Finite Group Databasebeta

← #18071638

Subgroups — #18071638

Order 4864.

478 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 87 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#14570006C211yesmaximal, characteristic
2#14565162C211yesmaximal, characteristic
3#14565108C211yesmaximal, characteristic, complemented
4#14565106C211yesmaximal, characteristic, complemented
5#14561457C211yesmaximal, characteristic, complemented
6#14561455C211yesmaximal, characteristic
7C19×#1271C211yesmaximal, characteristic, complemented
8C2×#10597343—21no—
9C2×#10597342—21no—
10C2×#10597275—21no—
11C2×#10597275—21no—
12C2×#10597264—21no—
13C2×#10597278—21no—
14#11926466—21no—
15#11926466—21no—
16#11926465—21no—
17#11926446C2211yescharacteristic
18#11926442C2211yescharacteristic
19#11926422—21no—
20#11926414C2211yescharacteristic
21#11926307—21no—
22#11926306—21no—
23#11926299C2211yescharacteristic
24C19×#389C2211yescharacteristic
25C19×#336C2211yescharacteristic
26C19×#336C2211yescharacteristic
27C22×D76D411yescharacteristic
28C22×C4×D19—21no—
29C22×Dic38—21no—
30C22×C8×C19—21no—
31C22×C8×C19—21no—
32C2×C4⋊C4×C19—21no—
33C2×C4⋊C4×C19D411yescharacteristic
34C2×C4⋊C4×C19D411yescharacteristic
35C2×C42×C19C2311yescharacteristic
36C2×(C2×D19)⋊C4—21no—
37C2×(C2×D19)⋊C4—21no—
38C2×(C2×D19)⋊C4—21no—
39C2×(C2×D19)⋊C4—21no—
40C2×(C2×D19)⋊C4—21no—
41C2×C4⋊Dic19—21no—
42C2×C4⋊Dic19—21no—
43C2×C4⋊Dic19—21no—
44C2×C4⋊Dic19—21no—
45C2×C4⋊Dic19D411yescharacteristic
46C2×C4⋊Dic19D411yescharacteristic
47C2×C4⋊Dic19D411yescharacteristic
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—21no—
50C22×C19⋊C8—21no—
51#10597343—42no—
52#10597343—42no—
53#10597342—42no—
54#10597342—42no—
55C19×#95—21no—
56C19⋊#95—21no—
57C19⋊#95—21no—
58#10597278—42no—
59#10597275—42no—
60#10597275—42no—
61#10597264—42no—
62C23×D19—21no—
63C22×C4×C19—21no—
64C22×C4×C19—21no—
65C22×C4×C19C2×D411yescharacteristic
66C22×C4×C19C2×D411yescharacteristic
67C22×C4×C19C2×D411yescharacteristic
68C22×Dic19—21no—
69C22×Dic19—21no—
70C22×Dic19—21no—
71C22×Dic19—41no—
72C2×D76—21no—
73C2×D76—41no—
74C2×D76—41no—
75C2×D76Q1612yes—
76C2×C4×D19—42no—
77C2×C4×D19—42no—
78C2×C4×D19—81no—
79C2×Dic38—42no—
80C2×Dic38—42no—
81C2×Dic38—81no—
82C2×C8×C19—22no—
83C2×C8×C19—22no—
84C2×C8×C19—41no—
85C2×C8×C19—41no—
86C2×C8×C19—41no—
87C2×C8×C19—41no—
88C4⋊C4×C19—21no—
89C4⋊C4×C19—41no—
90C4⋊C4×C19—41no—
91C4⋊C4×C19—41no—
92C4⋊C4×C19D812yes—
93C42×C19—41no—
94(C2×D19)⋊C4—42no—
95(C2×D19)⋊C4—42no—
96(C2×D19)⋊C4—41no—
97(C2×D19)⋊C4—41no—
98(C2×D19)⋊C4—41no—
99(C2×D19)⋊C4—41no—
100(C2×D19)⋊C4—81no—
101C4⋊Dic19—21no—
102C4⋊Dic19—42no—
103C4⋊Dic19—41no—
104C4⋊Dic19—41no—
105C4⋊Dic19—41no—
106C4⋊Dic19—41no—
107C4⋊Dic19—41no—
108C4⋊Dic19—41no—
109C4⋊Dic19—41no—
110C4⋊Dic19—41no—
111C4⋊Dic19D812yes—
112Dic19⋊C4—42no—
113Dic19⋊C4—41no—
114Dic19⋊C4—41no—
115C2×C19⋊C8—22no—
116C2×C19⋊C8—41no—
