Finite Group Databasebeta

← #37576077

Subgroups — #37576077

Order 24448.

666 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259303C211yesmaximal, characteristic, complemented
2C2×#20259303C211yesmaximal, characteristic, complemented
3C2×D4×Dic191C211yesmaximal, characteristic, complemented
4#27132596C211yesmaximal, characteristic, complemented
5#27132591C211yesmaximal, characteristic, complemented
6#27132586C211yesmaximal, characteristic, complemented
7#27132577C211yesmaximal, characteristic, complemented
8#27132558C211yesmaximal, characteristic, complemented
9#27132557C211yesmaximal, characteristic, complemented
10#27132543C211yesmaximal, characteristic, complemented
11#27132543C211yesmaximal, characteristic, complemented
12#27132536C211yesmaximal, characteristic, complemented
13#27132521C211yesmaximal, characteristic, complemented
14C2×C191⋊#95C211yesmaximal, characteristic, complemented
15C2×#121×C191C211yesmaximal, characteristic
16C23×Dic191C2211yescharacteristic
17C23×Dic191C2211yescharacteristic
18C23×Dic191C2211yescharacteristic
19#20259303—24no—
20#20259303—24no—
21D4×Dic191—24no—
22C2×C4⋊Dic191C2211yescharacteristic
23C2×Dic191⋊C4C2211yescharacteristic
24C2×Dic191⋊C4C2211yescharacteristic
25C2×Dic191⋊C4C2211yescharacteristic
26C2×Dic191⋊C4C2211yescharacteristic
27C2×Dic191⋊C4C2211yescharacteristic
28C2×Dic191⋊C4C2211yescharacteristic
29C2×C22⋊Dic191C2211yescharacteristic
30C2×C22⋊Dic191C2211yescharacteristic
31C2×C22⋊Dic191C2211yescharacteristic
32C2×C22⋊Dic191C2211yescharacteristic
33C2×C22⋊Dic191C2211yescharacteristic
34C2×C22⋊Dic191C2211yescharacteristic
35C2×C22⋊Dic191C2211yescharacteristic
36C2×C22⋊Dic191C2211yescharacteristic
37C2×C22⋊Dic191C2211yescharacteristic
38C2×C4×Dic191C2211yescharacteristic
39C191⋊#95C2211yescharacteristic
40C191⋊#95C2211yescharacteristic
41C191⋊#95C2211yescharacteristic
42C191⋊#95C2211yescharacteristic
43C191⋊#95C2211yescharacteristic
44C191⋊#95C2211yescharacteristic
45C191⋊#95C2211yescharacteristic
46C191⋊#95C2211yescharacteristic
47C22×D4×C191C2211yescharacteristic
48C22×D4×C191C2211yescharacteristic
49C22×D4×C191C2211yescharacteristic
50C23×C4×C191C2211yescharacteristic
51#121×C191—24no—
52C2×C4⋊C4×C191C2211yescharacteristic
53C2×C22⋊C4×C191C2211yescharacteristic
54C2×C22⋊C4×C191C2211yescharacteristic
55C22×Dic191—22no—
56C22×Dic191—22no—
57C22×Dic191—22no—
58C22×Dic191—22no—
59C22×Dic191—22no—
60C22×Dic191—22no—
61C22×Dic191—22no—
62C22×Dic191—41no—
63C22×Dic191—41no—
64C22×Dic191C2311yescharacteristic
65C22×Dic191C2311yescharacteristic
66C22×Dic191C2311yescharacteristic
67C22×Dic191C2311yescharacteristic
68C22×Dic191C2311yescharacteristic
69C22×Dic191C2311yescharacteristic
