Finite Group Databasebeta

← #37575959

Subgroups — #37575959

Order 24448.

788 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259296C211yesmaximal, characteristic, complemented
2C2×#20259295C211yesmaximal, characteristic, complemented
3C2×#20259294C211yesmaximal, characteristic, complemented
4C2×#20259294C211yesmaximal, characteristic, complemented
5C2×(C22⋊D191)⋊C4C211yesmaximal, characteristic, complemented
6C22×Dic191⋊C4C211yesmaximal, characteristic, complemented
7#27132587C211yesmaximal, characteristic, complemented
8#27132586C211yesmaximal, characteristic, complemented
9#27132581C211yesmaximal, characteristic, complemented
10#27132578C211yesmaximal, characteristic, complemented
11#27132563C211yesmaximal, characteristic, complemented
12#27132560C211yesmaximal, characteristic, complemented
13#27132540C211yesmaximal, characteristic, complemented
14#27132522C211yesmaximal, characteristic, complemented
15#386×C191C211yesmaximal, characteristic, complemented
16C22×D764C2211yescharacteristic
17C22×C22⋊D191C2211yescharacteristic
18C22×C22⋊D191C2211yescharacteristic
19C22×C22⋊D191C2211yescharacteristic
20C22×C22⋊D191C2211yescharacteristic
21C23×Dic191C2211yescharacteristic
22C23×Dic191C2211yescharacteristic
23C22×C4×D191C2211yescharacteristic
24#20259296—24no—
25#20259295—24no—
26#20259294—24no—
27#20259294—24no—
28(C22⋊D191)⋊C4—24no—
29C2×C4⋊Dic191C2211yescharacteristic
30C2×Dic191⋊C4—24no—
31C2×Dic191⋊C4C2211yescharacteristic
32C2×Dic191⋊C4C2211yescharacteristic
33C2×Dic191⋊C4C2211yescharacteristic
34C2×Dic191⋊C4C2211yescharacteristic
35C2×Dic191⋊C4C2211yescharacteristic
36C2×Dic191⋊C4C2211yescharacteristic
37C2×Dic191⋊C4C2211yescharacteristic
38C2×C22⋊Dic191C2211yescharacteristic
39C2×C22⋊Dic191C2211yescharacteristic
40C2×(C2×D191)⋊C4C2211yescharacteristic
41C2×(C2×D191)⋊C4C2211yescharacteristic
42C2×(C2×D191)⋊C4C2211yescharacteristic
43C2×(C2×D191)⋊C4C2211yescharacteristic
44C2×(C2×D191)⋊C4C2211yescharacteristic
45C2×(C2×D191)⋊C4C2211yescharacteristic
46C2×(C2×D191)⋊C4C2211yescharacteristic
47C2×C4×Dic191C2211yescharacteristic
48C191⋊#95C2211yescharacteristic
49C191⋊#95C2211yescharacteristic
50C22×D4×C191C2211yescharacteristic
51C23×C4×C191C2211yescharacteristic
52C2×C22⋊C4×C191C2211yescharacteristic
53C2×C22⋊C4×C191C2211yescharacteristic
54C2×C22⋊C4×C191C2211yescharacteristic
55#95×C191C2211yescharacteristic
56#95×C191C2211yescharacteristic
57C23×D191C2311yescharacteristic
58C23×D191C2311yescharacteristic
59C2×D764—22no—
60C2×D764—22no—
61C2×D764—41no—
62C2×C22⋊D191—22no—
63C2×C22⋊D191—22no—
64C2×C22⋊D191—22no—
65C2×C22⋊D191—22no—
66C2×C22⋊D191—22no—
67C2×C22⋊D191—22no—
68C2×C22⋊D191—22no—
69C2×C22⋊D191—22no—
70C2×C22⋊D191—22no—
71C2×C22⋊D191—22no—
72C2×C22⋊D191—41no—
73C2×C22⋊D191D414yescomplemented
74C22×Dic191—22no—
75C22×Dic191—22no—
76C22×Dic191—22no—
77C22×Dic191—22no—
78C22×Dic191—41no—
79C22×Dic191D414yescomplemented
80C22×Dic191C2311yescharacteristic
81C22×Dic191C2311yescharacteristic
82C22×Dic191C2311yescharacteristic
83C22×Dic191C2311yescharacteristic
