Finite Group Databasebeta

← C139×#33876 #48028472

Subgroups — C139×#33876 #48028472

Order 35584.

564 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3339×C139C211yesmaximal, characteristic, complemented
2#3287×C139C211yesmaximal, characteristic, complemented
3#2244×C139C211yesmaximal, characteristic, complemented
4#2234×C139C211yesmaximal, characteristic, complemented
5#2232×C139C211yesmaximal, characteristic, complemented
6#2229×C139C211yesmaximal, characteristic, complemented
7#2218×C139C211yesmaximal, characteristic, complemented
8#2215×C139C211yesmaximal, characteristic, complemented
9#2206×C139C211yesmaximal, characteristic, complemented
10#2186×C139C211yesmaximal, characteristic, complemented
11#2186×C139C211yesmaximal, characteristic, complemented
12#2175×C139C211yesmaximal, characteristic, complemented
13#2168×C139C211yesmaximal, characteristic, complemented
14#2139×C139C211yesmaximal, characteristic, complemented
15#2138×C139C211yesmaximal, characteristic, complemented
16C2×#135×C139C2211yescharacteristic
17C2×#135×C139C2211yescharacteristic
18#553×C139—21no—
19#550×C139—21no—
20C2×SD32×C139C2211yescharacteristic
21C2×D16×C139C2211yescharacteristic
22C2×D16×C139C2211yescharacteristic
23C2×M32×C139C2211yescharacteristic
24C22×C16×C139C2211yescharacteristic
25#499×C139C2211yescharacteristic
26#493×C139C2211yescharacteristic
27#482×C139—21no—
28#481×C139—21no—
29#478×C139—21no—
30#466×C139C2211yescharacteristic
31#466×C139C2211yescharacteristic
32#466×C139C2211yescharacteristic
33#466×C139C2211yescharacteristic
34#460×C139—21no—
35#449×C139—21no—
36#449×C139—21no—
37C4×Q16×C139C2211yescharacteristic
38C4×D8×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#357×C139C2211yescharacteristic
50#357×C139C2211yescharacteristic
51#357×C139C2211yescharacteristic
52#357×C139C2211yescharacteristic
53#357×C139C2211yescharacteristic
54#357×C139C2211yescharacteristic
55#357×C139C2211yescharacteristic
56C22⋊C16×C139C2211yescharacteristic
57C22⋊C16×C139C2211yescharacteristic
58#346×C139C2211yescharacteristic
59C2×#41×C139—21no—
60C2×#41×C139—21no—
61#135×C139—22no—
62#135×C139—22no—
63#135×C139—41no—
64#135×C139—41no—
65C2×Q16×C139C2311yescharacteristic
66C2×SD16×C139—21no—
67C2×SD16×C139—21no—
68C2×D8×C139—21no—
69C2×D8×C139C2311yescharacteristic
70C2×D8×C139C2311yescharacteristic
71C2×D8×C139C2311yescharacteristic
72C22×C8×C139C2311yescharacteristic
73C22×C8×C139C2311yescharacteristic
74#127×C139—21no—
75#127×C139—41no—
76#126×C139—41no—
77#125×C139—21no—
78#123×C139—41no—
79#121×C139—21no—
80#121×C139—21no—
81#121×C139—21no—
82#121×C139—21no—
83#121×C139—41no—
84#121×C139—41no—
85#121×C139—41no—
86C4×Q8×C139—21no—
87C4×D4×C139—21no—
88C4×D4×C139—41no—
89C4×D4×C139—41no—
90C4×D4×C139D411yescharacteristic
91#117×C139—21no—
92C2×C4⋊C4×C139—21no—
93SD32×C139—22no—
94D16×C139—41no—
95D16×C139—41no—
96M32×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#102×C139—21no—
112#102×C139—21no—
113#102×C139—21no—
114#102×C139—21no—
115#102×C139—21no—
116C22⋊C8×C139D411yescharacteristic
117C22⋊C8×C139D411yescharacteristic
118C4×C8×C139C2311yescharacteristic
119#41×C139—42no—
120#41×C139—42no—
121#41×C139—81no—
122#41×C139—81no—
123C2×Q8×C139—21no—
124C2×D4×C139—21no—
125C2×D4×C139—21no—
126C2×D4×C139—21no—
