Finite Group Databasebeta

← C139×#9340 #48003936

Subgroups — C139×#9340 #48003936

Order 35584.

480 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3217×C139C211yesmaximal, characteristic
2#2995×C139C211yesmaximal, characteristic, complemented
3#1965×C139C211yesmaximal, characteristic, complemented
4#1555×C139C211yesmaximal, characteristic, complemented
5#1529×C139C211yesmaximal, characteristic, complemented
6#1307×C139C211yesmaximal, characteristic, complemented
7#1291×C139C211yesmaximal, characteristic, complemented
8C2×#127×C139C2211yescharacteristic
9#529×C139C2211yescharacteristic
10#496×C139—21no—
11#490×C139—21no—
12#460×C139—21no—
13#459×C139—21no—
14#450×C139C412yes—
15#447×C139C412yes—
16#446×C139—21no—
17#436×C139—21no—
18#435×C139—21no—
19#435×C139—21no—
20#433×C139—21no—
21#432×C139C2211yescharacteristic
22#432×C139C2211yescharacteristic
23#432×C139C2211yescharacteristic
24#424×C139—21no—
25#423×C139C2211yescharacteristic
26C2×#100×C139—21no—
27C2×#100×C139—21no—
28C4×M16×C139C2211yescharacteristic
29#331×C139—21no—
30#331×C139—21no—
31#330×C139—21no—
32#329×C139—21no—
33C22×D4×C139—21no—
34C22×D4×C139—21no—
35C22×D4×C139C2×C412yes—
36C2×SD16×C139—22no—
37C2×D8×C139—22no—
38C2×M16×C139—21no—
39C2×M16×C139—21no—
40C2×M16×C139D411yescharacteristic
41C2×M16×C139D411yescharacteristic
42C22×C8×C139—21no—
43#127×C139—21no—
44#127×C139—21no—
45#127×C139—21no—
46#127×C139—21no—
47#126×C139—21no—
48#125×C139D411yescharacteristic
49#124×C139D411yescharacteristic
50#123×C139—21no—
51C22⋊Q8×C139C2×C411yescharacteristic
52#121×C139C2×C411yescharacteristic
53C4×Q8×C139D411yescharacteristic
54C4×D4×C139—21no—
55C4×D4×C139D411yescharacteristic
56#117×C139—21no—
57C2×C42×C139C2311yescharacteristic
58C4⋊C8×C139—21no—
59C4⋊C8×C139—21no—
60C4⋊C8×C139—21no—
61C4⋊C8×C139—21no—
62C4⋊C8×C139—21no—
63C4⋊C8×C139—21no—
64C4⋊C8×C139D411yescharacteristic
65C4⋊C8×C139D411yescharacteristic
66#102×C139—22no—
67#102×C139—22no—
68#100×C139—42no—
69#100×C139—42no—
70C22⋊C8×C139—21no—
71C22⋊C8×C139—21no—
72C22⋊C8×C139—21no—
73C22⋊C8×C139—21no—
74C22⋊C8×C139C2×C412yes—
75#97×C139—21no—
76#97×C139—21no—
77#97×C139—21no—
78#97×C139—21no—
79#97×C139—21no—
80C4×C8×C139—21no—
81C4×C8×C139—21no—
82C24×C139—22no—
83C2×Q8×C139C22⋊C411yescharacteristic
84C2×D4×C139—21no—
85C2×D4×C139—22no—
86C2×D4×C139—22no—
87C2×D4×C139—41no—
88C2×D4×C139—41no—
89C2×D4×C139—41no—
90C2×D4×C139—41no—
91C2×D4×C139—41no—
92C2×D4×C139—41no—
93C2×D4×C139—41no—
94C2×D4×C139—41no—
95C2×D4×C139—82no—
96C2×D4×C139—82no—
97C2×D4×C139C22⋊C411yescharacteristic
98C22×C4×C139—21no—
99C22×C4×C139C22×C411yescharacteristic
100C22×C4×C139C2×D411yescharacteristic
101C22×C4×C139#4111yescharacteristic
102SD16×C139—82no—
103D8×C139—82no—
104M16×C139—22no—
105M16×C139—41no—
106M16×C139—41no—
107M16×C139—41no—
108M16×C139—81no—
109C2×C8×C139—22no—
110C2×C8×C139—21no—
111C2×C8×C139—21no—
112C2×C8×C139—21no—
113C2×C8×C139—21no—
114C2×C8×C139—41no—
115C2×C8×C139—41no—
116C2×C8×C139—81no—
117C4⋊C4×C139—21no—
118C4⋊C4×C139—21no—
119C4⋊C4×C139—21no—
120C4⋊C4×C139—21no—
121C4⋊C4×C139C22⋊C411yescharacteristic
