Finite Group Databasebeta

← #18083034

Subgroups — #18083034

Order 4864.

744 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 744 conjugacy classes of subgroups — too many to draw. Only its 105 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×#11926699C211yesmaximal, characteristic
2#14567280C211yesmaximal, characteristic
3#14564621C211yesmaximal, characteristic
4#14563571C211yesmaximal, characteristic
5#14562207C211yesmaximal, characteristic
6#14561482C211yesmaximal, characteristic
7C19×#3189C211yesmaximal, characteristic
8C23×Dic38C2211yescharacteristic
9C22×#64528—21no—
10C2×#10597390—21no—
11#11926699—22no—
12#11926699—22no—
13C2×#10597273—22no—
14C2×#10597267—21no—
15C2×C22⋊(C19⋊C8)C2211yescharacteristic
16#11926464—22no—
17#11926449—21no—
18#11926416—22no—
19#11926404C2211yescharacteristic
20C4×C22⋊Dic19C2211yescharacteristic
21#11926311—22no—
22#11926281—22no—
23C2×C19×C22⋊Q8C2211yescharacteristic
24C2×C19×C22⋊Q8C2211yescharacteristic
25C19×#484—21no—
26C19×#484—21no—
27C19×#467—22no—
28C19×#451—21no—
29C19×#451—21no—
30C2×C19×C22⋊C8C2211yescharacteristic
31C22×Q8×C19D411yescharacteristic
32C22×Q8×C19D411yescharacteristic
33C23×C4×C19C2311yescharacteristic
34C23×Dic19—21no—
35C22×Dic38—21no—
36C22×Dic38—21no—
37C22×Dic38—21no—
38C22×Dic38—21no—
39C22×Dic38—21no—
40C22×Dic38—44no—
41C22×Dic38D412yes—
42C2×Q16×C19—22no—
43C22×C8×C19D412yes—
44C19×C22⋊Q8—21no—
45C19×C22⋊Q8—21no—
46C19×C22⋊Q8—21no—
47C19×C22⋊Q8—21no—
48C19×C22⋊Q8—21no—
49C19×C22⋊Q8—21no—
50C19×C22⋊Q8—21no—
51C19×C22⋊Q8—21no—
52C2×C4⋊C4×C19—21no—
53C2×C4⋊C4×C19—21no—
54C2×C4⋊C4×C19D411yescharacteristic
55C2×C4⋊C4×C19D411yescharacteristic
56C2×C22⋊C4×C19—21no—
57C2×C22⋊C4×C19—21no—
58C2×C22⋊Dic19—21no—
59C2×C22⋊Dic19D412yes—
60#10597390—44no—
61C2×#64528—24no—
62C2×#64528—44no—
63C2×C4⋊Dic19—21no—
64C2×Dic19⋊C4—24no—
65C2×C4×Dic19—21no—
66C22×C19⋊C8—21no—
67C19×#107—22no—
68C19×#103—22no—
69C19×#103—22no—
70C19×C22⋊C8—21no—
71C19×C22⋊C8—21no—
72C19⋊#95—24no—
73C19⋊#95—21no—
74C19⋊#95—21no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)D412yes—
77#10597273—44no—
78#10597267—24no—
79C24×C19C2×D411yescharacteristic
80C2×Q8×C19—21no—
81C2×Q8×C19—21no—
82C2×Q8×C19—21no—
83C2×Q8×C19—21no—
84C2×Q8×C19—42no—
85C2×Q8×C19—42no—
86C22×C4×C19—21no—
87C22×C4×C19—21no—
88C22×C4×C19—21no—
89C22×C4×C19—21no—
90C22×C4×C19—42no—
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C22×C4×C19C2×D411yescharacteristic
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19#4111yescharacteristic
97C22×Dic19—22no—
98C22×Dic19—22no—
99C22×Dic19—44no—
100C22×Dic19—41no—
101C22×Dic19—41no—
102C22×Dic19—41no—
103C2×Dic38—24no—
104C2×Dic38—24no—
105C2×Dic38—22no—
106C2×Dic38—22no—
107C2×Dic38—24no—
108C2×Dic38—44no—
109C2×Dic38—44no—
110C2×Dic38—44no—
111C2×Dic38—42no—
112C2×Dic38—42no—
113C2×Dic38—42no—
114C2×Dic38—41no—
115C2×Dic38—41no—
116Q16×C19—82no—
117C2×C8×C19—22no—
118C2×C8×C19—42no—
119C4⋊C4×C19—21no—
120C4⋊C4×C19—21no—
121C4⋊C4×C19—21no—
122C4⋊C4×C19—21no—
123C4⋊C4×C19—41no—