117C2×C19⋊C8—41no—
118#7797—191nomaximal, Sylow
119C23×C19#12011yescharacteristic
120C22×D19—22no—
121C22×D19—41no—
122C22×D19—41no—
123C22×D19—41no—
124C22×D19—41no—
125C22×D19—41no—
126C22×D19—41no—
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—22no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—41no—
137C2×C4×C19—41no—
138C2×C4×C19—41no—
139C2×C4×C19C2×D811yescharacteristic
140C2×C4×C19C2×D811yescharacteristic
141C2×C4×C19C2×Q1611yescharacteristic
142C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C19#13711yescharacteristic
145C2×Dic19—22no—
146C2×Dic19—41no—
147C2×Dic19—41no—
148C2×Dic19—41no—
149C2×Dic19—41no—
150C2×Dic19—41no—
151C2×Dic19—41no—
152C2×Dic19—41no—
153C2×Dic19—41no—
154C2×Dic19—81no—
155C2×Dic19—81no—
156C2×Dic19—81no—
157D76—42no—
158D76—81no—
159C4×D19—84no—
160Dic38—84no—
161C8×C19—42no—
162C8×C19—42no—
163C19⋊C8—42no—
164#2683—191no—
165#2093—191no—
166#2083—191no—
167#2083—191no—
168#1271—191no—
169#1271D1911yescharacteristic, complemented
170#1270—191no—
171C22×C19#44711yescharacteristic
172C22×C19#44711yescharacteristic
173C22×C19#45111yescharacteristic
174C22×C19#45311yescharacteristic
175C22×C19#45611yescharacteristic
176C22×C19#45611yescharacteristic
177C22×C19#45811yescharacteristic
178C2×D19—42no—
179C2×D19—42no—
180C2×D19—42no—
181C2×D19—81no—
182C2×D19—81no—
183C2×D19—81no—
184C2×D19—81no—
185C4×C19—21no—
186C4×C19—21no—
187C4×C19—21no—
188C4×C19—21no—
189C4×C19—21no—
190C4×C19—21no—
191C4×C19—42no—
192C4×C19—81no—
193Dic19—42no—
194Dic19—81no—
195Dic19—81no—
196Dic19—161no—
197C2×C22⋊Q8—381no—
198C2×C22⋊Q8—381no—
199C2×#107—381no—
200C2×#107—381no—
201C2×#107—381no—
202C2×#102—381no—
203#396—381no—
204#396—381no—
205#395—381no—
206#390—191no—
207#389—191no—
208#389C2×D1911yescharacteristic
209#386—381no—
210#384—191no—
211#340—381no—
212#340—381no—
213#336—191no—
214#336C2×D1911yescharacteristic
215#336C2×D1911yescharacteristic
216C2×C19#161011yescharacteristic
217C2×C19#161011yescharacteristic
218C2×C19#161411yescharacteristic
219C2×C19#161911yescharacteristic
220C2×C19#164911yescharacteristic
221C2×C19#164911yescharacteristic
222C2×C19#166011yescharacteristic
223D19—82no—
224C22×Q8—381no—
225C22×D4—191no—
226C23×C4—381no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—381no—
230C22⋊Q8—762no—
231C22⋊Q8—762no—
232C22⋊Q8—762no—
233C22⋊Q8—762no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—191no—
236C2×C4⋊C4—191no—
237C2×C4⋊C4—191no—
238C2×C4⋊C4—381no—
239C2×C4⋊C4—381no—
240C2×C4⋊C4—381no—
241C2×C4⋊C4—381no—
242C2×C4⋊C4—381no—
243C2×C4⋊C4—381no—
244C2×C4⋊C4D7611yescharacteristic
245C2×C4⋊C4D7611yescharacteristic
246C2×C22⋊C4—381no—
247C2×C22⋊C4—381no—
248C2×C22⋊C4—381no—
249C2×C22⋊C4—381no—
250C2×C22⋊C4—381no—
251C2×C42C22×D1911yescharacteristic
252#107—762no—
253#107—762no—
254#107—762no—
255#102—762no—
256#95—21no—
257#95—381no—
258#95—381no—
