Finite Group Databasebeta

← C139×#10002 #48004598

Subgroups — C139×#10002 #48004598

Order 35584.

548 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3104×C139C211yesmaximal, characteristic, complemented
2#3077×C139C211yesmaximal, characteristic
3#2580×C139C211yesmaximal, characteristic
4#1518×C139C211yesmaximal, characteristic, complemented
5#1487×C139C211yesmaximal, characteristic, complemented
6#1478×C139C211yesmaximal, characteristic
7#1286×C139C211yesmaximal, characteristic, complemented
8#533×C139C2211yescharacteristic
9C2×C4×Q8×C139C2211yescharacteristic
10C2×C4×D4×C139C2211yescharacteristic
11#484×C139—21no—
12#478×C139—22no—
13#477×C139—21no—
14#476×C139—21no—
15#474×C139—21no—
16#462×C139—21no—
17#451×C139—21no—
18C4×Q16×C139—22no—
19#431×C139C2211yescharacteristic
20#431×C139C2211yescharacteristic
21#428×C139—21no—
22#423×C139C2211yescharacteristic
23#418×C139—21no—
24#399×C139—21no—
25#393×C139—21no—
26#390×C139—21no—
27#389×C139—21no—
28#385×C139—22no—
29#382×C139C2211yescharacteristic
30#328×C139—22no—
31Q8⋊C8×C139—22no—
32D4⋊C8×C139—22no—
33C22×Q8×C139D411yescharacteristic
34C22×D4×C139D411yescharacteristic
35C23×C4×C139—21no—
36C2×Q16×C139—22no—
37C2×M16×C139—21no—
38C4⋊Q8×C139D411yescharacteristic
39C4⋊Q8×C139D411yescharacteristic
40#125×C139—21no—
41C22⋊Q8×C139—21no—
42C22⋊Q8×C139—21no—
43C4×Q8×C139—21no—
44C4×Q8×C139—21no—
45C4×Q8×C139—21no—
46C4×Q8×C139—21no—
47C4×Q8×C139—21no—
48C4×Q8×C139—21no—
49C4×D4×C139—21no—
50C4×D4×C139—21no—
51C4×D4×C139—21no—
52C4×D4×C139—21no—
53#117×C139—21no—
54C2×C4⋊C4×C139—21no—
55C2×C4⋊C4×C139—21no—
56C2×C4⋊C4×C139—22no—
57C2×C4⋊C4×C139D411yescharacteristic
58C2×C4⋊C4×C139D411yescharacteristic
59C2×C22⋊C4×C139—22no—
60C2×C22⋊C4×C139—21no—
61C2×C22⋊C4×C139—22no—
62C2×C42×C139—21no—
63C2×C42×C139C2311yescharacteristic
64#107×C139—22no—
65#107×C139—22no—
66#106×C139—22no—
67C4⋊C8×C139—21no—
68C4⋊C8×C139—21no—
69C4⋊C8×C139—21no—
70C4⋊C8×C139D412yes—
71#103×C139—22no—
72#103×C139—22no—
73#102×C139—22no—
74#102×C139—22no—
75C22⋊C8×C139—21no—
76C22⋊C8×C139—21no—
77C4×C8×C139—21no—
78C4×C8×C139D412yes—
79#95×C139—22no—
80#95×C139—21no—
81#95×C139D412yes—
82C24×C139—21no—
83C2×Q8×C139—21no—
84C2×Q8×C139—21no—
85C2×Q8×C139—21no—
86C2×Q8×C139—21no—
87C2×Q8×C139—42no—
88C2×D4×C139—21no—
89C2×D4×C139—21no—
90C2×D4×C139—21no—
91C2×D4×C139—21no—
92C2×D4×C139—21no—
93C2×D4×C139Q1612yescomplemented
94C22×C4×C139—21no—
95C22×C4×C139—22no—
96C22×C4×C139—21no—
97C22×C4×C139—21no—
98C22×C4×C139—41no—
99C22×C4×C139—41no—
100C22×C4×C139—82no—
101C22×C4×C139C2×D411yescharacteristic
102C22×C4×C139C2×D411yescharacteristic
103C22×C4×C139C2×D411yescharacteristic
104Q16×C139—44no—
105M16×C139—41no—
106M16×C139—41no—
107C2×C8×C139—22no—
108C2×C8×C139—22no—
109C2×C8×C139—41no—
110C4⋊C4×C139—21no—
111C4⋊C4×C139—21no—
112C4⋊C4×C139—21no—
113C4⋊C4×C139—21no—
114C4⋊C4×C139—21no—
115C4⋊C4×C139—21no—
116C4⋊C4×C139—21no—
117C4⋊C4×C139—21no—
118C4⋊C4×C139—41no—
119C4⋊C4×C139—41no—
120C4⋊C4×C139—41no—
121C4⋊C4×C139—41no—
122C4⋊C4×C139—41no—
123C4⋊C4×C139—41no—
124C4⋊C4×C139—82no—
125C22⋊C4×C139—44no—
126C22⋊C4×C139—41no—
127C22⋊C4×C139—41no—
128C22⋊C4×C139—41no—
129C22⋊C4×C139—82no—
130C42×C139—41no—
