Finite Group Databasebeta

← #18074183

Subgroups — #18074183

Order 4864.

750 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 750 conjugacy classes of subgroups — too many to draw. Only its 115 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×#11927234C211yesmaximal, characteristic
2C4×#10597290C211yesmaximal, characteristic
3#14562238C212yesmaximal, complemented
4#14562081C212yesmaximal, complemented
5C19×#1466C211yesmaximal, characteristic
6#11927234—24no—
7#11927234—24no—
8C2×#10597325—21no—
9C2×#10597316C2211yescharacteristic
10C2×#10597335—21no—
11C2×#10597381—21no—
12C2×#10597370C411yescharacteristic
13C2×#10597370C411yescharacteristic
14C2×C4×Dic38C2211yescharacteristic
15C2×#10597372C411yescharacteristic
16C2×#10597323—21no—
17C22×C4⋊Dic19C411yescharacteristic
18C2×#10597290—21no—
19C4×#64520C2212yes—
20#11926313—21no—
21#11926285—24no—
22#11926274—24no—
23C2×C4×D4×C19C2211yescharacteristic
24C19×#432C2212yes—
25C19×#323—21no—
26C19×#323—21no—
27C22×D4×C19D411yescharacteristic
28C23×C4×C19C2×C411yescharacteristic
29C23×C4×C19C2×C411yescharacteristic
30C23×Dic19—21no—
31C22×Dic38C2×C411yescharacteristic
32C4×D4×C19—22no—
33C4×D4×C19—22no—
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C22⋊C4×C19D411yescharacteristic
36C2×C22⋊C4×C19D411yescharacteristic
37C2×C42×C19C2311yescharacteristic
38C2×C22⋊Dic19—21no—
39C2×C22⋊Dic19—21no—
40C2×C22⋊Dic19—21no—
41#10597381—28no—
42#10597372—22no—
43#10597372—22no—
44C2×C4⋊Dic19—21no—
45C2×C4⋊Dic19—22no—
46C2×C4⋊Dic19—22no—
47C2×C4⋊Dic19C2×C411yescharacteristic
48C2×C4⋊Dic19C2×C411yescharacteristic
49C2×C4⋊Dic19C2×C411yescharacteristic
50#10597370—22no—
51#10597370—22no—
52#10597370—22no—
53#10597370—22no—
54C2×Dic19⋊C4—21no—
55C2×Dic19⋊C4—21no—
56C2×Dic19⋊C4—21no—
57C2×Dic19⋊C4—21no—
58C2×Dic19⋊C4—21no—
59C2×C4×Dic19—21no—
60C2×C4×Dic19—21no—
61C2×#64520—22no—
62#10597335—28no—
63#10597325—28no—
64#10597323—28no—
65#10597316—22no—
66#10597316D414yes—
67C4×Dic38—22no—
68C4×Dic38D414yes—
69C19×C4⋊C8—22no—
70C19×C22⋊C8—22no—
71C19×#97—22no—
72#10597290—24no—
73#10597260—22no—
74C4×C19⋊C8—22no—
75C24×C19C22⋊C411yescharacteristic
76C24×C19C22⋊C411yescharacteristic
77C2×D4×C19—22no—
78C2×D4×C19—22no—
79C2×D4×C19—41no—
80C22×C4×C19—21no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—42no—
85C22×C4×C19—42no—
86C22×C4×C19C22⋊C411yescharacteristic
87C22×C4×C19C22⋊C411yescharacteristic
88C22×C4×C19C22×C411yescharacteristic
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×Dic19—24no—
92C22×Dic19—21no—
93C22×Dic19—21no—
94C22×Dic19—21no—
95C22×Dic19—21no—
96C22×Dic19—42no—
97C22×Dic19—42no—
98C2×Dic38—21no—
99C2×Dic38—42no—
100C2×Dic38C22⋊C412yes—
101C2×C8×C19—42no—
102C4⋊C4×C19—22no—
103C22⋊C4×C19—22no—
104C22⋊C4×C19—22no—
105C42×C19C2×D412yes—
106C42×C19C2×D412yes—
107C22⋊Dic19—24no—
108C22⋊Dic19—24no—
109C22⋊Dic19—24no—
110C4⋊Dic19—24no—
111C4⋊Dic19—21no—
