Finite Group Databasebeta

← #18082922

Subgroups — #18082922

Order 4864.

600 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 85 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#14573571C211yesmaximal, characteristic
2#14567922C211yesmaximal, characteristic, complemented
3#14563735C211yesmaximal, characteristic, complemented
4#14562164C211yesmaximal, characteristic
5#14561965C211yesmaximal, characteristic, complemented
6#14561488C211yesmaximal, characteristic, complemented
7C19×#2591C211yesmaximal, characteristic
8C2×#10597372C2211yescharacteristic
9#11926865—22no—
10#11926860—21no—
11#11926855—21no—
12#11926584—21no—
13#11926549—21no—
14#11926508C2211yescharacteristic
15#11926508C2211yescharacteristic
16#11926483—21no—
17#11926474—21no—
18#11926425—22no—
19#11926417—21no—
20#11926407—21no—
21#11926407C2211yescharacteristic
22#11926304—22no—
23#11926278—22no—
24#11926270—22no—
25C2×C19×#121C2211yescharacteristic
26C22×C4⋊C4×C19C2211yescharacteristic
27C19×#400—21no—
28C19×#394—21no—
29C19×#388—22no—
30C19×#386—21no—
31C19×#386—21no—
32C4×C22⋊C4×C19C2211yescharacteristic
33C22×D4×C19—21no—
34C22×D4×C19D411yescharacteristic
35C23×C4×C19D411yescharacteristic
36C23×C4×C19D411yescharacteristic
37C23×C4×C19C2311yescharacteristic
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—21no—
47C2×C4⋊C4×C19—21no—
48C2×C4⋊C4×C19D411yescharacteristic
49C2×C22⋊C4×C19—22no—
50C2×C22⋊C4×C19—21no—
51C2×C22⋊C4×C19—21no—
52C2×C22⋊C4×C19—22no—
53C2×C42×C19D412yes—
54C2×C22⋊Dic19—21no—
55C2×C22⋊Dic19—21no—
56#10597372—21no—
57#10597372—21no—
58#10597372—21no—
59#10597372—21no—
60C2×C4⋊Dic19D411yescharacteristic
61C2×C4⋊Dic19D411yescharacteristic
62C2×Dic19⋊C4—22no—
63C2×C4×Dic19—21no—
64C2×#64520—21no—
65C2×#64520—21no—
66C19×#95—22no—
67C19×#95—22no—
68C19×#95—21no—
69#10597289—22no—
70#10597289—22no—
71C19⋊#95—22no—
72C19⋊#95—22no—
73C19⋊#95—22no—
74C19⋊#95—21no—
75C19⋊#95D412yes—
76C22⋊(C19⋊C8)—21no—
77C22⋊(C19⋊C8)—21no—
78C22⋊(C19⋊C8)—21no—
79C22⋊(C19⋊C8)D412yes—
80#10597265—22no—
81#10597264—22no—
82C24×C19—21no—
83C24×C19C2×D411yescharacteristic
84C2×D4×C19—21no—
85C2×D4×C19—21no—
86C2×D4×C19—42no—
87C2×D4×C19—44no—
88C2×D4×C19—41no—
89C2×D4×C19—41no—
90C22×C4×C19—21no—
91C22×C4×C19—21no—
92C22×C4×C19—21no—
93C22×C4×C19—22no—
94C22×C4×C19—21no—
95C22×C4×C19—21no—
96C22×C4×C19—21no—
97C22×C4×C19—21no—
98C22×C4×C19—42no—
99C22×C4×C19—42no—
100C22×C4×C19—42no—
101C22×C4×C19C2×D411yescharacteristic
102C22×C4×C19C2×D411yescharacteristic
103C22×C4×C19C2×D411yescharacteristic
104C22×C4×C19C2×D411yescharacteristic
105C22×C4×C19C2×D411yescharacteristic
106C22×C4×C19#4111yescharacteristic
107C22×Dic19—22no—
108C22×Dic19—21no—
109C22×Dic19—21no—
110C4⋊C4×C19—21no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19—41no—
113C4⋊C4×C19—41no—
114C4⋊C4×C19—41no—
115C4⋊C4×C19—41no—
116C22⋊C4×C19—44no—
117C22⋊C4×C19—42no—
118C22⋊C4×C19—41no—
119C22⋊C4×C19—41no—
120C22⋊C4×C19—82no—
121C42×C19—42no—
