Finite Group Databasebeta

← #20275549

Subgroups — #20275549

Order 6784.

408 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#13133189C211yesmaximal, characteristic
2C2×#13133132C211yesmaximal, characteristic, complemented
3C2×#13133131C211yesmaximal, characteristic, complemented
4C2×#13133131C211yesmaximal, characteristic, complemented
5#16810481C211yesmaximal, characteristic, complemented
6C22⋊C4×Dic53C211yesmaximal, characteristic, complemented
7C2×#99×C53C211yesmaximal, characteristic, complemented
8C22×C22⋊D53C411yescharacteristic, complemented
9C22×C22⋊D53C2211yescharacteristic
10C23×Dic53C2211yescharacteristic
11#13133189—21no—
12#13133189—21no—
13#13133189—21no—
14#13133189—21no—
15C2×#11719919—21no—
16C2×#11719919C411yescharacteristic, complemented
17C2×C22⋊Dic53C411yescharacteristic, complemented
18C2×C22⋊Dic53C2211yescharacteristic
19C2×C22⋊Dic53C2211yescharacteristic
20C2×#11719921C411yescharacteristic, complemented
21C2×C4×Dic53—21no—
22#13133132—22no—
23#13133131—22no—
24#13133131—22no—
25#13133124—21no—
26#13133124—21no—
27C22×D4×C53C2211yescharacteristic
28C2×C22⋊C4×C53C2211yescharacteristic
29C2×C22⋊C4×C53C2211yescharacteristic
30#99×C53—22no—
31C24×C53C2×C411yescharacteristic
32C24×C53C2311yescharacteristic
33C23×D53C2×C411yescharacteristic
34C2×D4×C53—21no—
35C2×D4×C53—21no—
36C2×D4×C53—21no—
37C2×D4×C53—21no—
38C2×D4×C53—21no—
39C2×D4×C53—21no—
40C22×C4×C53—21no—
41C22×C4×C53—21no—
42C22×C4×C53C2×C411yescharacteristic
43C2×C22⋊D53—21no—
44C2×C22⋊D53—21no—
45C2×C22⋊D53—21no—
46C2×C22⋊D53—21no—
47C2×C22⋊D53—21no—
48C2×C22⋊D53—21no—
49C2×C22⋊D53—21no—
50C2×C22⋊D53—21no—
51C2×C22⋊D53—42no—
52C22×Dic53—21no—
53C22×Dic53—21no—
54C22×Dic53—42no—
55C22×Dic53C2×C411yescharacteristic
56C22×Dic53C2×C411yescharacteristic
57C22×Dic53C2×C411yescharacteristic
58C22×Dic53D411yescharacteristic
59C22×Dic53D411yescharacteristic
60C22×Dic53D411yescharacteristic
61C22×Dic53D411yescharacteristic
62C22⋊C4×C53—21no—
63C22⋊C4×C53—21no—
64C22⋊C4×C53—21no—
65C22⋊C4×C53D412yescomplemented
66C22⋊Dic53—21no—
67C22⋊Dic53—21no—
68C22⋊Dic53—21no—
69C22⋊Dic53—21no—
70C22⋊Dic53—21no—
71C22⋊Dic53D412yescomplemented
72#11719921—21no—
73#11719921—21no—
74#11719919—21no—
75#11719919—21no—
76#11719919—42no—
77C4×Dic53—42no—
78C23×C53—21no—
79C23×C53—21no—
80C23×C53—21no—
81C23×C53—41no—
82C23×C53—41no—
83C23×C53—41no—
84C23×C53—41no—
85C23×C53C22×C411yescharacteristic
86C23×C53C2×D411yescharacteristic
87C23×C53C2×D411yescharacteristic
88C23×C53C2×D411yescharacteristic
89C23×C53C2×D411yescharacteristic
90C23×C53#4111yescharacteristic
91C23×C53#4111yescharacteristic
92C22×D53—21no—
93C22×D53—21no—
94C22×D53—21no—
95C22×D53—41no—
96C22×D53—41no—
97D4×C53—41no—
98D4×C53—41no—
99D4×C53—41no—
