Finite Group Databasebeta

← #18083116

Subgroups — #18083116

Order 4864.

772 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 115 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×#11926858C211yesmaximal, characteristic, complemented
2C2×#11926855C211yesmaximal, characteristic, complemented
3#14569739C211yesmaximal, characteristic
4C2×#11926277C211yesmaximal, characteristic, complemented
5#14561904C211yesmaximal, characteristic, complemented
6#14561477C211yesmaximal, characteristic, complemented
7C2×C19×#327C211yesmaximal, characteristic, complemented
8C2×#10597376C2211yescharacteristic
9C2×#10597385—22no—
10C22×C4⋊Dic19C2211yescharacteristic
11#11926858—22no—
12#11926858—22no—
13#11926855—22no—
14#11926855—22no—
15C2×#10597275—21no—
16C2×#10597264—21no—
17C2×#10597278—21no—
18C2×#10597289—21no—
19C2×C22⋊(C19⋊C8)C2211yescharacteristic
20#11926480—21no—
21#11926479—21no—
22#11926453—21no—
23#11926452—21no—
24C2×C19⋊#95—22no—
25C2×C19⋊#95C2211yescharacteristic
26#11926277—22no—
27C2×C19×#121C2211yescharacteristic
28C2×C19×C22⋊C8C2211yescharacteristic
29C2×C19×#95C2211yescharacteristic
30C19×#327—22no—
31C22×D4×C19—21no—
32C22×D4×C19D411yescharacteristic
33C23×C4×C19—21no—
34C23×C4×C19C2311yescharacteristic
35C22×C22⋊D19—21no—
36C22×C22⋊D19—22no—
37C23×Dic19—21no—
38C23×Dic19D412yes—
39C22×D76D411yescharacteristic
40C22×C8×C19—21no—
41C19×#121—21no—
42C19×#121—21no—
43C19×#121—21no—
44C19×#121—21no—
45C2×C4⋊C4×C19D411yescharacteristic
46C2×C22⋊C4×C19—21no—
47C2×C22⋊Dic19—22no—
48#10597385—44no—
49#10597385—44no—
50#10597376—21no—
51#10597376—21no—
52#10597376—21no—
53#10597376—21no—
54C2×(C2×D19)⋊C4—22no—
55C2×(C2×D19)⋊C4—21no—
56C2×C4⋊Dic19—21no—
57C2×C4⋊Dic19—21no—
58C2×C4⋊Dic19—21no—
59C2×C4⋊Dic19—21no—
60C2×C4⋊Dic19—21no—
61C2×C4⋊Dic19D411yescharacteristic
62C2×C4⋊Dic19D412yescomplemented
63C2×Dic19⋊C4—22no—
64C22×C19⋊C8—21no—
65C19×C22⋊C8—21no—
66C19×C22⋊C8D412yescomplemented
67C19×#95—21no—
68C19×#95—21no—
69#10597289—24no—
70C19⋊#95—21no—
71C19⋊#95—21no—
72C19⋊#95—44no—
73C22⋊(C19⋊C8)—21no—
74C22⋊(C19⋊C8)D412yescomplemented
75#10597278—24no—
76#10597275—24no—
77#10597264—24no—
78C24×C19—21no—
79C24×C19C2×D411yescharacteristic
80C23×D19—21no—
81C2×D4×C19—21no—
82C2×D4×C19—21no—
83C2×D4×C19—42no—
84C2×D4×C19—41no—
85C2×D4×C19—41no—
86C2×D4×C19—42no—
87C2×D4×C19—42no—
88C22×C4×C19—22no—
89C22×C4×C19—21no—
90C22×C4×C19—42no—
91C22×C4×C19—41no—
92C22×C4×C19—42no—
93C22×C4×C19—41no—
94C22×C4×C19—42no—
95C22×C4×C19C2×D411yescharacteristic
96C22×C4×C19C2×D411yescharacteristic
97C22×C4×C19C2×D411yescharacteristic
98C22×C4×C19C2×D411yescharacteristic
99C22×C4×C19C2×D411yescharacteristic
100C22×C4×C19#4111yescharacteristic
101C2×C22⋊D19—44no—
