Finite Group Databasebeta

← #18078161

Subgroups — #18078161

Order 4864.

530 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11926599C211yesmaximal, characteristic
2#14571940C211yesmaximal, characteristic
3#14563398C211yesmaximal, characteristic
4C2×#11926286C211yesmaximal, characteristic, complemented
5#14561517C211yesmaximal, characteristic, complemented
6#14561517C211yesmaximal, characteristic, complemented
7C2×C19×#330C211yesmaximal, characteristic, complemented
8C2×C42×D19C2211yescharacteristic
9#11926599—22no—
10#11926599—22no—
11C2×Dic19⋊C8—21no—
12C2×(C2×D19)⋊C8—21no—
13C2×(C2×D19)⋊C8—21no—
14C2×#10597260C2211yescharacteristic
15C2×#10597260C2211yescharacteristic
16#11926440C411yescharacteristic
17#11926440C411yescharacteristic
18#11926425—21no—
19#11926425—21no—
20#11926415—21no—
21#11926415—21no—
22#11926410C2211yescharacteristic
23#11926401C411yescharacteristic
24#11926401C411yescharacteristic
25#11926298—21no—
26#11926286—22no—
27C2×C19×#125C2211yescharacteristic
28C2×C19×#97C2211yescharacteristic
29C2×C19×#97C2211yescharacteristic
30C19×#330—22no—
31C22×C4×D19C2×C411yescharacteristic
32C22×C4×D19D411yescharacteristic
33C22×C4×D19D411yescharacteristic
34C22×C8×C19—21no—
35C22×C8×C19—21no—
36C19×#125—21no—
37C19×#125—21no—
38C19×#125—21no—
39C19×#125—21no—
40C2×C4⋊C4×C19—21no—
41C2×C4⋊C4×C19—21no—
42C2×C4⋊C4×C19C2×C411yescharacteristic
43C2×C4⋊C4×C19C2×C411yescharacteristic
44C2×C42×C19C2311yescharacteristic
45C2×(C2×D19)⋊C4—21no—
46C2×(C2×D19)⋊C4—21no—
47C2×C4⋊Dic19C2×C411yescharacteristic
48C2×C4⋊Dic19C2×C411yescharacteristic
49C2×Dic19⋊C4—21no—
50C2×Dic19⋊C4—21no—
51C2×C4×Dic19C2×C411yescharacteristic
52C2×C4×Dic19D411yescharacteristic
53C2×C4×Dic19D411yescharacteristic
54C22×C19⋊C8—21no—
55C22×C19⋊C8—21no—
56C42×D19—21no—
57C42×D19—21no—
58C42×D19—21no—
59C42×D19—21no—
60C19×#97—21no—
61C19×#97—21no—
62C19×#97—21no—
63C19×#97D412yes—
64C19⋊#95—21no—
65C19⋊#95—21no—
66C19⋊#95—21no—
67C19⋊#95—21no—
68C19⋊#95—21no—
69C19⋊#95—21no—
70(C2×D19)⋊C8—24no—
71(C2×D19)⋊C8—24no—
72Dic19⋊C8—24no—
73#10597260—21no—
74#10597260—21no—
75#10597260—21no—
76#10597260D412yes—
77C23×D19C22⋊C411yescharacteristic
78C22×C4×C19—21no—
79C22×C4×C19—21no—
80C22×C4×C19C22×C411yescharacteristic
81C22×C4×C19C2×D411yescharacteristic
82C22×C4×C19C2×D411yescharacteristic
83C22×Dic19—21no—
84C22×Dic19—21no—
85C22×Dic19C22⋊C411yescharacteristic
86C22×Dic19C22⋊C411yescharacteristic
87C22×Dic19C22⋊C411yescharacteristic
88C2×C4×D19—22no—
89C2×C4×D19—21no—
90C2×C4×D19—21no—
91C2×C4×D19—21no—
92C2×C4×D19—21no—
93C2×C4×D19—21no—
94C2×C4×D19—21no—
95C2×C4×D19—22no—
96C2×C4×D19—41no—
97C2×C4×D19—41no—
98C2×C4×D19—41no—
99C2×C4×D19—41no—
100C2×C8×C19—22no—
101C2×C8×C19—22no—
102C2×C8×C19—41no—
103C2×C8×C19—41no—
104C2×C8×C19—41no—
105C2×C8×C19—41no—
106C4⋊C4×C19—21no—
107C4⋊C4×C19—21no—
108C4⋊C4×C19—21no—
109C4⋊C4×C19—21no—
110C4⋊C4×C19—41no—
111C4⋊C4×C19—41no—
112C4⋊C4×C19—41no—
113C4⋊C4×C19—41no—
114C42×C19C2×D411yescharacteristic
115C42×C19C2×D411yescharacteristic
116C42×C19#4111yescharacteristic
117C42×C19#4111yescharacteristic
118(C2×D19)⋊C4—42no—
119(C2×D19)⋊C4—42no—
120C4⋊Dic19—41no—
121C4⋊Dic19—41no—
122Dic19⋊C4—42no—
123Dic19⋊C4—42no—
124C4×Dic19—21no—
125C4×Dic19—21no—
126C4×Dic19—21no—
