Finite Group Databasebeta

← #18083057

Subgroups — #18083057

Order 4864.

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

normal subgroups only

This group has 650 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#14574392C211yesmaximal, characteristic
2C2×#11926874C211yesmaximal, characteristic, complemented
3#14564620C211yesmaximal, characteristic, complemented
4#14563721C211yesmaximal, characteristic, complemented
5#14562203C211yesmaximal, characteristic
6#14561483C211yesmaximal, characteristic, complemented
7C19×#2501C211yesmaximal, characteristic
8C2×#10597370C2211yescharacteristic
9#11926874—22no—
10#11926874—21no—
11#11926874—22no—
12#11926860—21no—
13#11926771—22no—
14#11926695—21no—
15#11926682—21no—
16C2×#10597265—21no—
17C2×#10597267—21no—
18C2×C22⋊(C19⋊C8)C2211yescharacteristic
19C2×C22⋊(C19⋊C8)C2211yescharacteristic
20#11926404C2211yescharacteristic
21#11926310—22no—
22#11926306—22no—
23#11926278—22no—
24C2×C19×#123—22no—
25C2×C19×#121C2211yescharacteristic
26C22×C4⋊C4×C19C2211yescharacteristic
27C19×#399—22no—
28C19×#390—21no—
29C19×#384—21no—
30C4×C22⋊C4×C19C2211yescharacteristic
31C22×D4×C19—21no—
32C22×D4×C19D411yescharacteristic
33C23×C4×C19—21no—
34C23×C4×C19C2311yescharacteristic
35C22×Dic38D411yescharacteristic
36C19×#123—44no—
37C19×#123—44no—
38C19×#121—21no—
39C19×#121—21no—
40C19×#121—21no—
41C19×#121—21no—
42C2×C4⋊C4×C19—21no—
43C2×C4⋊C4×C19—21no—
44C2×C4⋊C4×C19—21no—
45C2×C4⋊C4×C19—21no—
46C2×C4⋊C4×C19—24no—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C4⋊C4×C19D412yes—
50C2×C22⋊C4×C19—24no—
51C2×C22⋊C4×C19—21no—
52C2×C22⋊C4×C19D412yes—
53C2×C42×C19—21no—
54C2×C22⋊Dic19—21no—
55C2×C22⋊Dic19—21no—
56C2×#64526—22no—
57C2×C4⋊Dic19—21no—
58C2×C4⋊Dic19D411yescharacteristic
59#10597370—21no—
60#10597370—21no—
61#10597370—21no—
62#10597370—21no—
63C2×Dic19⋊C4—21no—
64C22×C19⋊C8—21no—
65C22×C19⋊C8D412yes—
66C19×#95—21no—
67#10597289—22no—
68C19⋊#95—21no—
69C22⋊(C19⋊C8)—21no—
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)D412yes—
73#10597267—24no—
74#10597267—22no—
75#10597265—24no—
76#10597265—22no—
77C24×C19—21no—
78C24×C19C2×D411yescharacteristic
79C2×D4×C19—21no—
80C2×D4×C19—21no—
81C2×D4×C19—42no—
82C2×D4×C19—41no—
83C2×D4×C19—41no—
84C2×D4×C19—42no—
85C2×D4×C19—42no—
86C22×C4×C19—22no—
87C22×C4×C19—22no—
88C22×C4×C19—21no—
89C22×C4×C19—42no—
90C22×C4×C19—41no—
91C22×C4×C19—41no—
92C22×C4×C19—42no—
93C22×C4×C19—42no—
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19C2×D411yescharacteristic
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19#4111yescharacteristic
100C22×Dic19—21no—
101C22×Dic19—21no—
102C22×Dic19—41no—
103C2×Dic38—21no—
104C2×Dic38—21no—
105C2×Dic38—42no—
106C4⋊C4×C19—22no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—22no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—48no—
111C4⋊C4×C19—41no—
112C4⋊C4×C19—41no—
113C22⋊C4×C19—22no—
114C22⋊C4×C19—48no—
115C22⋊C4×C19—41no—
116C22⋊C4×C19—41no—
117C22⋊C4×C19SD1614yescomplemented
118C42×C19—42no—
119C22⋊Dic19—41no—
120C22⋊Dic19—41no—
121C22⋊Dic19—42no—
122#64526—82no—
123C4⋊Dic19—21no—
124C4⋊Dic19—21no—
125C4⋊Dic19—42no—
126Dic19⋊C4—41no—
