Finite Group Databasebeta

← #18085137

Subgroups — #18085137

Order 4864.

562 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926896C211yesmaximal, characteristic, complemented
2C2×#11926824C211yesmaximal, characteristic
3#14564430C211yesmaximal, characteristic
4C2×#11926293C211yesmaximal, characteristic, complemented
5C2×#11926289C211yesmaximal, characteristic, complemented
6#14561469C211yesmaximal, characteristic, complemented
7C2×C19×#476C211yesmaximal, characteristic
8C2×#10597315C2211yescharacteristic
9#11926896—22no—
10#11926896—22no—
11#11926824—22no—
12#11926824—22no—
13C2×#10597264—21no—
14C2×C4⋊(C19⋊C8)C2211yescharacteristic
15C2×C4⋊(C19⋊C8)C2211yescharacteristic
16C2×#10597267—22no—
17C2×#10597289—21no—
18C2×C22⋊(C19⋊C8)—22no—
19C2×C4×C19⋊C8C2211yescharacteristic
20#11926293—22no—
21#11926289—22no—
22C2×C19×C4⋊Q8C2211yescharacteristic
23C2×C4×D4×C19C2211yescharacteristic
24C19×#476—22no—
25C19×#476—22no—
26C2×C19×#106—21no—
27C2×C19×C4⋊C8C2211yescharacteristic
28C2×C19×#102—21no—
29C22×Q8×C19—21no—
30C22×D4×C19D411yescharacteristic
31C23×C4×C19—21no—
32C22×Dic38—21no—
33C22×C8×C19—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8—21no—
36C19×C4⋊Q8—21no—
37C19×C4⋊Q8D412yes—
38C4×D4×C19—21no—
39C4×D4×C19—21no—
40C4×D4×C19—21no—
41C4×D4×C19—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19D411yescharacteristic
45C2×C22⋊C4×C19—21no—
46C2×C42×C19C2311yescharacteristic
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19—21no—
49C22×C19⋊C8—21no—
50C22×C19⋊C8—21no—
51C22×C19⋊C8D412yes—
52#10597315—21no—
53#10597315—21no—
54#10597315—21no—
55#10597315D412yes—
56C19×#106—24no—
57C19×C4⋊C8—21no—
58C19×C4⋊C8D412yes—
59C19×#102—24no—
60#10597289—24no—
61C22⋊(C19⋊C8)—44no—
62#10597267—28no—
63#10597264—24no—
64C4⋊(C19⋊C8)—21no—
65C4⋊(C19⋊C8)—21no—
66C4⋊(C19⋊C8)—21no—
67C4⋊(C19⋊C8)D412yes—
68C4×C19⋊C8—21no—
69C4×C19⋊C8—21no—
70C24×C19—21no—
71C2×Q8×C19—22no—
72C2×Q8×C19—41no—
73C2×Q8×C19—82no—
74C2×D4×C19—21no—
75C2×D4×C19—21no—
76C2×D4×C19—21no—
77C2×D4×C19—21no—
78C2×D4×C19—21no—
79C2×D4×C19Q1612yes—
80C22×C4×C19—21no—
81C22×C4×C19—41no—
82C22×C4×C19—41no—
83C22×C4×C19—41no—
84C22×C4×C19—42no—
85C22×C4×C19—42no—
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19#4111yescharacteristic
89C22×Dic19—41no—
90C2×Dic38—22no—
91C2×Dic38—42no—
92C2×Dic38—42no—
93C2×Dic38—41no—
94C2×C8×C19—22no—
95C2×C8×C19—41no—
96C2×C8×C19—41no—
97C4⋊C4×C19—22no—
98C4⋊C4×C19—22no—
99C4⋊C4×C19—21no—
100C4⋊C4×C19—21no—
101C4⋊C4×C19—41no—
102C4⋊C4×C19—41no—
103C22⋊C4×C19—41no—
104C22⋊C4×C19—41no—
105C42×C19C2×D411yescharacteristic
106C42×C19C2×D411yescharacteristic
107C42×C19C2×D411yescharacteristic
108C42×C19C2×D411yescharacteristic
109C4⋊Dic19—22no—
110C4⋊Dic19—22no—
111C4⋊Dic19—41no—
112C4⋊Dic19—41no—
113C2×C19⋊C8—22no—
114C2×C19⋊C8—22no—
115C2×C19⋊C8—22no—
116C2×C19⋊C8—22no—
117C2×C19⋊C8—41no—
118C2×C19⋊C8—41no—
119C2×C19⋊C8—41no—
120C2×C19⋊C8—42no—
121#10275—191nomaximal, Sylow