70C22×Dic191C2311yescharacteristic
71C22×Dic191C2311yescharacteristic
72C4⋊Dic191—22no—
73Dic191⋊C4—22no—
74Dic191⋊C4—22no—
75Dic191⋊C4—22no—
76Dic191⋊C4—22no—
77Dic191⋊C4—22no—
78Dic191⋊C4—41no—
79C22⋊Dic191—22no—
80C22⋊Dic191—22no—
81C22⋊Dic191—22no—
82C22⋊Dic191—22no—
83C22⋊Dic191—22no—
84C22⋊Dic191—22no—
85C22⋊Dic191—22no—
86C22⋊Dic191—41no—
87C22⋊Dic191D414yescomplemented
88C4×Dic191—22no—
89C24×C191C2311yescharacteristic
90C24×C191C2311yescharacteristic
91C24×C191C2311yescharacteristic
92C2×D4×C191—22no—
93C2×D4×C191—22no—
94C2×D4×C191—22no—
95C2×D4×C191—22no—
96C2×D4×C191—22no—
97C2×D4×C191—22no—
98C2×D4×C191—22no—
99C2×D4×C191—41no—
100C2×D4×C191D414yes—
101C22×C4×C191—22no—
102C22×C4×C191—22no—
103C22×C4×C191—41no—
104C22×C4×C191C2311yescharacteristic
105C22×C4×C191C2311yescharacteristic
106C22×C4×C191C2311yescharacteristic
107C22×C4×C191C2311yescharacteristic
108C4⋊C4×C191—22no—
109C22⋊C4×C191—22no—
110C22⋊C4×C191—22no—
111C2×Dic191—21no—
112C2×Dic191—21no—
113C2×Dic191—21no—
114C2×Dic191—21no—
115C2×Dic191—21no—
116C2×Dic191—21no—
117C2×Dic191—21no—
118C2×Dic191—21no—
119C2×Dic191—21no—
120C2×Dic191—21no—
121C2×Dic191—21no—
122C2×Dic191—21no—
123C2×Dic191—21no—
124C2×Dic191—21no—
125C2×Dic191—21no—
126C2×Dic191—21no—
127C2×Dic191—21no—
128C2×Dic191—21no—
129C2×Dic191—21no—
130C2×Dic191—21no—
131C2×Dic191—21no—
132C2×Dic191—44no—
133C2×Dic191—44no—
134C2×Dic191—44no—
135C2×Dic191C2×D412yes—
136C2×Dic191C2×D412yes—
137C2×Dic191#4112yes—
138C23×C191—21no—
139C23×C191—21no—
140C23×C191—21no—
141C23×C191—21no—
142C23×C191—21no—
143C23×C191—21no—
144C23×C191—21no—
145C23×C191—21no—
146C23×C191—21no—
147C23×C191—21no—
148C23×C191—21no—
149C23×C191—21no—
150C23×C191—21no—
151C23×C191—21no—
152C23×C191—21no—
153C23×C191—21no—
154C23×C191—21no—
155C23×C191C2×D412yes—
156C23×C191C2×D412yes—
157C23×C191C2×D412yes—
158C23×C191#4112yes—
159C23×C191C2411yescharacteristic
160D4×C191—28no—
161D4×C191—44no—
162D4×C191—44no—
163C2×C4×C191—21no—
164C2×C4×C191—21no—
165C2×C4×C191—21no—
166C2×C4×C191—21no—
167C2×C4×C191—21no—
168C2×C4×C191—21no—
169C2×C4×C191—21no—
170C2×C4×C191—21no—
171C2×C4×C191—21no—
172C2×C4×C191—21no—
173C2×C4×C191—44no—
174C2×C4×C191C2×D412yes—
175C2×C4×C191#4112yes—
176C22×C191—22no—
177C22×C191—22no—
178C22×C191—22no—
179C22×C191—22no—
180C22×C191—22no—
181C22×C191—22no—
182C22×C191—22no—
183C22×C191—22no—
184C22×C191—22no—
185C22×C191—41no—
186C22×C191—41no—
187C22×C191—41no—
188C22×C191—41no—
189C22×C191—41no—
190C22×C191—41no—
191C22×C191—41no—
192C22×C191—41no—
193C22×C191—41no—
194C22×C191—41no—
195C22×C191—41no—
196C22×C191#12114yes—
197C22×C191C22×D411yescharacteristic
198C22×C191C22×D411yescharacteristic
