—
78C4×C8×C113C2×C414yes—
79#95×C113—21no—
80#95×C113—22no—
81#95×C113—21no—
82#95×C113—22no—
83#95×C113—22no—
84#95×C113—21no—
85#95×C113—21no—
86#95×C113—22no—
87#95×C113D411yescharacteristic
88#95×C113D411yescharacteristic
89C24×C113—21no—
90C2×Q8×C113—21no—
91C2×Q8×C113—21no—
92C2×Q8×C113—21no—
93C2×Q8×C113—21no—
94C2×Q8×C113—21no—
95C2×Q8×C113C22×C412yes—
96C2×D4×C113—21no—
97C2×D4×C113—21no—
98C2×D4×C113—21no—
99C2×D4×C113—21no—
100C2×D4×C113—21no—
101C2×D4×C113C22×C412yes—
102C22×C4×C113—21no—
103C22×C4×C113—21no—
104C22×C4×C113—21no—
105C22×C4×C113—24no—
106C22×C4×C113—22no—
107C22×C4×C113—22no—
108C22×C4×C113—82no—
109C22×C4×C113C2×D412yes—
110C22×C4×C113C2×D412yes—
111C22×C4×C113C2×D411yescharacteristic
112C22×C4×C113C2×D411yescharacteristic
113C22×C4×C113C2411yescharacteristic
114SD16×C113—28no—
115C2×C8×C113—21no—
116C2×C8×C113—21no—
117C2×C8×C113—22no—
118C2×C8×C113—22no—
119C2×C8×C113—22no—
120C2×C8×C113C22×C412yes—
121C2×C8×C113C22×C412yes—
122C2×C8×C113#4112yes—
123C2×C8×C113#4112yes—
124C4⋊C4×C113—24no—
125C4⋊C4×C113—21no—
126C4⋊C4×C113—21no—
127C4⋊C4×C113—22no—
128C4⋊C4×C113—22no—
129C4⋊C4×C113—22no—
130C4⋊C4×C113—22no—
131C4⋊C4×C113—42no—
132C4⋊C4×C113C22×C412yes—
133C4⋊C4×C113C22×C412yes—
134C22⋊C4×C113—24no—
135C22⋊C4×C113—44no—
136C22⋊C4×C113—82no—
137C42×C113—24no—
138C42×C113—22no—
139C42×C113—22no—
140C42×C113—44no—
141C42×C113—82no—
142C42×C113C22×C412yes—
143C42×C113#4112yes—
144C23×C113—22no—
145C23×C113—41no—
146C23×C113—41no—
147C23×C113—42no—
148C23×C113—42no—
149C23×C113C22×D411yescharacteristic
150Q8×C113—22no—
151Q8×C113—22no—
152Q8×C113—41no—
153Q8×C113—41no—
154D4×C113—22no—
155D4×C113—22no—
156D4×C113—41no—
157D4×C113—41no—
158C2×C4×C113—22no—
159C2×C4×C113—22no—
160C2×C4×C113—22no—
161C2×C4×C113—22no—
162C2×C4×C113—22no—
163C2×C4×C113—22no—
164C2×C4×C113—22no—
165C2×C4×C113—22no—
166C2×C4×C113—22no—
167C2×C4×C113—22no—
168C2×C4×C113—22no—
169C2×C4×C113—41no—
170C2×C4×C113—41no—
171C2×C4×C113—42no—
172C2×C4×C113—42no—
173C2×C4×C113—42no—
174C2×C4×C113—42no—
175C2×C4×C113—42no—
176C2×C4×C113—42no—
177C2×C4×C113—42no—
178C2×C4×C113—42no—
179C2×C4×C113—84no—
180C2×C4×C113C4×D412yes—
181C2×C4×C113C4×D412yes—
182C2×C4×C113C23×C411yescharacteristic
183C2×C4×C113C2×#4111yescharacteristic
184C2×C4×C113C2×#4111yescharacteristic
185C2×C4×C113C2×#4111yescharacteristic
186C2×C4×C113H(5,𝔽2)11yescharacteristic
187C2×C4×C1132−1+411yescharacteristic
188C8×C113—22no—
189C8×C113—42no—
190C8×C113#11714yes—
191C22×C113—42no—
192C22×C113—42no—
193C22×C113—42no—
194C22×C113—82no—
195C22×C113—82no—
196C22×C113C2×C4×D411yescharacteristic
197C22×C113#54711yescharacteristic
198C22×C113#55011yescharacteristic
199C22×C113#57512yes—
200C22×C113#57712yes—
201C4×C113—22no—
202C4×C113—22no—
203C4×C113—42no—
204C4×C113—42no—
205C4×C113—42no—
