Finite Group Databasebeta

← #18077402

Subgroups — #18077402

Order 4864.

500 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14573662C211yesmaximal, characteristic
2#14572586C211yesmaximal, characteristic, complemented
3#14564555C211yesmaximal, characteristic
4C4×#10597273C211yesmaximal, characteristic, complemented
5#14561536C211yesmaximal, characteristic, complemented
6#14561472C211yesmaximal, characteristic, complemented
7C19×#1492C211yesmaximal, characteristic
8C2×C4×Dic38C2211yescharacteristic
9#11926860—21no—
10#11926826C411yescharacteristic, complemented
11#11926826C411yescharacteristic, complemented
12#11926741C411yescharacteristic, complemented
13#11926741C411yescharacteristic, complemented
14#11926682—21no—
15#11926673—22no—
16#11926671—21no—
17#11926668—21no—
18C4×#64526—21no—
19C4×#64526—21no—
20#11926597C2211yescharacteristic
21#11926567—21no—
22C2×#10597294—21no—
23C2×#10597294—21no—
24C2×#10597273—21no—
25C4×#64520C2211yescharacteristic
26M16×Dic19—21no—
27C4×C4⋊Dic19C2211yescharacteristic
28#11926307—21no—
29C19×#532C2211yescharacteristic
30C19×#423C2211yescharacteristic
31C2×C4×C8×C19C2211yescharacteristic
32C19×D4⋊C8—22no—
33C2×#41×C19—21no—
34C22×Dic38D411yescharacteristic
35C2×M16×C19—21no—
36C22×C8×C19—21no—
37C19×C4⋊Q8C2×C411yescharacteristic
38C19×#127C2×C411yescharacteristic
39C19×#124—21no—
40C19×#121—21no—
41C19×#121—21no—
42C4×D4×C19—21no—
43C4×D4×C19—21no—
44C2×C42×C19C2311yescharacteristic
45C2×#64526—21no—
46C2×#64526—21no—
47C2×C4⋊Dic19—21no—
48C2×C4⋊Dic19D411yescharacteristic
49C2×Dic19⋊C4—21no—
50C2×C4×Dic19—21no—
51C2×C4×Dic19—21no—
52C2×#64520D411yescharacteristic
53C2×#64520D411yescharacteristic
54C4×Dic38—21no—
55C4×Dic38—21no—
56C4×Dic38C2×C411yescharacteristic
57C4×Dic38C2×C411yescharacteristic
58C4×Dic38D411yescharacteristic
59C4×Dic38D411yescharacteristic
60C19×C4⋊C8—21no—
61C19×C4⋊C8D412yes—
62C4×C8×C19—21no—
63C4×C8×C19—21no—
64#10597294—42no—
65#10597294—42no—
66#10597289—21no—
67#10597289—21no—
68C19⋊#95—21no—
69C22⋊(C19⋊C8)—21no—
70#10597273—24no—
71#10597272—22no—
72Dic19⋊C8—22no—
73Dic19⋊C8—22no—
74C8×Dic19—22no—
75#10597267—21no—
76#10597267—21no—
77#10597265—21no—
78#10597265—21no—
79C4⋊(C19⋊C8)C2×C411yescharacteristic
80C4⋊(C19⋊C8)C2×C411yescharacteristic
81#10597260—21no—
82C4×C19⋊C8—21no—
83C4×C19⋊C8—21no—
84#41×C19—41no—
85#41×C19—41no—
86#41×C19—41no—
87#41×C19—41no—
88C2×Q8×C19—21no—
89C2×D4×C19—21no—
90C2×D4×C19—21no—
91C2×D4×C19—21no—
92C2×D4×C19—41no—
93C22×C4×C19—41no—
94C22×C4×C19C2×D411yescharacteristic
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19#4111yescharacteristic
97C22×Dic19—21no—
98C22×Dic19—21no—
99C22×Dic19—41no—
100C2×Dic38—22no—
101C2×Dic38—21no—
102C2×Dic38—41no—
103C2×Dic38C22⋊C411yescharacteristic
104C2×Dic38C22⋊C411yescharacteristic
105M16×C19—41no—
106M16×C19—41no—
107C2×C8×C19—22no—
108C2×C8×C19—22no—
109C2×C8×C19—41no—
110C2×C8×C19—41no—
111C4⋊C4×C19—21no—
112C4⋊C4×C19—21no—
113C22⋊C4×C19—41no—
114C22⋊C4×C19—41no—
115C42×C19C22×C411yescharacteristic
116C42×C19C2×D411yescharacteristic
117C42×C19C2×D411yescharacteristic
118C42×C19#4111yescharacteristic
119#64526—42no—
120#64526—42no—
121C4⋊Dic19—21no—
122C4⋊Dic19—22no—
123C4⋊Dic19—41no—
124C4⋊Dic19C22⋊C411yescharacteristic
125C4⋊Dic19C22⋊C411yescharacteristic
126Dic19⋊C4—21no—
127Dic19⋊C4—21no—
128Dic19⋊C4—21no—
129Dic19⋊C4—21no—
130C4×Dic19—21no—
131C4×Dic19—21no—
132C4×Dic19—21no—
