Finite Group Databasebeta

← #18074972

Subgroups — #18074972

Order 4864.

728 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14564468C211yesmaximal, characteristic, complemented
2#14562297C211yesmaximal, characteristic, complemented
3#14562121C212yesmaximal, complemented
4#14562100C212yesmaximal, complemented
5C19×#3529C211yesmaximal, characteristic
6#11926597C2212yescomplemented
7#11926568C2211yescharacteristic, complemented
8C2×#10597294—21no—
9C2×#10597294—21no—
10#11926390C2211yescharacteristic, complemented
11#11926293—21no—
12#11926288—21no—
13#11926281—22no—
14#11926278—22no—
15Q8⋊(C19⋊C8)—22no—
16D4⋊(C19⋊C8)—22no—
17C19×#563—21no—
18C19×#563C411yescharacteristic, complemented
19C19×#562—22no—
20C19×#562C412yescomplemented
21C19×H(3,𝔽4)C411yescharacteristic, complemented
22C19×#560—21no—
23C19×#560—22no—
24C19×#532—21no—
25C19×#532C2211yescharacteristic
26C19×#529—22no—
27C19×#529C2212yes—
28C19×#525—21no—
29C19×#525—22no—
30C2×#41×C19—21no—
31C2×#41×C19D411yescharacteristic
32C2×#41×C19D411yescharacteristic
33C23×C4×C19—21no—
34C19×C4⋊Q8—21no—
35C19×C4⋊Q8D411yescharacteristic
36C19×#127—21no—
37C19×#127D411yescharacteristic
38C19×#126—22no—
39C19×#126—22no—
40C19×#126—22no—
41C19×#125—22no—
42C19×#125C2×C412yes—
43C19×#124—21no—
44C19×#124—22no—
45C19×#124—21no—
46C19×#124C2×C412yes—
47C19×#124C2×C411yescharacteristic
48C19×#124C2×C411yescharacteristic
49C19×#123—22no—
50C19×#123—21no—
51C19×#123—22no—
52C19×#123—21no—
53C19×#123—22no—
54C19×#123—22no—
55C19×#123—22no—
56C19×C22⋊Q8—22no—
57C19×C22⋊Q8—22no—
58C19×C22⋊Q8—22no—
59C19×C22⋊Q8—22no—
60C19×C22⋊Q8D412yes—
61C19×#121—22no—
62C19×#121—22no—
63C19×#121—22no—
64C19×#121—22no—
65C19×#121—22no—
66C19×#121—22no—
67C19×#121—22no—
68C19×#121D412yes—
69C19×#120—21no—
70C19×#120—22no—
71C19×#120—21no—
72C19×#120—22no—
73C4×Q8×C19D412yes—
74C4×D4×C19—22no—
75C4×D4×C19—22no—
76C4×D4×C19—22no—
77C4×D4×C19—22no—
78C4×D4×C19D412yes—
79C19×#117—21no—
80C19×#117—22no—
81C2×C42×C19—21no—
82C2×C42×C19C2311yescharacteristic
83C2×C4×Dic19—21no—
84C2×#64520—21no—
85#10597294—42no—
86#10597294—42no—
87C19⋊#95—22no—
88C22⋊(C19⋊C8)—22no—
89C4⋊(C19⋊C8)—22no—
90C4⋊(C19⋊C8)—22no—
91C4×C19⋊C8—22no—
92C24×C19—21no—
93#41×C19—41no—
94#41×C19—41no—
95#41×C19—41no—
96#41×C19—41no—
97#41×C19—81no—
98#41×C19—81no—
99C2×Q8×C19—21no—
100C2×Q8×C19C22⋊C412yes—
101C2×Q8×C19C22⋊C411yescharacteristic
102C2×Q8×C19C22⋊C411yescharacteristic
103C2×D4×C19—22no—
104C2×D4×C19—22no—
105C2×D4×C19—21no—
106C2×D4×C19—22no—
107C2×D4×C19—22no—
108C2×D4×C19—21no—
109C2×D4×C19—21no—
110C2×D4×C19—22no—
111C2×D4×C19C22⋊C412yes—
112C2×D4×C19C22⋊C411yescharacteristic
113C2×D4×C19C22⋊C411yescharacteristic
114C22×C4×C19—22no—
115C22×C4×C19—22no—
116C22×C4×C19—21no—
117C22×C4×C19—21no—
118C22×C4×C19—21no—
119C22×C4×C19—22no—
120C22×C4×C19—81no—
121C22×C4×C19—81no—
122C22×C4×C19C2×D411yescharacteristic
123C22×C4×C19C2×D412yes—
124C22×Dic19—41no—
125C4⋊C4×C19—22no—
126C4⋊C4×C19—22no—
127C4⋊C4×C19—22no—
128C4⋊C4×C19—22no—
129C4⋊C4×C19—22no—
130C4⋊C4×C19—22no—
131C4⋊C4×C19—22no—
132C4⋊C4×C19—22no—
133C4⋊C4×C19C22⋊C412yes—
134C4⋊C4×C19C22⋊C412yes—
135C22⋊C4×C19—21no—
136C22⋊C4×C19—21no—
137C22⋊C4×C19—22no—
138C22⋊C4×C19—22no—
139C22⋊C4×C19—22no—
140C22⋊C4×C19—22no—
