Finite Group Databasebeta

← #18074265

Subgroups — #18074265

Order 4864.

966 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 966 conjugacy classes of subgroups — too many to draw. Only its 147 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×Q8×D76C211yesmaximal, characteristic
2#14563631C211yesmaximal, characteristic, complemented
3#14562306C212yesmaximal, complemented
4#14562061C212yesmaximal
5C19×#1461C211yesmaximal, characteristic, complemented
6C22×Q8×D19—21no—
7Q8×D76—24no—
8Q8×D76—24no—
9C2×#10597315C412yes—
10C2×#10597315C2211yescharacteristic
11C2×#10597343—21no—
12C2×#10597343—22no—
13C2×C4×D76C412yes—
14C2×C4×D76C2211yescharacteristic
15#11926568C2212yes—
16C2×#10597293—21no—
17#11926313—21no—
18#11926289—24no—
19#11926273—24no—
20C2×C4×Q8×C19C2211yescharacteristic
21C19×#431C2212yes—
22C19×#324—22no—
23C22×Q8×C19D411yescharacteristic
24C2×Q8×D19—28no—
25C2×Q8×D19—44no—
26C2×Q8×D19—42no—
27C2×Q8×D19—42no—
28C22×D76C2×C411yescharacteristic
29C22×C4×D19—22no—
30C22×C4×D19—21no—
31C22×Dic38—22no—
32C22×Dic38—21no—
33C4×Q8×C19—22no—
34C4×Q8×C19—22no—
35C2×C4⋊C4×C19D411yescharacteristic
36C2×C4⋊C4×C19D412yes—
37C2×C42×C19C2×C412yes—
38C2×C42×C19C2311yescharacteristic
39C2×(C2×D19)⋊C4—22no—
40C2×(C2×D19)⋊C4—21no—
41C2×C4⋊Dic19—22no—
42C2×C4⋊Dic19—21no—
43C2×C4⋊Dic19C2×C411yescharacteristic
44C2×C4⋊Dic19C2×C412yes—
45C2×#64520—22no—
46#10597343—28no—
47#10597343—216no—
48C4×D76—24no—
49C4×D76—22no—
50C4×D76—24no—
51C4×D76D414yes—
52#10597315—22no—
53#10597315—24no—
54#10597315—24no—
55#10597315D414yes—
56C19×C4⋊C8—22no—
57C19×C22⋊C8—22no—
58C4×C8×C19—22no—
59#10597293—42no—
60C4⋊(C19⋊C8)—22no—
61C4⋊(C19⋊C8)—22no—
62C23×D19—21no—
63C2×Q8×C19—22no—
64C2×Q8×C19—22no—
65C2×Q8×C19D812yes—
66C2×Q8×C19SD1612yes—
67C22×C4×C19C22⋊C412yes—
68C22×C4×C19C22⋊C412yes—
69C22×C4×C19C22×C411yescharacteristic
70C22×C4×C19C2×D411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×Dic19—21no—
73C22×Dic19—22no—
74Q8×D19—416no—
75Q8×D19—416no—
76C2×D76—21no—
77C2×D76—24no—
78C2×D76C22⋊C412yes—
79C2×C4×D19—28no—
80C2×C4×D19—24no—
81C2×C4×D19—44no—
82C2×C4×D19—44no—
83C2×C4×D19—41no—
84C2×C4×D19—41no—
85C2×C4×D19—42no—
86C2×Dic38—28no—
87C2×Dic38—24no—
88C2×Dic38—44no—
89C2×Dic38—44no—
90C2×Dic38—41no—
91C2×Dic38—41no—
92C2×Dic38—42no—
93C2×C8×C19—42no—
94C4⋊C4×C19—24no—
95C4⋊C4×C19—22no—
96C42×C19—22no—
97C42×C19—22no—
98C42×C19C2×D412yes—
99C42×C19C2×D412yes—
100(C2×D19)⋊C4—28no—
101(C2×D19)⋊C4—24no—
102C4⋊Dic19—28no—
103C4⋊Dic19—21no—
104C4⋊Dic19—22no—
105C4⋊Dic19—24no—
106C4⋊Dic19C22⋊C412yes—
107C4⋊Dic19C22⋊C414yes—
