Finite Group Databasebeta

← #31817955

Subgroups — #31817955

Order 17792.

478 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17984872C211yesmaximal, characteristic, complemented
2C2×#17984862C211yesmaximal, characteristic, complemented
3#22581612C211yesmaximal, characteristic, complemented
4#22581345C211yesmaximal, characteristic, complemented
5#22581201C211yesmaximal, characteristic, complemented
6#22581192C211yesmaximal, characteristic, complemented
7#22581168C211yesmaximal, characteristic, complemented
8#22581160C211yesmaximal, characteristic, complemented
9#22581115C211yesmaximal, characteristic, complemented
10#22581113C211yesmaximal, characteristic, complemented
11#22581108C211yesmaximal, characteristic, complemented
12#22581098C211yesmaximal, characteristic, complemented
13#22581053C211yesmaximal, characteristic, complemented
14#22581025C211yesmaximal, characteristic, complemented
15#547×C139C211yesmaximal, characteristic, complemented
16C2×#14555785C2211yescharacteristic
17C22×Dic278C2211yescharacteristic
18#17984872—24no—
19#17984862—24no—
20C2×#14555775C2211yescharacteristic
21C2×#14555775C2211yescharacteristic
22C2×#14555775C2211yescharacteristic
23C2×#14555775C2211yescharacteristic
24C2×#14555773C2211yescharacteristic
25C2×#14555773C2211yescharacteristic
26C2×#14555772C2211yescharacteristic
27C2×#14555772C2211yescharacteristic
28C2×#14555770C2211yescharacteristic
29C2×#14555769C2211yescharacteristic
30C22×C139⋊C8C2211yescharacteristic
31#17984830C2211yescharacteristic
32#17984828—21no—
33#17984821C2211yescharacteristic
34#17984820—21no—
35#17984816C2211yescharacteristic
36#17984814—21no—
37C4×Dic278C2211yescharacteristic
38(C22⋊D139)⋊C4—21no—
39#17984775C2211yescharacteristic
40C4⋊(C139⋊C8)C2211yescharacteristic
41#17984766C2211yescharacteristic
42#17984766C2211yescharacteristic
43#17984765C2211yescharacteristic
44#17984765C2211yescharacteristic
45#17984763C2211yescharacteristic
46#17984762C2211yescharacteristic
47C22⋊(C139⋊C8)C2211yescharacteristic
48C22⋊(C139⋊C8)C2211yescharacteristic
49#17984753C2211yescharacteristic
50C2×#41×C139C2211yescharacteristic
51C2×#41×C139C2211yescharacteristic
52C4⋊Q8×C139C2211yescharacteristic
53#123×C139—21no—
54#123×C139—21no—
55C22⋊Q8×C139C2211yescharacteristic
56C22⋊Q8×C139C2211yescharacteristic
57#121×C139—21no—
58C4×D4×C139C2211yescharacteristic
59C4×D4×C139C2211yescharacteristic
60C2×C4⋊C4×C139—21no—
61#14555785—22no—
62#14555785—41no—
63C2×Dic278—22no—
64C2×Dic278—21no—
65C2×Dic278—41no—
66C2×Dic278C2311yescharacteristic
67C2×Dic278C2311yescharacteristic
68C2×D556C2311yescharacteristic
69C2×C22⋊D139—21no—
70C2×C22⋊D139—21no—
71C22×Dic139—21no—
72C2×C4×D139—21no—
73#14555775—22no—
74#14555775—22no—
75#14555775—22no—
76#14555775—41no—
77#14555773—22no—
78#14555773D414yescomplemented
79#14555772—22no—
80#14555772—41no—
81#14555770—22no—
82#14555769—22no—
83C2×C139⋊C8—22no—
84C2×C139⋊C8C2311yescharacteristic
85C2×C139⋊C8C2311yescharacteristic
86C2×C139⋊C8C2311yescharacteristic
87C2×C139⋊C8C2311yescharacteristic
88C4⋊Dic139C2311yescharacteristic
89Dic139⋊C4—21no—
90Dic139⋊C4—21no—
91C22⋊Dic139—21no—
92(C2×D139)⋊C4—21no—
93(C2×D139)⋊C4—21no—
94(C2×D139)⋊C4—21no—
95C4×Dic139—21no—
96#41×C139—22no—
97#41×C139—22no—
98#41×C139—41no—
99#41×C139—41no—
100C2×Q8×C139C2311yescharacteristic
101C2×Q8×C139C2311yescharacteristic
102C2×D4×C139—21no—
