Finite Group Databasebeta

← #37570768

Subgroups — #37570768

Order 24448.

736 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C2×D191)⋊C4C211yesmaximal, characteristic
2C22×(C2×D191)⋊C4C211yesmaximal, characteristic
3C22×(C2×D191)⋊C4C211yesmaximal, characteristic
4C2×C191⋊#95C211yesmaximal, characteristic, complemented
5C2×C191⋊#95C211yesmaximal, characteristic, complemented
6C2×C191⋊#95C211yesmaximal, characteristic, complemented
7C2×#95×C191C211yesmaximal, characteristic, complemented
8C24×D191C2211yescharacteristic
9C23×Dic191C2211yescharacteristic
10C23×Dic191C2211yescharacteristic
11C23×Dic191C2211yescharacteristic
12C2×(C2×D191)⋊C4—22no—
13C2×(C2×D191)⋊C4—22no—
14C2×(C2×D191)⋊C4—22no—
15C2×(C2×D191)⋊C4—22no—
16C2×(C2×D191)⋊C4—22no—
17C2×(C2×D191)⋊C4—22no—
18C2×(C2×D191)⋊C4—22no—
19C2×(C2×D191)⋊C4—22no—
20C2×(C2×D191)⋊C4C414yescomplemented
21C191⋊#95—22no—
22C191⋊#95—22no—
23C191⋊#95—22no—
24C23×C4×C191C2211yescharacteristic
25C23×C4×C191C2211yescharacteristic
26C23×C4×C191C2211yescharacteristic
27#95×C191—22no—
28C23×D191—21no—
29C23×D191—21no—
30C23×D191—21no—
31C23×D191—21no—
32C23×D191—21no—
33C23×D191—21no—
34C23×D191—21no—
35C23×D191—21no—
36C23×D191—21no—
37C23×D191—21no—
38C23×D191—21no—
39C23×D191—21no—
40C23×D191C2×C412yes—
41C23×D191D412yes—
42C23×D191D412yes—
43C22×Dic191—21no—
44C22×Dic191—21no—
45C22×Dic191—21no—
46C22×Dic191—21no—
47C22×Dic191—21no—
48C22×Dic191—21no—
49C22×Dic191—21no—
50C22×Dic191—21no—
51C22×Dic191—21no—
52C22×Dic191—21no—
53C22×Dic191—21no—
54C22×Dic191—21no—
55C22×Dic191—21no—
56C22×Dic191—21no—
57C22×Dic191—21no—
58C22×Dic191—21no—
59C22×Dic191—21no—
60C22×Dic191—21no—
61C22×Dic191C2×C412yes—
62C22×Dic191D412yes—
63C22×Dic191D412yes—
64(C2×D191)⋊C4—28no—
65(C2×D191)⋊C4—28no—
66(C2×D191)⋊C4—28no—
67C24×C191C2311yescharacteristic
68C22×C4×C191—21no—
69C22×C4×C191—21no—
70C22×C4×C191—21no—
71C22×C4×C191—21no—
72C22×C4×C191—21no—
73C22×C4×C191—21no—
74C22×C4×C191—21no—
75C22×C4×C191—21no—
76C22×C4×C191—21no—
77C22×C4×C191—21no—
78C22×C4×C191—21no—
79C22×C4×C191—21no—
80C22×C4×C191—21no—
81C22×C4×C191—21no—
82C22×C4×C191—21no—
83C22×C4×C191—21no—
84C22×C4×C191—21no—
85C22×C4×C191—21no—
86C22×C4×C191C2×C412yes—
87C22×C4×C191D412yes—
88C22×C4×C191D412yes—
89C22×D191—22no—
90C22×D191—22no—
91C22×D191—22no—
92C22×D191—22no—
93C22×D191—22no—
94C22×D191—22no—
95C22×D191—22no—
96C22×D191—22no—
97C22×D191—22no—
98C22×D191—22no—
99C22×D191—22no—
100C22×D191—22no—
101C22×D191—22no—
102C22×D191—22no—
103C22×D191—22no—
104C22×D191—22no—
105C22×D191—22no—
106C22×D191—22no—
107C22×D191—41no—
108C22×D191—41no—
109C22×D191—41no—
110C22×D191—41no—
111C22×D191—41no—
112C22×D191—41no—
113C22×D191—41no—
114C22×D191—41no—
115C22×D191—41no—
116C22×D191—41no—
117C22×D191—41no—
118C22×D191—41no—
119C22×D191—41no—
120C22×D191—41no—
121C22×D191—41no—
122C22×D191—41no—
123C22×D191C22⋊C414yes—
124C2×Dic191—22no—
125C2×Dic191—22no—
126C2×Dic191—22no—
127C2×Dic191—22no—
128C2×Dic191—22no—
