Finite Group Databasebeta

← C113×#10023 #43278043

Subgroups — C113×#10023 #43278043

Order 28928.

518 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3166C211yesmaximal, characteristic, complemented
2C113×#3110C211yesmaximal, characteristic
3C113×#2633C211yesmaximal, characteristic
4C113×#1534C211yesmaximal, characteristic, complemented
5C113×#1515C211yesmaximal, characteristic, complemented
6C113×#1490C211yesmaximal, characteristic
7C113×#1288C211yesmaximal, characteristic, complemented
8#533×C113C2211yescharacteristic
9C2×#125×C113C2211yescharacteristic
10C2×C4×D4×C113C2211yescharacteristic
11#501×C113—21no—
12#501×C113—21no—
13#499×C113—22no—
14#484×C113—21no—
15#474×C113—21no—
16#461×C113—21no—
17#450×C113—21no—
18#440×C113—22no—
19#432×C113C2211yescharacteristic
20#432×C113C2211yescharacteristic
21#428×C113—21no—
22#428×C113—21no—
23C4×M16×C113C2211yescharacteristic
24#399×C113—21no—
25#398×C113—21no—
26#397×C113—21no—
27#394×C113—21no—
28#385×C113—22no—
29#383×C113C2211yescharacteristic
30#330×C113—22no—
31#328×C113—22no—
32D4⋊C8×C113—22no—
33C22×D4×C113D411yescharacteristic
34C23×C4×C113—21no—
35C2×SD16×C113—22no—
36C2×M16×C113—21no—
37C4⋊Q8×C113D411yescharacteristic
38C4⋊Q8×C113D411yescharacteristic
39#125×C113—21no—
40#125×C113—21no—
41#125×C113—21no—
42#125×C113—21no—
43#125×C113—21no—
44C22⋊Q8×C113—21no—
45C22⋊Q8×C113—21no—
46C4×Q8×C113—21no—
47C4×Q8×C113—21no—
48C4×D4×C113—21no—
49C4×D4×C113—21no—
50C4×D4×C113—21no—
51C4×D4×C113—21no—
52#117×C113—21no—
53C2×C4⋊C4×C113—21no—
54C2×C4⋊C4×C113—21no—
55C2×C4⋊C4×C113—22no—
56C2×C4⋊C4×C113D411yescharacteristic
57C2×C4⋊C4×C113D411yescharacteristic
58C2×C4⋊C4×C113D411yescharacteristic
59C2×C22⋊C4×C113—22no—
60C2×C22⋊C4×C113—21no—
61C2×C22⋊C4×C113—22no—
62C2×C42×C113C2311yescharacteristic
63#107×C113—22no—
64#107×C113—22no—
65#107×C113—22no—
66#106×C113—22no—
67#106×C113—22no—
68C4⋊C8×C113—21no—
69C4⋊C8×C113—21no—
70#103×C113—22no—
71#102×C113—22no—
72C22⋊C8×C113—21no—
73C22⋊C8×C113—21no—
74#97×C113—21no—
75#97×C113—21no—
76#97×C113D412yes—
77C4×C8×C113D412yes—
78#95×C113—22no—
79#95×C113—21no—
80#95×C113—21no—
81#95×C113D412yes—
82C24×C113—21no—
83C2×Q8×C113—21no—
84C2×Q8×C113—21no—
85C2×D4×C113—21no—
86C2×D4×C113—21no—
87C2×D4×C113—42no—
88C22×C4×C113—22no—
89C22×C4×C113—21no—
90C22×C4×C113—21no—
91C22×C4×C113—21no—
92C22×C4×C113—41no—
93C22×C4×C113—41no—
94C22×C4×C113—82no—
95C22×C4×C113C2×D411yescharacteristic
96C22×C4×C113C2×D411yescharacteristic
97C22×C4×C113C2×D411yescharacteristic
98SD16×C113—44no—
99M16×C113—24no—
100C2×C8×C113—22no—
101C2×C8×C113—22no—
102C2×C8×C113—41no—
103C4⋊C4×C113—21no—
104C4⋊C4×C113—21no—
105C4⋊C4×C113—21no—
106C4⋊C4×C113—21no—
107C4⋊C4×C113—21no—
108C4⋊C4×C113—21no—
109C4⋊C4×C113—21no—
110C4⋊C4×C113—21no—
111C4⋊C4×C113—21no—
112C4⋊C4×C113—21no—
113C4⋊C4×C113—41no—
114C4⋊C4×C113—41no—
115C4⋊C4×C113—41no—
