Finite Group Databasebeta

← #18074185

Subgroups — #18074185

Order 4864.

788 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 788 conjugacy classes of subgroups — too many to draw. Only its 119 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×#11927254C211yesmaximal, characteristic
2#14562236C212yesmaximal, complemented
3#14562079C212yesmaximal
4#14561979C211yesmaximal, characteristic, complemented
5C4×C19×#101C211yesmaximal, characteristic, complemented
6#11927254—24no—
7#11927254—24no—
8C2×#10597315C411yescharacteristic
9C2×#10597316C411yescharacteristic
10C2×#10597316C2211yescharacteristic
11C2×#10597342—21no—
12C2×#10597342—21no—
13C2×#10597392—21no—
14C2×C4×D76C411yescharacteristic
15C2×C4×D76C411yescharacteristic
16C2×C4×D76C2211yescharacteristic
17C2×C4⋊C4×D19—21no—
18#11926601C2212yes—
19#11926285—24no—
20#11926273—24no—
21#11926270—21no—
22#11926270—21no—
23C2×C4×Q8×C19C2211yescharacteristic
24C2×C19×#101—21no—
25C4×M16×C19C2212yes—
26C19×#343—21no—
27C22×Q8×C19D411yescharacteristic
28C22×D76C2×C411yescharacteristic
29C22×C4×D19—21no—
30C22×C4×D19—21no—
31C22×C4×D19—21no—
32C22×Dic38—21no—
33C2×M16×C19—22no—
34C4×Q8×C19—22no—
35C4×Q8×C19—22no—
36C2×C4⋊C4×C19D411yescharacteristic
37C2×C4⋊C4×C19D411yescharacteristic
38C2×C4⋊C4×C19D411yescharacteristic
39C2×C42×C19C2×C411yescharacteristic
40C2×C42×C19C2×C411yescharacteristic
41C2×C42×C19C2311yescharacteristic
42#10597392—28no—
43C2×(C2×D19)⋊C4—21no—
44C2×(C2×D19)⋊C4—21no—
45C2×(C2×D19)⋊C4—21no—
46C2×C4⋊Dic19—21no—
47C2×C4⋊Dic19C2×C411yescharacteristic
48C2×C4⋊Dic19C2×C411yescharacteristic
49C2×C4⋊Dic19C2×C411yescharacteristic
50C2×Dic19⋊C4—21no—
51C2×Dic19⋊C4—21no—
52C2×Dic19⋊C4—21no—
53C2×Dic19⋊C4—21no—
54#10597342—28no—
55#10597342—28no—
56C4⋊C4×D19—28no—
57C4×D76—22no—
58C4×D76—22no—
59C4×D76—22no—
60C4×D76—22no—
61C4×D76—22no—
62C4×D76D414yes—
63#10597316—22no—
64#10597316—22no—
65#10597316—22no—
66#10597316D414yes—
67#10597315—22no—
68#10597315—22no—
69C19×#101—24no—
70C19×#97—22no—
71C4×C8×C19—22no—
72C22⋊(C19⋊C8)—22no—
73C4⋊(C19⋊C8)—22no—
74#10597260—22no—
75C23×D19—21no—
76C2×Q8×C19—22no—
77C2×Q8×C19—22no—
78C2×Q8×C19—41no—
79C22×C4×C19C22⋊C411yescharacteristic
80C22×C4×C19C22⋊C411yescharacteristic
81C22×C4×C19C22⋊C411yescharacteristic
82C22×C4×C19C22⋊C411yescharacteristic
83C22×C4×C19C22×C411yescharacteristic
84C22×C4×C19C2×D411yescharacteristic
85C22×C4×C19C2×D411yescharacteristic
86C22×Dic19—21no—
87C22×Dic19—21no—
88C22×Dic19—21no—
89C2×D76—21no—
90C2×D76—24no—
91C2×D76C22⋊C412yes—
92C2×C4×D19—24no—
93C2×C4×D19—24no—
94C2×C4×D19—24no—
95C2×C4×D19—42no—
96C2×C4×D19—42no—
97C2×C4×D19—82no—
98C2×C4×D19—82no—
99C2×Dic38—24no—
100C2×Dic38—82no—
101M16×C19—24no—
102M16×C19—42no—
103C2×C8×C19—42no—
104C4⋊C4×C19—22no—
105C4⋊C4×C19—22no—
106C4⋊C4×C19—22no—
107C42×C19—21no—
108C42×C19—21no—
109C42×C19—21no—
