Finite Group Databasebeta

← C139×#8496 #48003092

Subgroups — C139×#8496 #48003092

Order 35584.

676 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3550×C139C211yesmaximal, characteristic
2#1995×C139C211yesmaximal, characteristic, complemented
3#1559×C139C211yesmaximal, characteristic, complemented
4#1557×C139C211yesmaximal, characteristic
5#1537×C139C211yesmaximal, characteristic, complemented
6#1506×C139C211yesmaximal, characteristic, complemented
7#1505×C139C211yesmaximal, characteristic
8#563×C139—22no—
9#559×C139—21no—
10Q82×C139—21no—
11#556×C139—21no—
12#556×C139C412yescomplemented
13D4×Q8×C139—21no—
14D4×Q8×C139C412yescomplemented
15#542×C139—22no—
16#542×C139—22no—
17#536×C139—22no—
18#533×C139C2211yescharacteristic
19#533×C139C2211yescharacteristic
20#532×C139C2211yescharacteristic
21#432×C139C2211yescharacteristic
22#432×C139C2211yescharacteristic
23#423×C139C2211yescharacteristic
24#376×C139C2211yescharacteristic
25#339×C139—22no—
26#333×C139—21no—
27#332×C139—21no—
28#332×C139—21no—
29#331×C139—21no—
30#330×C139—22no—
31#328×C139—22no—
32#327×C139—22no—
33C2×#41×C139—21no—
34C22×Q8×C139—22no—
35C2×M16×C139—21no—
36C4⋊Q8×C139—24no—
37C4⋊Q8×C139—22no—
38C4⋊Q8×C139—22no—
39C4⋊Q8×C139C2×C411yescharacteristic
40C4⋊Q8×C139C2×C411yescharacteristic
41C4⋊Q8×C139D411yescharacteristic
42C4⋊Q8×C139D411yescharacteristic
43C4⋊Q8×C139D411yescharacteristic
44#127×C139D411yescharacteristic
45#126×C139—24no—
46#126×C139—24no—
47#125×C139—21no—
48#125×C139D412yes—
49#124×C139—24no—
50#124×C139—22no—
51#124×C139—22no—
52#124×C139—21no—
53#123×C139—24no—
54#123×C139—24no—
55C22⋊Q8×C139—24no—
56C22⋊Q8×C139—22no—
57C22⋊Q8×C139—21no—
58C22⋊Q8×C139—21no—
59C22⋊Q8×C139—21no—
60C22⋊Q8×C139—22no—
61C22⋊Q8×C139—24no—
62C22⋊Q8×C139D412yes—
63#121×C139—21no—
64#121×C139D412yes—
65C4×Q8×C139—22no—
66C4×Q8×C139—22no—
67C4×Q8×C139—21no—
68C4×Q8×C139—21no—
69C4×Q8×C139—21no—
70C4×Q8×C139C2×C412yes—
71C4×D4×C139—22no—
72C4×D4×C139—22no—
73C4×D4×C139—21no—
74C4×D4×C139C2×C412yes—
75#117×C139—21no—
76#117×C139—22no—
77#117×C139D412yes—
78C2×C42×C139—21no—
79C2×C42×C139C2311yescharacteristic
80C4⋊C8×C139—21no—
81C4⋊C8×C139—21no—
82C4⋊C8×C139—21no—
83C4⋊C8×C139—21no—
84C22⋊C8×C139—21no—
85C22⋊C8×C139—21no—
86#97×C139—21no—
87#97×C139—21no—
88#95×C139—21no—
89#95×C139—21no—
90#41×C139—82no—
91C2×Q8×C139—24no—
92C2×Q8×C139—21no—
93C2×Q8×C139—21no—
94C2×Q8×C139—21no—
95C2×Q8×C139—21no—
96C2×Q8×C139—84no—
97C2×Q8×C139C22⋊C412yes—
98C2×D4×C139—22no—
99C2×D4×C139—21no—
100C2×D4×C139—21no—
101C2×D4×C139C22⋊C412yes—
102C22×C4×C139—24no—
103C22×C4×C139—22no—
104C22×C4×C139—41no—
105C22×C4×C139C2×D411yescharacteristic
106C22×C4×C139C2×D411yescharacteristic
107C22×C4×C139C2×D411yescharacteristic
108M16×C139—42no—
109C2×C8×C139—41no—
110C2×C8×C139—41no—
111C2×C8×C139—41no—
112C4⋊C4×C139—24no—
113C4⋊C4×C139—24no—
114C4⋊C4×C139—21no—
115C4⋊C4×C139—21no—
116C4⋊C4×C139—22no—
117C4⋊C4×C139—21no—
118C4⋊C4×C139—21no—
119C4⋊C4×C139—21no—
120C4⋊C4×C139—21no—
121C4⋊C4×C139—22no—
122C4⋊C4×C139—22no—
123C4⋊C4×C139—22no—
124C4⋊C4×C139C22⋊C412yes—
125C4⋊C4×C139C22⋊C412yes—
126C4⋊C4×C139C22⋊C412yes—
127C4⋊C4×C139C22⋊C412yes—
128C22⋊C4×C139—24no—
129C22⋊C4×C139—24no—