127C2×D4×C139—41no—
128C2×D4×C139—41no—
129C2×D4×C139—41no—
130C2×D4×C139—41no—
131C2×D4×C139—41no—
132C2×D4×C139—41no—
133C2×D4×C139—41no—
134C2×D4×C139—41no—
135C2×D4×C139D811yescharacteristic
136C22×C4×C139—41no—
137C22×C4×C139—41no—
138C22×C4×C139—41no—
139C22×C4×C139—41no—
140C22×C4×C139C2×D411yescharacteristic
141C22×C4×C139C2×D411yescharacteristic
142Q16×C139—21no—
143Q16×C139#4112yes—
144SD16×C139—42no—
145SD16×C139—42no—
146D8×C139—21no—
147D8×C139—21no—
148D8×C139—21no—
149D8×C139—21no—
150D8×C139—21no—
151D8×C139—21no—
152D8×C139—81no—
153C2×C8×C139—21no—
154C2×C8×C139—21no—
155C2×C8×C139—21no—
156C2×C8×C139—21no—
157C2×C8×C139C2×D411yescharacteristic
158C2×C8×C139C2×D411yescharacteristic
159C2×C8×C139C2×D411yescharacteristic
160C2×C8×C139C2411yescharacteristic
161C4⋊C4×C139—21no—
162C4⋊C4×C139—21no—
163C4⋊C4×C139—21no—
164C4⋊C4×C139—21no—
165C4⋊C4×C139—41no—
166C4⋊C4×C139—41no—
167C4⋊C4×C139—41no—
168C4⋊C4×C139—41no—
169C4⋊C4×C139D811yescharacteristic
170C22⋊C4×C139—41no—
171C22⋊C4×C139—41no—
172C22⋊C4×C139—41no—
173C22⋊C4×C139—41no—
174C22⋊C4×C139—41no—
175C22⋊C4×C139—41no—
176C22⋊C4×C139D811yescharacteristic
177C22⋊C4×C139D811yescharacteristic
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×C139—41no—
187C23×C139—41no—
188C23×C139C2×D811yescharacteristic
189C23×C139C2×D811yescharacteristic
190Q8×C139—22no—
191Q8×C139—41no—
192D4×C139—41no—
193D4×C139—41no—
194D4×C139—41no—
195D4×C139—41no—
196D4×C139—41no—
197D4×C139—41no—
198D4×C139—41no—
199D4×C139—82no—
200D4×C139—82no—
201D4×C139—82no—
202D4×C139—82no—
203D4×C139—161no—
204D4×C139—161no—
205D4×C139—161no—
206D4×C139—161no—
207C2×C4×C139—21no—
208C2×C4×C139—21no—
209C2×C4×C139—21no—
210C2×C4×C139—21no—
211C2×C4×C139—41no—
212C2×C4×C139—41no—
213C2×C4×C139—41no—
214C2×C4×C139—41no—
215C2×C4×C139—41no—
216C2×C4×C139—82no—
217C2×C4×C139—82no—
218C2×C4×C139—161no—
219C2×C4×C139—161no—
220C2×C4×C139C2×D811yescharacteristic
221C2×C4×C139C2×D811yescharacteristic
222C2×C4×C139C2×D811yescharacteristic
223C2×C4×C139C2×D811yescharacteristic
224C2×C4×C139C22×D411yescharacteristic
225C8×C139—21no—
226C8×C139—21no—
227C8×C139—21no—
228C8×C139C2×#4111yescharacteristic
229C8×C139H(5,𝔽2)11yescharacteristic
230C22×C139—21no—
231C22×C139—21no—
232C22×C139—21no—
233C22×C139—21no—
234C22×C139—21no—
235C22×C139—21no—
236C22×C139—81no—
237C22×C139—81no—
238C22×C139—81no—
239C22×C139—81no—
240C22×C139—81no—
241C22×C139—81no—
242C22×C139—81no—
243C22×C139—81no—
244C22×C139—81no—
245C22×C139C22×D811yescharacteristic
246C4×C139—21no—
247C4×C139—21no—
248C4×C139—21no—
249C4×C139—21no—
250C4×C139—42no—
251C4×C139—81no—
252C4×C139—81no—
253C4×C139—81no—
254C4×C139—81no—
255C4×C139#54611yescharacteristic
256C4×C139#57711yescharacteristic
257C2×C139—41no—
258C2×C139—41no—
259C2×C139—161no—
260C2×C139—161no—
261C2×C139—161no—
262C2×C139#329411yescharacteristic
263C2×C139#341411yescharacteristic
264C2×C139#341511yescharacteristic
265#33876C13911yesmaximal, characteristic, direct product factor, Sylow
266C139#3387611yescharacteristic, direct product factor, Sylow
267#3339C2×C13911yescharacteristic, complemented
268#3287C2×C13911yescharacteristic, complemented
269#2244C2×C13911yescharacteristic, complemented
270#2234C2×C13911yescharacteristic, complemented
