Finite Group Databasebeta

← #18079067

Subgroups — #18079067

Order 4864.

496 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574756C211yesmaximal, characteristic
2#14572378C211yesmaximal, characteristic
3#14564480C211yesmaximal, characteristic, complemented
4#14562310C211yesmaximal, characteristic
5#14561532C211yesmaximal, characteristic, complemented
6#14561485C211yesmaximal, characteristic, complemented
7C2×C19×#332C211yesmaximal, characteristic, complemented
8C2×#10597347—21no—
9#11927094C2211yescharacteristic
10#11926947—21no—
11#11926892—21no—
12#11926857C414yes—
13#11926821—22no—
14#11926621—21no—
15#11926614—22no—
16#11926609—21no—
17#11926597C2211yescharacteristic
18#11926568C2211yescharacteristic
19C2×#10597293—21no—
20C2×#10597293—21no—
21#11926510—21no—
22C4×#64520C2211yescharacteristic
23#11926289—21no—
24#11926287—21no—
25C2×C19×C4⋊Q8C2211yescharacteristic
26C2×C19×C4⋊C8C2211yescharacteristic
27C2×C19×C4⋊C8C2211yescharacteristic
28C19×#332—21no—
29C19×#332—21no—
30C22×Q8×C19—21no—
31C2×#64541—21no—
32C22×C8×C19—21no—
33C22×C8×C19—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8—21no—
38C2×C4⋊C4×C19—21no—
39C2×C4⋊C4×C19C2×C412yes—
40C2×C42×C19C2311yescharacteristic
41#10597376—21no—
42#10597376C2×C412yes—
43C2×#64520—21no—
44C2×#64520D411yescharacteristic
45C2×#64520D411yescharacteristic
46#10597347—42no—
47#10597347—42no—
48C2×#64515—22no—
49C2×C8×D19—22no—
50#10597321—21no—
51#10597320D411yescharacteristic
52C4×D76—21no—
53C4×D76D412yes—
54#10597315D411yescharacteristic
55C19×C4⋊C8—21no—
56C19×C4⋊C8—21no—
57C19×C4⋊C8—21no—
58C19×C4⋊C8D411yescharacteristic
59C19×C4⋊C8D411yescharacteristic
60#10597293—42no—
61#10597293—42no—
62C22⋊(C19⋊C8)C2×C412yes—
63(C2×D19)⋊C8—22no—
64(C2×D19)⋊C8—22no—
65#10597266—24no—
66#10597264—24no—
67C4⋊(C19⋊C8)—21no—
68C4⋊(C19⋊C8)—21no—
69C4⋊(C19⋊C8)—21no—
70#10597260—21no—
71C4×C19⋊C8—21no—
72C4×C19⋊C8—21no—
73C2×Q8×C19—41no—
74C2×Q8×C19—41no—
75C2×Q8×C19—41no—
76C2×Q8×C19—41no—
77C2×Q8×C19—41no—
78C2×Q8×C19—41no—
79C22×C4×C19—22no—
80C22×C4×C19C22×C411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19#4111yescharacteristic
83C2×C22⋊D19—22no—
84#64541—41no—
85#64541—41no—
86#64541—41no—
87#64541—41no—
88C2×D76—21no—
89C2×D76—21no—
90C2×D76C22⋊C412yes—
91C2×C4×D19—22no—
92C2×Dic38—21no—
93C2×C8×C19—21no—
94C2×C8×C19—21no—
95C2×C8×C19—41no—
96C2×C8×C19—41no—
97C2×C8×C19—41no—
98C2×C8×C19—81no—
99C4⋊C4×C19—22no—
100C4⋊C4×C19—22no—
101C4⋊C4×C19—41no—
102C4⋊C4×C19—41no—
103C42×C19C2×D411yescharacteristic
104C42×C19C2×D411yescharacteristic
105C42×C19C2×D411yescharacteristic
106C42×C19#4111yescharacteristic
107(C2×D19)⋊C4—22no—
108(C2×D19)⋊C4—22no—
109C4⋊Dic19—21no—
110C4⋊Dic19C22⋊C412yes—
111#64520—21no—
112#64520—21no—
113#64520—21no—
114#64520—41no—
115#64520—41no—
116#64520D812yes—
117C2×C19⋊C8—21no—
118C2×C19⋊C8—22no—
119C2×C19⋊C8—21no—
120C2×C19⋊C8—41no—
121#64515—44no—
122C8×D19—44no—
123#9271—191nomaximal, Sylow
124C23×C19C4×D411yescharacteristic
125C22×D19—22no—
126Q8×C19—81no—
127Q8×C19—81no—
128Q8×C19—81no—
129Q8×C19—81no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—41no—
133C2×C4×C19—42no—
134C2×C4×C19—42no—
135C2×C4×C19—42no—
136C2×C4×C19C2×C22⋊C411yescharacteristic
137C2×C4×C19C4×D411yescharacteristic
138C2×C4×C19#12011yescharacteristic
139C2×C4×C19#12111yescharacteristic
140C2×C4×C19#12111yescharacteristic
141C2×C4×C19#12311yescharacteristic
142C2×C4×C19C2×D811yescharacteristic
143C2×C4×C19#13511yescharacteristic
144C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
146C22⋊D19—42no—
147C22⋊D19—42no—
148C2×Dic19—22no—
149D76—42no—
150D76—41no—
151D76—41no—
152D76—41no—
153D76—41no—
154C4×D19—42no—
155C4×D19—42no—
156Dic38—41no—
157Dic38—41no—
158C8×C19—41no—
159C8×C19—41no—
160C8×C19—81no—
161C19⋊C8—22no—
162C19⋊C8—42no—
163C19⋊C8—41no—
164C19⋊C8—81no—
165#3226—191no—
166#2935—191no—
167#1966—191no—
168#1547—191no—
169C2×#332D1911yescharacteristic, complemented
170#1301—191no—
171#1283—191no—
172C22×C19—21no—
173C22×C19—21no—
174C22×C19#38611yescharacteristic
175C22×C19C4×D811yescharacteristic
176C22×C19#44211yescharacteristic
177C2×D19—42no—
178C2×D19—42no—
179C2×D19—42no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—21no—
183C4×C19—82no—
184C4×C19#44711yescharacteristic