103C2×D4×C139—21no—
104C2×D4×C139D411yescharacteristic
105C2×D4×C139C2311yescharacteristic
106C22×C4×C139—21no—
107C22×C4×C139—21no—
108C22×C4×C139—21no—
109C22×C4×C139C2311yescharacteristic
110C22×C4×C139C2311yescharacteristic
111C4⋊C4×C139—21no—
112C4⋊C4×C139—21no—
113C4⋊C4×C139—21no—
114C4⋊C4×C139—21no—
115C4⋊C4×C139D411yescharacteristic
116C4⋊C4×C139C2311yescharacteristic
117C22⋊C4×C139—21no—
118C22⋊C4×C139—21no—
119C22⋊C4×C139—21no—
120C22⋊C4×C139D411yescharacteristic
121C22⋊C4×C139D411yescharacteristic
122C42×C139C2311yescharacteristic
123C22×D139—21no—
124Dic278—21no—
125Dic278—21no—
126Dic278—21no—
127Dic278—42no—
128Dic278C2×D412yes—
129D556—21no—
130D556—21no—
131C22⋊D139—42no—
132C22⋊D139—42no—
133C2×Dic139—21no—
134C2×Dic139—21no—
135C2×Dic139—21no—
136C2×Dic139—42no—
137C4×D139—42no—
138C139⋊C8—21no—
139C139⋊C8—21no—
140C139⋊C8—21no—
141C139⋊C8C2×D412yes—
142C23×C139—21no—
143C23×C139C2×D411yescharacteristic
144C23×C139C2×D411yescharacteristic
145Q8×C139—21no—
146Q8×C139—21no—
147Q8×C139—21no—
148Q8×C139—21no—
149D4×C139—21no—
150D4×C139—41no—
151D4×C139—42no—
152D4×C139—42no—
153D4×C139C2×D412yes—
154C2×C4×C139—21no—
155C2×C4×C139—21no—
156C2×C4×C139—21no—
157C2×C4×C139—21no—
158C2×C4×C139—21no—
159C2×C4×C139—21no—
160C2×C4×C139—21no—
161C2×C4×C139—42no—
162C2×C4×C139—42no—
163C2×C4×C139—42no—
164C2×C4×C139C2×D411yescharacteristic
165C2×C4×C139C2×D411yescharacteristic
166C2×C4×C139C2×D411yescharacteristic
167C2×C4×C139C2×D411yescharacteristic
168C2×C4×C139C2411yescharacteristic
169C22×C139—21no—
170C22×C139—21no—
171C22×C139—22no—
172C22×C139—21no—
173C22×C139—21no—
174C22×C139—21no—
175C22×C139—21no—
176C22×C139—41no—
177C22×C139—41no—
178C22×C139C22×D411yescharacteristic
179C2×D139—41no—
180C2×D139—41no—
181C2×D139—41no—
182C4×C139—21no—
183C4×C139—21no—
184C4×C139—21no—
185C4×C139—21no—
186C4×C139—41no—
187C4×C139—41no—
188C4×C139—41no—
189C4×C139C22×D411yescharacteristic
190C4×C139H(5,𝔽2)11yescharacteristic
191Dic139—22no—
192Dic139—41no—
193Dic139—41no—
194C2×C139—41no—
195C2×C139—41no—
196C2×C139—42no—
197C2×C139D4211yescharacteristic
198C2×C139#57511yescharacteristic
199C2×C139#57811yescharacteristic
200D139—81no—
201C139#326911yescharacteristic, complemented, Sylow
202#3269—1391nomaximal, Sylow
203C2×#137—1391no—
204C2×#135—1391no—
205#548—1391no—
206#547D13911yescharacteristic, complemented
207#497—1391no—
208#468—1391no—
209#467—1391no—
210#463—1391no—
211#462—1391no—
212#452—1391no—
213#452—1391no—
214#451—1391no—
215#449—1391no—
216#440—1391no—
217#435—1391no—
218C2×#41—1391no—
219C2×#41C2×D13911yescharacteristic
220C2×#41C2×D13911yescharacteristic
221C22×Q8—1391no—
222#137—2784no—
223#135—2784no—
224C2×Q16—1391no—
225C2×Q16—1391no—
226C2×Q16—1391no—
227C2×Q16—1391no—
228C2×SD16—1391no—
229C2×SD16—1391no—
230C2×SD16—1391no—
231C2×SD16—1391no—
232C2×D8—1391no—
233C2×M16—1391no—
234C22×C8—1391no—
235C4⋊Q8C2×D13911yescharacteristic
236#124—2781no—
237#124—1391no—
238#123—21no—
239#123—21no—
240C22⋊Q8—2781no—
241C22⋊Q8—1391no—
242C22⋊Q8C2×D13911yescharacteristic
243C22⋊Q8C2×D13911yescharacteristic
244#121—21no—
245#121—2781no—
246#121—1391no—
247C4×Q8—1391no—
248C4×D4—2781no—
249C4×D4C2×D13911yescharacteristic
250C4×D4C2×D13911yescharacteristic
251C2×C4⋊C4—21no—
252#107—1391no—
253C4⋊C8—1391no—
254#103—1391no—
255#103—1391no—
256#103—1391no—
257#103—1391no—
