Finite Group Databasebeta

← #18083276

Subgroups — #18083276

Order 4864.

622 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 101 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#14573635C211yesmaximal, characteristic
2#14573107C211yesmaximal, characteristic, complemented
3#14562194C211yesmaximal, characteristic, complemented
4#14562060C211yesmaximal, characteristic, complemented
5#14562030C211yesmaximal, characteristic, complemented
6#14561493C211yesmaximal, characteristic, complemented
7C19×#2536C211yesmaximal, characteristic, complemented
8C2×#10597388—21no—
9#11927094C2211yescharacteristic
10#11926857—21no—
11#11926824—21no—
12#11926766—22no—
13#11926754—21no—
14#11926744—21no—
15#11926739—21no—
16#11926678—21no—
17C4×#64525—22no—
18#11926597C2211yescharacteristic
19#11926597C2211yescharacteristic
20#11926568C2211yescharacteristic
21#11926543—21no—
22#11926277—22no—
23Q8⋊(C19⋊C8)—22no—
24D4⋊(C19⋊C8)—22no—
25C2×C19×C22⋊Q8—21no—
26C2×C4×Q8×C19C2211yescharacteristic
27C2×C4×D4×C19C2211yescharacteristic
28C19×#398—21no—
29C19×#394—21no—
30C19×#388—22no—
31C19×#382C2211yescharacteristic
32C19×#380—21no—
33C22×Q8×C19D411yescharacteristic
34C22×D4×C19D411yescharacteristic
35C23×C4×C19—21no—
36C2×#64541—21no—
37C19×C22⋊Q8—42no—
38C19×C22⋊Q8—42no—
39C4×Q8×C19—21no—
40C4×Q8×C19—21no—
41C4×Q8×C19—21no—
42C4×Q8×C19—21no—
43C4×D4×C19—21no—
44C4×D4×C19—21no—
45C4×D4×C19—21no—
46C4×D4×C19—21no—
47C2×C4⋊C4×C19—22no—
48C2×C4⋊C4×C19—21no—
49C2×C4⋊C4×C19—21no—
50C2×C4⋊C4×C19D411yescharacteristic
51C2×C4⋊C4×C19D411yescharacteristic
52C2×C22⋊C4×C19—22no—
53C2×C22⋊C4×C19—22no—
54C2×C22⋊C4×C19—21no—
55C2×C42×C19—21no—
56C2×C42×C19C2311yescharacteristic
57C2×#64528—22no—
58#10597388—42no—
59#10597388—42no—
60C2×#64527—22no—
61C2×#64525—22no—
62#10597376—21no—
63#10597376—21no—
64C2×#64520—21no—
65#10597321—21no—
66#10597320D411yescharacteristic
67C4×D76—21no—
68C4×D76—21no—
69#10597315D411yescharacteristic
70C19×#95—22no—
71C19×#95—21no—
72C19×#95D412yes—
73#10597289—22no—
74C22⋊(C19⋊C8)—21no—
75C22⋊(C19⋊C8)—21no—
76#10597267—22no—
77#10597266—22no—
78#10597266—22no—
79#10597264—22no—
80C4⋊(C19⋊C8)—21no—
81C4⋊(C19⋊C8)—21no—
82C4⋊(C19⋊C8)—21no—
83C4⋊(C19⋊C8)D412yes—
84C4×C19⋊C8—21no—
85C4×C19⋊C8D412yes—
86C24×C19—21no—
87C2×Q8×C19—21no—
88C2×Q8×C19—21no—
89C2×Q8×C19—21no—
90C2×Q8×C19—21no—
91C2×Q8×C19—21no—
92C2×Q8×C19D812yescomplemented
93C2×D4×C19—21no—
94C2×D4×C19—21no—
95C2×D4×C19—42no—
96C22×C4×C19—21no—
97C22×C4×C19—21no—
98C22×C4×C19—22no—
99C22×C4×C19—21no—
100C22×C4×C19—41no—
101C22×C4×C19—41no—
102C22×C4×C19—41no—
103C22×C4×C19—41no—
104C22×C4×C19—41no—
105C22×C4×C19—41no—
106C22×C4×C19C2×D411yescharacteristic
107C22×C4×C19C2×D411yescharacteristic
108C22×C4×C19C2×D411yescharacteristic
109C2×C22⋊D19—41no—
110#64541—41no—
111#64541—41no—
112#64541—41no—
113#64541—41no—
114C2×D76—21no—
115C2×D76—21no—
116C2×D76—21no—
117C2×C4×D19—41no—
118C2×Dic38—21no—
119C4⋊C4×C19—21no—
120C4⋊C4×C19—21no—
121C4⋊C4×C19—21no—
122C4⋊C4×C19—21no—
123C4⋊C4×C19—44no—
124C4⋊C4×C19—41no—
125C4⋊C4×C19—41no—
126C4⋊C4×C19—41no—
127C4⋊C4×C19—41no—
128C22⋊C4×C19—44no—
129C22⋊C4×C19—44no—
130C22⋊C4×C19—41no—
131C22⋊C4×C19—41no—
132C42×C19—41no—
133C42×C19—41no—
134C42×C19C2×D411yescharacteristic
135C42×C19C2×D411yescharacteristic
136C42×C19C2×D411yescharacteristic
137C42×C19#4111yescharacteristic
138#64528—44no—
139#64527—44no—
140#64525—44no—
141(C2×D19)⋊C4—41no—
142(C2×D19)⋊C4—41no—
143C4⋊Dic19—21no—
