Finite Group Databasebeta

← #18081559

Subgroups — #18081559

Order 4864.

596 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14571990C211yesmaximal, characteristic
2#14563489C211yesmaximal, characteristic, complemented
3#14563383C211yesmaximal, characteristic, complemented
4C2×#11926284C211yesmaximal, characteristic, complemented
5C2×#11926283C211yesmaximal, characteristic, complemented
6C2×#11926283C211yesmaximal, characteristic, complemented
7C2×C19×#329C211yesmaximal, characteristic, complemented
8C2×#10597390C411yescharacteristic
9C2×#10597386C411yescharacteristic
10C2×#10597393C411yescharacteristic
11C2×#10597321C2211yescharacteristic
12C2×#10597382C411yescharacteristic
13C2×Dic19⋊C8—21no—
14C2×#10597260C2211yescharacteristic
15C2×#10597260C2211yescharacteristic
16#11926444—21no—
17#11926444—21no—
18#11926444—21no—
19#11926444—21no—
20C42×Dic19C2211yescharacteristic
21#11926298—21no—
22#11926298—21no—
23#11926298—21no—
24#11926284—22no—
25#11926283—22no—
26#11926283—22no—
27C2×C19×#124C2211yescharacteristic
28C2×C19×#97C2211yescharacteristic
29C2×C19×#97C2211yescharacteristic
30C19×#329—22no—
31C22×Q8×C19C2×C411yescharacteristic
32C22×D4×C19C2×C411yescharacteristic
33C22×C22⋊D19—21no—
34C22×C22⋊D19—21no—
35C22×D76C2×C411yescharacteristic
36C22×Dic38C2×C411yescharacteristic
37C22×C8×C19—21no—
38C22×C8×C19—21no—
39C19×#124—21no—
40C19×#124—21no—
41C19×#124—21no—
42C19×#124—21no—
43C2×C22⋊C4×C19—21no—
44C2×C22⋊C4×C19—21no—
45C2×C42×C19C2311yescharacteristic
46C2×C22⋊Dic19—21no—
47C2×C22⋊Dic19—21no—
48#10597393—42no—
49#10597390—42no—
50#10597386—42no—
51#10597382—42no—
52C2×(C2×D19)⋊C4—21no—
53C2×(C2×D19)⋊C4—21no—
54C2×(C2×D19)⋊C4—21no—
55C2×(C2×D19)⋊C4—21no—
56C2×Dic19⋊C4—21no—
57C2×Dic19⋊C4—21no—
58C2×C4×Dic19C2×C411yescharacteristic
59C2×C4×Dic19C2×C411yescharacteristic
60C2×C4×Dic19D411yescharacteristic
61C2×C4×Dic19D411yescharacteristic
62C2×C4×Dic19D411yescharacteristic
63C2×C4×Dic19D411yescharacteristic
64C22×C19⋊C8—21no—
65C22×C19⋊C8—21no—
66#10597321—21no—
67#10597321—21no—
68#10597321—21no—
69#10597321—21no—
70C19×#97—21no—
71C19×#97—21no—
72C19×#97—21no—
73C19×#97D412yescomplemented
74Dic19⋊C8—24no—
75#10597260—21no—
76#10597260—21no—
77#10597260—21no—
78#10597260D412yescomplemented
79C24×C19—21no—
80C23×D19—21no—
81C2×Q8×C19—21no—
82C2×Q8×C19—21no—
83C2×Q8×C19—41no—
84C2×Q8×C19—41no—
85C2×D4×C19—21no—
86C2×D4×C19—21no—
87C2×D4×C19—41no—
88C2×D4×C19—41no—
89C22×C4×C19—21no—
90C22×C4×C19C22×C411yescharacteristic
91C22×C4×C19C2×D411yescharacteristic
92C22×C4×C19C2×D411yescharacteristic
93C2×C22⋊D19—42no—
94C2×C22⋊D19—42no—
95C2×C22⋊D19—42no—
96C2×C22⋊D19—42no—
97C2×C22⋊D19—42no—
98C2×C22⋊D19—42no—
99C22×Dic19—21no—
100C22×Dic19C22⋊C411yescharacteristic
