Finite Group Databasebeta

← #18079102

Subgroups — #18079102

Order 4864.

522 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 107 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#14574407C211yesmaximal, characteristic
2#14566715C211yesmaximal, characteristic
3#14564621C211yesmaximal, characteristic
4#14562208C211yesmaximal, characteristic
5#14561514C211yesmaximal, characteristic
6#14561482C211yesmaximal, characteristic
7C2×C19×#328C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9#11926879C412yescomplemented
10#11926877—21no—
11#11926783—22no—
12#11926700C412yescomplemented
13#11926699—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15#11926448—21no—
16#11926429—21no—
17#11926426—21no—
18#11926417—21no—
19#11926404C2211yescharacteristic
20#11926395—21no—
21C4×C22⋊Dic19—21no—
22C4×C22⋊Dic19C2211yescharacteristic
23#11926311—21no—
24#11926311—21no—
25#11926282—22no—
26C2×C19×C22⋊Q8C2211yescharacteristic
27C2×C19×C22⋊C8C2211yescharacteristic
28C2×C19×#95C2211yescharacteristic
29C19×#328—21no—
30C19×#328—21no—
31C22×Q8×C19C2×C411yescharacteristic
32C23×C4×C19—21no—
33C23×C4×C19C2311yescharacteristic
34C22×Dic38D411yescharacteristic
35C22×C8×C19—21no—
36C19×C22⋊Q8—21no—
37C19×C22⋊Q8—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19C2×C411yescharacteristic
42C2×C22⋊C4×C19—21no—
43C2×C22⋊Dic19—21no—
44C2×C22⋊Dic19—21no—
45C2×C22⋊Dic19D411yescharacteristic
46C2×C22⋊Dic19D411yescharacteristic
47C2×#64528—22no—
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19D411yescharacteristic
50#10597370—21no—
51#10597370—21no—
52#10597370C2×C412yes—
53#10597370D412yes—
54C2×Dic19⋊C4—21no—
55C2×Dic19⋊C4—21no—
56C2×Dic19⋊C4—21no—
57C2×C4×Dic19—21no—
58C2×C4×Dic19—21no—
59C2×C4×Dic19—21no—
60C22×C19⋊C8—21no—
61C19×C22⋊C8—21no—
62C19×C22⋊C8—21no—
63C19×#95—21no—
64C19×#95D411yescharacteristic
65C19×#95D411yescharacteristic
66#10597292—22no—
67C19⋊#95—21no—
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)C2×C412yes—
75#10597267—22no—
76#10597264—22no—
77C24×C19C2×D411yescharacteristic
78C2×Q8×C19—21no—
79C2×Q8×C19—21no—
80C2×Q8×C19—81no—
81C22×C4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—21no—
85C22×C4×C19—42no—
86C22×C4×C19—41no—
87C22×C4×C19—41no—
88C22×C4×C19—81no—
89C22×C4×C19—81no—
90C22×C4×C19C22×C411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19#4111yescharacteristic
95C22×C4×C19#4111yescharacteristic
96C22×Dic19—21no—
97C22×Dic19—21no—
98C22×Dic19—21no—
99C22×Dic19—21no—
100C22×Dic19—41no—
101C2×Dic38—21no—
102C2×Dic38—81no—
103C2×Dic38C22⋊C412yes—
104C2×C8×C19—41no—
105C2×C8×C19—81no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—41no—
109C4⋊C4×C19—41no—
110C22⋊C4×C19—41no—
111C22⋊C4×C19—41no—
112C22⋊Dic19—22no—
113C22⋊Dic19—22no—
114C22⋊Dic19—21no—
115C22⋊Dic19—21no—
116C22⋊Dic19—21no—
117C22⋊Dic19—41no—
118C22⋊Dic19—41no—
119C22⋊Dic19Q1612yescomplemented
120#64528—82no—
121C4⋊Dic19—21no—
122C4⋊Dic19—81no—
123C4⋊Dic19C22⋊C412yes—
124Dic19⋊C4—22no—
125Dic19⋊C4—22no—
126Dic19⋊C4—42no—
127Dic19⋊C4—81no—
128C4×Dic19—42no—
129C4×Dic19—81no—
130C4×Dic19—81no—
131C2×C19⋊C8—22no—
132C2×C19⋊C8—81no—
133#9276—191nomaximal, Sylow
