Finite Group Databasebeta

← #31817940

Subgroups — #31817940

Order 17792.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17984868C211yesmaximal, characteristic, complemented
2C2×#17984862C211yesmaximal, characteristic, complemented
3#22581624C211yesmaximal, characteristic, complemented
4#22581343C211yesmaximal, characteristic, complemented
5#22581201C211yesmaximal, characteristic, complemented
6#22581187C211yesmaximal, characteristic, complemented
7#22581172C211yesmaximal, characteristic, complemented
8#22581148C211yesmaximal, characteristic, complemented
9#22581113C211yesmaximal, characteristic, complemented
10#22581098C211yesmaximal, characteristic, complemented
11#22581096C211yesmaximal, characteristic, complemented
12#22581087C211yesmaximal, characteristic, complemented
13#22581053C211yesmaximal, characteristic, complemented
14#22581025C211yesmaximal, characteristic, complemented
15#546×C139C211yesmaximal, characteristic, complemented
16C2×#14555785C2211yescharacteristic
17C2×#14555785C2211yescharacteristic, complemented
18#17984868—24no—
19#17984862—24no—
20C2×#14555775C2211yescharacteristic, complemented
21C2×#14555773C2211yescharacteristic
22C2×#14555773C2211yescharacteristic
23C2×#14555772C2211yescharacteristic, complemented
24C2×#14555772C2211yescharacteristic, complemented
25C2×#14555770C2211yescharacteristic
26C2×#14555770C2211yescharacteristic
27C2×#14555770C2211yescharacteristic
28C2×#14555770C2211yescharacteristic
29C2×#14555769C2211yescharacteristic
30C22×C139⋊C8C2211yescharacteristic, complemented
31#17984839C2211yescharacteristic, complemented
32#17984838—21no—
33#17984816C2211yescharacteristic
34#17984816C2211yescharacteristic, complemented
35#17984815—21no—
36#17984815—21no—
37C4×Dic278C2211yescharacteristic, complemented
38#17984804—21no—
39#17984775C2211yescharacteristic, complemented
40C4⋊(C139⋊C8)C2211yescharacteristic, complemented
41#17984766C2211yescharacteristic, complemented
42#17984765C2211yescharacteristic, complemented
43#17984763C2211yescharacteristic
44#17984763C2211yescharacteristic
45#17984762C2211yescharacteristic, complemented
46#17984762C2211yescharacteristic, complemented
47C22⋊(C139⋊C8)C2211yescharacteristic
48C22⋊(C139⋊C8)C2211yescharacteristic, complemented
49#17984753C2211yescharacteristic, complemented
50C2×#41×C139C2211yescharacteristic
51C22×D4×C139C2211yescharacteristic
52#124×C139C2211yescharacteristic
53#123×C139—21no—
54C22⋊Q8×C139C2211yescharacteristic
55#121×C139—21no—
56#121×C139C2211yescharacteristic
57#120×C139—21no—
58C4×D4×C139C2211yescharacteristic
59C4×D4×C139C2211yescharacteristic
60C2×C22⋊C4×C139—21no—
61#14555785—22no—
62#14555785—22no—
63#14555785—41no—
64#14555785—41no—
65C2×Dic278C2311yescharacteristic
66C2×D556—21no—
67C2×D556—21no—
68C2×D556C2311yescharacteristic
69C2×D556C2311yescharacteristic
70C2×C22⋊D139—21no—
71C2×C22⋊D139—21no—
72C2×C22⋊D139—21no—
73C2×C22⋊D139—21no—
74C2×C4×D139—21no—
75C2×C4×D139—21no—
76#14555775—22no—
77#14555773—22no—
78#14555773D414yescomplemented
79#14555772—22no—
80#14555772—41no—
81#14555770—22no—
82#14555770—22no—
83#14555770—22no—
84#14555770—41no—
85#14555769—22no—
86C2×C139⋊C8—22no—
87C2×C139⋊C8C2311yescharacteristic
88C2×C139⋊C8C2311yescharacteristic
89C2×C139⋊C8C2311yescharacteristic
90C2×C139⋊C8C2311yescharacteristic
91C4⋊Dic139C2311yescharacteristic
92Dic139⋊C4—21no—
93(C2×D139)⋊C4—21no—
94(C2×D139)⋊C4—21no—
95C4×Dic139—21no—
96C24×C139—21no—
97#41×C139—22no—
98#41×C139—41no—
99C2×Q8×C139C2311yescharacteristic
100C2×D4×C139—22no—
101C2×D4×C139—21no—
102C2×D4×C139—21no—
103C2×D4×C139—21no—
104C2×D4×C139—41no—
105C2×D4×C139D411yescharacteristic
106C2×D4×C139C2311yescharacteristic
