Finite Group Databasebeta

← #18080119

Subgroups — #18080119

Order 4864.

436 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14572631C211yesmaximal, characteristic, complemented
2#14562246C211yesmaximal, characteristic, complemented
3#14562195C211yesmaximal, characteristic, complemented
4#14562173C211yesmaximal, characteristic, complemented
5#14561534C211yesmaximal, characteristic, complemented
6#14561517C211yesmaximal, characteristic, complemented
7C19×#3180C211yesmaximal, characteristic
8#11926675—21no—
9#11926616—21no—
10#11926616—21no—
11D4×C19⋊C8—21no—
12#11926605—21no—
13#11926601C2211yescharacteristic
14#11926597C2211yescharacteristic
15#11926500—21no—
16C2×#10597260C2211yescharacteristic
17#11926410C2211yescharacteristic
18#11926284—21no—
19#11926284—21no—
20#11926281—21no—
21#11926278—21no—
22#11926278—21no—
23#11926278—21no—
24C19×#532C2211yescharacteristic
25C19×#529C2211yescharacteristic
26C19×#501C411yescharacteristic, complemented
27C19×#496C411yescharacteristic, complemented
28C19×#490C411yescharacteristic, complemented
29C19×#489C411yescharacteristic, complemented
30C19×#466—21no—
31C19×#465—21no—
32C19×#442—21no—
33C19×#440—21no—
34C2×C19×#97C2211yescharacteristic
35C2×#41×C19—21no—
36C2×SD16×C19—21no—
37C2×D8×C19—21no—
38C22×C8×C19—21no—
39C19×C4⋊Q8C2×C411yescharacteristic
40C19×#127C2×C411yescharacteristic
41C19×#126—21no—
42C19×#125C2×C411yescharacteristic
43C19×#124—21no—
44C19×#124C2×C411yescharacteristic
45C19×#123—21no—
46C19×C22⋊Q8D411yescharacteristic
47C19×#121—21no—
48C19×#121—21no—
49C19×#121D411yescharacteristic
50C4×Q8×C19D411yescharacteristic
51C4×D4×C19—21no—
52C4×D4×C19—21no—
53C4×D4×C19—21no—
54C4×D4×C19D411yescharacteristic
55C19×#117—21no—
56C2×C42×C19C2311yescharacteristic
57C2×C4⋊Dic19—21no—
58C2×#64520—21no—
59C22×C19⋊C8—21no—
60C22×C19⋊C8—21no—
61C19×#107—21no—
62C19×#106—21no—
63C19×#103—21no—
64C19×#102—21no—
65C19×#102—21no—
66C19×#102—21no—
67C19×#97—21no—
68C19×#97C2×C411yescharacteristic
69C19×#97C2×C411yescharacteristic
70C19⋊#95—21no—
71C19⋊#95—21no—
72C22⋊(C19⋊C8)—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)D411yescharacteristic
76C22⋊(C19⋊C8)D411yescharacteristic
77C4⋊(C19⋊C8)—21no—
78C4⋊(C19⋊C8)—21no—
79C4⋊(C19⋊C8)—21no—
80C4⋊(C19⋊C8)—21no—
81#10597260—21no—
82#10597260—21no—
83#10597260—21no—
84#10597260D411yescharacteristic
85#10597260D411yescharacteristic
86C4×C19⋊C8—21no—
87C4×C19⋊C8—21no—
88#41×C19—81no—
89#41×C19—81no—
90C2×Q8×C19—21no—
91C2×Q8×C19C22⋊C411yescharacteristic
92C2×D4×C19—21no—
93C2×D4×C19—21no—
94C2×D4×C19—21no—
95C2×D4×C19—21no—
96C2×D4×C19—41no—
97C2×D4×C19C22⋊C411yescharacteristic
98C22×C4×C19—21no—
99C22×C4×C19—41no—
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19#4111yescharacteristic
103C22×Dic19—41no—
104SD16×C19—42no—
105D8×C19—42no—
106C2×C8×C19—21no—
107C2×C8×C19—21no—
108C2×C8×C19—42no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19—21no—
113C4⋊C4×C19—21no—
114C4⋊C4×C19—21no—
115C4⋊C4×C19C22⋊C411yescharacteristic
116C4⋊C4×C19C22⋊C411yescharacteristic
117C22⋊C4×C19—21no—
118C22⋊C4×C19—21no—