108#64520—42no—
109#64520—42no—
110C2×C19⋊C8—42no—
111#8388—191nomaximal, Sylow
112C23×C19C2×C22⋊C411yescharacteristic
113C22×D19—24no—
114C22×D19—22no—
115C22×D19—42no—
116C22×D19—41no—
117C22×D19—41no—
118Q8×C19—24no—
119Q8×C19—24no—
120C2×C4×C19—22no—
121C2×C4×C19—22no—
122C2×C4×C19—22no—
123C2×C4×C19—22no—
124C2×C4×C19—41no—
125C2×C4×C19—42no—
126C2×C4×C19#10214yes—
127C2×C4×C19C2×C22⋊C411yescharacteristic
128C2×C4×C19C2×C22⋊C411yescharacteristic
129C2×C4×C19#12012yes—
130C2×C4×C19#12012yes—
131C2×C4×C19C2×D811yescharacteristic
132C2×C4×C19C2×SD1611yescharacteristic
133C2×C4×C19AGL(1,ℤ/8)12yes—
134C2×Dic19—22no—
135C2×Dic19—24no—
136C2×Dic19—41no—
137C2×Dic19—42no—
138C2×Dic19—41no—
139C2×Dic19—42no—
140D76—24no—
141D76—22no—
142D76#10114yescomplemented
143C4×D19—416no—
144C4×D19—44no—
145C4×D19—44no—
146Dic38—416no—
147Dic38—44no—
148Dic38—44no—
149C8×C19—82no—
150C19⋊C8—82no—
151C2×D4×Q8—191no—
152#1801—191no—
153#1546—192no—
154#1486—192no—
155#1461D1911yescharacteristic, complemented
156C22×C19—21no—
157C22×C19—21no—
158C22×C19#37911yescharacteristic
159C22×C19C2×#10211yescharacteristic
160C22×C19#41811yescharacteristic
161C2×D19—24no—
162C2×D19—44no—
163C2×D19—44no—
164C2×D19—42no—
165C2×D19—42no—
166C4×C19—22no—
167C4×C19—21no—
168C4×C19—24no—
169C4×C19—42no—
170C4×C19C2×#10112yes—
171C4×C19#44712yes—
172C4×C19#45012yes—
173Dic19—42no—
174Dic19—44no—
175C23×Q8—381no—
176D4×Q8—384no—
177D4×Q8—384no—
178C2×C4⋊Q8—192no—
179C2×C4⋊Q8—191no—
180C2×C22⋊Q8—381no—
181C2×C22⋊Q8—382no—
182C2×C4×Q8C2×D1911yescharacteristic
183C2×C4×D4—192no—
184C2×C4×D4—191no—
185#431C2×D1912yes—
186#423—192no—
187C2×#101—381no—
188#343—381no—
189#332—384no—
190D4⋊C8—384no—
191#324—22no—
192C2×C19—21no—
193C2×C19—21no—
194C2×C19#178411yescharacteristic
195C2×C19#178611yescharacteristic
196C2×C19#179611yescharacteristic
197D19—44no—
198C22×Q8—388no—
199C22×Q8—382no—
200C22×Q8—381no—
201C22×Q8—764no—
202C22×Q8—762no—
203C22×Q8—762no—
204C22×Q8D7611yescharacteristic
205C22×D4—191no—
206C23×C4—382no—
207C23×C4—381no—
208C2×M16—382no—
209C4⋊Q8—194no—
210C4⋊Q8—384no—
211C4⋊Q8—384no—
212C4⋊Q8—382no—
213C22⋊Q8—388no—
214C22⋊Q8—3816no—
215C4×Q8—22no—
216C4×Q8—22no—
217C4×D4—194no—
218C4×D4—384no—
219C4×D4—384no—
220C4×D4—382no—
221C2×C4⋊C4—191no—
222C2×C4⋊C4—192no—
223C2×C4⋊C4—382no—
224C2×C4⋊C4—381no—
225C2×C4⋊C4D7611yescharacteristic
226C2×C4⋊C4C22⋊D1912yes—
227C2×C22⋊C4—382no—
228C2×C22⋊C4—381no—
229C2×C42C4×D1912yes—
230C2×C42C22×D1911yescharacteristic
231C4⋊C8—22no—
232C4⋊C8—382no—
233C4⋊C8—382no—
234#101—762no—
