Finite Group Databasebeta

← C139×#8555 #48003151

Subgroups — C139×#8555 #48003151

Order 35584.

1102 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 166 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
1C22×C22⋊Q8×C139C211yesmaximal, characteristic
2#1821×C139C212yesmaximal, complemented
3#1463×C139C212yesmaximal, complemented
4#1462×C139C212yesmaximal
5C23×Q8×C139C411yescharacteristic
6C24×C4×C139C411yescharacteristic
7C2×C22⋊Q8×C139—24no—
8C2×C22⋊Q8×C139—24no—
9C2×C22⋊Q8×C139—24no—
10C22×C4⋊C4×C139C411yescharacteristic
11C22×C4⋊C4×C139C2211yescharacteristic
12C22×C4⋊C4×C139C2211yescharacteristic
13C22×C22⋊C4×C139C411yescharacteristic
14C22×C22⋊C4×C139C2211yescharacteristic
15#407×C139C2214yes—
16#343×C139—24no—
17#324×C139—24no—
18#323×C139—24no—
19C25×C139C2×C411yescharacteristic
20C22×Q8×C139—22no—
21C22×Q8×C139—22no—
22C22×Q8×C139—22no—
23C22×Q8×C139—44no—
24C23×C4×C139—22no—
25C23×C4×C139—22no—
26C23×C4×C139—22no—
27C23×C4×C139—44no—
28C23×C4×C139C2×C411yescharacteristic
29C23×C4×C139C2×C411yescharacteristic
30C23×C4×C139C2×C411yescharacteristic
31C23×C4×C139C2×C411yescharacteristic
32C23×C4×C139C2×C411yescharacteristic
33C23×C4×C139C2311yescharacteristic
34C2×M16×C139—24no—
35C22⋊Q8×C139—232no—
36C2×C4⋊C4×C139—22no—
37C2×C4⋊C4×C139—22no—
38C2×C4⋊C4×C139—22no—
39C2×C4⋊C4×C139—22no—
40C2×C4⋊C4×C139—22no—
41C2×C4⋊C4×C139—22no—
42C2×C4⋊C4×C139—22no—
43C2×C4⋊C4×C139D414yes—
44C2×C4⋊C4×C139D414yes—
45C2×C22⋊C4×C139—22no—
46C2×C22⋊C4×C139—22no—
47C2×C22⋊C4×C139—22no—
48C2×C22⋊C4×C139—22no—
49C2×C22⋊C4×C139—22no—
50C2×C22⋊C4×C139D414yes—
51C22⋊C8×C139—24no—
52C22⋊C8×C139—24no—
53C24×C139—24no—
54C24×C139—21no—
55C24×C139—21no—
56C24×C139—42no—
57C24×C139—42no—
58C24×C139C22⋊C412yes—
59C24×C139C22×C411yescharacteristic
60C2×Q8×C139—28no—
61C2×Q8×C139—48no—
62C2×Q8×C139—48no—
63C2×Q8×C139—44no—
64C2×Q8×C139—44no—
65C22×C4×C139—21no—
66C22×C4×C139—21no—
67C22×C4×C139—24no—
68C22×C4×C139—28no—
69C22×C4×C139—21no—
70C22×C4×C139—21no—
71C22×C4×C139—21no—
72C22×C4×C139—21no—
73C22×C4×C139—21no—
74C22×C4×C139—21no—
75C22×C4×C139—21no—
76C22×C4×C139—21no—
77C22×C4×C139—42no—
78C22×C4×C139—48no—
79C22×C4×C139—48no—
80C22×C4×C139—44no—
81C22×C4×C139—44no—
82C22×C4×C139—42no—
83C22×C4×C139—42no—
84C22×C4×C139—42no—
85C22×C4×C139—42no—
86C22×C4×C139C22⋊C412yes—
87C22×C4×C139C22⋊C412yes—
88C22×C4×C139C22⋊C412yes—
89C22×C4×C139C22⋊C412yes—
90C22×C4×C139C22⋊C412yes—
91C22×C4×C139C2×D412yes—
92C22×C4×C139C2×D412yes—
93C22×C4×C139C2×D412yes—
94M16×C139—48no—
95C2×C8×C139—44no—
96C4⋊C4×C139—28no—
97C4⋊C4×C139—28no—
98C4⋊C4×C139—28no—
99C22⋊C4×C139—28no—
100C22⋊C4×C139—28no—
101C23×C139—22no—
102C23×C139—22no—
103C23×C139—22no—
104C23×C139—24no—
105C23×C139—24no—
106C23×C139—22no—
107C23×C139—22no—
108C23×C139—42no—
109C23×C139—42no—
110C23×C139—42no—
111C23×C139—416no—
112C23×C139—42no—
113C23×C139—42no—
114C23×C139—42no—
115C23×C139#10114yes—
116C23×C139C2×C22⋊C411yescharacteristic
117C23×C139C2×C22⋊C411yescharacteristic
118C23×C139C2×C22⋊C411yescharacteristic
119Q8×C139—416no—
120C2×C4×C139—24no—
121C2×C4×C139—24no—
122C2×C4×C139—22no—
123C2×C4×C139—24no—
124C2×C4×C139—22no—
125C2×C4×C139—22no—
126C2×C4×C139—22no—
127C2×C4×C139—22no—
128C2×C4×C139—22no—
129C2×C4×C139—42no—
130C2×C4×C139—42no—
131C2×C4×C139—416no—
132C2×C4×C139—42no—
133C2×C4×C139—42no—
134C2×C4×C139—42no—
135C2×C4×C139—42no—
136C2×C4×C139—42no—
137C2×C4×C139—42no—
138C2×C4×C139—42no—
139C2×C4×C139—42no—
140C2×C4×C139—42no—
141C2×C4×C139—42no—
142C2×C4×C139—42no—
143C2×C4×C139—42no—
144C2×C4×C139#10014yes—
145C2×C4×C139#12014yes—
146C8×C139—84no—
147C22×C139—28no—
148C22×C139—21no—
149C22×C139—21no—
150C22×C139—21no—
151C22×C139—21no—
152C22×C139—21no—
153C22×C139—21no—
154C22×C139—24no—
155C22×C139—44no—
156C22×C139—48no—
157C22×C139—48no—
158C22×C139—44no—
159C22×C139—42no—
160C22×C139—42no—