130C22⋊C4×C139—24no—
131C22⋊C4×C139—22no—
132C22⋊C4×C139—22no—
133C22⋊C4×C139—22no—
134C22⋊C4×C139—22no—
135C42×C139—24no—
136C42×C139—22no—
137C42×C139—22no—
138C42×C139—22no—
139C42×C139—41no—
140C42×C139C22×C411yescharacteristic
141C42×C139C2×D411yescharacteristic
142C42×C139C2×D411yescharacteristic
143C42×C139C2×D411yescharacteristic
144C23×C139—22no—
145C23×C139#12011yescharacteristic
146Q8×C139—42no—
147Q8×C139—42no—
148Q8×C139—42no—
149Q8×C139—41no—
150Q8×C139—41no—
151Q8×C139—81no—
152Q8×C139—84no—
153D4×C139—42no—
154D4×C139—41no—
155D4×C139—41no—
156D4×C139—81no—
157D4×C139—82no—
158C2×C4×C139—21no—
159C2×C4×C139—21no—
160C2×C4×C139—22no—
161C2×C4×C139—22no—
162C2×C4×C139—22no—
163C2×C4×C139—22no—
164C2×C4×C139—22no—
165C2×C4×C139—41no—
166C2×C4×C139—41no—
167C2×C4×C139—44no—
168C2×C4×C139—42no—
169C2×C4×C139—84no—
170C2×C4×C139—81no—
171C2×C4×C139—81no—
172C2×C4×C139C2×C22⋊C411yescharacteristic
173C2×C4×C139C2×C22⋊C411yescharacteristic
174C2×C4×C139C2×C22⋊C411yescharacteristic
175C2×C4×C139#12011yescharacteristic
176C2×C4×C139#12011yescharacteristic
177C2×C4×C139#12011yescharacteristic
178C8×C139—81no—
179C8×C139—81no—
180C8×C139—81no—
181C22×C139—21no—
182C22×C139—21no—
183C22×C139—21no—
184C22×C139—42no—
185C22×C139—42no—
186C22×C139—42no—
187C22×C139#37911yescharacteristic
188C4×C139—21no—
189C4×C139—21no—
190C4×C139—21no—
191C4×C139—21no—
192C4×C139—21no—
193C4×C139—42no—
194C4×C139—42no—
195C4×C139—42no—
196C4×C139—42no—
197C4×C139—42no—
198C4×C139—82no—
199C4×C139#45411yescharacteristic
200C4×C139#45611yescharacteristic
201C2×C139—41no—
202C2×C139—82no—
203C2×C139#179311yescharacteristic
204C2×C139#179511yescharacteristic
205C2×C139#179611yescharacteristic
206#8496C13911yesmaximal, characteristic, direct product factor, Sylow
207C139#849611yescharacteristic, direct product factor, Sylow
208#3550C2×C13911yescharacteristic
209#1995C2×C13911yescharacteristic, complemented
210#1559C2×C13911yescharacteristic, complemented
211#1557C2×C13911yescharacteristic
212#1537C2×C13911yescharacteristic, complemented
213#1506C2×C13911yescharacteristic, complemented
214#1505C2×C13911yescharacteristic
215#563—22no—
216#559—21no—
217Q82—21no—
218#556—21no—
219#556C4×C13912yescomplemented
220D4×Q8—21no—
221D4×Q8C4×C13912yescomplemented
222#542—22no—
223#542—22no—
224#536—22no—
225#533C22×C13911yescharacteristic
226#533C22×C13911yescharacteristic
227#532C22×C13911yescharacteristic
228#432C22×C13911yescharacteristic
229#432C22×C13911yescharacteristic
230#423C22×C13911yescharacteristic
231#376C22×C13911yescharacteristic
232#339—22no—
233#333—21no—
234#332—21no—
235#332—21no—
236#331—21no—
237#330—22no—
238#328—22no—
239#327—22no—
240C2×#41—21no—
241C22×Q8—22no—
242C2×M16—21no—
243C4⋊Q8—24no—
244C4⋊Q8—22no—
245C4⋊Q8—22no—
246C4⋊Q8C2×C4×C13911yescharacteristic
247C4⋊Q8C2×C4×C13911yescharacteristic
248C4⋊Q8D4×C13911yescharacteristic
249C4⋊Q8D4×C13911yescharacteristic
250C4⋊Q8D4×C13911yescharacteristic
251#127D4×C13911yescharacteristic
252#126—24no—
253#126—24no—
254#125—21no—
255#125D4×C13912yes—
256#124—24no—
257#124—22no—
258#124—22no—
259#124—21no—
260#123—24no—
261#123—24no—
262C22⋊Q8—24no—
263C22⋊Q8—22no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—21no—