122C22⋊Dic19—42no—
123C22⋊Dic19—41no—
124C22⋊Dic19—41no—
125C4⋊Dic19—21no—
126C4⋊Dic19—21no—
127C4⋊Dic19—21no—
128C4⋊Dic19—21no—
129Dic19⋊C4—44no—
130C4×Dic19—41no—
131C4×Dic19—41no—
132#64520—42no—
133#64520—42no—
134C2×C19⋊C8—22no—
135C2×C19⋊C8—41no—
136#9941—191nomaximal, Sylow
137C23×C19—22no—
138C23×C19—22no—
139C23×C19—41no—
140C23×C19—42no—
141C23×C19—42no—
142C23×C19—41no—
143C23×C19—42no—
144C23×C19#12011yescharacteristic
145C23×C19#12011yescharacteristic
146C23×C19#12111yescharacteristic
147D4×C19—42no—
148D4×C19—81no—
149D4×C19—82no—
150D4×C19—82no—
151C2×C4×C19—22no—
152C2×C4×C19—22no—
153C2×C4×C19—22no—
154C2×C4×C19—22no—
155C2×C4×C19—22no—
156C2×C4×C19—41no—
157C2×C4×C19—41no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—41no—
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—42no—
168C2×C4×C19—41no—
169C2×C4×C19—41no—
170C2×C4×C19—42no—
171C2×C4×C19—42no—
172C2×C4×C19—81no—
173C2×C4×C19#12011yescharacteristic
174C2×C4×C19#12111yescharacteristic
175C2×C4×C19#12111yescharacteristic
176C2×C4×C19#12711yescharacteristic
177C2×Dic19—42no—
178C2×Dic19—42no—
179C2×Dic19—42no—
180C2×Dic19—41no—
181C2×Dic19—41no—
182C2×Dic19—42no—
183C2×Dic19—42no—
184C19⋊C8—42no—
185C19⋊C8—81no—
186#3094—191no—
187#2591D1911yescharacteristic
188#2484—191no—
189#1826—191no—
190#1510—191no—
191#1463—191no—
192#1284—191no—
193C22×C19—21no—
194C22×C19—21no—
195C22×C19—21no—
196C22×C19—21no—
197C22×C19—21no—
198C22×C19—21no—
199C22×C19—21no—
200C22×C19—44no—
201C22×C19—84no—
202C22×C19—81no—
203C22×C19—81no—
204C22×C19—81no—
205C22×C19#39211yescharacteristic
206C22×C19#45412yes—
207C22×C19#45812yes—
208C4×C19—21no—
209C4×C19—21no—
210C4×C19—21no—
211C4×C19—21no—
212C4×C19—42no—
213C4×C19—82no—
214C4×C19—81no—
215C4×C19—81no—
216Dic19—82no—
217Dic19—81no—
218Dic19—81no—
219C2×#121C2×D1911yescharacteristic
220C2×#117—191no—
221C22×C4⋊C4C2×D1911yescharacteristic
222#482—382no—
223#481—381no—
224#480—381no—
225#428—381no—
226#418—381no—
227#407—191no—
228#407—191no—
229#400—21no—
230#400—381no—
231#398—381no—
232#394—21no—
233#388—22no—
234#387—382no—
235#386—21no—
236#386—21no—
237#385—381no—
238#381—191no—
239#381—381no—
240C4×C22⋊C4C2×D1911yescharacteristic
241#339—382no—
242#327—382no—
243#324—382no—
244C2×C19—22no—
245C2×C19—22no—
246C2×C19—41no—
247C2×C19—161no—
248C2×C19#200311yescharacteristic
249C2×C19#201011yescharacteristic
250C2×C19#202211yescharacteristic
251C22×D4—21no—
252C22×D4C22⋊D1911yescharacteristic
253C23×C4C22⋊D1911yescharacteristic
254C23×C4C22⋊D1911yescharacteristic
255C23×C4C22×D1911yescharacteristic
256C2×M16—381no—
257C2×M16—381no—
258#121—21no—
259#121—21no—
260#121—21no—
261#121—21no—
262#117—381no—
263#117—381no—
264#117—381no—
265#117—381no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—191no—
273C2×C4⋊C4—191no—
274C2×C4⋊C4—382no—
275C2×C4⋊C4C22⋊D1911yescharacteristic
276C2×C22⋊C4—22no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—22no—
