Finite Group Databasebeta

← #18082839

Subgroups — #18082839

Order 4864.

610 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C2×#11926877C211yesmaximal, characteristic
2#14569450C211yesmaximal, characteristic
3C2×#11926484C211yesmaximal, characteristic
4#14563726C211yesmaximal, characteristic
5C2×#11926269C211yesmaximal, characteristic
6#14561514C211yesmaximal, characteristic
7C2×C19×#328C211yesmaximal, characteristic
8C22×C4⋊Dic19C2211yescharacteristic
9C22×Dic19⋊C4C2211yescharacteristic
10#11926877—22no—
11#11926877—22no—
12C2×#10597264—21no—
13C2×#10597292—21no—
14C2×C22⋊(C19⋊C8)C2211yescharacteristic
15#11926484—22no—
16#11926484—22no—
17#11926482—21no—
18#11926477—22no—
19#11926463—21no—
20#11926416—21no—
21#11926405—21no—
22#11926404C2211yescharacteristic
23C2×C19⋊#95—21no—
24C2×C19⋊#95—21no—
25#11926307—22no—
26#11926269—22no—
27C2×C19×C22⋊Q8C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C2×C19×#95C2211yescharacteristic
30C19×#328—22no—
31C22×Q8×C19D411yescharacteristic
32C23×C4×C19—21no—
33C23×C4×C19C2311yescharacteristic
34C23×Dic19—21no—
35C23×Dic19D411yescharacteristic
36C23×Dic19D411yescharacteristic
37C22×C8×C19—21no—
38C19×C22⋊Q8—21no—
39C19×C22⋊Q8—21no—
40C19×C22⋊Q8—21no—
41C19×C22⋊Q8—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19D411yescharacteristic
44C2×C22⋊C4×C19—21no—
45C2×C22⋊Dic19—21no—
46C2×C4⋊Dic19—21no—
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19—21no—
49C2×C4⋊Dic19—21no—
50C2×C4⋊Dic19—21no—
51C2×C4⋊Dic19D412yes—
52C2×C4⋊Dic19D412yes—
53C2×Dic19⋊C4—21no—
54C2×Dic19⋊C4—21no—
55C2×Dic19⋊C4—21no—
56C2×Dic19⋊C4—21no—
57C2×Dic19⋊C4—21no—
58C2×Dic19⋊C4—21no—
59C2×Dic19⋊C4—22no—
60C22×C19⋊C8—21no—
61C19×C22⋊C8—21no—
62C19×C22⋊C8—21no—
63C19×#95—21no—
64C19×#95D412yes—
65#10597292—24no—
66C19⋊#95—24no—
67C19⋊#95—24no—
68C19⋊#95—22no—
69C19⋊#95—22no—
70C19⋊#95—22no—
71C19⋊#95—21no—
72C22⋊(C19⋊C8)—21no—
73C22⋊(C19⋊C8)D412yes—
74#10597264—24no—
75C24×C19C2×D411yescharacteristic
76C2×Q8×C19—21no—
77C2×Q8×C19—21no—
78C2×Q8×C19—42no—
79C22×C4×C19—21no—
80C22×C4×C19—21no—
81C22×C4×C19—22no—
82C22×C4×C19—42no—
83C22×C4×C19—42no—
84C22×C4×C19—42no—
85C22×C4×C19—41no—
86C22×C4×C19—41no—
87C22×C4×C19C2×D411yescharacteristic
88C22×C4×C19C2×D411yescharacteristic
89C22×C4×C19C2×D411yescharacteristic
90C22×C4×C19C2×D411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19#4111yescharacteristic
93C22×Dic19—21no—
94C22×Dic19—21no—
95C22×Dic19—21no—
96C22×Dic19—21no—
97C22×Dic19—21no—
98C22×Dic19—21no—
99C22×Dic19—22no—
100C22×Dic19—22no—
101C22×Dic19—21no—
102C22×Dic19—21no—
103C22×Dic19—21no—
104C22×Dic19—42no—
105C22×Dic19—44no—
106C22×Dic19—41no—
107C22×Dic19—41no—
108C22×Dic19Q1612yes—
109C2×C8×C19—42no—
110C2×C8×C19—41no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19—21no—
113C4⋊C4×C19—41no—
114C4⋊C4×C19—41no—
115C22⋊C4×C19—41no—
116C22⋊C4×C19—41no—
117C22⋊Dic19—41no—
118C22⋊Dic19—41no—
119C4⋊Dic19—22no—
120C4⋊Dic19—22no—
121C4⋊Dic19—41no—
122C4⋊Dic19—41no—
123C4⋊Dic19—42no—
124Dic19⋊C4—41no—
125Dic19⋊C4—41no—
126Dic19⋊C4—41no—
127Dic19⋊C4—41no—
128Dic19⋊C4—82no—
129C2×C19⋊C8—22no—