129C2×Dic191—22no—
130C2×Dic191—22no—
131C2×Dic191—22no—
132C2×Dic191—22no—
133C2×Dic191—41no—
134C2×Dic191—41no—
135C2×Dic191—41no—
136C2×Dic191—41no—
137C2×Dic191—41no—
138C2×Dic191—41no—
139C2×Dic191—41no—
140C2×Dic191—41no—
141C2×Dic191—41no—
142C2×Dic191—41no—
143C2×Dic191—41no—
144C2×Dic191—41no—
145C23×C191C22×C411yescharacteristic
146C23×C191C2×D411yescharacteristic
147C23×C191C2×D411yescharacteristic
148C23×C191C2×D411yescharacteristic
149C23×C191C2×D411yescharacteristic
150C23×C191C2×D411yescharacteristic
151C23×C191C2×D411yescharacteristic
152C23×C191#4111yescharacteristic
153C23×C191#4111yescharacteristic
154C23×C191#4111yescharacteristic
155C23×C191#4111yescharacteristic
156C23×C191#4111yescharacteristic
157C23×C191#4111yescharacteristic
158C23×C191#4111yescharacteristic
159C23×C191#4111yescharacteristic
160C2×C4×C191—22no—
161C2×C4×C191—22no—
162C2×C4×C191—22no—
163C2×C4×C191—22no—
164C2×C4×C191—22no—
165C2×C4×C191—22no—
166C2×C4×C191—22no—
167C2×C4×C191—22no—
168C2×C4×C191—22no—
169C2×C4×C191—41no—
170C2×C4×C191—41no—
171C2×C4×C191—41no—
172C2×C4×C191—41no—
173C2×C4×C191—41no—
174C2×C4×C191—41no—
175C2×C4×C191—41no—
176C2×C4×C191—41no—
177C2×C4×C191—41no—
178C2×C4×C191—41no—
179C2×C4×C191—41no—
180C2×C4×C191—41no—
181C22×C191C2×C22⋊C411yescharacteristic
182C22×C191#11711yescharacteristic
183C22×C191#11711yescharacteristic
184C22×C191C4×D411yescharacteristic
185C22×C191C4×D411yescharacteristic
186C22×C191C4×D411yescharacteristic
187C22×C191C4×D411yescharacteristic
188C22×C191#12011yescharacteristic
189C22×C191#12011yescharacteristic
190C22×C191#12111yescharacteristic
191C22×C191#12111yescharacteristic
192C22×C191#12111yescharacteristic
193C22×C191#12111yescharacteristic
194C22×C191#12111yescharacteristic
195C22×C191#12111yescharacteristic
196C22×C191#12111yescharacteristic
197C22×C191#12111yescharacteristic
198C22×C191#12311yescharacteristic
199C22×C191#12311yescharacteristic
200C22×C191#12311yescharacteristic
201C22×C191#12311yescharacteristic
202C22×C191#12311yescharacteristic
203C22×C191#12311yescharacteristic
204C22×C191#12311yescharacteristic
205C22×C191#12311yescharacteristic
206C22×C191#12311yescharacteristic
207C22×C191#12311yescharacteristic
208C22×C191#12411yescharacteristic
209C22×C191#12411yescharacteristic
210C22×C191#12411yescharacteristic
211C22×C191#12411yescharacteristic
212C22×C191#12611yescharacteristic
213C22×C191#12611yescharacteristic
214C22×C191#12611yescharacteristic
215C22×C191#12611yescharacteristic
216C2×D191—24no—
217C2×D191—24no—
218C2×D191—24no—
219C2×D191—42no—
220C2×D191—42no—
221C2×D191—42no—
222C2×D191—42no—
223C2×D191—42no—
224C2×D191—42no—
225C2×D191—42no—
226C2×D191—42no—
227C2×D191—42no—
228C2×D191—42no—
229C2×D191—42no—
230C2×D191—42no—
231C4×C191—42no—
232C4×C191—42no—
233C4×C191—42no—
234Dic191—42no—
235Dic191—42no—
236Dic191—42no—
237C2×C191#38111yescharacteristic
238C2×C191#38611yescharacteristic
239C2×C191#38611yescharacteristic