161C22×C139#37911yescharacteristic
162C22×C139#41012yes—
163C22×C139C2×#10012yes—
164C22×C139C2×#10112yes—
165C4×C139—24no—
166C4×C139—24no—
167C4×C139—42no—
168C4×C139—42no—
169C4×C139—42no—
170C4×C139—42no—
171C2×C139—22no—
172C2×C139—22no—
173C2×C139—22no—
174C2×C139—44no—
175C2×C139#178211yescharacteristic
176C2×C139#178311yescharacteristic
177C2×C139#178411yescharacteristic
178#8555C13911yesmaximal, characteristic, direct product factor, Sylow
179C139#855511yescharacteristic, direct product factor, Sylow
180C22×C22⋊Q8C2×C13911yescharacteristic
181#1821C2×C13912yescomplemented
182#1463C2×C13912yescomplemented
183#1462C2×C13912yes—
184C23×Q8C4×C13911yescharacteristic
185C24×C4C4×C13911yescharacteristic
186C2×C22⋊Q8—24no—
187C2×C22⋊Q8—24no—
188C2×C22⋊Q8—24no—
189C22×C4⋊C4C4×C13911yescharacteristic
190C22×C4⋊C4C22×C13911yescharacteristic
191C22×C4⋊C4C22×C13911yescharacteristic
192C22×C22⋊C4C4×C13911yescharacteristic
193C22×C22⋊C4C22×C13911yescharacteristic
194#407C22×C13914yes—
195#343—24no—
196#324—24no—
197#323—24no—
198C25C2×C4×C13911yescharacteristic
199C22×Q8—22no—
200C22×Q8—22no—
201C22×Q8—22no—
202C22×Q8—44no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—44no—
207C23×C4C2×C4×C13911yescharacteristic
208C23×C4C2×C4×C13911yescharacteristic
209C23×C4C2×C4×C13911yescharacteristic
210C23×C4C2×C4×C13911yescharacteristic
211C23×C4C2×C4×C13911yescharacteristic
212C23×C4C23×C13911yescharacteristic
213C2×M16—24no—
214C22⋊Q8—232no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4D4×C13914yes—
223C2×C4⋊C4D4×C13914yes—
224C2×C22⋊C4—22no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4D4×C13914yes—
230C22⋊C8—24no—
231C22⋊C8—24no—
232C24—24no—
233C24—21no—
234C24—21no—
235C24—42no—
236C24—42no—
237C24C22⋊C4×C13912yes—
238C24C22×C4×C13911yescharacteristic
239C2×Q8—28no—
240C2×Q8—48no—
241C2×Q8—48no—
242C2×Q8—44no—
243C2×Q8—44no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—24no—
247C22×C4—28no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—42no—
257C22×C4—48no—
258C22×C4—48no—
259C22×C4—44no—
260C22×C4—44no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4C22⋊C4×C13912yes—
266C22×C4C22⋊C4×C13912yes—
267C22×C4C22⋊C4×C13912yes—
268C22×C4C22⋊C4×C13912yes—
269C22×C4C22⋊C4×C13912yes—
270C22×C4C2×D4×C13912yes—
271C22×C4C2×D4×C13912yes—
272C22×C4C2×D4×C13912yes—
273M16—48no—
274C2×C8—44no—
275C4⋊C4—28no—
276C4⋊C4—28no—
277C4⋊C4—28no—
278C22⋊C4—28no—
279C22⋊C4—28no—
280C23—22no—
281C23—22no—
282C23—22no—
283C23—24no—
284C23—24no—
285C23—22no—
286C23—22no—
287C23—42no—
288C23—42no—
289C23—42no—
290C23—416no—
291C23—42no—
292C23—42no—
293C23—42no—
294C23#101×C13914yes—
295C23C2×C22⋊C4×C13911yescharacteristic
296C23C2×C22⋊C4×C13911yescharacteristic
297C23C2×C22⋊C4×C13911yescharacteristic
298Q8—416no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—416no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4#100×C13914yes—
324C2×C4#120×C13914yes—
325C8—84no—
326C22—28no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—24no—
334C22—44no—
335C22—48no—
336C22—48no—
337C22—44no—
338C22—42no—
339C22—42no—
340C22#379×C13911yescharacteristic
341C22#410×C13912yes—
342C22C2×#100×C13912yes—
343C22C2×#101×C13912yes—
344C4—24no—
345C4—24no—
346C4—42no—
347C4—42no—
348C4—42no—
349C4—42no—
350C2—22no—
351C2—22no—
352C2—22no—
353C2—44no—
354C2#1782×C13911yescharacteristic
355C2#1783×C13911yescharacteristic
356C2#1784×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#379
commutatorC24C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC25×C139C2×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1821×C139C2semidirect
3. #1463×C139C2semidirect
178. #8555C139direct (N × H)
179. C139#8555direct (N × H)
181. #1821C2×C139semidirect
182. #1463C2×C139semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1392
#1821×C1392
#1463×C1392
#1462×C1392
#8555139