124C4⋊C4×C19—41no—
125C4⋊C4×C19—41no—
126C4⋊C4×C19—41no—
127C22⋊C4×C19—41no—
128C22⋊C4×C19—41no—
129C22⋊C4×C19—41no—
130C22⋊C4×C19—41no—
131C22⋊Dic19—22no—
132C22⋊Dic19—42no—
133C22⋊Dic19Q1614yescomplemented
134#64528—48no—
135C4⋊Dic19—42no—
136Dic19⋊C4—48no—
137C4×Dic19—42no—
138C2×C19⋊C8—22no—
139C2×C19⋊C8—42no—
140#9957—191nomaximal, Sylow
141C23×C19—41no—
142C23×C19—41no—
143C23×C19#12011yescharacteristic
144C23×C19#12111yescharacteristic
145C23×C19#12711yescharacteristic
146C23×C19C2×Q1612yes—
147C23×C19#13712yes—
148Q8×C19—42no—
149Q8×C19—42no—
150Q8×C19—42no—
151Q8×C19—81no—
152C2×C4×C19—22no—
153C2×C4×C19—22no—
154C2×C4×C19—22no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—42no—
159C2×C4×C19—42no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—81no—
165C2×C4×C19—81no—
166C2×C4×C19#12011yescharacteristic
167C2×C4×C19#12011yescharacteristic
168C2×C4×C19#12111yescharacteristic
169C2×C4×C19#12111yescharacteristic
170C2×Dic19—24no—
171C2×Dic19—24no—
172C2×Dic19—42no—
173C2×Dic19—44no—
174C2×Dic19—44no—
175C2×Dic19—42no—
176C2×Dic19—42no—
177C2×Dic19—42no—
178C2×Dic19—81no—
179C2×Dic19—81no—
180C2×Dic19—81no—
181Dic38—24no—
182Dic38—24no—
183Dic38—42no—
184Dic38—42no—
185Dic38—44no—
186Dic38—44no—
187C8×C19—42no—
188C19⋊C8—42no—
189#3189D1911yescharacteristic
190C2×#451—191no—
191#2434—191no—
192#1996—191no—
193#1787—191no—
194#1520—191no—
195#1282—191no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—42no—
203C22×C19—42no—
204C22×C19#39211yescharacteristic
205C22×C19#45112yes—
206C22×C19#46212yes—
207C22×C19#49411yescharacteristic
208C22×C19#49711yescharacteristic
209C4×C19—21no—
210C4×C19—21no—
211C4×C19—21no—
212C4×C19—81no—
213C4×C19—81no—
214C4×C19—81no—
215C4×C19—81no—
216C4×C19B(4,𝔽2)12yes—
217Dic19—44no—
218Dic19—44no—
219Dic19—161no—
220C23×Q8—191no—
221C22×Q16—381no—
222C2×C4⋊Q8—381no—
223C2×C22⋊Q8C2×D1911yescharacteristic
224C2×C22⋊Q8C2×D1911yescharacteristic
225#484—21no—
226#484—21no—
227#467—22no—
228#451—21no—
229#451—21no—
230#451—382no—
231#451—382no—
232C2×#103—381no—
233C2×#103—382no—
234C2×C22⋊C8—191no—
235C2×C22⋊C8C2×D1911yescharacteristic
236#395—382no—
237#391—381no—
238#385—382no—
239#380—191no—
240C4×C22⋊C4—191no—
241#342—382no—
242#328—382no—
243C2×C19—22no—
244C2×C19—21no—
245C2×C19—22no—
246C2×C19—21no—
247C2×C19#200911yescharacteristic
248C2×C19#201611yescharacteristic
249C2×C19#202111yescharacteristic
250C22×Q8—192no—
251C22×Q8—381no—
252C22×Q8—381no—
253C22×Q8—381no—
254C22×Q8—381no—
255C22×Q8—381no—
256C22×Q8—764no—
257C22×Q8C22⋊D1911yescharacteristic
258C22×Q8C22⋊D1911yescharacteristic
259C23×C4—381no—
260C23×C4C22×D1911yescharacteristic
261C2×Q16—22no—
262C2×Q16—384no—
263C2×Q16—764no—
264C22×C8—381no—
265C22×C8C22⋊D1912yes—
266C4⋊Q8—764no—
267C22⋊Q8—21no—
268C22⋊Q8—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273C22⋊Q8—21no—
274C22⋊Q8—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—384no—
278C2×C4⋊C4—381no—
279C2×C4⋊C4C22⋊D1911yescharacteristic
