Finite Group Databasebeta

← #18078606

Subgroups — #18078606

Order 4864.

622 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 113 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#14569380C211yesmaximal, characteristic
2#14566252C211yesmaximal, characteristic, complemented
3#14562204C211yesmaximal, characteristic
4#14562202C211yesmaximal, characteristic
5C2×#11926269C211yesmaximal, characteristic, complemented
6#14561502C211yesmaximal, characteristic, complemented
7C19×#1289C211yesmaximal, characteristic, complemented
8C2×#10597332—21no—
9C2×#10597376C2211yescharacteristic
10C2×#10597323—21no—
11C22×Dic19⋊C4C2211yescharacteristic
12C2×C22⋊(C19⋊C8)C2211yescharacteristic
13#11926476C412yescomplemented
14#11926466—22no—
15#11926462C412yescomplemented
16#11926441—22no—
17#11926439—22no—
18#11926421—21no—
19#11926404C2211yescharacteristic
20#11926402—21no—
21#11926279—22no—
22#11926277—22no—
23#11926269—22no—
24C2×C19×C22⋊C8C2211yescharacteristic
25C19×#380C2211yescharacteristic
26C19×#380C2211yescharacteristic
27C23×C4×C19C2311yescharacteristic
28C22×C22⋊D19—21no—
29C23×Dic19D411yescharacteristic
30C23×Dic19D411yescharacteristic
31C22×D76C2×C411yescharacteristic
32C22×C8×C19—21no—
33C2×C4⋊C4×C19—21no—
34C2×C4⋊C4×C19—21no—
35C2×C22⋊C4×C19—21no—
36C2×C22⋊C4×C19—21no—
37C2×C22⋊Dic19—21no—
38#10597376—21no—
39#10597376—21no—
40#10597376—21no—
41#10597376—21no—
42C2×(C2×D19)⋊C4—21no—
43C2×(C2×D19)⋊C4—22no—
44C2×(C2×D19)⋊C4—22no—
45C2×C4⋊Dic19—22no—
46C2×C4⋊Dic19—21no—
47C2×C4⋊Dic19C2×C411yescharacteristic
48C2×Dic19⋊C4—21no—
49C2×Dic19⋊C4—21no—
50C2×Dic19⋊C4—21no—
51C2×Dic19⋊C4—21no—
52C2×Dic19⋊C4—22no—
53C2×Dic19⋊C4—22no—
54C2×Dic19⋊C4C2×C412yes—
55C2×Dic19⋊C4D412yes—
56C2×C4×Dic19—22no—
57C22×C19⋊C8—21no—
58#10597332—42no—
59#10597332—42no—
60#10597323—42no—
61#10597323—42no—
62C19×C22⋊C8—21no—
63C19×C22⋊C8—21no—
64C19×#95C2×C412yes—
65C19×#95D412yes—
66C19⋊#95—22no—
67C19⋊#95—22no—
68C19⋊#95D412yes—
69C22⋊(C19⋊C8)—21no—
70C22⋊(C19⋊C8)—21no—
71C24×C19C2×D411yescharacteristic
72C23×D19—21no—
73C22×C4×C19—22no—
74C22×C4×C19—22no—
75C22×C4×C19—81no—
76C22×C4×C19C22×C411yescharacteristic
77C22×C4×C19C2×D411yescharacteristic
78C22×C4×C19C2×D411yescharacteristic
79C22×C4×C19C2×D411yescharacteristic
80C22×C4×C19#4111yescharacteristic
81C22×C4×C19#4111yescharacteristic
82C2×C22⋊D19—41no—
83C2×C22⋊D19—41no—
84C2×C22⋊D19—41no—
85C2×C22⋊D19—41no—
86C2×C22⋊D19—41no—
87C2×C22⋊D19—41no—
88C22×Dic19—21no—
89C22×Dic19—21no—
90C22×Dic19—21no—
91C22×Dic19—21no—
92C22×Dic19—21no—
93C22×Dic19—21no—
94C22×Dic19—21no—
95C22×Dic19—22no—
96C22×Dic19—81no—
97C22×Dic19C22⋊C412yes—
98C22×Dic19C22⋊C412yes—
99C22×Dic19D812yes—
100C22×Dic19SD1612yes—
101C2×D76—21no—
102C2×D76—21no—
103C2×D76—81no—
104C2×C8×C19—41no—
105C2×C8×C19—81no—
106C4⋊C4×C19—81no—
107C4⋊C4×C19—81no—
108C22⋊C4×C19—41no—
109C22⋊C4×C19—41no—
110C22⋊C4×C19—41no—
111C22⋊C4×C19—41no—
112C22⋊Dic19—41no—
113C22⋊Dic19—41no—
114(C2×D19)⋊C4—41no—
115(C2×D19)⋊C4—41no—
116(C2×D19)⋊C4—44no—
117(C2×D19)⋊C4—82no—
118C4⋊Dic19—21no—
119C4⋊Dic19—21no—
120C4⋊Dic19—44no—
121C4⋊Dic19—81no—
122Dic19⋊C4—22no—
123Dic19⋊C4—22no—
124Dic19⋊C4—22no—
125Dic19⋊C4—22no—
126Dic19⋊C4—44no—
127Dic19⋊C4—82no—
128C4×Dic19—44no—
129C2×C19⋊C8—41no—
130C2×C19⋊C8—81no—
131#9204—191nomaximal, Sylow
132C23×C19—41no—
133C23×C19—41no—
