Finite Group Databasebeta

← C139×#35854 #48030450

Subgroups — C139×#35854 #48030450

Order 35584.

2286 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C139C211yesmaximal, characteristic, complemented
2C2×#548×C139C211yesmaximal, characteristic
3#2640×C139C213yesmaximal, complemented
4#2592×C139C213yesmaximal, complemented
5#2563×C139C213yesmaximal, complemented
6#2490×C139C216yesmaximal, complemented
7#2489×C139C216yesmaximal, complemented
8#2398×C139C213yesmaximal, complemented
9#2341×C139C212yesmaximal, complemented
10Q8×C22⋊C4×C139C212yesmaximal, complemented
11#2276×C139C211yesmaximal, characteristic, complemented
12C22×#41×C139C2211yescharacteristic
13C23×Q8×C139C2211yescharacteristic
14#557×C139—28no—
15#548×C139—28no—
16C2×C4⋊Q8×C139C2213yes—
17C2×#125×C139C2216yes—
18C2×#124×C139C2213yes—
19C2×C22⋊Q8×C139C2213yes—
20C2×#121×C139C2213yes—
21C2×C4×Q8×C139C2212yes—
22C2×C4×Q8×C139C2213yes—
23C2×C4×Q8×C139C2212yes—
24C2×C4×Q8×C139C2211yescharacteristic
25C2×C4×D4×C139C2213yes—
26#400×C139C2216yes—
27#397×C139C2213yes—
28#397×C139C22112yes—
29#397×C139C2211yescharacteristic
30#394×C139C2216yes—
31#393×C139C2213yes—
32#393×C139C2216yes—
33#393×C139C2213yes—
34#391×C139C2216yes—
35#391×C139C2216yes—
36#390×C139C2216yes—
37#390×C139C2216yes—
38#390×C139C2216yes—
39#388×C139C22112yes—
40#382×C139C2216yes—
41#380×C139C2216yes—
42#380×C139C2216yes—
43C4×C4⋊C4×C139C2213yes—
44C4×C4⋊C4×C139C2216yes—
45C4×C22⋊C4×C139C2216yes—
46C4×C22⋊C4×C139C2216yes—
47#376×C139C2213yes—
48C2×#41×C139—24no—
49C2×#41×C139—28no—
50C22×Q8×C139—24no—
51C22×Q8×C139—28no—
52C22×Q8×C139C2313yes—
53C22×Q8×C139C2313yes—
54C22×Q8×C139C2311yescharacteristic
55C22×D4×C139C2313yes—
56C22×D4×C139C2313yes—
57C23×C4×C139C2313yes—
58C23×C4×C139C2313yes—
59C4⋊Q8×C139—212no—
60#125×C139—224no—
61#124×C139—212no—
62C22⋊Q8×C139—212no—
63#121×C139—212no—
64C4×Q8×C139—28no—
65C4×Q8×C139—28no—
66C4×Q8×C139—212no—
67C4×Q8×C139D418yes—
68C4×D4×C139—212no—
69C2×C4⋊C4×C139C2311yescharacteristic
70C2×C4⋊C4×C139C2316yes—
71C2×C4⋊C4×C139C2313yes—
72C2×C4⋊C4×C139C2316yes—
73C2×C4⋊C4×C139C2316yes—
74C2×C4⋊C4×C139C2316yes—
75C2×C4⋊C4×C139C2313yes—
76C2×C22⋊C4×C139C2316yes—
77C2×C22⋊C4×C139C2311yescharacteristic
78C2×C22⋊C4×C139C2313yes—
79C2×C22⋊C4×C139C2312yes—
80C2×C22⋊C4×C139C2316yes—
81C2×C22⋊C4×C139C2316yes—
82C2×C22⋊C4×C139C23112yes—
83C2×C22⋊C4×C139C2316yes—
84C2×C42×C139C2316yes—
85C2×C42×C139C2316yes—
86C2×C42×C139C2316yes—
87C2×C42×C139C2313yes—
88#95×C139C2316yes—
89#95×C139C2316yes—
90#95×C139C2312yes—
91#95×C139C2316yes—
92#95×C139C2311yescharacteristic
93#95×C139C2313yes—
94#95×C139C23112yes—
95#95×C139C2316yes—
96C24×C139C2413yes—
97C24×C139C2411yescharacteristic
98#41×C139—416no—
99C2×Q8×C139—26no—