119C22⋊C4×C19—21no—
120C22⋊C4×C19—21no—
121C22⋊C4×C19—21no—
122C22⋊C4×C19—41no—
123C22⋊C4×C19—41no—
124C42×C19—21no—
125C42×C19C22×C411yescharacteristic
126C42×C19C2×D411yescharacteristic
127C42×C19C2×D411yescharacteristic
128C42×C19#4111yescharacteristic
129C4⋊Dic19—81no—
130#64520—42no—
131C2×C19⋊C8—21no—
132C2×C19⋊C8—21no—
133C2×C19⋊C8—21no—
134C2×C19⋊C8—21no—
135C2×C19⋊C8—42no—
136C2×C19⋊C8—42no—
137C2×C19⋊C8—41no—
138#9432—191nomaximal, Sylow
139C23×C19—21no—
140C23×C19—41no—
141C23×C19#12111yescharacteristic
142Q8×C19—41no—
143Q8×C19—81no—
144D4×C19—41no—
145D4×C19—41no—
146D4×C19—41no—
147D4×C19—41no—
148D4×C19—41no—
149D4×C19—81no—
150D4×C19—81no—
151D4×C19—81no—
152D4×C19—81no—
153C2×C4×C19—21no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—82no—
164C2×C4×C19C2×C22⋊C411yescharacteristic
165C2×C4×C19C4×D411yescharacteristic
166C2×C4×C19C4×D411yescharacteristic
167C2×C4×C19#12011yescharacteristic
168C2×C4×C19#12111yescharacteristic
169C2×C4×C19#12311yescharacteristic
170C2×Dic19—81no—
171C2×Dic19—81no—
172C2×Dic19—81no—
173C8×C19—22no—
174C8×C19—41no—
175C19⋊C8—22no—
176C19⋊C8—41no—
177C19⋊C8—41no—
178C19⋊C8—41no—
179C19⋊C8—81no—
180#3180D1911yescharacteristic
181#2968—191no—
182#1530—191no—
183#1517—191no—
184#1512—191no—
185#1302—191no—
186#1295—191no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—41no—
190C22×C19—41no—
191C22×C19—41no—
192C22×C19—81no—
193C22×C19—81no—
194C22×C19—81no—
195C22×C19#38611yescharacteristic
196C22×C19#47111yescharacteristic
197C22×C19#47211yescharacteristic
198C4×C19—21no—
199C4×C19—21no—
200C4×C19—21no—
201C4×C19—21no—
202C4×C19—21no—
203C4×C19—21no—
204C4×C19—41no—
205C4×C19—41no—
206C4×C19—41no—
207C4×C19—81no—
208Dic19—161no—
209#532C2×D1911yescharacteristic
210#529C2×D1911yescharacteristic
211#501Dic1911yescharacteristic, complemented
212#496Dic1911yescharacteristic, complemented
213#490Dic1911yescharacteristic, complemented
214#489Dic1911yescharacteristic, complemented
215#466—21no—
216#465—21no—
217#446—381no—
218#442—21no—
219#440—21no—
220#435—381no—
221#435—381no—
222C8×D4—381no—
223#433—381no—
224#432—191no—
225#431—191no—
226#405—381no—
227C2×#97—191no—
228C2×#97C2×D1911yescharacteristic
229#382—191no—
230#329—381no—
231#329—381no—
232#328—381no—
233#327—381no—
234#327—381no—
235#327—381no—
236C2×C19—21no—
237C2×C19—21no—
238C2×C19—81no—
239C2×C19—161no—
240C2×C19#188411yescharacteristic
241C2×C19#190611yescharacteristic
242C2×C19#190711yescharacteristic
243C2×#41—21no—
244C2×SD16—21no—
245C2×D8—21no—
246C2×M16—381no—
247C22×C8—21no—
248C22×C8—381no—
249C22×C8—381no—
250C4⋊Q8C2×Dic1911yescharacteristic
251#127C2×Dic1911yescharacteristic
252#126—21no—
253#125C2×Dic1911yescharacteristic
254#124—21no—
255#124C2×Dic1911yescharacteristic
256#123—21no—
257C22⋊Q8C22⋊D1911yescharacteristic
258#121—21no—
259#121—21no—
260#121C22⋊D1911yescharacteristic
261C4×Q8C22⋊D1911yescharacteristic
262C4×D4—21no—
263C4×D4—21no—
264C4×D4—21no—
265C4×D4C22⋊D1911yescharacteristic
266#117—21no—
267C2×C4⋊C4—381no—
268C2×C42C22×D1911yescharacteristic
269#107—21no—