127Dic19⋊C4—41no—
128C2×C19⋊C8—22no—
129C2×C19⋊C8—22no—
130C2×C19⋊C8—42no—
131C2×C19⋊C8—42no—
132#9960—191nomaximal, Sylow
133C23×C19—41no—
134C23×C19—41no—
135C23×C19—42no—
136C23×C19—42no—
137C23×C19—41no—
138C23×C19—42no—
139C23×C19#12011yescharacteristic
140C23×C19#12111yescharacteristic
141C23×C19#12711yescharacteristic
142C23×C19C2×SD1612yes—
143C23×C19AGL(1,ℤ/8)12yes—
144D4×C19—42no—
145D4×C19—81no—
146D4×C19—82no—
147D4×C19—81no—
148D4×C19—81no—
149C2×C4×C19—22no—
150C2×C4×C19—22no—
151C2×C4×C19—22no—
152C2×C4×C19—24no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—42no—
157C2×C4×C19—42no—
158C2×C4×C19—41no—
159C2×C4×C19—42no—
160C2×C4×C19—44no—
161C2×C4×C19—42no—
162C2×C4×C19—82no—
163C2×C4×C19—81no—
164C2×C4×C19—81no—
165C2×C4×C19#12011yescharacteristic
166C2×C4×C19#12011yescharacteristic
167C2×C4×C19#12111yescharacteristic
168C2×C4×C19#12111yescharacteristic
169C2×Dic19—41no—
170C2×Dic19—41no—
171C2×Dic19—81no—
172C2×Dic19—81no—
173C2×Dic19—81no—
174C2×Dic19—81no—
175C2×Dic19—81no—
176Dic38—42no—
177Dic38—42no—
178C19⋊C8—42no—
179C19⋊C8—42no—
180#3187—191no—
181C2×#483—191no—
182#2501D1911yescharacteristic
183#1996—191no—
184#1823—191no—
185#1519—191no—
186#1282—191no—
187C22×C19—21no—
188C22×C19—21no—
189C22×C19—21no—
190C22×C19—21no—
191C22×C19—21no—
192C22×C19—21no—
193C22×C19—42no—
194C22×C19—42no—
195C22×C19—84no—
196C22×C19—81no—
197C22×C19—81no—
198C22×C19—81no—
199C22×C19#39211yescharacteristic
200C22×C19#45012yes—
201C22×C19#46012yes—
202C22×C19#49211yescharacteristic
203C22×C19#49611yescharacteristic
204C4×C19—21no—
205C4×C19—21no—
206C4×C19—21no—
207C4×C19—44no—
208C4×C19—82no—
209C4×C19—81no—
210C4×C19#45812yes—
211Dic19—81no—
212Dic19—81no—
213Dic19—161no—
214C2×#123—22no—
215C2×C22⋊Q8—191no—
216C2×#121C2×D1911yescharacteristic
217C22×C4⋊C4C2×D1911yescharacteristic
218#483—382no—
219#483—382no—
220#483—381no—
221#481—381no—
222#465—382no—
223#450—381no—
224#448—381no—
225C2×#106—381no—
226C2×#103—381no—
227C2×C22⋊C8—191no—
228C2×C22⋊C8—191no—
229#399—22no—
230#390—21no—
231#384—21no—
232#380—191no—
233C4×C22⋊C4C2×D1911yescharacteristic
234#342—382no—
235#340—382no—
236#327—382no—
237C2×C19—21no—
238C2×C19—22no—
239C2×C19—22no—
240C2×C19—21no—
241C2×C19—161no—
242C2×C19#200911yescharacteristic
243C2×C19#201411yescharacteristic
244C2×C19#202211yescharacteristic
245C22×Q8—191no—
246C22×D4—21no—
247C22×D4C22⋊D1911yescharacteristic
248C23×C4—21no—
249C23×C4C22×D1911yescharacteristic
250C2×SD16—382no—
251C22×C8—192no—
252C22×C8—381no—
253#123—44no—
254#123—44no—
255C22⋊Q8—381no—
256C22⋊Q8—381no—
257C22⋊Q8—381no—
258C22⋊Q8—381no—
259#121—21no—
260#121—21no—
261#121—21no—
262#121—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—191no—
270C2×C4⋊C4—381no—
271C2×C4⋊C4—381no—
272C2×C4⋊C4C22⋊D1912yes—
273C2×C4⋊C4C22⋊D1911yescharacteristic
274C2×C22⋊C4—24no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—381no—
277C2×C22⋊C4—381no—
278C2×C22⋊C4C22⋊D1912yes—
279C2×C42—21no—
280#106—384no—
281#106—382no—
282#103—384no—
283#103—382no—
284#102—382no—
285C22⋊C8—192no—
286C22⋊C8—381no—
287C22⋊C8—381no—
288C22⋊C8—381no—
289#95—21no—