84C22×Dic191C2311yescharacteristic
85C22×Dic191C2311yescharacteristic
86C2×C4×D191—22no—
87C2×C4×D191—22no—
88C2×C4×D191—22no—
89C4⋊Dic191—22no—
90Dic191⋊C4—22no—
91Dic191⋊C4—22no—
92Dic191⋊C4—22no—
93Dic191⋊C4—22no—
94Dic191⋊C4—22no—
95Dic191⋊C4—22no—
96Dic191⋊C4D414yescomplemented
97C22⋊Dic191—22no—
98C22⋊Dic191—22no—
99(C2×D191)⋊C4—22no—
100(C2×D191)⋊C4—22no—
101(C2×D191)⋊C4—22no—
102(C2×D191)⋊C4—22no—
103(C2×D191)⋊C4—22no—
104(C2×D191)⋊C4—22no—
105(C2×D191)⋊C4—41no—
106C4×Dic191—22no—
107C24×C191C2311yescharacteristic
108C24×C191C2311yescharacteristic
109C2×D4×C191—22no—
110C2×D4×C191—22no—
111C2×D4×C191—22no—
112C22×C4×C191—22no—
113C22×C4×C191—22no—
114C22×C4×C191—41no—
115C22×C4×C191C2311yescharacteristic
116C22×C4×C191C2311yescharacteristic
117C22×C4×C191C2311yescharacteristic
118C22×C4×C191C2311yescharacteristic
119C22×C4×C191C2311yescharacteristic
120C22⋊C4×C191—22no—
121C22⋊C4×C191—22no—
122C22⋊C4×C191—41no—
123C22×D191—21no—
124C22×D191—21no—
125C22×D191—21no—
126C22×D191—21no—
127C22×D191—21no—
128C22×D191—21no—
129C22×D191—21no—
130C22×D191—21no—
131C22×D191—21no—
132C22×D191—21no—
133C22×D191—21no—
134C22×D191—21no—
135C22×D191—21no—
136C22×D191C2×D412yes—
137D764—44no—
138C22⋊D191—28no—
139C22⋊D191—44no—
140C22⋊D191—44no—
141C22⋊D191—44no—
142C2×Dic191—21no—
143C2×Dic191—21no—
144C2×Dic191—21no—
145C2×Dic191—21no—
146C2×Dic191—21no—
147C2×Dic191—21no—
148C2×Dic191—28no—
149C2×Dic191—21no—
150C2×Dic191—21no—
151C2×Dic191—21no—
152C2×Dic191—21no—
153C2×Dic191—21no—
154C2×Dic191—21no—
155C2×Dic191—44no—
156C2×Dic191C2×D412yes—
157C2×Dic191C2×D412yes—
158C2×Dic191C2×D412yes—
159C2×Dic191C2×D412yes—
160C2×Dic191C2×D412yes—
161C2×Dic191#4112yes—
162C4×D191—44no—
163C23×C191—21no—
164C23×C191—21no—
165C23×C191—21no—
166C23×C191—21no—
167C23×C191—21no—
168C23×C191—21no—
169C23×C191—21no—
170C23×C191—21no—
171C23×C191—21no—
172C23×C191—21no—
173C23×C191—21no—
174C23×C191C2×D412yes—
175C23×C191C2×D412yes—
176C23×C191#4112yes—
177C23×C191C2411yescharacteristic
178D4×C191—44no—
179C2×C4×C191—21no—
180C2×C4×C191—21no—
181C2×C4×C191—21no—
182C2×C4×C191—21no—
183C2×C4×C191—21no—
184C2×C4×C191—21no—
185C2×C4×C191—21no—
186C2×C4×C191—21no—
187C2×C4×C191—21no—
188C2×C4×C191—21no—
189C2×C4×C191—21no—
190C2×C4×C191—21no—
191C2×C4×C191—21no—
192C2×C4×C191—21no—
193C2×C4×C191—44no—
194C2×C4×C191C2×D412yes—
195C22×C191—22no—
196C22×C191—22no—
197C22×C191—22no—
198C22×C191—22no—
199C22×C191—22no—
200C22×C191—22no—
201C22×C191—41no—
202C22×C191—41no—
203C22×C191—41no—
204C22×C191—41no—
205C22×C191—41no—
206C22×C191—41no—
207C22×C191—41no—
208C22×C191#12114yescomplemented
209C22×C191C22×D411yescharacteristic
210C22×C191C22×D411yescharacteristic
211C22×C191C22×D411yescharacteristic
212C22×C191C2×#4111yescharacteristic
213C22×C191C2×#4111yescharacteristic
214C22×C191H(5,𝔽2)11yescharacteristic
215C22×C1912−1+411yescharacteristic
216C2×D191—22no—
217C2×D191—22no—
218C2×D191—22no—
219C2×D191—41no—
220C2×D191—41no—
221C2×D191—41no—
222C2×D191—41no—
223C2×D191—41no—
224C2×D191—41no—
225C2×D191—41no—