141C22⋊C4×C19—22no—
142C22⋊C4×C19—22no—
143C22⋊C4×C19—22no—
144C22⋊C4×C19—22no—
145C22⋊C4×C19—22no—
146C22⋊C4×C19—22no—
147C22⋊C4×C19—22no—
148C42×C19—21no—
149C42×C19—21no—
150C42×C19—22no—
151C42×C19C22×C411yescharacteristic
152C42×C19C2×D412yes—
153C42×C19C2×D411yescharacteristic
154C4×Dic19—22no—
155C4×Dic19—41no—
156#64520—41no—
157#64520—41no—
158C2×C19⋊C8—42no—
159C2×C19⋊C8—41no—
160#8504—191nomaximal, Sylow
161C23×C19—21no—
162C23×C19—22no—
163C23×C19—21no—
164C23×C19—81no—
165C23×C19—82no—
166C23×C19#12011yescharacteristic
167Q8×C19—42no—
168Q8×C19—41no—
169Q8×C19—41no—
170Q8×C19—81no—
171D4×C19—42no—
172D4×C19—41no—
173D4×C19—41no—
174D4×C19—82no—
175D4×C19—82no—
176D4×C19—81no—
177D4×C19—81no—
178D4×C19—82no—
179D4×C19—82no—
180D4×C19—82no—
181D4×C19—81no—
182C2×C4×C19—21no—
183C2×C4×C19—21no—
184C2×C4×C19—22no—
185C2×C4×C19—22no—
186C2×C4×C19—21no—
187C2×C4×C19—21no—
188C2×C4×C19—22no—
189C2×C4×C19—42no—
190C2×C4×C19—41no—
191C2×C4×C19—42no—
192C2×C4×C19—41no—
193C2×C4×C19—41no—
194C2×C4×C19—42no—
195C2×C4×C19—41no—
196C2×C4×C19—82no—
197C2×C4×C19—82no—
198C2×C4×C19—81no—
199C2×C4×C19C2×C22⋊C412yes—
200C2×C4×C19C2×C22⋊C411yescharacteristic
201C2×C4×C19#12012yes—
202C2×C4×C19#12011yescharacteristic
203C2×Dic19—42no—
204C2×Dic19—82no—
205C19⋊C8—82no—
206C19⋊C8—81no—
207#3529D1911yescharacteristic
208#1963—191no—
209#1543—191no—
210#1500—192no—
211#1495—192no—
212C22×C19—21no—
213C22×C19—22no—
214C22×C19—41no—
215C22×C19—42no—
216C22×C19—41no—
217C22×C19—42no—
218C22×C19—42no—
219C22×C19—42no—
220C22×C19—42no—
221C22×C19—84no—
222C22×C19#37911yescharacteristic
223C4×C19—21no—
224C4×C19—22no—
225C4×C19—22no—
226C4×C19—41no—
227C4×C19—42no—
228C4×C19—41no—
229C4×C19—42no—
230C4×C19—42no—
231C4×C19#45311yescharacteristic
232C4×C19#45511yescharacteristic
233Dic19—82no—
234#563—21no—
235#563Dic1911yescharacteristic, complemented
236#562—22no—
237#562Dic1912yescomplemented
238H(3,𝔽4)Dic1911yescharacteristic, complemented
239#560—21no—
240#560—22no—
241#532—21no—
242#532C2×D1911yescharacteristic
243#529—22no—
244#529C2×D1912yes—
245#525—21no—
246#525—22no—
247#431—192no—
248#423—191no—
249C2×#104—381no—
250C2×#104—381no—
251#376—191no—
252#333—381no—
253#331—381no—
254#328—382no—
255#327—382no—
256Q8⋊C8—382no—
257D4⋊C8—382no—
258C2×C19—41no—
259C2×C19—81no—
260C2×C19—81no—
261C2×C19—82no—
262C2×C19#179211yescharacteristic
263C2×C19#179412yes—
264C2×#41—21no—
265C2×#41C22⋊D1911yescharacteristic
266C2×#41C22⋊D1911yescharacteristic
267C23×C4—21no—
268C2×M16—381no—
269C4⋊Q8—21no—
270C4⋊Q8C22⋊D1911yescharacteristic
271#127—21no—
272#127C22⋊D1911yescharacteristic
273#126—22no—
274#126—22no—
275#126—22no—
276#125—22no—
277#125C2×Dic1912yes—
278#124—21no—
279#124—22no—
280#124—21no—
281#124C2×Dic1912yes—
282#124C2×Dic1911yescharacteristic
283#124C2×Dic1911yescharacteristic
284#123—22no—
285#123—21no—
286#123—22no—
287#123—21no—
288#123—22no—
289#123—22no—
290#123—22no—
291C22⋊Q8—22no—
292C22⋊Q8—22no—
293C22⋊Q8—22no—
294C22⋊Q8—22no—
295C22⋊Q8C22⋊D1912yes—
296#121—22no—
297#121—22no—
298#121—22no—
299#121—22no—
300#121—22no—
301#121—22no—
302#121—22no—
303#121C22⋊D1912yes—
304#120—21no—
305#120—22no—
306#120—21no—
307#120—22no—
308C4×Q8C22⋊D1912yes—
309C4×D4—22no—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4C22⋊D1912yes—