100C2×Q8×C139—26no—
101C2×Q8×C139—212no—
102C2×Q8×C139—46no—
103C2×Q8×C139—416no—
104C2×Q8×C139C2×D414yes—
105C2×Q8×C139#4118yes—
106C2×D4×C139—26no—
107C2×D4×C139—26no—
108C2×D4×C139—26no—
109C2×D4×C139—212no—
110C2×D4×C139—43no—
111C22×C4×C139—26no—
112C22×C4×C139—26no—
113C22×C4×C139—212no—
114C22×C4×C139—212no—
115C22×C4×C139C2412yes—
116C22×C4×C139C2413yes—
117C22×C4×C139C2411yescharacteristic
118C22×C4×C139C2416yes—
119C22×C4×C139C2412yes—
120C22×C4×C139C2416yes—
121C22×C4×C139C2411yescharacteristic
122C22×C4×C139C2413yes—
123C22×C4×C139C2413yes—
124C4⋊C4×C139—26no—
125C4⋊C4×C139—22no—
126C4⋊C4×C139—212no—
127C4⋊C4×C139—212no—
128C4⋊C4×C139—212no—
129C4⋊C4×C139—212no—
130C4⋊C4×C139C2×D4112yes—
131C22⋊C4×C139—24no—
132C22⋊C4×C139—22no—
133C22⋊C4×C139—26no—
134C22⋊C4×C139—212no—
135C22⋊C4×C139—46no—
136C22⋊C4×C139—46no—
137C22⋊C4×C139—46no—
138C22⋊C4×C139—412no—
139C42×C139—212no—
140C42×C139—212no—
141C42×C139—46no—
142C42×C139C2×D4112yes—
143C23×C139—21no—
144C23×C139—22no—
145C23×C139—22no—
146C23×C139—21no—
147C23×C139—23no—
148C23×C139—26no—
149C23×C139—23no—
150C23×C139—26no—
151C23×C139—23no—
152C23×C1392−1+412yes—
153C23×C139C2511yescharacteristic
154Q8×C139—412no—
155Q8×C139—412no—
156Q8×C139#124116yes—
157D4×C139—412no—
158D4×C139—412no—
159C2×C4×C139—23no—
160C2×C4×C139—23no—
161C2×C4×C139—22no—
162C2×C4×C139—22no—
163C2×C4×C139—26no—
164C2×C4×C139—23no—
165C2×C4×C139—21no—
166C2×C4×C139—22no—
167C2×C4×C139—26no—
168C2×C4×C139—22no—
169C2×C4×C139—26no—
170C2×C4×C139—22no—
171C2×C4×C139—22no—
172C2×C4×C139—26no—
173C2×C4×C139—22no—
174C2×C4×C139—22no—
175C2×C4×C139—26no—
176C2×C4×C139—26no—
177C2×C4×C139—26no—
178C2×C4×C139—412no—
179C2×C4×C139—412no—
180C2×C4×C139C22×D412yes—
181C2×C4×C139C22×D416yes—
182C2×C4×C139C22×D416yes—
183C2×C4×C139C2×#41112yes—
184C22×C139—22no—
185C22×C139—24no—
186C22×C139—41no—
187C22×C139—41no—
188C22×C139—42no—
189C22×C139—43no—
190C22×C139—43no—
191C22×C139—43no—
192C22×C139—46no—
193C22×C139—46no—
194C22×C139C23×D411yescharacteristic
195C22×C139C22×#4112yes—
196C22×C139C2×2−1+411yescharacteristic
197C22×C139#58512yes—
198C22×C139#58511yescharacteristic
199C4×C139—22no—
200C4×C139—26no—
201C4×C139—41no—
202C4×C139—43no—
203C4×C139—46no—
204C4×C139—42no—
205C4×C139—42no—
206C4×C139—46no—
207C4×C139C2×#124112yes—
208C2×C139—42no—
209C2×C139—83no—
210C2×C139C22×#12411yescharacteristic
211C2×C139#348711yescharacteristic
212C2×C139#348911yescharacteristic
213C2×C139#351612yes—
214C2×C139#352412yes—
215#35854C13911yesmaximal, characteristic, direct product factor, Sylow
216C139#3585411yescharacteristic, direct product factor, Sylow
217C2×#557C2×C13911yescharacteristic, complemented
218C2×#548C2×C13911yescharacteristic
