Finite Group Databasebeta

← #18081901

Subgroups — #18081901

Order 4864.

502 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14574061C211yesmaximal, characteristic
2#14563505C211yesmaximal, characteristic, complemented
3#14562381C211yesmaximal, characteristic, complemented
4#14562131C211yesmaximal, characteristic, complemented
5#14562130C211yesmaximal, characteristic, complemented
6#14562033C211yesmaximal, characteristic, complemented
7C19×#1480C211yesmaximal, characteristic, complemented
8C2×#10597396—21no—
9C2×#10597396—21no—
10#11927094C2211yescharacteristic
11#11926926—21no—
12#11926926—21no—
13#11926923C411yescharacteristic, complemented
14#11926920C411yescharacteristic, complemented
15#11926918C411yescharacteristic, complemented
16#11926916C411yescharacteristic, complemented
17#11926597C2211yescharacteristic
18C2×#10597272—21no—
19C2×C4×C19⋊C8C2211yescharacteristic
20C4×C4⋊Dic19C2211yescharacteristic
21#11926298—21no—
22#11926296—21no—
23#11926294—21no—
24#11926279—22no—
25#11926278—22no—
26#11926271—22no—
27C19×#532C2211yescharacteristic
28C19×#431C2211yescharacteristic
29C2×C19×C4⋊C8C2211yescharacteristic
30C19×D4⋊C8—22no—
31C2×#41×C19—21no—
32C2×#64541—21no—
33C22×C8×C19—21no—
34C19×C4⋊Q8C2×C411yescharacteristic
35C19×#127C2×C411yescharacteristic
36C19×#124—21no—
37C19×#121—21no—
38C19×#121—21no—
39C4×D4×C19—21no—
40C4×D4×C19—21no—
41C2×C42×C19C2311yescharacteristic
42#10597396—42no—
43#10597396—42no—
44#10597396—42no—
45#10597396—42no—
46C2×#64528—21no—
47C2×#64528—21no—
48C2×#64527—21no—
49C2×#64527—21no—
50C2×#64526—21no—
51C2×#64526—21no—
52C2×#64525—21no—
53C2×#64525—21no—
54#10597376—21no—
55#10597376—21no—
56C2×C4⋊Dic19—21no—
57C2×C4×Dic19—21no—
58C22×C19⋊C8D411yescharacteristic
59C22×C19⋊C8D411yescharacteristic
60#10597321—21no—
61#10597320C2×C411yescharacteristic
62C4×D76—21no—
63C4×D76—21no—
64#10597315C2×C411yescharacteristic
65C19×C4⋊C8—21no—
66C19×C4⋊C8—21no—
67C19×C4⋊C8D412yes—
68C19×C22⋊C8—21no—
69C4×C8×C19—21no—
70C19⋊#95D412yes—
71C22⋊(C19⋊C8)—21no—
72#10597272—42no—
73C4⋊(C19⋊C8)—21no—
74C4×C19⋊C8—21no—
75C4×C19⋊C8C2×C411yescharacteristic
76C4×C19⋊C8C2×C411yescharacteristic
77C4×C19⋊C8D411yescharacteristic
78C4×C19⋊C8D411yescharacteristic
79#41×C19—41no—
80#41×C19—41no—
81#41×C19—41no—
82#41×C19—41no—
83C2×Q8×C19—21no—
84C2×D4×C19—21no—
85C2×D4×C19—21no—
86C2×D4×C19—21no—
87C2×D4×C19—41no—
88C22×C4×C19—41no—
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19#4111yescharacteristic
92C2×C22⋊D19—41no—
93C22×Dic19—22no—
94#64541—41no—
95#64541—41no—
96#64541—41no—
97#64541—41no—
98C2×D76—21no—
99C2×D76—21no—
100C2×D76—21no—
101C2×C4×D19—41no—
102C2×Dic38—21no—
103C2×C8×C19—22no—
104C2×C8×C19—41no—
105C2×C8×C19—41no—
106C2×C8×C19—41no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—21no—
109C22⋊C4×C19—41no—
110C22⋊C4×C19—41no—
111C42×C19C22×C411yescharacteristic
112C42×C19C2×D411yescharacteristic
113C42×C19C2×D411yescharacteristic
114C42×C19#4111yescharacteristic
115#64528—42no—
116#64528—42no—
117#64527—42no—
118#64527—42no—
119#64526—42no—
120#64526—42no—
121#64525—42no—
122#64525—42no—
123(C2×D19)⋊C4—41no—
124(C2×D19)⋊C4—41no—
125C4⋊Dic19—21no—
126C4⋊Dic19—21no—
127C4⋊Dic19—42no—
128C4×Dic19—41no—
129C4×Dic19—41no—
130C2×C19⋊C8—21no—
131C2×C19⋊C8—21no—
132C2×C19⋊C8—41no—
133C2×C19⋊C8C22⋊C411yescharacteristic