199C22×C191C2×#4111yescharacteristic
200C22×C191C2×#4111yescharacteristic
201C22×C191C2×#4111yescharacteristic
202C22×C191H(5,𝔽2)11yescharacteristic
203C22×C1912−1+411yescharacteristic
204C4×C191—22no—
205C4×C191—22no—
206C4×C191—41no—
207C4×C191—41no—
208Dic191—22no—
209Dic191—22no—
210Dic191—22no—
211Dic191—41no—
212Dic191—41no—
213Dic191—41no—
214Dic191—41no—
215Dic191—41no—
216C2×C191—24no—
217C2×C191—42no—
218C2×C191—81no—
219C2×C191C2×#12111yescharacteristic
220C2×C191#52911yescharacteristic
221C2×C191#53911yescharacteristic
222C2×C191#54611yescharacteristic
223C2×C191#54611yescharacteristic
224C2×C191#54711yescharacteristic
225C2×C191#54711yescharacteristic
226C191#242511yescharacteristic, complemented, Sylow
227#2425—1911nomaximal, Sylow
228C2×#123—1911no—
229C2×#123—1911no—
230C2×#121D19111yescharacteristic
231C2×C4×D4—1911no—
232#398—1911no—
233#397—1911no—
234#396—1911no—
235#394—1911no—
236#389—1911no—
237#388—1911no—
238#386—1911no—
239#386—1911no—
240#385—1911no—
241#380—1911no—
242C2×#95—1911no—
243C22×D4C2×D19111yescharacteristic
244C22×D4C2×D19111yescharacteristic
245C22×D4C2×D19111yescharacteristic
246C23×C4—1911no—
247C23×C4—1911no—
248C23×C4—1911no—
249C23×C4C2×D19111yescharacteristic
250#123—3824no—
251#123—3824no—
252#121—24no—
253C4×D4—3824no—
254C2×C4⋊C4—1911no—
255C2×C4⋊C4—1911no—
256C2×C4⋊C4—1911no—
257C2×C4⋊C4—1911no—
258C2×C4⋊C4—1911no—
259C2×C4⋊C4—1911no—
260C2×C4⋊C4—1911no—
261C2×C4⋊C4C2×D19111yescharacteristic
262C2×C22⋊C4—1911no—
263C2×C22⋊C4—1911no—
264C2×C22⋊C4—1911no—
265C2×C22⋊C4—1911no—
266C2×C22⋊C4—1911no—
267C2×C22⋊C4—1911no—
268C2×C22⋊C4—1911no—
269C2×C22⋊C4—1911no—
270C2×C22⋊C4—1911no—
271C2×C22⋊C4C2×D19111yescharacteristic
272C2×C22⋊C4C2×D19111yescharacteristic
273C2×C42—1911no—
274#95—1911no—
275#95—1911no—
276#95—1911no—
277#95—1911no—
278#95—1911no—
279#95—1911no—
280#95—1911no—
281#95—1911no—
282C24C22×D19111yescharacteristic
283C24C22×D19111yescharacteristic
284C24C22×D19111yescharacteristic
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—41no—
293C2×D4C22⋊D19114yes—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—41no—
297C22×C4—3822no—
298C22×C4—3822no—
299C22×C4—3822no—
300C22×C4—3822no—
301C22×C4—3822no—
302C22×C4—3822no—
303C22×C4—3822no—
304C22×C4—1911no—
305C22×C4—1911no—
306C22×C4—1911no—
307C22×C4—1911no—
308C22×C4—1911no—
309C22×C4—1911no—
310C22×C4—1911no—
311C22×C4—1911no—
312C22×C4—7641no—
313C22×C4—7641no—
314C22×C4C22×D19111yescharacteristic
315C22×C4C22×D19111yescharacteristic
316C22×C4C22×D19111yescharacteristic
317C22×C4C22×D19111yescharacteristic
318C4⋊C4—22no—
319C4⋊C4—3822no—
320C4⋊C4—3822no—
321C4⋊C4—3822no—
322C4⋊C4—3822no—
323C4⋊C4—3822no—