131C42×C139—41no—
132C42×C139—41no—
133C42×C139C2×D411yescharacteristic
134C42×C139C2×D411yescharacteristic
135C42×C139C2×D411yescharacteristic
136C42×C139#4111yescharacteristic
137C23×C139—22no—
138C23×C139—42no—
139C23×C139—42no—
140C23×C139—41no—
141C23×C139—41no—
142C23×C139#12011yescharacteristic
143Q8×C139—22no—
144Q8×C139—22no—
145Q8×C139—41no—
146Q8×C139—41no—
147Q8×C139—42no—
148Q8×C139—81no—
149D4×C139—22no—
150D4×C139—22no—
151D4×C139—41no—
152D4×C139—41no—
153C2×C4×C139—22no—
154C2×C4×C139—41no—
155C2×C4×C139—41no—
156C2×C4×C139—41no—
157C2×C4×C139—41no—
158C2×C4×C139—42no—
159C2×C4×C139—41no—
160C2×C4×C139—42no—
161C2×C4×C139—41no—
162C2×C4×C139—42no—
163C2×C4×C139—41no—
164C2×C4×C139—41no—
165C2×C4×C139—41no—
166C2×C4×C139—41no—
167C2×C4×C139—42no—
168C2×C4×C139—82no—
169C2×C4×C139—82no—
170C2×C4×C139#12011yescharacteristic
171C2×C4×C139#12011yescharacteristic
172C2×C4×C139#12111yescharacteristic
173C2×C4×C139#12111yescharacteristic
174C2×C4×C139#12111yescharacteristic
175C2×C4×C139#12711yescharacteristic
176C2×C4×C139C2×Q1611yescharacteristic
177C2×C4×C139#13511yescharacteristic
178C2×C4×C139#13711yescharacteristic
179C2×C4×C139#13711yescharacteristic
180C8×C139—42no—
181C8×C139—42no—
182C8×C139—81no—
183C22×C139—21no—
184C22×C139—21no—
185C22×C139—44no—
186C22×C139—42no—
187C22×C139—82no—
188C22×C139—81no—
189C22×C139—81no—
190C22×C139#39211yescharacteristic
191C22×C139#45111yescharacteristic
192C22×C139#45211yescharacteristic
193C4×C139—21no—
194C4×C139—21no—
195C4×C139—21no—
196C4×C139—21no—
197C4×C139—42no—
198C4×C139—82no—
199C4×C139—81no—
200C4×C139—81no—
201C4×C139—81no—
202C4×C139—81no—
203C4×C139#45111yescharacteristic
204C4×C139#45211yescharacteristic
205C4×C139#46711yescharacteristic
206C4×C139#47011yescharacteristic
207C2×C139—21no—
208C2×C139—21no—
209C2×C139—82no—
210C2×C139#200111yescharacteristic
211C2×C139#200811yescharacteristic
212C2×C139#201011yescharacteristic
213#10002C13911yesmaximal, characteristic, direct product factor, Sylow
214C139#1000211yescharacteristic, direct product factor, Sylow
215#3104C2×C13911yescharacteristic, complemented
216#3077C2×C13911yescharacteristic
217#2580C2×C13911yescharacteristic
218#1518C2×C13911yescharacteristic, complemented
219#1487C2×C13911yescharacteristic, complemented
220#1478C2×C13911yescharacteristic
221#1286C2×C13911yescharacteristic, complemented
222#533C22×C13911yescharacteristic
223C2×C4×Q8C22×C13911yescharacteristic
224C2×C4×D4C22×C13911yescharacteristic
225#484—21no—
226#478—22no—
227#477—21no—
228#476—21no—
229#474—21no—
230#462—21no—
231#451—21no—
232C4×Q16—22no—
233#431C22×C13911yescharacteristic
234#431C22×C13911yescharacteristic
235#428—21no—
236#423C22×C13911yescharacteristic
237#418—21no—
238#399—21no—
239#393—21no—
240#390—21no—
241#389—21no—
242#385—22no—
243#382C22×C13911yescharacteristic
244#328—22no—
245Q8⋊C8—22no—
246D4⋊C8—22no—
247C22×Q8D4×C13911yescharacteristic
248C22×D4D4×C13911yescharacteristic
249C23×C4—21no—
250C2×Q16—22no—
251C2×M16—21no—
252C4⋊Q8D4×C13911yescharacteristic
253C4⋊Q8D4×C13911yescharacteristic
254#125—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4—21no—
267#117—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4D4×C13911yescharacteristic