127C4×Dic19—21no—
128C4×Dic19—21no—
129C4×Dic19—21no—
130C2×C19⋊C8—22no—
131C2×C19⋊C8—22no—
132C2×C19⋊C8—41no—
133C2×C19⋊C8—41no—
134C2×C19⋊C8—41no—
135C2×C19⋊C8—41no—
136#9125—191nomaximal, Sylow
137C23×C19C2×C22⋊C411yescharacteristic
138C22×D19—21no—
139C22×D19—21no—
140C22×D19—21no—
141C22×D19—21no—
142C22×D19—21no—
143C22×D19—21no—
144C22×D19#10412yes—
145C2×C4×C19—21no—
146C2×C4×C19—21no—
147C2×C4×C19—21no—
148C2×C4×C19—21no—
149C2×C4×C19—21no—
150C2×C4×C19—21no—
151C2×C4×C19—41no—
152C2×C4×C19—41no—
153C2×C4×C19—41no—
154C2×C4×C19—41no—
155C2×C4×C19—41no—
156C2×C4×C19—41no—
157C2×C4×C19C4×D411yescharacteristic
158C2×C4×C19C4×D411yescharacteristic
159C2×C4×C19#12011yescharacteristic
160C2×C4×C19#12111yescharacteristic
161C2×C4×C19#12111yescharacteristic
162C2×C4×C19#12311yescharacteristic
163C2×Dic19—21no—
164C2×Dic19—21no—
165C2×Dic19—21no—
166C2×Dic19—21no—
167C2×Dic19—21no—
168C2×Dic19—21no—
169C2×Dic19—21no—
170C2×Dic19—21no—
171C2×Dic19—41no—
172C2×Dic19—41no—
173C2×Dic19—41no—
174C2×Dic19—41no—
175C2×Dic19—41no—
176C2×Dic19—41no—
177C2×Dic19#10112yes—
178C4×D19—42no—
179C4×D19—42no—
180C4×D19—42no—
181C4×D19—42no—
182C4×D19—42no—
183C4×D19—42no—
184C8×C19—42no—
185C8×C19—42no—
186C19⋊C8—42no—
187C19⋊C8—42no—
188C2×#432—191no—
189#2851—191no—
190#1749—191no—
191C2×#330—191no—
192C2×#330D1911yescharacteristic, complemented
193#1295—191no—
194#1295—191no—
195C22×C19#38611yescharacteristic
196C22×C19C2×#10111yescharacteristic
197C22×C19#41311yescharacteristic
198C22×C19C2×#10411yescharacteristic
199C22×C19#42111yescharacteristic
200C22×C19#42111yescharacteristic
201C22×C19#42111yescharacteristic
202C2×D19—22no—
203C2×D19—22no—
204C2×D19—22no—
205C2×D19—41no—
206C2×D19—41no—
207C2×D19—41no—
208C2×D19—41no—
209C4×C19—21no—
210C4×C19—21no—
211C4×C19—21no—
212C4×C19—21no—
213C4×C19—21no—
214C4×C19—21no—
215C4×C19—81no—
216C4×C19—81no—
217Dic19—22no—
218Dic19—41no—
219Dic19—41no—
220Dic19—81no—
221Dic19—81no—
222C2×#125C2×D1911yescharacteristic
223C22×C42—191no—
224#432—382no—
225#432—382no—
226C2×C4⋊C8—381no—
227C2×C22⋊C8—381no—
228C2×C22⋊C8—381no—
229C2×#97—191no—
230C2×#97—191no—
231C2×#97C2×D1911yescharacteristic
232C2×#97C2×D1911yescharacteristic
233#389—191no—
234#389—191no—
235#387—381no—
236#387—381no—
237#385—381no—
238#385—381no—
239#382—191no—
240#380—191no—
241#380—191no—
242#336—381no—
243#330—22no—
244#330—382no—
245C2×C19#152811yescharacteristic
246C2×C19#153211yescharacteristic
247C2×C19#153511yescharacteristic
248C2×C19#153711yescharacteristic
249C2×C19#187111yescharacteristic
250C2×C19#189711yescharacteristic
251C2×C19#190111yescharacteristic
252D19—42no—
253C23×C4—191no—
254C23×C4—191no—
255C23×C4—191no—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8—381no—
259C22×C8—381no—
260#125—21no—
261#125—21no—
262#125—21no—
263#125—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—191no—
267C2×C4⋊C4—191no—
268C2×C4⋊C4—381no—
269C2×C4⋊C4—381no—
270C2×C4⋊C4C4×D1911yescharacteristic
271C2×C4⋊C4C4×D1911yescharacteristic
272C2×C22⋊C4—381no—
273C2×C22⋊C4—381no—
274C2×C42—191no—
275C2×C42—191no—
276C2×C42—191no—
277C2×C42—381no—
278C2×C42—381no—
279C2×C42—381no—
280C2×C42—381no—
281C2×C42C22×D1911yescharacteristic
282C4⋊C8—384no—
283C22⋊C8—384no—
284C22⋊C8—384no—
