Finite Group Databasebeta

← C139×#33867 #48028463

Subgroups — C139×#33867 #48028463

Order 35584.

546 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3336×C139C211yesmaximal, characteristic, complemented
2#3285×C139C211yesmaximal, characteristic
3#2242×C139C211yesmaximal, characteristic, complemented
4#2237×C139C211yesmaximal, characteristic, complemented
5#2232×C139C211yesmaximal, characteristic, complemented
6#2229×C139C211yesmaximal, characteristic, complemented
7#2217×C139C211yesmaximal, characteristic, complemented
8#2216×C139C211yesmaximal, characteristic, complemented
9#2211×C139C211yesmaximal, characteristic, complemented
10#2189×C139C211yesmaximal, characteristic, complemented
11#2188×C139C211yesmaximal, characteristic, complemented
12C4×Q32×C139C211yesmaximal, characteristic, complemented
13D4×C16×C139C211yesmaximal, characteristic, complemented
14#2138×C139C211yesmaximal, characteristic, complemented
15C2×#358×C139C211yesmaximal, characteristic, complemented
16C2×#135×C139C2211yescharacteristic
17C22×Q16×C139C2211yescharacteristic
18#552×C139—21no—
19#548×C139—21no—
20C2×Q32×C139C2211yescharacteristic
21C2×Q32×C139C2211yescharacteristic
22C2×SD32×C139C2211yescharacteristic
23C22×C16×C139C2211yescharacteristic
24C22×C16×C139C2211yescharacteristic
25#499×C139C2211yescharacteristic
26#495×C139C2211yescharacteristic
27#485×C139—21no—
28#483×C139—21no—
29#479×C139—21no—
30#467×C139C2211yescharacteristic
31#467×C139C2211yescharacteristic
32#467×C139C2211yescharacteristic
33#466×C139C2211yescharacteristic
34#464×C139—21no—
35#452×C139—21no—
36#448×C139—21no—
37C4×Q16×C139C2211yescharacteristic
38C4×Q16×C139C2211yescharacteristic
39C8×D4×C139C2211yescharacteristic
40#427×C139C2211yescharacteristic
41C2×#107×C139C2211yescharacteristic
42#367×C139C2211yescharacteristic
43#366×C139C2211yescharacteristic
44#366×C139C2211yescharacteristic
45C4⋊C16×C139C2211yescharacteristic
46#358×C139C2211yescharacteristic
47#358×C139C2211yescharacteristic
48#358×C139C2211yescharacteristic
49#358×C139C2211yescharacteristic
50#358×C139C2211yescharacteristic
51#358×C139C2211yescharacteristic
52#358×C139C2211yescharacteristic
53#357×C139C2211yescharacteristic
54#357×C139C2211yescharacteristic
55#357×C139C2211yescharacteristic
56C22⋊C16×C139C2211yescharacteristic
57C22⋊C16×C139C2211yescharacteristic
58C4×C16×C139C2211yescharacteristic
59C2×#41×C139—21no—
60C22×Q8×C139—21no—
61#135×C139—22no—
62#135×C139—41no—
63C2×Q16×C139—22no—
64C2×Q16×C139—21no—
65C2×Q16×C139—41no—
66C2×Q16×C139C2311yescharacteristic
67C2×Q16×C139C2311yescharacteristic
68C2×Q16×C139C2311yescharacteristic
69C2×SD16×C139—21no—
70C2×SD16×C139—21no—
71C2×D8×C139C2311yescharacteristic
72C22×C8×C139C2311yescharacteristic
73C22×C8×C139C2311yescharacteristic
74#126×C139—41no—
75#125×C139—21no—
76#125×C139—41no—
77#124×C139—21no—
78#124×C139—41no—
79#123×C139—41no—
80C22⋊Q8×C139—21no—
81C22⋊Q8×C139—21no—
82C22⋊Q8×C139—21no—
83C22⋊Q8×C139—41no—
84#121×C139—21no—
85#121×C139—41no—
86C4×Q8×C139—21no—
87C4×Q8×C139—21no—
88C4×D4×C139—41no—
89C4×D4×C139D411yescharacteristic
90#117×C139—21no—
91#117×C139—41no—
92C2×C4⋊C4×C139—21no—
93Q32×C139—22no—
94Q32×C139—41no—
95SD32×C139—41no—
96C2×C16×C139—41no—
97C2×C16×C139—41no—
98C2×C16×C139C2311yescharacteristic
99C2×C16×C139C2311yescharacteristic
100C2×C16×C139C2311yescharacteristic
101C2×C16×C139C2311yescharacteristic
102#107×C139—21no—
103#107×C139C2311yescharacteristic