122C23×C19—22no—
123C23×C19—41no—
124C23×C19—42no—
125C23×C19—41no—
126C23×C19—42no—
127C23×C19#12111yescharacteristic
128Q8×C19—82no—
129Q8×C19—82no—
130D4×C19—22no—
131D4×C19—22no—
132D4×C19—41no—
133D4×C19—41no—
134C2×C4×C19—22no—
135C2×C4×C19—41no—
136C2×C4×C19—42no—
137C2×C4×C19—42no—
138C2×C4×C19—82no—
139C2×C4×C19—82no—
140C2×C4×C19—81no—
141C2×C4×C19—81no—
142C2×C4×C19#12011yescharacteristic
143C2×C4×C19#12011yescharacteristic
144C2×C4×C19#12011yescharacteristic
145C2×C4×C19#12111yescharacteristic
146C2×C4×C19#12111yescharacteristic
147C2×C4×C19#12711yescharacteristic
148C2×C4×C19C2×Q1611yescharacteristic
149C2×C4×C19#13511yescharacteristic
150C2×C4×C19#13512yes—
151C2×C4×C19AGL(1,ℤ/8)12yes—
152C2×C4×C19#13711yescharacteristic
153C2×C4×C19#13711yescharacteristic
154C2×Dic19—42no—
155C2×Dic19—82no—
156Dic38—44no—
157Dic38—81no—
158Dic38—81no—
159C8×C19—42no—
160C19⋊C8—42no—
161C19⋊C8—42no—
162C19⋊C8—81no—
163C2×#487—191no—
164C2×#476D1911yescharacteristic
165C2×#474—191no—
166#1954—191no—
167C2×#333—191no—
168C2×#332—191no—
169#1277—191no—
170C22×C19—44no—
171C22×C19—42no—
172C22×C19—82no—
173C22×C19—81no—
174C22×C19—81no—
175C22×C19#39211yescharacteristic
176C22×C19#46312yes—
177C22×C19#46711yescharacteristic
178C22×C19#47011yescharacteristic
179C22×C19#47112yes—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—81no—
183C4×C19—82no—
184C4×C19#44912yes—
185C4×C19#45111yescharacteristic
186C4×C19#45111yescharacteristic
187C4×C19#45211yescharacteristic
188C4×C19#45211yescharacteristic
189C4×C19#49511yescharacteristic
190C4×C19#49611yescharacteristic
191Dic19—82no—
192C2×C4⋊Q8—191no—
193C2×C4⋊Q8C2×D1911yescharacteristic
194C2×C4×D4C2×D1911yescharacteristic
195#487—382no—
196#487—382no—
197#476—22no—
198#476—22no—
199#474—382no—
200#474—382no—
201C2×#107—381no—
202C2×#106—21no—
203C2×C4⋊C8—191no—
204C2×C4⋊C8—191no—
205C2×C4⋊C8C2×D1911yescharacteristic
206C2×#103—382no—
207C2×#102—21no—
208C2×#102—381no—
209C2×C22⋊C8—382no—
210C2×C4×C8—191no—
211#333—382no—
212#332—382no—
213C2×C19—82no—
214C2×C19#168312yes—
215C2×C19#170312yes—
216C2×C19#200111yescharacteristic
217C2×C19#201211yescharacteristic
218C2×C19#201911yescharacteristic
219C22×Q8—21no—
220C22×Q8—381no—
221C22×D4C22⋊D1911yescharacteristic
222C23×C4—21no—
223C22×C8—21no—
224C22×C8—192no—
225C22×C8—381no—
226C22×C8—381no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—21no—
230C4⋊Q8—192no—
231C4⋊Q8—381no—
232C4⋊Q8—381no—
233C4⋊Q8—381no—
234C4⋊Q8C22⋊D1912yes—
235C4×D4—21no—
236C4×D4—21no—
237C4×D4—21no—
238C4×D4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—381no—
242C2×C4⋊C4—381no—
243C2×C4⋊C4C22⋊D1911yescharacteristic
244C2×C22⋊C4—21no—
245C2×C42C22×D1911yescharacteristic
246#107—384no—
247#106—24no—
248C4⋊C8—21no—
249C4⋊C8—192no—
250C4⋊C8—381no—
251C4⋊C8—381no—
252C4⋊C8—381no—
253C4⋊C8C22⋊D1912yes—
254#103—388no—
255#102—24no—
256#102—384no—
257C22⋊C8—764no—
258C4×C8—381no—
259C4×C8—381no—