130C2×C19⋊C8—42no—
131#9929—191nomaximal, Sylow
132C23×C19—22no—
133C23×C19—22no—
134C23×C19#12011yescharacteristic
135C23×C19#12011yescharacteristic
136C23×C19#12111yescharacteristic
137C23×C19C2×Q1611yescharacteristic
138C23×C19#13511yescharacteristic
139C23×C19#13711yescharacteristic
140C23×C19#13711yescharacteristic
141Q8×C19—42no—
142Q8×C19—81no—
143C2×C4×C19—22no—
144C2×C4×C19—22no—
145C2×C4×C19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—42no—
150C2×C4×C19—42no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—42no—
154C2×C4×C19—42no—
155C2×C4×C19—42no—
156C2×C4×C19—82no—
157C2×C4×C19—82no—
158C2×C4×C19#12011yescharacteristic
159C2×C4×C19#12111yescharacteristic
160C2×C4×C19#12111yescharacteristic
161C2×C4×C19#12711yescharacteristic
162C2×Dic19—22no—
163C2×Dic19—22no—
164C2×Dic19—22no—
165C2×Dic19—41no—
166C2×Dic19—41no—
167C2×Dic19—41no—
168C2×Dic19—41no—
169C2×Dic19—44no—
170C2×Dic19—42no—
171C2×Dic19—41no—
172C2×Dic19—42no—
173C2×Dic19—42no—
174C2×Dic19—42no—
175C2×Dic19—42no—
176C2×Dic19—42no—
177C2×Dic19—82no—
178C2×Dic19—82no—
179C2×Dic19—81no—
180C8×C19—81no—
181C19⋊C8—42no—
182C2×#484—191no—
183#2627—191no—
184C2×#400—191no—
185#1824—191no—
186C2×#328D1911yescharacteristic
187C2×#324—191no—
188#1294—191no—
189C22×C19—22no—
190C22×C19—22no—
191C22×C19—22no—
192C22×C19—22no—
193C22×C19—21no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19#39211yescharacteristic
198C22×C19#45111yescharacteristic
199C22×C19#45111yescharacteristic
200C22×C19#45211yescharacteristic
201C22×C19#45211yescharacteristic
202C22×C19#45412yes—
203C22×C19#45812yes—
204C22×C19#46711yescharacteristic
205C22×C19#47011yescharacteristic
206C4×C19—21no—
207C4×C19—21no—
208C4×C19—21no—
209C4×C19—21no—
210C4×C19—82no—
211C4×C19—81no—
212C4×C19—81no—
213Dic19—42no—
214Dic19—82no—
215Dic19—82no—
216Dic19—81no—
217C2×C22⋊Q8C2×D1911yescharacteristic
218C22×C4⋊C4—191no—
219C22×C4⋊C4—191no—
220#484—382no—
221#484—382no—
222C2×#107—381no—
223C2×#103—381no—
224C2×C22⋊C8—191no—
225C2×C22⋊C8C2×D1911yescharacteristic
226#400—382no—
227#400—381no—
228#400—382no—
229#398—382no—
230#395—381no—
231#385—381no—
232#381—381no—
233#380—191no—
234C2×#95—381no—
235C2×#95—381no—
236C2×#95C2×D1911yescharacteristic
237#340—382no—
238#328—22no—
239#324—382no—
240C2×C19—21no—
241C2×C19—21no—
242C2×C19—21no—
243C2×C19—21no—
244C2×C19#161512yes—
245C2×C19#161712yes—
246C2×C19#200111yescharacteristic
247C2×C19#200311yescharacteristic
248C2×C19#202211yescharacteristic
249C22×Q8D7611yescharacteristic
250C23×C4—21no—
251C23×C4—191no—
252C23×C4—191no—
253C23×C4—381no—
254C23×C4C22×D1911yescharacteristic
255C22×C8—21no—
256C22×C8—381no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—192no—
263C2×C4⋊C4—192no—
264C2×C4⋊C4—381no—
265C2×C4⋊C4—381no—
266C2×C4⋊C4—381no—
267C2×C4⋊C4—381no—
268C2×C4⋊C4—381no—
269C2×C4⋊C4—381no—
270C2×C4⋊C4—381no—
271C2×C4⋊C4—381no—
272C2×C4⋊C4—381no—
273C2×C4⋊C4—381no—
274C2×C4⋊C4—381no—
275C2×C4⋊C4—382no—
276C2×C4⋊C4D7611yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—381no—
279#107—384no—
280#103—384no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—192no—
