Finite Group Databasebeta

← #21435645

Subgroups — #21435645

Order 7552.

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×#14273748C211yesmaximal, characteristic, complemented
2#16838063C211yesmaximal, characteristic, complemented
3#16838051C211yesmaximal, characteristic, complemented
4#16837795C211yesmaximal, characteristic, complemented
5#16837648C211yesmaximal, characteristic, complemented
6#16837640C211yesmaximal, characteristic, complemented
7#16837619C211yesmaximal, characteristic, complemented
8#16837610C211yesmaximal, characteristic, complemented
9#16837563C211yesmaximal, characteristic, complemented
10#16837561C211yesmaximal, characteristic, complemented
11#16837558C211yesmaximal, characteristic, complemented
12#16837547C211yesmaximal, characteristic, complemented
13#16837503C211yesmaximal, characteristic, complemented
14#16837471C211yesmaximal, characteristic, complemented
15C2×#137×C59C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×#11745687C2211yescharacteristic
18#14273748—24no—
19C2×#11745672C2211yescharacteristic
20C2×#11745672C2211yescharacteristic
21C2×#11745660C2211yescharacteristic
22C2×#11745671C2211yescharacteristic
23C2×#11745669C2211yescharacteristic
24C2×C8×D59C2211yescharacteristic
25#14273725C2211yescharacteristic
26#14273716—21no—
27#14273716C2211yescharacteristic
28#14273710—21no—
29#14273708—21no—
30#14273706C2211yescharacteristic
31#14273703—21no—
32#14273703C2211yescharacteristic
33#14273703C2211yescharacteristic
34#14273701—21no—
35#14273701C2211yescharacteristic
36#14273699—21no—
37Q8×Dic59C2211yescharacteristic
38D4×Dic59C2211yescharacteristic
39C4×C22⋊D59—21no—
40C4×C22⋊D59C2211yescharacteristic
41C2×Dic59⋊C4—21no—
42#14273661C2211yescharacteristic
43Dic59⋊C8C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273651C2211yescharacteristic
47#14273651C2211yescharacteristic
48#14273649C2211yescharacteristic
49#14273648C2211yescharacteristic
50C22⋊(C59⋊C8)C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52#14273637C2211yescharacteristic
53C2×#41×C59C2211yescharacteristic
54C22×Q8×C59C2211yescharacteristic
55#137×C59—24no—
56C2×Q16×C59C2211yescharacteristic
57C2×Q16×C59C2211yescharacteristic
58C2×SD16×C59C2211yescharacteristic
59C2×SD16×C59C2211yescharacteristic
60C2×M16×C59C2211yescharacteristic
61#41×C59—22no—
62#41×C59—41no—
63C2×Q8×C59—21no—
64C2×Q8×C59—22no—
65C2×Q8×C59—41no—
66C2×Q8×C59C2311yescharacteristic
67C2×Q8×C59C2311yescharacteristic
68C2×Q8×C59C2311yescharacteristic
69C2×D4×C59—21no—
70C2×D4×C59C2311yescharacteristic
71C22×C4×C59—21no—
72C22×C4×C59—21no—
73C22×C4×C59C2311yescharacteristic
74C2×C22⋊D59—21no—
75C2×C22⋊D59—21no—
76C2×C22⋊D59D411yescharacteristic
77C22×Dic59—21no—
78C22×Dic59—21no—
79#11745689—22no—
80#11745689—41no—
81#11745687—22no—
82#11745687—41no—
83C2×D236—21no—
84C2×D236C2311yescharacteristic
85C2×C4×D59—21no—
86C2×C4×D59C2311yescharacteristic
87C2×Dic118C2311yescharacteristic
88Q16×C59—22no—
89Q16×C59—22no—
90SD16×C59—22no—
91SD16×C59D414yescomplemented
92M16×C59—22no—
93C2×C8×C59C2311yescharacteristic
94C2×C8×C59C2311yescharacteristic
95C22⋊Dic59—21no—
96C22⋊Dic59—21no—
97C22⋊Dic59D411yescharacteristic