219#2640C2×C13913yescomplemented
220#2592C2×C13913yescomplemented
221#2563C2×C13913yescomplemented
222#2490C2×C13916yescomplemented
223#2489C2×C13916yescomplemented
224#2398C2×C13913yescomplemented
225#2341C2×C13912yescomplemented
226Q8×C22⋊C4C2×C13912yescomplemented
227#2276C2×C13911yescharacteristic, complemented
228C22×#41C22×C13911yescharacteristic
229C23×Q8C22×C13911yescharacteristic
230#557—28no—
231#548—28no—
232C2×C4⋊Q8C22×C13913yes—
233C2×#125C22×C13916yes—
234C2×#124C22×C13913yes—
235C2×C22⋊Q8C22×C13913yes—
236C2×#121C22×C13913yes—
237C2×C4×Q8C22×C13913yes—
238C2×C4×Q8C22×C13912yes—
239C2×C4×Q8C22×C13912yes—
240C2×C4×Q8C22×C13911yescharacteristic
241C2×C4×D4C22×C13913yes—
242#400C22×C13916yes—
243#397C22×C13913yes—
244#397C22×C139112yes—
245#397C22×C13911yescharacteristic
246#394C22×C13916yes—
247#393C22×C13913yes—
248#393C22×C13916yes—
249#393C22×C13913yes—
250#391C22×C13916yes—
251#391C22×C13916yes—
252#390C22×C13916yes—
253#390C22×C13916yes—
254#390C22×C13916yes—
255#388C22×C139112yes—
256#382C22×C13916yes—
257#380C22×C13916yes—
258#380C22×C13916yes—
259C4×C4⋊C4C22×C13913yes—
260C4×C4⋊C4C22×C13916yes—
261C4×C22⋊C4C22×C13916yes—
262C4×C22⋊C4C22×C13916yes—
263#376C22×C13913yes—
264C2×#41—24no—
265C2×#41—28no—
266C22×Q8—24no—
267C22×Q8—28no—
268C22×Q8C23×C13913yes—
269C22×Q8C23×C13913yes—
270C22×Q8C23×C13911yescharacteristic
271C22×D4C23×C13913yes—
272C22×D4C23×C13913yes—
273C23×C4C23×C13913yes—
274C23×C4C23×C13913yes—
275C4⋊Q8—212no—
276#125—224no—
277#124—212no—
278C22⋊Q8—212no—
279#121—212no—
280C4×Q8—28no—
281C4×Q8—28no—
282C4×Q8—212no—
283C4×Q8D4×C13918yes—
284C4×D4—212no—
285C2×C4⋊C4C23×C13913yes—
286C2×C4⋊C4C23×C13911yescharacteristic
287C2×C4⋊C4C23×C13916yes—
288C2×C4⋊C4C23×C13916yes—
289C2×C4⋊C4C23×C13916yes—
290C2×C4⋊C4C23×C13916yes—
291C2×C4⋊C4C23×C13913yes—
292C2×C22⋊C4C23×C13911yescharacteristic
293C2×C22⋊C4C23×C13913yes—
294C2×C22⋊C4C23×C13916yes—
295C2×C22⋊C4C23×C13912yes—
296C2×C22⋊C4C23×C13916yes—
297C2×C22⋊C4C23×C13916yes—
298C2×C22⋊C4C23×C13916yes—
299C2×C22⋊C4C23×C139112yes—
300C2×C42C23×C13916yes—
301C2×C42C23×C13916yes—
302C2×C42C23×C13916yes—
303C2×C42C23×C13913yes—
304#95C23×C13911yescharacteristic
305#95C23×C13913yes—
306#95C23×C13916yes—
307#95C23×C13912yes—
308#95C23×C13916yes—
309#95C23×C13916yes—
310#95C23×C13916yes—
311#95C23×C139112yes—
312C24C24×C13913yes—
313C24C24×C13911yescharacteristic
314#41—416no—
315C2×Q8—26no—
316C2×Q8—26no—
317C2×Q8—212no—
318C2×Q8—46no—
319C2×Q8—416no—
320C2×Q8C2×D4×C13914yes—
321C2×Q8#41×C13918yes—
322C2×D4—26no—
323C2×D4—26no—
324C2×D4—26no—
325C2×D4—212no—
326C2×D4—43no—
327C22×C4—26no—
328C22×C4—26no—
329C22×C4—212no—
330C22×C4—212no—
331C22×C4C24×C13912yes—
332C22×C4C24×C13913yes—