271#2232C2×C13911yescharacteristic, complemented
272#2229C2×C13911yescharacteristic, complemented
273#2218C2×C13911yescharacteristic, complemented
274#2215C2×C13911yescharacteristic, complemented
275#2206C2×C13911yescharacteristic, complemented
276#2186C2×C13911yescharacteristic, complemented
277#2186C2×C13911yescharacteristic, complemented
278#2175C2×C13911yescharacteristic, complemented
279#2168C2×C13911yescharacteristic, complemented
280#2139C2×C13911yescharacteristic, complemented
281#2138C2×C13911yescharacteristic, complemented
282C2×#135C22×C13911yescharacteristic
283C2×#135C22×C13911yescharacteristic
284#553—21no—
285#550—21no—
286C2×SD32C22×C13911yescharacteristic
287C2×D16C22×C13911yescharacteristic
288C2×D16C22×C13911yescharacteristic
289C2×M32C22×C13911yescharacteristic
290C22×C16C22×C13911yescharacteristic
291#499C22×C13911yescharacteristic
292#493C22×C13911yescharacteristic
293#482—21no—
294#481—21no—
295#478—21no—
296#466C22×C13911yescharacteristic
297#466C22×C13911yescharacteristic
298#466C22×C13911yescharacteristic
299#466C22×C13911yescharacteristic
300#460—21no—
301#449—21no—
302#449—21no—
303C4×Q16C22×C13911yescharacteristic
304C4×D8C22×C13911yescharacteristic
305C8×D4C22×C13911yescharacteristic
306#427C22×C13911yescharacteristic
307C2×#107C22×C13911yescharacteristic
308#367C22×C13911yescharacteristic
309#366C22×C13911yescharacteristic
310#366C22×C13911yescharacteristic
311C4⋊C16C22×C13911yescharacteristic
312#358C22×C13911yescharacteristic
313#358C22×C13911yescharacteristic
314#358C22×C13911yescharacteristic
315#357C22×C13911yescharacteristic
316#357C22×C13911yescharacteristic
317#357C22×C13911yescharacteristic
318#357C22×C13911yescharacteristic
319#357C22×C13911yescharacteristic
320#357C22×C13911yescharacteristic
321#357C22×C13911yescharacteristic
322C22⋊C16C22×C13911yescharacteristic
323C22⋊C16C22×C13911yescharacteristic
324#346C22×C13911yescharacteristic
325C2×#41—21no—
326C2×#41—21no—
327#135—22no—
328#135—22no—
329#135—41no—
330#135—41no—
331C2×Q16C23×C13911yescharacteristic
332C2×SD16—21no—
333C2×SD16—21no—
334C2×D8—21no—
335C2×D8C23×C13911yescharacteristic
336C2×D8C23×C13911yescharacteristic
337C2×D8C23×C13911yescharacteristic
338C22×C8C23×C13911yescharacteristic
339C22×C8C23×C13911yescharacteristic
340#127—21no—
341#127—41no—
342#126—41no—
343#125—21no—
344#123—41no—
345#121—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349#121—41no—
350#121—41no—
351#121—41no—
352C4×Q8—21no—
353C4×D4—21no—
354C4×D4—41no—
355C4×D4—41no—
356C4×D4D4×C13911yescharacteristic
357#117—21no—
358C2×C4⋊C4—21no—
359SD32—22no—
360D16—41no—
361D16—41no—
362M32—41no—
363C2×C16—41no—
364C2×C16C23×C13911yescharacteristic
365C2×C16C23×C13911yescharacteristic
366C2×C16C23×C13911yescharacteristic
367C2×C16C23×C13911yescharacteristic
368#107—21no—
369#107C23×C13911yescharacteristic
370#107C23×C13911yescharacteristic
371#107C23×C13911yescharacteristic
372#107C23×C13911yescharacteristic
373#106—21no—
374#106—21no—
375C4⋊C8D4×C13911yescharacteristic
376#103—21no—
377#102—21no—
378#102—21no—
379#102—21no—
380#102—21no—
381#102—21no—
382C22⋊C8D4×C13911yescharacteristic
383C22⋊C8D4×C13911yescharacteristic
384C4×C8C23×C13911yescharacteristic
385#41—42no—
386#41—42no—
387#41—81no—
388#41—81no—
