Finite Group Databasebeta

← C113×#26082 #43294102

Subgroups — C113×#26082 #43294102

Order 28928.

674 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3164C211yesmaximal, characteristic, complemented
2C113×#3084C212yesmaximal
3C113×#2913C211yesmaximal, characteristic
4C113×#2090C212yesmaximal, complemented
5C113×#2061C212yesmaximal, complemented
6C113×#1952C211yesmaximal, characteristic, complemented
7C113×#1945C211yesmaximal, characteristic, complemented
8C113×#1860C212yesmaximal
9C113×#1846C211yesmaximal, characteristic, complemented
10C113×#1816C211yesmaximal, characteristic
11C113×#1764C211yesmaximal, characteristic
12C2×#131×C113C2211yescharacteristic
13#544×C113C2212yes—
14#520×C113C2212yes—
15#501×C113—22no—
16#500×C113—21no—
17#499×C113—21no—
18#479×C113—22no—
19#478×C113—22no—
20#476×C113—22no—
21#475×C113—22no—
22C2×#108×C113C2211yescharacteristic
23#428×C113—22no—
24#428×C113C2212yes—
25#428×C113C2212yes—
26#428×C113C2212yes—
27#427×C113—21no—
28#427×C113C2211yescharacteristic
29C2×#107×C113—21no—
30C2×#107×C113C2211yescharacteristic
31C2×#107×C113C2211yescharacteristic
32C2×#106×C113C2212yes—
33#424×C113C2212yes—
34C2×#104×C113C2211yescharacteristic
35#417×C113C2212yes—
36#416×C113C2211yescharacteristic
37#405×C113C2211yescharacteristic
38C2×C4×C8×C113C2211yescharacteristic
39#382×C113C2212yes—
40#343×C113C2212yes—
41#343×C113C2212yes—
42#341×C113C2211yescharacteristic
43#339×C113C2211yescharacteristic
44#339×C113C2212yes—
45C2×#41×C113C2311yescharacteristic
46#131×C113—22no—
47#131×C113Q814yescomplemented
48C2×M16×C113—21no—
49C2×M16×C113C2312yes—
50C2×M16×C113C2311yescharacteristic
51C2×M16×C113C2311yescharacteristic
52C22×C8×C113—21no—
53C22×C8×C113C2311yescharacteristic
54C22×C8×C113C2311yescharacteristic
55C4⋊Q8×C113—22no—
56C4⋊Q8×C113—22no—
57#125×C113—22no—
58#125×C113—22no—
59C22⋊Q8×C113—42no—
60C4×Q8×C113—22no—
61C4×D4×C113—22no—
62C4×D4×C113—42no—
63#117×C113—22no—
64#117×C113C2312yes—
65#117×C113C2311yescharacteristic
66C2×C4⋊C4×C113—22no—
67C2×C4⋊C4×C113C2312yes—
68C2×C4⋊C4×C113C2312yes—
69C2×C42×C113C2311yescharacteristic
70#108×C113—22no—
71#107×C113—21no—
72#107×C113—21no—
73#107×C113—21no—
74#107×C113—21no—
75#107×C113—22no—
76#107×C113—22no—
77#107×C113—22no—
78#107×C113D411yescharacteristic
79#107×C113D411yescharacteristic
80#106×C113—22no—
81#106×C113—22no—
82#106×C113—22no—
83#106×C113—22no—
84#106×C113—22no—
85#106×C113D412yes—
86C4⋊C8×C113—22no—
87C4⋊C8×C113—22no—
88#104×C113Q814yescomplemented
89#103×C113—22no—
90#103×C113D411yescharacteristic
91#103×C113D411yescharacteristic
92#102×C113—22no—
93#102×C113D411yescharacteristic
94#102×C113D411yescharacteristic
95#97×C113—21no—
96C4×C8×C113—21no—
97C4×C8×C113—22no—
98#95×C113—42no—
99#41×C113—21no—
