Finite Group Databasebeta

← #18083646

Subgroups — #18083646

Order 4864.

634 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926891C211yesmaximal, characteristic
2C2×#11926744C211yesmaximal, characteristic
3#14568847C211yesmaximal, characteristic, complemented
4#14564561C211yesmaximal, characteristic
5C2×#11926291C211yesmaximal, characteristic, complemented
6#14561475C211yesmaximal, characteristic, complemented
7C2×C19×Q8⋊C8C211yesmaximal, characteristic, complemented
8C22×#64527—21no—
9C2×#10597315C2211yescharacteristic
10C2×#10597320C2211yescharacteristic
11#11926891—22no—
12#11926891—22no—
13#11926744—22no—
14#11926744—22no—
15C2×C4⋊(C19⋊C8)C2211yescharacteristic
16C2×#10597278—22no—
17C2×#10597278—22no—
18C2×#10597266—21no—
19#11926483—22no—
20#11926451—21no—
21#11926450—22no—
22#11926409—21no—
23C4×C4⋊Dic19C2211yescharacteristic
24#11926291—22no—
25C2×C4×Q8×C19C2211yescharacteristic
26C2×C19×C4⋊C8C2211yescharacteristic
27C2×C4×C8×C19C2211yescharacteristic
28C19×Q8⋊C8—22no—
29C22×Q8×C19D411yescharacteristic
30C22×D76—21no—
31C22×D76—21no—
32C22×D76—21no—
33C22×Dic38—21no—
34C22×C8×C19—21no—
35C22×C8×C19—21no—
36C4×Q8×C19—21no—
37C4×Q8×C19—21no—
38C4×Q8×C19—21no—
39C4×Q8×C19—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19D411yescharacteristic
42C2×C42×C19—21no—
43C2×C42×C19C2311yescharacteristic
44C2×#64527—24no—
45C2×#64527—42no—
46C2×#64527—42no—
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19D412yes—
49C2×C4⋊Dic19D412yes—
50C2×C4×Dic19—21no—
51C22×C19⋊C8—21no—
52#10597320—21no—
53#10597320—21no—
54#10597320—21no—
55#10597320D412yes—
56#10597315—21no—
57#10597315—21no—
58#10597315—21no—
59#10597315—21no—
60C19×C4⋊C8—21no—
61C19×C4⋊C8—21no—
62C4×C8×C19—21no—
63C4×C8×C19D412yes—
64C19⋊#95—24no—
65C19⋊#95—24no—
66C19⋊#95—21no—
67#10597278—28no—
68#10597278—44no—
69#10597266—24no—
70C4⋊(C19⋊C8)—21no—
71C4⋊(C19⋊C8)D412yes—
72C23×D19—41no—
73C2×Q8×C19—21no—
74C2×Q8×C19—21no—
75C2×Q8×C19—21no—
76C2×Q8×C19—21no—
77C2×Q8×C19—21no—
78C2×Q8×C19SD1612yes—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×C4×C19C2×D411yescharacteristic
84C22×Dic19—22no—
85C22×Dic19—22no—
86C2×D76—22no—
87C2×D76—22no—
88C2×D76—22no—
89C2×D76—44no—
90C2×D76—41no—
91C2×D76—41no—
92C2×D76—42no—
93C2×D76—41no—
94C2×D76—42no—
95C2×D76—41no—
96C2×D76—41no—
97C2×D76—41no—
98C2×D76—41no—
99C2×Dic38—41no—
100C2×Dic38—41no—
101C2×Dic38—42no—
102C2×Dic38—42no—
103C2×C8×C19—22no—
104C2×C8×C19—42no—
105C2×C8×C19—41no—
106C2×C8×C19—42no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—21no—
109C4⋊C4×C19—41no—
110C4⋊C4×C19—41no—
111C42×C19—41no—
112C42×C19—41no—
113C42×C19C2×D411yescharacteristic
114C42×C19C2×D411yescharacteristic
115C42×C19C2×D411yescharacteristic
116C42×C19#4111yescharacteristic
117#64527—48no—
118C4⋊Dic19—22no—
119C4⋊Dic19—22no—
120C4⋊Dic19—22no—
121C4⋊Dic19—22no—
122C4⋊Dic19—41no—
123C4⋊Dic19—41no—
124C4×Dic19—41no—
125C4×Dic19—41no—
126C2×C19⋊C8—22no—
127C2×C19⋊C8—41no—
128C2×C19⋊C8—41no—
129#10053—191nomaximal, Sylow
130C23×C19#12011yescharacteristic
131C22×D19—42no—
132C22×D19—81no—
