Finite Group Databasebeta

← #28484166

Subgroups — #28484166

Order 15104.

514 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C8×#11745685C211yesmaximal, characteristic
2C4×#14273758C211yesmaximal, characteristic
3#21422481C211yesmaximal, characteristic
4#21422420C211yesmaximal, characteristic, complemented
5#21421946C211yesmaximal, characteristic, complemented
6#21421933C211yesmaximal, characteristic, complemented
7C2×C59×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#14273758C411yescharacteristic
9C4×#11745685C2211yescharacteristic
10C8×Dic118—21no—
11#16837507—21no—
12#16837500—21no—
13C4×#11745672—21no—
14C4×#11745671—21no—
15C8×D236—21no—
16C8×C22⋊D59—22no—
17#16837455C2211yescharacteristic
18#16837455C2211yescharacteristic
19#16837453—21no—
20#16837442C411yescharacteristic
21#16837411C411yescharacteristic
22#16837401C411yescharacteristic
23C4×#11745664C2211yescharacteristic
24C4×C8×D59—21no—
25#16837132—21no—
26#16837129—21no—
27#16837128—22no—
28C2×C4×Q8×C59C2211yescharacteristic
29C2×C4⋊C8×C59C2211yescharacteristic
30C2×C4×C8×C59C2211yescharacteristic
31C59×Q8⋊C8—21no—
32C59×Q8⋊C8—21no—
33C2×#11745685C2×C411yescharacteristic
34#14273758—22no—
35#14273758C814yescomplemented
36C2×#11745672—21no—
37C2×#11745671—21no—
38C2×#11745664C2×C411yescharacteristic
39C2×#11745664C2×C411yescharacteristic
40C2×C8×D59—22no—
41C4×Dic118D411yescharacteristic
42C4×Dic118D411yescharacteristic
43C4×D236D411yescharacteristic
44C4×D236D411yescharacteristic
45C4×C22⋊D59—21no—
46C4×C22⋊D59—21no—
47#14273686C2×C411yescharacteristic
48#14273684—21no—
49C42×D59—21no—
50#14273660—21no—
51#14273658—21no—
52C4⋊(C59⋊C8)—21no—
53C4⋊(C59⋊C8)—21no—
54Dic59⋊C8—22no—
55#14273651—21no—
56#14273651—21no—
57#14273650—21no—
58#14273647—21no—
59C22⋊(C59⋊C8)—21no—
60C22⋊(C59⋊C8)D412yes—
61(C2×D59)⋊C8—22no—
62#14273638—21no—
63C4×C59⋊C8—21no—
64C4×C59⋊C8—21no—
65C4×C59⋊C8—21no—
66C8×Dic59—22no—
67C22×Q8×C59C2×C411yescharacteristic
68C22×C8×C59—21no—
69C22×C8×C59—21no—
70C4×Q8×C59—21no—
71C4×Q8×C59—21no—
72C4×Q8×C59—21no—
73C4×Q8×C59—21no—
74C2×C4⋊C4×C59—21no—
75C2×C4⋊C4×C59C2×C411yescharacteristic
76C2×C42×C59—21no—
77C2×C42×C59C2311yescharacteristic
78C4⋊C8×C59—21no—
79C4⋊C8×C59—21no—
80C4×C8×C59—21no—
81C4×C8×C59D411yescharacteristic
82C4×C8×C59D411yescharacteristic
83C2×Q8×C59—21no—
84C2×Q8×C59—21no—
85C2×Q8×C59—21no—
86C2×Q8×C59—21no—
87C2×Q8×C59—21no—
88C2×Q8×C59C2×C812yescomplemented
89C22×C4×C59—21no—
90C22×C4×C59—21no—
91C22×C4×C59C22×C411yescharacteristic
92C22×C4×C59C2×D411yescharacteristic
93C22×C4×C59#4111yescharacteristic
94C2×C22⋊D59—21no—
95#11745685—21no—
96#11745685—21no—
97#11745685C2×C812yes—
98#11745685M1612yes—
99C2×D236C22⋊C411yescharacteristic
100C2×C4×D59—21no—
101C2×C4×D59—21no—
102C2×C4×D59—21no—
103C2×Dic118C22⋊C411yescharacteristic
104C2×C8×C59—21no—
105C2×C8×C59—21no—
106C2×C8×C59—42no—
107C2×C8×C59—41no—
108C2×C8×C59—81no—
109C4⋊C4×C59—21no—
110C4⋊C4×C59—21no—
111C4⋊C4×C59—41no—
112C4⋊C4×C59—41no—
113C42×C59—41no—
114C42×C59—41no—
115C42×C59C2×D411yescharacteristic
116C42×C59C2×D411yescharacteristic
117C42×C59C2×D411yescharacteristic
118C42×C59#4111yescharacteristic
119C22⋊Dic59—21no—
120#11745672—24no—
121#11745671—24no—
122(C2×D59)⋊C4—21no—
123(C2×D59)⋊C4—21no—
124C4⋊Dic59C22⋊C411yescharacteristic
125C4⋊Dic59C22⋊C411yescharacteristic
126Dic59⋊C4—21no—
127Dic59⋊C4—21no—
128C4×Dic59—21no—