267C22⋊Q8—22no—
268C22⋊Q8—24no—
269C22⋊Q8D4×C13912yes—
270#121—21no—
271#121D4×C13912yes—
272C4×Q8—22no—
273C4×Q8—22no—
274C4×Q8—21no—
275C4×Q8—21no—
276C4×Q8—21no—
277C4×Q8C2×C4×C13912yes—
278C4×D4—22no—
279C4×D4—22no—
280C4×D4—21no—
281C4×D4C2×C4×C13912yes—
282#117—21no—
283#117—22no—
284#117D4×C13912yes—
285C2×C42—21no—
286C2×C42C23×C13911yescharacteristic
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293#97—21no—
294#97—21no—
295#95—21no—
296#95—21no—
297#41—82no—
298C2×Q8—24no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—84no—
304C2×Q8C22⋊C4×C13912yes—
305C2×D4—22no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4C22⋊C4×C13912yes—
309C22×C4—24no—
310C22×C4—22no—
311C22×C4—41no—
312C22×C4C2×D4×C13911yescharacteristic
313C22×C4C2×D4×C13911yescharacteristic
314C22×C4C2×D4×C13911yescharacteristic
315M16—42no—
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C4⋊C4—24no—
320C4⋊C4—24no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—22no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4C22⋊C4×C13912yes—
332C4⋊C4C22⋊C4×C13912yes—
333C4⋊C4C22⋊C4×C13912yes—
334C4⋊C4C22⋊C4×C13912yes—
335C22⋊C4—24no—
336C22⋊C4—24no—
337C22⋊C4—24no—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—22no—
342C42—24no—
343C42—22no—
344C42—22no—
345C42—22no—
346C42—41no—
347C42C22×C4×C13911yescharacteristic
348C42C2×D4×C13911yescharacteristic
349C42C2×D4×C13911yescharacteristic
350C42C2×D4×C13911yescharacteristic
351C23—22no—
352C23#120×C13911yescharacteristic
353Q8—42no—
354Q8—42no—
355Q8—42no—
356Q8—41no—
357Q8—41no—
358Q8—81no—
359Q8—84no—
360D4—42no—
361D4—41no—
362D4—41no—
363D4—81no—
364D4—82no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—44no—
375C2×C4—42no—
376C2×C4—84no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4C2×C22⋊C4×C13911yescharacteristic
380C2×C4C2×C22⋊C4×C13911yescharacteristic
381C2×C4C2×C22⋊C4×C13911yescharacteristic
382C2×C4#120×C13911yescharacteristic
383C2×C4#120×C13911yescharacteristic
384C2×C4#120×C13911yescharacteristic
385C8—81no—
386C8—81no—
387C8—81no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22#379×C13911yescharacteristic
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—42no—
401C4—42no—
402C4—42no—
403C4—42no—
404C4—42no—
405C4—82no—
406C4#454×C13911yescharacteristic
407C4#456×C13911yescharacteristic
408C2—41no—
409C2—82no—
410C2#1793×C13911yescharacteristic
411C2#1795×C13911yescharacteristic
412C2#1796×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#379
commutatorC42C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radical#532×C139C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1995×C139C2semidirect
3. #1559×C139C2semidirect
5. #1537×C139C2semidirect
6. #1506×C139C2semidirect
12. #556×C139C4semidirect
14. D4×Q8×C139C4semidirect
206. #8496C139direct (N × H)
207. C139#8496direct (N × H)
209. #1995C2×C139semidirect
210. #1559C2×C139semidirect
212. #1537C2×C139semidirect
213. #1506C2×C139semidirect
219. #556C4×C139semidirect
221. D4×Q8C4×C139semidirect

Maximal subgroups

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

subgroupindex
#3550×C1392
#1995×C1392
#1559×C1392
#1557×C1392
#1537×C1392
#1506×C1392
#1505×C1392
#8496139