100D4×C53—41no—
101C2×C4×C53—21no—
102C2×C4×C53—21no—
103C2×C4×C53—21no—
104C2×C4×C53—22no—
105C2×C4×C53—41no—
106C2×C4×C53—41no—
107C2×C4×C53—41no—
108C2×C4×C53—41no—
109C2×C4×C53—41no—
110C22⋊D53—42no—
111C22⋊D53—41no—
112C22⋊D53—41no—
113C22⋊D53—41no—
114C22⋊D53—41no—
115C22⋊D53—42no—
116C2×Dic53—22no—
117C2×Dic53—22no—
118C2×Dic53—22no—
119C2×Dic53—21no—
120C2×Dic53—21no—
121C2×Dic53—21no—
122C2×Dic53—22no—
123C2×Dic53—41no—
124C2×Dic53—41no—
125C2×Dic53—41no—
126C2×Dic53—41no—
127C2×Dic53—41no—
128C2×Dic53—41no—
129C2×Dic53—41no—
130C2×Dic53—41no—
131C2×Dic53C22⋊C411yescharacteristic
132C2×Dic53C22⋊C411yescharacteristic
133C2×Dic53C22⋊C411yescharacteristic
134C2×Dic53C22⋊C411yescharacteristic
135C22×C53—21no—
136C22×C53—21no—
137C22×C53—21no—
138C22×C53—21no—
139C22×C53—21no—
140C22×C53—21no—
141C22×C53—41no—
142C22×C53—41no—
143C22×C53—41no—
144C22×C53—41no—
145C22×C53—41no—
146C22×C53—41no—
147C22×C53—41no—
148C22×C53—81no—
149C22×C53—81no—
150C22×C53C2×C22⋊C411yescharacteristic
151C22×C53C4×D411yescharacteristic
152C22×C53C4×D411yescharacteristic
153C22×C53#12111yescharacteristic
154C22×C53#12111yescharacteristic
155C22×C53#12411yescharacteristic
156C22×C53#12711yescharacteristic
157C2×D53—41no—
158C2×D53—41no—
159C2×D53—41no—
160C2×D53—81no—
161C2×D53—81no—
162C4×C53—42no—
163C4×C53—41no—
164C4×C53—81no—
165Dic53—21no—
166Dic53—21no—
167Dic53—21no—
168Dic53—42no—
169Dic53—41no—
170Dic53—81no—
171Dic53#9912yescomplemented
172#1964—531nomaximal, Sylow
173C2×C53—21no—
174C2×C53—21no—
175C2×C53—21no—
176C2×C53—21no—
177C2×C53—21no—
178C2×C53—21no—
179C2×C53—81no—
180C2×C53#39011yescharacteristic
181C2×C53C2×#9911yescharacteristic
182C2×C53#41011yescharacteristic
183D53—81no—
184C2×#121—531no—
185C2×#99—531no—
186C2×#99—531no—
187C2×#99—531no—
188C2×#99D5311yescharacteristic, complemented
189#380—531no—
190C4×C22⋊C4—531no—
191C53#196411yescharacteristic, complemented, Sylow
192C22×D4—531no—
193C22×D4—531no—
194C22×D4C2×D5311yescharacteristic
195C23×C4—531no—
196#121—1061no—
197#121—1061no—
198#121—1061no—
199#121—1061no—
200C2×C4⋊C4—531no—
201C2×C4⋊C4—1061no—
202C2×C22⋊C4—531no—
203C2×C22⋊C4—531no—
204C2×C22⋊C4—531no—
205C2×C22⋊C4—531no—
206C2×C22⋊C4C2×D5311yescharacteristic
207C2×C22⋊C4C2×D5311yescharacteristic
208C2×C42—1061no—
209#99—22no—
210#99—1062no—
211#99—1062no—
212#99—1062no—
213#95—1061no—
214#95—1061no—
215C24—531no—
216C24C4×D5311yescharacteristic
217C24C22×D5311yescharacteristic
218C2×D4—21no—
219C2×D4—21no—
220C2×D4—21no—
221C2×D4—21no—
222C2×D4—21no—
223C2×D4—21no—
224C2×D4—1061no—
225C2×D4—1061no—
226C2×D4—1061no—
227C2×D4—1061no—
228C2×D4—1061no—
229C2×D4—1061no—
230C2×D4—1061no—
231C2×D4—1061no—
232C2×D4—2122no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—531no—
