Finite Group Databasebeta

← #14569484

Subgroups — #14569484

Order 2432.

562 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10597340C211yesmaximal, characteristic, complemented
2C2×C4×D76C211yesmaximal, characteristic, complemented
3#11926478C211yesmaximal, characteristic, complemented
4#11926473C211yesmaximal, characteristic, complemented
5#11926468C211yesmaximal, characteristic, complemented
6#11926466C211yesmaximal, characteristic, complemented
7#11926462C211yesmaximal, characteristic, complemented
8#11926462C211yesmaximal, characteristic, complemented
9#11926461C211yesmaximal, characteristic, complemented
10#11926454C211yesmaximal, characteristic
11#11926435C211yesmaximal, characteristic, complemented
12#11926422C211yesmaximal, characteristic, complemented
13#11926415C211yesmaximal, characteristic, complemented
14#11926403C211yesmaximal, characteristic, complemented
15C19×#387C211yesmaximal, characteristic, complemented
16C22×D76C2211yescharacteristic
17C22×D76C2211yescharacteristic
18C22×D76C2211yescharacteristic
19C22×C4×D19C2211yescharacteristic
20C22×C4×D19C2211yescharacteristic
21C2×C4⋊C4×C19C2211yescharacteristic
22C2×C4⋊C4×C19C2211yescharacteristic
23C2×C42×C19C2211yescharacteristic
24C2×(C2×D19)⋊C4C2211yescharacteristic
25C2×(C2×D19)⋊C4C2211yescharacteristic
26C2×(C2×D19)⋊C4C2211yescharacteristic
27C2×(C2×D19)⋊C4C2211yescharacteristic
28C2×(C2×D19)⋊C4C2211yescharacteristic
29C2×(C2×D19)⋊C4C2211yescharacteristic
30C2×(C2×D19)⋊C4C2211yescharacteristic
31C2×(C2×D19)⋊C4C2211yescharacteristic
32C2×(C2×D19)⋊C4C2211yescharacteristic
33C2×(C2×D19)⋊C4C2211yescharacteristic
34C2×(C2×D19)⋊C4C2211yescharacteristic
35C2×(C2×D19)⋊C4C2211yescharacteristic
36C2×(C2×D19)⋊C4C2211yescharacteristic
37C2×C4⋊Dic19C2211yescharacteristic
38C2×Dic19⋊C4C2211yescharacteristic
39C2×Dic19⋊C4C2211yescharacteristic
40C2×Dic19⋊C4C2211yescharacteristic
41C2×Dic19⋊C4C2211yescharacteristic
42C2×Dic19⋊C4C2211yescharacteristic
43#10597340—24no—
44C4×D76—24no—
45C19×#95C2211yescharacteristic
46C19×#95C2211yescharacteristic
47C19×#95C2211yescharacteristic
48C19×#95C2211yescharacteristic
49C19⋊#95C2211yescharacteristic
50C19⋊#95C2211yescharacteristic
51C19⋊#95C2211yescharacteristic
52C19⋊#95C2211yescharacteristic
53C23×D19C2311yescharacteristic
54C23×D19C2311yescharacteristic
55C23×D19C2311yescharacteristic
56C22×C4×C19C2311yescharacteristic
57C22×C4×C19C2311yescharacteristic
58C22×C4×C19C2311yescharacteristic
59C22×C4×C19C2311yescharacteristic
60C22×C4×C19C2311yescharacteristic
61C22×C4×C19C2311yescharacteristic
62C22×C4×C19C2311yescharacteristic
63C22×Dic19C2311yescharacteristic
64C22×Dic19C2311yescharacteristic
65C22×Dic19C2311yescharacteristic
66C22×Dic19C2311yescharacteristic
67C22×Dic19C2311yescharacteristic
68C2×D76—22no—
69C2×D76—22no—
70C2×D76—22no—
71C2×D76—22no—
72C2×D76—22no—
73C2×D76—41no—
74C2×D76—41no—
75C2×D76—41no—
76C2×D76—41no—
77C2×C4×D19—22no—
78C2×C4×D19—41no—
79C2×C4×D19—41no—
80C2×C4×D19—41no—
81C2×C4×D19—41no—
82C2×C4×D19D414yescomplemented
83C4⋊C4×C19—22no—
84C4⋊C4×C19—22no—
85C42×C19—22no—
86(C2×D19)⋊C4—22no—
87(C2×D19)⋊C4—22no—
88(C2×D19)⋊C4—22no—
89(C2×D19)⋊C4—22no—
90(C2×D19)⋊C4—22no—
91(C2×D19)⋊C4—22no—
92(C2×D19)⋊C4—22no—
93(C2×D19)⋊C4—41no—
94(C2×D19)⋊C4—41no—
95(C2×D19)⋊C4—41no—
96(C2×D19)⋊C4—41no—
97(C2×D19)⋊C4—41no—
98(C2×D19)⋊C4—41no—
99C4⋊Dic19—22no—
100Dic19⋊C4—22no—
101Dic19⋊C4—41no—
102Dic19⋊C4—41no—
103Dic19⋊C4—41no—
104Dic19⋊C4—41no—
