Finite Group Databasebeta

← C19×#11175 #18017134

Subgroups — C19×#11175 #18017134

Order 4864.

890 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C19×#413C211yesmaximal, characteristic
2C19×#2879C211yesmaximal, characteristic
3C19×#2297C211yesmaximal, characteristic
4C2×C19×#344C212yesmaximal, complemented
5C19×#1728C212yesmaximal, complemented
6C22×#41×C19C2211yescharacteristic
7C22×M16×C19C2212yes—
8C22×M16×C19C2212yes—
9C2×C19×#117C2211yescharacteristic
10C22×C42×C19C2211yescharacteristic
11C19×#413—24no—
12C2×C19×#101—21no—
13C2×C19×#100—21no—
14C19×#408—24no—
15C19×#407—22no—
16C19×#391—21no—
17C19×#390—21no—
18C19×#386C414yes—
19C4×C22⋊C4×C19—22no—
20C19×#344—24no—
21C19×#336—24no—
22C2×#41×C19—22no—
23C2×#41×C19—22no—
24C2×#41×C19—22no—
25C2×#41×C19—22no—
26C2×#41×C19—22no—
27C2×#41×C19—22no—
28C22×Q8×C19D411yescharacteristic
29C22×D4×C19C2×C412yes—
30C22×D4×C19D411yescharacteristic
31C23×C4×C19C2×C412yes—
32C23×C4×C19D412yes—
33C23×C4×C19C2311yescharacteristic
34C2×M16×C19—22no—
35C2×M16×C19—22no—
36C2×M16×C19—22no—
37C2×M16×C19—22no—
38C2×M16×C19—22no—
39C2×M16×C19—22no—
40C2×M16×C19—22no—
41C2×M16×C19—22no—
42C2×M16×C19—22no—
43C2×M16×C19—22no—
44C2×M16×C19—22no—
45C2×M16×C19D414yes—
46C22×C8×C19—22no—
47C22×C8×C19D414yes—
48C19×#117—22no—
49C19×#117—22no—
50C2×C4⋊C4×C19—21no—
51C2×C22⋊C4×C19—24no—
52C2×C22⋊C4×C19C2×C412yes—
53C2×C42×C19—21no—
54C2×C42×C19—21no—
55C2×C42×C19—21no—
56C2×C42×C19—22no—
57C2×C42×C19—22no—
58C19×#101—24no—
59C19×#100—24no—
60C19×C22⋊C8—28no—
61C19×#95—24no—
62C24×C19C22⋊C412yes—
63C24×C19C22×C411yescharacteristic
64#41×C19—42no—
65#41×C19—42no—
66#41×C19—42no—
67#41×C19—42no—
68#41×C19—42no—
69#41×C19—42no—
70#41×C19—42no—
71#41×C19—42no—
72C2×Q8×C19—21no—
73C2×Q8×C19—22no—
74C2×Q8×C19—22no—
75C2×Q8×C19—21no—
76C2×D4×C19—22no—
77C2×D4×C19—22no—
78C2×D4×C19—24no—
79C2×D4×C19—24no—
80C2×D4×C19—21no—
81C2×D4×C19—22no—
82C2×D4×C19—22no—
83C2×D4×C19—21no—
84C22×C4×C19—22no—
85C22×C4×C19—24no—
86C22×C4×C19—22no—
87C22×C4×C19—24no—
88C22×C4×C19—24no—
89C22×C4×C19—22no—
90C22×C4×C19—22no—
91C22×C4×C19—44no—
92C22×C4×C19C22⋊C412yes—
93C22×C4×C19C2×D412yes—
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D412yes—
96C22×C4×C19C2×D411yescharacteristic
97C22×C4×C19#4112yes—
98C22×C4×C19#4112yes—
99C22×C4×C19#4112yes—
100C22×C4×C19#4112yes—
101M16×C19—24no—
102M16×C19—24no—
103M16×C19—42no—
104M16×C19—42no—
105M16×C19—42no—
106M16×C19—42no—
107M16×C19—42no—
108M16×C19—42no—
109C2×C8×C19—24no—
110C2×C8×C19—24no—
111C2×C8×C19—24no—
112C2×C8×C19—24no—
113C2×C8×C19—42no—
114C2×C8×C19—42no—
115C4⋊C4×C19—41no—
116C4⋊C4×C19—41no—
117C22⋊C4×C19—24no—
118C22⋊C4×C19—48no—
119C42×C19—41no—
120C42×C19—42no—
121C42×C19—42no—
122C42×C19—41no—
123#11175C1911yesmaximal, characteristic, direct product factor, Sylow
124C23×C19—22no—
125C23×C19—22no—
126C23×C19—22no—
127C23×C19—42no—
