Finite Group Databasebeta

← C19×#9177 #18015136

Subgroups — C19×#9177 #18015136

Order 4864.

494 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
1C19×#3077C211yesmaximal, characteristic
2C19×#2357C211yesmaximal, characteristic
3C19×#1518C211yesmaximal, characteristic, complemented
4C19×#1503C211yesmaximal, characteristic, complemented
5C19×#1478C211yesmaximal, characteristic
6C19×#1303C211yesmaximal, characteristic, complemented
7C19×#1286C211yesmaximal, characteristic, complemented
8C19×#533C2211yescharacteristic
9C2×C4×D4×C19C2211yescharacteristic
10C19×#478—22no—
11C19×#476C412yescomplemented
12C19×#474C412yescomplemented
13C19×#431C2211yescharacteristic
14C19×#431C2211yescharacteristic
15C19×#428—21no—
16C19×#423C2211yescharacteristic
17C19×#418—21no—
18C19×#390—21no—
19C19×#388—22no—
20C19×#382C2211yescharacteristic
21C19×#381—21no—
22C4×C4⋊C4×C19—21no—
23C4×C4⋊C4×C19C2211yescharacteristic
24C4×C22⋊C4×C19—21no—
25C19×#328—21no—
26C19×#328—21no—
27C19×#328—22no—
28C19×D4⋊C8—22no—
29C22×D4×C19D411yescharacteristic
30C23×C4×C19—21no—
31C2×M16×C19—21no—
32C19×C4⋊Q8C2×C411yescharacteristic
33C19×C4⋊Q8C2×C411yescharacteristic
34C19×#125—21no—
35C19×C22⋊Q8—21no—
36C19×C22⋊Q8—21no—
37C4×Q8×C19—21no—
38C4×Q8×C19—21no—
39C4×D4×C19—21no—
40C4×D4×C19—21no—
41C4×D4×C19C2×C412yes—
42C4×D4×C19D412yes—
43C19×#117—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19D411yescharacteristic
47C2×C22⋊C4×C19—21no—
48C2×C22⋊C4×C19—22no—
49C2×C22⋊C4×C19—22no—
50C2×C42×C19—21no—
51C2×C42×C19—22no—
52C2×C42×C19C2311yescharacteristic
53C19×#107—22no—
54C19×#106—22no—
55C19×C4⋊C8—21no—
56C19×C4⋊C8—21no—
57C19×C4⋊C8—21no—
58C19×C4⋊C8C2×C412yes—
59C19×#102—22no—
60C19×#102—22no—
61C19×C22⋊C8—21no—
62C19×C22⋊C8—21no—
63C4×C8×C19—21no—
64C4×C8×C19—21no—
65C19×#95—22no—
66C19×#95—21no—
67C19×#95D411yescharacteristic
68C19×#95D411yescharacteristic
69C19×#95D412yes—
70C24×C19—21no—
71C2×Q8×C19—21no—
72C2×Q8×C19—21no—
73C2×D4×C19—21no—
74C2×D4×C19—21no—
75C2×D4×C19—21no—
76C2×D4×C19—21no—
77C2×D4×C19—21no—
78C2×D4×C19C22⋊C412yes—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—22no—
82C22×C4×C19—22no—
83C22×C4×C19—22no—
84C22×C4×C19—21no—
85C22×C4×C19—82no—
86C22×C4×C19C2×D411yescharacteristic
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89M16×C19—41no—
90M16×C19—41no—
91C2×C8×C19—22no—
92C2×C8×C19—41no—
93C2×C8×C19—41no—
94C4⋊C4×C19—21no—
95C4⋊C4×C19—21no—
96C4⋊C4×C19—21no—
97C4⋊C4×C19—21no—
98C4⋊C4×C19—21no—
99C4⋊C4×C19—42no—
100C4⋊C4×C19—41no—
101C4⋊C4×C19—41no—
102C4⋊C4×C19—41no—
103C4⋊C4×C19—41no—
104C4⋊C4×C19C22⋊C412yes—
105C22⋊C4×C19—22no—
106C22⋊C4×C19—22no—
107C22⋊C4×C19—44no—
108C22⋊C4×C19—41no—
109C22⋊C4×C19—82no—
110C42×C19—41no—
111C42×C19—41no—
112C42×C19—41no—
113C42×C19—82no—
114C42×C19C22×C411yescharacteristic
115C42×C19C2×D411yescharacteristic
116C42×C19#4111yescharacteristic
117C42×C19#4111yescharacteristic
118#9177C1911yesmaximal, characteristic, direct product factor, Sylow
119C23×C19—22no—
120C23×C19—42no—