226C2×D191—41no—
227C2×D191—41no—
228C2×D191—41no—
229C2×D191—41no—
230C4×C191—22no—
231C4×C191—41no—
232C4×C191—41no—
233C4×C191—41no—
234C4×C191—41no—
235Dic191—22no—
236Dic191—22no—
237Dic191—22no—
238Dic191—41no—
239Dic191—41no—
240Dic191#12114yescomplemented
241C2×C191—24no—
242C2×C191—81no—
243C2×C191C2×#12111yescharacteristic
244C2×C191C2×#12111yescharacteristic
245C2×C191#53711yescharacteristic
246C2×C191D4211yescharacteristic
247C2×C191#54711yescharacteristic
248C2×C191#54811yescharacteristic
249C2×C191#55311yescharacteristic
250D191—42no—
251D191—81no—
252C191#241611yescharacteristic, complemented, Sylow
253#2416—1911nomaximal, Sylow
254C2×#121—1911no—
255C2×#121—1911no—
256C2×#121—1911no—
257C2×#121—1911no—
258C2×C4×D4—1911no—
259C22×C4⋊C4—1911no—
260#396—1911no—
261#396—1911no—
262#394—1911no—
263#394—1911no—
264#390—1911no—
265#389—1911no—
266#386—1911no—
267#386D19111yescharacteristic, complemented
268#380—1911no—
269C22×D4—1911no—
270C22×D4—1911no—
271C22×D4—1911no—
272C22×D4—1911no—
273C22×D4—1911no—
274C22×D4C2×D19111yescharacteristic
275C23×C4—1911no—
276C23×C4—1911no—
277C23×C4—1911no—
278C23×C4C2×D19111yescharacteristic
279#121—3824no—
280#121—3824no—
281#121—3824no—
282#121—3824no—
283C4×D4—3824no—
284C2×C4⋊C4—3824no—
285C2×C4⋊C4—1911no—
286C2×C4⋊C4—1911no—
287C2×C4⋊C4—1911no—
288C2×C4⋊C4—1911no—
289C2×C4⋊C4—1911no—
290C2×C4⋊C4—1911no—
291C2×C4⋊C4—1911no—
292C2×C4⋊C4—1911no—
293C2×C22⋊C4—1911no—
294C2×C22⋊C4—1911no—
295C2×C22⋊C4—1911no—
296C2×C22⋊C4—1911no—
297C2×C22⋊C4—1911no—
298C2×C22⋊C4—1911no—
299C2×C22⋊C4—1911no—
300C2×C22⋊C4—1911no—
301C2×C22⋊C4—1911no—
302C2×C22⋊C4C2×D19111yescharacteristic
303C2×C22⋊C4C2×D19111yescharacteristic
304C2×C22⋊C4C2×D19111yescharacteristic
305C2×C42—1911no—
306#95—1911no—
307#95—1911no—
308#95C2×D19111yescharacteristic
309#95C2×D19111yescharacteristic
310C24—1911no—
311C24—1911no—
312C24C22×D19111yescharacteristic
313C24C22×D19111yescharacteristic
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—3822no—
318C2×D4—3822no—
319C2×D4—3822no—
320C2×D4—3822no—
321C2×D4—3822no—
322C2×D4—3822no—
323C2×D4—3822no—
324C2×D4—3822no—
325C2×D4—3822no—
326C2×D4—3822no—
327C2×D4—3822no—
328C2×D4—3822no—
329C2×D4—1914no—
330C2×D4—7641no—
331C2×D4—7641no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—41no—
335C22×C4—3822no—
336C22×C4—3822no—
337C22×C4—3822no—
338C22×C4—3822no—
339C22×C4—3822no—
340C22×C4—3822no—
341C22×C4—3822no—
342C22×C4—1911no—
343C22×C4—1911no—
344C22×C4—1914no—
345C22×C4—1911no—
346C22×C4—1911no—
347C22×C4—1911no—
348C22×C4—1911no—
349C22×C4—7641no—
350C22×C4C22×D19111yescharacteristic
351C22×C4C22×D19111yescharacteristic
352C22×C4C22×D19111yescharacteristic
353C22×C4C22×D19111yescharacteristic
354C22×C4C22×D19111yescharacteristic
355C4⋊C4—3822no—
356C4⋊C4—3822no—
357C4⋊C4—3822no—
358C4⋊C4—3822no—
359C4⋊C4—3822no—
360C4⋊C4—3822no—
361C4⋊C4—3822no—
362C4⋊C4—1914no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—41no—
366C22⋊C4—3822no—
367C22⋊C4—3822no—
368C22⋊C4—3822no—
369C22⋊C4—3822no—