133C22×D19—81no—
134C22×D19—82no—
135C22×D19—82no—
136Q8×C19—22no—
137Q8×C19—22no—
138Q8×C19—41no—
139Q8×C19—41no—
140C2×C4×C19—22no—
141C2×C4×C19—22no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—42no—
146C2×C4×C19#12011yescharacteristic
147C2×C4×C19#12011yescharacteristic
148C2×C4×C19#12111yescharacteristic
149C2×C4×C19#12111yescharacteristic
150C2×C4×C19#12111yescharacteristic
151C2×C4×C19#12711yescharacteristic
152C2×C4×C19C2×SD1611yescharacteristic
153C2×C4×C19#13511yescharacteristic
154C2×C4×C19#13512yes—
155C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C19AGL(1,ℤ/8)12yes—
157C2×C4×C19#13711yescharacteristic
158C2×Dic19—42no—
159C2×Dic19—42no—
160C2×Dic19—42no—
161C2×Dic19—44no—
162C2×Dic19—42no—
163D76—44no—
164D76—42no—
165D76—42no—
166D76—44no—
167D76—82no—
168D76—81no—
169D76—81no—
170D76—81no—
171D76—81no—
172Dic38—82no—
173Dic38—81no—
174Dic38—81no—
175C8×C19—42no—
176C8×C19—81no—
177C19⋊C8—42no—
178C2×#486—191no—
179C2×#460—191no—
180#2568—191no—
181#1982—191no—
182C2×#332—191no—
183C2×Q8⋊C8D1911yescharacteristic, complemented
184#1279—191no—
185C22×C19#39211yescharacteristic
186C22×C19#44811yescharacteristic
187C22×C19#44911yescharacteristic
188C22×C19#44912yes—
189C22×C19#45412yes—
190C2×D19—82no—
191C2×D19—82no—
192C2×D19—82no—
193C2×D19—162no—
194C2×D19—162no—
195C4×C19—21no—
196C4×C19—21no—
197C4×C19—42no—
198C4×C19—81no—
199C4×C19#45011yescharacteristic
200C4×C19#45211yescharacteristic
201C4×C19#46312yes—
202C4×C19#46511yescharacteristic
203C4×C19#46811yescharacteristic
204C4×C19#49511yescharacteristic
205C4×C19#49611yescharacteristic
206Dic19—82no—
207Dic19—82no—
208C22×SD16—381no—
209C2×C4⋊Q8—191no—
210C2×#127—191no—
211C2×C4×Q8C2×D1911yescharacteristic
212#486—382no—
213#486—382no—
214#460—382no—
215#460—382no—
216C2×C4⋊C8—191no—
217C2×C4⋊C8C2×D1911yescharacteristic
218C2×#102—382no—
219C2×#102—381no—
220C2×#102—382no—
221C2×C4×C8C2×D1911yescharacteristic
222#400—382no—
223#391—382no—
224#391—381no—
225#382—381no—
226C4×C4⋊C4—191no—
227#332—382no—
228Q8⋊C8—22no—
229C2×C19#162612yes—
230C2×C19#162812yes—
231C2×C19#200011yescharacteristic
232C2×C19#200311yescharacteristic
233C2×C19#201211yescharacteristic
234D19—162no—
235C22×Q8—381no—
236C22×Q8D7611yescharacteristic
237C22×D4—381no—
238C22×D4—381no—
239C22×D4—381no—
240C2×SD16—384no—
241C2×SD16—762no—
242C2×SD16—762no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—381no—
246C4⋊Q8—381no—
247C4⋊Q8—381no—
248C4⋊Q8—381no—
249C4⋊Q8—381no—
250#127—192no—
251#127—381no—
252#127—381no—
253#127—381no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—192no—
260C2×C4⋊C4—192no—
261C2×C4⋊C4—381no—
262C2×C4⋊C4D7611yescharacteristic
263C2×C42—21no—
264C2×C42—381no—
265C2×C42C22×D1911yescharacteristic
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—192no—
269C4⋊C8—381no—
270#102—384no—
271#102—388no—
272#102—764no—
273C4×C8—21no—
274C4×C8C22⋊D1912yes—
275#95—384no—
276#95—384no—
277#95—381no—
278C19#1005311yescharacteristic, complemented, Sylow
279C24—761no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—761no—