102C2×C22⋊D19—41no—
103C2×C22⋊D19—41no—
104C2×C22⋊D19—42no—
105C2×C22⋊D19—42no—
106C2×C22⋊D19—82no—
107C2×C22⋊D19—82no—
108C22×Dic19—22no—
109C22×Dic19—22no—
110C22×Dic19—21no—
111C22×Dic19—22no—
112C22×Dic19—42no—
113C22×Dic19—42no—
114C22×Dic19—41no—
115C22×Dic19—41no—
116C22×Dic19—42no—
117C22×Dic19—42no—
118C22×Dic19D814yes—
119C2×D76—21no—
120C2×D76—21no—
121C2×D76—42no—
122C2×C8×C19—22no—
123C2×C8×C19—42no—
124C4⋊C4×C19—21no—
125C4⋊C4×C19—21no—
126C22⋊C4×C19—41no—
127C22⋊C4×C19—41no—
128C22⋊Dic19—44no—
129(C2×D19)⋊C4—44no—
130(C2×D19)⋊C4—41no—
131(C2×D19)⋊C4—41no—
132C4⋊Dic19—21no—
133C4⋊Dic19—22no—
134C4⋊Dic19—22no—
135C4⋊Dic19—21no—
136C4⋊Dic19—41no—
137C4⋊Dic19—41no—
138Dic19⋊C4—44no—
139C2×C19⋊C8—22no—
140C2×C19⋊C8—42no—
141#9970—191nomaximal, Sylow
142C23×C19—21no—
143C23×C19—21no—
144C23×C19—22no—
145C23×C19—41no—
146C23×C19—42no—
147C23×C19—41no—
148C23×C19—41no—
149C23×C19—42no—
150C23×C19#12011yescharacteristic
151C23×C19#12111yescharacteristic
152C23×C19#12711yescharacteristic
153C23×C19C2×D812yes—
154C23×C19AGL(1,ℤ/8)12yes—
155C22×D19—41no—
156C22×D19—42no—
157C22×D19—41no—
158C22×D19—41no—
159C22×D19—42no—
160D4×C19—42no—
161D4×C19—81no—
162D4×C19—82no—
163D4×C19—81no—
164D4×C19—81no—
165C2×C4×C19—22no—
166C2×C4×C19—22no—
167C2×C4×C19—41no—
168C2×C4×C19—41no—
169C2×C4×C19—41no—
170C2×C4×C19—41no—
171C2×C4×C19—44no—
172C2×C4×C19—42no—
173C2×C4×C19—41no—
174C2×C4×C19—42no—
175C2×C4×C19—82no—
176C2×C4×C19—81no—
177C2×C4×C19—81no—
178C2×C4×C19#12011yescharacteristic
179C2×C4×C19#12011yescharacteristic
180C2×C4×C19#12111yescharacteristic
181C2×C4×C19#12111yescharacteristic
182C22⋊D19—88no—
183C22⋊D19—82no—
184C22⋊D19—81no—
185C22⋊D19—81no—
186C2×Dic19—24no—
187C2×Dic19—42no—
188C2×Dic19—42no—
189C2×Dic19—44no—
190C2×Dic19—42no—
191C2×Dic19—41no—
192C2×Dic19—42no—
193C2×Dic19—44no—
194C2×Dic19—82no—
195C2×Dic19—82no—
196C2×Dic19—81no—
197C2×Dic19—81no—
198D76—42no—
199D76—81no—
200C8×C19—42no—
201C19⋊C8—42no—
202C2×#480—191no—
203C2×#480—191no—
204#2656—191no—
205C2×#327—191no—
206C2×#327D1911yescharacteristic, complemented
207#1445—191no—
208#1280—191no—
209C22×C19—22no—
210C22×C19—22no—
211C22×C19—22no—
212C22×C19—22no—
213C22×C19—21no—
214C22×C19—21no—
215C22×C19—21no—
216C22×C19—21no—
217C22×C19—82no—
218C22×C19—82no—
219C22×C19—81no—
220C22×C19—81no—
221C22×C19—81no—
222C22×C19#39211yescharacteristic
223C22×C19#44712yes—
224C22×C19#45511yescharacteristic
225C22×C19#45611yescharacteristic
226C22×C19#45812yes—
227C22×C19#45912yes—
228C22×C19#49311yescharacteristic
229C22×C19#49611yescharacteristic
230C2×D19—82no—
231C2×D19—82no—
232C2×D19—81no—
233C2×D19—81no—
234C2×D19—81no—
235C4×C19—21no—
236C4×C19—21no—
237C4×C19—21no—
