Finite Group Databasebeta

← #28485005

Subgroups — #28485005

Order 15104.

452 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
1#21432754C211yesmaximal, characteristic
2#21424195C211yesmaximal, characteristic
3#21422616C211yesmaximal, characteristic
4#21422460C211yesmaximal, characteristic
5#21421973C211yesmaximal, characteristic
6#21421943C211yesmaximal, characteristic
7C2×C59×#485C211yesmaximal, characteristic
8#16837463—22no—
9#16837459—21no—
10#16837455—21no—
11#16837429—21no—
12#16837366C2211yescharacteristic
13#16837366C2211yescharacteristic
14C2×C22⋊(C59⋊C8)C2211yescharacteristic
15#16837358—21no—
16C4×C22⋊Dic59C2211yescharacteristic
17#16837161—21no—
18#16837161—21no—
19#16837139—22no—
20#16837128—21no—
21#16837128—21no—
22C2×C22⋊Q8×C59C2211yescharacteristic
23C2×#117×C59C2211yescharacteristic
24C59×#485—21no—
25C59×#485—21no—
26C59×#485—21no—
27C59×#485—21no—
28C2×#107×C59C411yescharacteristic, complemented
29C2×#106×C59C411yescharacteristic, complemented
30C2×#103×C59C411yescharacteristic, complemented
31C2×#103×C59C411yescharacteristic, complemented
32C2×C22⋊C8×C59C2211yescharacteristic
33C2×#11745664—21no—
34C2×#11745664—21no—
35C22×C59⋊C8—21no—
36C2×C22⋊Dic59—21no—
37C2×C4×Dic59—21no—
38C4⋊(C59⋊C8)—22no—
39C4⋊(C59⋊C8)—22no—
40C22⋊(C59⋊C8)—21no—
41C22⋊(C59⋊C8)—21no—
42C22⋊(C59⋊C8)—21no—
43C22⋊(C59⋊C8)—21no—
44C22⋊(C59⋊C8)D411yescharacteristic
45C22⋊(C59⋊C8)D411yescharacteristic
46C22⋊(C59⋊C8)D412yes—
47#14273638—22no—
48C4×C59⋊C8—22no—
49C59⋊#95—21no—
50C22×Q8×C59C2×C411yescharacteristic
51C23×C4×C59C2311yescharacteristic
52C22×C8×C59C2×C411yescharacteristic
53C22×C8×C59C2×C411yescharacteristic
54C22⋊Q8×C59—21no—
55C22⋊Q8×C59—21no—
56C22⋊Q8×C59—21no—
57C22⋊Q8×C59—21no—
58#117×C59—21no—
59#117×C59—21no—
60#117×C59D411yescharacteristic
61#117×C59D411yescharacteristic
62#117×C59D411yescharacteristic
63#117×C59D411yescharacteristic
64C2×C4⋊C4×C59—21no—
65C2×C4⋊C4×C59C2×C411yescharacteristic
66C2×C4⋊C4×C59C2×C411yescharacteristic
67C2×C4⋊C4×C59C2×C411yescharacteristic
68C2×C22⋊C4×C59—21no—
69C2×C22⋊C4×C59—21no—
70C2×C42×C59—21no—
71#107×C59—21no—
72#107×C59—21no—
73#106×C59—21no—
74#106×C59—21no—
75#103×C59—21no—
76#103×C59—21no—
77#103×C59—21no—
78#103×C59—21no—
79C22⋊C8×C59—21no—
80C22⋊C8×C59—21no—
81C24×C59#4111yescharacteristic
82C2×Q8×C59—21no—
83C2×Q8×C59—21no—
84C2×Q8×C59—41no—
85C2×Q8×C59—41no—
86C22×C4×C59—21no—
87C22×C4×C59—21no—
88C22×C4×C59—21no—
89C22×C4×C59—21no—
90C22×C4×C59—41no—
91C22×C4×C59—41no—
92C22×C4×C59C22×C411yescharacteristic
93C22×C4×C59C2×D411yescharacteristic
94C22×C4×C59C2×D411yescharacteristic
95C22×C4×C59C2×D411yescharacteristic
96C22×C4×C59C2×D411yescharacteristic
97C22×C4×C59#4111yescharacteristic
98C22×Dic59—41no—
99C2×C8×C59—21no—
100C2×C8×C59—21no—
101C2×C8×C59—41no—
102C2×C8×C59—41no—
103C4⋊C4×C59—21no—
104C4⋊C4×C59—21no—
105C4⋊C4×C59—21no—
106C4⋊C4×C59—21no—
107C4⋊C4×C59—41no—
108C4⋊C4×C59—41no—
109C4⋊C4×C59C22⋊C411yescharacteristic
110C4⋊C4×C59C22⋊C411yescharacteristic
111C4⋊C4×C59C22⋊C411yescharacteristic
112C4⋊C4×C59C22⋊C411yescharacteristic
113C22⋊C4×C59—21no—
114C22⋊C4×C59—21no—
115C22⋊C4×C59—21no—
116C22⋊C4×C59—21no—
117C22⋊C4×C59—41no—