272C2×C4⋊C4D4×C13911yescharacteristic
273C2×C22⋊C4—22no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—22no—
276C2×C42—21no—
277C2×C42C23×C13911yescharacteristic
278#107—22no—
279#107—22no—
280#106—22no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8D4×C13912yes—
285#103—22no—
286#103—22no—
287#102—22no—
288#102—22no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291C4×C8—21no—
292C4×C8D4×C13912yes—
293#95—22no—
294#95—21no—
295#95D4×C13912yes—
296C24—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8—42no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4Q16×C13912yescomplemented
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—82no—
315C22×C4C2×D4×C13911yescharacteristic
316C22×C4C2×D4×C13911yescharacteristic
317C22×C4C2×D4×C13911yescharacteristic
318Q16—44no—
319M16—41no—
320M16—41no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—41no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—82no—
339C22⋊C4—44no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—82no—
344C42—41no—
345C42—41no—
346C42—41no—
347C42C2×D4×C13911yescharacteristic
348C42C2×D4×C13911yescharacteristic
349C42C2×D4×C13911yescharacteristic
350C42#41×C13911yescharacteristic
351C23—22no—
352C23—42no—
353C23—42no—
354C23—41no—
355C23—41no—
356C23#120×C13911yescharacteristic
357Q8—22no—
358Q8—22no—
359Q8—41no—
360Q8—41no—
361Q8—42no—
362Q8—81no—
363D4—22no—
364D4—22no—
365D4—41no—
366D4—41no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—82no—
383C2×C4—82no—
384C2×C4#120×C13911yescharacteristic
385C2×C4#120×C13911yescharacteristic
386C2×C4#121×C13911yescharacteristic
387C2×C4#121×C13911yescharacteristic
388C2×C4#121×C13911yescharacteristic
389C2×C4#127×C13911yescharacteristic
390C2×C4C2×Q16×C13911yescharacteristic
391C2×C4#135×C13911yescharacteristic
392C2×C4#137×C13911yescharacteristic
393C2×C4#137×C13911yescharacteristic
394C8—42no—
395C8—42no—
396C8—81no—
397C22—21no—
398C22—21no—
399C22—44no—
400C22—42no—
401C22—82no—
402C22—81no—
403C22—81no—
404C22#392×C13911yescharacteristic
405C22#451×C13911yescharacteristic
406C22#452×C13911yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—42no—
412C4—82no—
413C4—81no—
414C4—81no—
415C4—81no—
416C4—81no—
417C4#451×C13911yescharacteristic
418C4#452×C13911yescharacteristic
419C4#467×C13911yescharacteristic
420C4#470×C13911yescharacteristic
421C2—21no—
422C2—21no—
423C2—82no—
424C2#2001×C13911yescharacteristic
425C2#2008×C13911yescharacteristic
426C2#2010×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#392
commutator, Frattini, cosocleC2×C42C23×C139
prime radicalC22×D4×C139D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3104×C139C2semidirect
4. #1518×C139C2semidirect
5. #1487×C139C2semidirect
7. #1286×C139C2semidirect
93. C2×D4×C139Q16semidirect
213. #10002C139direct (N × H)
214. C139#10002direct (N × H)
215. #3104C2×C139semidirect
218. #1518C2×C139semidirect
219. #1487C2×C139semidirect
221. #1286C2×C139semidirect
307. C2×D4Q16×C139semidirect

Maximal subgroups

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

subgroupindex
#3104×C1392
#3077×C1392
#2580×C1392
#1518×C1392
#1487×C1392
#1478×C1392
#1286×C1392
#10002139