258#102—1391no—
259#102—1391no—
260C22⋊C8—1391no—
261C22⋊C8—1391no—
262#97—1391no—
263#41—22no—
264#41—22no—
265#41—41no—
266#41—41no—
267#41—2782no—
268#41—5561no—
269C2×Q8—2782no—
270C2×Q8—2781no—
271C2×Q8—5561no—
272C2×Q8—1391no—
273C2×Q8—1391no—
274C2×Q8C22×D13911yescharacteristic
275C2×Q8C22×D13911yescharacteristic
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—2781no—
279C2×D4—2781no—
280C2×D4—1391no—
281C2×D4C22⋊D13911yescharacteristic
282C2×D4C22×D13911yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—2781no—
287C22×C4—2781no—
288C22×C4C22×D13911yescharacteristic
289C22×C4C22×D13911yescharacteristic
290Q16—2782no—
291Q16—2782no—
292Q16—2782no—
293Q16—5561no—
294SD16—2782no—
295SD16—2782no—
296SD16—5561no—
297SD16—1394no—
298D8—2782no—
299M16—2782no—
300C2×C8—2782no—
301C2×C8—1391no—
302C2×C8—1391no—
303C2×C8—1391no—
304C2×C8—1391no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—2781no—
310C4⋊C4—2781no—
311C4⋊C4—1391no—
312C4⋊C4C22⋊D13911yescharacteristic
313C4⋊C4C22×D13911yescharacteristic
314C22⋊C4—21no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—2781no—
318C22⋊C4—2781no—
319C22⋊C4—2781no—
320C22⋊C4—2781no—
321C22⋊C4C22⋊D13911yescharacteristic
322C22⋊C4C22⋊D13911yescharacteristic
323C42—2781no—
324C42C22×D13911yescharacteristic
325C23—21no—
326C23—2781no—
327C23C2×C22⋊D13911yescharacteristic
328C23C2×C22⋊D13911yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—2781no—
334Q8—2781no—
335Q8—2781no—
336Q8—5562no—
337Q8—1392no—
338D4—21no—
339D4—41no—
340D4—42no—
341D4—42no—
342D4—2781no—
343D4—2781no—
344D4—5562no—
345D4—5562no—
346D4D4×D13912yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—2781no—
358C2×C4—2781no—
359C2×C4—2781no—
360C2×C4—5562no—
361C2×C4—5562no—
362C2×C4C2×C22⋊D13911yescharacteristic
363C2×C4C2×C22⋊D13911yescharacteristic
364C2×C4C2×C22⋊D13911yescharacteristic
365C2×C4C2×C22⋊D13911yescharacteristic
366C2×C4C23×D13911yescharacteristic
367C8—2781no—
368C8—2781no—
369C8—2781no—
370C8—1392no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—22no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—5561no—
381C22—5561no—
382C22—5561no—
383C22C22×C22⋊D13911yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—2782no—
392C4—5561no—
393C4—5561no—
394C4C2×D4×D13911yescharacteristic
395C4#1798488711yescharacteristic
396C2—41no—
397C2—41no—
398C2—42no—
399C2—11121no—
400C2D4×C22⋊D13911yescharacteristic
401C2#2258175111yescharacteristic
402C2#2258176811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#547×C139C2
socleC22×C139C22×D4
hypercenter#547D139
hypocenterC139#3269
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C2×#17984872C2semidirect
2. C2×#17984862C2semidirect
3. #22581612C2semidirect
4. #22581345C2semidirect
5. #22581201C2semidirect
6. #22581192C2semidirect
7. #22581168C2semidirect
8. #22581160C2semidirect
9. #22581115C2semidirect
10. #22581113C2semidirect
11. #22581108C2semidirect
12. #22581098C2semidirect
13. #22581053C2semidirect
14. #22581025C2semidirect
15. #547×C139C2semidirect
78. #14555773D4semidirect
201. C139#3269semidirect
206. #547D139semidirect

Maximal subgroups

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

subgroupindex
C2×#179848722
C2×#179848622
#225816122
#225813452
#225812012
#225811922
#225811682
#225811602
#225811152
#225811132
#225811082
#225810982
#225810532
#225810252
#547×C1392
#3269139