Finite Group Databasebeta

← #37575957

Subgroups — #37575957

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×#20259294C211yesmaximal, characteristic, complemented
2C2×#20259294C211yesmaximal, characteristic, complemented
3C2×#20259294C211yesmaximal, characteristic, complemented
4C2×D4×Dic191C211yesmaximal, characteristic, complemented
5C22×Dic191⋊C4C211yesmaximal, characteristic, complemented
6#27132586C211yesmaximal, characteristic, complemented
7#27132585C211yesmaximal, characteristic, complemented
8#27132578C211yesmaximal, characteristic, complemented
9#27132577C211yesmaximal, characteristic, complemented
10#27132563C211yesmaximal, characteristic, complemented
11#27132558C211yesmaximal, characteristic, complemented
12#27132543C211yesmaximal, characteristic, complemented
13#27132542C211yesmaximal, characteristic, complemented
14#27132521C211yesmaximal, characteristic, complemented
15C2×#121×C191C211yesmaximal, characteristic, complemented
16C22×C22⋊D191C2211yescharacteristic
17C22×C22⋊D191C2211yescharacteristic
18C22×C22⋊D191C2211yescharacteristic
19C23×Dic191C2211yescharacteristic
20C23×Dic191C2211yescharacteristic
21C23×Dic191C2211yescharacteristic
22#20259294—24no—
23#20259294—24no—
24#20259294—24no—
25D4×Dic191—24no—
26C2×C4⋊Dic191C2211yescharacteristic
27C2×Dic191⋊C4—24no—
28C2×Dic191⋊C4C2211yescharacteristic
29C2×Dic191⋊C4C2211yescharacteristic
30C2×Dic191⋊C4C2211yescharacteristic
31C2×Dic191⋊C4C2211yescharacteristic
32C2×Dic191⋊C4C2211yescharacteristic
33C2×Dic191⋊C4C2211yescharacteristic
34C2×C22⋊Dic191C2211yescharacteristic
35C2×C22⋊Dic191C2211yescharacteristic
36C2×C22⋊Dic191C2211yescharacteristic
37C2×C22⋊Dic191C2211yescharacteristic
38C2×C22⋊Dic191C2211yescharacteristic
39C2×C22⋊Dic191C2211yescharacteristic
40C2×(C2×D191)⋊C4C2211yescharacteristic
41C2×(C2×D191)⋊C4C2211yescharacteristic
42C2×(C2×D191)⋊C4C2211yescharacteristic
43C2×(C2×D191)⋊C4C2211yescharacteristic
44C2×C4×Dic191C2211yescharacteristic
45C191⋊#95C2211yescharacteristic
46C191⋊#95C2211yescharacteristic
47C191⋊#95C2211yescharacteristic
48C191⋊#95C2211yescharacteristic
49C22×D4×C191C2211yescharacteristic
50C22×D4×C191C2211yescharacteristic
51C22×D4×C191C2211yescharacteristic
52C23×C4×C191C2211yescharacteristic
53#121×C191—24no—
54C2×C4⋊C4×C191C2211yescharacteristic
55C2×C22⋊C4×C191C2211yescharacteristic
56C2×C22⋊C4×C191C2211yescharacteristic
57C23×D191C2311yescharacteristic
58C2×C22⋊D191—22no—
59C2×C22⋊D191—22no—
60C2×C22⋊D191—22no—
61C2×C22⋊D191—22no—
62C2×C22⋊D191—22no—
63C2×C22⋊D191—22no—
64C2×C22⋊D191—22no—
65C2×C22⋊D191—22no—
66C2×C22⋊D191—41no—
67C22×Dic191—22no—
68C22×Dic191—22no—
69C22×Dic191—22no—
70C22×Dic191—22no—
71C22×Dic191—22no—
72C22×Dic191—22no—
73C22×Dic191—22no—
74C22×Dic191—41no—
75C22×Dic191D414yescomplemented
76C22×Dic191C2311yescharacteristic
77C22×Dic191C2311yescharacteristic
78C22×Dic191C2311yescharacteristic
79C22×Dic191C2311yescharacteristic
80C22×Dic191C2311yescharacteristic
81C22×Dic191C2311yescharacteristic
82C22×Dic191C2311yescharacteristic
83C4⋊Dic191—22no—
84Dic191⋊C4—22no—
85Dic191⋊C4—22no—
86Dic191⋊C4—22no—
87Dic191⋊C4—22no—
88Dic191⋊C4—22no—
89Dic191⋊C4D414yescomplemented
90C22⋊Dic191—22no—
91C22⋊Dic191—22no—
92C22⋊Dic191—22no—
93C22⋊Dic191—22no—
94C22⋊Dic191—22no—
95C22⋊Dic191—41no—
96(C2×D191)⋊C4—22no—
97(C2×D191)⋊C4—22no—
98(C2×D191)⋊C4—22no—
99(C2×D191)⋊C4—41no—
100C4×Dic191—22no—
101C24×C191C2311yescharacteristic
102C24×C191C2311yescharacteristic
103C24×C191C2311yescharacteristic
104C2×D4×C191—22no—
105C2×D4×C191—22no—
106C2×D4×C191—22no—