389C2×Q8—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4D8×C13911yescharacteristic
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4C2×D4×C13911yescharacteristic
407C22×C4C2×D4×C13911yescharacteristic
408Q16—21no—
409Q16#41×C13912yes—
410SD16—42no—
411SD16—42no—
412D8—21no—
413D8—21no—
414D8—21no—
415D8—21no—
416D8—21no—
417D8—21no—
418D8—81no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8C2×D4×C13911yescharacteristic
424C2×C8C2×D4×C13911yescharacteristic
425C2×C8C2×D4×C13911yescharacteristic
426C2×C8C24×C13911yescharacteristic
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C4⋊C4—41no—
435C4⋊C4D8×C13911yescharacteristic
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4D8×C13911yescharacteristic
443C22⋊C4D8×C13911yescharacteristic
444C42—41no—
445C42—41no—
446C42C2×D4×C13911yescharacteristic
447C16—21no—
448C16—21no—
449C16—21no—
450C16—21no—
451C23—41no—
452C23—41no—
453C23—41no—
454C23C2×D8×C13911yescharacteristic
455C23C2×D8×C13911yescharacteristic
456Q8—22no—
457Q8—41no—
458D4—41no—
459D4—41no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—41no—
464D4—41no—
465D4—82no—
466D4—82no—
467D4—82no—
468D4—82no—
469D4—161no—
470D4—161no—
471D4—161no—
472D4—161no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4—161no—
485C2×C4—161no—
486C2×C4C2×D8×C13911yescharacteristic
487C2×C4C2×D8×C13911yescharacteristic
488C2×C4C2×D8×C13911yescharacteristic
489C2×C4C2×D8×C13911yescharacteristic
490C2×C4C22×D4×C13911yescharacteristic
491C8—21no—
492C8—21no—
493C8—21no—
494C8C2×#41×C13911yescharacteristic
495C8H(5,𝔽2)×C13911yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—81no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22C22×D8×C13911yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—42no—
517C4—81no—
518C4—81no—
519C4—81no—
520C4—81no—
521C4#546×C13911yescharacteristic
522C4#577×C13911yescharacteristic
523C2—41no—
524C2—41no—
525C2—161no—
526C2—161no—
527C2—161no—
528C2#3294×C13911yescharacteristic
529C2#3414×C13911yescharacteristic
530C2#3415×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C22×D8
commutator, Frattini, cosocleC2×C8C24×C139
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. #3339×C139C2semidirect
2. #3287×C139C2semidirect
3. #2244×C139C2semidirect
4. #2234×C139C2semidirect
5. #2232×C139C2semidirect
6. #2229×C139C2semidirect
7. #2218×C139C2semidirect
8. #2215×C139C2semidirect
9. #2206×C139C2semidirect
10. #2186×C139C2semidirect
11. #2186×C139C2semidirect
12. #2175×C139C2semidirect
13. #2168×C139C2semidirect
14. #2139×C139C2semidirect
15. #2138×C139C2semidirect
265. #33876C139direct (N × H)
266. C139#33876direct (N × H)
267. #3339C2×C139semidirect
268. #3287C2×C139semidirect
269. #2244C2×C139semidirect
270. #2234C2×C139semidirect
271. #2232C2×C139semidirect
272. #2229C2×C139semidirect
273. #2218C2×C139semidirect
274. #2215C2×C139semidirect
275. #2206C2×C139semidirect
276. #2186C2×C139semidirect
277. #2186C2×C139semidirect
278. #2175C2×C139semidirect
279. #2168C2×C139semidirect
280. #2139C2×C139semidirect
281. #2138C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3339×C1392
#3287×C1392
#2244×C1392
#2234×C1392
#2232×C1392
#2229×C1392
#2218×C1392
#2215×C1392
#2206×C1392
#2186×C1392
#2175×C1392
#2168×C1392
#2139×C1392
#2138×C1392
#33876139