112C4⋊Dic19—21no—
113C4⋊Dic19—21no—
114C4⋊Dic19C22⋊C412yes—
115C4⋊Dic19C22⋊C412yes—
116C4⋊Dic19C22⋊C412yes—
117Dic19⋊C4—24no—
118Dic19⋊C4—24no—
119Dic19⋊C4—24no—
120Dic19⋊C4—24no—
121Dic19⋊C4—24no—
122C4×Dic19—24no—
123C4×Dic19—24no—
124#64520—24no—
125#64520—42no—
126C2×C19⋊C8—42no—
127#8371—191nomaximal, Sylow
128C23×C19—21no—
129C23×C19—21no—
130C23×C19—21no—
131C23×C19—21no—
132C23×C19—21no—
133C23×C19—41no—
134C23×C19—41no—
135C23×C19—41no—
136C23×C19—41no—
137C23×C19#10412yes—
138C23×C19C2×C22⋊C411yescharacteristic
139D4×C19—44no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—22no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—41no—
146C2×C4×C19—42no—
147C2×C4×C19—42no—
148C2×C4×C19—42no—
149C2×C4×C19—42no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19C2×C22⋊C411yescharacteristic
153C2×C4×C19C2×C22⋊C411yescharacteristic
154C2×C4×C19#12012yes—
155C2×C4×C19#12012yes—
156C2×Dic19—22no—
157C2×Dic19—22no—
158C2×Dic19—22no—
159C2×Dic19—22no—
160C2×Dic19—42no—
161C2×Dic19—42no—
162C2×Dic19—48no—
163C2×Dic19—41no—
164C2×Dic19—41no—
165C2×Dic19—41no—
166C2×Dic19—41no—
167Dic38—24no—
168Dic38—42no—
169C8×C19—82no—
170C19⋊C8—44no—
171C2×#552—191no—
172C4×#100—191no—
173#1528—192no—
174#1491—192no—
175#1466D1911yescharacteristic
176C22×C19—21no—
177C22×C19—21no—
178C22×C19—22no—
179C22×C19—42no—
180C22×C19—42no—
181C22×C19—41no—
182C22×C19—41no—
183C22×C19—41no—
184C22×C19—41no—
185C22×C19—41no—
186C22×C19—81no—
187C22×C19—81no—
188C22×C19#37911yescharacteristic
189C22×C19C2×#10411yescharacteristic
190C22×C19#42111yescharacteristic
191C4×C19—22no—
192C4×C19—21no—
193C4×C19—22no—
194C4×C19—41no—
195C4×C19—41no—
196C4×C19#41312yes—
197Dic19—42no—
198Dic19—42no—
199Dic19—42no—
200Dic19—42no—
201#552—384no—
202#552—384no—
203C2×#126—381no—
204C2×#125—191no—
205C2×#125—381no—
206C2×#123—381no—
207C2×C22⋊Q8—191no—
208C2×C22⋊Q8—191no—
209C2×C4×Q8—191no—
210C2×C4×D4C2×D1911yescharacteristic
211C2×#117—191no—
212C2×#117—381no—
213C22×C4⋊C4—191no—
214#432C2×D1912yes—
215C2×#100—381no—
216C4×M16—192no—
217#343—381no—
218#330—384no—
219Q8⋊C8—384no—
220#323—21no—
221#323—21no—
222C2×C19—21no—
223C2×C19—21no—
224C2×C19—42no—
225C2×C19—81no—
226C2×C19#178511yescharacteristic
227C2×C19#178911yescharacteristic
228C2×C19#179611yescharacteristic
229C22×Q8—191no—
230C22×D4D7611yescharacteristic
231C23×C4—381no—
232C23×C4C4×D1911yescharacteristic
233C23×C4C4×D1911yescharacteristic
234C2×M16—382no—
235#126—388no—
236#125—194no—
237#125—388no—
238#125—382no—
239#123—388no—
240C22⋊Q8—382no—
241C22⋊Q8—382no—
242C22⋊Q8—382no—
243C22⋊Q8—382no—
244C4×Q8—194no—
245C4×Q8—382no—
246C4×D4—22no—
247C4×D4—22no—
248#117—388no—
249#117—382no—
250#117—382no—
251C2×C4⋊C4—191no—
252C2×C4⋊C4—191no—
253C2×C4⋊C4—191no—
254C2×C4⋊C4—382no—
255C2×C4⋊C4—382no—
256C2×C4⋊C4—381no—
257C2×C4⋊C4—381no—
258C2×C4⋊C4—381no—
259C2×C4⋊C4—381no—
260C2×C4⋊C4—381no—
261C2×C4⋊C4—381no—