133C4×Dic19—21no—
134C4×Dic19—41no—
135C4×Dic19—41no—
136#64520—21no—
137#64520—21no—
138#64520—21no—
139#64520SD1612yescomplemented
140C2×C19⋊C8—21no—
141C2×C19⋊C8—21no—
142C2×C19⋊C8—21no—
143C2×C19⋊C8—21no—
144#8992—191nomaximal, Sylow
145C23×C19—41no—
146C23×C19#12111yescharacteristic
147Q8×C19—41no—
148Q8×C19—41no—
149D4×C19—42no—
150D4×C19—41no—
151D4×C19—41no—
152D4×C19—41no—
153D4×C19—41no—
154D4×C19—81no—
155D4×C19—81no—
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—41no—
159C2×C4×C19—41no—
160C2×C4×C19—81no—
161C2×C4×C19—81no—
162C2×C4×C19C2×C22⋊C411yescharacteristic
163C2×C4×C19C4×D411yescharacteristic
164C2×C4×C19C4×D411yescharacteristic
165C2×C4×C19#12011yescharacteristic
166C2×C4×C19#12111yescharacteristic
167C2×C4×C19#12311yescharacteristic
168C2×C4×C19C2×SD1611yescharacteristic
169C2×C4×C19#13511yescharacteristic
170C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C19#13711yescharacteristic
172C2×Dic19—21no—
173C2×Dic19—21no—
174C2×Dic19—21no—
175C2×Dic19—21no—
176C2×Dic19—42no—
177C2×Dic19—42no—
178C2×Dic19—81no—
179C2×Dic19—81no—
180C2×Dic19—81no—
181Dic38—21no—
182Dic38—21no—
183Dic38—21no—
184Dic38—42no—
185Dic38#10412yescomplemented
186C8×C19—42no—
187C8×C19—42no—
188C19⋊C8—22no—
189C19⋊C8—41no—
190C19⋊C8—41no—
191C19⋊C8—41no—
192#3103—191no—
193Q8×M16—191no—
194#1980—191no—
195C4×#103—191no—
196#1492D1911yescharacteristic
197#1303—191no—
198#1278—191no—
199C22×C19—21no—
200C22×C19—21no—
201C22×C19—81no—
202C22×C19—81no—
203C22×C19—81no—
204C22×C19#38611yescharacteristic
205C22×C19#46011yescharacteristic
206C22×C19#46411yescharacteristic
207C4×C19—21no—
208C4×C19—21no—
209C4×C19—21no—
210C4×C19—81no—
211C4×C19C2×#10411yescharacteristic
212C4×C19#42111yescharacteristic
213C4×C19C4×SD1611yescharacteristic
214C4×C19#44011yescharacteristic
215C4×C19#44811yescharacteristic
216C4×C19#44911yescharacteristic
217Dic19—22no—
218Dic19—41no—
219Dic19—41no—
220Dic19—41no—
221Dic19—82no—
222#532C2×D1911yescharacteristic
223C2×C4×Q8—191no—
224#481—381no—
225#475—191no—
226#475—191no—
227#460—191no—
228#460—191no—
229#448—381no—
230#446—381no—
231#446—382no—
232C8×Q8—381no—
233C4×SD16—381no—
234C4×SD16—381no—
235#431—191no—
236#423—381no—
237#423C2×D1911yescharacteristic
238C2×#104—381no—
239C2×#104—381no—
240C2×#103—381no—
241C4×M16—191no—
242C4×M16—381no—
243C2×C4×C8C2×D1911yescharacteristic
244C4×C4⋊C4—191no—
245#340—381no—
246D4⋊C8—22no—
247C2×C19—21no—
248C2×C19—21no—
249C2×C19—161no—
250C2×C19#187111yescharacteristic
251C2×C19#188011yescharacteristic
252C2×C19#188111yescharacteristic
253C2×#41—21no—
254C22×Q8—191no—
255C2×SD16—381no—
256C2×SD16—381no—
257C2×M16—21no—
258C2×M16—191no—
259C2×M16—191no—
260C22×C8—21no—
261C4⋊Q8C4×D1911yescharacteristic
262#127C4×D1911yescharacteristic
263#124—21no—
264#121—21no—
265#121—21no—
266C4×Q8—191no—
267C4×Q8—191no—
268C4×Q8—191no—
269C4×Q8—191no—
270C4×Q8—381no—
271C4×Q8—381no—
272C4×D4—21no—
273C4×D4—21no—
274C2×C4⋊C4—191no—
275C2×C4⋊C4—381no—
276C2×C4⋊C4—381no—
277C2×C42—381no—
278C2×C42—381no—
279C2×C42C22×D1911yescharacteristic
280#106—381no—
281#106—381no—
282C4⋊C8—21no—
283C4⋊C8—191no—
284C4⋊C8—191no—
285C4⋊C8—382no—
286C4⋊C8—382no—
287C4⋊C8C22⋊D1912yes—
288#104—762no—
289#104—762no—
290#103—381no—
291#103—381no—
292#103—384no—
293#102—381no—
294#102—381no—
295C22⋊C8—381no—
296#97—382no—
297#97—381no—
298C4×C8—21no—
299C4×C8—21no—
300C4×C8—382no—
301C4×C8—381no—