290#95—381no—
291C19#996011yescharacteristic, complemented, Sylow
292C24—21no—
293C24C2×C22⋊D1911yescharacteristic
294C2×Q8—381no—
295C2×Q8—381no—
296C2×Q8—762no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—42no—
302C2×D4—41no—
303C2×D4—41no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—21no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—381no—
313C22×C4—381no—
314C22×C4—761no—
315C22×C4D4×D1911yescharacteristic
316C22×C4D4×D1911yescharacteristic
317C22×C4D4×D1911yescharacteristic
318C22×C4#6454311yescharacteristic
319C22×C4C2×C22⋊D1911yescharacteristic
320C22×C4C2×C22⋊D1911yescharacteristic
321SD16—1522no—
322C2×C8—382no—
323C2×C8—382no—
324C2×C8—762no—
325C2×C8—762no—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—22no—
329C4⋊C4—21no—
330C4⋊C4—48no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—381no—
334C4⋊C4—381no—
335C4⋊C4—762no—
336C4⋊C4—761no—
337C4⋊C4—761no—
338C22⋊C4—22no—
339C22⋊C4—48no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—761no—
343C22⋊C4—761no—
344C22⋊C4—762no—
345C22⋊C4#6452614yescomplemented
346C42—42no—
347C23—41no—
348C23—41no—
349C23—42no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23#1059737812yes—
354C23C2×#6452612yes—
355C23#1059738411yescharacteristic
356C23#1059738611yescharacteristic
357C23#1059739911yescharacteristic
358Q8—762no—
359Q8—762no—
360D4—42no—
361D4—81no—
362D4—81no—
363D4—81no—
364D4—82no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—24no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—44no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—42no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—82no—
381C2×C4—761no—
382C2×C4—761no—
383C2×C4—1521no—
384C2×C4—1521no—
385C2×C4—1521no—
386C2×C4—1521no—
387C2×C4—1521no—
388C2×C4#1059738311yescharacteristic
389C2×C4#1059738311yescharacteristic
390C2×C4#1059738511yescharacteristic
391C2×C4#1059738511yescharacteristic
392C8—762no—
393C8—762no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—42no—
401C22—42no—
402C22—84no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22#1192645211yescharacteristic
407C22#1192669512yes—
408C22#1192674112yes—
409C22#1192691611yescharacteristic
410C22#1192693111yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—44no—
415C4—82no—
416C4—81no—
417C4—3041no—
418C4—1521no—
419C4—1521no—
420C4#1192673312yes—
421C2—22no—
422C2—21no—
423C2—21no—
424C2—22no—
425C2—161no—
426C2#1456469511yescharacteristic
427C2#1456472311yescharacteristic
428C2#1456476311yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2501C2
socleC22×C19#392
prime radicalC2×C19×#121C22
hypercenter#2501D19
hypocenterC19#9960
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2501

Complements

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

NH ≅ G/Ntype
2. C2×#11926874C2semidirect
3. #14564620C2semidirect
4. #14563721C2semidirect
6. #14561483C2semidirect
117. C22⋊C4×C19SD16semidirect
291. C19#9960semidirect
345. C22⋊C4#64526semidirect

Maximal subgroups

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

subgroupindex
#145743922
C2×#119268742
#145646202
#145637212
#145622032
#145614832
C19×#25012
#996019