134C23×C19C2×C22⋊C411yescharacteristic
135C23×C19#12011yescharacteristic
136C23×C19#12311yescharacteristic
137C23×C19C2×D811yescharacteristic
138C23×C19C2×SD1611yescharacteristic
139C23×C19AGL(1,ℤ/8)11yescharacteristic
140C23×C19#13711yescharacteristic
141C22×D19—42no—
142C22×D19—42no—
143C22×D19—41no—
144C22×D19—41no—
145C22×D19—41no—
146C2×C4×C19—41no—
147C2×C4×C19—41no—
148C2×C4×C19—41no—
149C2×C4×C19—41no—
150C2×C4×C19—41no—
151C2×C4×C19—41no—
152C2×C4×C19—42no—
153C2×C4×C19—42no—
154C2×C4×C19—42no—
155C2×C4×C19—42no—
156C2×C4×C19—42no—
157C2×C4×C19—42no—
158C2×C4×C19C4×D411yescharacteristic
159C2×C4×C19C4×D411yescharacteristic
160C2×C4×C19#12111yescharacteristic
161C2×C4×C19#12111yescharacteristic
162C22⋊D19—81no—
163C22⋊D19—81no—
164C22⋊D19—81no—
165C22⋊D19—81no—
166C2×Dic19—22no—
167C2×Dic19—22no—
168C2×Dic19—22no—
169C2×Dic19—22no—
170C2×Dic19—22no—
171C2×Dic19—22no—
172C2×Dic19—22no—
173C2×Dic19—42no—
174C2×Dic19—42no—
175C2×Dic19—42no—
176C2×Dic19—42no—
177C2×Dic19—41no—
178C2×Dic19—41no—
179C2×Dic19—41no—
180C2×Dic19—42no—
181C2×Dic19—81no—
182C2×Dic19#10214yes—
183D76—81no—
184D76—81no—
185C8×C19—81no—
186C19⋊C8—81no—
187#2618—191no—
188#2316—191no—
189#1519—191no—
190#1519—191no—
191C2×#324—191no—
192#1289—191no—
193#1289D1911yescharacteristic, complemented
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—41no—
201C22×C19—41no—
202C22×C19—41no—
203C22×C19—41no—
204C22×C19#38611yescharacteristic
205C22×C19C2×#10211yescharacteristic
206C22×C19#41711yescharacteristic
207C22×C19#44711yescharacteristic
208C22×C19#44811yescharacteristic
209C22×C19#48011yescharacteristic
210C22×C19#48111yescharacteristic
211C2×D19—82no—
212C2×D19—82no—
213C2×D19—81no—
214C2×D19—81no—
215C2×D19—81no—
216C4×C19—21no—
217C4×C19—21no—
218C4×C19—21no—
219C4×C19—21no—
220C4×C19—82no—
221C4×C19—82no—
222Dic19—24no—
223Dic19—42no—
224Dic19—82no—
225Dic19—81no—
226C2×#123—381no—
227C2×#121—191no—
228C2×#117—381no—
229C22×C4⋊C4—191no—
230C2×C22⋊C8—191no—
231C2×C22⋊C8C2×D1911yescharacteristic
232#398—192no—
233#396—382no—
234#394—192no—
235#389—382no—
236#389—382no—
237#386—381no—
238#380—191no—
239#380—381no—
240#380C2×D1911yescharacteristic
241#380C2×D1911yescharacteristic
242#327—382no—
243#327—382no—
244#324—382no—
245C2×C19—21no—
246C2×C19—21no—
247C2×C19—21no—
248C2×C19—21no—
249C2×C19—21no—
250C2×C19—21no—
251C2×C19#187411yescharacteristic
252C2×C19#191211yescharacteristic
253C2×C19#191311yescharacteristic
254D19—161no—
255C22×D4—191no—
256C22×D4—381no—
257C23×C4—191no—
258C23×C4—191no—
259C23×C4C22×D1911yescharacteristic
260C22×C8—21no—
261C22×C8—381no—
262#123—762no—
263#123—762no—
264#121—381no—
265#121—381no—
266#121—381no—
267#121—381no—
268#117—762no—
269#117—762no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—192no—
273C2×C4⋊C4—192no—
274C2×C4⋊C4—191no—
275C2×C4⋊C4—381no—
276C2×C4⋊C4—381no—
277C2×C4⋊C4—381no—
278C2×C4⋊C4—381no—
279C2×C4⋊C4—382no—
280C2×C4⋊C4—382no—
281C2×C4⋊C4—382no—
282C2×C4⋊C4—381no—
283C2×C22⋊C4—21no—
284C2×C22⋊C4—21no—
285C2×C22⋊C4—382no—
286C2×C22⋊C4—381no—
287C2×C22⋊C4—381no—
288C2×C22⋊C4—382no—
289C2×C42—382no—
290C22⋊C8—21no—
291C22⋊C8—21no—
292C22⋊C8—381no—
293C22⋊C8—381no—
294#95—192no—
295#95—382no—
296#95—382no—
297#95C4×D1912yes—
298#95D7612yes—
299C19#920411yescharacteristic, complemented, Sylow
