Finite Group Databasebeta

← #18080581

Subgroups — #18080581

Order 4864.

472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 107 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#14572683C211yesmaximal, characteristic
2#14563721C211yesmaximal, characteristic, complemented
3#14563715C211yesmaximal, characteristic, complemented
4#14562178C211yesmaximal, characteristic
5#14561542C211yesmaximal, characteristic, complemented
6#14561511C211yesmaximal, characteristic, complemented
7C19×#3092C211yesmaximal, characteristic
8#11926622—21no—
9#11926616—21no—
10#11926616—21no—
11D4×C19⋊C8—21no—
12#11926605—21no—
13#11926511—21no—
14#11926508C2211yescharacteristic
15#11926508C2211yescharacteristic
16C2×C22⋊(C19⋊C8)C2211yescharacteristic
17#11926404C2211yescharacteristic
18#11926313—21no—
19#11926313—21no—
20#11926306—21no—
21#11926306—21no—
22#11926281—21no—
23#11926278—21no—
24C19×#525C2211yescharacteristic
25C22×C4⋊C4×C19C2211yescharacteristic
26C19×#484C412yescomplemented
27C19×#483—21no—
28C19×#481C412yescomplemented
29C19×#480—21no—
30C19×#428—21no—
31C19×#417—21no—
32C19×#407C2211yescharacteristic
33C2×#41×C19D411yescharacteristic
34C23×C4×C19—21no—
35C23×C4×C19C2311yescharacteristic
36C2×M16×C19—21no—
37C19×#123—21no—
38C19×C22⋊Q8C2×C411yescharacteristic
39C19×C22⋊Q8D411yescharacteristic
40C19×#121C2×C411yescharacteristic
41C19×#121D411yescharacteristic
42C19×#120—21no—
43C4×D4×C19—21no—
44C4×D4×C19—21no—
45C19×#117D411yescharacteristic
46C2×C4⋊C4×C19—21no—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19—21no—
49C2×C4⋊C4×C19—21no—
50C2×C4⋊C4×C19—21no—
51C2×C4⋊C4×C19C2×C412yes—
52C2×C22⋊Dic19—21no—
53C2×C4⋊Dic19—21no—
54C2×#64520—21no—
55C2×#64520—21no—
56C2×#64520D411yescharacteristic
57C2×#64520D411yescharacteristic
58C22×C19⋊C8—21no—
59C22×C19⋊C8D411yescharacteristic
60C22×C19⋊C8D411yescharacteristic
61C19×#107—22no—
62C19×#106—22no—
63C19×#103—22no—
64C19×#102—22no—
65C19×C22⋊C8—21no—
66C19×C22⋊C8C2×C412yes—
67C19⋊#95—21no—
68C22⋊(C19⋊C8)—21no—
69C22⋊(C19⋊C8)—21no—
70C22⋊(C19⋊C8)—21no—
71C22⋊(C19⋊C8)—21no—
72C22⋊(C19⋊C8)—21no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76C4⋊(C19⋊C8)—21no—
77C4⋊(C19⋊C8)—21no—
78#10597260—21no—
79C4×C19⋊C8—21no—
80C24×C19#4111yescharacteristic
81#41×C19—41no—
82#41×C19—41no—
83C2×Q8×C19C22⋊C411yescharacteristic
84C2×D4×C19—21no—
85C2×D4×C19—21no—
86C2×D4×C19—21no—
87C2×D4×C19C22⋊C411yescharacteristic
88C22×C4×C19—21no—
89C22×C4×C19—22no—
90C22×C4×C19—41no—
91C22×C4×C19—41no—
92C22×C4×C19—41no—
93C22×C4×C19—41no—
94C22×C4×C19—81no—
95C22×C4×C19—81no—
96C22×C4×C19C22×C411yescharacteristic
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19C2×D411yescharacteristic
101C22×C4×C19#4111yescharacteristic
102C22×Dic19—41no—
103M16×C19—41no—
104M16×C19—41no—
105C2×C8×C19—22no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—22no—
109C4⋊C4×C19—22no—
110C4⋊C4×C19—41no—
111C4⋊C4×C19—41no—
112C4⋊C4×C19C22⋊C411yescharacteristic
113C4⋊C4×C19C22⋊C411yescharacteristic
114C22⋊C4×C19—21no—
115C22⋊C4×C19—21no—
116C22⋊C4×C19—21no—
117C22⋊C4×C19—21no—
118C22⋊C4×C19—21no—
119C42×C19—21no—
