Finite Group Databasebeta

← #18083036

Subgroups — #18083036

Order 4864.

744 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 744 conjugacy classes of subgroups — too many to draw. Only its 109 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
2C2×#11926700C211yesmaximal, characteristic
3#14564620C211yesmaximal, characteristic
4#14563570C211yesmaximal, characteristic
5#14562207C211yesmaximal, characteristic
6#14561483C211yesmaximal, characteristic
7C19×#2434C211yesmaximal, characteristic
8C22×#64528—21no—
9C2×#10597370C2211yescharacteristic
10#11926879—21no—
11#11926877—21no—
12#11926783—22no—
13#11926700—22no—
14#11926700—22no—
15#11926700—21no—
16#11926699—21no—
17C2×#10597292—21no—
18C2×#10597292—22no—
19C2×C22⋊(C19⋊C8)C2211yescharacteristic
20C2×C22⋊(C19⋊C8)C2211yescharacteristic
21#11926404C2211yescharacteristic
22#11926310—22no—
23#11926281—22no—
24C23×Q8×C19C2211yescharacteristic
25C2×C19×C4⋊Q8—21no—
26C2×C19×C22⋊Q8C2211yescharacteristic
27C19×#395—22no—
28C19×#391—21no—
29C19×#385—22no—
30C4×C22⋊C4×C19C2211yescharacteristic
31C22×Q8×C19—21no—
32C22×Q8×C19—21no—
33C22×Q8×C19—21no—
34C22×Q8×C19—21no—
35C22×Q8×C19—21no—
36C22×Q8×C19—44no—
37C22×Q8×C19D412yes—
38C22×Q8×C19D411yescharacteristic
39C23×C4×C19—21no—
40C23×C4×C19C2311yescharacteristic
41C22×Dic38D411yescharacteristic
42C19×C4⋊Q8—44no—
43C19×C22⋊Q8—21no—
44C19×C22⋊Q8—21no—
45C19×C22⋊Q8—21no—
46C19×C22⋊Q8—21no—
47C2×C4⋊C4×C19—24no—
48C2×C4⋊C4×C19—21no—
49C2×C4⋊C4×C19D411yescharacteristic
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19D412yes—
52C2×C42×C19—21no—
53C2×C22⋊Dic19—21no—
54C2×C22⋊Dic19—21no—
55C2×#64528—24no—
56C2×#64528—22no—
57C2×#64528—44no—
58C2×C4⋊Dic19—21no—
59C2×C4⋊Dic19D411yescharacteristic
60#10597370—21no—
61#10597370—21no—
62#10597370—21no—
63#10597370—21no—
64C2×Dic19⋊C4—21no—
65C22×C19⋊C8—21no—
66C22×C19⋊C8D412yes—
67C19×#95—24no—
68C19×#95—21no—
69#10597292—24no—
70#10597292—22no—
71#10597292—44no—
72C19⋊#95—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76C22⋊(C19⋊C8)D412yes—
77#10597267—22no—
78#10597264—22no—
79C24×C19C2×D411yescharacteristic
80C2×Q8×C19—24no—
81C2×Q8×C19—24no—
82C2×Q8×C19—24no—
83C2×Q8×C19—22no—
84C2×Q8×C19—21no—
85C2×Q8×C19—22no—
86C2×Q8×C19—21no—
87C2×Q8×C19—44no—
88C2×Q8×C19—42no—
89C2×Q8×C19—42no—
90C2×Q8×C19—42no—
91C2×Q8×C19—42no—
92C2×Q8×C19—44no—
93C2×Q8×C19—44no—
94C2×Q8×C19—41no—
95C2×Q8×C19—41no—
96C22×C4×C19—22no—
97C22×C4×C19—22no—
98C22×C4×C19—21no—
99C22×C4×C19—21no—
100C22×C4×C19—42no—
101C22×C4×C19—44no—
102C22×C4×C19—41no—
103C22×C4×C19—41no—
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19C2×D411yescharacteristic
106C22×C4×C19C2×D411yescharacteristic
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19C2×D411yescharacteristic
109C22×C4×C19#4111yescharacteristic
110C22×Dic19—21no—
111C22×Dic19—21no—
112C22×Dic19—41no—
113C2×Dic38—21no—
114C2×Dic38—21no—
115C2×Dic38—42no—
116C4⋊C4×C19—21no—
117C4⋊C4×C19—21no—
118C4⋊C4×C19—48no—