107C2×D4×C139C2311yescharacteristic
108C22×C4×C139—21no—
109C22×C4×C139—21no—
110C22×C4×C139C2311yescharacteristic
111C22×C4×C139C2311yescharacteristic
112C4⋊C4×C139—21no—
113C4⋊C4×C139D411yescharacteristic
114C4⋊C4×C139C2311yescharacteristic
115C22⋊C4×C139—21no—
116C22⋊C4×C139—21no—
117C22⋊C4×C139—21no—
118C22⋊C4×C139—21no—
119C22⋊C4×C139—21no—
120C22⋊C4×C139D411yescharacteristic
121C22⋊C4×C139D411yescharacteristic
122C42×C139C2311yescharacteristic
123C22×D139—21no—
124C22×D139—21no—
125Dic278—21no—
126Dic278C2×D412yes—
127D556—21no—
128D556—21no—
129D556—21no—
130D556—21no—
131D556—42no—
132D556—81no—
133C22⋊D139—42no—
134C22⋊D139—42no—
135C22⋊D139—81no—
136C22⋊D139—81no—
137C2×Dic139—21no—
138C2×Dic139—21no—
139C4×D139—42no—
140C4×D139—42no—
141C139⋊C8—21no—
142C139⋊C8—21no—
143C139⋊C8—21no—
144C139⋊C8C2×D412yes—
145C23×C139—21no—
146C23×C139—21no—
147C23×C139—42no—
148C23×C139—42no—
149C23×C139—81no—
150C23×C139C2×D411yescharacteristic
151C23×C139C2×D411yescharacteristic
152Q8×C139—21no—
153Q8×C139—21no—
154D4×C139—21no—
155D4×C139—21no—
156D4×C139—21no—
157D4×C139—41no—
158D4×C139—42no—
159D4×C139—42no—
160D4×C139—81no—
161D4×C139C2×D412yes—
162C2×C4×C139—21no—
163C2×C4×C139—21no—
164C2×C4×C139—21no—
165C2×C4×C139—21no—
166C2×C4×C139—21no—
167C2×C4×C139—21no—
168C2×C4×C139—42no—
169C2×C4×C139—81no—
170C2×C4×C139C2×D411yescharacteristic
171C2×C4×C139C2×D411yescharacteristic
172C2×C4×C139C2×D411yescharacteristic
173C2×C4×C139C2×D411yescharacteristic
174C2×C4×C139C2411yescharacteristic
175C22×C139—21no—
176C22×C139—21no—
177C22×C139—22no—
178C22×C139—21no—
179C22×C139—21no—
180C22×C139—21no—
181C22×C139—21no—
182C22×C139—41no—
183C22×C139—41no—
184C22×C139—41no—
185C22×C139—41no—
186C22×C139—41no—
187C22×C139—84no—
188C22×C139C22×D411yescharacteristic
189C2×D139—41no—
190C2×D139—41no—
191C2×D139—41no—
192C2×D139—41no—
193C2×D139—41no—
194C2×D139—41no—
195C4×C139—21no—
196C4×C139—21no—
197C4×C139—21no—
198C4×C139—21no—
199C4×C139—41no—
200C4×C139—41no—
201C4×C139C22×D411yescharacteristic
202C4×C139H(5,𝔽2)11yescharacteristic
203Dic139—22no—
204Dic139—41no—
205C2×C139—41no—
206C2×C139—41no—
207C2×C139—42no—
208C2×C139—81no—
209C2×C139D4211yescharacteristic
210C2×C139#57511yescharacteristic
211C2×C139#57611yescharacteristic
212D139—81no—
213D139—81no—
214C139#326811yescharacteristic, complemented, Sylow
215#3268—1391nomaximal, Sylow
216C2×AGL(1,ℤ/8)—1391no—
217C2×#135—1391no—
218#550—1391no—
219#546D13911yescharacteristic, complemented
220#496—1391no—
221#468—1391no—
222#466—1391no—
223#464—1391no—
224#459—1391no—
225#452—1391no—
226#449—1391no—
227#449—1391no—
228#447—1391no—
229#440—1391no—
230#435—1391no—
231C2×#41—1391no—
232C2×#41—1391no—
233C2×#41C2×D13911yescharacteristic
234C22×D4C2×D13911yescharacteristic
235AGL(1,ℤ/8)—2784no—
236#135—2784no—
237C2×Q16—1391no—
238C2×SD16—1391no—
239C2×SD16—1391no—
240C2×SD16—1391no—
241C2×SD16—1391no—
242C2×D8—1391no—
243C2×D8—1391no—
244C2×D8—1391no—
245C2×D8—1391no—
246C2×M16—1391no—
247C22×C8—1391no—
248#127—2781no—
249#127—1391no—
250#124C2×D13911yescharacteristic
251#123—21no—
252C22⋊Q8C2×D13911yescharacteristic
253#121—21no—
254#121—2781no—
255#121—2781no—
256#121—1391no—
257#121—1391no—
258#121C2×D13911yescharacteristic
259#120—21no—
260C4×Q8—1391no—
261C4×D4—2781no—
262C4×D4C2×D13911yescharacteristic
263C4×D4C2×D13911yescharacteristic
264C2×C22⋊C4—21no—
265#107—1391no—
266C4⋊C8—1391no—
267#103—1391no—
268#103—1391no—
269#102—1391no—
270#102—1391no—
271#102—1391no—
272#102—1391no—
273C22⋊C8—1391no—
274C22⋊C8—1391no—
275#97—1391no—
276C24—21no—
277#41—22no—
278#41—41no—
279#41—2782no—
280#41—2782no—
281#41—5561no—
282#41—5561no—
