Finite Group Databasebeta

← #18071076

Subgroups — #18071076

Order 4864.

532 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 107 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#14571966C211yesmaximal, characteristic
2#14563615C211yesmaximal, characteristic, complemented
3#14561459C212yesmaximal, complemented
4#14561455C212yesmaximal, complemented
5C19×#1749C211yesmaximal, characteristic, complemented
6C2×#10597375—21no—
7C2×#10597376C411yescharacteristic
8C2×C4⋊(C19⋊C8)—21no—
9C2×C22⋊(C19⋊C8)—21no—
10#11926446C411yescharacteristic
11#11926446C2211yescharacteristic
12#11926442C411yescharacteristic
13#11926442C2211yescharacteristic
14#11926435—21no—
15#11926435—21no—
16#11926423—21no—
17#11926404C411yescharacteristic
18#11926299C2212yes—
19C22×C42×C19C2211yescharacteristic
20C2×C19×C22⋊C8—21no—
21C2×C19×#97—21no—
22C19×#336C2212yes—
23C23×C4×C19C2×C411yescharacteristic
24C23×C4×C19D411yescharacteristic
25C23×C4×C19D411yescharacteristic
26C22×C22⋊D19—21no—
27C22×D76C2×C411yescharacteristic
28C22×C8×C19—22no—
29C2×C42×C19—42no—
30C2×C42×C19C2×C411yescharacteristic
31C2×C42×C19D411yescharacteristic
32C2×C42×C19D411yescharacteristic
33C2×C42×C19C2311yescharacteristic
34C2×C22⋊Dic19—21no—
35#10597376—42no—
36#10597375—44no—
37C2×(C2×D19)⋊C4—21no—
38C2×(C2×D19)⋊C4—21no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×(C2×D19)⋊C4—21no—
42C2×C4⋊Dic19C2×C411yescharacteristic
43C2×C4⋊Dic19C2×C411yescharacteristic
44C2×C4⋊Dic19C2×C411yescharacteristic
45C2×Dic19⋊C4—21no—
46C2×Dic19⋊C4—21no—
47C22×C19⋊C8—22no—
48C19×C22⋊C8—24no—
49C19×#97—42no—
50C19⋊#95—21no—
51C19⋊#95—21no—
52C19⋊#95—21no—
53C22⋊(C19⋊C8)—42no—
54C4⋊(C19⋊C8)—42no—
55C24×C19C22⋊C411yescharacteristic
56C23×D19—21no—
57C22×C4×C19—22no—
58C22×C4×C19—22no—
59C22×C4×C19—22no—
60C22×C4×C19—21no—
61C22×C4×C19—22no—
62C22×C4×C19—21no—
63C22×C4×C19—41no—
64C22×C4×C19—41no—
65C22×C4×C19—41no—
66C22×C4×C19—41no—
67C22×C4×C19C22⋊C411yescharacteristic
68C22×C4×C19C22⋊C411yescharacteristic
69C22×C4×C19C22⋊C411yescharacteristic
70C22×C4×C19C22×C411yescharacteristic
71C22×C4×C19C2×D411yescharacteristic
72C22×C4×C19C2×D411yescharacteristic
73C2×C22⋊D19—42no—
74C2×C22⋊D19—42no—
75C2×C22⋊D19—42no—
76C22×Dic19—21no—
77C22×Dic19—21no—
78C22×Dic19—21no—
79C2×D76—22no—
80C2×D76—41no—
81C2×D76—41no—
82C2×C8×C19—24no—
83C2×C8×C19—42no—
84C2×C8×C19—42no—
85C42×C19—22no—
86C42×C19—22no—
87C42×C19—41no—
88C42×C19—41no—
89C22⋊Dic19—42no—
90(C2×D19)⋊C4—42no—
91(C2×D19)⋊C4—42no—
92(C2×D19)⋊C4—42no—
93(C2×D19)⋊C4—41no—
94(C2×D19)⋊C4—42no—
95(C2×D19)⋊C4—41no—
96C4⋊Dic19—22no—
97C4⋊Dic19—41no—
98C4⋊Dic19—41no—
99Dic19⋊C4—42no—
100Dic19⋊C4—42no—
101C2×C19⋊C8—42no—
102C2×C19⋊C8—42no—
103C2×C19⋊C8—42no—
104#7698—191nomaximal, Sylow
105C23×C19—21no—
106C23×C19—21no—
107C23×C19—21no—
108C23×C19—21no—
109C23×C19—21no—
110C23×C19—21no—
111C23×C19#10412yes—