120C22⋊Dic19—81no—
121C4⋊Dic19—41no—
122C4⋊Dic19—41no—
123#64520—41no—
124#64520—41no—
125#64520—41no—
126#64520—41no—
127#64520—81no—
128C2×C19⋊C8—21no—
129C2×C19⋊C8—21no—
130C2×C19⋊C8—21no—
131C2×C19⋊C8—21no—
132C2×C19⋊C8—41no—
133C2×C19⋊C8—41no—
134C2×C19⋊C8—41no—
135C2×C19⋊C8—81no—
136#9522—191nomaximal, Sylow
137C23×C19—21no—
138C23×C19—21no—
139C23×C19—21no—
140C23×C19—41no—
141C23×C19—41no—
142C23×C19C4×D411yescharacteristic
143C23×C19#12111yescharacteristic
144C23×C19#12311yescharacteristic
145Q8×C19—41no—
146D4×C19—41no—
147D4×C19—41no—
148D4×C19—41no—
149D4×C19—81no—
150D4×C19—81no—
151C2×C4×C19—21no—
152C2×C4×C19—21no—
153C2×C4×C19—21no—
154C2×C4×C19—21no—
155C2×C4×C19—21no—
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—21no—
159C2×C4×C19—21no—
160C2×C4×C19—41no—
161C2×C4×C19—41no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—41no—
165C2×C4×C19—42no—
166C2×C4×C19—82no—
167C2×C4×C19—81no—
168C2×C4×C19—81no—
169C2×C4×C19—82no—
170C2×C4×C19C2×C22⋊C411yescharacteristic
171C2×C4×C19C4×D411yescharacteristic
172C2×C4×C19#12011yescharacteristic
173C2×C4×C19#12111yescharacteristic
174C2×Dic19—81no—
175C2×Dic19—81no—
176C2×Dic19—81no—
177C8×C19—42no—
178C19⋊C8—41no—
179C19⋊C8—41no—
180C19⋊C8—41no—
181C19⋊C8—41no—
182C19⋊C8—81no—
183#3092D1911yescharacteristic
184#2976—191no—
185#1823—191no—
186#1821—191no—
187#1513—191no—
188#1305—191no—
189#1293—191no—
190C22×C19—21no—
191C22×C19—21no—
192C22×C19—21no—
193C22×C19—21no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—42no—
199C22×C19—42no—
200C22×C19—41no—
201C22×C19—41no—
202C22×C19—41no—
203C22×C19#38611yescharacteristic
204C22×C19#47111yescharacteristic
205C22×C19#47211yescharacteristic
206C4×C19—21no—
207C4×C19—21no—
208C4×C19—21no—
209C4×C19—41no—
210C4×C19—41no—
211C4×C19—41no—
212C4×C19—82no—
213C4×C19#45811yescharacteristic
214C4×C19#45811yescharacteristic
215Dic19—161no—
216#525C2×D1911yescharacteristic
217C22×C4⋊C4C2×D1911yescharacteristic
218#484Dic1912yescomplemented
219#483—21no—
220#481Dic1912yescomplemented
221#480—21no—
222#436—381no—
223#435—381no—
224#435—381no—
225C8×D4—381no—
226#433—381no—
227#428—21no—
228#417—21no—
229#408—381no—
230#407—191no—
231#407—191no—
232#407C2×D1911yescharacteristic
233C2×C22⋊C8—191no—
234#380—191no—
235#343—381no—
236#343—381no—
237#340—381no—
238#340—381no—
239#328—381no—
240#327—381no—
241C2×C19—21no—
242C2×C19—21no—
243C2×C19—41no—
244C2×C19—41no—
245C2×C19—81no—
246C2×C19#189011yescharacteristic
247C2×C19#190211yescharacteristic
248C2×C19#190711yescharacteristic
249C2×#41C22⋊D1911yescharacteristic
250C23×C4—21no—
251C23×C4C22×D1911yescharacteristic
252C2×M16—21no—
253C2×M16—191no—
254C2×M16—191no—
255C2×M16—381no—
256C2×M16—381no—
257C22×C8—191no—
258C22×C8—191no—
259C22×C8—381no—
260#123—21no—
261C22⋊Q8C2×Dic1911yescharacteristic
262C22⋊Q8C22⋊D1911yescharacteristic
263#121C2×Dic1911yescharacteristic
264#121C22⋊D1911yescharacteristic
265#120—21no—
266C4×D4—21no—
267C4×D4—21no—
268#117C22⋊D1911yescharacteristic
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—381no—
275C2×C4⋊C4C2×Dic1912yes—
276C2×C22⋊C4—381no—
277#107—22no—