105C23×C19C2411yescharacteristic
106C22×D19—21no—
107C22×D19—21no—
108C22×D19—21no—
109C22×D19—21no—
110C22×D19—21no—
111C22×D19—21no—
112C22×D19—21no—
113C22×D19—21no—
114C22×D19—21no—
115C22×D19—21no—
116C22×D19—21no—
117C22×D19—21no—
118C22×D19—21no—
119C22×D19—21no—
120C22×D19—21no—
121C22×D19—21no—
122C22×D19—21no—
123C22×D19—21no—
124C22×D19—21no—
125C22×D19C2×D412yes—
126C22×D19#4112yes—
127C2×C4×C19—21no—
128C2×C4×C19—21no—
129C2×C4×C19—21no—
130C2×C4×C19—21no—
131C2×C4×C19—21no—
132C2×C4×C19—21no—
133C2×C4×C19—21no—
134C2×C4×C19—21no—
135C2×C4×C19—21no—
136C2×C4×C19—21no—
137C2×C4×C19—21no—
138C2×C4×C19—21no—
139C2×C4×C19—21no—
140C2×C4×C19—21no—
141C2×C4×C19—21no—
142C2×C4×C19—21no—
143C2×C4×C19—21no—
144C2×C4×C19—21no—
145C2×C4×C19—21no—
146C2×C4×C19C2×D412yes—
147C2×C4×C19#4112yes—
148C2×Dic19—21no—
149C2×Dic19—21no—
150C2×Dic19—21no—
151C2×Dic19—21no—
152C2×Dic19—21no—
153C2×Dic19—21no—
154C2×Dic19—21no—
155C2×Dic19—21no—
156C2×Dic19—21no—
157C2×Dic19—21no—
158C2×Dic19—21no—
159C2×Dic19—21no—
160C2×Dic19—21no—
161C2×Dic19—21no—
162C2×Dic19C2×D412yes—
163D76—28no—
164D76—44no—
165D76—44no—
166C4×D19—44no—
167C4×D19—44no—
168#2630—191nomaximal, Sylow
169C22×C19C22×D411yescharacteristic
170C22×C19C2×#4111yescharacteristic
171C22×C19C2×#4111yescharacteristic
172C22×C19H(5,𝔽2)11yescharacteristic
173C22×C19H(5,𝔽2)11yescharacteristic
174C22×C19H(5,𝔽2)11yescharacteristic
175C22×C192−1+411yescharacteristic
176C2×D19—22no—
177C2×D19—22no—
178C2×D19—22no—
179C2×D19—22no—
180C2×D19—22no—
181C2×D19—22no—
182C2×D19—41no—
183C2×D19—41no—
184C2×D19—41no—
185C2×D19—41no—
186C2×D19—41no—
187C2×D19—41no—
188C2×D19—41no—
189C2×D19—41no—
190C2×D19—41no—
191C2×D19—41no—
192C2×D19—41no—
193C2×D19—41no—
194C2×D19—41no—
195C2×D19—41no—
196C2×D19—41no—
197C4×C19—22no—
198C4×C19—22no—
199C4×C19—41no—
200C4×C19—41no—
201C4×C19—41no—
202C4×C19—41no—
203C4×C19—41no—
204Dic19—22no—
205Dic19—41no—
206Dic19—41no—
207Dic19—41no—
208Dic19—41no—
209C2×#123—191no—
210C2×C4×D4—191no—
211#398—191no—
212#397—191no—
213#396—191no—
214#396—191no—
215#394—191no—
216#394—191no—
217#394—191no—
218#392—191no—
219#388—191no—
220#387D1911yescharacteristic, complemented
221#386—191no—
222#385—191no—
223#380—191no—
224C2×C19#52511yescharacteristic
225C2×C19#53411yescharacteristic
226C2×C19#53711yescharacteristic
227C2×C19#53811yescharacteristic
228C2×C19#53911yescharacteristic
229C2×C19#54011yescharacteristic
230C2×C19#54211yescharacteristic
231D19—42no—
232D19—42no—
233D19—81no—
234C22×D4—191no—
235C22×D4—191no—
236C22×D4—191no—
237C23×C4—191no—
238C23×C4—191no—
239#123—384no—
240C4×D4—384no—
241C2×C4⋊C4—191no—
242C2×C4⋊C4—191no—
243C2×C4⋊C4—191no—
244C2×C4⋊C4—191no—
245C2×C4⋊C4—191no—
246C2×C4⋊C4—191no—
247C2×C4⋊C4C2×D1911yescharacteristic
248C2×C4⋊C4C2×D1911yescharacteristic
249C2×C22⋊C4—191no—
250C2×C22⋊C4—191no—
251C2×C22⋊C4—191no—
252C2×C22⋊C4—191no—
253C2×C22⋊C4—191no—
254C2×C22⋊C4—191no—
255C2×C22⋊C4—191no—
256C2×C22⋊C4—191no—
257C2×C22⋊C4—191no—
258C2×C22⋊C4—191no—
259C2×C22⋊C4—191no—
260C2×C22⋊C4—191no—
261C2×C22⋊C4—191no—
262C2×C42C2×D1911yescharacteristic
263#95—191no—
264#95—191no—
265#95—191no—
266#95—191no—
267#95C2×D1911yescharacteristic
268#95C2×D1911yescharacteristic
269#95C2×D1911yescharacteristic
270#95C2×D1911yescharacteristic
271C19#263011yescharacteristic, complemented, Sylow
272C24—191no—
273C24—191no—
274C24—191no—
275C2×D4—382no—
276C2×D4—382no—
277C2×D4—382no—
278C2×D4—382no—
279C2×D4—382no—