240C2×C191#38811yescharacteristic
241C2×C191#38811yescharacteristic
242C2×C191#38811yescharacteristic
243C2×C191#38811yescharacteristic
244C2×C191#39411yescharacteristic
245C2×C191#39411yescharacteristic
246C2×C191#39411yescharacteristic
247C2×C191#39411yescharacteristic
248C2×C191#39711yescharacteristic
249C2×C191#39711yescharacteristic
250C2×C191#39711yescharacteristic
251C2×C191#39711yescharacteristic
252D191—44no—
253C191#144011yescharacteristic, complemented, Sylow
254#1440—1911nomaximal, Sylow
255C22×C22⋊C4—1911no—
256C22×C22⋊C4—1911no—
257C22×C22⋊C4—1911no—
258C2×#95—1911no—
259C2×#95—1911no—
260C2×#95—1911no—
261C2×#95D19111yescharacteristic, complemented
262C25—1911no—
263C23×C4—1911no—
264C23×C4—1911no—
265C23×C4—1911no—
266C23×C4C2×D19111yescharacteristic
267C23×C4C2×D19111yescharacteristic
268C23×C4C2×D19111yescharacteristic
269C2×C22⋊C4—3822no—
270C2×C22⋊C4—3822no—
271C2×C22⋊C4—3822no—
272C2×C22⋊C4—3822no—
273C2×C22⋊C4—3822no—
274C2×C22⋊C4—3822no—
275C2×C22⋊C4—3822no—
276C2×C22⋊C4—3822no—
277C2×C22⋊C4—1914no—
278#95—22no—
279#95—3822no—
280#95—3822no—
281#95—3822no—
282C24—3821no—
283C24—3821no—
284C24—3821no—
285C24—3821no—
286C24—3821no—
287C24—3821no—
288C24—3821no—
289C24—3821no—
290C24—3821no—
291C24—3821no—
292C24—3821no—
293C24—3821no—
294C24—1912no—
295C24—1912no—
296C24—1912no—
297C24C22×D19111yescharacteristic
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—3821no—
317C22×C4—3821no—
318C22×C4—3821no—
319C22×C4—3821no—
320C22×C4—3821no—
321C22×C4—3821no—
322C22×C4—3821no—
323C22×C4—3821no—
324C22×C4—3821no—
325C22×C4—3821no—
326C22×C4—3821no—
327C22×C4—3821no—
328C22×C4—3821no—
329C22×C4—3821no—
330C22×C4—3821no—
331C22×C4—3821no—
332C22×C4—3821no—
333C22×C4—3821no—
334C22×C4—1912no—
335C22×C4—1912no—
336C22×C4—1912no—
337C22×C4C4×D19112yes—
338C22×C4C22⋊D19112yes—
339C22×C4D76412yes—
340C22⋊C4—3828no—
341C22⋊C4—3828no—
342C22⋊C4—3828no—
343C23—3822no—
344C23—3822no—
345C23—3822no—
346C23—3822no—
347C23—3822no—
348C23—3822no—
349C23—3822no—
350C23—3822no—
351C23—3822no—
352C23—3822no—
353C23—3822no—
354C23—3822no—
355C23—3822no—
356C23—3822no—
357C23—3822no—
358C23—3822no—
359C23—3822no—
360C23—3822no—
361C23—1914no—
362C23—7641no—
363C23—7641no—
364C23—7641no—
365C23—7641no—
366C23—7641no—
367C23—7641no—
368C23—7641no—
369C23—7641no—
370C23—7641no—
371C23—7641no—
372C23—7641no—
373C23—7641no—
374C23—7641no—
375C23—7641no—
376C23—7641no—
377C23—7641no—
378C23C2×C4×D19111yescharacteristic
379C23D4×D19111yescharacteristic
380C23D4×D19111yescharacteristic
381C23D4×D19111yescharacteristic
382C23D4×D19111yescharacteristic
383C23C2×C22⋊D19111yescharacteristic
384C23C2×D76411yescharacteristic
385C23#1569028611yescharacteristic
386C23#1569028611yescharacteristic
387C23#1569028711yescharacteristic
388C23#1569028711yescharacteristic
389C23#1569028711yescharacteristic
390C23#1569028711yescharacteristic
391C23#1569028811yescharacteristic
392C23#1569028811yescharacteristic