104#107×C139C2311yescharacteristic
105#107×C139C2311yescharacteristic
106#107×C139C2311yescharacteristic
107#106×C139—21no—
108#106×C139—21no—
109C4⋊C8×C139D411yescharacteristic
110#103×C139—21no—
111#103×C139—21no—
112#103×C139—21no—
113#103×C139—21no—
114#103×C139—21no—
115#102×C139—21no—
116C22⋊C8×C139D411yescharacteristic
117C22⋊C8×C139D411yescharacteristic
118C4×C8×C139C2311yescharacteristic
119#41×C139—42no—
120#41×C139—81no—
121C2×Q8×C139—21no—
122C2×Q8×C139—21no—
123C2×Q8×C139—21no—
124C2×Q8×C139—42no—
125C2×Q8×C139—41no—
126C2×Q8×C139—81no—
127C2×D4×C139—21no—
128C2×D4×C139—41no—
129C2×D4×C139—41no—
130C2×D4×C139D811yescharacteristic
131C22×C4×C139—41no—
132C22×C4×C139—41no—
133C22×C4×C139—41no—
134C22×C4×C139C2×D411yescharacteristic
135C22×C4×C139C2×D411yescharacteristic
136Q16×C139—21no—
137Q16×C139—21no—
138Q16×C139—21no—
139Q16×C139—21no—
140Q16×C139—21no—
141Q16×C139—42no—
142Q16×C139#4112yes—
143SD16×C139—42no—
144SD16×C139—81no—
145D8×C139—21no—
146D8×C139—21no—
147C2×C8×C139—21no—
148C2×C8×C139—21no—
149C2×C8×C139—21no—
150C2×C8×C139—21no—
151C2×C8×C139C2×D411yescharacteristic
152C2×C8×C139C2×D411yescharacteristic
153C2×C8×C139C2×D411yescharacteristic
154C2×C8×C139C2411yescharacteristic
155C4⋊C4×C139—21no—
156C4⋊C4×C139—21no—
157C4⋊C4×C139—21no—
158C4⋊C4×C139—21no—
159C4⋊C4×C139—41no—
160C4⋊C4×C139—41no—
161C4⋊C4×C139—41no—
162C4⋊C4×C139—41no—
163C4⋊C4×C139—41no—
164C4⋊C4×C139—41no—
165C4⋊C4×C139—41no—
166C4⋊C4×C139—41no—
167C4⋊C4×C139D811yescharacteristic
168C22⋊C4×C139—41no—
169C22⋊C4×C139—41no—
170C22⋊C4×C139—41no—
171C22⋊C4×C139—41no—
172C22⋊C4×C139—41no—
173C22⋊C4×C139—41no—
174C22⋊C4×C139—41no—
175C22⋊C4×C139D811yescharacteristic
176C22⋊C4×C139D811yescharacteristic
177C42×C139—41no—
178C42×C139—41no—
179C42×C139—41no—
180C42×C139C2×D411yescharacteristic
181C16×C139—21no—
182C16×C139—21no—
183C16×C139—21no—
184C16×C139—21no—
185C23×C139—41no—
186C23×C139C2×D811yescharacteristic
187C23×C139C2×D811yescharacteristic
188Q8×C139—22no—
189Q8×C139—41no—
190Q8×C139—41no—
191Q8×C139—41no—
192Q8×C139—41no—
193Q8×C139—41no—
194Q8×C139—82no—
195D4×C139—22no—
196D4×C139—41no—
197D4×C139—41no—
198D4×C139—82no—
199D4×C139—82no—
200C2×C4×C139—21no—
201C2×C4×C139—21no—
202C2×C4×C139—21no—
203C2×C4×C139—21no—
204C2×C4×C139—41no—
205C2×C4×C139—41no—
206C2×C4×C139—41no—
207C2×C4×C139—41no—
208C2×C4×C139—41no—
209C2×C4×C139—41no—
210C2×C4×C139—41no—
211C2×C4×C139—82no—
212C2×C4×C139—82no—
213C2×C4×C139—82no—
214C2×C4×C139C2×D811yescharacteristic
215C2×C4×C139C2×D811yescharacteristic
216C2×C4×C139C2×D811yescharacteristic
217C2×C4×C139C2×D811yescharacteristic
218C2×C4×C139C22×D411yescharacteristic
219C8×C139—21no—
220C8×C139—21no—
221C8×C139—21no—
222C8×C139C2×#4111yescharacteristic
223C8×C139H(5,𝔽2)11yescharacteristic
224C22×C139—21no—
225C22×C139—21no—
226C22×C139—21no—
227C22×C139—21no—
228C22×C139—21no—
229C22×C139—81no—
230C22×C139—81no—
231C22×C139—81no—
232C22×C139#50812yes—
233C22×C139C22×D811yescharacteristic
234C4×C139—21no—
235C4×C139—21no—
236C4×C139—21no—
237C4×C139—21no—
238C4×C139—42no—
239C4×C139—81no—
240C4×C139—81no—
241C4×C139—81no—
242C4×C139—81no—
243C4×C139—81no—
244C4×C139—81no—
245C4×C139#54611yescharacteristic
246C4×C139#57711yescharacteristic
247C2×C139—22no—
248C2×C139—41no—
249C2×C139—161no—
250C2×C139#329411yescharacteristic
251C2×C139C2×#50811yescharacteristic
252C2×C139#341711yescharacteristic
253#33867C13911yesmaximal, characteristic, direct product factor, Sylow