235C22⋊C8—22no—
236C4×C8—22no—
237C19#838811yescharacteristic, complemented, Sylow
238C24—381no—
239C2×Q8—22no—
240C2×Q8—22no—
241C2×Q8—388no—
242C2×Q8—384no—
243C2×Q8—764no—
244C2×Q8—7616no—
245C2×Q8—7616no—
246C2×Q8—764no—
247C2×Q8—761no—
248C2×Q8—761no—
249C2×Q8—762no—
250C2×Q8#6451612yes—
251C2×Q8D15212yes—
252C2×D4—192no—
253C2×D4—384no—
254C2×D4—381no—
255C22×C4—388no—
256C22×C4—382no—
257C22×C4—381no—
258C22×C4—384no—
259C22×C4—764no—
260C22×C4—764no—
261C22×C4—761no—
262C22×C4—761no—
263C22×C4—762no—
264C22×C4(C2×D19)⋊C412yes—
265C22×C4(C2×D19)⋊C412yes—
266C22×C4C2×C4×D1911yescharacteristic
267C22×C4C2×D7611yescharacteristic
268C22×C4C2×C22⋊D1911yescharacteristic
269M16—762no—
270M16—762no—
271C2×C8—42no—
272C2×C8—762no—
273C4⋊C4—24no—
274C4⋊C4—22no—
275C4⋊C4—192no—
276C4⋊C4—194no—
277C4⋊C4—388no—
278C4⋊C4—384no—
279C4⋊C4—381no—
280C4⋊C4—382no—
281C22⋊C4—388no—
282C22⋊C4—384no—
283C42—22no—
284C42—22no—
285C42D4×D1912yes—
286C42D4×D1912yes—
287C23—384no—
288C23—382no—
289C23—762no—
290C23—761no—
291C23—761no—
292C23C2×(C2×D19)⋊C411yescharacteristic
293Q8—24no—
294Q8—24no—
295Q8—7616no—
296Q8—764no—
297Q8—764no—
298D4—194no—
299D4—384no—
300D4—382no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—384no—
308C2×C4—382no—
309C2×C4—7616no—
310C2×C4—762no—
311C2×C4—761no—
312C2×C4—762no—
313C2×C4—761no—
314C2×C4—764no—
315C2×C4—764no—
316C2×C4#1059727814yes—
317C2×C4C22⋊C4×D1911yescharacteristic
318C2×C4C22⋊C4×D1911yescharacteristic
319C2×C4#1059732812yes—
320C2×C4C2×#6451611yescharacteristic
321C2×C4C2×D15211yescharacteristic
322C2×C4#1059735412yes—
323C2×C4#1059738312yes—
324C8—82no—
325C8—1522no—
326C22—21no—
327C22—21no—
328C22—384no—
329C22—764no—
330C22—764no—
331C22—762no—
332C22—762no—
333C22#1192639911yescharacteristic
334C22C2×#1059727811yescharacteristic
335C22#1192655011yescharacteristic
336C4—22no—
337C4—21no—
338C4—24no—
339C4—42no—
340C4—764no—
341C4—762no—
342C4#101×D1912yes—
343C4#1192668012yes—
344C4#1192669712yes—
345C2—21no—
346C2—21no—
347C2—764no—
348C2#1456355711yescharacteristic
349C2#1456356711yescharacteristic
350C2#1456360811yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1461C2
socleC22×C19#379
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenter#1461D19
hypocenterC19#8388
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. #14563631C2semidirect
3. #14562306C2semidirect
5. C19×#1461C2semidirect
142. D76#101semidirect
155. #1461D19semidirect
237. C19#8388semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×D762
#145636312
#145623062
#145620612
C19×#14612
#838819