278#106—22no—
279C4⋊C8—381no—
280C4⋊C8—381no—
281#103—22no—
282#102—22no—
283C22⋊C8—21no—
284C22⋊C8—381no—
285C22⋊C8—381no—
286C22⋊C8—381no—
287C22⋊C8—381no—
288C22⋊C8—381no—
289C22⋊C8—381no—
290C22⋊C8—381no—
291C22⋊C8—381no—
292C22⋊C8C2×Dic1912yes—
293#97—381no—
294C4×C8—381no—
295#95—381no—
296C19#952211yescharacteristic, complemented, Sylow
297C24#6454311yescharacteristic
298#41—41no—
299#41—41no—
300C2×Q8C22⋊Dic1911yescharacteristic
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4C22⋊Dic1911yescharacteristic
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—81no—
312C22×C4—81no—
313C22×C4—761no—
314C22×C4D4×D1911yescharacteristic
315C22×C4D4×D1911yescharacteristic
316C22×C4#6454311yescharacteristic
317C22×C4C22×Dic1911yescharacteristic
318C22×C4C2×C22⋊D1911yescharacteristic
319C22×C4C2×C22⋊D1911yescharacteristic
320M16—41no—
321M16—41no—
322M16—761no—
323M16—761no—
324M16—761no—
325M16—761no—
326M16—1521no—
327C2×C8—22no—
328C2×C8—381no—
329C2×C8—381no—
330C2×C8—381no—
331C2×C8—381no—
332C2×C8—761no—
333C2×C8—761no—
334C2×C8—761no—
335C2×C8—1521no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—761no—
343C4⋊C4—761no—
344C4⋊C4C22⋊Dic1911yescharacteristic
345C4⋊C4C22⋊Dic1911yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—1521no—
352C42—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—41no—
357C23—41no—
358C23D4×Dic1911yescharacteristic
359C23#1059738111yescharacteristic
360C23#1059738511yescharacteristic
361Q8—41no—
362D4—41no—
363D4—41no—
364D4—41no—
365D4—81no—
366D4—81no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—82no—
386C2×C4—1521no—
387C2×C4—1521no—
388C2×C4—1521no—
389C2×C4D4×Dic1911yescharacteristic
390C2×C4#1059738311yescharacteristic
391C2×C4#1059738511yescharacteristic
392C2×C4C2×C22⋊Dic1911yescharacteristic
393C8—42no—
394C8—761no—
395C8—761no—
396C8—761no—
397C8—761no—
398C8—1521no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—42no—
408C22—42no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22#1192642411yescharacteristic
413C22#1192680511yescharacteristic
414C22#1192681211yescharacteristic
415C4—21no—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—82no—
422C4—3041no—
423C4#1192673311yescharacteristic
424C4#1192673311yescharacteristic
425C2—21no—
426C2—21no—
427C2—41no—
428C2—41no—
429C2—81no—
430C2#1456404911yescharacteristic
431C2#1456411011yescharacteristic
432C2#1456414511yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#3092C2
socleC22×C19#386
prime radicalC19×#525C22
cosocleC23×C4×C19C23
hypercenter#3092D19
hypocenterC19#9522
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3092

Complements

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

NH ≅ G/Ntype
2. #14563721C2semidirect
3. #14563715C2semidirect
5. #14561542C2semidirect
6. #14561511C2semidirect
26. C19×#484C4semidirect
28. C19×#481C4semidirect
218. #484Dic19semidirect
220. #481Dic19semidirect
296. C19#9522semidirect

Maximal subgroups

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

subgroupindex
#145726832
#145637212
#145637152
#145621782
#145615422
#145615112
C19×#30922
#952219