Finite Group Databasebeta

← #18079723

Subgroups — #18079723

Order 4864.

732 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 115 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#14566476C211yesmaximal, characteristic
2#14564621C211yesmaximal, characteristic, complemented
3#14563579C211yesmaximal, characteristic
4#14562155C211yesmaximal, characteristic, complemented
5#14561540C211yesmaximal, characteristic, complemented
6#14561520C211yesmaximal, characteristic, complemented
7C19×#3007C211yesmaximal, characteristic
8C2×Q8×Dic19—21no—
9C2×#10597294—22no—
10#11926508C2211yescharacteristic
11#11926447—21no—
12#11926447—22no—
13#11926404—21no—
14#11926404C2211yescharacteristic
15C4×C22⋊Dic19—21no—
16C4×C22⋊Dic19C2211yescharacteristic
17C4×C22⋊Dic19C2211yescharacteristic
18#11926311—22no—
19#11926281—21no—
20#11926281—21no—
21C22×#41×C19C2211yescharacteristic
22C2×C19×#137C412yescomplemented
23C2×C19×C22⋊Q8C2211yescharacteristic
24C19×#452—22no—
25C19×#451—21no—
26C19×#450—21no—
27C19×#417C412yescomplemented
28C19×#407C2211yescharacteristic
29C2×#41×C19—21no—
30C2×#41×C19—21no—
31C2×#41×C19—44no—
32C2×#41×C19C2×C412yes—
33C2×#41×C19D412yes—
34C22×Q8×C19C2×C411yescharacteristic
35C22×Q8×C19D411yescharacteristic
36C22×D4×C19—21no—
37C22×D4×C19D411yescharacteristic
38C23×C4×C19—21no—
39C23×C4×C19C2311yescharacteristic
40C19×#137—44no—
41C2×Q16×C19—22no—
42C2×SD16×C19—22no—
43C2×M16×C19C2×C412yes—
44C19×C22⋊Q8—21no—
45C19×C22⋊Q8—21no—
46C19×C22⋊Q8—21no—
47C19×C22⋊Q8—21no—
48C2×C4⋊C4×C19—21no—
49C2×C4⋊C4×C19C2×C411yescharacteristic
50C2×C22⋊C4×C19—21no—
51C2×C22⋊Dic19—21no—
52C2×C22⋊Dic19—22no—
53C2×C22⋊Dic19—21no—
54C2×C22⋊Dic19—22no—
55C2×C22⋊Dic19D412yes—
56Q8×Dic19—44no—
57C2×C4⋊Dic19—22no—
58C2×C4⋊Dic19—21no—
59C2×C4×Dic19—22no—
60C2×C4×Dic19—21no—
61C2×C4×Dic19—21no—
62C2×#64520—21no—
63C19×#103—22no—
64C19×#102—22no—
65C19×C22⋊C8—21no—
66C19×C22⋊C8—21no—
67#10597294—44no—
68C19⋊#95—21no—
69C19⋊#95—21no—
70C19⋊#95D411yescharacteristic
71C19⋊#95D411yescharacteristic
72C22⋊(C19⋊C8)—21no—
73C22⋊(C19⋊C8)—21no—
74C24×C19—21no—
75C24×C19C2×D411yescharacteristic
76#41×C19—24no—
77#41×C19—24no—
78#41×C19—42no—
79#41×C19—42no—
80#41×C19—44no—
81#41×C19—44no—
82C2×Q8×C19—24no—
83C2×Q8×C19—21no—
84C2×Q8×C19—21no—
85C2×Q8×C19—21no—
86C2×Q8×C19—42no—
87C2×Q8×C19C22⋊C412yes—
88C2×D4×C19—22no—
89C2×D4×C19—22no—
90C2×D4×C19—21no—
91C2×D4×C19—42no—
92C2×D4×C19—44no—
93C2×D4×C19C22⋊C412yes—
94C22×C4×C19—21no—
95C22×C4×C19—22no—
96C22×C4×C19—22no—
97C22×C4×C19—21no—
98C22×C4×C19—21no—
99C22×C4×C19—42no—
100C22×C4×C19—44no—
101C22×C4×C19C22×C411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19C2×D411yescharacteristic
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19#4111yescharacteristic
106C22×C4×C19#4111yescharacteristic
107C22×Dic19—21no—
108C22×Dic19—21no—
109C22×Dic19—22no—
110C22×Dic19—41no—
111Q16×C19—44no—
112SD16×C19—44no—
113M16×C19—42no—
114C2×C8×C19—22no—
115C4⋊C4×C19—21no—
116C4⋊C4×C19—21no—
117C4⋊C4×C19—41no—
118C4⋊C4×C19—41no—
119C22⋊C4×C19—41no—
120C22⋊C4×C19—41no—
121C22⋊Dic19—22no—
122C22⋊Dic19—42no—
123C22⋊Dic19—44no—
124C22⋊Dic19—41no—
125C22⋊Dic19—42no—
126C22⋊Dic19—82no—
127C4⋊Dic19—44no—
128C4⋊Dic19—42no—