107C2×D4×C191—22no—
108C2×D4×C191—22no—
109C2×D4×C191—22no—
110C2×D4×C191—22no—
111C2×D4×C191—41no—
112C2×D4×C191D414yescomplemented
113C22×C4×C191—22no—
114C22×C4×C191—22no—
115C22×C4×C191—41no—
116C22×C4×C191C2311yescharacteristic
117C22×C4×C191C2311yescharacteristic
118C22×C4×C191C2311yescharacteristic
119C22×C4×C191C2311yescharacteristic
120C4⋊C4×C191—22no—
121C22⋊C4×C191—22no—
122C22⋊C4×C191—22no—
123C22×D191—21no—
124C22×D191—21no—
125C22×D191—21no—
126C22×D191—21no—
127C22×D191—21no—
128C22×D191—21no—
129C22×D191—21no—
130C22⋊D191—44no—
131C22⋊D191—44no—
132C22⋊D191—44no—
133C2×Dic191—21no—
134C2×Dic191—21no—
135C2×Dic191—21no—
136C2×Dic191—21no—
137C2×Dic191—28no—
138C2×Dic191—21no—
139C2×Dic191—21no—
140C2×Dic191—21no—
141C2×Dic191—21no—
142C2×Dic191—21no—
143C2×Dic191—21no—
144C2×Dic191—21no—
145C2×Dic191—21no—
146C2×Dic191—21no—
147C2×Dic191—21no—
148C2×Dic191—21no—
149C2×Dic191—21no—
150C2×Dic191—44no—
151C2×Dic191—44no—
152C2×Dic191C2×D412yes—
153C2×Dic191C2×D412yes—
154C2×Dic191C2×D412yes—
155C2×Dic191C2×D412yes—
156C2×Dic191#4112yes—
157C23×C191—21no—
158C23×C191—21no—
159C23×C191—21no—
160C23×C191—21no—
161C23×C191—21no—
162C23×C191—21no—
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×C191C2×D412yes—
177C23×C191#4112yes—
178C23×C191C2411yescharacteristic
179D4×C191—28no—
180D4×C191—44no—
181D4×C191—44no—
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—44no—
193C2×C4×C191C2×D412yes—
194C2×C4×C191C2×D412yes—
195C22×C191—22no—
196C22×C191—22no—
197C22×C191—22no—
198C22×C191—22no—
199C22×C191—22no—
200C22×C191—22no—
201C22×C191—22no—
202C22×C191—22no—
203C22×C191—22no—
204C22×C191—41no—
205C22×C191—41no—
206C22×C191—41no—
207C22×C191—41no—
208C22×C191—41no—
209C22×C191—41no—
210C22×C191—41no—
211C22×C191—41no—
212C22×C191—41no—
213C22×C191—41no—
214C22×C191—41no—
215C22×C191#12114yescomplemented
216C22×C191C22×D411yescharacteristic
217C22×C191C22×D411yescharacteristic
218C22×C191C22×D411yescharacteristic
219C22×C191C2×#4111yescharacteristic
220C22×C191C2×#4111yescharacteristic
221C22×C191H(5,𝔽2)11yescharacteristic
222C22×C1912−1+411yescharacteristic
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—22no—
232C4×C191—41no—
233C4×C191—41no—
234Dic191—22no—
235Dic191—22no—
236Dic191—41no—
237Dic191—41no—
238Dic191—41no—
239Dic191—41no—
240Dic191#12114yescomplemented
241C2×C191—24no—
242C2×C191—42no—
243C2×C191—81no—
244C2×C191C2×#12111yescharacteristic
245C2×C191C2×#12111yescharacteristic
246C2×C191#53711yescharacteristic
247C2×C191D4211yescharacteristic
248C2×C191#54711yescharacteristic
249C2×C191#54811yescharacteristic
250C2×C191#55311yescharacteristic
251D191—81no—
252C191#241611yescharacteristic, complemented, Sylow
253#2416—1911nomaximal, Sylow
254C2×#121—1911no—
255C2×#121—1911no—
256C2×#121—1911no—
257C2×#121D19111yescharacteristic, complemented
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#386—1911no—
268#380—1911no—
269C22×D4—1911no—
270C22×D4—1911no—
271C22×D4—1911no—
272C22×D4C2×D19111yescharacteristic
273C22×D4C2×D19111yescharacteristic
274C22×D4C2×D19111yescharacteristic
275C23×C4—1911no—
276C23×C4—1911no—
277C23×C4—1911no—
278C23×C4C2×D19111yescharacteristic
279#121—24no—
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⋊C4C2×D19111yescharacteristic
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⋊C4—1911no—
303C2×C22⋊C4C2×D19111yescharacteristic
304C2×C22⋊C4C2×D19111yescharacteristic
305C2×C42—1911no—
306#95—1911no—
307#95—1911no—
308#95—1911no—
309#95—1911no—
310C24—1911no—
311C24C22×D19111yescharacteristic