144C4⋊Dic19—21no—
145#64520—41no—
146#64520—41no—
147C2×C19⋊C8—22no—
148C2×C19⋊C8—22no—
149C2×C19⋊C8—41no—
150#9997—191nomaximal, Sylow
151C23×C19—22no—
152C23×C19—41no—
153C23×C19—41no—
154C23×C19—41no—
155C23×C19—41no—
156C23×C19—41no—
157C23×C19—41no—
158C23×C19#12011yescharacteristic
159C22×D19—41no—
160Q8×C19—22no—
161Q8×C19—22no—
162Q8×C19—41no—
163Q8×C19—41no—
164D4×C19—22no—
165D4×C19—22no—
166D4×C19—41no—
167D4×C19—41no—
168C2×C4×C19—22no—
169C2×C4×C19—41no—
170C2×C4×C19—41no—
171C2×C4×C19—41no—
172C2×C4×C19—41no—
173C2×C4×C19—42no—
174C2×C4×C19—42no—
175C2×C4×C19—42no—
176C2×C4×C19—41no—
177C2×C4×C19—41no—
178C2×C4×C19—42no—
179C2×C4×C19—41no—
180C2×C4×C19—41no—
181C2×C4×C19—81no—
182C2×C4×C19—81no—
183C2×C4×C19—81no—
184C2×C4×C19—81no—
185C2×C4×C19#12011yescharacteristic
186C2×C4×C19#12011yescharacteristic
187C2×C4×C19#12111yescharacteristic
188C2×C4×C19#12111yescharacteristic
189C2×C4×C19#12111yescharacteristic
190C2×C4×C19#12711yescharacteristic
191C2×C4×C19C2×D811yescharacteristic
192C2×C4×C19#13511yescharacteristic
193C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C19AGL(1,ℤ/8)11yescharacteristic
195C22⋊D19—81no—
196C22⋊D19—81no—
197C2×Dic19—41no—
198D76—42no—
199D76—41no—
200D76—41no—
201D76—81no—
202C4×D19—81no—
203C4×D19—81no—
204Dic38—41no—
205Dic38—41no—
206C19⋊C8—42no—
207C19⋊C8—42no—
208C19⋊C8—81no—
209#3100—191no—
210#3037—191no—
211#2536D1911yescharacteristic, complemented
212#1517—191no—
213#1486—191no—
214#1479—191no—
215#1286—191no—
216C22×C19—21no—
217C22×C19—21no—
218C22×C19—42no—
219C22×C19—42no—
220C22×C19—42no—
221C22×C19—81no—
222C22×C19—81no—
223C22×C19—81no—
224C22×C19—81no—
225C22×C19#39211yescharacteristic
226C22×C19#44711yescharacteristic
227C22×C19#44911yescharacteristic
228C2×D19—81no—
229C2×D19—81no—
230C2×D19—81no—
231C4×C19—21no—
232C4×C19—21no—
233C4×C19—21no—
234C4×C19—21no—
235C4×C19—42no—
236C4×C19—82no—
237C4×C19—81no—
238C4×C19—81no—
239C4×C19#44711yescharacteristic
240C4×C19#44911yescharacteristic
241C4×C19#46611yescharacteristic
242C4×C19#46911yescharacteristic
243Dic19—81no—
244C2×#137—381no—
245#532—191no—
246C2×C22⋊Q8—21no—
247C2×C4×Q8C2×D1911yescharacteristic
248C2×C4×D4C2×D1911yescharacteristic
249#480—381no—
250#474—381no—
251#464—382no—
252#462—381no—
253#460—381no—
254#459—381no—
255#447—381no—
256C4×D8—382no—
257#431—191no—
258#431—191no—
259#423—191no—
260#417—381no—
261#398—21no—
262#394—21no—
263#388—22no—
264#382C2×D1911yescharacteristic
265#380—21no—
266#327—382no—
267Q8⋊C8—382no—
268D4⋊C8—382no—
269C2×C19—21no—
270C2×C19—21no—
271C2×C19—82no—
272C2×C19#199911yescharacteristic
273C2×C19#200911yescharacteristic
274C2×C19#201011yescharacteristic
275D19—161no—
276C2×#41—381no—
277C22×Q8C22⋊D1911yescharacteristic
278C22×D4C22⋊D1911yescharacteristic
279C23×C4—21no—
280#137—762no—
281#137—762no—
282C2×Q16—382no—
283C2×SD16—382no—
284C2×D8—382no—
285C2×M16—381no—
286C4⋊Q8—191no—
287#127—191no—
288#124—381no—
289C22⋊Q8—42no—
290C22⋊Q8—42no—
291#121—381no—
292#121—381no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×D4—21no—
298C4×D4—21no—
299C4×D4—21no—
300C4×D4—21no—
301C4×D4—381no—
302C4×D4—381no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4C22⋊D1911yescharacteristic
307C2×C4⋊C4C22⋊D1911yescharacteristic
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—21no—
311C2×C42—21no—
312C2×C42C22×D1911yescharacteristic
313#107—382no—
314C4⋊C8—192no—
315C4⋊C8—381no—
316C4⋊C8—381no—
317C4⋊C8—381no—