259C19#779711yescharacteristic, complemented, Sylow
260C24—381no—
261C2×Q8—762no—
262C2×Q8—762no—
263C2×Q8—1521no—
264C2×D4—192no—
265C2×D4—381no—
266C2×D4—761no—
267C2×D4—761no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—381no—
271C22×C4—381no—
272C22×C4—381no—
273C22×C4—762no—
274C22×C4—762no—
275C22×C4—761no—
276C22×C4—1521no—
277C22×C4C2×D7611yescharacteristic
278C22×C4D4×D1911yescharacteristic
279C22×C4D4×D1911yescharacteristic
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—382no—
287C2×C8—761no—
288C2×C8—761no—
289C4⋊C4—21no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—192no—
294C4⋊C4—381no—
295C4⋊C4—761no—
296C4⋊C4—761no—
297C4⋊C4—762no—
298C4⋊C4—761no—
299C4⋊C4—761no—
300C4⋊C4—762no—
301C4⋊C4—761no—
302C4⋊C4—761no—
303C4⋊C4—761no—
304C4⋊C4—761no—
305C4⋊C4—761no—
306C4⋊C4—761no—
307C4⋊C4D15212yes—
308C22⋊C4—762no—
309C22⋊C4—762no—
310C22⋊C4—761no—
311C22⋊C4—761no—
312C22⋊C4—761no—
313C22⋊C4—761no—
314C22⋊C4—1521no—
315C42—41no—
316C23—382no—
317C23—761no—
318C23—761no—
319C23—761no—
320C23—761no—
321C23—761no—
322C23—761no—
323C23#1059732811yescharacteristic
324Q8—1524no—
325D4—762no—
326D4—1521no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—382no—
340C2×C4—761no—
341C2×C4—761no—
342C2×C4—761no—
343C2×C4—761no—
344C2×C4—761no—
345C2×C4—761no—
346C2×C4—761no—
347C2×C4—761no—
348C2×C4—1524no—
349C2×C4—1521no—
350C2×C4—1521no—
351C2×C4—1521no—
352C2×C4C2×D15211yescharacteristic
353C2×C4#1059735411yescharacteristic
354C2×C4D8×D1911yescharacteristic
355C2×C4#1059736011yescharacteristic
356C2×C4#1059736111yescharacteristic
357C2×C4Q16×D1911yescharacteristic
358C8—42no—
359C8—42no—
360C8—762no—
361C22—762no—
362C22—762no—
363C22—762no—
364C22—1521no—
365C22—1521no—
366C22—1521no—
367C22—1521no—
368C22#1192667911yescharacteristic
369C22#1192668011yescharacteristic
370C22#1192670111yescharacteristic
371C22#1192671311yescharacteristic
372C22#1192672811yescharacteristic
373C22#1192672911yescharacteristic
374C22#1192673511yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—42no—
382C4—81no—
383C4—3041no—
384C4—762no—
385C4—1521no—
386C4—1521no—
387C2—1522no—
388C2#1456263911yescharacteristic
389C2#1456264011yescharacteristic
390C2#1456266111yescharacteristic
391C2#1456269111yescharacteristic
392C2#1456288511yescharacteristic
393C2#1456288611yescharacteristic
394C2#1456294811yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#1271C2
socleC23×C19#120
prime radicalC22×D76D4
hypercenter#1271D19
hypocenterC19#7797
LCSG ▷ C2×C42×C19 ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
3. #14565108C2semidirect
4. #14565106C2semidirect
5. #14561457C2semidirect
7. C19×#1271C2semidirect
169. #1271D19semidirect
259. C19#7797semidirect

Maximal subgroups

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

subgroupindex
#145700062
#145651622
#145651082
#145651062
#145614572
#145614552
C19×#12712
#779719