100#41×C113—21no—
101#41×C113C2×Q812yes—
102#41×C113C2×Q812yes—
103C2×Q8×C113—42no—
104C2×Q8×C113C2×D411yescharacteristic
105C2×D4×C113—21no—
106C2×D4×C113C2×D411yescharacteristic
107C22×C4×C113—21no—
108C22×C4×C113—21no—
109C22×C4×C113—22no—
110C22×C4×C113—22no—
111C22×C4×C113—42no—
112C22×C4×C113C2411yescharacteristic
113M16×C113—21no—
114M16×C113—21no—
115M16×C113—24no—
116M16×C113—22no—
117M16×C113—22no—
118M16×C113C2×Q812yes—
119M16×C113C2×Q812yes—
120C2×C8×C113—21no—
121C2×C8×C113—21no—
122C2×C8×C113—21no—
123C2×C8×C113—21no—
124C2×C8×C113—24no—
125C2×C8×C113—22no—
126C2×C8×C113C2×D411yescharacteristic
127C2×C8×C113C2×D411yescharacteristic
128C2×C8×C113C2×D411yescharacteristic
129C2×C8×C113C2×D411yescharacteristic
130C2×C8×C113C2×Q812yes—
131C2×C8×C113#4112yes—
132C4⋊C4×C113—22no—
133C4⋊C4×C113—22no—
134C4⋊C4×C113—22no—
135C4⋊C4×C113—22no—
136C4⋊C4×C113—42no—
137C4⋊C4×C113—42no—
138C4⋊C4×C113—42no—
139C4⋊C4×C113—42no—
140C4⋊C4×C113C2×D411yescharacteristic
141C4⋊C4×C113C2×D411yescharacteristic
142C4⋊C4×C113C2×D412yes—
143C4⋊C4×C113C2×D412yes—
144C22⋊C4×C113—22no—
145C22⋊C4×C113—21no—
146C22⋊C4×C113—42no—
147C42×C113—21no—
148C42×C113—22no—
149C42×C113—21no—
150C42×C113—42no—
151C42×C113C2×Q812yes—
152C23×C113—21no—
153C23×C113H(5,𝔽2)11yescharacteristic
154Q8×C113—21no—
155Q8×C113—162no—
156Q8×C113C4⋊Q812yes—
157D4×C113—22no—
158D4×C113—22no—
159D4×C113—21no—
160D4×C113C4⋊Q812yes—
161C2×C4×C113—21no—
162C2×C4×C113—22no—
163C2×C4×C113—22no—
164C2×C4×C113—22no—
165C2×C4×C113—21no—
166C2×C4×C113—22no—
167C2×C4×C113—21no—
168C2×C4×C113—22no—
169C2×C4×C113—41no—
170C2×C4×C113—41no—
171C2×C4×C113—42no—
172C2×C4×C113—42no—
173C2×C4×C113—82no—
174C2×C4×C113—82no—
175C2×C4×C113—162no—
176C2×C4×C113C22×D411yescharacteristic
177C2×C4×C113C22×D411yescharacteristic
178C2×C4×C113C22×Q811yescharacteristic
179C2×C4×C113C22×Q811yescharacteristic
180C2×C4×C113C2×#4111yescharacteristic
181C2×C4×C1132−1+411yescharacteristic
182C8×C113—22no—
183C8×C113—21no—
184C8×C113—21no—
185C8×C113—22no—
186C8×C113—42no—
187C8×C113C22⋊Q812yes—
188C8×C113C22⋊Q812yes—
189C22×C113—21no—
190C22×C113—21no—
191C22×C113—22no—
192C22×C113—41no—
193C22×C113—41no—
194C22×C113#54411yescharacteristic
195C22×C113D4211yescharacteristic
196C22×C113#55411yescharacteristic
197C4×C113—22no—
198C4×C113—42no—
199C4×C113—41no—
200C4×C113—42no—
201C4×C113—42no—
202C4×C113—41no—
203C4×C113—82no—
204C4×C113—82no—
205C4×C113C2×C22⋊Q811yescharacteristic
206C4×C113C2×C4⋊Q811yescharacteristic
207C4×C113#54711yescharacteristic
208C4×C113D4×Q811yescharacteristic
209#26082C11311yesmaximal, characteristic, direct product factor, Sylow
210C2×C113—21no—
211C2×C113—21no—
212C2×C113—42no—
213C2×C113#244011yescharacteristic
214C2×C113#329011yescharacteristic