285#97—21no—
286#97—21no—
287#97—21no—
288#97—192no—
289#97—381no—
290#97—381no—
291#97—381no—
292#97C22⋊D1912yes—
293#95—381no—
294#95—381no—
295#95—381no—
296#95—381no—
297#95—381no—
298#95—381no—
299C19#912511yescharacteristic, complemented, Sylow
300C24—191no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—191no—
304C22×C4—191no—
305C22×C4—191no—
306C22×C4—382no—
307C22×C4—382no—
308C22×C4—381no—
309C22×C4—381no—
310C22×C4—381no—
311C22×C4—381no—
312C22×C4—381no—
313C22×C4—381no—
314C22×C4—381no—
315C22×C4—381no—
316C22×C4—761no—
317C22×C4—761no—
318C22×C4—761no—
319C22×C4—761no—
320C22×C4C2×C4×D1911yescharacteristic
321C22×C4D4×D1911yescharacteristic
322C22×C4D4×D1911yescharacteristic
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—382no—
330C2×C8—382no—
331C2×C8—761no—
332C2×C8—761no—
333C2×C8—761no—
334C2×C8—761no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—761no—
344C4⋊C4—761no—
345C4⋊C4—762no—
346C4⋊C4—762no—
347C22⋊C4—762no—
348C22⋊C4—762no—
349C42—381no—
350C42—381no—
351C42—381no—
352C42—381no—
353C42—381no—
354C42—381no—
355C42#6454111yescharacteristic
356C42D4×D1911yescharacteristic
357C42#6454311yescharacteristic
358C42C2×C22⋊D1911yescharacteristic
359C23—192no—
360C23—381no—
361C23—381no—
362C23—381no—
363C23—381no—
364C23—381no—
365C23—381no—
366C23C22⋊C4×D1911yescharacteristic
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—192no—
380C2×C4—381no—
381C2×C4—381no—
382C2×C4—381no—
383C2×C4—381no—
384C2×C4—381no—
385C2×C4—381no—
386C2×C4—381no—
387C2×C4—381no—
388C2×C4—762no—
389C2×C4—762no—
390C2×C4—762no—
391C2×C4—762no—
392C2×C4—762no—
393C2×C4—762no—
394C2×C4—761no—
395C2×C4—761no—
396C2×C4—761no—
397C2×C4—761no—
398C2×C4—761no—
399C2×C4—761no—
400C2×C4(C22⋊D19)⋊C411yescharacteristic
401C2×C4#1059732911yescharacteristic
402C2×C4#1059733011yescharacteristic
403C2×C4C4×C22⋊D1911yescharacteristic
404C2×C4#1059738311yescharacteristic
405C2×C4#1059738411yescharacteristic
406C8—42no—
407C8—42no—
408C8—762no—
409C8—762no—
410C22—382no—
411C22—382no—
412C22—382no—
413C22—761no—
414C22—761no—
415C22—761no—
416C22—761no—
417C22#1192642011yescharacteristic
418C22#101×D1911yescharacteristic
419C22#1192652711yescharacteristic
420C22#104×D1911yescharacteristic
421C22#1192655911yescharacteristic
422C22#1192655911yescharacteristic
423C22#1192655911yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—81no—
431C4—81no—
432C4—382no—
433C4—761no—
434C4—761no—
435C4—1521no—
436C4—1521no—
437C2—762no—
438C2#1456223511yescharacteristic
439C2#1456225411yescharacteristic
440C2#1456226511yescharacteristic
441C2#1456227111yescharacteristic
442C2#1456393411yescharacteristic
443C2#1456408011yescharacteristic
444C2#1456410011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#330C2
socleC23×C19C2×C22⋊C4
prime radicalC23×D19C22⋊C4
cosocleC2×C42×C19C23
hypercenterC2×#330D19
hypocenterC19#9125
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
4. C2×#11926286C2semidirect
5. #14561517C2semidirect
6. #14561517C2semidirect
7. C2×C19×#330C2semidirect
192. C2×#330D19semidirect
299. C19#9125semidirect

Maximal subgroups

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

subgroupindex
C2×#119265992
#145719402
#145633982
C2×#119262862
#145615172
C2×C19×#3302
#912519