134C2×C19⋊C8C22⋊C411yescharacteristic
135C2×C19⋊C8C22⋊C411yescharacteristic
136C2×C19⋊C8C22⋊C411yescharacteristic
137C2×C19⋊C8D812yes—
138C2×C19⋊C8SD1612yes—
139#9753—191nomaximal, Sylow
140C23×C19—41no—
141C23×C19#12111yescharacteristic
142C22×D19—41no—
143Q8×C19—41no—
144Q8×C19—41no—
145D4×C19—41no—
146D4×C19—41no—
147D4×C19—42no—
148D4×C19—81no—
149D4×C19—81no—
150D4×C19—81no—
151C2×C4×C19—22no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—81no—
155C2×C4×C19—81no—
156C2×C4×C19C2×C22⋊C411yescharacteristic
157C2×C4×C19C4×D411yescharacteristic
158C2×C4×C19C4×D411yescharacteristic
159C2×C4×C19#12111yescharacteristic
160C2×C4×C19#12411yescharacteristic
161C2×C4×C19#12711yescharacteristic
162C2×C4×C19C2×D811yescharacteristic
163C2×C4×C19C2×SD1611yescharacteristic
164C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
166C22⋊D19—81no—
167C22⋊D19—81no—
168C2×Dic19—42no—
169C2×Dic19—42no—
170C2×Dic19—41no—
171C2×Dic19—42no—
172D76—41no—
173D76—41no—
174D76—42no—
175D76—81no—
176C4×D19—81no—
177C4×D19—81no—
178Dic38—41no—
179Dic38—41no—
180C8×C19—42no—
181C8×C19—81no—
182C19⋊C8—21no—
183C19⋊C8—21no—
184C19⋊C8—81no—
185C19⋊C8#10212yes—
186C19⋊C8#10212yes—
187#3147—191no—
188#1770—191no—
189#1564—191no—
190#1502—191no—
191#1502—191no—
192#1480—191no—
193#1480D1911yescharacteristic, complemented
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—81no—
197C22×C19—81no—
198C22×C19—81no—
199C22×C19#39011yescharacteristic
200C22×C19#45911yescharacteristic
201C22×C19#46011yescharacteristic
202C2×D19—81no—
203C2×D19—81no—
204C2×D19—81no—
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—21no—
208C4×C19—81no—
209C4×C19C2×#10211yescharacteristic
210C4×C19#41811yescharacteristic
211C4×C19#44412yes—
212C4×C19#45911yescharacteristic
213C4×C19#46011yescharacteristic
214Dic19—82no—
215Dic19—81no—
216C2×#135—381no—
217C2×#135—381no—
218#532—191no—
219#532C2×D1911yescharacteristic
220#495—381no—
221#495—381no—
222#494—191no—
223#493—191no—
224#492—191no—
225#492—191no—
226#431—191no—
227#431C2×D1911yescharacteristic
228C2×C4⋊C8C2×D1911yescharacteristic
229C2×#97—381no—
230C2×C4×C8—191no—
231C4×C4⋊C4—191no—
232#336—381no—
233#335—381no—
234#334—381no—
235#327—382no—
236#327—382no—
237D4⋊C8—22no—
238D4⋊C8—382no—
239C2×C19—21no—
240C2×C19—21no—
241C2×C19—161no—
242C2×C19#197511yescharacteristic
243C2×C19#197611yescharacteristic
244C2×C19#198211yescharacteristic
245D19—161no—
246C2×#41—21no—
247C2×#41—381no—
248#135—762no—
249#135—762no—
250#135—762no—
251#135—762no—
252C2×Q16—381no—
253C2×Q16—381no—
254C2×SD16—381no—
255C2×SD16—381no—
256C2×SD16—381no—
257C2×SD16—381no—
258C2×D8—381no—
259C2×D8—381no—
260C22×C8—21no—
261C22×C8—191no—
262C22×C8—191no—
263C4⋊Q8—191no—
264C4⋊Q8C4×D1911yescharacteristic
265#127—191no—
266#127C4×D1911yescharacteristic
267#124—21no—
268#124—381no—
269#121—21no—
270#121—21no—
271#121—381no—
272#121—381no—
273C4×D4—21no—
274C4×D4—21no—
275C4×D4—381no—
276C4×D4—381no—
277C2×C4⋊C4—381no—
278C2×C42—381no—
279C2×C42C22×D1911yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—381no—
283C4⋊C8C22⋊D1912yes—
284C22⋊C8—21no—
285C22⋊C8—381no—
286#97—762no—
287C4×C8—21no—
288C4×C8—191no—
289C4×C8—191no—
290C4×C8—191no—
291C4×C8—191no—
292C4×C8—381no—
293#95—192no—
294C19#975311yescharacteristic, complemented, Sylow
295#41—41no—
296#41—41no—
297#41—41no—