262C2×C4⋊C4D7611yescharacteristic
263C2×C22⋊C4—381no—
264C2×C22⋊C4—381no—
265C2×C22⋊C4—381no—
266C2×C22⋊C4C22⋊D1911yescharacteristic
267C2×C22⋊C4C22⋊D1911yescharacteristic
268C2×C42—381no—
269C2×C42—381no—
270C2×C42C22×D1911yescharacteristic
271C4⋊C8—22no—
272#100—384no—
273C22⋊C8—22no—
274#97—22no—
275#97—382no—
276C4×C8—382no—
277C19#837111yescharacteristic, complemented, Sylow
278C24(C2×D19)⋊C411yescharacteristic
279C24(C2×D19)⋊C411yescharacteristic
280C2×Q8—192no—
281C2×Q8—381no—
282C2×Q8—762no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—41no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—384no—
293C22×C4—381no—
294C22×C4—381no—
295C22×C4—381no—
296C22×C4—381no—
297C22×C4—762no—
298C22×C4—762no—
299C22×C4(C2×D19)⋊C411yescharacteristic
300C22×C4(C2×D19)⋊C411yescharacteristic
301C22×C4C2×C4×D1911yescharacteristic
302C22×C4C2×D7611yescharacteristic
303C22×C4C2×C22⋊D1911yescharacteristic
304M16—384no—
305M16—762no—
306C2×C8—42no—
307C2×C8—762no—
308C4⋊C4—22no—
309C4⋊C4—192no—
310C4⋊C4—192no—
311C4⋊C4—192no—
312C4⋊C4—384no—
313C4⋊C4—384no—
314C4⋊C4—384no—
315C4⋊C4—384no—
316C4⋊C4—381no—
317C4⋊C4—381no—
318C4⋊C4—381no—
319C4⋊C4—384no—
320C4⋊C4—384no—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—384no—
324C22⋊C4—384no—
325C22⋊C4—384no—
326C42—384no—
327C42—384no—
328C42D4×D1912yes—
329C42D4×D1912yes—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23#1059728212yes—
340C23C2×(C2×D19)⋊C411yescharacteristic
341Q8—384no—
342Q8—762no—
343D4—44no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—22no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—382no—
357C2×C4—382no—
358C2×C4—382no—
359C2×C4—382no—
360C2×C4—768no—
361C2×C4—762no—
362C2×C4—762no—
363C2×C4—761no—
364C2×C4—761no—
365C2×C4—761no—
366C2×C4—761no—
367C2×C4C22⋊C4×D1911yescharacteristic
368C2×C4C22⋊C4×D1911yescharacteristic
369C2×C4#1059732812yes—
370C2×C4#1059738312yes—
371C8—82no—
372C8—764no—
373C22—21no—
374C22—21no—
375C22—22no—
376C22—42no—
377C22—42no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—81no—
384C22—81no—
385C22#1192639911yescharacteristic
386C22C2×#1059728211yescharacteristic
387C22#1192656011yescharacteristic
388C4—22no—
389C4—21no—
390C4—22no—
391C4—41no—
392C4—41no—
393C4—762no—
394C4—762no—
395C4—762no—
396C4—762no—
397C4#1192652512yes—
398C2—21no—
399C2—21no—
400C2—42no—
401C2—81no—
402C2#1456356011yescharacteristic
403C2#1456357811yescharacteristic
404C2#1456360811yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1466C2
socleC22×C19#379
prime radicalC22×D4×C19D4
cosocleC2×C42×C19C23
hypercenter#1466D19
hypocenterC19#8371
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #14562238C2semidirect
4. #14562081C2semidirect
277. C19#8371semidirect

Maximal subgroups

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

subgroupindex
C2×#119272342
C4×#105972902
#145622382
#145620812
C19×#14662
#837119