Finite Group Databasebeta

← #18085425

Subgroups — #18085425

Order 4864.

602 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 101 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#14571975C211yesmaximal, characteristic
3#14571969C211yesmaximal, characteristic
4#14563701C211yesmaximal, characteristic
5#14562208C211yesmaximal, characteristic
6#14561502C211yesmaximal, characteristic
7C19×#1520C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9C22×C4×Dic19C2211yescharacteristic
10#11926879—21no—
11#11926877—21no—
12#11926783—22no—
13#11926700—21no—
14#11926699—21no—
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16#11926451—21no—
17#11926449—21no—
18#11926443—21no—
19#11926440—21no—
20#11926429—22no—
21#11926425—22no—
22#11926419—21no—
23#11926416—21no—
24#11926405—21no—
25#11926405—21no—
26#11926404C2211yescharacteristic
27#11926298—22no—
28#11926282—22no—
29C2×C19×C22⋊Q8C2211yescharacteristic
30C2×C19×C22⋊C8C2211yescharacteristic
31C19×#380C2211yescharacteristic
32C19×#328—22no—
33C22×Q8×C19D411yescharacteristic
34C23×C4×C19C2311yescharacteristic
35C23×Dic19D411yescharacteristic
36C23×Dic19D411yescharacteristic
37C22×Dic38D411yescharacteristic
38C22×C8×C19—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C19×C22⋊Q8—21no—
42C19×C22⋊Q8—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19D411yescharacteristic
46C2×C22⋊C4×C19—21no—
47C2×C22⋊C4×C19—21no—
48C2×C22⋊Dic19—21no—
49C2×C22⋊Dic19—21no—
50C2×#64528—22no—
51C2×C4⋊Dic19—22no—
52C2×C4⋊Dic19—21no—
53C2×C4⋊Dic19D411yescharacteristic
54#10597370—21no—
55#10597370—21no—
56#10597370—21no—
57#10597370—21no—
58C2×Dic19⋊C4—22no—
59C2×Dic19⋊C4—21no—
60C2×C4×Dic19—21no—
61C2×C4×Dic19—21no—
62C2×C4×Dic19—21no—
63C2×C4×Dic19—21no—
64C2×C4×Dic19—21no—
65C2×C4×Dic19—21no—
66C22×C19⋊C8D412yes—
67C19×C22⋊C8—21no—
68C19×C22⋊C8—21no—
69C19×#95D412yes—
70#10597292—22no—
71C19⋊#95—22no—
72C19⋊#95—22no—
73C19⋊#95—22no—
74C19⋊#95—22no—
75C19⋊#95—22no—
76C19⋊#95—22no—
77C19⋊#95D412yes—
78C22⋊(C19⋊C8)—21no—
79C22⋊(C19⋊C8)—21no—
80#10597267—22no—
81#10597264—22no—
82C24×C19C2×D411yescharacteristic
83C2×Q8×C19—21no—
84C2×Q8×C19—21no—
85C2×Q8×C19—42no—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—22no—
89C22×C4×C19—42no—
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19#4111yescharacteristic
96C22×Dic19—21no—
97C22×Dic19—21no—
98C22×Dic19—21no—
99C22×Dic19—21no—
100C22×Dic19—21no—
101C22×Dic19—21no—
102C22×Dic19—21no—
103C22×Dic19—21no—
104C22×Dic19—21no—
105C22×Dic19—21no—
106C22×Dic19—22no—
107C22×Dic19—21no—
108C22×Dic19—42no—
109C22×Dic19Q1612yescomplemented
110C2×Dic38—21no—
111C2×Dic38—21no—
112C2×Dic38—42no—
113C2×C8×C19—42no—
114C2×C8×C19—41no—
115C4⋊C4×C19—21no—
116C4⋊C4×C19—21no—
117C4⋊C4×C19—42no—
118C4⋊C4×C19—41no—
119C4⋊C4×C19—41no—
120C22⋊C4×C19—41no—
121C22⋊C4×C19—41no—
122C22⋊C4×C19—41no—
123C22⋊C4×C19—41no—
124C22⋊Dic19—41no—
125C22⋊Dic19—41no—
126C22⋊Dic19—41no—
127C22⋊Dic19—41no—
128#64528—82no—
129C4⋊Dic19—21no—
130C4⋊Dic19—21no—
131C4⋊Dic19—44no—
132C4⋊Dic19—42no—
133Dic19⋊C4—44no—
134Dic19⋊C4—41no—
135Dic19⋊C4—41no—
136C4×Dic19—41no—
137C4×Dic19—41no—
138C4×Dic19—41no—
139C4×Dic19—41no—
140C2×C19⋊C8—22no—
141C2×C19⋊C8—42no—
142#10325—191nomaximal, Sylow
143C23×C19—41no—
144C23×C19—41no—