122C4⋊C4×C139C22⋊C411yescharacteristic
123C22⋊C4×C139—21no—
124C22⋊C4×C139—21no—
125C22⋊C4×C139—21no—
126C22⋊C4×C139—21no—
127C22⋊C4×C139—21no—
128C42×C139—21no—
129C42×C139C2×D411yescharacteristic
130C42×C139C2×D411yescharacteristic
131C42×C139C2×D411yescharacteristic
132C42×C139#4111yescharacteristic
133C23×C139—21no—
134C23×C139—42no—
135C23×C139—42no—
136C23×C139—42no—
137C23×C139—82no—
138C23×C139—82no—
139C23×C139C4×D411yescharacteristic
140Q8×C139—41no—
141D4×C139—41no—
142D4×C139—42no—
143D4×C139—42no—
144D4×C139—82no—
145D4×C139—81no—
146D4×C139—81no—
147D4×C139—82no—
148D4×C139—82no—
149D4×C139—81no—
150D4×C139—81no—
151D4×C139—81no—
152C2×C4×C139—21no—
153C2×C4×C139—21no—
154C2×C4×C139—21no—
155C2×C4×C139—21no—
156C2×C4×C139—21no—
157C2×C4×C139—41no—
158C2×C4×C139—41no—
159C2×C4×C139—41no—
160C2×C4×C139—41no—
161C2×C4×C139C2×C22⋊C411yescharacteristic
162C2×C4×C139C4×D411yescharacteristic
163C2×C4×C139#12011yescharacteristic
164C2×C4×C139#12111yescharacteristic
165C2×C4×C139#12111yescharacteristic
166C2×C4×C139#12311yescharacteristic
167C8×C139—42no—
168C8×C139—42no—
169C8×C139—41no—
170C8×C139—41no—
171C8×C139—41no—
172C8×C139—41no—
173C8×C139—81no—
174C22×C139—21no—
175C22×C139—21no—
176C22×C139—21no—
177C22×C139—41no—
178C22×C139—41no—
179C22×C139—41no—
180C22×C139—82no—
181C22×C139—82no—
182C22×C139—82no—
183C22×C139—162no—
184C22×C139—162no—
185C22×C139#38611yescharacteristic
186C4×C139—21no—
187C4×C139—21no—
188C4×C139—21no—
189C4×C139—21no—
190C4×C139—21no—
191C4×C139—41no—
192C4×C139—41no—
193C4×C139—41no—
194C4×C139#45311yescharacteristic
195C4×C139#45411yescharacteristic
196C2×C139—41no—
197C2×C139—81no—
198C2×C139—162no—
199C2×C139#188311yescharacteristic
200C2×C139#190311yescharacteristic
201C2×C139#191411yescharacteristic
202#9340C13911yesmaximal, characteristic, direct product factor, Sylow
203C139#934011yescharacteristic, direct product factor, Sylow
204#3217C2×C13911yescharacteristic
205#2995C2×C13911yescharacteristic, complemented
206#1965C2×C13911yescharacteristic, complemented
207#1555C2×C13911yescharacteristic, complemented
208#1529C2×C13911yescharacteristic, complemented
209#1307C2×C13911yescharacteristic, complemented
210#1291C2×C13911yescharacteristic, complemented
211C2×#127C22×C13911yescharacteristic
212#529C22×C13911yescharacteristic
213#496—21no—
214#490—21no—
215#460—21no—
216#459—21no—
217#450C4×C13912yes—
218#447C4×C13912yes—
219#446—21no—
220#436—21no—
221#435—21no—
222#435—21no—
223#433—21no—
224#432C22×C13911yescharacteristic
225#432C22×C13911yescharacteristic
226#432C22×C13911yescharacteristic
227#424—21no—
228#423C22×C13911yescharacteristic
229C2×#100—21no—
230C2×#100—21no—
231C4×M16C22×C13911yescharacteristic
232#331—21no—
233#331—21no—
234#330—21no—
235#329—21no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4C2×C4×C13912yes—
239C2×SD16—22no—
240C2×D8—22no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16D4×C13911yescharacteristic
244C2×M16D4×C13911yescharacteristic
245C22×C8—21no—
246#127—21no—
247#127—21no—
248#127—21no—
249#127—21no—
250#126—21no—
