Finite Group Databasebeta

← C113×#12178 #43280198

Subgroups — C113×#12178 #43280198

Order 28928.

422 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2742C211yesmaximal, characteristic, complemented
2C113×#2044C211yesmaximal, characteristic
3C113×#1613C211yesmaximal, characteristic
4C113×#1601C211yesmaximal, characteristic
5C113×#1352C211yesmaximal, characteristic, complemented
6C113×#1351C211yesmaximal, characteristic, complemented
7C113×#1326C211yesmaximal, characteristic, complemented
8#534×C113C2211yescharacteristic
9#481×C113—21no—
10#448×C113—21no—
11C2×#99×C113—21no—
12#400×C113—21no—
13#399×C113C2211yescharacteristic
14#395×C113—21no—
15#393×C113C2211yescharacteristic
16#389×C113—21no—
17#388×C113—21no—
18#387×C113—21no—
19#386×C113—21no—
20#385×C113C2211yescharacteristic
21#380×C113—21no—
22#342×C113C2211yescharacteristic
23#327×C113—21no—
24#327×C113—21no—
25#323×C113C2211yescharacteristic
26#323×C113C2211yescharacteristic
27C22×Q8×C113D411yescharacteristic
28C22×D4×C113—21no—
29C23×C4×C113D411yescharacteristic
30C2×SD16×C113—41no—
31#123×C113—41no—
32#121×C113—21no—
33#121×C113—21no—
34#120×C113—41no—
35C2×C4⋊C4×C113—21no—
36C2×C4⋊C4×C113—21no—
37C2×C4⋊C4×C113—21no—
38C2×C4⋊C4×C113—21no—
39C2×C4⋊C4×C113—21no—
40C2×C4⋊C4×C113D411yescharacteristic
41C2×C22⋊C4×C113—21no—
42C2×C22⋊C4×C113—21no—
43C2×C22⋊C4×C113—21no—
44C2×C22⋊C4×C113—41no—
45C2×C22⋊C4×C113D411yescharacteristic
46C2×C22⋊C4×C113C2311yescharacteristic
47C2×C42×C113—21no—
48#106×C113—41no—
49#103×C113—41no—
50#102×C113—41no—
51#99×C113—42no—
52C22⋊C8×C113—21no—
53C22⋊C8×C113—21no—
54#95×C113—21no—
55#95×C113—21no—
56#95×C113—21no—
57#95×C113—21no—
58#95×C113—21no—
59#95×C113—21no—
60#95×C113—41no—
61#95×C113D411yescharacteristic
62#95×C113D411yescharacteristic
63C24×C113—21no—
64C24×C113C2×D411yescharacteristic
65C2×Q8×C113—41no—
66C2×Q8×C113—81no—
67C2×D4×C113—21no—
68C2×D4×C113—21no—
69C2×D4×C113—41no—
70C2×D4×C113—41no—
71C2×D4×C113—41no—
72C2×D4×C113—41no—
73C2×D4×C113—41no—
74C2×D4×C113—41no—
75C22×C4×C113—21no—
76C22×C4×C113—21no—
77C22×C4×C113—21no—
78C22×C4×C113—21no—
79C22×C4×C113—21no—
80C22×C4×C113—21no—
81C22×C4×C113—21no—
82C22×C4×C113—42no—
83C22×C4×C113—41no—
84C22×C4×C113—41no—
85C22×C4×C113C2×D411yescharacteristic
86C22×C4×C113C2×D411yescharacteristic
87SD16×C113—82no—
88C2×C8×C113—41no—
89C2×C8×C113—41no—
90C4⋊C4×C113—21no—
91C4⋊C4×C113—21no—
92C4⋊C4×C113—41no—
93C4⋊C4×C113—42no—
94C4⋊C4×C113—42no—
95C4⋊C4×C113—81no—
96C4⋊C4×C113—81no—
97C4⋊C4×C113—81no—
98C22⋊C4×C113—21no—
99C22⋊C4×C113—41no—
100C22⋊C4×C113—41no—
101C22⋊C4×C113—41no—
102C22⋊C4×C113—41no—
103C22⋊C4×C113—41no—
104C22⋊C4×C113—81no—
105C22⋊C4×C113—81no—
106C22⋊C4×C113—82no—
107C22⋊C4×C113SD1612yescomplemented
108C42×C113—81no—
109C23×C113—21no—
110C23×C113—21no—
111C23×C113—41no—
112C23×C113—41no—
113C23×C113—41no—
114C23×C113—41no—
115C23×C113—41no—
116C23×C113—81no—
117C23×C113—81no—
118C23×C113#12011yescharacteristic
119C23×C113C2×SD1611yescharacteristic
120C23×C113#13711yescharacteristic
121Q8×C113—42no—
122Q8×C113—81no—
123D4×C113—81no—
124D4×C113—81no—
125D4×C113—81no—
126D4×C113—81no—
127D4×C113—81no—
128D4×C113—81no—
129C2×C4×C113—22no—
130C2×C4×C113—22no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113—41no—
134C2×C4×C113—41no—
135C2×C4×C113—41no—
136C2×C4×C113—41no—
137C2×C4×C113—41no—
138C2×C4×C113—41no—
139C2×C4×C113—42no—
140C2×C4×C113—41no—
141C2×C4×C113—41no—
142C2×C4×C113—41no—
143C2×C4×C113—41no—
144C2×C4×C113—41no—
145C2×C4×C113—41no—
146C2×C4×C113—41no—
147C2×C4×C113—41no—
148C2×C4×C113—41no—
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—81no—
156C2×C4×C113—81no—
157C2×C4×C113—81no—
158C2×C4×C113—81no—
159C8×C113—81no—
160C8×C113—81no—
161C22×C113—21no—
162C22×C113—21no—
163C22×C113—21no—
164C22×C113—21no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113—81no—
170C22×C113—82no—
171C22×C113—81no—
172C22×C113—81no—
173C22×C113—81no—
174C22×C113—161no—
175C22×C113#44811yescharacteristic
176C22×C113#45411yescharacteristic
