Finite Group Databasebeta

← #16822825

Subgroups — #16822825

Order 3712.

864 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#90805C211yesmaximal, characteristic
2C2×#11745256C211yesmaximal, characteristic, complemented
3C2×#11745245C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×D29C211yesmaximal, characteristic, complemented
5#14271084C211yesmaximal, characteristic, complemented
6#14271083C211yesmaximal, characteristic, complemented
7#14271079C211yesmaximal, characteristic, complemented
8#14271078C211yesmaximal, characteristic, complemented
9#14271041C211yesmaximal, characteristic, complemented
10#14271039C211yesmaximal, characteristic, complemented
11#14271037C211yesmaximal, characteristic, complemented
12#14271036C211yesmaximal, characteristic, complemented
13#14271034C211yesmaximal, characteristic, complemented
14#14271025C211yesmaximal, characteristic, complemented
15C29×#385C211yesmaximal, characteristic, complemented
16C23×C4×C29C2211yescharacteristic
17C22×C22⋊D29C2211yescharacteristic
18C22×C22⋊D29C2211yescharacteristic
19C2×#90805—24no—
20C2×#90805—24no—
21C2×#90805—24no—
22C22×D116C2211yescharacteristic
23C22×C4×D29C2211yescharacteristic
24C22×C4×D29C2211yescharacteristic
25C22×C4×D29C2211yescharacteristic
26C22×C4×D29C2211yescharacteristic
27C22×Dic58C2211yescharacteristic
28C2×C4⋊C4×C29C2211yescharacteristic
29C2×C4⋊C4×C29C2211yescharacteristic
30C2×C22⋊C4×C29C2211yescharacteristic
31C2×C22⋊C4×C29C2211yescharacteristic
32C2×C22⋊Dic29C2211yescharacteristic
33C2×C22⋊Dic29C2211yescharacteristic
34C2×#90781C2211yescharacteristic
35C2×#90781C2211yescharacteristic
36C2×#90781C2211yescharacteristic
37C2×#90781C2211yescharacteristic
38C2×#90781C2211yescharacteristic
39C2×#90781C2211yescharacteristic
40C2×C4⋊Dic29C2211yescharacteristic
41C2×C4⋊Dic29C2211yescharacteristic
42C2×#90779C2211yescharacteristic
43C2×#90779C2211yescharacteristic
44C2×#90779C2211yescharacteristic
45C2×#90779C2211yescharacteristic
46#11745256—24no—
47C4⋊C4×D29—24no—
48#11745245—24no—
49C29×#95C2211yescharacteristic
50C29×#95C2211yescharacteristic
51#11745179C2211yescharacteristic
52#11745179C2211yescharacteristic
53#11745179C2211yescharacteristic
54#11745179C2211yescharacteristic
55#11745179C2211yescharacteristic
56#11745179C2211yescharacteristic
57C24×C29C2311yescharacteristic
58C23×D29C2311yescharacteristic
59C23×D29C2311yescharacteristic
60C22×C4×C29—22no—
61C22×C4×C29—22no—
62C22×C4×C29—22no—
63C22×C4×C29C2311yescharacteristic
64C22×C4×C29C2311yescharacteristic
65C22×C4×C29C2311yescharacteristic
66C22×C4×C29C2311yescharacteristic
67C22×C4×C29C2311yescharacteristic
68C22×C4×C29C2311yescharacteristic
69C2×C22⋊D29—22no—
70C2×C22⋊D29—22no—
71C2×C22⋊D29—22no—
72C2×C22⋊D29—22no—
73C2×C22⋊D29—22no—
74C2×C22⋊D29D414yes—
75C22×Dic29C2311yescharacteristic
76C22×Dic29C2311yescharacteristic
77C22×Dic29C2311yescharacteristic
78C22×Dic29C2311yescharacteristic
79C22×Dic29C2311yescharacteristic