283C2×Q8—1391no—
284C2×Q8C22×D13911yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—2781no—
291C2×D4—2781no—
292C2×D4—2781no—
293C2×D4—2781no—
294C2×D4—2781no—
295C2×D4—2781no—
296C2×D4—1391no—
297C2×D4—1391no—
298C2×D4C22⋊D13911yescharacteristic
299C2×D4C22×D13911yescharacteristic
300C2×D4C22×D13911yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—2781no—
304C22×C4—2781no—
305C22×C4C22×D13911yescharacteristic
306C22×C4C22×D13911yescharacteristic
307Q16—2782no—
308SD16—2782no—
309SD16—2782no—
310SD16—5561no—
311SD16—1394no—
312D8—2782no—
313D8—2782no—
314D8—2782no—
315D8—5561no—
316M16—2782no—
317C2×C8—2782no—
318C2×C8—1391no—
319C2×C8—1391no—
320C2×C8—1391no—
321C2×C8—1391no—
322C4⋊C4—21no—
323C4⋊C4—2781no—
324C4⋊C4—1391no—
325C4⋊C4C22⋊D13911yescharacteristic
326C4⋊C4C22×D13911yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—2781no—
333C22⋊C4—2781no—
334C22⋊C4C22⋊D13911yescharacteristic
335C22⋊C4C22⋊D13911yescharacteristic
336C42—2781no—
337C42C22×D13911yescharacteristic
338C23—21no—
339C23—21no—
340C23—42no—
341C23—42no—
342C23—81no—
343C23—2781no—
344C23—2781no—
345C23C2×C22⋊D13911yescharacteristic
346C23C2×C22⋊D13911yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—2781no—
350Q8—1392no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—41no—
355D4—42no—
356D4—42no—
357D4—81no—
358D4—2781no—
359D4—2781no—
360D4—2781no—
361D4—2781no—
362D4—5562no—
363D4—5562no—
364D4—5562no—
365D4—11121no—
366D4—11121no—
367D4—11121no—
368D4D4×D13912yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—81no—
377C2×C4—2781no—
378C2×C4—2781no—
379C2×C4—5562no—
380C2×C4—5562no—
381C2×C4C2×C22⋊D13911yescharacteristic
382C2×C4C2×C22⋊D13911yescharacteristic
383C2×C4C2×C22⋊D13911yescharacteristic
384C2×C4C2×C22⋊D13911yescharacteristic
385C2×C4C23×D13911yescharacteristic
386C8—2781no—
387C8—2781no—
388C8—2781no—
389C8—1392no—
390C22—21no—
391C22—21no—
392C22—22no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—5561no—
404C22—5561no—
405C22—5561no—
406C22—5561no—
407C22—5561no—
408C22—5561no—
409C22C22×C22⋊D13911yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—2782no—
417C4—5561no—
418C4C2×D4×D13911yescharacteristic
419C4#1798488711yescharacteristic
420C2—41no—
421C2—41no—
422C2—42no—
423C2—81no—
424C2—11121no—
425C2—11121no—
426C2D4×C22⋊D13911yescharacteristic
427C2#2258175111yescharacteristic
428C2#2258175611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#546×C139C2
socleC22×C139C22×D4
hypercenter#546D139
hypocenterC139#3268
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#17984868C2semidirect
2. C2×#17984862C2semidirect
3. #22581624C2semidirect
4. #22581343C2semidirect
5. #22581201C2semidirect
6. #22581187C2semidirect
7. #22581172C2semidirect
8. #22581148C2semidirect
9. #22581113C2semidirect
10. #22581098C2semidirect
11. #22581096C2semidirect
12. #22581087C2semidirect
13. #22581053C2semidirect
14. #22581025C2semidirect
15. #546×C139C2semidirect
17. C2×#14555785C22semidirect
20. C2×#14555775C22semidirect
23. C2×#14555772C22semidirect
24. C2×#14555772C22semidirect
30. C22×C139⋊C8C22semidirect
31. #17984839C22semidirect
34. #17984816C22semidirect
37. C4×Dic278C22semidirect
39. #17984775C22semidirect
40. C4⋊(C139⋊C8)C22semidirect
41. #17984766C22semidirect
42. #17984765C22semidirect
45. #17984762C22semidirect
46. #17984762C22semidirect
48. C22⋊(C139⋊C8)C22semidirect
49. #17984753C22semidirect
78. #14555773D4semidirect
214. C139#3268semidirect
219. #546D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848682
C2×#179848622
#225816242
#225813432
#225812012
#225811872
#225811722
#225811482
#225811132
#225810982
#225810962
#225810872
#225810532
#225810252
#546×C1392
#3268139