177C22×C113B(4,𝔽2)11yescharacteristic
178C4×C113—42no—
179C4×C113—41no—
180C4×C113—42no—
181C4×C113—41no—
182C4×C113—81no—
183C4×C113—81no—
184C4×C113—81no—
185C4×C113—81no—
186C4×C113—81no—
187C4×C113—161no—
188#12178C11311yesmaximal, characteristic, direct product factor, Sylow
189C2×C113—21no—
190C2×C113—21no—
191C2×C113—41no—
192C2×C113—41no—
193C2×C113—161no—
194C2×C113#159911yescharacteristic
195C2×C113#219711yescharacteristic
196C2×C113#220011yescharacteristic
197#2742C2×C11311yescharacteristic, complemented
198#2044C2×C11311yescharacteristic
199#1613C2×C11311yescharacteristic
200#1601C2×C11311yescharacteristic
201#1352C2×C11311yescharacteristic, complemented
202#1351C2×C11311yescharacteristic, complemented
203#1326C2×C11311yescharacteristic, complemented
204C113#1217811yescharacteristic, direct product factor, Sylow
205#534C22×C11311yescharacteristic
206#481—21no—
207#448—21no—
208C2×#99—21no—
209#400—21no—
210#399C22×C11311yescharacteristic
211#395—21no—
212#393C22×C11311yescharacteristic
213#389—21no—
214#388—21no—
215#387—21no—
216#386—21no—
217#385C22×C11311yescharacteristic
218#380—21no—
219#342C22×C11311yescharacteristic
220#327—21no—
221#327—21no—
222#323C22×C11311yescharacteristic
223#323C22×C11311yescharacteristic
224C22×Q8D4×C11311yescharacteristic
225C22×D4—21no—
226C23×C4D4×C11311yescharacteristic
227C2×SD16—41no—
228#123—41no—
229#121—21no—
230#121—21no—
231#120—41no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4D4×C11311yescharacteristic
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—41no—
242C2×C22⋊C4D4×C11311yescharacteristic
243C2×C22⋊C4C23×C11311yescharacteristic
244C2×C42—21no—
245#106—41no—
246#103—41no—
247#102—41no—
248#99—42no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—41no—
258#95D4×C11311yescharacteristic
259#95D4×C11311yescharacteristic
260C24—21no—
261C24C2×D4×C11311yescharacteristic
262C2×Q8—41no—
263C2×Q8—81no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—42no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4C2×D4×C11311yescharacteristic
283C22×C4C2×D4×C11311yescharacteristic
284SD16—82no—
285C2×C8—41no—
286C2×C8—41no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—41no—
290C4⋊C4—42no—
291C4⋊C4—42no—
292C4⋊C4—81no—
293C4⋊C4—81no—
294C4⋊C4—81no—
295C22⋊C4—21no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—81no—
302C22⋊C4—81no—
303C22⋊C4—82no—
304C22⋊C4SD16×C11312yescomplemented
305C42—81no—
306C23—21no—
307C23—21no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—81no—
314C23—81no—
315C23#120×C11311yescharacteristic
316C23C2×SD16×C11311yescharacteristic
317C23#137×C11311yescharacteristic
318Q8—42no—
319Q8—81no—
320D4—81no—
321D4—81no—
322D4—81no—
323D4—81no—
324D4—81no—
325D4—81no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C8—81no—
357C8—81no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—81no—
367C22—82no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—161no—
372C22#448×C11311yescharacteristic
373C22#454×C11311yescharacteristic
374C22B(4,𝔽2)×C11311yescharacteristic
375C4—42no—
376C4—41no—
377C4—42no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—81no—
382C4—81no—
383C4—81no—
384C4—161no—
385C2—21no—
386C2—21no—
387C2—41no—
388C2—41no—
389C2—161no—
390C2C113×#159911yescharacteristic
391C2C113×#219711yescharacteristic
392C2C113×#220011yescharacteristic
subgroupG/H
center, socleC22×C113B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C113
prime radical#534×C113C22
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C23×C113 ◁ C2×C22⋊C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#2742C2semidirect
5. C113×#1352C2semidirect
6. C113×#1351C2semidirect
7. C113×#1326C2semidirect
107. C22⋊C4×C113SD16semidirect
188. #12178C113direct (N × H)
197. #2742C2×C113semidirect
201. #1352C2×C113semidirect
202. #1351C2×C113semidirect
203. #1326C2×C113semidirect
204. C113#12178direct (N × H)
304. C22⋊C4SD16×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#27422
C113×#20442
C113×#16132
C113×#16012
C113×#13522
C113×#13512
C113×#13262
#12178113