215C2×C113#329011yescharacteristic
216#3164C2×C11311yescharacteristic, complemented
217#3084C2×C11312yes—
218#2913C2×C11311yescharacteristic
219#2090C2×C11312yescomplemented
220#2061C2×C11312yescomplemented
221#1952C2×C11311yescharacteristic, complemented
222#1945C2×C11311yescharacteristic, complemented
223#1860C2×C11312yes—
224#1846C2×C11311yescharacteristic, complemented
225#1816C2×C11311yescharacteristic
226#1764C2×C11311yescharacteristic
227C113#2608211yescharacteristic, direct product factor, Sylow
228C2×#131C22×C11311yescharacteristic
229#544C22×C11312yes—
230#520C22×C11312yes—
231#501—22no—
232#500—21no—
233#499—21no—
234#479—22no—
235#478—22no—
236#476—22no—
237#475—22no—
238C2×#108C22×C11311yescharacteristic
239#428—22no—
240#428C22×C11312yes—
241#428C22×C11312yes—
242#428C22×C11312yes—
243#427—21no—
244#427C22×C11311yescharacteristic
245C2×#107—21no—
246C2×#107C22×C11311yescharacteristic
247C2×#107C22×C11311yescharacteristic
248C2×#106C22×C11312yes—
249#424C22×C11312yes—
250C2×#104C22×C11311yescharacteristic
251#417C22×C11312yes—
252#416C22×C11311yescharacteristic
253#405C22×C11311yescharacteristic
254C2×C4×C8C22×C11311yescharacteristic
255#382C22×C11312yes—
256#343C22×C11312yes—
257#343C22×C11312yes—
258#341C22×C11311yescharacteristic
259#339C22×C11311yescharacteristic
260#339C22×C11312yes—
261C2×#41C23×C11311yescharacteristic
262#131—22no—
263#131Q8×C11314yescomplemented
264C2×M16—21no—
265C2×M16C23×C11312yes—
266C2×M16C23×C11311yescharacteristic
267C2×M16C23×C11311yescharacteristic
268C22×C8—21no—
269C22×C8C23×C11311yescharacteristic
270C22×C8C23×C11311yescharacteristic
271C4⋊Q8—22no—
272C4⋊Q8—22no—
273#125—22no—
274#125—22no—
275C22⋊Q8—42no—
276C4×Q8—22no—
277C4×D4—22no—
278C4×D4—42no—
279#117—22no—
280#117C23×C11312yes—
281#117C23×C11311yescharacteristic
282C2×C4⋊C4—22no—
283C2×C4⋊C4C23×C11312yes—
284C2×C4⋊C4C23×C11312yes—
285C2×C42C23×C11311yescharacteristic
286#108—22no—
287#107—21no—
288#107—21no—
289#107—21no—
290#107—21no—
291#107—22no—
292#107—22no—
293#107—22no—
294#107D4×C11311yescharacteristic
295#107D4×C11311yescharacteristic
296#106—22no—
297#106—22no—
298#106—22no—
299#106—22no—
300#106—22no—
301#106D4×C11312yes—
302C4⋊C8—22no—
303C4⋊C8—22no—
304#104Q8×C11314yescomplemented
305#103—22no—
306#103D4×C11311yescharacteristic
307#103D4×C11311yescharacteristic
308#102—22no—
309#102D4×C11311yescharacteristic
310#102D4×C11311yescharacteristic
311#97—21no—
312C4×C8—21no—
313C4×C8—22no—
314#95—42no—
315#41—21no—
316#41—21no—
317#41C2×Q8×C11312yes—
318#41C2×Q8×C11312yes—
319C2×Q8—42no—
320C2×Q8C2×D4×C11311yescharacteristic
321C2×D4—21no—
322C2×D4C2×D4×C11311yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—42no—
328C22×C4C24×C11311yescharacteristic
