Finite Group Databasebeta

← #18074215

Subgroups — #18074215

Order 4864.

844 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#11927240C211yesmaximal, characteristic
2#14563726C212yesmaximal, complemented
3#14563623C211yesmaximal, characteristic, complemented
4#14562204C212yesmaximal, complemented
5C19×#1459C211yesmaximal, characteristic, complemented
6#11927240—24no—
7#11927240—24no—
8C2×#10597344—21no—
9C2×#10597316C411yescharacteristic, complemented
10C2×#10597329—21no—
11C2×#10597376C411yescharacteristic, complemented
12C2×#10597376C2211yescharacteristic
13C2×#10597385—21no—
14C2×C4×D76C411yescharacteristic, complemented
15C2×(C22⋊D19)⋊C4—21no—
16C2×#10597372C411yescharacteristic, complemented
17C22×C4⋊Dic19C2211yescharacteristic
18C2×#10597291—21no—
19#11926404C2212yes—
20#11926311—21no—
21#11926307—24no—
22#11926279—24no—
23C2×C4×D4×C19C2211yescharacteristic
24C2×C19×C22⋊C8C2212yes—
25C19×#324—21no—
26C19×#323—21no—
27C22×D4×C19D411yescharacteristic
28C23×C4×C19C2×C411yescharacteristic
29C23×C4×C19C2311yescharacteristic
30C22×C22⋊D19—21no—
31C22×C22⋊D19—21no—
32C23×Dic19—21no—
33C22×D76C2×C411yescharacteristic
34C22×C4×D19—21no—
35C22×C8×C19—22no—
36C4×D4×C19—22no—
37C4×D4×C19—22no—
38C2×C4⋊C4×C19D411yescharacteristic
39C2×C22⋊C4×C19D411yescharacteristic
40C2×C22⋊C4×C19D411yescharacteristic
41C2×C42×C19C2×C411yescharacteristic
42C2×C22⋊Dic19—21no—
43C2×C22⋊Dic19—22no—
44#10597385—28no—
45#10597376—22no—
46#10597376—22no—
47#10597376—22no—
48#10597376D414yes—
49C2×(C2×D19)⋊C4—21no—
50C2×(C2×D19)⋊C4—21no—
51C2×(C2×D19)⋊C4—21no—
52#10597372—22no—
53#10597372—22no—
54C2×C4⋊Dic19—21no—
55C2×C4⋊Dic19—22no—
56C2×C4⋊Dic19—22no—
57C2×C4⋊Dic19C2×C411yescharacteristic
58C2×C4⋊Dic19C2×C411yescharacteristic
59C2×C4⋊Dic19C2×C411yescharacteristic
60C2×C4⋊Dic19D414yes—
61C2×Dic19⋊C4—21no—
62C2×Dic19⋊C4—21no—
63C2×C4×Dic19—21no—
64#10597344—28no—
65#10597329—28no—
66(C22⋊D19)⋊C4—28no—
67C4×D76—22no—
68C4×D76—22no—
69#10597316—22no—
70#10597316—22no—
71C19×C22⋊C8—22no—
72C19×C22⋊C8—22no—
73#10597291—42no—
74C19⋊#95—22no—
75C24×C19C22⋊C411yescharacteristic
76C24×C19C2×D411yescharacteristic
77C23×D19—21no—
78C2×D4×C19—22no—
79C2×D4×C19—22no—
80C2×D4×C19—21no—
81C2×D4×C19—21no—
82C22×C4×C19—21no—
83C22×C4×C19—21no—
84C22×C4×C19—42no—
85C22×C4×C19—42no—
86C22×C4×C19C22⋊C411yescharacteristic
87C22×C4×C19C22⋊C411yescharacteristic
88C22×C4×C19C22⋊C411yescharacteristic
89C22×C4×C19C22×C411yescharacteristic
90C22×C4×C19C2×D412yes—
91C22×C4×C19C2×D412yes—
92C22×C4×C19C2×D411yescharacteristic
93C2×C22⋊D19—24no—
94C2×C22⋊D19—24no—
95C2×C22⋊D19—42no—
96C2×C22⋊D19—41no—
97C2×C22⋊D19—41no—
98C2×C22⋊D19—82no—
99C22×Dic19—21no—
100C22×Dic19—21no—
101C22×Dic19—21no—
102C22×Dic19—24no—
103C22×Dic19—42no—
104C22×Dic19—82no—
105C2×D76—21no—
106C2×D76—42no—
107C2×D76C22⋊C412yes—
108C2×C4×D19—24no—
109C2×C4×D19—82no—
110C2×C8×C19—44no—
111C2×C8×C19—42no—
112C4⋊C4×C19—22no—
113C22⋊C4×C19—22no—
114C22⋊C4×C19—22no—
115C42×C19—21no—
116C42×C19—21no—
117C22⋊Dic19—24no—
118C22⋊Dic19—42no—
119C22⋊Dic19—42no—
120(C2×D19)⋊C4—24no—
121(C2×D19)⋊C4—24no—
122(C2×D19)⋊C4—24no—
123C4⋊Dic19—21no—
124C4⋊Dic19—21no—
125C4⋊Dic19—21no—
126C4⋊Dic19—24no—
127C4⋊Dic19—44no—
128C4⋊Dic19C22⋊C412yes—
129C4⋊Dic19C22⋊C412yes—
130C4⋊Dic19C22⋊C412yes—
131Dic19⋊C4—24no—