312C24C22×D19111yescharacteristic
313C24C22×D19111yescharacteristic
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—41no—
322C2×D4—3822no—
323C2×D4—3822no—
324C2×D4—3822no—
325C2×D4—3822no—
326C2×D4—3822no—
327C2×D4—3822no—
328C2×D4—3822no—
329C2×D4—3822no—
330C2×D4—7641no—
331C2×D4C22⋊D19114yescomplemented
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—1911no—
345C22×C4—1911no—
346C22×C4—1914no—
347C22×C4—1911no—
348C22×C4—1911no—
349C22×C4—1911no—
350C22×C4—7641no—
351C22×C4C22×D19111yescharacteristic
352C22×C4C22×D19111yescharacteristic
353C22×C4C22×D19111yescharacteristic
354C22×C4C22×D19111yescharacteristic
355C4⋊C4—22no—
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—3822no—
366C22⋊C4—3822no—
367C22⋊C4—3822no—
368C22⋊C4—3822no—
369C22⋊C4—3822no—
370C22⋊C4—3822no—
371C22⋊C4—3822no—
372C22⋊C4—3822no—
373C22⋊C4—7641no—
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—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—3821no—
394C23—3821no—
395C23—3821no—
396C23—3821no—
397C23—3821no—
398C23—3821no—
399C23—3821no—
400C23D4×D19112yes—
401C23C2×C22⋊D19112yes—
402C23C2×C22⋊D19112yes—
403C23#1569028612yes—
404C23C23×D19111yescharacteristic
405D4—28no—
406D4—44no—
407D4—44no—
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—44no—
422C2×C4—3821no—
423C2×C4—3821no—
424C2×C4—3821no—
425C2×C4—3821no—
426C2×C4—3828no—
427C2×C4—3821no—
428C2×C4—3821no—
429C2×C4—3821no—
430C2×C4—3821no—
431C2×C4—3821no—
432C2×C4—3821no—
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—7644no—
445C2×C4—7644no—
446C2×C4D4×D19112yes—
447C2×C4C2×C22⋊D19112yes—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—7641no—
469C22—7641no—
470C22—7641no—
471C22—7641no—
472C22—7641no—
473C22—7641no—
474C22—7641no—
475C22#2025929414yescomplemented
476C22C2×D4×D19111yescharacteristic
477C22C2×D4×D19111yescharacteristic
478C22C22×C22⋊D19111yescharacteristic
479C22#41×D19111yescharacteristic
480C22C2×#1569028611yescharacteristic
481C22#2025936711yescharacteristic
482C22#2025936911yescharacteristic
483C4—22no—
484C4—22no—
485C4—41no—
486C4—41no—
487C4—3822no—
488C4—3822no—
489C4—1914no—
490C4—7641no—
491C4—7641no—
492C4—7641no—
493C4—7641no—
494C2—24no—
495C2—42no—
496C2—81no—
497C2—15281no—
498C2#121×D19111yescharacteristic
499C2C2×#2025929411yescharacteristic
500C2#2713324011yescharacteristic
501C2D4×C22⋊D19111yescharacteristic
502C2#2713331211yescharacteristic
503C2#2713331911yescharacteristic
504C2#2713335611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
FittingC2×#121×C191C2
hypercenterC2×#121D191
hypocenterC191#2416
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#20259294C2semidirect
2. C2×#20259294C2semidirect
3. C2×#20259294C2semidirect
4. C2×D4×Dic191C2semidirect
5. C22×Dic191⋊C4C2semidirect
6. #27132586C2semidirect
7. #27132585C2semidirect
8. #27132578C2semidirect
9. #27132577C2semidirect
10. #27132563C2semidirect
11. #27132558C2semidirect
12. #27132543C2semidirect
13. #27132542C2semidirect
14. #27132521C2semidirect
15. C2×#121×C191C2semidirect
75. C22×Dic191D4semidirect
89. Dic191⋊C4D4semidirect
112. C2×D4×C191D4semidirect
215. C22×C191#121semidirect
240. Dic191#121semidirect
252. C191#2416semidirect
257. C2×#121D191semidirect
331. C2×D4C22⋊D191semidirect
475. C22#20259294semidirect

Maximal subgroups

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

subgroupindex
C2×#202592942
C2×D4×Dic1912
C22×Dic191⋊C42
#271325862
#271325852
#271325782
#271325772
#271325632
#271325582
#271325432
#271325422
#271325212
C2×#121×C1912
#2416191