300C24—381no—
301C24D4×D1911yescharacteristic
302C2×D4—381no—
303C2×D4—381no—
304C2×D4—761no—
305C2×D4—761no—
306C2×D4—761no—
307C2×D4—761no—
308C2×D4—761no—
309C2×D4—761no—
310C2×D4—1521no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—81no—
314C22×C4—192no—
315C22×C4—192no—
316C22×C4—192no—
317C22×C4—192no—
318C22×C4—381no—
319C22×C4—381no—
320C22×C4—381no—
321C22×C4—381no—
322C22×C4—381no—
323C22×C4—381no—
324C22×C4—381no—
325C22×C4—382no—
326C22×C4—1521no—
327C22×C4C2×C4×D1911yescharacteristic
328C22×C4C2×D7611yescharacteristic
329C22×C4#6454111yescharacteristic
330C22×C4D4×D1911yescharacteristic
331C22×C4D4×D1911yescharacteristic
332C22×C4#6454511yescharacteristic
333C2×C8—41no—
334C2×C8—81no—
335C2×C8—761no—
336C2×C8—1521no—
337C4⋊C4—81no—
338C4⋊C4—81no—
339C4⋊C4—382no—
340C4⋊C4—382no—
341C4⋊C4—382no—
342C4⋊C4—382no—
343C4⋊C4—381no—
344C4⋊C4—381no—
345C4⋊C4—764no—
346C4⋊C4—764no—
347C4⋊C4—1522no—
348C4⋊C4—1521no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C22⋊C4—41no—
353C22⋊C4—764no—
354C22⋊C4—761no—
355C22⋊C4—761no—
356C22⋊C4—761no—
357C22⋊C4—761no—
358C22⋊C4—1522no—
359C42—764no—
360C23—41no—
361C23—41no—
362C23—762no—
363C23—762no—
364C23—761no—
365C23—761no—
366C23—761no—
367C23C22⋊C4×D1911yescharacteristic
368C23#1059732811yescharacteristic
369C23#1059734011yescharacteristic
370C23D8×D1911yescharacteristic
371C23SD16×D1911yescharacteristic
372C23#1059736011yescharacteristic
373C23#1059736411yescharacteristic
374D4—1521no—
375D4—1521no—
376D4—1521no—
377D4—1521no—
378D4—1521no—
379D4—1521no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—194no—
393C2×C4—382no—
394C2×C4—382no—
395C2×C4—382no—
396C2×C4—382no—
397C2×C4—382no—
398C2×C4—382no—
399C2×C4—382no—
400C2×C4—762no—
401C2×C4—762no—
402C2×C4—762no—
403C2×C4—762no—
404C2×C4—761no—
405C2×C4—761no—
406C2×C4—761no—
407C2×C4—762no—
408C2×C4—1521no—
409C2×C4C4×D7611yescharacteristic
410C2×C4#1059733011yescharacteristic
411C2×C4#1059733911yescharacteristic
412C2×C4#1059734111yescharacteristic
413C8—81no—
414C8—1521no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—1522no—
426C22—1522no—
427C22—1521no—
428C22—1521no—
429C22—1521no—
430C22#1192642211yescharacteristic
431C22#102×D1911yescharacteristic
432C22#1192654411yescharacteristic
433C22#1192667911yescharacteristic
434C22#1192668411yescharacteristic
435C22#1192685911yescharacteristic
436C22#1192686411yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—82no—
442C4—82no—
443C4—384no—
444C4—762no—
445C4—1522no—
446C4—1521no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—3041no—
454C2#1456395111yescharacteristic
455C2#1456417111yescharacteristic
456C2#1456417611yescharacteristic
subgroupG/H
centerC22#11926422
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1289C2
socleC22×C19#386
prime radicalC2×#10597376C22
cosocleC23×C4×C19C23
hypercenter#1289D19
hypocenterC19#9204
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
2. #14566252C2semidirect
5. C2×#11926269C2semidirect
6. #14561502C2semidirect
7. C19×#1289C2semidirect
13. #11926476C4semidirect
15. #11926462C4semidirect
193. #1289D19semidirect
299. C19#9204semidirect

Maximal subgroups

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

subgroupindex
#145693802
#145662522
#145622042
#145622022
C2×#119262692
#145615022
C19×#12892
#920419