112C23×C19C2×C22⋊C411yescharacteristic
113C22×D19—41no—
114C22×D19—41no—
115C22×D19—41no—
116C22×D19—41no—
117C22×D19—41no—
118C22×D19—41no—
119C22×D19—41no—
120C2×C4×C19—21no—
121C2×C4×C19—21no—
122C2×C4×C19—21no—
123C2×C4×C19—21no—
124C2×C4×C19—21no—
125C2×C4×C19—21no—
126C2×C4×C19—21no—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—44no—
135C2×C4×C19—44no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19#9912yes—
139C2×C4×C19#13112yes—
140C2×C4×C19AGL(1,ℤ/8)12yes—
141C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C19#13711yescharacteristic
143C22⋊D19—84no—
144C2×Dic19—41no—
145C2×Dic19—41no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150C2×Dic19—41no—
151C2×Dic19—41no—
152C2×Dic19—41no—
153D76—82no—
154C8×C19—44no—
155C19⋊C8—82no—
156#2854—191no—
157#1797—191no—
158#1749D1911yescharacteristic, complemented
159#1271—192no—
160#1270—192no—
161C22×C19—22no—
162C22×C19—22no—
163C22×C19—22no—
164C22×C19—41no—
165C22×C19—41no—
166C22×C19—41no—
167C22×C19—41no—
168C22×C19#40811yescharacteristic
169C22×C19C2×#9911yescharacteristic
170C22×C19#41311yescharacteristic
171C22×C19#41711yescharacteristic
172C22×C19#41811yescharacteristic
173C22×C19C2×#10411yescharacteristic
174C22×C19#42111yescharacteristic
175C2×D19—81no—
176C2×D19—81no—
177C2×D19—81no—
178C2×D19—81no—
179C2×D19—81no—
180C2×D19—81no—
181C2×D19—81no—
182C4×C19—22no—
183C4×C19—22no—
184C4×C19—22no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—41no—
188C4×C19—41no—
189Dic19—81no—
190Dic19—81no—
191Dic19—81no—
192C2×#123—381no—
193C2×#121—191no—
194C22×C42C2×D1911yescharacteristic
195C2×C4⋊C8—381no—
196C2×C22⋊C8—21no—
197C2×C22⋊C8—381no—
198C2×#97—21no—
199#390—191no—
200#390—191no—
201#389—191no—
202#389—191no—
203#388—381no—
204#388—381no—
205#386—381no—
206#380—191no—
207#336—192no—
208#336C2×D1912yes—
209C2×C19—42no—
210C2×C19#146811yescharacteristic
211C2×C19#148311yescharacteristic
212C2×C19#149611yescharacteristic
213C2×C19#150711yescharacteristic
214C2×C19#151311yescharacteristic
215C2×C19#153211yescharacteristic
216C2×C19#155711yescharacteristic
217D19—161no—
218C22×D4—191no—
219C22×D4—381no—
220C23×C4C4×D1911yescharacteristic
221C23×C4D7611yescharacteristic
222C23×C4C22⋊D1911yescharacteristic
223C22×C8—22no—
224C22×C8—382no—
225#123—764no—
226#121—762no—
227C2×C4⋊C4—191no—
228C2×C4⋊C4—191no—
229C2×C4⋊C4—191no—
230C2×C4⋊C4—381no—
231C2×C4⋊C4—381no—
232C2×C22⋊C4—381no—
233C2×C22⋊C4—381no—
234C2×C22⋊C4—381no—
235C2×C22⋊C4—381no—
236C2×C22⋊C4—381no—
237C2×C22⋊C4—381no—
238C2×C42—42no—
239C2×C42C4×D1911yescharacteristic
240C2×C42D7611yescharacteristic
241C2×C42C22⋊D1911yescharacteristic
242C2×C42C22×D1911yescharacteristic
243C4⋊C8—762no—
244C22⋊C8—24no—
245C22⋊C8—762no—
246#97—42no—
247#95—381no—
248#95—381no—
249#95—381no—
250C19#769811yescharacteristic, complemented, Sylow
