Finite Group Databasebeta

← C2×C113×#1470 #43285395

Subgroups — C2×C113×#1470 #43285395

Order 28928.

1002 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#125×C113C211yesmaximal, characteristic
2C2×#432×C113C211yesmaximal, characteristic
3C2×#431×C113C211yesmaximal, characteristic
4C113×#1470C218yesmaximal, direct product factor
5C2×#324×C113C214yesmaximal
6C2×#125×C113—21no—
7C2×#125×C113—21no—
8C2×#125×C113—21no—
9C2×#125×C113—21no—
10C2×#125×C113—22no—
11C2×#125×C113—22no—
12C2×#125×C113C414yes—
13C2×#125×C113C2214yes—
14C22×C4⋊C4×C113C411yescharacteristic
15C22×C4⋊C4×C113C412yes—
16C22×C4⋊C4×C113C411yescharacteristic
17C22×C4⋊C4×C113C2212yes—
18C22×C42×C113C2211yescharacteristic
19#432×C113—22no—
20#432×C113C2214yes—
21#431×C113—22no—
22#431×C113C2214yes—
23C2×C4⋊C8×C113—21no—
24C2×C4⋊C8×C113—21no—
25C2×C22⋊C8×C113C2212yes—
26C2×C22⋊C8×C113C2212yes—
27C2×#97×C113—21no—
28C2×C4×C8×C113—21no—
29#324×C113C22116yes—
30C23×C4×C113C2×C412yes—
31C23×C4×C113C2×C411yescharacteristic
32C23×C4×C113C2×C411yescharacteristic
33C23×C4×C113C2×C412yes—
34C23×C4×C113C2311yescharacteristic
35C22×C8×C113—22no—
36C22×C8×C113—22no—
37#125×C113—24no—
38#125×C113—24no—
39#125×C113—24no—
40#125×C113—24no—
41#125×C113—24no—
42#125×C113—24no—
43#125×C113—24no—
44#125×C113—24no—
45C2×C4⋊C4×C113—24no—
46C2×C4⋊C4×C113—22no—
47C2×C4⋊C4×C113—22no—
48C2×C4⋊C4×C113—21no—
49C2×C4⋊C4×C113—22no—
50C2×C4⋊C4×C113—22no—
51C2×C4⋊C4×C113—21no—
52C2×C4⋊C4×C113—21no—
53C2×C4⋊C4×C113—21no—
54C2×C4⋊C4×C113—22no—
55C2×C4⋊C4×C113—22no—
56C2×C4⋊C4×C113—22no—
57C2×C4⋊C4×C113—22no—
58C2×C4⋊C4×C113C2×C414yes—
59C2×C4⋊C4×C113C2×C418yes—
60C2×C4⋊C4×C113C2×C414yes—
61C2×C4⋊C4×C113C2×C414yes—
62C2×C4⋊C4×C113C2314yes—
63C2×C42×C113C2×C412yes—
64C2×C42×C113D411yescharacteristic
65C2×C42×C113D411yescharacteristic
66C2×C42×C113D411yescharacteristic
67C2×C42×C113D411yescharacteristic
68C2×C42×C113D412yes—
69C2×C42×C113D412yes—
70C2×C42×C113C2312yes—
71C4⋊C8×C113—24no—
72C4⋊C8×C113—24no—
73C22⋊C8×C113—22no—
74C22⋊C8×C113—22no—
75C22⋊C8×C113C2314yes—
76C22⋊C8×C113C2314yes—
77#97×C113—24no—
78C4×C8×C113—24no—
79C24×C113C22×C411yescharacteristic
80C22×C4×C113—24no—
81C22×C4×C113—24no—
82C22×C4×C113—22no—
83C22×C4×C113—22no—
84C22×C4×C113—22no—
85C22×C4×C113—22no—
86C22×C4×C113—28no—
87C22×C4×C113—42no—
88C22×C4×C113—44no—
89C22×C4×C113C22⋊C412yes—
90C22×C4×C113C22⋊C412yes—
91C22×C4×C113C22⋊C411yescharacteristic
92C22×C4×C113C22⋊C411yescharacteristic
93C22×C4×C113C22⋊C411yescharacteristic
94C22×C4×C113C22⋊C411yescharacteristic
95C22×C4×C113C22×C414yes—
96C22×C4×C113C22×C412yes—
97C22×C4×C113C22×C412yes—
98C22×C4×C113C22×C414yes—
99C22×C4×C113C22×C411yescharacteristic
100C22×C4×C113C2×D411yescharacteristic
101C22×C4×C113C2×D411yescharacteristic
102C22×C4×C113C2×D411yescharacteristic
103C22×C4×C113C2×D411yescharacteristic
104C22×C4×C113C2411yescharacteristic
105C2×C8×C113—24no—
106C2×C8×C113—24no—
107C2×C8×C113—44no—
108C2×C8×C113—44no—
109C4⋊C4×C113—24no—
110C4⋊C4×C113—24no—
111C4⋊C4×C113—24no—
112C4⋊C4×C113—28no—
113C4⋊C4×C113—28no—
114C4⋊C4×C113—24no—
115C4⋊C4×C113—24no—
116C4⋊C4×C113—24no—
117C4⋊C4×C113—24no—