119C4⋊C4×C19—41no—
120C4⋊C4×C19—41no—
121C22⋊C4×C19—22no—
122C22⋊C4×C19—41no—
123C22⋊C4×C19—41no—
124C22⋊C4×C19Q1614yescomplemented
125C42×C19—42no—
126C22⋊Dic19—41no—
127C22⋊Dic19—41no—
128C22⋊Dic19—42no—
129#64528—48no—
130#64528—82no—
131C4⋊Dic19—21no—
132C4⋊Dic19—21no—
133C4⋊Dic19—42no—
134Dic19⋊C4—41no—
135Dic19⋊C4—41no—
136C2×C19⋊C8—22no—
137C2×C19⋊C8—22no—
138C2×C19⋊C8—42no—
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—24no—
149Q8×C19—24no—
150Q8×C19—42no—
151Q8×C19—42no—
152Q8×C19—44no—
153Q8×C19—44no—
154Q8×C19—42no—
155Q8×C19—81no—
156C2×C4×C19—22no—
157C2×C4×C19—22no—
158C2×C4×C19—22no—
159C2×C4×C19—24no—
160C2×C4×C19—24no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—42no—
165C2×C4×C19—42no—
166C2×C4×C19—42no—
167C2×C4×C19—44no—
168C2×C4×C19—44no—
169C2×C4×C19—42no—
170C2×C4×C19—42no—
171C2×C4×C19—42no—
172C2×C4×C19—41no—
173C2×C4×C19—41no—
174C2×C4×C19#12011yescharacteristic
175C2×C4×C19#12011yescharacteristic
176C2×C4×C19#12111yescharacteristic
177C2×C4×C19#12111yescharacteristic
178C2×Dic19—41no—
179C2×Dic19—41no—
180C2×Dic19—81no—
181C2×Dic19—81no—
182C2×Dic19—81no—
183C2×Dic19—81no—
184C2×Dic19—81no—
185Dic38—42no—
186Dic38—42no—
187C19⋊C8—42no—
188C19⋊C8—42no—
189#3189—191no—
190C2×#451—191no—
191#2434D1911yescharacteristic
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—44no—
213C4×C19—44no—
214C4×C19—81no—
215C4×C19—81no—
216C4×C19B(4,𝔽2)12yes—
217Dic19—81no—
218Dic19—81no—
219Dic19—161no—
220C23×Q8C2×D1911yescharacteristic
221C22×Q16—381no—
222C2×C4⋊Q8—21no—
223C2×C22⋊Q8—191no—
224C2×C22⋊Q8C2×D1911yescharacteristic
225#484—381no—
226#484—381no—
227#467—382no—
228#451—382no—
229#451—381no—
230#451—381no—
231#451—382no—
232C2×#103—381no—
233C2×#103—382no—
234C2×C22⋊C8—191no—
235C2×C22⋊C8—191no—
236#395—22no—
237#391—21no—
238#385—22no—
239#380—191no—
240C4×C22⋊C4C2×D1911yescharacteristic
241#342—382no—
242#328—382no—
243C2×C19—21no—
244C2×C19—22no—
245C2×C19—22no—
246C2×C19—21no—
247C2×C19#200911yescharacteristic
248C2×C19#201611yescharacteristic
249C2×C19#202111yescharacteristic
250C22×Q8—21no—
251C22×Q8—21no—
252C22×Q8—21no—
253C22×Q8—21no—
254C22×Q8—21no—
255C22×Q8—44no—
256C22×Q8—191no—
257C22×Q8C22⋊D1911yescharacteristic
258C22×Q8C22⋊D1912yes—
259C23×C4—21no—
260C23×C4C22×D1911yescharacteristic
261C2×Q16—384no—
262C2×Q16—382no—
263C2×Q16—764no—
264C22×C8—192no—
265C22×C8—381no—
266C4⋊Q8—44no—
267C22⋊Q8—21no—
268C22⋊Q8—21no—
269C22⋊Q8—21no—
270C22⋊Q8—21no—
271C22⋊Q8—381no—
272C22⋊Q8—381no—
273C22⋊Q8—381no—
274C22⋊Q8—381no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—191no—
278C2×C4⋊C4—381no—
279C2×C4⋊C4—381no—
280C2×C4⋊C4C22⋊D1911yescharacteristic
281C2×C22⋊C4—21no—
282C2×C22⋊C4—381no—
283C2×C22⋊C4—381no—
284C2×C22⋊C4C22⋊D1912yes—
285C2×C42—21no—
286#107—382no—
287#103—382no—
288#103—384no—
289#103—382no—
290#103—764no—
291C22⋊C8—192no—
292C22⋊C8—381no—
293C22⋊C8—381no—
294C22⋊C8—381no—
295#95—24no—
296#95—21no—
297#95—381no—