298#41—41no—
299#41—761no—
300#41—761no—
301#41—761no—
302#41—761no—
303C2×Q8—21no—
304C2×Q8—381no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—41no—
309C2×D4—381no—
310C2×D4—381no—
311C2×D4—381no—
312C2×D4—761no—
313C22×C4—41no—
314C22×C4—382no—
315C22×C4—761no—
316C22×C4#6454111yescharacteristic
317C22×C4D4×D1911yescharacteristic
318C22×C4D4×D1911yescharacteristic
319Q16—762no—
320Q16—762no—
321SD16—762no—
322SD16—762no—
323SD16—762no—
324SD16—762no—
325D8—762no—
326D8—762no—
327C2×C8—22no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—191no—
332C2×C8—191no—
333C2×C8—192no—
334C2×C8—192no—
335C2×C8—191no—
336C2×C8—191no—
337C2×C8—381no—
338C2×C8—381no—
339C2×C8—761no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—381no—
343C4⋊C4—381no—
344C4⋊C4—762no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—761no—
348C22⋊C4—761no—
349C42—761no—
350C42—761no—
351C42C2×C4×D1911yescharacteristic
352C42D4×D1911yescharacteristic
353C42#6454311yescharacteristic
354C42C2×C22⋊D1911yescharacteristic
355C23—41no—
356C23—761no—
357C23#1059733011yescharacteristic
358Q8—41no—
359Q8—41no—
360Q8—761no—
361Q8—761no—
362D4—41no—
363D4—41no—
364D4—42no—
365D4—81no—
366D4—81no—
367D4—81no—
368D4—761no—
369D4—761no—
370D4—762no—
371D4—1521no—
372D4—1521no—
373D4—1521no—
374C2×C4—22no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—762no—
380C2×C4—762no—
381C2×C4—761no—
382C2×C4—762no—
383C2×C4—1521no—
384C2×C4—1521no—
385C2×C4C22⋊C4×D1911yescharacteristic
386C2×C4(C22⋊D19)⋊C411yescharacteristic
387C2×C4#1059733111yescharacteristic
388C2×C4D8×D1911yescharacteristic
389C2×C4#1059735711yescharacteristic
390C2×C4SD16×D1911yescharacteristic
391C2×C4#1059736011yescharacteristic
392C2×C4C4×C22⋊D1911yescharacteristic
393C2×C4#1059738511yescharacteristic
394C2×C4#1059738611yescharacteristic
395C8—42no—
396C8—81no—
397C8—192no—
398C8—192no—
399C8—381no—
400C8—381no—
401C8—1521no—
402C22—21no—
403C22—21no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—1521no—
408C22—1521no—
409C22—1521no—
410C22#1192644411yescharacteristic
411C22#1192673811yescharacteristic
412C22#1192674311yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—81no—
417C4—1522no—
418C4—1521no—
419C4#102×D1911yescharacteristic
420C4#1192654711yescharacteristic
421C4#1192666412yes—
422C4#1192673711yescharacteristic
423C4#1192674211yescharacteristic
424C2—21no—
425C2—21no—
426C2—161no—
427C2—3041no—
428C2#1456452711yescharacteristic
429C2#1456453211yescharacteristic
430C2#1456456011yescharacteristic
subgroupG/H
centerC2×C4#10597385
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1480C2
socleC22×C19#390
prime radical#14574061C2
cosocleC2×C42×C19C23
hypercenter#1480D19
hypocenterC19#9753
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1480

Complements

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

NH ≅ G/Ntype
2. #14563505C2semidirect
3. #14562381C2semidirect
4. #14562131C2semidirect
5. #14562130C2semidirect
6. #14562033C2semidirect
7. C19×#1480C2semidirect
13. #11926923C4semidirect
14. #11926920C4semidirect
15. #11926918C4semidirect
16. #11926916C4semidirect
193. #1480D19semidirect
294. C19#9753semidirect

Maximal subgroups

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

subgroupindex
#145740612
#145635052
#145623812
#145621312
#145621302
#145620332
C19×#14802
#975319