118C4⋊C4×C113—24no—
119C42×C113C22⋊C412yes—
120C42×C113C22⋊C412yes—
121C42×C113C22⋊C412yes—
122C42×C113C22⋊C412yes—
123C42×C113C2×D412yes—
124C42×C113C2×D412yes—
125C42×C113C2×D412yes—
126C42×C113C2×D412yes—
127C23×C113—22no—
128C23×C113—22no—
129C23×C113C2×C22⋊C411yescharacteristic
130C23×C113C2×C22⋊C411yescharacteristic
131C23×C113#13114yes—
132C23×C113C23×C411yescharacteristic
133C2×C4×C113—24no—
134C2×C4×C113—24no—
135C2×C4×C113—22no—
136C2×C4×C113—22no—
137C2×C4×C113—22no—
138C2×C4×C113—22no—
139C2×C4×C113—22no—
140C2×C4×C113—24no—
141C2×C4×C113—24no—
142C2×C4×C113—24no—
143C2×C4×C113—24no—
144C2×C4×C113—28no—
145C2×C4×C113—41no—
146C2×C4×C113—41no—
147C2×C4×C113—41no—
148C2×C4×C113—41no—
149C2×C4×C113—44no—
150C2×C4×C113—44no—
151C2×C4×C113—44no—
152C2×C4×C113—44no—
153C2×C4×C113—44no—
154C2×C4×C113#10114yes—
155C2×C4×C113C2×C22⋊C411yescharacteristic
156C2×C4×C113C2×C22⋊C411yescharacteristic
157C2×C4×C113C2×C22⋊C412yes—
158C2×C4×C113C2×C22⋊C412yes—
159C2×C4×C113C2×C22⋊C412yes—
160C2×C4×C113C2×C22⋊C412yes—
161C2×C4×C113C22×D411yescharacteristic
162C2×C4×C113C22×D411yescharacteristic
163C8×C113—44no—
164C8×C113—44no—
165C22×C113—21no—
166C22×C113—21no—
167C22×C113—21no—
168C22×C113—21no—
169C22×C113—28no—
170C22×C113#40812yes—
171C22×C113#40812yes—
172C22×C113#41012yes—
173C22×C113C2×#10112yes—
174C22×C113C22×C22⋊C411yescharacteristic
175C22×C113C2×#13112yes—
176C4×C113—22no—
177C4×C113—22no—
178C4×C113—21no—
179C4×C113—21no—
180C4×C113—21no—
181C4×C113—21no—
182C4×C113—22no—
183C4×C113—44no—
184C4×C113—44no—
185C4×C113C2×#10114yes—
186C2×#1470C11311yesmaximal, characteristic, direct product factor, Sylow
187C2×C113—22no—
188C2×C113—22no—
189C2×C113#147014yesdirect product factor
190C2×C113C2×#40811yescharacteristic
191C2×C113C2×#41011yescharacteristic
192C2×C113C22×#10111yescharacteristic
193C22×#125C2×C11311yescharacteristic
194C2×#432C2×C11311yescharacteristic
195C2×#431C2×C11311yescharacteristic
196#1470C2×C11318yesdirect product factor
197C2×#324C2×C11314yes—
198C113C2×#147011yescharacteristic, direct product factor, Sylow
199C2×#125—21no—
200C2×#125—21no—
201C2×#125—21no—
202C2×#125—21no—
203C2×#125—22no—
204C2×#125—22no—
205C2×#125C4×C11314yes—
206C2×#125C22×C11314yes—
207C22×C4⋊C4C4×C11311yescharacteristic
208C22×C4⋊C4C4×C11312yes—
209C22×C4⋊C4C4×C11311yescharacteristic
210C22×C4⋊C4C22×C11312yes—
211C22×C42C22×C11311yescharacteristic
212#432—22no—
213#432C22×C11314yes—
214#431—22no—
215#431C22×C11314yes—
216C2×C4⋊C8—21no—
217C2×C4⋊C8—21no—
218C2×C22⋊C8C22×C11312yes—
219C2×C22⋊C8C22×C11312yes—
220C2×#97—21no—
221C2×C4×C8—21no—
222#324C22×C113116yes—
223C23×C4C2×C4×C11312yes—
224C23×C4C2×C4×C11311yescharacteristic
225C23×C4C2×C4×C11311yescharacteristic
226C23×C4C2×C4×C11312yes—
227C23×C4C23×C11311yescharacteristic
228C22×C8—22no—
229C22×C8—22no—
230#125—24no—
231#125—24no—
232#125—24no—
233#125—24no—
234#125—24no—
235#125—24no—
236#125—24no—
237#125—24no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4C2×C4×C11314yes—
252C2×C4⋊C4C2×C4×C11318yes—
253C2×C4⋊C4C2×C4×C11314yes—
254C2×C4⋊C4C2×C4×C11314yes—
255C2×C4⋊C4C23×C11314yes—
256C2×C42C2×C4×C11312yes—