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—3822no—
415C2×C4—3822no—
416C2×C4—3822no—
417C2×C4—3822no—
418C2×C4—3822no—
419C2×C4—3822no—
420C2×C4—3822no—
421C2×C4—3822no—
422C2×C4—3822no—
423C2×C4—7641no—
424C2×C4—7641no—
425C2×C4—7641no—
426C2×C4—7641no—
427C2×C4—7641no—
428C2×C4—7641no—
429C2×C4—7641no—
430C2×C4—7641no—
431C2×C4—7641no—
432C2×C4—7641no—
433C2×C4—7641no—
434C2×C4—7641no—
435C22—3824no—
436C22—3824no—
437C22—3824no—
438C22—7642no—
439C22—7642no—
440C22—7642no—
441C22—7642no—
442C22—7642no—
443C22—7642no—
444C22—7642no—
445C22—7642no—
446C22—7642no—
447C22—7642no—
448C22—7642no—
449C22—7642no—
450C22C22⋊C4×D19111yescharacteristic
451C22#2025927911yescharacteristic
452C22#2025928011yescharacteristic
453C22(C22⋊D191)⋊C411yescharacteristic
454C22C4×C22⋊D19111yescharacteristic
455C22#2025928411yescharacteristic
456C22C4×D76411yescharacteristic
457C22#2025929011yescharacteristic
458C22#2025929211yescharacteristic
459C22#2025929311yescharacteristic
460C22#2025929411yescharacteristic
461C22#2025929511yescharacteristic
462C22#2025929511yescharacteristic
463C22#2025929511yescharacteristic
464C22#2025929611yescharacteristic
465C22#2025929711yescharacteristic
466C22#2025929711yescharacteristic
467C22#2025930411yescharacteristic
468C22#2025930411yescharacteristic
469C22#2025930411yescharacteristic
470C22#2025930511yescharacteristic
471C22#2025930611yescharacteristic
472C22#2025930711yescharacteristic
473C22#2025930711yescharacteristic
474C22#2025930711yescharacteristic
475C22#2025930711yescharacteristic
476C22#2025930711yescharacteristic
477C22#2025930811yescharacteristic
478C22#2025930811yescharacteristic
479C22#2025931011yescharacteristic
480C22#2025931111yescharacteristic
481C22#2025931611yescharacteristic
482C22#2025931711yescharacteristic
483C22#2025931711yescharacteristic
484C22#2025931711yescharacteristic
485C4—42no—
486C4—42no—
487C4—42no—
488C4—7642no—
489C4—7642no—
490C4—7642no—
491C2—7644no—
492C2#2713252511yescharacteristic
493C2#2713253911yescharacteristic
494C2#2713254111yescharacteristic
495C2#2713255211yescharacteristic
496C2#2713255311yescharacteristic
497C2#2713255411yescharacteristic
498C2#2713255511yescharacteristic
499C2#2713257811yescharacteristic
500C2#2713257911yescharacteristic
501C2#2713258011yescharacteristic
502C2#2713258111yescharacteristic
503C2#2713258911yescharacteristic
504C2#2713259011yescharacteristic
505C2#2713259211yescharacteristic
506C2#2713259211yescharacteristic
subgroupG/H
center, FrattiniC24C22×D191
commutatorC23×C191C22×C4
FittingC2×#95×C191C2
socle, cosocleC24×C191C23
prime radicalC24×D191C22
hypercenterC2×#95D191
hypocenterC191#1440
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
4. C2×C191⋊#95C2semidirect
5. C2×C191⋊#95C2semidirect
6. C2×C191⋊#95C2semidirect
7. C2×#95×C191C2semidirect
20. C2×(C2×D191)⋊C4C4semidirect
253. C191#1440semidirect
261. C2×#95D191semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D191)⋊C42
C2×C191⋊#952
C2×#95×C1912
#1440191