Finite Group Databasebeta

← #29591040

Subgroups — #29591040

Order 15616.

522 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450775C211yesmaximal, characteristic
2#21444140C211yesmaximal, characteristic, complemented
3#21443818C212yesmaximal, complemented
4#21443815C212yesmaximal, complemented
5C61×#1799C211yesmaximal, characteristic, complemented
6C2×#14519751C411yescharacteristic, complemented
7C2×#14519749—21no—
8#16839815—21no—
9#16839692C411yescharacteristic, complemented
10#16839687C2211yescharacteristic
11#16839679C411yescharacteristic, complemented
12#16839671C2211yescharacteristic
13#16839653—21no—
14#16839641—21no—
15#16839639—21no—
16C2×#14519684C411yescharacteristic, complemented
17#16839486—21no—
18#16839486C2212yes—
19C2×C4×D4×C61C2211yescharacteristic
20C2×#99×C61—21no—
21C61×#380—21no—
22C61×#342C2212yes—
23C22×D244C2×C411yescharacteristic
24C22×C22⋊D61—21no—
25C22×C22⋊D61—21no—
26C23×Dic61—21no—
27#14519751—41no—
28#14519751—41no—
29#14519749—42no—
30#14519749—42no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×#11758196—21no—
33C2×C22⋊Dic61—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C4⋊#92418—41no—
39C22⋊#92418—22no—
40C4×#92418—41no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684C2×C411yescharacteristic
45#14519684C2×C411yescharacteristic
46C22×D4×C61D411yescharacteristic
47C23×C4×C61C2×C411yescharacteristic
48C23×C4×C61D411yescharacteristic
49C4×D4×C61—41no—
50C4×D4×C61—41no—
51C2×C4⋊C4×C61—41no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C22⋊C4×C61—22no—
54C2×C22⋊C4×C61D411yescharacteristic
55C2×C22⋊C4×C61C2311yescharacteristic
56C2×C42×C61D411yescharacteristic
57#99×C61—42no—
58#95×C61—41no—
59C24×C61C22⋊C411yescharacteristic
60C24×C61C2×D411yescharacteristic
61C23×D61—21no—
62C2×D4×C61—41no—
63C2×D4×C61—41no—
64C2×D4×C61D812yes—
65C2×D4×C61SD1612yes—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—42no—
71C22×C4×C61—81no—
72C22×C4×C61—81no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C2×C22⋊D61—42no—
79C2×C22⋊D61—42no—
80C2×C22⋊D61—42no—
81C2×C22⋊D61—42no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61—41no—
84C2×C22⋊D61—81no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—42no—
89C22×Dic61—42no—
90C22×Dic61—81no—
91C2×D244—41no—
92C2×D244—81no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—82no—
95C22⋊C4×C61—41no—
96C22⋊C4×C61—41no—
97C22⋊C4×C61—42no—
98C22⋊C4×C61—42no—
99C42×C61—21no—
100C42×C61—21no—
101C22⋊Dic61—41no—
102C22⋊Dic61—41no—
103#11758198—42no—
104#11758198—41no—
105#11758198—41no—
106#11758198—42no—
107#11758198—81no—
108C4⋊Dic61—41no—
109#11758196—42no—
110C2×#92418—42no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61#10212yes—
120C23×C61C2×C22⋊C411yescharacteristic
121C23×C61C2×D811yescharacteristic
122C23×C61C2×SD1611yescharacteristic
123C22×D61—41no—
124C22×D61—41no—
125C22×D61—41no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130D4×C61—42no—
131D4×C61—42no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—41no—
138C2×C4×C61—42no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—81no—
143C2×C4×C61—81no—
144C2×C4×C61—81no—
145C2×C4×C61—82no—
146C2×C4×C61—82no—
147C2×C4×C61—82no—
148C2×C4×C61#9911yescharacteristic
149C2×C4×C61#9911yescharacteristic
150C2×C4×C61#10212yes—
151C22⋊D61—82no—
152C22⋊D61—82no—
153C22⋊D61—84no—
154C2×Dic61—22no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—84no—
164D244—82no—
165#92418—82no—
166#11876—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—22no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—42no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—42no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—81no—
181C22×C61C2×#9911yescharacteristic
182C22×C61C2×#10211yescharacteristic
183C22×C61#42111yescharacteristic
184C2×D61—81no—
185C2×D61—81no—
186C2×D61—81no—
187C2×D61—81no—
188C2×D61—81no—
189C2×D61—81no—
190C2×D61—81no—
191C4×C61—21no—
192C4×C61—21no—
193C4×C61—22no—
194C4×C61—41no—
195C4×C61—41no—
196C4×C61—41no—
197C4×C61—162no—
198Dic61—42no—
199Dic61—81no—
200Dic61—81no—
201#2543—611no—
202#1799D6111yescharacteristic, complemented
203#1460—611no—
204#1344—612no—
205#1343—612no—
206C2×C61—21no—
207C2×C61—21no—
208C2×C61—41no—
209C2×C61—42no—