236C22×C4—531no—
237C22×C4—531no—
238C22×C4—531no—
239C22×C4—531no—
240C22×C4—531no—
241C22×C4—531no—
242C22×C4—1061no—
243C22×C4—1061no—
244C22×C4—2122no—
245C22×C4C4×D5311yescharacteristic
246C4⋊C4—1061no—
247C4⋊C4—1061no—
248C4⋊C4—2122no—
249C22⋊C4—21no—
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—532no—
253C22⋊C4—1061no—
254C22⋊C4—1061no—
255C22⋊C4—1061no—
256C22⋊C4—1061no—
257C22⋊C4—1061no—
258C22⋊C4—1061no—
259C22⋊C4—1061no—
260C22⋊C4C22⋊D5312yescomplemented
261C42—2122no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23—1061no—
270C23—1061no—
271C23—1061no—
272C23—2121no—
273C23—2121no—
274C23C2×C4×D5311yescharacteristic
275C23#1171994511yescharacteristic
276C23D4×D5311yescharacteristic
277C23D4×D5311yescharacteristic
278C23D4×D5311yescharacteristic
279C23#1171994711yescharacteristic
280C23C2×C22⋊D5311yescharacteristic
281D4—41no—
282D4—41no—
283D4—41no—
284D4—41no—
285D4—2122no—
286D4—2122no—
287D4—2121no—
288D4—2121no—
289D4—2121no—
290D4—2121no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—531no—
301C2×C4—531no—
302C2×C4—531no—
303C2×C4—531no—
304C2×C4—1062no—
305C2×C4—1062no—
306C2×C4—1062no—
307C2×C4—1061no—
308C2×C4—1061no—
309C2×C4—1061no—
310C2×C4—1062no—
311C2×C4—2121no—
312C2×C4—2121no—
313C2×C4—2121no—
314C2×C4—2121no—
315C2×C4—2121no—
316C2×C4—2121no—
317C2×C4—2121no—
318C2×C4—2121no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22—81no—
334C22—4241no—
335C22—4241no—
336C22—2121no—
337C22—2121no—
338C22—2121no—
339C22C22⋊C4×D5311yescharacteristic
340C22#1313317711yescharacteristic
341C22C4×C22⋊D5311yescharacteristic
342C22#1313318911yescharacteristic
343C22#1313319011yescharacteristic
344C22#1313320311yescharacteristic
345C22#1313321311yescharacteristic
346C4—42no—
347C4—41no—
348C4—81no—
349C4—532no—
350C4—1061no—
351C4—1061no—
352C4—1061no—
353C4—4241no—
354C4—2122no—
355C4—2121no—
356C2—21no—
357C2—21no—
358C2—21no—
359C2—21no—
360C2—21no—
361C2—21no—
362C2—81no—
363C2—4241no—
364C2#1681052311yescharacteristic
365C2#99×D5311yescharacteristic
366C2#1681059511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D53
commutatorC23×C53C22×C4
FrattiniC24C22×D53
FittingC2×#99×C53C2
socleC22×C53C2×C22⋊C4
hypercenterC2×#99D53
hypocenterC53#1964
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#13133132C2semidirect
3. C2×#13133131C2semidirect
4. C2×#13133131C2semidirect
5. #16810481C2semidirect
6. C22⋊C4×Dic53C2semidirect
7. C2×#99×C53C2semidirect
8. C22×C22⋊D53C4semidirect
16. C2×#11719919C4semidirect
17. C2×C22⋊Dic53C4semidirect
20. C2×#11719921C4semidirect
65. C22⋊C4×C53D4semidirect
71. C22⋊Dic53D4semidirect
171. Dic53#99semidirect
188. C2×#99D53semidirect
191. C53#1964semidirect
260. C22⋊C4C22⋊D53semidirect