238C4×C19—21no—
239C4×C19—82no—
240C4×C19—81no—
241Dic19—44no—
242Dic19—82no—
243Dic19—81no—
244C2×#121—191no—
245C2×#121—382no—
246C2×#121C2×D1911yescharacteristic
247C22×C4⋊C4—191no—
248#480—382no—
249#480—382no—
250#480—382no—
251#480—382no—
252C2×#107—381no—
253C2×#107—381no—
254C2×#102—381no—
255C2×#102—381no—
256C2×C22⋊C8—191no—
257C2×C22⋊C8C2×D1911yescharacteristic
258#399—381no—
259#399—381no—
260#392—381no—
261#392—381no—
262C2×#95—191no—
263C2×#95—382no—
264C2×#95C2×D1911yescharacteristic
265#327—22no—
266#327—382no—
267C2×C19—21no—
268C2×C19—22no—
269C2×C19—21no—
270C2×C19—161no—
271C2×C19#160712yes—
272C2×C19#161012yes—
273C2×C19#200711yescharacteristic
274C2×C19#201111yescharacteristic
275C2×C19#202211yescharacteristic
276D19—161no—
277C22×D4—21no—
278C22×D4—191no—
279C22×D4—381no—
280C22×D4—382no—
281C22×D4D7611yescharacteristic
282C23×C4—21no—
283C23×C4—192no—
284C23×C4—381no—
285C23×C4C22×D1911yescharacteristic
286C22×C8—21no—
287C22×C8—381no—
288#121—21no—
289#121—21no—
290#121—21no—
291#121—21no—
292#121—381no—
293#121—381no—
294#121—381no—
295#121—381no—
296#121—764no—
297#121—764no—
298C2×C4⋊C4—192no—
299C2×C4⋊C4—191no—
300C2×C4⋊C4—381no—
301C2×C4⋊C4—381no—
302C2×C4⋊C4—381no—
303C2×C4⋊C4—381no—
304C2×C4⋊C4—382no—
305C2×C4⋊C4—381no—
306C2×C4⋊C4D7611yescharacteristic
307C2×C22⋊C4—21no—
308C2×C22⋊C4—382no—
309C2×C22⋊C4—382no—
310C2×C22⋊C4—381no—
311#107—384no—
312#107—384no—
313#102—384no—
314#102—384no—
315C22⋊C8—21no—
316C22⋊C8—192no—
317C22⋊C8—381no—
318C22⋊C8C22⋊D1912yescomplemented
319#95—21no—
320#95—21no—
321#95—381no—
322#95—381no—
323#95—764no—
324C19#997011yescharacteristic, complemented, Sylow
325C24—21no—
326C24—381no—
327C24D4×D1911yescharacteristic
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—42no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—42no—
334C2×D4—42no—
335C2×D4—381no—
336C2×D4—381no—
337C2×D4—762no—
338C2×D4—764no—
339C2×D4—761no—
340C2×D4—761no—
341C2×D4—762no—
342C2×D4—762no—
343C2×D4—1522no—
344C2×D4—1522no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—42no—
348C22×C4—41no—
349C22×C4—42no—
350C22×C4—41no—
351C22×C4—42no—
352C22×C4—194no—
353C22×C4—382no—
354C22×C4—382no—
355C22×C4—381no—
356C22×C4—382no—
357C22×C4—762no—
358C22×C4—762no—
359C22×C4—761no—
360C22×C4—761no—
361C22×C4—762no—
362C22×C4—762no—
363C22×C4C2×D7611yescharacteristic
364C22×C4#6454111yescharacteristic
365C22×C4D4×D1911yescharacteristic
366C22×C4D4×D1911yescharacteristic
367C22×C4D4×D1911yescharacteristic
368C22×C4C2×C22⋊D1911yescharacteristic
369C2×C8—22no—
370C2×C8—42no—
371C2×C8—382no—
372C2×C8—762no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—382no—
376C4⋊C4—381no—
377C4⋊C4—382no—
378C4⋊C4—381no—