280C2×D4—761no—
281C2×D4—761no—
282C2×D4—761no—
283C2×D4—761no—
284C22×C4—191no—
285C22×C4—194no—
286C22×C4—191no—
287C22×C4—191no—
288C22×C4—191no—
289C22×C4—191no—
290C22×C4—382no—
291C22×C4—761no—
292C22×C4—761no—
293C22×C4—761no—
294C22×C4—761no—
295C22×C4C22×D1911yescharacteristic
296C22×C4C22×D1911yescharacteristic
297C22×C4C22×D1911yescharacteristic
298C22×C4C22×D1911yescharacteristic
299C22×C4C22×D1911yescharacteristic
300C22×C4C22×D1911yescharacteristic
301C22×C4C22×D1911yescharacteristic
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—382no—
305C4⋊C4—382no—
306C4⋊C4—761no—
307C4⋊C4—761no—
308C4⋊C4—761no—
309C4⋊C4—761no—
310C22⋊C4—382no—
311C22⋊C4—382no—
312C22⋊C4—382no—
313C22⋊C4—382no—
314C22⋊C4—382no—
315C22⋊C4—382no—
316C22⋊C4—382no—
317C22⋊C4—761no—
318C22⋊C4—761no—
319C22⋊C4—761no—
320C22⋊C4—761no—
321C22⋊C4—761no—
322C22⋊C4—761no—
323C42—22no—
324C23—192no—
325C23—192no—
326C23—381no—
327C23—381no—
328C23—381no—
329C23—381no—
330C23—381no—
331C23—381no—
332C23—381no—
333C23—381no—
334C23—381no—
335C23—381no—
336C23—381no—
337C23—381no—
338C23—381no—
339C23—381no—
340C23—381no—
341C23—381no—
342C23—381no—
343C23—381no—
344C23—381no—
345C23C23×D1911yescharacteristic
346D4—388no—
347D4—764no—
348D4—764no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—192no—
369C2×C4—381no—
370C2×C4—381no—
371C2×C4—381no—
372C2×C4—381no—
373C2×C4—381no—
374C2×C4—381no—
375C2×C4—381no—
376C2×C4—381no—
377C2×C4—381no—
378C2×C4—381no—
379C2×C4—381no—
380C2×C4—381no—
381C2×C4—381no—
382C2×C4—381no—
383C2×C4—764no—
384C2×C4—764no—
385C2×C4#6454112yes—
386C2×C4D4×D1912yes—
387C22—382no—
388C22—382no—
389C22—382no—
390C22—382no—
391C22—382no—
392C22—382no—
393C22—761no—
394C22—761no—
395C22—761no—
396C22—761no—
397C22—761no—
398C22—761no—
399C22—761no—
400C22—761no—
401C22—761no—
402C22—761no—
403C22—761no—
404C22—761no—
405C22—761no—
406C22—761no—
407C22—761no—
408C22C2×#6454111yescharacteristic
409C22C2×D4×D1911yescharacteristic
410C22#1059743311yescharacteristic
411C22#41×D1911yescharacteristic
412C22#1059743511yescharacteristic
413C22#1059743511yescharacteristic
414C22#1059743511yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—41no—
422C4—382no—
423C4—761no—
424C4—761no—
425C4—761no—
426C4—761no—
427C2—762no—
428C2—762no—
429C2—1521no—
430C2#1192705311yescharacteristic
431C2#1192710511yescharacteristic
432C2#1192712411yescharacteristic
433C2#1192713311yescharacteristic
434C2#1192714211yescharacteristic
435C2#1192714911yescharacteristic
436C2#1192716611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D19
commutator, socle, cosocleC23×C19C24
FittingC19×#387C2
prime radical#11926454C2
hypercenter#387D19
hypocenterC19#2630
LCSG ▷ C23×C19 ▷ C19
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#10597340C2semidirect
2. C2×C4×D76C2semidirect
3. #11926478C2semidirect
4. #11926473C2semidirect
5. #11926468C2semidirect
6. #11926466C2semidirect
7. #11926462C2semidirect
8. #11926462C2semidirect
9. #11926461C2semidirect
11. #11926435C2semidirect
12. #11926422C2semidirect
13. #11926415C2semidirect
14. #11926403C2semidirect
15. C19×#387C2semidirect
82. C2×C4×D19D4semidirect
220. #387D19semidirect
271. C19#2630semidirect

Maximal subgroups

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

subgroupindex
C2×#105973402
C2×C4×D762
#119264782
#119264732
#119264682
#119264662
#119264622
#119264612
#119264542
#119264352
#119264222
#119264152
#119264032
C19×#3872
#263019