254C139#3386711yescharacteristic, direct product factor, Sylow
255#3336C2×C13911yescharacteristic, complemented
256#3285C2×C13911yescharacteristic
257#2242C2×C13911yescharacteristic, complemented
258#2237C2×C13911yescharacteristic, complemented
259#2232C2×C13911yescharacteristic, complemented
260#2229C2×C13911yescharacteristic, complemented
261#2217C2×C13911yescharacteristic, complemented
262#2216C2×C13911yescharacteristic, complemented
263#2211C2×C13911yescharacteristic, complemented
264#2189C2×C13911yescharacteristic, complemented
265#2188C2×C13911yescharacteristic, complemented
266C4×Q32C2×C13911yescharacteristic, complemented
267D4×C16C2×C13911yescharacteristic, complemented
268#2138C2×C13911yescharacteristic, complemented
269C2×#358C2×C13911yescharacteristic, complemented
270C2×#135C22×C13911yescharacteristic
271C22×Q16C22×C13911yescharacteristic
272#552—21no—
273#548—21no—
274C2×Q32C22×C13911yescharacteristic
275C2×Q32C22×C13911yescharacteristic
276C2×SD32C22×C13911yescharacteristic
277C22×C16C22×C13911yescharacteristic
278C22×C16C22×C13911yescharacteristic
279#499C22×C13911yescharacteristic
280#495C22×C13911yescharacteristic
281#485—21no—
282#483—21no—
283#479—21no—
284#467C22×C13911yescharacteristic
285#467C22×C13911yescharacteristic
286#467C22×C13911yescharacteristic
287#466C22×C13911yescharacteristic
288#464—21no—
289#452—21no—
290#448—21no—
291C4×Q16C22×C13911yescharacteristic
292C4×Q16C22×C13911yescharacteristic
293C8×D4C22×C13911yescharacteristic
294#427C22×C13911yescharacteristic
295C2×#107C22×C13911yescharacteristic
296#367C22×C13911yescharacteristic
297#366C22×C13911yescharacteristic
298#366C22×C13911yescharacteristic
299C4⋊C16C22×C13911yescharacteristic
300#358C22×C13911yescharacteristic
301#358C22×C13911yescharacteristic
302#358C22×C13911yescharacteristic
303#358C22×C13911yescharacteristic
304#358C22×C13911yescharacteristic
305#358C22×C13911yescharacteristic
306#358C22×C13911yescharacteristic
307#357C22×C13911yescharacteristic
308#357C22×C13911yescharacteristic
309#357C22×C13911yescharacteristic
310C22⋊C16C22×C13911yescharacteristic
311C22⋊C16C22×C13911yescharacteristic
312C4×C16C22×C13911yescharacteristic
313C2×#41—21no—
314C22×Q8—21no—
315#135—22no—
316#135—41no—
317C2×Q16—22no—
318C2×Q16—21no—
319C2×Q16—41no—
320C2×Q16C23×C13911yescharacteristic
321C2×Q16C23×C13911yescharacteristic
322C2×Q16C23×C13911yescharacteristic
323C2×SD16—21no—
324C2×SD16—21no—
325C2×D8C23×C13911yescharacteristic
326C22×C8C23×C13911yescharacteristic
327C22×C8C23×C13911yescharacteristic
328#126—41no—
329#125—21no—
330#125—41no—
331#124—21no—
332#124—41no—
333#123—41no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336C22⋊Q8—21no—
337C22⋊Q8—41no—
338#121—21no—
339#121—41no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×D4—41no—
343C4×D4D4×C13911yescharacteristic
344#117—21no—
345#117—41no—
346C2×C4⋊C4—21no—
347Q32—22no—
348Q32—41no—
349SD32—41no—
350C2×C16—41no—
351C2×C16—41no—
352C2×C16C23×C13911yescharacteristic
353C2×C16C23×C13911yescharacteristic
354C2×C16C23×C13911yescharacteristic
355C2×C16C23×C13911yescharacteristic
356#107—21no—
357#107C23×C13911yescharacteristic
358#107C23×C13911yescharacteristic
359#107C23×C13911yescharacteristic
360#107C23×C13911yescharacteristic
361#106—21no—
362#106—21no—
363C4⋊C8D4×C13911yescharacteristic
364#103—21no—
365#103—21no—
366#103—21no—
367#103—21no—
368#103—21no—
369#102—21no—
370C22⋊C8D4×C13911yescharacteristic