116C4⋊C4×C113—41no—
117C4⋊C4×C113—41no—
118C4⋊C4×C113—41no—
119C4⋊C4×C113—82no—
120C22⋊C4×C113—44no—
121C22⋊C4×C113—41no—
122C22⋊C4×C113—41no—
123C22⋊C4×C113—41no—
124C22⋊C4×C113—82no—
125C42×C113—41no—
126C42×C113C2×D411yescharacteristic
127C42×C113C2×D411yescharacteristic
128C42×C113C2×D411yescharacteristic
129C42×C113#4111yescharacteristic
130C23×C113—22no—
131C23×C113—42no—
132C23×C113—41no—
133C23×C113—41no—
134C23×C113—42no—
135C23×C113#12011yescharacteristic
136Q8×C113—42no—
137Q8×C113—81no—
138D4×C113—22no—
139D4×C113—22no—
140D4×C113—41no—
141D4×C113—41no—
142C2×C4×C113—22no—
143C2×C4×C113—41no—
144C2×C4×C113—41no—
145C2×C4×C113—42no—
146C2×C4×C113—42no—
147C2×C4×C113—41no—
148C2×C4×C113—42no—
149C2×C4×C113—41no—
150C2×C4×C113—42no—
151C2×C4×C113—41no—
152C2×C4×C113—41no—
153C2×C4×C113—41no—
154C2×C4×C113—41no—
155C2×C4×C113—41no—
156C2×C4×C113—42no—
157C2×C4×C113—82no—
158C2×C4×C113—82no—
159C2×C4×C113#12011yescharacteristic
160C2×C4×C113#12011yescharacteristic
161C2×C4×C113#12111yescharacteristic
162C2×C4×C113#12111yescharacteristic
163C2×C4×C113#12111yescharacteristic
164C2×C4×C113#12711yescharacteristic
165C8×C113—24no—
166C8×C113—42no—
167C8×C113—81no—
168C22×C113—21no—
169C22×C113—21no—
170C22×C113—44no—
171C22×C113—42no—
172C22×C113—82no—
173C22×C113—81no—
174C22×C113—81no—
175C22×C113#39211yescharacteristic
176C22×C113#45612yes—
177C4×C113—21no—
178C4×C113—21no—
179C4×C113—21no—
180C4×C113—21no—
181C4×C113—21no—
182C4×C113—21no—
183C4×C113—82no—
184C4×C113—81no—
185C4×C113—81no—
186C4×C113—81no—
187C4×C113—81no—
188C4×C113—81no—
189#10023C11311yesmaximal, characteristic, direct product factor, Sylow
190C2×C113—22no—
191C2×C113—82no—
192C2×C113#200511yescharacteristic
193C2×C113#200811yescharacteristic
194C2×C113#201011yescharacteristic
195#3166C2×C11311yescharacteristic, complemented
196#3110C2×C11311yescharacteristic
197#2633C2×C11311yescharacteristic
198#1534C2×C11311yescharacteristic, complemented
199#1515C2×C11311yescharacteristic, complemented
200#1490C2×C11311yescharacteristic
201#1288C2×C11311yescharacteristic, complemented
202C113#1002311yescharacteristic, direct product factor, Sylow
203#533C22×C11311yescharacteristic
204C2×#125C22×C11311yescharacteristic
205C2×C4×D4C22×C11311yescharacteristic
206#501—21no—
207#501—21no—
208#499—22no—
209#484—21no—
210#474—21no—
211#461—21no—
212#450—21no—
213#440—22no—
214#432C22×C11311yescharacteristic
215#432C22×C11311yescharacteristic
216#428—21no—
217#428—21no—
218C4×M16C22×C11311yescharacteristic
219#399—21no—
220#398—21no—
221#397—21no—
222#394—21no—
223#385—22no—
224#383C22×C11311yescharacteristic
225#330—22no—
226#328—22no—
227D4⋊C8—22no—
228C22×D4D4×C11311yescharacteristic
229C23×C4—21no—
230C2×SD16—22no—
231C2×M16—21no—
232C4⋊Q8D4×C11311yescharacteristic
233C4⋊Q8D4×C11311yescharacteristic
234#125—21no—
235#125—21no—
236#125—21no—