284C22⋊C8—381no—
285#95—21no—
286#95—384no—
287#95—384no—
288#95—382no—
289#95—382no—
290#95—382no—
291#95—381no—
292#95C22⋊D1912yes—
293C19#992911yescharacteristic, complemented, Sylow
294C24D4×D1911yescharacteristic
295C2×Q8—21no—
296C2×Q8—21no—
297C2×Q8—42no—
298C22×C4—22no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—192no—
307C22×C4—381no—
308C22×C4—381no—
309C22×C4—381no—
310C22×C4—381no—
311C22×C4—381no—
312C22×C4—381no—
313C22×C4—382no—
314C22×C4—381no—
315C22×C4—382no—
316C22×C4—381no—
317C22×C4—381no—
318C22×C4—762no—
319C22×C4—764no—
320C22×C4—761no—
321C22×C4—761no—
322C22×C4C2×D7611yescharacteristic
323C22×C4#6454111yescharacteristic
324C22×C4D4×D1911yescharacteristic
325C22×C4D4×D1911yescharacteristic
326C22×C4D4×D1911yescharacteristic
327C22×C4C2×C22⋊D1911yescharacteristic
328C2×C8—42no—
329C2×C8—41no—
330C2×C8—382no—
331C2×C8—762no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—382no—
337C4⋊C4—382no—
338C4⋊C4—762no—
339C4⋊C4—761no—
340C4⋊C4—761no—
341C4⋊C4—761no—
342C4⋊C4—761no—
343C4⋊C4—761no—
344C4⋊C4—761no—
345C4⋊C4—1522no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—761no—
349C22⋊C4—761no—
350C23—22no—
351C23—22no—
352C23#1059732811yescharacteristic
353C23#1059733011yescharacteristic
354C23#1059736111yescharacteristic
355C23#1059736211yescharacteristic
356C23Q16×D1911yescharacteristic
357C23#1059736411yescharacteristic
358C23#1059738311yescharacteristic
359Q8—42no—
360Q8—81no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—82no—
375C2×C4—82no—
376C2×C4—382no—
377C2×C4—382no—
378C2×C4—382no—
379C2×C4—761no—
380C2×C4—761no—
381C2×C4—761no—
382C2×C4—761no—
383C2×C4—764no—
384C2×C4—762no—
385C2×C4—762no—
386C2×C4—761no—
387C2×C4—762no—
388C2×C4—762no—
389C2×C4—762no—
390C2×C4—762no—
391C2×C4—1522no—
392C2×C4—1522no—
393C2×C4—1521no—
394C2×C4#1059732811yescharacteristic
395C2×C4#1059733011yescharacteristic
396C2×C4#1059737611yescharacteristic
397C2×C4#1059738611yescharacteristic
398C8—81no—
399C8—762no—
400C22—21no—
401C22—21no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—21no—
407C22—21no—
408C22#1192645311yescharacteristic
409C22#1192669811yescharacteristic
410C22#1192670111yescharacteristic
411C22#1192670311yescharacteristic
412C22#1192670911yescharacteristic
413C22#1192671812yes—
414C22#1192673512yes—
415C22#1192678411yescharacteristic
416C22#1192680111yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—82no—
422C4—81no—
423C4—81no—
424C4—762no—
425C4—1522no—
426C4—1522no—
427C4—1521no—
428C2—21no—
429C2—21no—
430C2—21no—
431C2—21no—
432C2#1456266912yes—
433C2#1456267812yes—
434C2#1456464411yescharacteristic
435C2#1456465611yescharacteristic
436C2#1456476511yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC2×C19×#328C2
socleC23×C19#120
prime radicalC24×C19C2×D4
hypercenterC2×#328D19
hypocenterC19#9929
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
293. C19#9929semidirect

Maximal subgroups

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

subgroupindex
C2×#119268772
#145694502
C2×#119264842
#145637262
C2×#119262692
#145615142
C2×C19×#3282
#992919