280C2×C22⋊C4—381no—
281C2×C22⋊C4—381no—
282C2×C42—381no—
283C2×C42C22⋊D1912yes—
284#107—382no—
285#106—382no—
286#102—382no—
287#102—382no—
288C22⋊C8—192no—
289C22⋊C8—381no—
290C22⋊C8—381no—
291C22⋊C8—381no—
292#95—22no—
293#95—22no—
294#95—21no—
295#95—192no—
296#95—382no—
297#95—382no—
298#95—382no—
299#95—381no—
300C19#994111yescharacteristic, complemented, Sylow
301C24—21no—
302C24C2×C22⋊D1911yescharacteristic
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—42no—
306C2×D4—44no—
307C2×D4—41no—
308C2×D4—41no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—382no—
321C22×C4—381no—
322C22×C4—381no—
323C22×C4D4×D1911yescharacteristic
324C22×C4D4×D1911yescharacteristic
325C22×C4D4×D1911yescharacteristic
326C22×C4#6454311yescharacteristic
327C22×C4C2×C22⋊D1911yescharacteristic
328C22×C4C2×C22⋊D1911yescharacteristic
329M16—762no—
330M16—762no—
331C2×C8—382no—
332C2×C8—761no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—41no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—41no—
339C4⋊C4—381no—
340C4⋊C4—381no—
341C4⋊C4—381no—
342C4⋊C4—381no—
343C4⋊C4—764no—
344C22⋊C4—44no—
345C22⋊C4—42no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—82no—
349C22⋊C4—762no—
350C22⋊C4—761no—
351C22⋊C4—761no—
352C42—42no—
353C42—761no—
354C42—761no—
355C23—22no—
356C23—22no—
357C23—41no—
358C23—42no—
359C23—42no—
360C23—41no—
361C23—42no—
362C23#1059738311yescharacteristic
363C23#1059738511yescharacteristic
364C23#1059739911yescharacteristic
365D4—42no—
366D4—81no—
367D4—82no—
368D4—82no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—81no—
391C2×C4—762no—
392C2×C4—762no—
393C2×C4—762no—
394C2×C4—761no—
395C2×C4—761no—
396C2×C4—762no—
397C2×C4—762no—
398C2×C4#1059738311yescharacteristic
399C2×C4#1059738411yescharacteristic
400C2×C4#1059738511yescharacteristic
401C2×C4#1059738611yescharacteristic
402C8—762no—
403C8—1521no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—44no—
412C22—84no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22#1192645211yescharacteristic
417C22#1192671612yes—
418C22#1192673412yes—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—21no—
423C4—42no—
424C4—82no—
425C4—81no—
426C4—81no—
427C4—1522no—
428C4—1521no—
429C4—1521no—
430C2—22no—
431C2—22no—
432C2—41no—
433C2—161no—
434C2#1456465711yescharacteristic
435C2#1456470011yescharacteristic
436C2#1456476411yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC19×#2591C2
socleC22×C19#392
prime radicalC2×C19×#121C22
hypercenter#2591D19
hypocenterC19#9941
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2591

Complements

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

NH ≅ G/Ntype
2. #14567922C2semidirect
3. #14563735C2semidirect
5. #14561965C2semidirect
6. #14561488C2semidirect
300. C19#9941semidirect

Maximal subgroups

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

subgroupindex
#145735712
#145679222
#145637352
#145621642
#145619652
#145614882
C19×#25912
#994119