118C22⋊C4×C59—41no—
119C42×C59—21no—
120C42×C59—21no—
121C42×C59—21no—
122C42×C59—21no—
123C22⋊Dic59—22no—
124C22⋊Dic59—41no—
125C4×Dic59—41no—
126C4×Dic59—41no—
127#11745664—41no—
128#11745664—41no—
129#11745664—41no—
130#11745664—41no—
131C2×C59⋊C8—21no—
132C2×C59⋊C8—22no—
133C2×C59⋊C8—21no—
134C2×C59⋊C8—41no—
135C2×C59⋊C8—41no—
136C2×C59⋊C8—41no—
137C23×C59—21no—
138C23×C59—21no—
139C23×C59—41no—
140C23×C59—41no—
141C23×C59C4×D411yescharacteristic
142C23×C59#12111yescharacteristic
143C23×C59#12311yescharacteristic
144Q8×C59—41no—
145Q8×C59—41no—
146Q8×C59—81no—
147C2×C4×C59—21no—
148C2×C4×C59—21no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—21no—
152C2×C4×C59—21no—
153C2×C4×C59—21no—
154C2×C4×C59—21no—
155C2×C4×C59—21no—
156C2×C4×C59—21no—
157C2×C4×C59—41no—
158C2×C4×C59—41no—
159C2×C4×C59—41no—
160C2×C4×C59—41no—
161C2×C4×C59—41no—
162C2×C4×C59—41no—
163C2×C4×C59—41no—
164C2×C4×C59—41no—
165C2×C4×C59—41no—
166C2×C4×C59—81no—
167C2×C4×C59—81no—
168C2×C4×C59C2×C22⋊C411yescharacteristic
169C2×C4×C59C4×D411yescharacteristic
170C2×C4×C59#12011yescharacteristic
171C2×C4×C59#12111yescharacteristic
172C2×Dic59—42no—
173C2×Dic59—81no—
174C2×Dic59—81no—
175C8×C59—41no—
176C8×C59—41no—
177C59⋊C8—41no—
178C59⋊C8—41no—
179C59⋊C8—42no—
180C59⋊C8—81no—
181#9240—591nomaximal, Sylow
182C22×C59—21no—
183C22×C59—21no—
184C22×C59—21no—
185C22×C59—21no—
186C22×C59—21no—
187C22×C59—21no—
188C22×C59—21no—
189C22×C59—21no—
190C22×C59—81no—
191C22×C59—81no—
192C22×C59#38611yescharacteristic
193C22×C59#44311yescharacteristic
194C22×C59#44411yescharacteristic
195C4×C59—21no—
196C4×C59—21no—
197C4×C59—21no—
198C4×C59—41no—
199C4×C59—41no—
200C4×C59—41no—
201C4×C59—41no—
202C4×C59—81no—
203C4×C59—81no—
204C4×C59#41011yescharacteristic
205C4×C59#41011yescharacteristic
206Dic59—82no—
207C2×#485D5911yescharacteristic
208#2924—591no—
209#1826—591no—
210#1508—591no—
211#1472—591no—
212#1293—591no—
213#1282—591no—
214C2×C59—21no—
215C2×C59—21no—
216C2×C59—41no—
217C2×C59—41no—
218C2×C59#187611yescharacteristic
219C2×C59#189911yescharacteristic
220C2×C59#190211yescharacteristic
221C2×C22⋊Q8C2×D5911yescharacteristic
222C2×#117C2×D5911yescharacteristic
223#485—21no—
224#485—21no—
225#485—21no—
226#485—21no—
227#433—1182no—
228#432—1181no—
229#431—1181no—
230C2×#107Dic5911yescharacteristic, complemented
231C2×#106Dic5911yescharacteristic, complemented
232#424—1181no—
233C2×#103Dic5911yescharacteristic, complemented
234C2×#103Dic5911yescharacteristic, complemented
235#407—591no—
236#407—591no—
237C2×C22⋊C8—591no—
238C2×C22⋊C8C2×D5911yescharacteristic
239#405—1181no—
240C4×C22⋊C4—591no—
241#339—1181no—
242#339—1181no—
243#328—1182no—
244#324—1181no—
245#324—1181no—
246C59#924011yescharacteristic, complemented, Sylow
247C22×Q8C2×Dic5911yescharacteristic
248C23×C4C22×D5911yescharacteristic
249C2×M16—1181no—
250C2×M16—1181no—
251C22×C8—1181no—
252C22×C8C2×Dic5911yescharacteristic
253C22×C8C2×Dic5911yescharacteristic
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—21no—
258#117—21no—
259#117—21no—
260#117C22⋊D5911yescharacteristic
261#117C22⋊D5911yescharacteristic
262#117C22⋊D5911yescharacteristic
263#117C22⋊D5911yescharacteristic