134C23×C19—41no—
135C23×C19—41no—
136C23×C19C4×D411yescharacteristic
137C23×C19#12011yescharacteristic
138C23×C19#12111yescharacteristic
139C23×C19C2×Q1611yescharacteristic
140C23×C19#13511yescharacteristic
141C23×C19#13711yescharacteristic
142C23×C19#13711yescharacteristic
143Q8×C19—42no—
144Q8×C19—81no—
145C2×C4×C19—22no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—82no—
160C2×C4×C19—82no—
161C2×C4×C19—81no—
162C2×C4×C19—81no—
163C2×C4×C19C2×C22⋊C411yescharacteristic
164C2×C4×C19C4×D411yescharacteristic
165C2×C4×C19#12111yescharacteristic
166C2×C4×C19#12311yescharacteristic
167C2×Dic19—22no—
168C2×Dic19—22no—
169C2×Dic19—22no—
170C2×Dic19—41no—
171C2×Dic19—41no—
172C2×Dic19—41no—
173C2×Dic19—41no—
174C2×Dic19—41no—
175C2×Dic19—41no—
176C2×Dic19—41no—
177C2×Dic19—41no—
178C2×Dic19—41no—
179C2×Dic19—81no—
180C2×Dic19—81no—
181C2×Dic19—81no—
182Dic38—42no—
183Dic38—81no—
184C8×C19—81no—
185C19⋊C8—42no—
186#3189—191no—
187#2368—191no—
188#1996—191no—
189#1520—191no—
190C2×#328D1911yescharacteristic
191#1294—191no—
192#1282—191no—
193C22×C19—21no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—41no—
200C22×C19—41no—
201C22×C19—41no—
202C22×C19—41no—
203C22×C19#38611yescharacteristic
204C22×C19C4×Q1611yescharacteristic
205C22×C19#44111yescharacteristic
206C22×C19#45111yescharacteristic
207C22×C19#45211yescharacteristic
208C22×C19#46211yescharacteristic
209C22×C19#46411yescharacteristic
210C4×C19—21no—
211C4×C19—21no—
212C4×C19—21no—
213C4×C19—21no—
214C4×C19—42no—
215C4×C19—81no—
216C4×C19—81no—
217C4×C19—81no—
218Dic19—42no—
219Dic19—42no—
220Dic19—42no—
221Dic19—81no—
222Dic19—161no—
223C2×C22⋊Q8—191no—
224C2×C22⋊Q8C2×D1911yescharacteristic
225#484—192no—
226#484—381no—
227#467—382no—
228#451—192no—
229#451—381no—
230C2×C22⋊C8—191no—
231C2×C22⋊C8C2×D1911yescharacteristic
232#391—381no—
233#387—381no—
234#387—381no—
235#385—381no—
236#380—191no—
237C4×C4⋊C4—381no—
238C4×C22⋊C4—191no—
239C4×C22⋊C4—381no—
240C2×#95C2×D1911yescharacteristic
241#342—381no—
242#342—381no—
243#328—21no—
244#328—21no—
245#328—382no—
246C2×C19—21no—
247C2×C19—21no—
248C2×C19—21no—
249C2×C19—21no—
250C2×C19—21no—
251C2×C19—21no—
252C2×C19#187811yescharacteristic
253C2×C19#190611yescharacteristic
254C2×C19#191311yescharacteristic
255C22×Q8—191no—
256C22×Q8C4×D1911yescharacteristic
257C23×C4—21no—
258C23×C4C22×D1911yescharacteristic
259C2×Q16—382no—
260C22×C8—21no—
261C22×C8—381no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264C22⋊Q8—21no—
265C22⋊Q8—21no—
266C22⋊Q8—192no—
267C22⋊Q8—192no—
268C22⋊Q8—381no—
269C22⋊Q8—381no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—191no—
272C2×C4⋊C4—381no—
273C2×C4⋊C4—381no—
274C2×C4⋊C4—381no—
275C2×C4⋊C4—381no—
276C2×C4⋊C4C4×D1911yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—191no—
279C2×C22⋊C4—191no—
280C2×C22⋊C4—381no—
281C2×C22⋊C4—381no—
282C2×C42—381no—
283C2×C42—381no—
284C2×C42—381no—
285#107—382no—
286#103—382no—
287#103—382no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—192no—
291C22⋊C8—381no—
292#95—21no—
293#95—381no—
294#95—381no—
295#95—381no—
296#95—381no—
297#95—381no—
298#95—381no—
299#95C22⋊D1911yescharacteristic