132Dic19⋊C4—24no—
133C4×Dic19—24no—
134#8378—191nomaximal, Sylow
135C23×C19—21no—
136C23×C19—21no—
137C23×C19—21no—
138C23×C19—41no—
139C23×C19—41no—
140C23×C19—41no—
141C23×C19—41no—
142C23×C19C2×C22⋊C411yescharacteristic
143C23×C19#12012yes—
144C23×C19#13512yes—
145C23×C19AGL(1,ℤ/8)11yescharacteristic
146C23×C19#13711yescharacteristic
147C22×D19—22no—
148C22×D19—42no—
149C22×D19—42no—
150C22×D19—41no—
151C22×D19—41no—
152D4×C19—42no—
153D4×C19—42no—
154C2×C4×C19—24no—
155C2×C4×C19—22no—
156C2×C4×C19—21no—
157C2×C4×C19—21no—
158C2×C4×C19—21no—
159C2×C4×C19—21no—
160C2×C4×C19—21no—
161C2×C4×C19—42no—
162C2×C4×C19—41no—
163C2×C4×C19—42no—
164C2×C4×C19—42no—
165C2×C4×C19—41no—
166C2×C4×C19—41no—
167C2×C4×C19C2×C22⋊C411yescharacteristic
168C2×C4×C19C2×C22⋊C411yescharacteristic
169C2×C4×C19#12012yes—
170C22⋊D19—44no—
171C22⋊D19—44no—
172C22⋊D19—84no—
173C2×Dic19—22no—
174C2×Dic19—22no—
175C2×Dic19—22no—
176C2×Dic19—42no—
177C2×Dic19—42no—
178C2×Dic19—41no—
179C2×Dic19—41no—
180C2×Dic19—84no—
181C2×Dic19—82no—
182C2×Dic19—82no—
183C2×Dic19—82no—
184D76—42no—
185D76—42no—
186C4×D19—84no—
187C8×C19—82no—
188C2×#553—191no—
189#1824—192no—
190#1799—191no—
191#1519—192no—
192#1459D1911yescharacteristic, complemented
193C22×C19—21no—
194C22×C19—22no—
195C22×C19—22no—
196C22×C19—21no—
197C22×C19—42no—
198C22×C19—41no—
199C22×C19—41no—
200C22×C19—41no—
201C22×C19—41no—
202C22×C19—41no—
203C22×C19—81no—
204C22×C19—81no—
205C22×C19#37911yescharacteristic
206C22×C19#41611yescharacteristic
207C22×C19#41711yescharacteristic
208C22×C19#44912yes—
209C22×C19#45212yes—
210C2×D19—42no—
211C2×D19—42no—
212C2×D19—42no—
213C2×D19—82no—
214C2×D19—82no—
215C4×C19—22no—
216C4×C19—21no—
217C4×C19—41no—
218C4×C19—41no—
219C4×C19—41no—
220C4×C19#41012yes—
221Dic19—42no—
222Dic19—42no—
223Dic19—42no—
224Dic19—162no—
225#553—384no—
226#553—384no—
227C2×#126—381no—
228C2×#125—191no—
229C2×#123—381no—
230C2×#121—191no—
231C2×#121—191no—
232C2×#121—381no—
233C2×C4×D4—191no—
234C2×C4×D4—381no—
235C2×C4×D4C2×D1911yescharacteristic
236C2×#117—191no—
237C22×C4⋊C4—191no—
238C2×#99—381no—
239C2×C22⋊C8C2×D1912yes—
240#380—192no—
241#342—381no—
242#340—384no—
243#327—384no—
244#324—21no—
245#323—21no—
246C2×C19—22no—
247C2×C19—21no—
248C2×C19—21no—
249C2×C19—22no—
250C2×C19—81no—
251C2×C19#178211yescharacteristic
252C2×C19#178811yescharacteristic
253C2×C19#179511yescharacteristic
254D19—82no—
255C22×D4—191no—
256C22×D4—381no—
257C22×D4—381no—
258C22×D4D7611yescharacteristic
259C23×C4—381no—
260C23×C4—381no—
261C23×C4C4×D1911yescharacteristic
262C23×C4C22×D1911yescharacteristic
263C22×C8—22no—
264#126—388no—
265#125—382no—
266#125—382no—
267#123—388no—
268#121—194no—
269#121—382no—
270#121—382no—
271#121—388no—
272#121—382no—
273C4×D4—22no—
274C4×D4—22no—
275C4×D4—382no—
276C4×D4—382no—
277C4×D4—388no—
278#117—382no—
279#117—382no—
280C2×C4⋊C4—191no—
281C2×C4⋊C4—191no—
282C2×C4⋊C4—191no—
283C2×C4⋊C4—194no—
284C2×C4⋊C4—381no—
285C2×C4⋊C4—381no—
286C2×C4⋊C4—382no—
287C2×C4⋊C4—381no—
288C2×C4⋊C4—382no—
289C2×C4⋊C4C22⋊D1911yescharacteristic
290C2×C22⋊C4—381no—
291C2×C22⋊C4—381no—
292C2×C22⋊C4—381no—
293C2×C22⋊C4—381no—
294C2×C22⋊C4—382no—
295C2×C22⋊C4D7611yescharacteristic
296C2×C22⋊C4C22⋊D1911yescharacteristic
297C2×C42—381no—
298C2×C42C4×D1911yescharacteristic
299#99—762no—