98#11745672—22no—
99#11745672—41no—
100#11745671—41no—
101#11745669—22no—
102(C2×D59)⋊C4—21no—
103(C2×D59)⋊C4—21no—
104(C2×D59)⋊C4—21no—
105(C2×D59)⋊C4—21no—
106(C2×D59)⋊C4—21no—
107(C2×D59)⋊C4D411yescharacteristic
108C4⋊Dic59—21no—
109C4⋊Dic59C2311yescharacteristic
110C4⋊Dic59C2311yescharacteristic
111Dic59⋊C4—21no—
112Dic59⋊C4—21no—
113Dic59⋊C4—21no—
114Dic59⋊C4—21no—
115Dic59⋊C4—21no—
116Dic59⋊C4D411yescharacteristic
117C4×Dic59—21no—
118C4×Dic59C2311yescharacteristic
119C2×C59⋊C8C2311yescharacteristic
120C2×C59⋊C8C2311yescharacteristic
121#11745660—22no—
122C8×D59—22no—
123C23×C59—21no—
124C23×C59C2×D411yescharacteristic
125C22×D59—21no—
126C22×D59C2×D411yescharacteristic
127Q8×C59—21no—
128Q8×C59—21no—
129Q8×C59—21no—
130Q8×C59—21no—
131Q8×C59—21no—
132Q8×C59—42no—
133Q8×C59C2×D412yes—
134D4×C59—21no—
135D4×C59—42no—
136D4×C59C2×D412yes—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59—42no—
143C2×C4×C59—42no—
144C2×C4×C59C2×D411yescharacteristic
145C2×C4×C59C2411yescharacteristic
146C22⋊D59—41no—
147C22⋊D59—42no—
148C22⋊D59—42no—
149C2×Dic59—21no—
150C2×Dic59—21no—
151C2×Dic59—21no—
152C2×Dic59—42no—
153C2×Dic59—42no—
154C2×Dic59C2×D411yescharacteristic
155C2×Dic59C2×D411yescharacteristic
156C2×Dic59C2×D411yescharacteristic
157D236—21no—
158D236—21no—
159D236—42no—
160C4×D59—21no—
161C4×D59—21no—
162C4×D59—42no—
163Dic118—21no—
164Dic118—21no—
165C8×C59—21no—
166C8×C59C2×D412yes—
167C59⋊C8—21no—
168C59⋊C8—21no—
169C22×C59—22no—
170C22×C59—21no—
171C22×C59—21no—
172C22×C59—21no—
173C22×C59—41no—
174C22×C59—41no—
175C22×C59C22×D411yescharacteristic
176C2×D59—21no—
177C2×D59—21no—
178C2×D59—21no—
179C2×D59—41no—
180C2×D59—41no—
181C2×D59—41no—
182C4×C59—22no—
183C4×C59—21no—
184C4×C59—41no—
185C4×C59—41no—
186C4×C59C22×D411yescharacteristic
187C4×C59H(5,𝔽2)11yescharacteristic
188Dic59—21no—
189Dic59—21no—
190Dic59—21no—
191Dic59—41no—
192Dic59—41no—
193Dic59—41no—
194#3269—591nomaximal, Sylow
195C2×C59—41no—
196C2×C59—42no—
197C2×C59D4211yescharacteristic
198C2×C59#57511yescharacteristic
199C2×C59#57811yescharacteristic
200D59—41no—
201D59—81no—
202C2×#137D5911yescharacteristic, complemented
203C2×#135—591no—
204#548—591no—
205#547—591no—
206#497—591no—
207#468—591no—
208#467—591no—
209#463—591no—
210#462—591no—
211#452—591no—
212#452—591no—
213#451—591no—
214#449—591no—
215#440—591no—
216#435—591no—
217C59#326911yescharacteristic, complemented, Sylow
218C2×#41—591no—
219C2×#41—591no—
220C2×#41C2×D5911yescharacteristic
221C22×Q8C2×D5911yescharacteristic
222#137—24no—
223#135—1184no—
224C2×Q16—591no—
225C2×Q16—591no—
226C2×Q16C2×D5911yescharacteristic
227C2×Q16C2×D5911yescharacteristic
228C2×SD16—591no—
229C2×SD16—591no—
230C2×SD16C2×D5911yescharacteristic
231C2×SD16C2×D5911yescharacteristic
232C2×D8—591no—
233C2×M16C2×D5911yescharacteristic
234C22×C8—591no—
235C4⋊Q8—591no—
236#124—591no—
237#124—1181no—
238#123—1181no—
239#123—1181no—
240C22⋊Q8—591no—
241C22⋊Q8—591no—
242C22⋊Q8—591no—
243C22⋊Q8—1181no—
244#121—591no—
245#121—1181no—
246#121—1181no—
247C4×Q8—591no—
248C4×D4—591no—
249C4×D4—591no—
250C4×D4—1181no—
251C2×C4⋊C4—1181no—
252#107—591no—
253C4⋊C8—591no—
254#103—591no—
255#103—591no—