318#103—382no—
319#102—382no—
320#102—382no—
321#102—382no—
322C22⋊C8—381no—
323C22⋊C8—381no—
324C4×C8—192no—
325C4×C8—381no—
326#95—22no—
327#95—21no—
328#95C22⋊D1912yes—
329C19#999711yescharacteristic, complemented, Sylow
330C24—21no—
331#41—761no—
332#41—761no—
333#41—761no—
334#41—761no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—381no—
341C2×Q8#6452512yescomplemented
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—42no—
345C2×D4—381no—
346C2×D4—381no—
347C2×D4—381no—
348C2×D4—761no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—761no—
360C22×C4C2×C22⋊D1911yescharacteristic
361C22×C4C2×C22⋊D1911yescharacteristic
362C22×C4C2×C22⋊D1911yescharacteristic
363Q16—764no—
364SD16—764no—
365D8—764no—
366M16—761no—
367M16—761no—
368C2×C8—382no—
369C2×C8—382no—
370C2×C8—761no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—44no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—381no—
381C4⋊C4—381no—
382C22⋊C4—44no—
383C22⋊C4—44no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—761no—
387C22⋊C4—761no—
388C42—41no—
389C42—41no—
390C42D4×D1911yescharacteristic
391C42D4×D1911yescharacteristic
392C42D4×D1911yescharacteristic
393C42#6454311yescharacteristic
394C23—22no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—761no—
402C23#1059739911yescharacteristic
403Q8—22no—
404Q8—22no—
405Q8—41no—
406Q8—41no—
407Q8—761no—
408Q8—761no—
409D4—22no—
410D4—22no—
411D4—41no—
412D4—41no—
413D4—762no—
414D4—761no—
415D4—761no—
416D4—1521no—
417D4—1521no—
418D4—1521no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—761no—
437C2×C4—1521no—
438C2×C4—1521no—
439C2×C4C2×#6452511yescharacteristic
440C2×C4#1059737811yescharacteristic
441C2×C4#1059738311yescharacteristic
442C2×C4#1059738311yescharacteristic
443C2×C4#1059738411yescharacteristic
444C2×C4#1059738511yescharacteristic
445C2×C4#1059738511yescharacteristic
446C2×C4#1059738611yescharacteristic
447C2×C4#1059739511yescharacteristic
448C2×C4#1059739611yescharacteristic
449C8—762no—
450C8—762no—
451C8—1521no—
452C22—21no—
453C22—21no—
454C22—42no—
455C22—42no—
456C22—42no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—1521no—
462C22—1521no—
463C22—1521no—
464C22#1192645211yescharacteristic
465C22#1192667811yescharacteristic
466C22#1192668911yescharacteristic
467C4—21no—
468C4—21no—
469C4—21no—
470C4—21no—
471C4—42no—
472C4—82no—
473C4—81no—
474C4—81no—
475C4—1521no—
476C4#1192667711yescharacteristic
477C4#1192668711yescharacteristic
478C4#1192677811yescharacteristic
479C4#1192679511yescharacteristic
480C2—21no—
481C2—21no—
482C2—82no—
483C2—3041no—
484C2#1456463111yescharacteristic
485C2#1456469511yescharacteristic
486C2#1456470011yescharacteristic
subgroupG/H
centerC22#11926452
commutator, cosocleC2×C42×C19C23
FrattiniC2×C42C22×D19
FittingC19×#2536C2
socleC22×C19#392
prime radical#14573635C2
hypercenter#2536D19
hypocenterC19#9997
LCSG ▷ C2×C42×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2536

Complements

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

NH ≅ G/Ntype
2. #14573107C2semidirect
3. #14562194C2semidirect
4. #14562060C2semidirect
5. #14562030C2semidirect
6. #14561493C2semidirect
7. C19×#2536C2semidirect
92. C2×Q8×C19D8semidirect
211. #2536D19semidirect
329. C19#9997semidirect
341. C2×Q8#64525semidirect

Maximal subgroups

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

subgroupindex
#145736352
#145731072
#145621942
#145620602
#145620302
#145614932
C19×#25362
#999719