129C4×Dic59—21no—
130C4×Dic59—21no—
131#11745664—21no—
132#11745664—21no—
133#11745664—21no—
134#11745664C2×C812yescomplemented
135C2×C59⋊C8—21no—
136C2×C59⋊C8—21no—
137C2×C59⋊C8—22no—
138C2×C59⋊C8—41no—
139C8×D59—44no—
140C23×C59C4×D411yescharacteristic
141C22×D59—21no—
142Q8×C59—22no—
143Q8×C59—22no—
144Q8×C59—41no—
145Q8×C59—41no—
146C2×C4×C59—21no—
147C2×C4×C59—21no—
148C2×C4×C59—22no—
149C2×C4×C59—41no—
150C2×C4×C59—41no—
151C2×C4×C59—41no—
152C2×C4×C59—41no—
153C2×C4×C59—81no—
154C2×C4×C59C2×C22⋊C411yescharacteristic
155C2×C4×C59C4×D411yescharacteristic
156C2×C4×C59#12011yescharacteristic
157C2×C4×C59#12111yescharacteristic
158C2×C4×C59#12111yescharacteristic
159C2×C4×C59#12311yescharacteristic
160C2×C4×C59C22×C811yescharacteristic
161C2×C4×C59C2×M1611yescharacteristic
162C2×C4×C59#13111yescharacteristic
163C2×C4×C59#13111yescharacteristic
164C22⋊D59—22no—
165C22⋊D59—22no—
166C2×Dic59—21no—
167C2×Dic59—21no—
168C2×Dic59—21no—
169D236—21no—
170D236C22⋊C812yes—
171C4×D59—22no—
172C4×D59—22no—
173C4×D59—42no—
174C4×D59—41no—
175C4×D59—41no—
176Dic118—21no—
177Dic118C22⋊C812yes—
178C8×C59—22no—
179C8×C59—41no—
180C8×C59—81no—
181C59⋊C8—22no—
182C59⋊C8—42no—
183C59⋊C8—41no—
184C59⋊C8—81no—
185#9096—591nomaximal, Sylow
186C22×C59—21no—
187C22×C59—21no—
188C22×C59#38611yescharacteristic
189C22×C59C8×D411yescharacteristic
190C22×C59#43511yescharacteristic
191C2×D59—22no—
192C2×D59—41no—
193C2×D59—41no—
194C4×C59—21no—
195C4×C59—21no—
196C4×C59—21no—
197C4×C59—42no—
198C4×C59—81no—
199C4×C59C2×C22⋊C811yescharacteristic
200C4×C59#40811yescharacteristic
201C4×C59C8×D411yescharacteristic
202C4×C59#43511yescharacteristic
203C4×C59#47111yescharacteristic
204C4×C59#47311yescharacteristic
205Dic59—22no—
206Dic59—41no—
207Dic59—41no—
208C8×#41—591no—
209C4×#137—591no—
210#1477—591no—
211C2×Q8⋊C8D5911yescharacteristic, complemented
212#1461—591no—
213#1283—591no—
214#1278—591no—
215C2×C59—21no—
216C2×C59—21no—
217C2×C59#186911yescharacteristic
218C2×C59#190611yescharacteristic
219C2×C59#190811yescharacteristic
220D59—42no—
221C2×#137—591no—
222C4×#41—591no—
223C2×C4×Q8C2×D5911yescharacteristic
224C8×Q8—1181no—
225#441—1181no—
226#440—1181no—
227C4×Q16—1181no—
228C4×SD16—1181no—
229C8×D4—1181no—
230C8×D4—1182no—
231#431—591no—
232#431—591no—
233#431—1181no—
234#428—591no—
235C2×C4⋊C8C2×D5911yescharacteristic
236#419—591no—
237#417—591no—
238C4×M16—591no—
239C2×C4×C8—1181no—
240C2×C4×C8C2×D5911yescharacteristic
241Q8⋊C8—21no—
242Q8⋊C8—21no—
243Q8⋊C8—1181no—
244D4⋊C8—1181no—
245#324—1182no—
246C59#909611yescharacteristic, complemented, Sylow
247C2×#41—591no—
248C22×Q8C4×D5911yescharacteristic
249#137—594no—
250#137—1182no—
251C2×Q16—1181no—
252C2×SD16—1181no—
253C2×M16—591no—
254C2×M16—591no—
255C22×C8—21no—
256C22×C8—21no—
257C22×C8—1182no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×Q8—591no—
263C4×Q8—591no—
264C4×D4—591no—
265C4×D4—591no—
266C4×D4—1181no—
267C4×D4—1181no—
268#117—591no—
269#117—1181no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4C4×D5911yescharacteristic
272C2×C42—21no—
273C2×C42—1181no—
274C2×C42C22×D5911yescharacteristic
275#107—1181no—
276#106—1181no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279C4⋊C8—1182no—
280C4⋊C8—1181no—
281C4⋊C8—1181no—
282#103—1181no—
283#103—1181no—
284#103—1181no—
285#102—1181no—
286C22⋊C8—592no—
287C22⋊C8—1182no—
288C22⋊C8—1181no—
289#97—1181no—