128C23×C19—44no—
129C23×C19C2×C22⋊C411yescharacteristic
130C23×C19#11711yescharacteristic
131C23×C19#11711yescharacteristic
132C23×C19C4×D412yes—
133C23×C19C4×D412yes—
134Q8×C19—42no—
135Q8×C19—42no—
136D4×C19—44no—
137D4×C19—44no—
138D4×C19—42no—
139D4×C19—42no—
140C2×C4×C19—24no—
141C2×C4×C19—28no—
142C2×C4×C19—22no—
143C2×C4×C19—22no—
144C2×C4×C19—22no—
145C2×C4×C19—42no—
146C2×C4×C19—44no—
147C2×C4×C19—42no—
148C2×C4×C19—44no—
149C2×C4×C19—44no—
150C2×C4×C19—44no—
151C2×C4×C19—42no—
152C2×C4×C19#12011yescharacteristic
153C2×C4×C19#12011yescharacteristic
154C2×C4×C19#12112yes—
155C2×C4×C19#12112yes—
156C2×C4×C19#12112yes—
157C2×C4×C19#12112yes—
158C2×C4×C19#12312yes—
159C2×C4×C19#12312yes—
160C2×C4×C19#12312yes—
161C2×C4×C19#12312yes—
162C2×C4×C19#12311yescharacteristic
163C2×C4×C19#12311yescharacteristic
164C2×C4×C19#12412yes—
165C2×C4×C19#12412yes—
166C2×C4×C19#12612yes—
167C2×C4×C19#12612yes—
168C8×C19—44no—
169C8×C19—44no—
170C2×#413C2×C1911yescharacteristic
171#2879C2×C1911yescharacteristic
172#2297C2×C1911yescharacteristic
173C2×#344C2×C1912yescomplemented
174#1728C2×C1912yescomplemented
175C22×C19—22no—
176C22×C19—24no—
177C22×C19—41no—
178C22×C19—41no—
179C22×C19—42no—
180C22×C19—44no—
181C22×C19—44no—
182C22×C19—42no—
183C22×C19—82no—
184C22×C19#38111yescharacteristic
185C22×C19#38611yescharacteristic
186C22×C19#38611yescharacteristic
187C22×C19#38812yes—
188C22×C19#38812yes—
189C4×C19—44no—
190C4×C19—42no—
191C4×C19—82no—
192C4×C19#39412yes—
193C4×C19#39412yes—
194C4×C19#39712yes—
195C4×C19#39712yes—
196C22×#41C22×C1911yescharacteristic
197C22×M16C22×C1912yes—
198C22×M16C22×C1912yes—
199C2×#117C22×C1911yescharacteristic
200C22×C42C22×C1911yescharacteristic
201#413—24no—
202C2×#101—21no—
203C2×#100—21no—
204#408—24no—
205#407—22no—
206#391—21no—
207#390—21no—
208#386C4×C1914yes—
209C4×C22⋊C4—22no—
210#344—24no—
211#336—24no—
212C2×C19—21no—
213C2×C19—21no—
214C2×C19—22no—
215C2×C19—22no—
216C2×C19—82no—
217C2×C19#144011yescharacteristic
218C2×C19#189112yes—
219C2×#41—22no—
220C2×#41—22no—
221C2×#41—22no—
222C2×#41—22no—
223C2×#41—22no—
224C2×#41—22no—
225C22×Q8D4×C1911yescharacteristic
226C22×D4C2×C4×C1912yes—
227C22×D4D4×C1911yescharacteristic
228C23×C4C2×C4×C1912yes—
229C23×C4D4×C1912yes—
230C23×C4C23×C1911yescharacteristic
231C2×M16—22no—
232C2×M16—22no—
233C2×M16—22no—
234C2×M16—22no—
235C2×M16—22no—
236C2×M16—22no—
237C2×M16—22no—
238C2×M16—22no—
239C2×M16—22no—
240C2×M16—22no—
241C2×M16—22no—
242C2×M16D4×C1914yes—
243C22×C8—22no—
244C22×C8D4×C1914yes—
245#117—22no—
246#117—22no—
247C2×C4⋊C4—21no—
248C2×C22⋊C4—24no—
249C2×C22⋊C4C2×C4×C1912yes—
250C2×C42—21no—
251C2×C42—22no—
252C2×C42—21no—
253C2×C42—21no—
254C2×C42—22no—
255#101—24no—
256#100—24no—
257C22⋊C8—28no—
258#95—24no—
259C19#1117511yescharacteristic, direct product factor, Sylow
260C24C22⋊C4×C1912yes—
261C24C22×C4×C1911yescharacteristic