210C2×C61—41no—
211C2×C61#151911yescharacteristic
212C2×C61#212111yescharacteristic
213C2×C61#212611yescharacteristic
214D61—161no—
215C2×#121—611no—
216C2×#121—1221no—
217C2×C4×D4C2×D6111yescharacteristic
218#431—1221no—
219C2×#99—21no—
220#398—611no—
221#397—611no—
222#394—611no—
223#392—611no—
224#388—1221no—
225#386—1221no—
226#386—1221no—
227#380—21no—
228C2×#95—611no—
229#342C2×D6112yes—
230#323—612no—
231#323—1221no—
232C61#1187611yescharacteristic, complemented, Sylow
233C22×D4—611no—
234C22×D4—1221no—
235C22×D4—1221no—
236C22×D4C22⋊D6111yescharacteristic
237C23×C4—1221no—
238C23×C4C4×D6111yescharacteristic
239C23×C4C22⋊D6111yescharacteristic
240#121—2442no—
241#121—2442no—
242#121—2441no—
243#121—2441no—
244C4×D4—41no—
245C4×D4—41no—
246C2×C4⋊C4—41no—
247C2×C4⋊C4—611no—
248C2×C4⋊C4—1221no—
249C2×C4⋊C4C4×D6111yescharacteristic
250C2×C22⋊C4—22no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C22⋊C4—1221no—
255C2×C22⋊C4—1221no—
256C2×C22⋊C4D24411yescharacteristic
257C2×C22⋊C4C22×D6111yescharacteristic
258C2×C42D24411yescharacteristic
259C4⋊C8—2441no—
260#99—42no—
261C22⋊C8—1222no—
262C4×C8—2441no—
263#95—41no—
264#95—611no—
265#95—611no—
266#95—1221no—
267#95—1221no—
268#95—1221no—
269C24—1221no—
270C24#1175819811yescharacteristic
271C24C2×C22⋊D6111yescharacteristic
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—4881no—
275C2×D4—4881no—
276C2×D4—2441no—
277C2×D4—2442no—
278C2×D4—2442no—
279C2×D4—2442no—
280C2×D4—2442no—
281C2×D4—2441no—
282C2×D4—2441no—
283C2×D4#1175819912yes—
284C2×D4#1175820112yes—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—42no—
290C22×C4—81no—
291C22×C4—81no—
292C22×C4—1221no—
293C22×C4—1221no—
294C22×C4—1221no—
295C22×C4—4881no—
296C22×C4—2442no—
297C22×C4—2442no—
298C22×C4#1175819811yescharacteristic
299C22×C4#1175819811yescharacteristic
300C22×C4#1175819811yescharacteristic
301C22×C4C2×C4×D6111yescharacteristic
302C22×C4C2×D24411yescharacteristic
303C2×C8—2442no—
304C4⋊C4—41no—
305C4⋊C4—82no—
306C4⋊C4—2441no—
307C4⋊C4—2442no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—42no—
311C22⋊C4—42no—
312C22⋊C4—4881no—
313C22⋊C4—2442no—
314C22⋊C4—2441no—
315C22⋊C4—2441no—
316C22⋊C4—2441no—
317C22⋊C4—2441no—
318C22⋊C4—2442no—
319C42—21no—
320C42—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—2441no—
330C23—2441no—
331C23—2441no—
332C23—2441no—
333C23—2441no—
334C23—2441no—
335C23—2441no—
336C23#1451969712yes—
337C23C2×#1175819811yescharacteristic
338C23C2×#1175819911yescharacteristic
339C23C2×#1175820111yescharacteristic
340D4—42no—
341D4—42no—
342D4—4882no—
343D4—4884no—
344D4—4882no—
345D4—4882no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—82no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4—1222no—
363C2×C4—4884no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4#1451969111yescharacteristic
373C2×C4#1451969111yescharacteristic
374C2×C4#1451969712yes—
375C8—4882no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—21no—
381C22—42no—
382C22—41no—
383C22—41no—
384C22—42no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—81no—
390C22—4881no—
391C22—4881no—
392C22—4881no—
393C22—4881no—
394C22—4881no—
395C22—4881no—
396C22—4881no—
397C22C2×#1451969111yescharacteristic
398C22C2×#1451969711yescharacteristic
399C22#1683978011yescharacteristic
400C4—22no—
401C4—21no—
402C4—21no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—162no—
407C4—4881no—
408C4—4881no—
409C4—2442no—
410C2—21no—
411C2—21no—
412C2—41no—
413C2—42no—
414C2—41no—
415C2—9761no—
416C2#2144438611yescharacteristic
417C2#2144746311yescharacteristic
418C2#2144748211yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1799C2
socleC22×C61C2×#99
prime radical#21450775C2
cosocleC2×C22⋊C4×C61C23
hypercenter#1799D61
hypocenterC61#11876
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #21444140C2semidirect
3. #21443818C2semidirect
4. #21443815C2semidirect
5. C61×#1799C2semidirect
6. C2×#14519751C4semidirect
9. #16839692C4semidirect
11. #16839679C4semidirect
16. C2×#14519684C4semidirect
202. #1799D61semidirect
232. C61#11876semidirect

Maximal subgroups

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

subgroupindex
#214507752
#214441402
#214438182
#214438152
C61×#17992
#1187661