Finite Group Databasebeta

← #19135845

Subgroups — #19135845

Order 5504.

382 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 69 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#14583458C211yesmaximal, characteristic
2C2×#13063239C211yesmaximal, characteristic, complemented
3#14582779C211yesmaximal, characteristic, complemented
4#14582776C211yesmaximal, characteristic, complemented
5#14582774C211yesmaximal, characteristic, complemented
6#14582665C211yesmaximal, characteristic, complemented
7C2×#99×C43C211yesmaximal, characteristic, complemented
8C22×C22⋊D43C2211yescharacteristic
9C23×Dic43C2211yescharacteristic
10#13063308—21no—
11#13063306—21no—
12#13063297—21no—
13#13063297—21no—
14#13063294—21no—
15#13063293—21no—
16C2×C4⋊Dic43—21no—
17C2×C22⋊Dic43—21no—
18C2×C22⋊Dic43C2211yescharacteristic
19C2×C22⋊Dic43C2211yescharacteristic
20C2×(C2×D43)⋊C4—21no—
21#13063239—22no—
22C43⋊#95—21no—
23C43⋊#95—21no—
24C43⋊#95—21no—
25C22×D4×C43C2211yescharacteristic
26C2×C22⋊C4×C43C2211yescharacteristic
27C2×C22⋊C4×C43C2211yescharacteristic
28#99×C43—22no—
29C24×C43D411yescharacteristic
30C24×C43C2311yescharacteristic
31C23×D43D411yescharacteristic
32C2×D4×C43—21no—
33C2×D4×C43—21no—
34C2×D4×C43—21no—
35C2×D4×C43—21no—
36C2×D4×C43—21no—
37C2×D4×C43—21no—
38C22×C4×C43—21no—
39C22×C4×C43—21no—
40C22×C4×C43D411yescharacteristic
41C2×C22⋊D43—21no—
42C2×C22⋊D43—21no—
43C2×C22⋊D43—21no—
44C2×C22⋊D43—21no—
45C2×C22⋊D43—21no—
46C2×C22⋊D43—21no—
47C2×C22⋊D43—21no—
48C2×C22⋊D43—21no—
49C22×Dic43—21no—
50C22×Dic43—21no—
51C22×Dic43—21no—
52C22×Dic43—21no—
53C22×Dic43—42no—
54C22×Dic43D411yescharacteristic
55C22×Dic43D411yescharacteristic
56C22×Dic43D411yescharacteristic
57C22⋊C4×C43—21no—
58C22⋊C4×C43—21no—
59C22⋊C4×C43—21no—
60C22⋊C4×C43D412yescomplemented
61C22⋊Dic43—21no—
62C22⋊Dic43—21no—
63C22⋊Dic43—21no—
64C22⋊Dic43—21no—
65C22⋊Dic43—21no—
66C22⋊Dic43—21no—
67C22⋊Dic43—42no—
68(C2×D43)⋊C4—21no—
69(C2×D43)⋊C4—21no—
70(C2×D43)⋊C4—42no—
71C4⋊Dic43—42no—
72Dic43⋊C4—21no—
73Dic43⋊C4—21no—
74C23×C43—21no—
75C23×C43—21no—
76C23×C43—21no—
77C23×C43—41no—
78C23×C43—41no—
79C23×C43—41no—
80C23×C43—41no—
81C23×C43C2×D411yescharacteristic
82C23×C43C2×D411yescharacteristic
83C23×C43C2×D411yescharacteristic
84C23×C43C2×D411yescharacteristic
85C23×C43#4111yescharacteristic
86C23×C43#4111yescharacteristic
87C23×C43#4111yescharacteristic
88C22×D43—21no—
89C22×D43—21no—
90C22×D43—21no—
91C22×D43—41no—
92C22×D43—41no—
93D4×C43—41no—
94D4×C43—41no—
95D4×C43—41no—
96D4×C43—41no—
97C2×C4×C43—21no—
98C2×C4×C43—22no—
99C2×C4×C43—21no—
100C2×C4×C43—21no—
101C2×C4×C43—41no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C22⋊D43—41no—
107C22⋊D43—41no—
108C22⋊D43—41no—
109C22⋊D43—41no—
110C22⋊D43—81no—
111C22⋊D43—81no—
112C2×Dic43—22no—
113C2×Dic43—22no—
114C2×Dic43—22no—
115C2×Dic43—21no—
116C2×Dic43—21no—
117C2×Dic43—21no—
118C2×Dic43—21no—
119C2×Dic43—21no—
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C22×C43—21no—
130C22×C43—21no—
131C22×C43—21no—
132C22×C43—21no—
133C22×C43—21no—
134C22×C43—21no—
135C22×C43—41no—
136C22×C43—41no—
137C22×C43—41no—
138C22×C43—41no—
139C22×C43—42no—
140C22×C43—41no—
141C22×C43—41no—
142C22×C43—41no—
143C22×C43—81no—
144C22×C43#12011yescharacteristic
145C22×C43#12111yescharacteristic
146C22×C43#12111yescharacteristic
147C22×C43#12111yescharacteristic
148C22×C43#12311yescharacteristic
149C22×C43#12311yescharacteristic
150C22×C43#12411yescharacteristic
151C2×D43—42no—
152C2×D43—41no—
153C2×D43—41no—
154C2×D43—41no—
155C2×D43—81no—
156C4×C43—42no—
157C4×C43—41no—
158C4×C43—81no—
159Dic43—41no—
160Dic43—42no—