300C22⋊C8—22no—
301C22⋊C8—22no—
302#95—382no—
303C19#837811yescharacteristic, complemented, Sylow
304C24—381no—
305C24(C2×D19)⋊C411yescharacteristic
306C24C2×D7611yescharacteristic
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—192no—
312C2×D4—384no—
313C2×D4—384no—
314C2×D4—381no—
315C2×D4—762no—
316C2×D4—762no—
317C2×D4—761no—
318C2×D4—761no—
319C2×D4—1522no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—42no—
323C22×C4—42no—
324C22×C4—384no—
325C22×C4—381no—
326C22×C4—381no—
327C22×C4—381no—
328C22×C4—384no—
329C22×C4—762no—
330C22×C4—1522no—
331C22×C4—1522no—
332C22×C4(C2×D19)⋊C411yescharacteristic
333C22×C4(C2×D19)⋊C411yescharacteristic
334C22×C4(C2×D19)⋊C411yescharacteristic
335C22×C4C2×C4×D1911yescharacteristic
336C22×C4D4×D1912yes—
337C22×C4D4×D1912yes—
338C22×C4C2×C22⋊D1911yescharacteristic
339C2×C8—44no—
340C2×C8—42no—
341C4⋊C4—22no—
342C4⋊C4—192no—
343C4⋊C4—192no—
344C4⋊C4—192no—
345C4⋊C4—384no—
346C4⋊C4—384no—
347C4⋊C4—384no—
348C4⋊C4—381no—
349C4⋊C4—381no—
350C4⋊C4—381no—
351C4⋊C4—764no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—384no—
355C22⋊C4—384no—
356C22⋊C4—384no—
357C22⋊C4—384no—
358C22⋊C4—762no—
359C22⋊C4—762no—
360C42—21no—
361C42—21no—
362C42—384no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—382no—
371C23—762no—
372C23—762no—
373C23—761no—
374C23—761no—
375C23#1059732812yes—
376C23#1059735012yes—
377C23#1059735411yescharacteristic
378C23#1059735511yescharacteristic
379C23C2×(C2×D19)⋊C411yescharacteristic
380D4—42no—
381D4—42no—
382D4—762no—
383D4—764no—
384D4—764no—
385D4—762no—
386D4—1524no—
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—382no—
401C2×C4—382no—
402C2×C4—382no—
403C2×C4—762no—
404C2×C4—762no—
405C2×C4—761no—
406C2×C4—761no—
407C2×C4—1524no—
408C2×C4—1522no—
409C2×C4—1522no—
410C2×C4—1522no—
411C2×C4—1524no—
412C2×C4C22⋊C4×D1911yescharacteristic
413C2×C4C22⋊C4×D1911yescharacteristic
414C2×C4#1059738312yes—
415C8—82no—
416C22—21no—
417C22—22no—
418C22—21no—
419C22—22no—
420C22—42no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—81no—
427C22—81no—
428C22—762no—
429C22—762no—
430C22—762no—
431C22—1522no—
432C22—1522no—
433C22#1192639911yescharacteristic
434C22#1192654111yescharacteristic
435C22#1192654611yescharacteristic
436C22#1192669112yes—
437C22#1192670812yes—
438C4—22no—
439C4—21no—
440C4—41no—
441C4—41no—
442C4—41no—
443C4—3042no—
444C4—762no—
445C4—762no—
446C4—762no—
447C4#1192651612yes—
448C2—22no—
449C2—21no—
450C2—21no—
451C2—22no—
452C2—81no—
453C2—1522no—
454C2#1456355111yescharacteristic
455C2#1456357611yescharacteristic
456C2#1456360611yescharacteristic
subgroupG/H
centerC22#11926399
commutatorC22×C4×C19C22×C4
FrattiniC23×C4C22×D19
FittingC19×#1459C2
socleC22×C19#379
prime radicalC2×#11927240C2
cosocleC23×C4×C19C23
hypercenter#1459D19
hypocenterC19#8378
LCSG ▷ C22×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. #14563726C2semidirect
3. #14563623C2semidirect
4. #14562204C2semidirect
5. C19×#1459C2semidirect
9. C2×#10597316C4semidirect
11. C2×#10597376C4semidirect
14. C2×C4×D76C4semidirect
16. C2×#10597372C4semidirect
192. #1459D19semidirect
303. C19#8378semidirect

Maximal subgroups

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

subgroupindex
C2×#119272402
#145637262
#145636232
#145622042
C19×#14592
#837819