Finite Group Databasebeta

← #14578127

Subgroups — #14578127

Order 2432.

890 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C19⋊#564C214yesmaximal, complemented
2#11927273C211yesmaximal, characteristic, complemented
3#11927272C212yesmaximal, complemented
4#11927272C211yesmaximal, characteristic, complemented
5#11927271C212yesmaximal, complemented
6#11927270C212yesmaximal, complemented
7#11927269C212yesmaximal, complemented
8#11927269C211yesmaximal, characteristic, complemented
9#11927157C212yesmaximal
10#11927155C212yesmaximal
11#11927153C214yesmaximal
12#11927152C212yesmaximal
13#11927152C212yesmaximal
14#11927099C211yesmaximal, characteristic
15#11927098C211yesmaximal, characteristic
16#11927098C211yesmaximal, characteristic
17C19×#557C211yesmaximal, characteristic, complemented
18C19×C4⋊Q8C2211yescharacteristic
19C19×C4⋊Q8C2212yes—
20C19×#125C2214yes—
21C19×#125C2212yes—
22C4×Q8×C19C2211yescharacteristic
23C4×Q8×C19C2211yescharacteristic
24C4×Q8×C19C2212yes—
25C4×Q8×C19C2212yes—
26#10597392C2211yescharacteristic
27#10597392C2211yescharacteristic
28#10597392C2212yes—
29Q8×Dic19C2212yes—
30Q8×Dic19C2212yes—
31Q8×Dic19C2212yes—
32#10597390C2211yescharacteristic
33#10597390C2211yescharacteristic
34#10597390C2212yes—
35#10597390C2212yes—
36#10597344C2214yes—
37#10597344C2214yes—
38#10597344C2214yes—
39#10597343C2211yescharacteristic
40#10597343C2211yescharacteristic
41#10597343C2212yes—
42#10597342C2212yes—
43#10597342C2212yes—
44#10597338C2212yes—
45#10597336C2212yes—
46#10597336C2214yes—
47#10597336C2214yes—
48#10597336C2214yes—
49#10597336C2212yes—
50#10597336C2212yes—
51#10597335C2212yes—
52#10597335C2212yes—
53#10597335C2214yes—
54#10597335C2214yes—
55#10597335C2214yes—
56#10597335C2214yes—
57#10597335C2214yes—
58#10597335C2214yes—
59#10597335C2214yes—
60#10597334C2211yescharacteristic
61#10597334C2211yescharacteristic
62#10597334C2214yes—
63#10597333C2212yes—
64#10597333C2214yes—
65#10597333C2212yes—
66#10597333C2212yes—
67#10597322C2214yes—
68#10597318C2212yes—
69#10597318C2212yes—
70C42×D19C2211yescharacteristic
71#10597316C2214yes—
72#10597316C2214yes—
73#10597316C2212yes—
74#10597315C2211yescharacteristic
75#10597315C2212yes—
76C4×Dic38C2212yes—
77C4×Dic38C2211yescharacteristic
78C4×Dic38C2211yescharacteristic
79C4×Dic38C2212yes—
80C4×Dic38C2212yes—
81C4×Dic38C2212yes—
82C4×Dic38C2214yes—
83C2×Q8×C19C2311yescharacteristic
84C2×Q8×C19C2311yescharacteristic
85C2×Q8×C19C2312yes—
86C2×C4×D19C2311yescharacteristic
87C2×C4×D19C2311yescharacteristic
88C2×C4×D19C2311yescharacteristic
89C2×Dic38C2311yescharacteristic
90C2×Dic38C2311yescharacteristic
91C2×Dic38C2312yes—
92C2×Dic38C2312yes—
93C2×Dic38C2312yes—
94C4⋊C4×C19C2311yescharacteristic
95C4⋊C4×C19C2311yescharacteristic
96C4⋊C4×C19C2314yes—
97C4⋊C4×C19C2312yes—
98C4⋊C4×C19C2312yes—
99C4⋊C4×C19C2312yes—
100C4⋊C4×C19C2314yes—
101C4⋊C4×C19C2314yes—
102C4⋊C4×C19C2312yes—
103C42×C19C2312yes—
104C42×C19C2314yes—
105C42×C19C2311yescharacteristic
106C42×C19C2312yes—
107(C2×D19)⋊C4C2312yes—
108(C2×D19)⋊C4C2312yes—
109(C2×D19)⋊C4C2314yes—
110(C2×D19)⋊C4C2312yes—