370C22⋊C4—3822no—
371C22⋊C4—3822no—
372C22⋊C4—3822no—
373C22⋊C4—3822no—
374C22⋊C4—7641no—
375C42—3822no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—3821no—
388C23—3821no—
389C23—3821no—
390C23—3821no—
391C23—3821no—
392C23—3821no—
393C23—3821no—
394C23—3821no—
395C23—3821no—
396C23—3821no—
397C23—3821no—
398C23—3821no—
399C23—3821no—
400C23—1912no—
401C23D4×D19112yes—
402C23D4×D19112yes—
403C23#1569028712yes—
404C23C23×D19111yescharacteristic
405D4—44no—
406D4—3828no—
407D4—7644no—
408D4—7644no—
409D4—7644no—
410D4—7644no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—44no—
426C2×C4—3821no—
427C2×C4—3821no—
428C2×C4—3821no—
429C2×C4—3821no—
430C2×C4—3821no—
431C2×C4—3821no—
432C2×C4—3828no—
433C2×C4—3821no—
434C2×C4—3821no—
435C2×C4—3821no—
436C2×C4—3821no—
437C2×C4—3821no—
438C2×C4—3821no—
439C2×C4—1912no—
440C2×C4—1912no—
441C2×C4—1912no—
442C2×C4—1912no—
443C2×C4—1912no—
444C2×C4—1912no—
445C2×C4—7644no—
446C2×C4—7644no—
447C2×C4D4×D19112yes—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—41no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—3822no—
462C22—3822no—
463C22—3822no—
464C22—7641no—
465C22—7641no—
466C22—7641no—
467C22—7641no—
468C22—7641no—
469C22—7641no—
470C22—7641no—
471C22—7641no—
472C22—7641no—
473C22—7641no—
474C22—7641no—
475C22#2025929514yescomplemented
476C22C2×D4×D19111yescharacteristic
477C22C2×D4×D19111yescharacteristic
478C22C2×D4×D19111yescharacteristic
479C22#41×D19111yescharacteristic
480C22C2×#1569028711yescharacteristic
481C22#2025936711yescharacteristic
482C22#2025936911yescharacteristic
483C4—22no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—3822no—
489C4—3822no—
490C4—3822no—
491C4—1914no—
492C4—7641no—
493C4—7641no—
494C2—24no—
495C2—81no—
496C2—15281no—
497C2—7642no—
498C2#121×D19111yescharacteristic
499C2C2×#2025929511yescharacteristic
500C2#2713324011yescharacteristic
501C2#2713329511yescharacteristic
502C2#2713331111yescharacteristic
503C2#2713332211yescharacteristic
504C2#2713336211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
Fitting#386×C191C2
hypercenter#386D191
hypocenterC191#2416
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#20259296C2semidirect
2. C2×#20259295C2semidirect
3. C2×#20259294C2semidirect
4. C2×#20259294C2semidirect
5. C2×(C22⋊D191)⋊C4C2semidirect
6. C22×Dic191⋊C4C2semidirect
7. #27132587C2semidirect
8. #27132586C2semidirect
9. #27132581C2semidirect
10. #27132578C2semidirect
11. #27132563C2semidirect
12. #27132560C2semidirect
13. #27132540C2semidirect
14. #27132522C2semidirect
15. #386×C191C2semidirect
73. C2×C22⋊D191D4semidirect
79. C22×Dic191D4semidirect
96. Dic191⋊C4D4semidirect
208. C22×C191#121semidirect
240. Dic191#121semidirect
252. C191#2416semidirect
267. #386D191semidirect
475. C22#20259295semidirect

Maximal subgroups

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

subgroupindex
C2×#202592962
C2×#202592952
C2×#202592942
C2×(C22⋊D191)⋊C42
C22×Dic191⋊C42
#271325872
#271325862
#271325812
#271325782
#271325632
#271325602
#271325402
#271325222
#386×C1912
#2416191