251C24—381no—
252C24(C2×D19)⋊C411yescharacteristic
253C2×D4—382no—
254C2×D4—761no—
255C2×D4—761no—
256C2×D4—762no—
257C2×D4—762no—
258C2×D4—762no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—41no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—381no—
270C22×C4—381no—
271C22×C4—381no—
272C22×C4(C2×D19)⋊C411yescharacteristic
273C22×C4(C2×D19)⋊C411yescharacteristic
274C22×C4(C2×D19)⋊C411yescharacteristic
275C22×C4C2×C4×D1911yescharacteristic
276C22×C4C2×D7611yescharacteristic
277C22×C4C2×C22⋊D1911yescharacteristic
278C2×C8—24no—
279C2×C8—42no—
280C2×C8—42no—
281C2×C8—762no—
282C2×C8—762no—
283C2×C8—762no—
284C4⋊C4—382no—
285C4⋊C4—761no—
286C4⋊C4—761no—
287C4⋊C4—762no—
288C4⋊C4—762no—
289C22⋊C4—762no—
290C22⋊C4—762no—
291C22⋊C4—762no—
292C22⋊C4—762no—
293C22⋊C4—762no—
294C22⋊C4—761no—
295C22⋊C4—761no—
296C42—22no—
297C42—22no—
298C42—41no—
299C42—41no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—761no—
307C23—761no—
308C23—761no—
309C23—761no—
310C23—761no—
311C23—761no—
312C23—761no—
313C23#1059726212yes—
314C23C2×(C2×D19)⋊C411yescharacteristic
315D4—1522no—
316D4—1524no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—761no—
336C2×C4—761no—
337C2×C4—761no—
338C2×C4—761no—
339C2×C4—761no—
340C2×C4—761no—
341C2×C4—761no—
342C2×C4—761no—
343C2×C4—761no—
344C2×C4#1059726312yes—
345C2×C4#1059735312yes—
346C2×C4#1059735411yescharacteristic
347C2×C4#1059735511yescharacteristic
348C2×C4#1059739512yes—
349C8—44no—
350C8—1522no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—1521no—
359C22—1521no—
360C22—1521no—
361C22—1521no—
362C22—1521no—
363C22—1521no—
364C22—1521no—
365C22#1192651211yescharacteristic
366C22C2×#1059726311yescharacteristic
367C22#1192652611yescharacteristic
368C22#1192654611yescharacteristic
369C22#1192654811yescharacteristic
370C22C2×#1059726211yescharacteristic
371C22#1192656011yescharacteristic
372C4—22no—
373C4—21no—
374C4—21no—
375C4—22no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—1521no—
380C4—1521no—
381C4—1521no—
382C2—42no—
383C2—3041no—
384C2#1456198411yescharacteristic
385C2#1456204911yescharacteristic
386C2#1456210311yescharacteristic
387C2#1456215011yescharacteristic
388C2#1456217911yescharacteristic
389C2#1456225311yescharacteristic
390C2#1456235811yescharacteristic
subgroupG/H
centerC23C2×(C2×D19)⋊C4
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1749C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597376C4
cosocleC2×C42×C19C23
hypercenter#1749D19
hypocenterC19#7698
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
2. #14563615C2semidirect
3. #14561459C2semidirect
4. #14561455C2semidirect
5. C19×#1749C2semidirect
158. #1749D19semidirect
250. C19#7698semidirect

Maximal subgroups

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

subgroupindex
#145719662
#145636152
#145614592
#145614552
C19×#17492
#769819