206C4×C113—42no—
207C4×C113—42no—
208C4×C113—82no—
209C4×C113—82no—
210C4×C113C2×#11711yescharacteristic
211C4×C113#52011yescharacteristic
212C4×C113#55511yescharacteristic
213C4×C113#55611yescharacteristic
214#22812C11311yesmaximal, characteristic, direct product factor, Sylow
215C2×C113—82no—
216C2×C113#235411yescharacteristic
217C2×C113#294311yescharacteristic
218C2×C113#294911yescharacteristic
219C2×C113#335112yes—
220C2×C113#340112yes—
221C2×C4×SD16C2×C11311yescharacteristic
222#2357C2×C11311yescharacteristic
223#2356C2×C11311yescharacteristic, complemented
224#1973C2×C11312yes—
225#1927C2×C11312yescomplemented
226#1926C2×C11312yes—
227#1846C2×C11311yescharacteristic, complemented
228#1805C2×C11311yescharacteristic, complemented
229#1804C2×C11311yescharacteristic
230#1776C2×C11312yescomplemented
231#1770C2×C11311yescharacteristic, complemented
232C113#2281211yescharacteristic, direct product factor, Sylow
233C22×SD16C22×C11311yescharacteristic
234C2×C4×Q8C22×C11311yescharacteristic
235C2×C4×D4C22×C11311yescharacteristic
236C4×SD16C4×C11318yescomplemented
237C2×#107C22×C11312yes—
238C2×#106C22×C11312yes—
239C2×#106C22×C11311yescharacteristic
240C2×C4⋊C8C22×C11311yescharacteristic
241C2×#103C22×C11312yes—
242C2×#103C22×C11311yescharacteristic
243C2×#102C22×C11312yes—
244C2×#102C22×C11311yescharacteristic
245C2×#97C22×C11312yes—
246C2×C4×C8C22×C11311yescharacteristic
247#391C22×C11312yes—
248#390C22×C11312yes—
249#388—22no—
250#387—22no—
251#383—21no—
252#382C22×C11311yescharacteristic
253#382C22×C11311yescharacteristic
254#381—21no—
255C4×C4⋊C4C22×C11312yes—
256C4×C4⋊C4C22×C11312yes—
257C4×C4⋊C4C22×C11311yescharacteristic
258C4×C22⋊C4—21no—
259#376—21no—
260#340C22×C11312yes—
261#340C22×C11312yes—
262#336C22×C11312yes—
263C22×Q8C23×C11311yescharacteristic
264C22×D4C23×C11311yescharacteristic
265C23×C4—21no—
266C2×SD16—22no—
267C2×SD16—22no—
268C2×SD16C2×C4×C11314yes—
269C22×C8C23×C11312yes—
270C22×C8C23×C11311yescharacteristic
271C22×C8C23×C11311yescharacteristic
272C4×Q8—22no—
273C4×Q8C2×C4×C11314yes—
274C4×D4—22no—
275C4×D4C2×C4×C11314yes—
276C2×C4⋊C4—21no—
277C2×C4⋊C4D4×C11312yes—
278C2×C4⋊C4C23×C11312yes—
279C2×C4⋊C4C23×C11312yes—
280C2×C4⋊C4C23×C11311yescharacteristic
281C2×C4⋊C4C23×C11311yescharacteristic
282C2×C22⋊C4—21no—
283C2×C22⋊C4—22no—
284C2×C22⋊C4—22no—
285C2×C42—21no—
286C2×C42—22no—
287C2×C42—22no—
288C2×C42C23×C11312yes—
289C2×C42C23×C11311yescharacteristic
290#107—24no—
291#106—42no—
292#106C2×C4×C11314yes—
293C4⋊C8—22no—
294#103—42no—
295#103C2×C4×C11314yes—
296#102—42no—
297#102C2×C4×C11314yes—
298#97—24no—
299C4×C8C2×C4×C11314yes—
300#95—21no—
301#95—22no—
302#95—21no—
303#95—22no—
304#95—22no—
305#95—21no—
306#95—21no—
307#95—22no—
308#95D4×C11311yescharacteristic
309#95D4×C11311yescharacteristic
310C24—21no—
311C2×Q8—21no—