129C4×Dic19—44no—
130C4×Dic19—42no—
131C4×Dic19—42no—
132#64520—42no—
133C2×C19⋊C8—41no—
134#9364—191nomaximal, Sylow
135C23×C19—21no—
136C23×C19—21no—
137C23×C19—22no—
138C23×C19—41no—
139C23×C19—41no—
140C23×C19—42no—
141C23×C19—42no—
142C23×C19—41no—
143C23×C19—41no—
144C23×C19C4×D411yescharacteristic
145C23×C19#12011yescharacteristic
146C23×C19#12111yescharacteristic
147Q8×C19—24no—
148Q8×C19—22no—
149Q8×C19—42no—
150Q8×C19—81no—
151Q8×C19#9914yes—
152D4×C19—22no—
153D4×C19—22no—
154D4×C19—44no—
155D4×C19—44no—
156D4×C19—42no—
157C2×C4×C19—24no—
158C2×C4×C19—22no—
159C2×C4×C19—22no—
160C2×C4×C19—22no—
161C2×C4×C19—22no—
162C2×C4×C19—41no—
163C2×C4×C19—41no—
164C2×C4×C19—41no—
165C2×C4×C19—44no—
166C2×C4×C19—44no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19—81no—
170C2×C4×C19—81no—
171C2×C4×C19C2×C22⋊C411yescharacteristic
172C2×C4×C19C4×D411yescharacteristic
173C2×C4×C19#12111yescharacteristic
174C2×C4×C19#12311yescharacteristic
175C2×Dic19—22no—
176C2×Dic19—41no—
177C2×Dic19—41no—
178C2×Dic19—41no—
179C2×Dic19—42no—
180C2×Dic19—42no—
181C2×Dic19—41no—
182C2×Dic19—42no—
183C2×Dic19—42no—
184C2×Dic19—41no—
185C2×Dic19—81no—
186C2×Dic19—81no—
187C8×C19—42no—
188C19⋊C8—81no—
189#3007D1911yescharacteristic
190#2341—191no—
191#1996—191no—
192#1789—191no—
193#1508—191no—
194#1305—191no—
195#1297—191no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—21no—
202C22×C19—21no—
203C22×C19—21no—
204C22×C19—42no—
205C22×C19—42no—
206C22×C19—42no—
207C22×C19—81no—
208C22×C19—81no—
209C22×C19—82no—
210C22×C19—82no—
211C22×C19#38611yescharacteristic
212C22×C19#45511yescharacteristic
213C22×C19#45611yescharacteristic
214C4×C19—21no—
215C4×C19—24no—
216C4×C19—21no—
217C4×C19—21no—
218C4×C19—81no—
219C4×C19—81no—
220C4×C19C2×#9912yes—
221Dic19—42no—
222Dic19—82no—
223Dic19—81no—
224Dic19—82no—
225C22×#41C2×D1911yescharacteristic
226C2×#137Dic1912yescomplemented
227C2×C22⋊Q8C2×D1911yescharacteristic
228C2×C4×Q8—381no—
229#452—22no—
230#451—21no—
231#450—21no—
232C2×#104—382no—
233#417Dic1912yescomplemented
234#407—191no—
235#407C2×D1911yescharacteristic
236#390—382no—
237#390—381no—
238#380—191no—
239#380—381no—
240C4×C22⋊C4—191no—
241C4×C22⋊C4—191no—
242C4×C22⋊C4—381no—
243#342—382no—
244#328—381no—
245#328—381no—
246C2×C19—21no—
247C2×C19—21no—
248C2×C19—41no—
249C2×C19—41no—
250C2×C19—82no—
251C2×C19#188211yescharacteristic
252C2×C19#189811yescharacteristic
253C2×C19#190611yescharacteristic
254C2×#41—21no—
255C2×#41—21no—
256C2×#41—44no—
257C2×#41C2×Dic1912yes—
258C2×#41C22⋊D1912yes—
259C22×Q8C2×Dic1911yescharacteristic
260C22×Q8C22⋊D1911yescharacteristic
261C22×D4—21no—
262C22×D4C22⋊D1911yescharacteristic
263C23×C4—21no—
264C23×C4C22×D1911yescharacteristic
265#137—44no—
266C2×Q16—22no—
267C2×SD16—22no—
268C2×M16—381no—
269C2×M16C2×Dic1912yes—
270C22⋊Q8—21no—
271C22⋊Q8—21no—
272C22⋊Q8—21no—
273C22⋊Q8—21no—
274C4×Q8—764no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—382no—
277C2×C4⋊C4—381no—
278C2×C4⋊C4C2×Dic1911yescharacteristic
279C2×C22⋊C4—21no—
280C2×C22⋊C4—192no—
281C2×C22⋊C4—381no—
282C2×C22⋊C4—382no—
283C2×C22⋊C4—381no—
284C2×C22⋊C4—382no—
285C2×C42—382no—
286C2×C42—381no—
287C2×C42—381no—
288#104—764no—