161Dic43—41no—
162Dic43—41no—
163Dic43—81no—
164#2044—431nomaximal, Sylow
165C2×C43—21no—
166C2×C43—21no—
167C2×C43—21no—
168C2×C43—21no—
169C2×C43—21no—
170C2×C43—21no—
171C2×C43—81no—
172C2×C43#39411yescharacteristic
173C2×C43B(4,𝔽2)11yescharacteristic
174C2×C43#45811yescharacteristic
175D43—81no—
176#534—431no—
177C2×#99—431no—
178C2×#99D4311yescharacteristic, complemented
179#386—431no—
180#386—431no—
181#385—431no—
182#342—431no—
183C43#204411yescharacteristic, complemented, Sylow
184C22×D4—431no—
185C22×D4C2×D4311yescharacteristic
186C23×C4—431no—
187#123—861no—
188#123—861no—
189#121—861no—
190#121—861no—
191#120—861no—
192#120—861no—
193C2×C4⋊C4—861no—
194C2×C22⋊C4—431no—
195C2×C22⋊C4—431no—
196C2×C22⋊C4—861no—
197C2×C22⋊C4—861no—
198C2×C22⋊C4C2×D4311yescharacteristic
199C2×C22⋊C4C2×D4311yescharacteristic
200#99—22no—
201#99—862no—
202#95—861no—
203#95—861no—
204#95—861no—
205C24—431no—
206C24D17211yescharacteristic
207C24C22×D4311yescharacteristic
208C2×D4—21no—
209C2×D4—21no—
210C2×D4—21no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—21no—
214C2×D4—861no—
215C2×D4—861no—
216C2×D4—861no—
217C2×D4—861no—
218C2×D4—861no—
219C2×D4—861no—
220C2×D4—861no—
221C2×D4—861no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—431no—
225C22×C4—431no—
226C22×C4—431no—
227C22×C4—861no—
228C22×C4—861no—
229C22×C4—861no—
230C22×C4—861no—
231C22×C4—1722no—
232C22×C4D17211yescharacteristic
233C4⋊C4—861no—
234C4⋊C4—861no—
235C4⋊C4—1722no—
236C22⋊C4—21no—
237C22⋊C4—21no—
238C22⋊C4—21no—
239C22⋊C4—861no—
240C22⋊C4—861no—
241C22⋊C4—861no—
242C22⋊C4—861no—
243C22⋊C4—861no—
244C22⋊C4—861no—
245C22⋊C4—861no—
246C22⋊C4—861no—
247C22⋊C4—1722no—
248C22⋊C4—1722no—
249C22⋊C4C22⋊D4312yescomplemented
250C23—21no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23—861no—
258C23—861no—
259C23—861no—
260C23—1721no—
261C23—1721no—
262C23C2×D17211yescharacteristic
263C23#1062189811yescharacteristic
264C23D4×D4311yescharacteristic
265C23D4×D4311yescharacteristic
266C23#1062190011yescharacteristic
267C23#1062190011yescharacteristic
268C23C2×C22⋊D4311yescharacteristic
269D4—41no—
270D4—41no—
271D4—41no—
272D4—41no—
273D4—3441no—
274D4—3441no—
275D4—1721no—
276D4—1721no—
277D4—1721no—
278D4—1721no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—862no—
289C2×C4—862no—
290C2×C4—862no—
291C2×C4—861no—
292C2×C4—861no—
293C2×C4—861no—
294C2×C4—861no—
295C2×C4—861no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4—1721no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—81no—
320C22—3441no—
321C22—1722no—
322C22—1721no—
323C22—1721no—
324C22—1721no—
325C22#1306329511yescharacteristic
326C22#1306329611yescharacteristic
327C22#1306329711yescharacteristic
328C22#1306329911yescharacteristic
329C22#1306330711yescharacteristic
330C22#1306330911yescharacteristic
331C22#1306331111yescharacteristic
332C4—42no—
333C4—41no—
334C4—81no—
335C4—3441no—
336C4—1721no—
337C4—1722no—
338C4—1721no—
339C4—1721no—
340C2—21no—
341C2—21no—
342C2—21no—
343C2—21no—
344C2—21no—
345C2—21no—
346C2—81no—
347C2—3441no—
348C2#1458281511yescharacteristic
349C2#1458308711yescharacteristic
350C2#1458309011yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC24×C43C23
FrattiniC24C22×D43
FittingC2×#99×C43C2
socleC22×C43#120
hypercenterC2×#99D43
hypocenterC43#2044
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#13063239C2semidirect
3. #14582779C2semidirect
4. #14582776C2semidirect
5. #14582774C2semidirect
6. #14582665C2semidirect
7. C2×#99×C43C2semidirect
60. C22⋊C4×C43D4semidirect
178. C2×#99D43semidirect
183. C43#2044semidirect
249. C22⋊C4C22⋊D43semidirect