286C2×Q8—761no—
287C2×Q8—762no—
288C2×Q8—762no—
289C2×Q8#6451612yes—
290C2×D4—382no—
291C2×D4—382no—
292C2×D4—382no—
293C2×D4—764no—
294C2×D4—761no—
295C2×D4—761no—
296C2×D4—761no—
297C2×D4—761no—
298C2×D4—761no—
299C2×D4—761no—
300C2×D4—761no—
301C2×D4—762no—
302C2×D4—762no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—382no—
306C22×C4—382no—
307C22×C4C2×D7611yescharacteristic
308C22×C4D4×D1911yescharacteristic
309C22×C4D4×D1911yescharacteristic
310SD16—768no—
311C2×C8—22no—
312C2×C8—42no—
313C2×C8—41no—
314C2×C8—42no—
315C2×C8—382no—
316C2×C8—761no—
317C2×C8—761no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—382no—
323C4⋊C4—382no—
324C4⋊C4—382no—
325C4⋊C4—382no—
326C4⋊C4—761no—
327C4⋊C4—761no—
328C42—41no—
329C42—41no—
330C42—761no—
331C42—761no—
332C42#6454111yescharacteristic
333C42D4×D1911yescharacteristic
334C42D4×D1911yescharacteristic
335C42C2×C22⋊D1911yescharacteristic
336C23—762no—
337C23—1521no—
338C23—1521no—
339C23—1522no—
340C23—1522no—
341C23#1059732811yescharacteristic
342Q8—22no—
343Q8—22no—
344Q8—41no—
345Q8—41no—
346Q8—1521no—
347Q8—1521no—
348Q8—1522no—
349D4—764no—
350D4—762no—
351D4—762no—
352D4—764no—
353D4—1522no—
354D4—1521no—
355D4—1521no—
356D4—1521no—
357D4—1521no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—762no—
365C2×C4—762no—
366C2×C4—764no—
367C2×C4—762no—
368C2×C4—762no—
369C2×C4#1059732811yescharacteristic
370C2×C4#1059733011yescharacteristic
371C2×C4#1059733011yescharacteristic
372C2×C4C2×#6451611yescharacteristic
373C2×C4#1059735011yescharacteristic
374C2×C4#1059735411yescharacteristic
375C2×C4#1059735511yescharacteristic
376C2×C4#1059736012yes—
377C2×C4#1059736512yes—
378C2×C4#1059737611yescharacteristic
379C2×C4#1059738311yescharacteristic
380C2×C4#1059738611yescharacteristic
381C8—42no—
382C8—81no—
383C8—762no—
384C22—3042no—
385C22—3042no—
386C22—1522no—
387C22—1522no—
388C22—1522no—
389C22#1192645311yescharacteristic
390C22#1192668511yescharacteristic
391C22#1192669111yescharacteristic
392C22#1192669212yes—
393C22#1192671812yes—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—81no—
398C4—1522no—
399C4—1522no—
400C4#1192669711yescharacteristic
401C4#1192670811yescharacteristic
402C4#1192676212yes—
403C4#1192677311yescharacteristic
404C4#1192679011yescharacteristic
405C4#1192692911yescharacteristic
406C4#1192693011yescharacteristic
407C2—3042no—
408C2#1456273412yes—
409C2#1456274812yes—
410C2#1456464011yescharacteristic
411C2#1456465611yescharacteristic
412C2#1456471311yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC2×C19×Q8⋊C8C2
socleC23×C19#120
prime radicalC2×#10597320C22
hypercenterC2×Q8⋊C8D19
hypocenterC19#10053
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #14568847C2semidirect
5. C2×#11926291C2semidirect
6. #14561475C2semidirect
7. C2×C19×Q8⋊C8C2semidirect
183. C2×Q8⋊C8D19semidirect
278. C19#10053semidirect

Maximal subgroups

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

subgroupindex
C2×#119268912
C2×#119267442
#145688472
#145645612
C2×#119262912
#145614752
C2×C19×Q8⋊C82
#1005319