145C23×C19#12011yescharacteristic
146C23×C19#12011yescharacteristic
147C23×C19#12111yescharacteristic
148C23×C19C2×Q1611yescharacteristic
149C23×C19#13511yescharacteristic
150C23×C19#13711yescharacteristic
151C23×C19#13711yescharacteristic
152Q8×C19—42no—
153Q8×C19—81no—
154C2×C4×C19—22no—
155C2×C4×C19—22no—
156C2×C4×C19—22no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—42no—
161C2×C4×C19—42no—
162C2×C4×C19—42no—
163C2×C4×C19—42no—
164C2×C4×C19—41no—
165C2×C4×C19—41no—
166C2×C4×C19—42no—
167C2×C4×C19#12011yescharacteristic
168C2×C4×C19#12111yescharacteristic
169C2×C4×C19#12111yescharacteristic
170C2×C4×C19#12711yescharacteristic
171C2×Dic19—22no—
172C2×Dic19—22no—
173C2×Dic19—22no—
174C2×Dic19—22no—
175C2×Dic19—22no—
176C2×Dic19—22no—
177C2×Dic19—41no—
178C2×Dic19—41no—
179C2×Dic19—41no—
180C2×Dic19—41no—
181C2×Dic19—41no—
182C2×Dic19—41no—
183C2×Dic19—41no—
184C2×Dic19—41no—
185C2×Dic19—42no—
186C2×Dic19—42no—
187C2×Dic19—42no—
188C2×Dic19—42no—
189C2×Dic19—41no—
190C2×Dic19—41no—
191C2×Dic19—42no—
192Dic38—42no—
193Dic38—81no—
194C8×C19—81no—
195C19⋊C8—42no—
196#3189—191no—
197#2855—191no—
198#2855—191no—
199#1817—191no—
200#1520—191no—
201#1520D1911yescharacteristic
202#1289—191no—
203C22×C19—21no—
204C22×C19—21no—
205C22×C19—21no—
206C22×C19—21no—
207C22×C19—21no—
208C22×C19—21no—
209C22×C19—41no—
210C22×C19—41no—
211C22×C19—41no—
212C22×C19—41no—
213C22×C19#39211yescharacteristic
214C22×C19#45111yescharacteristic
215C22×C19#45111yescharacteristic
216C22×C19#45211yescharacteristic
217C22×C19#45211yescharacteristic
218C22×C19#46711yescharacteristic
219C22×C19#47011yescharacteristic
220C4×C19—21no—
221C4×C19—21no—
222C4×C19—21no—
223C4×C19—82no—
224C4×C19—81no—
225C4×C19—81no—
226C4×C19#45812yes—
227Dic19—42no—
228Dic19—42no—
229Dic19—82no—
230Dic19—81no—
231Dic19—81no—
232C2×C22⋊Q8—191no—
233C2×C22⋊Q8C2×D1911yescharacteristic
234C22×C42—191no—
235#484—381no—
236#484—381no—
237#467—382no—
238#451—381no—
239#451—381no—
240C2×C22⋊C8—191no—
241C2×C22⋊C8C2×D1911yescharacteristic
242#391—381no—
243#391—381no—
244#389—381no—
245#389—381no—
246#387—382no—
247#387—382no—
248#385—381no—
249#385—381no—
250#381—381no—
251#381—381no—
252#380—191no—
253#380C2×D1911yescharacteristic
254#336—382no—
255#328—22no—
256#328—382no—
257C2×C19—21no—
258C2×C19—21no—
259C2×C19—21no—
260C2×C19—21no—
261C2×C19—21no—
262C2×C19—21no—
263C2×C19#200111yescharacteristic
264C2×C19#201011yescharacteristic
265C2×C19#202211yescharacteristic
266C22×Q8—191no—
267C22×Q8D7611yescharacteristic
268C23×C4—191no—
269C23×C4—191no—
270C23×C4C22×D1911yescharacteristic
271C2×Q16—382no—
272C22×C8—21no—
273C22×C8—192no—
274C22⋊Q8—21no—
275C22⋊Q8—21no—
276C22⋊Q8—21no—
277C22⋊Q8—21no—
278C22⋊Q8—381no—
279C22⋊Q8—381no—
280C22⋊Q8—381no—
281C22⋊Q8—381no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—191no—
285C2×C4⋊C4—382no—
286C2×C4⋊C4—382no—
287C2×C4⋊C4—381no—
288C2×C4⋊C4—381no—
289C2×C4⋊C4D7611yescharacteristic
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—381no—
293C2×C22⋊C4—381no—
294C2×C42—381no—
295C2×C42—381no—
296C2×C42—381no—
297C2×C42—381no—
298C2×C42—381no—
299C2×C42—381no—
300#107—382no—
301#103—382no—
302#103—382no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8—381no—
306C22⋊C8—381no—
307#95—192no—