121C23×C19—42no—
122C23×C19—41no—
123C23×C19—41no—
124C23×C19#12011yescharacteristic
125Q8×C19—81no—
126Q8×C19—81no—
127D4×C19—22no—
128D4×C19—22no—
129D4×C19—41no—
130D4×C19—41no—
131C2×C4×C19—22no—
132C2×C4×C19—22no—
133C2×C4×C19—41no—
134C2×C4×C19—41no—
135C2×C4×C19—41no—
136C2×C4×C19—42no—
137C2×C4×C19—41no—
138C2×C4×C19—42no—
139C2×C4×C19—42no—
140C2×C4×C19—41no—
141C2×C4×C19—41no—
142C2×C4×C19—41no—
143C2×C4×C19—41no—
144C2×C4×C19—41no—
145C2×C4×C19—42no—
146C2×C4×C19—82no—
147C2×C4×C19—82no—
148C2×C4×C19C2×C22⋊C411yescharacteristic
149C2×C4×C19C4×D411yescharacteristic
150C2×C4×C19C4×D411yescharacteristic
151C2×C4×C19#12111yescharacteristic
152C2×C4×C19#12111yescharacteristic
153C2×C4×C19#12311yescharacteristic
154C2×C4×C19#13511yescharacteristic
155C2×C4×C19#13511yescharacteristic
156C2×C4×C19#13711yescharacteristic
157C2×C4×C19#13711yescharacteristic
158C8×C19—42no—
159C8×C19—81no—
160C8×C19—81no—
161#3077C2×C1911yescharacteristic
162#2357C2×C1911yescharacteristic
163#1518C2×C1911yescharacteristic, complemented
164#1503C2×C1911yescharacteristic, complemented
165#1478C2×C1911yescharacteristic
166#1303C2×C1911yescharacteristic, complemented
167#1286C2×C1911yescharacteristic, complemented
168C22×C19—21no—
169C22×C19—21no—
170C22×C19—42no—
171C22×C19—42no—
172C22×C19—42no—
173C22×C19—82no—
174C22×C19—82no—
175C22×C19#38611yescharacteristic
176C22×C19#45211yescharacteristic
177C22×C19#45211yescharacteristic
178C4×C19—21no—
179C4×C19—21no—
180C4×C19—21no—
181C4×C19—21no—
182C4×C19—42no—
183C4×C19—42no—
184C4×C19—81no—
185C4×C19—82no—
186C4×C19—81no—
187C4×C19—81no—
188C4×C19#41611yescharacteristic
189C4×C19#41911yescharacteristic
190C4×C19#48511yescharacteristic
191C4×C19#48511yescharacteristic
192#533C22×C1911yescharacteristic
193C2×C4×D4C22×C1911yescharacteristic
194#478—22no—
195#476C4×C1912yescomplemented
196#474C4×C1912yescomplemented
197#431C22×C1911yescharacteristic
198#431C22×C1911yescharacteristic
199#428—21no—
200#423C22×C1911yescharacteristic
201#418—21no—
202#390—21no—
203#388—22no—
204#382C22×C1911yescharacteristic
205#381—21no—
206C4×C4⋊C4—21no—
207C4×C4⋊C4C22×C1911yescharacteristic
208C4×C22⋊C4—21no—
209#328—21no—
210#328—21no—
211#328—22no—
212D4⋊C8—22no—
213C2×C19—21no—
214C2×C19—21no—
215C2×C19—82no—
216C2×C19#187311yescharacteristic
217C2×C19#190411yescharacteristic
218C2×C19#190611yescharacteristic
219C22×D4D4×C1911yescharacteristic
220C23×C4—21no—
221C2×M16—21no—
222C4⋊Q8C2×C4×C1911yescharacteristic
223C4⋊Q8C2×C4×C1911yescharacteristic
224#125—21no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×D4—21no—
230C4×D4—21no—
231C4×D4C2×C4×C1912yes—
232C4×D4D4×C1912yes—
233#117—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4D4×C1911yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C42—21no—
241C2×C42—22no—
242C2×C42C23×C1911yescharacteristic
243#107—22no—
244#106—22no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8C2×C4×C1912yes—
249#102—22no—