379C4⋊C4—764no—
380C4⋊C4—761no—
381C4⋊C4—761no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—764no—
385C22⋊C4—764no—
386C22⋊C4—761no—
387C22⋊C4—761no—
388C23—21no—
389C23—21no—
390C23—22no—
391C23—42no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—42no—
396C23—762no—
397C23—761no—
398C23—761no—
399C23—761no—
400C23—762no—
401C23#1059732811yescharacteristic
402C23#1059733011yescharacteristic
403C23D8×D1912yes—
404C23#1059736012yes—
405C23#1059738611yescharacteristic
406D4—42no—
407D4—81no—
408D4—81no—
409D4—81no—
410D4—82no—
411D4—762no—
412D4—1521no—
413D4—1528no—
414D4—1521no—
415D4—1521no—
416D4—1522no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—82no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—384no—
431C2×C4—762no—
432C2×C4—762no—
433C2×C4—764no—
434C2×C4—762no—
435C2×C4—761no—
436C2×C4—762no—
437C2×C4—764no—
438C2×C4—1522no—
439C2×C4—1521no—
440C2×C4—1521no—
441C2×C4—1522no—
442C2×C4#1059732811yescharacteristic
443C2×C4#1059733011yescharacteristic
444C2×C4#1059737611yescharacteristic
445C2×C4#1059738311yescharacteristic
446C8—42no—
447C8—762no—
448C22—22no—
449C22—22no—
450C22—21no—
451C22—21no—
452C22—22no—
453C22—22no—
454C22—21no—
455C22—21no—
456C22—82no—
457C22—81no—
458C22—82no—
459C22—81no—
460C22—81no—
461C22—1522no—
462C22—1521no—
463C22—1522no—
464C22—1521no—
465C22—1521no—
466C22#1192645311yescharacteristic
467C22#1192667912yes—
468C22#1192672311yescharacteristic
469C22#1192672811yescharacteristic
470C22#1192673512yes—
471C22#1192673812yes—
472C22#1192691911yescharacteristic
473C22#1192693011yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—21no—
478C4—82no—
479C4—81no—
480C4—764no—
481C4—1522no—
482C4—1521no—
483C2—21no—
484C2—21no—
485C2—22no—
486C2—161no—
487C2—3041no—
488C2#1456262212yes—
489C2#1456263912yes—
490C2#1456468311yescharacteristic
491C2#1456470711yescharacteristic
492C2#1456476511yescharacteristic
subgroupG/H
centerC23#10597328
commutator, cosocleC23×C4×C19C23
FrattiniC23×C4C22×D19
FittingC2×C19×#327C2
socleC23×C19#120
prime radical#14569739C2
hypercenterC2×#327D19
hypocenterC19#9970
LCSG ▷ C23×C4×C19 ▷ C22×C19 ▷ C19
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
1. C2×#11926858C2semidirect
2. C2×#11926855C2semidirect
4. C2×#11926277C2semidirect
5. #14561904C2semidirect
6. #14561477C2semidirect
7. C2×C19×#327C2semidirect
62. C2×C4⋊Dic19D4semidirect
66. C19×C22⋊C8D4semidirect
74. C22⋊(C19⋊C8)D4semidirect
206. C2×#327D19semidirect
318. C22⋊C8C22⋊D19semidirect
324. C19#9970semidirect

Maximal subgroups

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

subgroupindex
C2×#119268582
C2×#119268552
#145697392
C2×#119262772
#145619042
#145614772
C2×C19×#3272
#997019