111(C2×D19)⋊C4C2312yes—
112C4⋊Dic19C2312yes—
113C4⋊Dic19C2311yescharacteristic
114C4⋊Dic19C2314yes—
115C4⋊Dic19C2314yes—
116C4⋊Dic19C2314yes—
117C4⋊Dic19C2311yescharacteristic
118C4⋊Dic19C2314yes—
119C4⋊Dic19C2312yes—
120C4⋊Dic19C2312yes—
121C4⋊Dic19C2312yes—
122Dic19⋊C4C2312yes—
123Dic19⋊C4C2314yes—
124Dic19⋊C4C2314yes—
125Dic19⋊C4C2312yes—
126Dic19⋊C4C2312yes—
127Dic19⋊C4C2314yes—
128Dic19⋊C4C2312yes—
129Dic19⋊C4C2314yes—
130Dic19⋊C4C2312yes—
131Dic19⋊C4C2312yes—
132Dic19⋊C4C2314yes—
133Dic19⋊C4C2314yes—
134Dic19⋊C4C2312yes—
135Dic19⋊C4C2312yes—
136Dic19⋊C4C2312yes—
137Dic19⋊C4C2314yes—
138Dic19⋊C4C2312yes—
139C4×Dic19C2311yescharacteristic
140C4×Dic19C2312yes—
141C4×Dic19C2311yescharacteristic
142C4×Dic19C2312yes—
143C4×Dic19C2314yes—
144C4×Dic19C2314yes—
145C4×Dic19C2314yes—
146C4×Dic19C2314yes—
147C4×Dic19C2311yescharacteristic
148C22×D19C2411yescharacteristic
149Q8×C19—22no—
150Q8×C19—22no—
151Q8×C19—24no—
152C2×C4×C19C2414yes—
153C2×C4×C19C2412yes—
154C2×C4×C19C2412yes—
155C2×C4×C19C2411yescharacteristic
156C2×C4×C19C2412yes—
157C2×C4×C19C2412yes—
158C2×C4×C19C2411yescharacteristic
159C2×C4×C19C2411yescharacteristic
160C2×Dic19C2412yes—
161C2×Dic19C2412yes—
162C2×Dic19C2412yes—
163C2×Dic19C2412yes—
164C2×Dic19C2414yes—
165C2×Dic19C2411yescharacteristic
166C2×Dic19C2411yescharacteristic
167C2×Dic19C2411yescharacteristic
168C4×D19—22no—
169C4×D19—22no—
170C4×D19—22no—
171Dic38—22no—
172Dic38—24no—
173Dic38—22no—
174Dic38—24no—
175Dic38—24no—
176#3556—191nomaximal, Sylow
177C22×C19C2511yescharacteristic
178C2×D19—21no—
179C2×D19—21no—
180C2×D19—21no—
181C4×C19—22no—
182C4×C19—22no—
183C4×C19—21no—
184C4×C19—24no—
185C4×C19—22no—
186C4×C19—22no—
187C4×C192−1+412yes—
188C4×C192−1+412yes—
189Dic19—22no—
190Dic19—22no—
191Dic19—22no—
192Dic19—22no—
193Dic19—24no—
194Dic19—21no—
195Dic19—21no—
196Dic192−1+412yes—
197#564—194no—
198#557—192no—
199#557—191no—
200#557—192no—
201#557—192no—
202#557—192no—
203#557—191no—
204#557—191no—
205#557D1911yescharacteristic, complemented
206#541—192no—
207#541—194no—
208#541—192no—
209#541—192no—
210#541—192no—
211#533—191no—
212#533—191no—
213#533—191no—
214C2×C19C2×2−1+411yescharacteristic
215C2×C19C2×2−1+411yescharacteristic
216C2×C19C2×2−1+411yescharacteristic
217D19—41no—
218C4⋊Q8—191no—
219C4⋊Q8—191no—
220C4⋊Q8—192no—
221C4⋊Q8—192no—
222C4⋊Q8—191no—
223C4⋊Q8—191no—
224C4⋊Q8—194no—
225C4⋊Q8—191no—
226C4⋊Q8—192no—
227C4⋊Q8C2×D1911yescharacteristic
228C4⋊Q8C2×D1912yes—
229#126—194no—
230#126—194no—
231#126—194no—
232#126—194no—
233#125—192no—
234#125—192no—
235#125—192no—
236#125—194no—
237#125—192no—
238#125—192no—
239#125—194no—
240#125—194no—
241#125—194no—
242#125—194no—
243#125—194no—
244#125—194no—
245#125—194no—
246#125—194no—
247#125—194no—
248#125—192no—
249#125—194no—
250#125—194no—
251#125C2×D1912yes—
252#125C2×D1914yes—
253C22⋊Q8—191no—
254C22⋊Q8—192no—
255C22⋊Q8—191no—
256C22⋊Q8—192no—
257C22⋊Q8—192no—
258C22⋊Q8—192no—
259C22⋊Q8—191no—
260C22⋊Q8—191no—
261C4×Q8—192no—
262C4×Q8—192no—
263C4×Q8—192no—
264C4×Q8—192no—
265C4×Q8—194no—
266C4×Q8—192no—
267C4×Q8—192no—
268C4×Q8—192no—