256#103—591no—
257#103—591no—
258#102—591no—
259#102—591no—
260C22⋊C8—591no—
261C22⋊C8—591no—
262#97—591no—
263#41—22no—
264#41—41no—
265#41—1182no—
266#41—1182no—
267#41—2361no—
268#41—2361no—
269C2×Q8—21no—
270C2×Q8—22no—
271C2×Q8—41no—
272C2×Q8—591no—
273C2×Q8C22×D5911yescharacteristic
274C2×Q8C22×D5911yescharacteristic
275C2×Q8C22×D5911yescharacteristic
276C2×D4—21no—
277C2×D4—591no—
278C2×D4—591no—
279C2×D4—1181no—
280C2×D4—1181no—
281C2×D4—1181no—
282C2×D4C22×D5911yescharacteristic
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—591no—
286C22×C4—1181no—
287C22×C4—1181no—
288C22×C4—1181no—
289C22×C4C22×D5911yescharacteristic
290Q16—22no—
291Q16—22no—
292Q16—1182no—
293Q16—2361no—
294SD16—22no—
295SD16—1182no—
296SD16—2361no—
297SD16C22⋊D5914yescomplemented
298D8—1182no—
299M16—22no—
300C2×C8—591no—
301C2×C8—591no—
302C2×C8—1182no—
303C2×C8C22×D5911yescharacteristic
304C2×C8C22×D5911yescharacteristic
305C4⋊C4—591no—
306C4⋊C4—591no—
307C4⋊C4—591no—
308C4⋊C4—1181no—
309C4⋊C4—1181no—
310C4⋊C4—1181no—
311C4⋊C4—1181no—
312C4⋊C4—1181no—
313C4⋊C4—1181no—
314C22⋊C4—591no—
315C22⋊C4—591no—
316C22⋊C4—1181no—
317C22⋊C4—1181no—
318C22⋊C4—1181no—
319C22⋊C4—1181no—
320C22⋊C4—1181no—
321C22⋊C4—1181no—
322C22⋊C4—1181no—
323C42—591no—
324C42—1181no—
325C23—21no—
326C23—591no—
327C23—1181no—
328C23D4×D5911yescharacteristic
329Q8—21no—
330Q8—21no—
331Q8—21no—
332Q8—21no—
333Q8—21no—
334Q8—42no—
335Q8—1181no—
336Q8—1181no—
337Q8C2×C22⋊D5912yes—
338D4—21no—
339D4—42no—
340D4—1181no—
341D4—1181no—
342D4—2362no—
343D4—2361no—
344D4—2362no—
345D4—2362no—
346D4C2×C22⋊D5912yes—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—591no—
355C2×C4—591no—
356C2×C4—591no—
357C2×C4—1181no—
358C2×C4—1181no—
359C2×C4—1181no—
360C2×C4—1181no—
361C2×C4—1181no—
362C2×C4—2362no—
363C2×C4—2362no—
364C2×C4—2362no—
365C2×C4D4×D5911yescharacteristic
366C2×C4C23×D5911yescharacteristic
367C8—21no—
368C8—1181no—
369C8—1181no—
370C8C2×C22⋊D5912yes—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—22no—
375C22—41no—
376C22—41no—
377C22—1181no—
378C22—1181no—
379C22—1181no—
380C22—2361no—
381C22—2361no—
382C22—2361no—
383C22C2×D4×D5911yescharacteristic
384C4—21no—
385C4—22no—
386C4—41no—
387C4—41no—
388C4—1181no—
389C4—1181no—
390C4—1181no—
391C4—2361no—
392C4—2361no—
393C4—2361no—
394C4C22×C22⋊D5911yescharacteristic
395C4#1427377211yescharacteristic
396C2—41no—
397C2—42no—
398C2—4721no—
399C2—2361no—
400C2D4×C22⋊D5911yescharacteristic
401C2#1683820111yescharacteristic
402C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC2×#137×C59C2
socleC22×C59C22×D4
hypercenterC2×#137D59
hypocenterC59#3269
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#14273748C2semidirect
2. #16838063C2semidirect
3. #16838051C2semidirect
4. #16837795C2semidirect
5. #16837648C2semidirect
6. #16837640C2semidirect
7. #16837619C2semidirect
8. #16837610C2semidirect
9. #16837563C2semidirect
10. #16837561C2semidirect
11. #16837558C2semidirect
12. #16837547C2semidirect
13. #16837503C2semidirect
14. #16837471C2semidirect
15. C2×#137×C59C2semidirect
91. SD16×C59D4semidirect
202. C2×#137D59semidirect
217. C59#3269semidirect
297. SD16C22⋊D59semidirect