257C2×C42D4×C11311yescharacteristic
258C2×C42D4×C11311yescharacteristic
259C2×C42D4×C11311yescharacteristic
260C2×C42D4×C11311yescharacteristic
261C2×C42D4×C11312yes—
262C2×C42D4×C11312yes—
263C2×C42C23×C11312yes—
264C4⋊C8—24no—
265C4⋊C8—24no—
266C22⋊C8—22no—
267C22⋊C8—22no—
268C22⋊C8C23×C11314yes—
269C22⋊C8C23×C11314yes—
270#97—24no—
271C4×C8—24no—
272C24C22×C4×C11311yescharacteristic
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—28no—
280C22×C4—42no—
281C22×C4—44no—
282C22×C4C22⋊C4×C11312yes—
283C22×C4C22⋊C4×C11311yescharacteristic
284C22×C4C22⋊C4×C11311yescharacteristic
285C22×C4C22⋊C4×C11311yescharacteristic
286C22×C4C22⋊C4×C11312yes—
287C22×C4C22⋊C4×C11311yescharacteristic
288C22×C4C22×C4×C11314yes—
289C22×C4C22×C4×C11312yes—
290C22×C4C22×C4×C11312yes—
291C22×C4C22×C4×C11314yes—
292C22×C4C22×C4×C11311yescharacteristic
293C22×C4C2×D4×C11311yescharacteristic
294C22×C4C2×D4×C11311yescharacteristic
295C22×C4C2×D4×C11311yescharacteristic
296C22×C4C2×D4×C11311yescharacteristic
297C22×C4C24×C11311yescharacteristic
298C2×C8—24no—
299C2×C8—24no—
300C2×C8—44no—
301C2×C8—44no—
302C4⋊C4—24no—
303C4⋊C4—24no—
304C4⋊C4—24no—
305C4⋊C4—28no—
306C4⋊C4—28no—
307C4⋊C4—24no—
308C4⋊C4—24no—
309C4⋊C4—24no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C42C22⋊C4×C11312yes—
313C42C22⋊C4×C11312yes—
314C42C22⋊C4×C11312yes—
315C42C22⋊C4×C11312yes—
316C42C2×D4×C11312yes—
317C42C2×D4×C11312yes—
318C42C2×D4×C11312yes—
319C42C2×D4×C11312yes—
320C23—22no—
321C23—22no—
322C23C2×C22⋊C4×C11311yescharacteristic
323C23C2×C22⋊C4×C11311yescharacteristic
324C23#131×C11314yes—
325C23C23×C4×C11311yescharacteristic
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—28no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4#101×C11314yes—
348C2×C4C2×C22⋊C4×C11311yescharacteristic
349C2×C4C2×C22⋊C4×C11311yescharacteristic
350C2×C4C2×C22⋊C4×C11312yes—
351C2×C4C2×C22⋊C4×C11312yes—
352C2×C4C2×C22⋊C4×C11312yes—
353C2×C4C2×C22⋊C4×C11312yes—
354C2×C4C22×D4×C11311yescharacteristic
355C2×C4C22×D4×C11311yescharacteristic
356C8—44no—
357C8—44no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—28no—
363C22#408×C11312yes—
364C22#408×C11312yes—
365C22#410×C11312yes—
366C22C2×#101×C11312yes—
367C22C22×C22⋊C4×C11311yescharacteristic
368C22C2×#131×C11312yes—
369C4—22no—
370C4—22no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—22no—
376C4—44no—
377C4—44no—
378C4C2×#101×C11314yes—
379C2—22no—
380C2—22no—
381C2C113×#147014yesdirect product factor
382C2C2×#408×C11311yescharacteristic
383C2C2×#410×C11311yescharacteristic
384C2C22×#101×C11311yescharacteristic
subgroupG/H
center, socleC23×C113C2×C22⋊C4
commutatorC23C23×C4×C113
Frattini, cosocleC22×C4C24×C113
prime radicalC24×C113C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C22×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
4. C113×#1470C2direct (N × H)
186. C2×#1470C113direct (N × H)
189. C2×C113#1470direct (N × H)
196. #1470C2×C113direct (N × H)
198. C113C2×#1470direct (N × H)
381. C2C113×#1470direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#125×C1132
C2×#432×C1132
C2×#431×C1132
C113×#14702
C2×#324×C1132
C2×#1470113