110C42×C19—21no—
111C42×C19C2×D412yes—
112C42×C19C2×D412yes—
113(C2×D19)⋊C4—24no—
114(C2×D19)⋊C4—24no—
115(C2×D19)⋊C4—24no—
116C4⋊Dic19—24no—
117C4⋊Dic19—21no—
118C4⋊Dic19—21no—
119C4⋊Dic19—21no—
120C4⋊Dic19C22⋊C412yes—
121C4⋊Dic19C22⋊C412yes—
122C4⋊Dic19C22⋊C412yes—
123Dic19⋊C4—24no—
124Dic19⋊C4—24no—
125Dic19⋊C4—24no—
126Dic19⋊C4—24no—
127C2×C19⋊C8—42no—
128#8372—191nomaximal, Sylow
129C23×C19C2×C22⋊C411yescharacteristic
130C22×D19—24no—
131C22×D19—22no—
132C22×D19—42no—
133C22×D19—41no—
134C22×D19—41no—
135Q8×C19—44no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—22no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19#10412yes—
150C2×C4×C19C2×C22⋊C411yescharacteristic
151C2×C4×C19C2×C22⋊C411yescharacteristic
152C2×C4×C19#12012yes—
153C2×C4×C19#12012yes—
154C2×Dic19—22no—
155C2×Dic19—22no—
156C2×Dic19—22no—
157C2×Dic19—42no—
158C2×Dic19—42no—
159C2×Dic19—41no—
160C2×Dic19—41no—
161D76—24no—
162D76—22no—
163D76#10114yescomplemented
164C4×D19—48no—
165C4×D19—84no—
166C4×D19—84no—
167Dic38—84no—
168C8×C19—44no—
169C19⋊C8—82no—
170C2×#554—191no—
171C4×#101D1911yescharacteristic, complemented
172#1528—192no—
173#1490—192no—
174#1467—191no—
175C22×C19—21no—
176C22×C19—21no—
177C22×C19#37911yescharacteristic
178C22×C19C2×#10411yescharacteristic
179C22×C19#42111yescharacteristic
180C2×D19—24no—
181C2×D19—44no—
182C2×D19—44no—
183C2×D19—42no—
184C2×D19—42no—
185C4×C19—22no—
186C4×C19—21no—
187C4×C19—22no—
188C4×C19—22no—
189C4×C19—41no—
190C4×C19—41no—
191C4×C19—41no—
192C4×C19C2×#10112yes—
193Dic19—42no—
194Dic19—42no—
195Dic19—42no—
196#554—384no—
197#554—384no—
198C2×C4⋊Q8—191no—
199C2×#125—191no—
200C2×#125—191no—
201C2×C22⋊Q8—381no—
202C2×C22⋊Q8—381no—
203C2×C22⋊Q8—381no—
204C2×C4×Q8C2×D1911yescharacteristic
205C2×C4×D4—191no—
206C2×C4×D4—191no—
207C2×C4×D4—191no—
208C22×C4⋊C4—381no—
209#432—192no—
210C2×#101—21no—
211C4×M16C2×D1912yes—
212#343—21no—
213#330—384no—
214D4⋊C8—384no—
215#324—381no—
216#324—381no—
217C2×C19—21no—
218C2×C19—21no—
219C2×C19#178411yescharacteristic
220C2×C19#178911yescharacteristic
221C2×C19#179511yescharacteristic
222D19—44no—
223C22×Q8—381no—
224C22×Q8C22⋊D1911yescharacteristic
225C22×D4—191no—
226C23×C4—381no—
227C23×C4—381no—
228C23×C4—381no—
229C2×M16—22no—
230C4⋊Q8—382no—
231C4⋊Q8—382no—
232#125—194no—
233#125—382no—
234#125—382no—
235#125—382no—
236C22⋊Q8—388no—
237C22⋊Q8—388no—
238C22⋊Q8—388no—
239C4×Q8—22no—
240C4×Q8—22no—
241C4×D4—194no—
242C4×D4—382no—
243C4×D4—382no—
244C4×D4—382no—
245C4×D4—382no—
246C4×D4—382no—
247C2×C4⋊C4—191no—
248C2×C4⋊C4—191no—
249C2×C4⋊C4—191no—
250C2×C4⋊C4—388no—
251C2×C4⋊C4—381no—
252C2×C4⋊C4—381no—
253C2×C4⋊C4—381no—
254C2×C4⋊C4—381no—
255C2×C4⋊C4—381no—
256C2×C4⋊C4D7611yescharacteristic
257C2×C4⋊C4D7611yescharacteristic
258C2×C4⋊C4C22⋊D1911yescharacteristic
259C2×C22⋊C4—381no—
260C2×C22⋊C4—381no—