237#125—21no—
238#125—21no—
239C22⋊Q8—21no—
240C22⋊Q8—21no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—21no—
246C4×D4—21no—
247#117—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4D4×C11311yescharacteristic
252C2×C4⋊C4D4×C11311yescharacteristic
253C2×C4⋊C4D4×C11311yescharacteristic
254C2×C22⋊C4—22no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—22no—
257C2×C42C23×C11311yescharacteristic
258#107—22no—
259#107—22no—
260#107—22no—
261#106—22no—
262#106—22no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265#103—22no—
266#102—22no—
267C22⋊C8—21no—
268C22⋊C8—21no—
269#97—21no—
270#97—21no—
271#97D4×C11312yes—
272C4×C8D4×C11312yes—
273#95—22no—
274#95—21no—
275#95—21no—
276#95D4×C11312yes—
277C24—21no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—42no—
283C22×C4—22no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—82no—
290C22×C4C2×D4×C11311yescharacteristic
291C22×C4C2×D4×C11311yescharacteristic
292C22×C4C2×D4×C11311yescharacteristic
293SD16—44no—
294M16—24no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—41no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—82no—
315C22⋊C4—44no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—82no—
320C42—41no—
321C42C2×D4×C11311yescharacteristic
322C42C2×D4×C11311yescharacteristic
323C42C2×D4×C11311yescharacteristic
324C42#41×C11311yescharacteristic
325C23—22no—
326C23—42no—
327C23—41no—
328C23—41no—
329C23—42no—
330C23#120×C11311yescharacteristic
331Q8—42no—
332Q8—81no—
333D4—22no—
334D4—22no—
335D4—41no—
336D4—41no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—42no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4#120×C11311yescharacteristic
355C2×C4#120×C11311yescharacteristic
356C2×C4#121×C11311yescharacteristic
357C2×C4#121×C11311yescharacteristic
358C2×C4#121×C11311yescharacteristic
359C2×C4#127×C11311yescharacteristic
360C8—24no—
361C8—42no—
362C8—81no—
363C22—21no—
364C22—21no—
365C22—44no—
366C22—42no—
367C22—82no—
368C22—81no—
369C22—81no—
370C22#392×C11311yescharacteristic
371C22#456×C11312yes—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—82no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—81no—
383C4—81no—
384C2—22no—
385C2—82no—
386C2C113×#200511yescharacteristic
387C2C113×#200811yescharacteristic
388C2C113×#201011yescharacteristic
subgroupG/H
center, socleC22×C113#392
commutator, Frattini, cosocleC2×C42C23×C113
prime radicalC22×D4×C113D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3166C2semidirect
4. C113×#1534C2semidirect
5. C113×#1515C2semidirect
7. C113×#1288C2semidirect
189. #10023C113direct (N × H)
195. #3166C2×C113semidirect
198. #1534C2×C113semidirect
199. #1515C2×C113semidirect
201. #1288C2×C113semidirect
202. C113#10023direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#31662
C113×#31102
C113×#26332
C113×#15342
C113×#15152
C113×#14902
C113×#12882
#10023113