371C22⋊C8D4×C13911yescharacteristic
372C4×C8C23×C13911yescharacteristic
373#41—42no—
374#41—81no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—42no—
379C2×Q8—41no—
380C2×Q8—81no—
381C2×D4—21no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4D8×C13911yescharacteristic
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4C2×D4×C13911yescharacteristic
389C22×C4C2×D4×C13911yescharacteristic
390Q16—21no—
391Q16—21no—
392Q16—21no—
393Q16—21no—
394Q16—21no—
395Q16—42no—
396Q16#41×C13912yes—
397SD16—42no—
398SD16—81no—
399D8—21no—
400D8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8C2×D4×C13911yescharacteristic
406C2×C8C2×D4×C13911yescharacteristic
407C2×C8C2×D4×C13911yescharacteristic
408C2×C8C24×C13911yescharacteristic
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4D8×C13911yescharacteristic
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4D8×C13911yescharacteristic
430C22⋊C4D8×C13911yescharacteristic
431C42—41no—
432C42—41no—
433C42—41no—
434C42C2×D4×C13911yescharacteristic
435C16—21no—
436C16—21no—
437C16—21no—
438C16—21no—
439C23—41no—
440C23C2×D8×C13911yescharacteristic
441C23C2×D8×C13911yescharacteristic
442Q8—22no—
443Q8—41no—
444Q8—41no—
445Q8—41no—
446Q8—41no—
447Q8—41no—
448Q8—82no—
449D4—22no—
450D4—41no—
451D4—41no—
452D4—82no—
453D4—82no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—82no—
466C2×C4—82no—
467C2×C4—82no—
468C2×C4C2×D8×C13911yescharacteristic
469C2×C4C2×D8×C13911yescharacteristic
470C2×C4C2×D8×C13911yescharacteristic
471C2×C4C2×D8×C13911yescharacteristic
472C2×C4C22×D4×C13911yescharacteristic
473C8—21no—
474C8—21no—
475C8—21no—
476C8C2×#41×C13911yescharacteristic
477C8H(5,𝔽2)×C13911yescharacteristic
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22#508×C13912yes—
487C22C22×D8×C13911yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—42no—
493C4—81no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4—81no—
498C4—81no—
499C4#546×C13911yescharacteristic
500C4#577×C13911yescharacteristic
501C2—22no—
502C2—41no—
503C2—161no—
504C2#3294×C13911yescharacteristic
505C2C2×#508×C13911yescharacteristic
506C2#3417×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C22×D8
commutator, Frattini, cosocleC2×C8C24×C139
prime radical#3285×C139C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C4×D4×C139 ◁ C8×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3336×C139C2semidirect
3. #2242×C139C2semidirect
4. #2237×C139C2semidirect
5. #2232×C139C2semidirect
6. #2229×C139C2semidirect
7. #2217×C139C2semidirect
8. #2216×C139C2semidirect
9. #2211×C139C2semidirect
10. #2189×C139C2semidirect
11. #2188×C139C2semidirect
12. C4×Q32×C139C2semidirect
13. D4×C16×C139C2semidirect
14. #2138×C139C2semidirect
15. C2×#358×C139C2semidirect
253. #33867C139direct (N × H)
254. C139#33867direct (N × H)
255. #3336C2×C139semidirect
257. #2242C2×C139semidirect
258. #2237C2×C139semidirect
259. #2232C2×C139semidirect
260. #2229C2×C139semidirect
261. #2217C2×C139semidirect
262. #2216C2×C139semidirect
263. #2211C2×C139semidirect
264. #2189C2×C139semidirect
265. #2188C2×C139semidirect
266. C4×Q32C2×C139semidirect
267. D4×C16C2×C139semidirect
268. #2138C2×C139semidirect
269. C2×#358C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3336×C1392
#3285×C1392
#2242×C1392
#2237×C1392
#2232×C1392
#2229×C1392
#2217×C1392
#2216×C1392
#2211×C1392
#2189×C1392
#2188×C1392
C4×Q32×C1392
D4×C16×C1392
#2138×C1392
C2×#358×C1392
#33867139