333C22×C4C24×C13911yescharacteristic
334C22×C4C24×C13916yes—
335C22×C4C24×C13912yes—
336C22×C4C24×C13916yes—
337C22×C4C24×C13911yescharacteristic
338C22×C4C24×C13913yes—
339C22×C4C24×C13913yes—
340C4⋊C4—26no—
341C4⋊C4—22no—
342C4⋊C4—212no—
343C4⋊C4—212no—
344C4⋊C4—212no—
345C4⋊C4—212no—
346C4⋊C4C2×D4×C139112yes—
347C22⋊C4—24no—
348C22⋊C4—22no—
349C22⋊C4—26no—
350C22⋊C4—212no—
351C22⋊C4—46no—
352C22⋊C4—46no—
353C22⋊C4—46no—
354C22⋊C4—412no—
355C42—212no—
356C42—212no—
357C42—46no—
358C42C2×D4×C139112yes—
359C23—21no—
360C23—22no—
361C23—22no—
362C23—21no—
363C23—23no—
364C23—26no—
365C23—23no—
366C23—26no—
367C23—23no—
368C232−1+4×C13912yes—
369C23C25×C13911yescharacteristic
370Q8—412no—
371Q8—412no—
372Q8#124×C139116yes—
373D4—412no—
374D4—412no—
375C2×C4—23no—
376C2×C4—23no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—26no—
380C2×C4—23no—
381C2×C4—21no—
382C2×C4—22no—
383C2×C4—26no—
384C2×C4—22no—
385C2×C4—26no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—26no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—26no—
392C2×C4—26no—
393C2×C4—26no—
394C2×C4—412no—
395C2×C4—412no—
396C2×C4C22×D4×C13912yes—
397C2×C4C22×D4×C13916yes—
398C2×C4C22×D4×C13916yes—
399C2×C4C2×#41×C139112yes—
400C22—22no—
401C22—24no—
402C22—41no—
403C22—41no—
404C22—42no—
405C22—43no—
406C22—43no—
407C22—43no—
408C22—46no—
409C22—46no—
410C22C23×D4×C13911yescharacteristic
411C22C22×#41×C13912yes—
412C22C2×2−1+4×C13911yescharacteristic
413C22#585×C13912yes—
414C22#585×C13911yescharacteristic
415C4—22no—
416C4—26no—
417C4—41no—
418C4—43no—
419C4—46no—
420C4—42no—
421C4—42no—
422C4—46no—
423C4C2×#124×C139112yes—
424C2—42no—
425C2—83no—
426C2C22×#124×C13911yescharacteristic
427C2#3487×C13911yescharacteristic
428C2#3489×C13911yescharacteristic
429C2#3516×C13912yes—
430C2#3524×C13912yes—
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radicalC2×#548×C139C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#557×C139C2semidirect
3. #2640×C139C2semidirect
4. #2592×C139C2semidirect
5. #2563×C139C2semidirect
6. #2490×C139C2semidirect
7. #2489×C139C2semidirect
8. #2398×C139C2semidirect
9. #2341×C139C2semidirect
10. Q8×C22⋊C4×C139C2semidirect
11. #2276×C139C2semidirect
215. #35854C139direct (N × H)
216. C139#35854direct (N × H)
217. C2×#557C2×C139semidirect
219. #2640C2×C139semidirect
220. #2592C2×C139semidirect
221. #2563C2×C139semidirect
222. #2490C2×C139semidirect
223. #2489C2×C139semidirect
224. #2398C2×C139semidirect
225. #2341C2×C139semidirect
226. Q8×C22⋊C4C2×C139semidirect
227. #2276C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#557×C1392
C2×#548×C1392
#2640×C1392
#2592×C1392
#2563×C1392
#2490×C1392
#2489×C1392
#2398×C1392
#2341×C1392
Q8×C22⋊C4×C1392
#2276×C1392
#35854139