289#103—22no—
290#102—22no—
291C22⋊C8—21no—
292C22⋊C8—21no—
293C22⋊C8—381no—
294C22⋊C8—381no—
295#95—191no—
296#95—191no—
297#95—381no—
298#95—381no—
299C19#936411yescharacteristic, complemented, Sylow
300C24—21no—
301C24D4×D1911yescharacteristic
302#41—24no—
303#41—24no—
304#41—42no—
305#41—42no—
306#41—44no—
307#41—44no—
308C2×Q8—24no—
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—21no—
312C2×Q8—42no—
313C2×Q8C22⋊Dic1912yes—
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—21no—
317C2×D4—42no—
318C2×D4—44no—
319C2×D4C22⋊Dic1912yes—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—42no—
326C22×C4—44no—
327C22×C4—381no—
328C22×C4—381no—
329C22×C4—382no—
330C22×C4—761no—
331C22×C4D4×D1911yescharacteristic
332C22×C4#6454311yescharacteristic
333C22×C4#6454311yescharacteristic
334C22×C4C22×Dic1911yescharacteristic
335C22×C4C2×C22⋊D1911yescharacteristic
336C22×C4C2×C22⋊D1911yescharacteristic
337Q16—44no—
338SD16—44no—
339M16—42no—
340M16—762no—
341C2×C8—22no—
342C2×C8—761no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—764no—
348C4⋊C4—762no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—382no—
352C22⋊C4—762no—
353C22⋊C4—764no—
354C22⋊C4—761no—
355C22⋊C4—762no—
356C22⋊C4—1522no—
357C42—764no—
358C42—762no—
359C42—762no—
360C23—21no—
361C23—21no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—42no—
367C23—41no—
368C23—41no—
369C23D4×Dic1911yescharacteristic
370C23#1059738311yescharacteristic
371C23#1059738511yescharacteristic
372Q8—24no—
373Q8—22no—
374Q8—42no—
375Q8—81no—
376Q8#1059729114yes—
377D4—22no—
378D4—22no—
379D4—44no—
380D4—44no—
381D4—42no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—382no—
397C2×C4—761no—
398C2×C4—761no—
399C2×C4—761no—
400C2×C4—762no—
401C2×C4—762no—
402C2×C4—761no—
403C2×C4—762no—
404C2×C4—762no—
405C2×C4—761no—
406C2×C4—1521no—
407C2×C4—1521no—
408C2×C4D4×Dic1911yescharacteristic
409C2×C4#1059738111yescharacteristic
410C2×C4#1059738511yescharacteristic
411C2×C4C2×C22⋊Dic1911yescharacteristic
412C8—42no—
413C8—1521no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—81no—
426C22—81no—
427C22—82no—
428C22—82no—
429C22#1192642411yescharacteristic
430C22#1192672011yescharacteristic
431C22#1192672511yescharacteristic
432C4—21no—
433C4—24no—
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—762no—
439C4—1522no—
440C4—1521no—
441C4—1522no—
442C4C2×#1059729112yes—
443C2—21no—
444C2—21no—
445C2—41no—
446C2—41no—
447C2—82no—
448C2#1456400611yescharacteristic
449C2#1456408911yescharacteristic
450C2#1456413811yescharacteristic
subgroupG/H
centerC22#11926424
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#3007C2
socleC22×C19#386
prime radicalC22×#41×C19C22
cosocleC23×C4×C19C23
hypercenter#3007D19
hypocenterC19#9364
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
2. #14564621C2semidirect
4. #14562155C2semidirect
5. #14561540C2semidirect
6. #14561520C2semidirect
22. C2×C19×#137C4semidirect
27. C19×#417C4semidirect
226. C2×#137Dic19semidirect
233. #417Dic19semidirect
299. C19#9364semidirect

Maximal subgroups

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

subgroupindex
#145664762
#145646212
#145635792
#145621552
#145615402
#145615202
C19×#30072
#936419