101C22×Dic19C22⋊C411yescharacteristic
102C22×Dic19C22⋊C411yescharacteristic
103C22×Dic19C22⋊C411yescharacteristic
104C2×D76—21no—
105C2×D76—21no—
106C2×D76—41no—
107C2×D76—41no—
108C2×Dic38—21no—
109C2×Dic38—21no—
110C2×Dic38—41no—
111C2×Dic38—41no—
112C2×C8×C19—22no—
113C2×C8×C19—22no—
114C2×C8×C19—41no—
115C2×C8×C19—41no—
116C2×C8×C19—41no—
117C2×C8×C19—41no—
118C22⋊C4×C19—41no—
119C22⋊C4×C19—41no—
120C22⋊C4×C19—41no—
121C22⋊C4×C19—41no—
122C42×C19C2×D411yescharacteristic
123C42×C19C2×D411yescharacteristic
124C42×C19#4111yescharacteristic
125C42×C19#4111yescharacteristic
126C22⋊Dic19—42no—
127C22⋊Dic19—42no—
128(C2×D19)⋊C4—42no—
129(C2×D19)⋊C4—41no—
130(C2×D19)⋊C4—41no—
131(C2×D19)⋊C4—41no—
132(C2×D19)⋊C4—41no—
133(C2×D19)⋊C4—42no—
134Dic19⋊C4—42no—
135Dic19⋊C4—42no—
136C4×Dic19—22no—
137C4×Dic19—22no—
138C4×Dic19—22no—
139C4×Dic19—41no—
140C4×Dic19—41no—
141C4×Dic19—41no—
142C2×C19⋊C8—22no—
143C2×C19⋊C8—22no—
144C2×C19⋊C8—41no—
145C2×C19⋊C8—41no—
146C2×C19⋊C8—41no—
147C2×C19⋊C8—41no—
148#9689—191nomaximal, Sylow
149C23×C19—41no—
150C23×C19—41no—
151C23×C19—41no—
152C23×C19—41no—
153C23×C19—41no—
154C23×C19—41no—
155C23×C19—41no—
156C23×C19C2×C22⋊C411yescharacteristic
157C22×D19—41no—
158C22×D19—41no—
159C22×D19—41no—
160C22×D19—41no—
161C22×D19—41no—
162C22×D19—41no—
163C22×D19—41no—
164Q8×C19—81no—
165Q8×C19—81no—
166D4×C19—81no—
167D4×C19—81no—
168C2×C4×C19—21no—
169C2×C4×C19—21no—
170C2×C4×C19—21no—
171C2×C4×C19—21no—
172C2×C4×C19—21no—
173C2×C4×C19—21no—
174C2×C4×C19—41no—
175C2×C4×C19—41no—
176C2×C4×C19—41no—
177C2×C4×C19C4×D411yescharacteristic
178C2×C4×C19C4×D411yescharacteristic
179C2×C4×C19#12111yescharacteristic
180C2×C4×C19#12111yescharacteristic
181C2×C4×C19#12411yescharacteristic
182C2×C4×C19#12711yescharacteristic
183C22⋊D19—84no—
184C22⋊D19—84no—
185C2×Dic19—21no—
186C2×Dic19—21no—
187C2×Dic19—21no—
188C2×Dic19—21no—
189C2×Dic19—21no—
190C2×Dic19—21no—
191C2×Dic19—21no—
192C2×Dic19—21no—
193C2×Dic19—21no—
194C2×Dic19—41no—
195C2×Dic19—41no—
196C2×Dic19—41no—
197C2×Dic19#10012yes—
198C2×Dic19#10012yes—
199C2×Dic19#10412yes—
200D76—81no—
201D76—81no—
202Dic38—81no—
203Dic38—81no—
204C8×C19—42no—
205C8×C19—42no—
206C19⋊C8—42no—
207C19⋊C8—42no—
208#2858—191no—
209#1767—191no—
210#1745—191no—
211C2×#329—191no—
212C2×#329—191no—
213C2×#329—191no—
214C2×#329D1911yescharacteristic, complemented
215C22×C19—81no—
216C22×C19—81no—
217C22×C19—81no—
218C22×C19—81no—
219C22×C19—81no—
220C22×C19—81no—
221C22×C19—81no—
222C22×C19#39011yescharacteristic
223C22×C19C2×#10011yescharacteristic
224C22×C19C2×#10011yescharacteristic
225C22×C19C2×#10411yescharacteristic
226C22×C19#42111yescharacteristic
227C22×C19#42111yescharacteristic
228C22×C19#42111yescharacteristic
229C2×D19—81no—