251#125D4×C13911yescharacteristic
252#124D4×C13911yescharacteristic
253#123—21no—
254C22⋊Q8C2×C4×C13911yescharacteristic
255#121C2×C4×C13911yescharacteristic
256C4×Q8D4×C13911yescharacteristic
257C4×D4—21no—
258C4×D4D4×C13911yescharacteristic
259#117—21no—
260C2×C42C23×C13911yescharacteristic
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8D4×C13911yescharacteristic
268C4⋊C8D4×C13911yescharacteristic
269#102—22no—
270#102—22no—
271#100—42no—
272#100—42no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8C2×C4×C13912yes—
278#97—21no—
279#97—21no—
280#97—21no—
281#97—21no—
282#97—21no—
283C4×C8—21no—
284C4×C8—21no—
285C24—22no—
286C2×Q8C22⋊C4×C13911yescharacteristic
287C2×D4—21no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—82no—
299C2×D4—82no—
300C2×D4C22⋊C4×C13911yescharacteristic
301C22×C4—21no—
302C22×C4C22×C4×C13911yescharacteristic
303C22×C4C2×D4×C13911yescharacteristic
304C22×C4#41×C13911yescharacteristic
305SD16—82no—
306D8—82no—
307M16—22no—
308M16—41no—
309M16—41no—
310M16—41no—
311M16—81no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—81no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4C22⋊C4×C13911yescharacteristic
325C4⋊C4C22⋊C4×C13911yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C42—21no—
332C42C2×D4×C13911yescharacteristic
333C42C2×D4×C13911yescharacteristic
334C42C2×D4×C13911yescharacteristic
335C42#41×C13911yescharacteristic
336C23—21no—
337C23—42no—
338C23—42no—
339C23—42no—
340C23—82no—
341C23—82no—
342C23C4×D4×C13911yescharacteristic
343Q8—41no—
344D4—41no—
345D4—42no—
346D4—42no—
347D4—82no—
348D4—81no—
349D4—81no—
350D4—82no—
351D4—82no—
352D4—81no—
353D4—81no—
354D4—81no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4C2×C22⋊C4×C13911yescharacteristic
365C2×C4C4×D4×C13911yescharacteristic
366C2×C4#120×C13911yescharacteristic
367C2×C4#121×C13911yescharacteristic
368C2×C4#121×C13911yescharacteristic
369C2×C4#123×C13911yescharacteristic
370C8—42no—
371C8—42no—
372C8—41no—
373C8—41no—
374C8—41no—
375C8—41no—
376C8—81no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—82no—
384C22—82no—
385C22—82no—
386C22—162no—
387C22—162no—
388C22#386×C13911yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4#453×C13911yescharacteristic
398C4#454×C13911yescharacteristic
399C2—41no—
400C2—81no—
401C2—162no—
402C2#1883×C13911yescharacteristic
403C2#1903×C13911yescharacteristic
404C2#1914×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC22×C4C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radical#3217×C139C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2995×C139C2semidirect
3. #1965×C139C2semidirect
4. #1555×C139C2semidirect
5. #1529×C139C2semidirect
6. #1307×C139C2semidirect
7. #1291×C139C2semidirect
202. #9340C139direct (N × H)
203. C139#9340direct (N × H)
205. #2995C2×C139semidirect
206. #1965C2×C139semidirect
207. #1555C2×C139semidirect
208. #1529C2×C139semidirect
209. #1307C2×C139semidirect
210. #1291C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3217×C1392
#2995×C1392
#1965×C1392
#1555×C1392
#1529×C1392
#1307×C1392
#1291×C1392
#9340139