80C22×Dic29C2311yescharacteristic
81#90805—232no—
82C2×D116—22no—
83C2×D116—22no—
84C2×D116D414yes—
85C2×C4×D29—22no—
86C2×C4×D29—22no—
87C2×C4×D29—22no—
88C2×C4×D29—22no—
89C2×C4×D29—22no—
90C2×C4×D29—22no—
91C2×C4×D29—22no—
92C2×C4×D29—22no—
93C2×C4×D29—22no—
94C2×C4×D29—22no—
95C2×C4×D29—22no—
96C2×C4×D29D414yes—
97C2×Dic58—22no—
98C2×Dic58—22no—
99C2×Dic58—22no—
100C4⋊C4×C29—22no—
101C4⋊C4×C29—22no—
102C22⋊C4×C29—22no—
103C22⋊C4×C29—22no—
104C22⋊Dic29—22no—
105C22⋊Dic29—22no—
106#90781—22no—
107#90781—22no—
108#90781—22no—
109#90781—22no—
110#90781—22no—
111#90781—22no—
112C4⋊Dic29—22no—
113C4⋊Dic29—22no—
114#90779—22no—
115#90779—22no—
116#90779—22no—
117#90779—22no—
118C23×C29—21no—
119C23×C29—21no—
120C23×C29—21no—
121C23×C29—21no—
122C23×C29—21no—
123C23×C29—21no—
124C23×C29C2×D412yes—
125C23×C29C2411yescharacteristic
126C22×D29—21no—
127C22×D29—21no—
128C22×D29—21no—
129C22×D29—21no—
130C22×D29—21no—
131C22×D29—21no—
132C22×D29—21no—
133C22×D29—21no—
134C22×D29—21no—
135C22×D29—21no—
136C22×D29C2×D412yes—
137C22×D29C2×D412yes—
138C22×D29C2×D412yes—
139C22×D29C2×D412yes—
140C2×C4×C29—28no—
141C2×C4×C29—21no—
142C2×C4×C29—21no—
143C2×C4×C29—21no—
144C2×C4×C29—21no—
145C2×C4×C29—21no—
146C2×C4×C29—21no—
147C2×C4×C29—21no—
148C2×C4×C29—21no—
149C2×C4×C29—21no—
150C2×C4×C29—21no—
151C2×C4×C29—21no—
152C2×C4×C29—21no—
153C2×C4×C29—21no—
154C2×C4×C29—21no—
155C2×C4×C29—21no—
156C2×C4×C29C2×D412yes—
157C2×C4×C29C2×D412yes—
158C2×C4×C29#4112yescomplemented
159C22⋊D29—28no—
160C22⋊D29—28no—
161C2×Dic29—21no—
162C2×Dic29—21no—
163C2×Dic29—21no—
164C2×Dic29—21no—
165C2×Dic29—21no—
166C2×Dic29—21no—
167C2×Dic29—21no—
168C2×Dic29—21no—
169C2×Dic29—21no—
170C2×Dic29—21no—
171C2×Dic29—21no—
172C2×Dic29—21no—
173C2×Dic29—21no—
174C2×Dic29—21no—
175C2×Dic29—21no—
176C2×Dic29C2×D412yes—
177C2×Dic29C2×D412yes—
178C2×Dic29#4112yescomplemented
179D116—28no—
180C4×D29—28no—
181C4×D29—28no—
182C4×D29—28no—
183C4×D29—44no—
184Dic58—28no—
185#2406—291nomaximal, Sylow
186C22×C29—22no—
187C22×C29—22no—
188C22×C29—22no—
189C22×C29—41no—
190C22×C29—41no—
191C22×C29—41no—
192C22×C29—41no—
193C22×C29C22×D411yescharacteristic
194C22×C29C22×D411yescharacteristic
195C22×C29C22×D411yescharacteristic
196C22×C29C2×#4111yescharacteristic
197C22×C29C2×#4111yescharacteristic
198C22×C292−1+411yescharacteristic
199C22×C292−1+411yescharacteristic
200C2×D29—22no—
201C2×D29—22no—
202C2×D29—22no—
203C2×D29—22no—
204C2×D29—22no—
205C2×D29—22no—
206C2×D29—22no—
207C2×D29—22no—
208C2×D29—22no—
209C2×D29—41no—
210C2×D29—41no—
211C2×D29—41no—
212C2×D29—41no—
213C2×D29#12014yes—
214C4×C29—22no—
215C4×C29—22no—
216C4×C29—22no—
217C4×C29—41no—
218C4×C29—41no—
219C4×C29—41no—
220Dic29—22no—
221Dic29—22no—
222Dic29—22no—
223Dic29—41no—
224Dic29—41no—
225Dic29—41no—
226C22×#41—291no—
227C2×#123—291no—
228C2×#123—291no—
229C22×C4⋊C4—291no—
230#395—291no—
231#395—291no—
232#394—291no—
233#394—291no—
234#386—291no—