230C2×D19—81no—
231C2×D19—81no—
232C2×D19—81no—
233C2×D19—81no—
234C2×D19—81no—
235C2×D19—81no—
236C4×C19—21no—
237C4×C19—21no—
238C4×C19—21no—
239C4×C19—21no—
240C4×C19—21no—
241C4×C19—21no—
242C4×C19—81no—
243Dic19—22no—
244Dic19—22no—
245Dic19—22no—
246Dic19—41no—
247Dic19—81no—
248C2×C4⋊Q8—191no—
249C2×#127—191no—
250C2×#124—191no—
251C2×#124—191no—
252C2×#124—191no—
253C2×#124C2×D1911yescharacteristic
254C2×C4⋊C8—381no—
255C2×#97—191no—
256C2×#97—191no—
257C2×#97C2×D1911yescharacteristic
258C2×#97C2×D1911yescharacteristic
259#390—381no—
260#390—381no—
261#390—381no—
262#390—381no—
263C43—191no—
264#336—381no—
265#336—381no—
266#336—381no—
267#329—22no—
268#329—382no—
269#329—382no—
270#329—382no—
271C2×C19—161no—
272C2×C19#152711yescharacteristic
273C2×C19#153011yescharacteristic
274C2×C19#153311yescharacteristic
275C2×C19#153611yescharacteristic
276C2×C19#196311yescharacteristic
277C2×C19#196511yescharacteristic
278C2×C19#198011yescharacteristic
279D19—161no—
280C22×Q8—191no—
281C22×Q8C4×D1911yescharacteristic
282C22×D4—191no—
283C22×D4—381no—
284C22×D4—381no—
285C22×D4C4×D1911yescharacteristic
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—381no—
289C22×C8—381no—
290C4⋊Q8—762no—
291#127—762no—
292#124—21no—
293#124—21no—
294#124—21no—
295#124—21no—
296#124—381no—
297#124—381no—
298#124—381no—
299#124—381no—
300#124—762no—
301#124—762no—
302C2×C4⋊C4—381no—
303C2×C4⋊C4—381no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—381no—
307C2×C22⋊C4—381no—
308C2×C22⋊C4—381no—
309C2×C22⋊C4—381no—
310C2×C22⋊C4—381no—
311C2×C22⋊C4—381no—
312C2×C42—191no—
313C2×C42—191no—
314C2×C42—191no—
315C2×C42—191no—
316C2×C42—191no—
317C2×C42—191no—
318C2×C42C22×D1911yescharacteristic
319C4⋊C8—384no—
320#97—21no—
321#97—21no—
322#97—21no—
323#97—192no—
324#97—381no—
325#97—381no—
326#97—381no—
327#97C22⋊D1912yescomplemented
328C19#968911yescharacteristic, complemented, Sylow
329C24—21no—
330C24—381no—
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—41no—
334C2×Q8—41no—
335C2×Q8—381no—
336C2×Q8—381no—
337C2×Q8—761no—
338C2×Q8—761no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—381no—
344C2×D4—381no—
345C2×D4—761no—
346C2×D4—761no—
347C2×D4—762no—
348C2×D4—762no—
349C2×D4—762no—
350C2×D4—762no—
351C2×D4—762no—
352C2×D4—762no—
353C22×C4—21no—
354C22×C4—191no—
355C22×C4—191no—
356C22×C4—191no—
357C22×C4—191no—
358C22×C4—381no—
359C22×C4C2×C4×D1911yescharacteristic
360C22×C4D4×D1911yescharacteristic
361C22×C4D4×D1911yescharacteristic
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8—382no—
369C2×C8—382no—
370C2×C8—761no—
371C2×C8—761no—
372C2×C8—761no—
373C2×C8—761no—
374C4⋊C4—762no—
375C4⋊C4—762no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—762no—