250#102—22no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253C4×C8—21no—
254C4×C8—21no—
255#95—22no—
256#95—21no—
257#95D4×C1911yescharacteristic
258#95D4×C1911yescharacteristic
259#95D4×C1912yes—
260C19#917711yescharacteristic, direct product factor, Sylow
261C24—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4C22⋊C4×C1912yes—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—21no—
276C22×C4—82no—
277C22×C4C2×D4×C1911yescharacteristic
278C22×C4C2×D4×C1911yescharacteristic
279C22×C4C2×D4×C1911yescharacteristic
280M16—41no—
281M16—41no—
282C2×C8—22no—
283C2×C8—41no—
284C2×C8—41no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—42no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4C22⋊C4×C1912yes—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—44no—
299C22⋊C4—41no—
300C22⋊C4—82no—
301C42—41no—
302C42—41no—
303C42—41no—
304C42—82no—
305C42C22×C4×C1911yescharacteristic
306C42C2×D4×C1911yescharacteristic
307C42#41×C1911yescharacteristic
308C42#41×C1911yescharacteristic
309C23—22no—
310C23—42no—
311C23—42no—
312C23—41no—
313C23—41no—
314C23C19×#12011yescharacteristic
315Q8—81no—
316Q8—81no—
317D4—22no—
318D4—22no—
319D4—41no—
320D4—41no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4C2×C22⋊C4×C1911yescharacteristic
339C2×C4C4×D4×C1911yescharacteristic
340C2×C4C4×D4×C1911yescharacteristic
341C2×C4C19×#12111yescharacteristic
342C2×C4C19×#12111yescharacteristic
343C2×C4C19×#12311yescharacteristic
344C2×C4C19×#13511yescharacteristic
345C2×C4C19×#13511yescharacteristic
346C2×C4C19×#13711yescharacteristic
347C2×C4C19×#13711yescharacteristic
348C8—42no—
349C8—81no—
350C8—81no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—42no—
355C22—42no—
356C22—82no—
357C22—82no—
358C22C19×#38611yescharacteristic
359C22C19×#45211yescharacteristic
360C22C19×#45211yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—42no—
366C4—42no—
367C4—81no—
368C4—82no—
369C4—81no—
370C4—81no—
371C4C19×#41611yescharacteristic
372C4C19×#41911yescharacteristic
373C4C19×#48511yescharacteristic
374C4C19×#48511yescharacteristic
375C2—21no—
376C2—21no—
377C2—82no—
378C2C19×#187311yescharacteristic
379C2C19×#190411yescharacteristic
380C2C19×#190611yescharacteristic
subgroupG/H
center, socleC22×C19#386
commutatorC42C22×C4×C19
Frattini, cosocleC2×C42C23×C19
prime radicalC22×D4×C19D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G

Complements

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

NH ≅ G/Ntype
3. C19×#1518C2semidirect
4. C19×#1503C2semidirect
6. C19×#1303C2semidirect
7. C19×#1286C2semidirect
11. C19×#476C4semidirect
12. C19×#474C4semidirect
118. #9177C19direct (N × H)
163. #1518C2×C19semidirect
164. #1503C2×C19semidirect
166. #1303C2×C19semidirect
167. #1286C2×C19semidirect
195. #476C4×C19semidirect
196. #474C4×C19semidirect
260. C19#9177direct (N × H)

Maximal subgroups

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

subgroupindex
C19×#30772
C19×#23572
C19×#15182
C19×#15032
C19×#14782
C19×#13032
C19×#12862
#917719