270#106—21no—
271C4⋊C8—381no—
272C4⋊C8—381no—
273C4⋊C8—381no—
274C4⋊C8—381no—
275#103—21no—
276#102—21no—
277#102—21no—
278#102—21no—
279C22⋊C8—191no—
280C22⋊C8—191no—
281C22⋊C8—381no—
282C22⋊C8—381no—
283C22⋊C8—381no—
284#97—21no—
285#97—191no—
286#97—191no—
287#97—381no—
288#97—381no—
289#97—381no—
290#97C2×Dic1911yescharacteristic
291#97C2×Dic1911yescharacteristic
292C4×C8—381no—
293C4×C8—381no—
294#95—381no—
295#95—381no—
296C19#943211yescharacteristic, complemented, Sylow
297#41—81no—
298#41—81no—
299C2×Q8—21no—
300C2×Q8C22⋊Dic1911yescharacteristic
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4C22⋊Dic1911yescharacteristic
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—761no—
310C22×C4D4×D1911yescharacteristic
311C22×C4#6454311yescharacteristic
312C22×C4C2×C22⋊D1911yescharacteristic
313SD16—42no—
314D8—42no—
315M16—762no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—42no—
319C2×C8—381no—
320C2×C8—381no—
321C2×C8—381no—
322C2×C8—381no—
323C2×C8—762no—
324C2×C8—762no—
325C2×C8—761no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—1521no—
333C4⋊C4C22⋊Dic1911yescharacteristic
334C4⋊C4C22⋊Dic1911yescharacteristic
335C22⋊C4—21no—
336C22⋊C4—21no—
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—21no—
343C42D4×D1911yescharacteristic
344C42#6454311yescharacteristic
345C42C22×Dic1911yescharacteristic
346C42C2×C22⋊D1911yescharacteristic
347C23—21no—
348C23—41no—
349C23#1059738511yescharacteristic
350Q8—41no—
351Q8—81no—
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—82no—
372C2×C4—1521no—
373C2×C4—1521no—
374C2×C4—1521no—
375C2×C4D4×Dic1911yescharacteristic
376C2×C4D4×Dic1911yescharacteristic
377C2×C4#1059738111yescharacteristic
378C2×C4#1059738311yescharacteristic
379C2×C4#1059738511yescharacteristic
380C2×C4C2×C22⋊Dic1911yescharacteristic
381C8—22no—
382C8—41no—
383C8—382no—
384C8—761no—
385C8—761no—
386C8—761no—
387C8—1521no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22#1192642411yescharacteristic
397C22#1192680511yescharacteristic
398C22#1192681211yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—81no—
409C4—3041no—
410C2—21no—
411C2—21no—
412C2—81no—
413C2—161no—
414C2#1456401911yescharacteristic
415C2#1456413811yescharacteristic
416C2#1456414511yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3180C2
socleC22×C19#386
cosocleC2×C42×C19C23
hypercenter#3180D19
hypocenterC19#9432
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3180

Complements

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

NH ≅ G/Ntype
1. #14572631C2semidirect
2. #14562246C2semidirect
3. #14562195C2semidirect
4. #14562173C2semidirect
5. #14561534C2semidirect
6. #14561517C2semidirect
26. C19×#501C4semidirect
27. C19×#496C4semidirect
28. C19×#490C4semidirect
29. C19×#489C4semidirect
211. #501Dic19semidirect
212. #496Dic19semidirect
213. #490Dic19semidirect
214. #489Dic19semidirect
296. C19#9432semidirect

Maximal subgroups

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

subgroupindex
#145726312
#145622462
#145621952
#145621732
#145615342
#145615172
C19×#31802
#943219