300#95C22⋊D1911yescharacteristic
301C19#927611yescharacteristic, complemented, Sylow
302C24D4×D1911yescharacteristic
303C2×Q8—21no—
304C2×Q8—21no—
305C2×Q8—81no—
306C2×Q8—192no—
307C2×Q8—381no—
308C2×Q8—1521no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—42no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—81no—
317C22×C4—81no—
318C22×C4—381no—
319C22×C4—381no—
320C22×C4—381no—
321C22×C4—381no—
322C22×C4—761no—
323C22×C4C2×C4×D1911yescharacteristic
324C22×C4#6454111yescharacteristic
325C22×C4D4×D1911yescharacteristic
326C22×C4D4×D1911yescharacteristic
327C22×C4#6454311yescharacteristic
328C22×C4C2×C22⋊D1911yescharacteristic
329Q16—1522no—
330C2×C8—41no—
331C2×C8—81no—
332C2×C8—382no—
333C2×C8—1521no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—192no—
339C4⋊C4—382no—
340C4⋊C4—381no—
341C4⋊C4—382no—
342C4⋊C4—762no—
343C4⋊C4—1521no—
344C4⋊C4—1521no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—192no—
348C22⋊C4—382no—
349C22⋊C4—382no—
350C22⋊C4—381no—
351C22⋊C4—381no—
352C22⋊C4—381no—
353C22⋊C4—761no—
354C22⋊C4—761no—
355C42—762no—
356C42—1521no—
357C42—1521no—
358C23—41no—
359C23—41no—
360C23(C22⋊D19)⋊C411yescharacteristic
361C23#1059733011yescharacteristic
362C23#1059736111yescharacteristic
363C23#1059736211yescharacteristic
364C23Q16×D1911yescharacteristic
365C23#1059736411yescharacteristic
366C23#1059738311yescharacteristic
367Q8—42no—
368Q8—81no—
369Q8—762no—
370Q8—1521no—
371C2×C4—22no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—82no—
386C2×C4—82no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—382no—
390C2×C4—382no—
391C2×C4—382no—
392C2×C4—761no—
393C2×C4—761no—
394C2×C4—761no—
395C2×C4—761no—
396C2×C4—761no—
397C2×C4—761no—
398C2×C4—761no—
399C2×C4—761no—
400C2×C4—761no—
401C2×C4—1521no—
402C2×C4—1521no—
403C2×C4—1521no—
404C2×C4C22⋊C4×D1911yescharacteristic
405C2×C4#1059732911yescharacteristic
406C2×C4C4×C22⋊D1911yescharacteristic
407C2×C4#1059738411yescharacteristic
408C8—81no—
409C8—762no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22#1192642011yescharacteristic
421C22#1192663611yescharacteristic
422C22#1192664811yescharacteristic
423C22#1192669811yescharacteristic
424C22#1192670311yescharacteristic
425C22#1192675311yescharacteristic
426C22#1192676911yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—42no—
432C4—81no—
433C4—81no—
434C4—81no—
435C4—3041no—
436C4—762no—
437C4—762no—
438C4—762no—
439C4—1521no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—21no—
444C2—21no—
445C2—21no—
446C2#1456397311yescharacteristic
447C2#1456413911yescharacteristic
448C2#1456417411yescharacteristic
subgroupG/H
centerC22#11926420
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC2×C19×#328C2
socleC22×C19#386
prime radicalC24×C19C2×D4
cosocleC23×C4×C19C23
hypercenterC2×#328D19
hypocenterC19#9276
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
9. #11926879C4semidirect
12. #11926700C4semidirect
119. C22⋊Dic19Q16semidirect
301. C19#9276semidirect

Maximal subgroups

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

subgroupindex
#145744072
#145667152
#145646212
#145622082
#145615142
#145614822
C2×C19×#3282
#927619