290C4×C8—21no—
291C4×C8—1182no—
292C4×C8—1181no—
293C4×C8—1181no—
294C4×C8—1181no—
295C4×C8C22⋊D5911yescharacteristic
296C4×C8C22⋊D5911yescharacteristic
297#41—592no—
298#41—592no—
299#41—1181no—
300#41—1181no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—21no—
306C2×Q8—591no—
307C2×Q8C8×D5912yescomplemented
308C2×D4—591no—
309C2×D4—1181no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—1181no—
313C22×C4—1181no—
314C22×C4—1181no—
315C22×C4C2×C4×D5911yescharacteristic
316C22×C4D4×D5911yescharacteristic
317C22×C4#1174568711yescharacteristic
318Q16—1184no—
319SD16—1184no—
320M16—592no—
321M16—1181no—
322M16—1181no—
323M16—1181no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—42no—
327C2×C8—41no—
328C2×C8—81no—
329C2×C8—1181no—
330C2×C8—1181no—
331C2×C8—1182no—
332C2×C8—2364no—
333C2×C8—2361no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—591no—
339C4⋊C4—591no—
340C4⋊C4—1181no—
341C4⋊C4—1181no—
342C22⋊C4—1181no—
343C22⋊C4—1181no—
344C22⋊C4—1181no—
345C42—41no—
346C42—41no—
347C42—1181no—
348C42—1181no—
349C42—1181no—
350C42#1174568511yescharacteristic
351C42D4×D5911yescharacteristic
352C42D4×D5911yescharacteristic
353C42C2×C22⋊D5911yescharacteristic
354C23—1181no—
355C23(C22⋊D59)⋊C411yescharacteristic
356Q8—22no—
357Q8—22no—
358Q8—41no—
359Q8—41no—
360Q8—592no—
361Q8—1181no—
362D4—592no—
363D4—1182no—
364D4—1182no—
365D4—1181no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—1181no—
375C2×C4—1182no—
376C2×C4—1182no—
377C2×C4—1181no—
378C2×C4—1181no—
379C2×C4—2362no—
380C2×C4—2361no—
381C2×C4—2361no—
382C2×C4C22⋊C4×D5911yescharacteristic
383C2×C4C4×C22⋊D5911yescharacteristic
384C2×C4#1427369511yescharacteristic
385C2×C4#1427369811yescharacteristic
386C2×C4#1427370011yescharacteristic
387C2×C4#1427370911yescharacteristic
388C2×C4C2×C8×D5911yescharacteristic
389C2×C4M16×D5911yescharacteristic
390C2×C4#1427373311yescharacteristic
391C2×C4#1427373511yescharacteristic
392C8—22no—
393C8—41no—
394C8—81no—
395C8—1182no—
396C8—4721no—
397C8—2362no—
398C8—2361no—
399C22—21no—
400C22—21no—
401C22—1182no—
402C22—2361no—
403C22—2361no—
404C22#1683727811yescharacteristic
405C22(C22⋊D59)⋊C811yescharacteristic
406C22#1683747611yescharacteristic
407C4—21no—
408C4—21no—
409C4—21no—
410C4—42no—
411C4—81no—
412C4—1182no—
413C4—2361no—
414C4—2361no—
415C4C22⋊C8×D5911yescharacteristic
416C4#1683736711yescharacteristic
417C4C8×C22⋊D5911yescharacteristic
418C4#1683747111yescharacteristic
419C4#1683766211yescharacteristic
420C4#1683767411yescharacteristic
421C2—21no—
422C2—21no—
423C2—2362no—
424C2#2142438511yescharacteristic
425C2#2142460011yescharacteristic
426C2#2142461411yescharacteristic
subgroupG/H
centerC2×C4#14273698
commutatorC2×C4×C59C22×C8
FrattiniC2×C42C22×D59
FittingC2×C59×Q8⋊C8C2
socleC22×C59#386
prime radicalC2×#11745685C2×C4
cosocleC2×C42×C59C23
hypercenterC2×Q8⋊C8D59
hypocenterC59#9096
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. #21422420C2semidirect
5. #21421946C2semidirect
6. #21421933C2semidirect
7. C2×C59×Q8⋊C8C2semidirect
35. #14273758C8semidirect
88. C2×Q8×C59C2×C8semidirect
134. #11745664C2×C8semidirect
211. C2×Q8⋊C8D59semidirect
246. C59#9096semidirect
307. C2×Q8C8×D59semidirect

Maximal subgroups

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

subgroupindex
C8×#117456852
C4×#142737582
#214224812
#214224202
#214219462
#214219332
C2×C59×Q8⋊C82
#909659