280C2×C4⋊C4C22⋊D1911yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—192no—
284C2×C22⋊C4—381no—
285C2×C42—381no—
286#107—22no—
287#103—22no—
288#103—22no—
289#103—384no—
290#103—764no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—192no—
294C22⋊C8—381no—
295#95—384no—
296#95—381no—
297#95—381no—
298C19#995711yescharacteristic, complemented, Sylow
299C24D4×D1911yescharacteristic
300C2×Q8—21no—
301C2×Q8—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—42no—
305C2×Q8—42no—
306C2×Q8—384no—
307C2×Q8—384no—
308C2×Q8—384no—
309C2×Q8—382no—
310C2×Q8—382no—
311C2×Q8—762no—
312C2×Q8—762no—
313C2×Q8—762no—
314C2×Q8—764no—
315C2×Q8—764no—
316C2×Q8—764no—
317C2×Q8—761no—
318C2×Q8—761no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—42no—
324C22×C4—382no—
325C22×C4—382no—
326C22×C4—764no—
327C22×C4—761no—
328C22×C4—761no—
329C22×C4—761no—
330C22×C4D4×D1911yescharacteristic
331C22×C4D4×D1911yescharacteristic
332C22×C4#6454311yescharacteristic
333C22×C4C2×C22⋊D1911yescharacteristic
334C22×C4C2×C22⋊D1911yescharacteristic
335C22×C4C2×C22⋊D1911yescharacteristic
336Q16—82no—
337Q16—768no—
338C2×C8—22no—
339C2×C8—42no—
340C2×C8—382no—
341C2×C8—762no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—41no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—762no—
351C4⋊C4—768no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—194no—
357C22⋊C4—382no—
358C22⋊C4—762no—
359C42—762no—
360C23—41no—
361C23—41no—
362C23Q16×D1912yes—
363C23#1059736412yes—
364C23#1059738311yescharacteristic
365C23#1059738511yescharacteristic
366C23#1059738611yescharacteristic
367Q8—42no—
368Q8—42no—
369Q8—42no—
370Q8—81no—
371Q8—384no—
372Q8—384no—
373Q8—762no—
374Q8—762no—
375Q8—764no—
376Q8—764no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—384no—
392C2×C4—384no—
393C2×C4—762no—
394C2×C4—762no—
395C2×C4—762no—
396C2×C4—764no—
397C2×C4—764no—
398C2×C4—762no—
399C2×C4—1521no—
400C2×C4—1521no—
401C2×C4—1521no—
402C2×C4#1059738311yescharacteristic
403C2×C4#1059738411yescharacteristic
404C2×C4#1059738511yescharacteristic
405C2×C4#1059739911yescharacteristic
406C8—42no—
407C8—762no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—42no—
415C22—42no—
416C22#1192645211yescharacteristic
417C22#1192669812yes—
418C22#1192675212yes—
419C22#1192692211yescharacteristic
420C22#1192693711yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—81no—
425C4—81no—
426C4—81no—
427C4—81no—
428C4—3041no—
429C4—764no—
430C4—764no—
431C4#1192673112yes—
432C2—21no—
433C2—22no—
434C2—21no—
435C2—22no—
436C2#1456469211yescharacteristic
437C2#1456473311yescharacteristic
438C2#1456475911yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#3189C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#3189D19
hypocenterC19#9957
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
133. C22⋊Dic19Q16semidirect
298. C19#9957semidirect

Maximal subgroups

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

subgroupindex
C2×#119266992
#145672802
#145646212
#145635712
#145622072
#145614822
C19×#31892
#995719