302C4×C8—381no—
303#95—381no—
304C19#899211yescharacteristic, complemented, Sylow
305#41—41no—
306#41—41no—
307#41—41no—
308#41—41no—
309C2×Q8—21no—
310C2×Q8—191no—
311C2×Q8—191no—
312C2×Q8—382no—
313C2×Q8—381no—
314C2×Q8—761no—
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—21no—
318C2×D4—41no—
319C22×C4—41no—
320C22×C4—381no—
321C22×C4—381no—
322C22×C4—761no—
323C22×C4#6454111yescharacteristic
324C22×C4D4×D1911yescharacteristic
325C22×C4D4×D1911yescharacteristic
326SD16—762no—
327SD16—762no—
328M16—41no—
329M16—41no—
330M16—192no—
331M16—381no—
332M16—381no—
333M16—381no—
334C2×C8—22no—
335C2×C8—22no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—381no—
339C2×C8—381no—
340C2×C8—381no—
341C2×C8—381no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—191no—
345C4⋊C4—191no—
346C4⋊C4—382no—
347C4⋊C4—381no—
348C4⋊C4—381no—
349C4⋊C4—381no—
350C4⋊C4—381no—
351C4⋊C4—381no—
352C4⋊C4—761no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C42—381no—
356C42—381no—
357C42—381no—
358C42—381no—
359C42—761no—
360C42—761no—
361C42C2×C4×D1911yescharacteristic
362C42D4×D1911yescharacteristic
363C42#6454311yescharacteristic
364C42C2×C22⋊D1911yescharacteristic
365C23—41no—
366C23#1059733011yescharacteristic
367Q8—41no—
368Q8—41no—
369Q8—192no—
370Q8—381no—
371Q8—381no—
372Q8—381no—
373Q8—762no—
374D4—42no—
375D4—41no—
376D4—41no—
377D4—41no—
378D4—41no—
379D4—81no—
380D4—81no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—381no—
388C2×C4—381no—
389C2×C4—381no—
390C2×C4—381no—
391C2×C4—762no—
392C2×C4—762no—
393C2×C4—1521no—
394C2×C4—1521no—
395C2×C4—1521no—
396C2×C4C22⋊C4×D1911yescharacteristic
397C2×C4(C22⋊D19)⋊C411yescharacteristic
398C2×C4#1059732911yescharacteristic
399C2×C4#1059735711yescharacteristic
400C2×C4#1059735811yescharacteristic
401C2×C4SD16×D1911yescharacteristic
402C2×C4#1059736111yescharacteristic
403C2×C4C4×C22⋊D1911yescharacteristic
404C2×C4#1059738311yescharacteristic
405C2×C4#1059738411yescharacteristic
406C8—42no—
407C8—42no—
408C8—382no—
409C8—761no—
410C8—761no—
411C8—761no—
412C22—21no—
413C22—21no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22#1192642011yescharacteristic
418C22#1192674311yescharacteristic
419C22#1192676511yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—81no—
424C4—382no—
425C4—761no—
426C4—761no—
427C4—761no—
428C4—1522no—
429C4#104×D1911yescharacteristic
430C4#1192655911yescharacteristic
431C4#1192663511yescharacteristic
432C4#1192664111yescharacteristic
433C4#1192668111yescharacteristic
434C4#1192668611yescharacteristic
435C2—21no—
436C2—21no—
437C2—161no—
438C2#1456393411yescharacteristic
439C2#1456398711yescharacteristic
440C2#1456400011yescharacteristic
subgroupG/H
centerC2×C4#10597383
commutatorC42×C19C22×C4
FrattiniC2×C42C22×D19
FittingC19×#1492C2
socleC22×C19#386
prime radicalC19×#532C22
cosocleC2×C42×C19C23
hypercenter#1492D19
hypocenterC19#8992
LCSG ▷ C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. #14572586C2semidirect
4. C4×#10597273C2semidirect
5. #14561536C2semidirect
6. #14561472C2semidirect
10. #11926826C4semidirect
11. #11926826C4semidirect
12. #11926741C4semidirect
13. #11926741C4semidirect
139. #64520SD16semidirect
185. Dic38#104semidirect
304. C19#8992semidirect

Maximal subgroups

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

subgroupindex
#145736622
#145725862
#145645552
C4×#105972732
#145615362
#145614722
C19×#14922
#899219