298C19#995711yescharacteristic, complemented, Sylow
299C24C2×C22⋊D1911yescharacteristic
300C2×Q8—24no—
301C2×Q8—24no—
302C2×Q8—24no—
303C2×Q8—22no—
304C2×Q8—21no—
305C2×Q8—22no—
306C2×Q8—21no—
307C2×Q8—44no—
308C2×Q8—42no—
309C2×Q8—42no—
310C2×Q8—42no—
311C2×Q8—42no—
312C2×Q8—44no—
313C2×Q8—44no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×Q8—381no—
317C2×Q8—381no—
318C2×Q8—762no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—42no—
324C22×C4—44no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—381no—
328C22×C4—381no—
329C22×C4—761no—
330C22×C4D4×D1911yescharacteristic
331C22×C4D4×D1911yescharacteristic
332C22×C4D4×D1911yescharacteristic
333C22×C4#6454311yescharacteristic
334C22×C4C2×C22⋊D1911yescharacteristic
335C22×C4C2×C22⋊D1911yescharacteristic
336Q16—768no—
337Q16—1522no—
338C2×C8—382no—
339C2×C8—382no—
340C2×C8—762no—
341C2×C8—762no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—48no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—381no—
348C4⋊C4—381no—
349C4⋊C4—762no—
350C4⋊C4—761no—
351C4⋊C4—761no—
352C22⋊C4—22no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—761no—
356C22⋊C4—761no—
357C22⋊C4—762no—
358C22⋊C4#6452814yescomplemented
359C42—42no—
360C23—41no—
361C23—41no—
362C23#1059738411yescharacteristic
363C23#1059738611yescharacteristic
364C23#1059738812yes—
365C23C2×#6452812yes—
366C23#1059739911yescharacteristic
367Q8—24no—
368Q8—24no—
369Q8—42no—
370Q8—42no—
371Q8—44no—
372Q8—44no—
373Q8—42no—
374Q8—81no—
375Q8—762no—
376Q8—762no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—24no—
381C2×C4—24no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—761no—
396C2×C4—761no—
397C2×C4—1521no—
398C2×C4—1521no—
399C2×C4—1521no—
400C2×C4—1521no—
401C2×C4—1521no—
402C2×C4#1059738311yescharacteristic
403C2×C4#1059738311yescharacteristic
404C2×C4#1059738511yescharacteristic
405C2×C4#1059738511yescharacteristic
406C8—762no—
407C8—762no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—42no—
415C22—42no—
416C22#1192645211yescharacteristic
417C22#1192670012yes—
418C22#1192675112yes—
419C22#1192692311yescharacteristic
420C22#1192693611yescharacteristic
421C4—21no—
422C4—21no—
423C4—21no—
424C4—44no—
425C4—44no—
426C4—81no—
427C4—81no—
428C4—3041no—
429C4—1521no—
430C4—1521no—
431C4#1192673012yes—
432C2—22no—
433C2—21no—
434C2—21no—
435C2—22no—
436C2#1456469511yescharacteristic
437C2#1456473511yescharacteristic
438C2#1456475811yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2434C2
socleC22×C19#392
prime radicalC24×C19C2×D4
hypercenter#2434D19
hypocenterC19#9957
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2434

Complements

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

NH ≅ G/Ntype
124. C22⋊C4×C19Q16semidirect
298. C19#9957semidirect
358. C22⋊C4#64528semidirect

Maximal subgroups

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

subgroupindex
#145744072
C2×#119267002
#145646202
#145635702
#145622072
#145614832
C19×#24342
#995719