185C4×C19#44911yescharacteristic
186C4×C19#45911yescharacteristic
187C4×C19#46311yescharacteristic
188C4×C19#47111yescharacteristic
189C4×C19#47311yescharacteristic
190Dic19—42no—
191C2×#131—381no—
192#532—191no—
193C2×C4⋊Q8C2×D1911yescharacteristic
194#500—381no—
195#486—381no—
196#480—194no—
197#474—382no—
198#436—381no—
199#435—382no—
200C8×D4—381no—
201#431—191no—
202#423—191no—
203C2×C4⋊C8C2×D1911yescharacteristic
204C2×C4⋊C8C2×D1911yescharacteristic
205C2×#101—381no—
206C2×#101—381no—
207#408—381no—
208C4×M16—191no—
209#332—21no—
210#332—21no—
211#332—381no—
212#331—381no—
213C2×C19—21no—
214C2×C19—21no—
215C2×C19#187911yescharacteristic
216C2×C19#190811yescharacteristic
217C2×C19#191511yescharacteristic
218D19—82no—
219C2×#41—381no—
220C22×Q8—21no—
221#131—762no—
222#131—762no—
223C2×M16—191no—
224C2×M16—191no—
225C2×M16—382no—
226C2×M16—381no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—382no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—191no—
235#127—191no—
236#124—381no—
237#121—192no—
238#121—381no—
239C4×D4—192no—
240C4×D4—381no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4C4×D1912yes—
243C2×C42C22×D1911yescharacteristic
244#107—384no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—381no—
249C4⋊C8—381no—
250C4⋊C8—381no—
251C4⋊C8C22⋊D1911yescharacteristic
252C4⋊C8C22⋊D1911yescharacteristic
253#102—384no—
254#101—762no—
255#101—762no—
256C22⋊C8—192no—
257C22⋊C8—382no—
258C22⋊C8—382no—
259#97—381no—
260C4×C8—381no—
261C4×C8—381no—
262C19#927111yescharacteristic, complemented, Sylow
263#41—761no—
264#41—761no—
265#41—761no—
266#41—761no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—381no—
274C2×D4—192no—
275C2×D4—382no—
276C2×D4—381no—
277C2×D4—381no—
278C22×C4—22no—
279C22×C4—382no—
280C22×C4C2×C4×D1911yescharacteristic
281C22×C4D4×D1911yescharacteristic
282C22×C4#6454311yescharacteristic
283M16—192no—
284M16—381no—
285M16—381no—
286M16—381no—
287M16—764no—
288M16—761no—
289M16—761no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—81no—
296C2×C8—381no—
297C2×C8—381no—
298C2×C8—382no—
299C2×C8—764no—
300C2×C8—761no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—192no—
306C4⋊C4—381no—
307C22⋊C4—382no—
308C22⋊C4—382no—
309C42#6454111yescharacteristic
310C42D4×D1911yescharacteristic
311C42D4×D1911yescharacteristic
312C42C2×C22⋊D1911yescharacteristic
313C23—382no—
314C23(C22⋊D19)⋊C411yescharacteristic
315Q8—81no—
316Q8—81no—
317Q8—81no—
318Q8—81no—
319Q8—761no—
320Q8—761no—
321D4—762no—
322D4—762no—
323D4—762no—
324D4—761no—
325D4—761no—
326D4—761no—
327D4—761no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—382no—
335C2×C4—762no—
336C2×C4—762no—
337C2×C4C22⋊C4×D1911yescharacteristic
338C2×C4#1059732911yescharacteristic
339C2×C4#1059733011yescharacteristic
340C2×C4D8×D1911yescharacteristic
341C2×C4#1059735711yescharacteristic
342C2×C4#1059736011yescharacteristic
343C2×C4#1059736211yescharacteristic
344C2×C4C4×C22⋊D1911yescharacteristic
345C2×C4#1059738311yescharacteristic
346C2×C4#1059738411yescharacteristic
347C8—41no—
348C8—41no—
349C8—81no—
350C8—382no—
351C8—762no—
352C8—761no—
353C8—1521no—
354C22—21no—
355C22—21no—
356C22—762no—
357C22—762no—
358C22—762no—
359C22#1192642011yescharacteristic
360C22#1192662411yescharacteristic
361C22#1192665311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—82no—
366C4—762no—
367C4#1192667611yescharacteristic
368C4#1192668811yescharacteristic
369C4#1192673811yescharacteristic
370C4#1192675811yescharacteristic
371C4#1192680411yescharacteristic
372C4#1192681611yescharacteristic
373C2—21no—
374C2—21no—
375C2—1522no—
376C2#1456398011yescharacteristic
377C2#1456415311yescharacteristic
378C2#1456418411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#332C2
socleC22×C19#386
prime radical#11927094C22
cosocleC2×C42×C19C23
hypercenterC2×#332D19
hypocenterC19#9271
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
3. #14564480C2semidirect
5. #14561532C2semidirect
6. #14561485C2semidirect
7. C2×C19×#332C2semidirect
169. C2×#332D19semidirect
262. C19#9271semidirect

Maximal subgroups

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

subgroupindex
#145747562
#145723782
#145644802
#145623102
#145615322
#145614852
C2×C19×#3322
#927119