308#95—382no—
309#95—382no—
310#95—382no—
311#95—382no—
312#95—382no—
313#95—382no—
314#95C22⋊D1912yes—
315C19#1032511yescharacteristic, complemented, Sylow
316C24D4×D1911yescharacteristic
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—42no—
320C2×Q8—381no—
321C2×Q8—381no—
322C2×Q8—762no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—42no—
327C22×C4—192no—
328C22×C4—381no—
329C22×C4—381no—
330C22×C4—381no—
331C22×C4—381no—
332C22×C4—381no—
333C22×C4—381no—
334C22×C4—381no—
335C22×C4—381no—
336C22×C4—381no—
337C22×C4—381no—
338C22×C4—381no—
339C22×C4—382no—
340C22×C4—762no—
341C22×C4C2×D7611yescharacteristic
342C22×C4#6454111yescharacteristic
343C22×C4D4×D1911yescharacteristic
344C22×C4D4×D1911yescharacteristic
345C22×C4D4×D1911yescharacteristic
346C22×C4C2×C22⋊D1911yescharacteristic
347Q16—1522no—
348C2×C8—42no—
349C2×C8—41no—
350C2×C8—382no—
351C2×C8—762no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—42no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—381no—
358C4⋊C4—381no—
359C4⋊C4—762no—
360C4⋊C4—764no—
361C4⋊C4—764no—
362C4⋊C4—761no—
363C4⋊C4—761no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—41no—
368C22⋊C4—761no—
369C22⋊C4—761no—
370C22⋊C4—761no—
371C22⋊C4—761no—
372C42—761no—
373C42—761no—
374C42—761no—
375C42—761no—
376C23—41no—
377C23—41no—
378C23#1059732811yescharacteristic
379C23#1059733011yescharacteristic
380C23#1059736111yescharacteristic
381C23#1059736211yescharacteristic
382C23Q16×D1911yescharacteristic
383C23#1059736411yescharacteristic
384C23#1059738311yescharacteristic
385Q8—42no—
386Q8—81no—
387Q8—762no—
388Q8—1521no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—382no—
403C2×C4—382no—
404C2×C4—382no—
405C2×C4—382no—
406C2×C4—382no—
407C2×C4—382no—
408C2×C4—761no—
409C2×C4—761no—
410C2×C4—761no—
411C2×C4—761no—
412C2×C4—761no—
413C2×C4—761no—
414C2×C4—761no—
415C2×C4—761no—
416C2×C4—762no—
417C2×C4—762no—
418C2×C4—762no—
419C2×C4—762no—
420C2×C4—761no—
421C2×C4—761no—
422C2×C4—762no—
423C2×C4#1059732811yescharacteristic
424C2×C4#1059733011yescharacteristic
425C2×C4#1059737611yescharacteristic
426C2×C4#1059738611yescharacteristic
427C8—81no—
428C8—762no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22#1192645311yescharacteristic
440C22#1192669811yescharacteristic
441C22#1192670111yescharacteristic
442C22#1192670311yescharacteristic
443C22#1192670911yescharacteristic
444C22#1192678411yescharacteristic
445C22#1192680111yescharacteristic
446C4—21no—
447C4—21no—
448C4—21no—
449C4—82no—
450C4—81no—
451C4—81no—
452C4—762no—
453C4—762no—
454C4—1522no—
455C4—1521no—
456C4—1521no—
457C4#1192673512yes—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2—21no—
463C2—21no—
464C2#1456464411yescharacteristic
465C2#1456470111yescharacteristic
466C2#1456476511yescharacteristic
subgroupG/H
centerC22#11926453
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#1520C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#1520D19
hypocenterC19#10325
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
109. C22×Dic19Q16semidirect
315. C19#10325semidirect

Maximal subgroups

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

subgroupindex
#145744072
#145719752
#145719692
#145637012
#145622082
#145615022
C19×#15202
#1032519