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8C22×C4×C11312yes—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4C22×C4×C11312yes—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—24no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—82no—
330C22×C4C2×D4×C11312yes—
331C22×C4C2×D4×C11312yes—
332C22×C4C2×D4×C11311yescharacteristic
333C22×C4C2×D4×C11311yescharacteristic
334C22×C4C24×C11311yescharacteristic
335SD16—28no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8—22no—
341C2×C8C22×C4×C11312yes—
342C2×C8C22×C4×C11312yes—
343C2×C8#41×C11312yes—
344C2×C8#41×C11312yes—
345C4⋊C4—24no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—42no—
353C4⋊C4C22×C4×C11312yes—
354C4⋊C4C22×C4×C11312yes—
355C22⋊C4—24no—
356C22⋊C4—44no—
357C22⋊C4—82no—
358C42—24no—
359C42—22no—
360C42—22no—
361C42—44no—
362C42—82no—
363C42C22×C4×C11312yes—
364C42#41×C11312yes—
365C23—22no—
366C23—41no—
367C23—41no—
368C23—42no—
369C23—42no—
370C23C22×D4×C11311yescharacteristic
371Q8—22no—
372Q8—22no—
373Q8—41no—
374Q8—41no—
375D4—22no—
376D4—22no—
377D4—41no—
378D4—41no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—84no—
401C2×C4C4×D4×C11312yes—
402C2×C4C4×D4×C11312yes—
403C2×C4C23×C4×C11311yescharacteristic
404C2×C4C2×#41×C11311yescharacteristic
405C2×C4C2×#41×C11311yescharacteristic
406C2×C4C2×#41×C11311yescharacteristic
407C2×C4H(5,𝔽2)×C11311yescharacteristic
408C2×C42−1+4×C11311yescharacteristic
409C8—22no—
410C8—42no—
411C8#117×C11314yes—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—82no—
416C22—82no—
417C22C2×C4×D4×C11311yescharacteristic
418C22#547×C11311yescharacteristic
419C22#550×C11311yescharacteristic
420C22#575×C11312yes—
421C22#577×C11312yes—
422C4—22no—
423C4—22no—
424C4—42no—
425C4—42no—
426C4—42no—
427C4—42no—
428C4—42no—
429C4—82no—
430C4—82no—
431C4C2×#117×C11311yescharacteristic
432C4#520×C11311yescharacteristic
433C4#555×C11311yescharacteristic
434C4#556×C11311yescharacteristic
435C2—82no—
436C2C113×#235411yescharacteristic
437C2C113×#294311yescharacteristic
438C2C113×#294911yescharacteristic
439C2C113×#335112yes—
440C2C113×#340112yes—
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 ◁ C4×C4⋊C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
3. C113×#2356C2semidirect
5. C113×#1927C2semidirect
7. C113×#1846C2semidirect
8. C113×#1805C2semidirect
10. C113×#1776C2semidirect
11. C113×#1770C2semidirect
15. C4×SD16×C113C4semidirect
214. #22812C113direct (N × H)
223. #2356C2×C113semidirect
225. #1927C2×C113semidirect
227. #1846C2×C113semidirect
228. #1805C2×C113semidirect
230. #1776C2×C113semidirect
231. #1770C2×C113semidirect
232. C113#22812direct (N × H)
236. 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×#23572
C113×#23562
C113×#19732
C113×#19272
C113×#19262
C113×#18462
C113×#18052
C113×#18042
C113×#17762
C113×#17702
#22812113