264C2×C4⋊C4—21no—
265C2×C4⋊C4C2×Dic5911yescharacteristic
266C2×C4⋊C4C2×Dic5911yescharacteristic
267C2×C4⋊C4C2×Dic5911yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—1181no—
271C2×C42—21no—
272C2×C42—1181no—
273#107—21no—
274#107—21no—
275#106—21no—
276#106—21no—
277C4⋊C8—1182no—
278C4⋊C8—1182no—
279#103—21no—
280#103—21no—
281#103—21no—
282#103—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—591no—
286C22⋊C8—591no—
287C22⋊C8—592no—
288C22⋊C8—1181no—
289C22⋊C8—1181no—
290C22⋊C8—1181no—
291C22⋊C8—1181no—
292#97—1182no—
293C4×C8—1182no—
294#95—1181no—
295C24#1174568711yescharacteristic
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—41no—
299C2×Q8—41no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—2361no—
307C22×C4D4×D5911yescharacteristic
308C22×C4D4×D5911yescharacteristic
309C22×C4#1174568711yescharacteristic
310C22×C4C22×Dic5911yescharacteristic
311C22×C4C2×C22⋊D5911yescharacteristic
312C22×C4C2×C22⋊D5911yescharacteristic
313M16—2361no—
314M16—2361no—
315M16—2361no—
316M16—2361no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—1181no—
322C2×C8—1182no—
323C2×C8—1181no—
324C2×C8—2361no—
325C2×C8—2361no—
326C2×C8—2361no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4C22⋊Dic5911yescharacteristic
334C4⋊C4C22⋊Dic5911yescharacteristic
335C4⋊C4C22⋊Dic5911yescharacteristic
336C4⋊C4C22⋊Dic5911yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—1182no—
344C22⋊C4—2361no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42—21no—
349C42—2361no—
350C42—2361no—
351C23—21no—
352C23—21no—
353C23—41no—
354C23—41no—
355C23D4×Dic5911yescharacteristic
356C23#1427369911yescharacteristic
357C23#1427370811yescharacteristic
358Q8—41no—
359Q8—41no—
360Q8—81no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—4721no—
383C2×C4—4721no—
384C2×C4—2362no—
385C2×C4C2×C22⋊Dic5911yescharacteristic
386C2×C4D4×Dic5911yescharacteristic
387C2×C4#1427369511yescharacteristic
388C2×C4#1427369911yescharacteristic
389C8—41no—
390C8—41no—
391C8—4721no—
392C8—2361no—
393C8—2361no—
394C8—2362no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22#1683728211yescharacteristic
406C22#1683751911yescharacteristic
407C22#1683752411yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—41no—
415C4—81no—
416C4—81no—
417C4—4722no—
418C4#1683737611yescharacteristic
419C4#1683737611yescharacteristic
420C2—21no—
421C2—21no—
422C2—41no—
423C2—41no—
424C2#2142442511yescharacteristic
425C2#2142455511yescharacteristic
426C2#2142457111yescharacteristic
subgroupG/H
centerC22#16837282
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×#485C2
socleC22×C59#386
prime radicalC24×C59#41
cosocleC23×C4×C59C23
hypercenterC2×#485D59
hypocenterC59#9240
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
28. C2×#107×C59C4semidirect
29. C2×#106×C59C4semidirect
30. C2×#103×C59C4semidirect
31. C2×#103×C59C4semidirect
230. C2×#107Dic59semidirect
231. C2×#106Dic59semidirect
233. C2×#103Dic59semidirect
234. C2×#103Dic59semidirect
246. C59#9240semidirect

Maximal subgroups

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

subgroupindex
#214327542
#214241952
#214226162
#214224602
#214219732
#214219432
C2×C59×#4852
#924059