260C19#1027511yescharacteristic, complemented, Sylow
261C24—21no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—82no—
265C2×Q8—382no—
266C2×Q8—761no—
267C2×Q8—762no—
268C2×Q8—762no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4#6452812yes—
275C22×C4—21no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—761no—
282C22×C4D4×D1911yescharacteristic
283C22×C4#6454311yescharacteristic
284C22×C4C2×C22⋊D1911yescharacteristic
285C2×C8—22no—
286C2×C8—41no—
287C2×C8—41no—
288C2×C8—382no—
289C2×C8—382no—
290C2×C8—382no—
291C2×C8—382no—
292C2×C8—761no—
293C2×C8—761no—
294C2×C8—761no—
295C2×C8—762no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—382no—
303C4⋊C4—382no—
304C4⋊C4—761no—
305C4⋊C4—761no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42D4×D1911yescharacteristic
309C42D4×D1911yescharacteristic
310C42C2×C22⋊D1911yescharacteristic
311C42C2×C22⋊D1911yescharacteristic
312C23—22no—
313C23—41no—
314C23—42no—
315C23—41no—
316C23—42no—
317C23#1059738511yescharacteristic
318Q8—82no—
319Q8—82no—
320Q8—764no—
321Q8—1521no—
322Q8—1521no—
323D4—22no—
324D4—22no—
325D4—41no—
326D4—41no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—82no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—82no—
335C2×C4—762no—
336C2×C4—1522no—
337C2×C4#1059736012yes—
338C2×C4#1059736212yes—
339C2×C4#1059738311yescharacteristic
340C2×C4#1059738311yescharacteristic
341C2×C4#1059738411yescharacteristic
342C2×C4#1059738511yescharacteristic
343C2×C4#1059738611yescharacteristic
344C2×C4#1059738811yescharacteristic
345C2×C4C2×#6452811yescharacteristic
346C2×C4#1059739611yescharacteristic
347C2×C4#1059739711yescharacteristic
348C2×C4#1059739911yescharacteristic
349C8—42no—
350C8—762no—
351C8—762no—
352C8—1521no—
353C22—44no—
354C22—42no—
355C22—81no—
356C22—82no—
357C22—81no—
358C22#1192645211yescharacteristic
359C22#1192676112yes—
360C22#1192678311yescharacteristic
361C22#1192680011yescharacteristic
362C22#1192680512yes—
363C4—21no—
364C4—21no—
365C4—81no—
366C4—82no—
367C4—1522no—
368C4#1192668812yes—
369C4#1192669911yescharacteristic
370C4#1192670011yescharacteristic
371C4#1192670411yescharacteristic
372C4#1192670611yescharacteristic
373C4#1192692511yescharacteristic
374C4#1192693011yescharacteristic
375C2—82no—
376C2#1456308812yes—
377C2#1456321212yes—
378C2#1456464311yescharacteristic
379C2#1456470911yescharacteristic
380C2#1456474911yescharacteristic
subgroupG/H
centerC23#10597385
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC2×C19×#476C2
socleC23×C19#121
prime radicalC22×D4×C19D4
hypercenterC2×#476D19
hypocenterC19#10275
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#11926896C2semidirect
4. C2×#11926293C2semidirect
5. C2×#11926289C2semidirect
6. #14561469C2semidirect
260. C19#10275semidirect

Maximal subgroups

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

subgroupindex
C2×#119268962
C2×#119268242
#145644302
C2×#119262932
C2×#119262892
#145614692
C2×C19×#4762
#1027519