329M16—21no—
330M16—21no—
331M16—24no—
332M16—22no—
333M16—22no—
334M16C2×Q8×C11312yes—
335M16C2×Q8×C11312yes—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—21no—
339C2×C8—21no—
340C2×C8—24no—
341C2×C8—22no—
342C2×C8C2×D4×C11311yescharacteristic
343C2×C8C2×D4×C11311yescharacteristic
344C2×C8C2×D4×C11311yescharacteristic
345C2×C8C2×D4×C11311yescharacteristic
346C2×C8C2×Q8×C11312yes—
347C2×C8#41×C11312yes—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4—42no—
355C4⋊C4—42no—
356C4⋊C4C2×D4×C11311yescharacteristic
357C4⋊C4C2×D4×C11311yescharacteristic
358C4⋊C4C2×D4×C11312yes—
359C4⋊C4C2×D4×C11312yes—
360C22⋊C4—22no—
361C22⋊C4—21no—
362C22⋊C4—42no—
363C42—21no—
364C42—22no—
365C42—21no—
366C42—42no—
367C42C2×Q8×C11312yes—
368C23—21no—
369C23H(5,𝔽2)×C11311yescharacteristic
370Q8—21no—
371Q8—162no—
372Q8C4⋊Q8×C11312yes—
373D4—22no—
374D4—22no—
375D4—21no—
376D4C4⋊Q8×C11312yes—
377C2×C4—21no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—162no—
392C2×C4C22×D4×C11311yescharacteristic
393C2×C4C22×D4×C11311yescharacteristic
394C2×C4C22×Q8×C11311yescharacteristic
395C2×C4C22×Q8×C11311yescharacteristic
396C2×C4C2×#41×C11311yescharacteristic
397C2×C42−1+4×C11311yescharacteristic
398C8—22no—
399C8—21no—
400C8—21no—
401C8—22no—
402C8—42no—
403C8C22⋊Q8×C11312yes—
404C8C22⋊Q8×C11312yes—
405C22—21no—
406C22—21no—
407C22—22no—
408C22—41no—
409C22—41no—
410C22#544×C11311yescharacteristic
411C22D42×C11311yescharacteristic
412C22#554×C11311yescharacteristic
413C4—22no—
414C4—42no—
415C4—42no—
416C4—41no—
417C4—42no—
418C4—41no—
419C4—82no—
420C4—82no—
421C4C2×C22⋊Q8×C11311yescharacteristic
422C4C2×C4⋊Q8×C11311yescharacteristic
423C4#547×C11311yescharacteristic
424C4D4×Q8×C11311yescharacteristic
425C2—21no—
426C2—21no—
427C2—42no—
428C2C113×#244011yescharacteristic
429C2C113×#329011yescharacteristic
430C2C113×#329011yescharacteristic
subgroupG/H
center, socleC22×C113D42
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC2×#41×C113C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C22×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3164C2semidirect
4. C113×#2090C2semidirect
5. C113×#2061C2semidirect
6. C113×#1952C2semidirect
7. C113×#1945C2semidirect
9. C113×#1846C2semidirect
47. #131×C113Q8semidirect
88. #104×C113Q8semidirect
209. #26082C113direct (N × H)
216. #3164C2×C113semidirect
219. #2090C2×C113semidirect
220. #2061C2×C113semidirect
221. #1952C2×C113semidirect
222. #1945C2×C113semidirect
224. #1846C2×C113semidirect
227. C113#26082direct (N × H)
263. #131Q8×C113semidirect
304. #104Q8×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#31642
C113×#30842
C113×#29132
C113×#20902
C113×#20612
C113×#19522
C113×#19452
C113×#18602
C113×#18462
C113×#18162
C113×#17642
#26082113