269C4×Q8—192no—
270C4×Q8—191no—
271C4×Q8—191no—
272C4×Q8—194no—
273C4×Q8—192no—
274C4×Q8—192no—
275C4×Q8C2×D1911yescharacteristic
276C4×Q8C2×D1911yescharacteristic
277C4×Q8C2×D1912yes—
278C4×Q8C2×D1912yes—
279#117—192no—
280#117—192no—
281#117—192no—
282C2×C42—191no—
283C19#355611yescharacteristic, complemented, Sylow
284C2×Q8—192no—
285C2×Q8—192no—
286C2×Q8—192no—
287C2×Q8—191no—
288C2×Q8—191no—
289C2×Q8C22×D1912yes—
290C2×Q8C22×D1911yescharacteristic
291C2×Q8C22×D1911yescharacteristic
292C22×C4—191no—
293C22×C4—191no—
294C22×C4—191no—
295C4⋊C4—192no—
296C4⋊C4—192no—
297C4⋊C4—192no—
298C4⋊C4—192no—
299C4⋊C4—192no—
300C4⋊C4—192no—
301C4⋊C4—192no—
302C4⋊C4—192no—
303C4⋊C4—192no—
304C4⋊C4—194no—
305C4⋊C4—192no—
306C4⋊C4—194no—
307C4⋊C4—194no—
308C4⋊C4—194no—
309C4⋊C4—194no—
310C4⋊C4—194no—
311C4⋊C4—194no—
312C4⋊C4—192no—
313C4⋊C4—191no—
314C4⋊C4—192no—
315C4⋊C4—191no—
316C4⋊C4—194no—
317C4⋊C4—192no—
318C4⋊C4—192no—
319C4⋊C4—194no—
320C4⋊C4—194no—
321C4⋊C4—194no—
322C4⋊C4C22×D1912yes—
323C4⋊C4C22×D1912yes—
324C4⋊C4C22×D1911yescharacteristic
325C4⋊C4C22×D1914yes—
326C4⋊C4C22×D1911yescharacteristic
327C4⋊C4C22×D1912yes—
328C4⋊C4C22×D1912yes—
329C4⋊C4C22×D1914yes—
330C4⋊C4C22×D1914yes—
331C22⋊C4—192no—
332C22⋊C4—194no—
333C22⋊C4—192no—
334C22⋊C4—192no—
335C22⋊C4—192no—
336C42—191no—
337C42—191no—
338C42—191no—
339C42—194no—
340C42—192no—
341C42—192no—
342C42—194no—
343C42—194no—
344C42—194no—
345C42C22×D1911yescharacteristic
346C42C22×D1912yes—
347C42C22×D1912yes—
348C42C22×D1914yes—
349C23—191no—
350Q8—22no—
351Q8—24no—
352Q8—22no—
353Q8—384no—
354Q8—384no—
355Q8—384no—
356Q8—382no—
357Q8—382no—
358C2×C4—191no—
359C2×C4—192no—
360C2×C4—192no—
361C2×C4—192no—
362C2×C4—192no—
363C2×C4—194no—
364C2×C4—191no—
365C2×C4—191no—
366C2×C4—382no—
367C2×C4—382no—
368C2×C4—382no—
369C2×C4C23×D1914yes—
370C2×C4C23×D1912yes—
371C2×C4C23×D1912yes—
372C2×C4C23×D1911yescharacteristic
373C2×C4C23×D1912yes—
374C2×C4C23×D1912yes—
375C2×C4C23×D1911yescharacteristic
376C2×C4C23×D1911yescharacteristic
377C22—381no—
378C22—381no—
379C22—381no—
380C22C24×D1911yescharacteristic
381C4—21no—
382C4—22no—
383C4—22no—
384C4—24no—
385C4—22no—
386C4—22no—
387C4—192no—
388C4—382no—
389C4—382no—
390C4—381no—
391C4—382no—
392C4—381no—
393C4—382no—
394C4—384no—
395C4#1059743312yes—
396C4#1059743612yes—
397C2—761no—
398C22−1+4×D1911yescharacteristic
399C2C2×#1059743611yescharacteristic
400C2C2×#1059743311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#557C2
prime radicalC22×D19C24
hypercenter#557D19
hypocenterC19#3556
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C19⋊#564C2semidirect
2. #11927273C2semidirect
3. #11927272C2semidirect
4. #11927272C2semidirect
5. #11927271C2semidirect
6. #11927270C2semidirect
7. #11927269C2semidirect
8. #11927269C2semidirect
17. C19×#557C2semidirect
205. #557D19semidirect
283. C19#3556semidirect

Maximal subgroups

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

subgroupindex
C19⋊#5642
#119272732
#119272722
#119272712
#119272702
#119272692
#119271572
#119271552
#119271532
#119271522
#119270992
#119270982
C19×#5572
#355619