314#117—21no—
315#117—22no—
316C2×C42—21no—
317C2×C42—381no—
318C2×C42C22×D1911yescharacteristic
319C4⋊C8—382no—
320C4⋊C8—382no—
321#104—762no—
322#104—762no—
323C22⋊C8—382no—
324C4×C8—382no—
325#95—382no—
326C19#850411yescharacteristic, complemented, Sylow
327C24—21no—
328#41—41no—
329#41—41no—
330#41—41no—
331#41—41no—
332#41—81no—
333#41—81no—
334C2×Q8—21no—
335C2×Q8C22⋊Dic1912yes—
336C2×Q8C22⋊Dic1911yescharacteristic
337C2×Q8C22⋊Dic1911yescharacteristic
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—21no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—22no—
346C2×D4C22⋊Dic1912yes—
347C2×D4C22⋊Dic1911yescharacteristic
348C2×D4C22⋊Dic1911yescharacteristic
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—81no—
356C22×C4—81no—
357C22×C4—761no—
358C22×C4C2×C22⋊D1911yescharacteristic
359C22×C4C2×C22⋊D1912yes—
360M16—761no—
361M16—761no—
362C2×C8—762no—
363C2×C8—761no—
364C4⋊C4—22no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4C22⋊Dic1912yes—
373C4⋊C4C22⋊Dic1912yes—
374C22⋊C4—21no—
375C22⋊C4—21no—
376C22⋊C4—22no—
377C22⋊C4—22no—
378C22⋊C4—22no—
379C22⋊C4—22no—
380C22⋊C4—22no—
381C22⋊C4—22no—
382C22⋊C4—22no—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C42—21no—
388C42—21no—
389C42—22no—
390C42—382no—
391C42—761no—
392C42C22×Dic1911yescharacteristic
393C42C2×C22⋊D1911yescharacteristic
394C42C2×C22⋊D1912yes—
395C23—21no—
396C23—22no—
397C23—21no—
398C23—81no—
399C23—82no—
400C23#1059739911yescharacteristic
401Q8—41no—
402Q8—41no—
403Q8—42no—
404Q8—81no—
405D4—41no—
406D4—41no—
407D4—42no—
408D4—82no—
409D4—81no—
410D4—81no—
411D4—82no—
412D4—82no—
413D4—81no—
414D4—82no—
415D4—82no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—82no—
431C2×C4—81no—
432C2×C4—82no—
433C2×C4—762no—
434C2×C4—1522no—
435C2×C4C2×C22⋊Dic1912yes—
436C2×C4C2×C22⋊Dic1911yescharacteristic
437C2×C4#1059739912yes—
438C2×C4#1059739911yescharacteristic
439C8—1522no—
440C8—1521no—
441C22—21no—
442C22—22no—
443C22—41no—
444C22—42no—
445C22—41no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—84no—
451C22#1192640011yescharacteristic
452C4—21no—
453C4—22no—
454C4—22no—
455C4—41no—
456C4—42no—
457C4—41no—
458C4—42no—
459C4—42no—
460C4—1522no—
461C4#1192671211yescharacteristic
462C4#1192672211yescharacteristic
463C2—41no—
464C2—81no—
465C2—82no—
466C2—81no—
467C2#1456358911yescharacteristic
468C2#1456359912yes—
subgroupG/H
centerC2×C4#10597399
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
Fitting, prime radicalC19×#3529C2
socleC22×C19#379
cosocleC2×C42×C19C23
hypercenter#3529D19
hypocenterC19#8504
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3529

Complements

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

NH ≅ G/Ntype
1. #14564468C2semidirect
2. #14562297C2semidirect
3. #14562121C2semidirect
4. #14562100C2semidirect
6. #11926597C22semidirect
7. #11926568C22semidirect
10. #11926390C22semidirect
18. C19×#563C4semidirect
20. C19×#562C4semidirect
21. C19×H(3,𝔽4)C4semidirect
235. #563Dic19semidirect
237. #562Dic19semidirect
238. H(3,𝔽4)Dic19semidirect
326. C19#8504semidirect

Maximal subgroups

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

subgroupindex
#145644682
#145622972
#145621212
#145621002
C19×#35292
#850419