381C22⋊C4—762no—
382C22⋊C4—762no—
383C22⋊C4—762no—
384C22⋊C4—761no—
385C22⋊C4—761no—
386C22⋊C4—761no—
387C22⋊C4—761no—
388C42—382no—
389C42—382no—
390C42—382no—
391C42—761no—
392C42—761no—
393C42—761no—
394C42#6454111yescharacteristic
395C42D4×D1911yescharacteristic
396C42#6454311yescharacteristic
397C42C2×C22⋊D1911yescharacteristic
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—761no—
406C23—761no—
407C23—761no—
408C23—761no—
409C23—761no—
410C23—761no—
411C23—761no—
412C23C22⋊C4×D1911yescharacteristic
413Q8—81no—
414Q8—81no—
415Q8—1521no—
416Q8—1521no—
417D4—81no—
418D4—81no—
419D4—1521no—
420D4—1521no—
421D4—1524no—
422D4—1524no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—192no—
433C2×C4—192no—
434C2×C4—192no—
435C2×C4—381no—
436C2×C4—381no—
437C2×C4—381no—
438C2×C4—381no—
439C2×C4—381no—
440C2×C4—381no—
441C2×C4—381no—
442C2×C4—381no—
443C2×C4—381no—
444C2×C4—761no—
445C2×C4—761no—
446C2×C4—761no—
447C2×C4(C22⋊D19)⋊C411yescharacteristic
448C2×C4#1059733011yescharacteristic
449C2×C4#1059733111yescharacteristic
450C2×C4C4×C22⋊D1911yescharacteristic
451C2×C4#1059738511yescharacteristic
452C2×C4#1059738611yescharacteristic
453C8—42no—
454C8—42no—
455C8—762no—
456C8—762no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22—1521no—
465C22—1521no—
466C22—1521no—
467C22—1521no—
468C22—1521no—
469C22—1521no—
470C22—1521no—
471C22#1192644411yescharacteristic
472C22#100×D1911yescharacteristic
473C22#100×D1911yescharacteristic
474C22#104×D1911yescharacteristic
475C22#1192655911yescharacteristic
476C22#1192655911yescharacteristic
477C22#1192655911yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—21no—
483C4—21no—
484C4—81no—
485C4—382no—
486C4—382no—
487C4—382no—
488C4—761no—
489C4—1521no—
490C2—161no—
491C2—3041no—
492C2#1456223111yescharacteristic
493C2#1456224411yescharacteristic
494C2#1456225711yescharacteristic
495C2#1456226811yescharacteristic
496C2#1456446511yescharacteristic
497C2#1456447311yescharacteristic
498C2#1456455211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D19
commutatorC22×C4×C19C22×C4
FrattiniC2×C42C22×D19
FittingC2×C19×#329C2
socleC23×C19C2×C22⋊C4
prime radicalC2×#10597386C4
cosocleC2×C42×C19C23
hypercenterC2×#329D19
hypocenterC19#9689
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
2. #14563489C2semidirect
3. #14563383C2semidirect
4. C2×#11926284C2semidirect
5. C2×#11926283C2semidirect
6. C2×#11926283C2semidirect
7. C2×C19×#329C2semidirect
73. C19×#97D4semidirect
78. #10597260D4semidirect
214. C2×#329D19semidirect
327. #97C22⋊D19semidirect
328. C19#9689semidirect

Maximal subgroups

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

subgroupindex
#145719902
#145634892
#145633832
C2×#119262842
C2×#119262832
C2×C19×#3292
#968919