324C4⋊C4—3822no—
325C4⋊C4—7641no—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—3822no—
329C22⋊C4—3822no—
330C22⋊C4—3822no—
331C22⋊C4—3822no—
332C22⋊C4—3822no—
333C22⋊C4—3822no—
334C22⋊C4—3822no—
335C22⋊C4—1914no—
336C22⋊C4—7641no—
337C42—3822no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23D4×D19112yes—
356C23C2×C22⋊D19112yes—
357C23C2×C22⋊D19112yes—
358C23#1569028612yes—
359C23C23×D19111yescharacteristic
360D4—28no—
361D4—44no—
362D4—44no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—44no—
374C2×C4—3821no—
375C2×C4—3821no—
376C2×C4—3821no—
377C2×C4—3821no—
378C2×C4—3821no—
379C2×C4—3821no—
380C2×C4—3821no—
381C2×C4—3821no—
382C2×C4—3821no—
383C2×C4—3821no—
384C2×C4—3821no—
385C2×C4—3821no—
386C2×C4—3821no—
387C2×C4—3821no—
388C2×C4—3821no—
389C2×C4—3821no—
390C2×C4—3821no—
391C2×C4—3821no—
392C2×C4—3821no—
393C2×C4—3821no—
394C2×C4—3821no—
395C2×C4—1912no—
396C2×C4—1912no—
397C2×C4—1912no—
398C2×C4—7644no—
399C2×C4—7644no—
400C2×C4—7644no—
401C2×C4C2×C22⋊D19112yes—
402C2×C4#1569028612yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—22no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22#2025929414yes—
424C22C2×D4×D19111yescharacteristic
425C22C22×C22⋊D19111yescharacteristic
426C22#41×D19111yescharacteristic
427C22C2×#1569028611yescharacteristic
428C22C2×#1569028611yescharacteristic
429C22#2025936711yescharacteristic
430C22#2025936911yescharacteristic
431C4—22no—
432C4—22no—
433C4—41no—
434C4—41no—
435C4—3822no—
436C4—3822no—
437C4—3822no—
438C4—7641no—
439C4—7641no—
440C4—7641no—
441C4—7641no—
442C4—7641no—
443C2—24no—
444C2—42no—
445C2—81no—
446C2C2×#2025929411yescharacteristic
447C2#2713319411yescharacteristic
448C2#2713325811yescharacteristic
449C2#2713330211yescharacteristic
450C2#2713330711yescharacteristic
451C2#2713331211yescharacteristic
452C2#2713331311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
Fitting, prime radicalC2×#121×C191C2
hypercenterC2×#121D191
hypocenterC191#2425
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#20259303C2semidirect
2. C2×#20259303C2semidirect
3. C2×D4×Dic191C2semidirect
4. #27132596C2semidirect
5. #27132591C2semidirect
6. #27132586C2semidirect
7. #27132577C2semidirect
8. #27132558C2semidirect
9. #27132557C2semidirect
10. #27132543C2semidirect
11. #27132543C2semidirect
12. #27132536C2semidirect
13. #27132521C2semidirect
14. C2×C191⋊#95C2semidirect
87. C22⋊Dic191D4semidirect
226. C191#2425semidirect

Maximal subgroups

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

subgroupindex
C2×#202593032
C2×D4×Dic1912
#271325962
#271325912
#271325862
#271325772
#271325582
#271325572
#271325432
#271325362
#271325212
C2×C191⋊#952
C2×#121×C1912
#2425191