262#41—42no—
263#41—42no—
264#41—42no—
265#41—42no—
266#41—42no—
267#41—42no—
268#41—42no—
269#41—42no—
270C2×Q8—21no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8—21no—
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—24no—
277C2×D4—24no—
278C2×D4—21no—
279C2×D4—22no—
280C2×D4—22no—
281C2×D4—21no—
282C22×C4—22no—
283C22×C4—24no—
284C22×C4—22no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—44no—
290C22×C4C22⋊C4×C1912yes—
291C22×C4C2×D4×C1912yes—
292C22×C4C2×D4×C1912yes—
293C22×C4C2×D4×C1911yescharacteristic
294C22×C4C2×D4×C1911yescharacteristic
295C22×C4#41×C1912yes—
296C22×C4#41×C1912yes—
297C22×C4#41×C1912yes—
298C22×C4#41×C1912yes—
299M16—24no—
300M16—24no—
301M16—42no—
302M16—42no—
303M16—42no—
304M16—42no—
305M16—42no—
306M16—42no—
307C2×C8—24no—
308C2×C8—24no—
309C2×C8—24no—
310C2×C8—24no—
311C2×C8—42no—
312C2×C8—42no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C22⋊C4—24no—
316C22⋊C4—48no—
317C42—41no—
318C42—42no—
319C42—42no—
320C42—41no—
321C23—22no—
322C23—22no—
323C23—22no—
324C23—42no—
325C23—44no—
326C23C2×C22⋊C4×C1911yescharacteristic
327C23C19×#11711yescharacteristic
328C23C19×#11711yescharacteristic
329C23C4×D4×C1912yes—
330C23C4×D4×C1912yes—
331Q8—42no—
332Q8—42no—
333D4—44no—
334D4—44no—
335D4—42no—
336D4—42no—
337C2×C4—24no—
338C2×C4—28no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—42no—
343C2×C4—44no—
344C2×C4—42no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—44no—
348C2×C4—42no—
349C2×C4C19×#12011yescharacteristic
350C2×C4C19×#12011yescharacteristic
351C2×C4C19×#12112yes—
352C2×C4C19×#12112yes—
353C2×C4C19×#12112yes—
354C2×C4C19×#12112yes—
355C2×C4C19×#12312yes—
356C2×C4C19×#12312yes—
357C2×C4C19×#12312yes—
358C2×C4C19×#12312yes—
359C2×C4C19×#12311yescharacteristic
360C2×C4C19×#12311yescharacteristic
361C2×C4C19×#12412yes—
362C2×C4C19×#12412yes—
363C2×C4C19×#12612yes—
364C2×C4C19×#12612yes—
365C8—44no—
366C8—44no—
367C22—22no—
368C22—24no—
369C22—41no—
370C22—41no—
371C22—42no—
372C22—44no—
373C22—44no—
374C22—42no—
375C22—82no—
376C22C19×#38111yescharacteristic
377C22C19×#38611yescharacteristic
378C22C19×#38611yescharacteristic
379C22C19×#38812yes—
380C22C19×#38812yes—
381C4—44no—
382C4—42no—
383C4—82no—
384C4C19×#39412yes—
385C4C19×#39412yes—
386C4C19×#39712yes—
387C4C19×#39712yes—
388C2—21no—
389C2—21no—
390C2—22no—
391C2—22no—
392C2—82no—
393C2C19×#144011yescharacteristic
394C2C19×#189112yes—
subgroupG/H
centerC2×C4×C19#120
commutatorC24C22×C4×C19
Frattini, cosocleC23×C4C23×C19
socleC22×C19#386
prime radicalC22×#41×C19C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C19×#344C2semidirect
5. C19×#1728C2semidirect
123. #11175C19direct (N × H)
173. C2×#344C2×C19semidirect
174. #1728C2×C19semidirect
259. C19#11175direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C19×#4132
C19×#28792
C19×#22972
C2×C19×#3442
C19×#17282
#1117519