261C2×C22⋊C4—381no—
262C2×C42C4×D1911yescharacteristic
263C2×C42C4×D1911yescharacteristic
264C2×C42C22×D1911yescharacteristic
265C4⋊C8—382no—
266#101—24no—
267C22⋊C8—382no—
268#97—22no—
269#97—382no—
270C4×C8—22no—
271C19#837211yescharacteristic, complemented, Sylow
272C24—381no—
273C2×Q8—22no—
274C2×Q8—22no—
275C2×Q8—41no—
276C2×Q8—384no—
277C2×Q8—1522no—
278C2×D4—192no—
279C2×D4—384no—
280C2×D4—381no—
281C22×C4—384no—
282C22×C4—384no—
283C22×C4—381no—
284C22×C4—381no—
285C22×C4—381no—
286C22×C4—384no—
287C22×C4—762no—
288C22×C4—762no—
289C22×C4—1522no—
290C22×C4—1522no—
291C22×C4(C2×D19)⋊C411yescharacteristic
292C22×C4(C2×D19)⋊C411yescharacteristic
293C22×C4(C2×D19)⋊C411yescharacteristic
294C22×C4(C2×D19)⋊C411yescharacteristic
295C22×C4C2×C4×D1911yescharacteristic
296C22×C4C2×D7611yescharacteristic
297C22×C4C2×C22⋊D1911yescharacteristic
298M16—24no—
299M16—42no—
300C2×C8—42no—
301C2×C8—762no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—192no—
306C4⋊C4—192no—
307C4⋊C4—192no—
308C4⋊C4—384no—
309C4⋊C4—384no—
310C4⋊C4—384no—
311C4⋊C4—384no—
312C4⋊C4—381no—
313C4⋊C4—381no—
314C4⋊C4—381no—
315C4⋊C4—384no—
316C22⋊C4—384no—
317C22⋊C4—384no—
318C22⋊C4—384no—
319C42—21no—
320C42—21no—
321C42—21no—
322C42—21no—
323C42D4×D1912yes—
324C42D4×D1912yes—
325C23—384no—
326C23—382no—
327C23—762no—
328C23—761no—
329C23—761no—
330C23C2×(C2×D19)⋊C411yescharacteristic
331Q8—44no—
332Q8—1524no—
333D4—194no—
334D4—384no—
335D4—382no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—382no—
350C2×C4—382no—
351C2×C4—382no—
352C2×C4—768no—
353C2×C4—762no—
354C2×C4—762no—
355C2×C4—761no—
356C2×C4—761no—
357C2×C4—1524no—
358C2×C4—1524no—
359C2×C4#1059726212yes—
360C2×C4C22⋊C4×D1911yescharacteristic
361C2×C4C22⋊C4×D1911yescharacteristic
362C2×C4#1059732812yes—
363C2×C4#1059738312yes—
364C8—44no—
365C8—1522no—
366C22—21no—
367C22—21no—
368C22—384no—
369C22—764no—
370C22—764no—
371C22—762no—
372C22—762no—
373C22#1192639911yescharacteristic
374C22C2×#1059726211yescharacteristic
375C22#1192656211yescharacteristic
376C4—22no—
377C4—21no—
378C4—22no—
379C4—22no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—762no—
384C4—762no—
385C4—762no—
386C4#101×D1912yes—
387C2—21no—
388C2—21no—
389C2—764no—
390C2#1456355711yescharacteristic
391C2#1456358011yescharacteristic
392C2#1456360611yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC4×C19×#101C2
socleC22×C19#379
prime radicalC22×D76C2×C4
cosocleC2×C42×C19C23
hypercenterC4×#101D19
hypocenterC19#8372
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
2. #14562236C2semidirect
4. #14561979C2semidirect
5. C4×C19×#101C2semidirect
163. D76#101semidirect
171. C4×#101D19semidirect
271. C19#8372semidirect

Maximal subgroups

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

subgroupindex
C2×#119272542
#145622362
#145620792
#145619792
C4×C19×#1012
#837219