235#386—291no—
236#385—291no—
237#385—291no—
238#385—291no—
239#385D2911yescharacteristic, complemented
240#381—291no—
241C2×C29—42no—
242C2×C29C2×#12011yescharacteristic
243C2×C29#52511yescharacteristic
244C2×C29#53611yescharacteristic
245C2×C29#54711yescharacteristic
246C2×C29#54711yescharacteristic
247C2×C29#54711yescharacteristic
248C2×C29#54711yescharacteristic
249D29—24no—
250D29—42no—
251C2×#41—584no—
252C2×#41—584no—
253C2×#41—584no—
254C22×Q8—291no—
255C22×D4—291no—
256C22×D4—291no—
257C22×D4—291no—
258C23×C4—291no—
259C23×C4—291no—
260C23×C4—291no—
261C23×C4—291no—
262C23×C4C2×D2911yescharacteristic
263#123—584no—
264#123—584no—
265C2×C4⋊C4—291no—
266C2×C4⋊C4—291no—
267C2×C4⋊C4—291no—
268C2×C4⋊C4—291no—
269C2×C4⋊C4—291no—
270C2×C4⋊C4—291no—
271C2×C4⋊C4—584no—
272C2×C4⋊C4C2×D2911yescharacteristic
273C2×C4⋊C4C2×D2911yescharacteristic
274C2×C22⋊C4—291no—
275C2×C22⋊C4—291no—
276C2×C22⋊C4—291no—
277C2×C22⋊C4—291no—
278C2×C22⋊C4—291no—
279C2×C22⋊C4—291no—
280C2×C22⋊C4—291no—
281C2×C22⋊C4—291no—
282C2×C22⋊C4C2×D2911yescharacteristic
283C2×C22⋊C4C2×D2911yescharacteristic
284#95—291no—
285#95—291no—
286#95—291no—
287#95—291no—
288#95—291no—
289#95—291no—
290#95C2×D2911yescharacteristic
291#95C2×D2911yescharacteristic
292C29#240611yescharacteristic, complemented, Sylow
293C24—291no—
294C24—291no—
295C24C22×D2911yescharacteristic
296#41—5832no—
297C2×Q8—582no—
298C2×Q8—582no—
299C2×Q8—582no—
300C2×D4—294no—
301C2×D4—294no—
302C2×D4—582no—
303C2×D4—582no—
304C2×D4—582no—
305C2×D4—582no—
306C2×D4—582no—
307C2×D4—582no—
308C2×D4—582no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—291no—
313C22×C4—291no—
314C22×C4—291no—
315C22×C4—294no—
316C22×C4—291no—
317C22×C4—291no—
318C22×C4—291no—
319C22×C4—582no—
320C22×C4—582no—
321C22×C4—582no—
322C22×C4—582no—
323C22×C4—582no—
324C22×C4—582no—
325C22×C4—582no—
326C22×C4—582no—
327C22×C4—582no—
328C22×C4—582no—
329C22×C4—582no—
330C22×C4C22×D2911yescharacteristic
331C22×C4C22×D2911yescharacteristic
332C22×C4C22×D2911yescharacteristic
333C22×C4C22×D2911yescharacteristic
334C22×C4C22×D2911yescharacteristic
335C22×C4C22×D2911yescharacteristic
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—582no—
339C4⋊C4—582no—
340C4⋊C4—582no—
341C4⋊C4—582no—
342C4⋊C4—582no—
343C4⋊C4—582no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—582no—
347C22⋊C4—582no—
348C22⋊C4—582no—
349C22⋊C4—582no—
350C22⋊C4—582no—
351C22⋊C4—582no—
352C22⋊C4—582no—
353C22⋊C4—582no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—292no—
361C23—292no—
362C23—292no—
363C23—292no—
364C23—581no—
365C23—581no—
366C23—581no—
367C23—581no—
368C23—581no—
369C23—581no—
370C23—581no—
371C23—581no—
372C23—581no—
373C23—581no—
374C23D4×D2912yes—
375C23C23×D2911yescharacteristic
376Q8—588no—
377D4—588no—
378D4—588no—
379D4—588no—
380C2×C4—28no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—292no—
397C2×C4—292no—
398C2×C4—292no—
399C2×C4—588no—
400C2×C4—588no—
401C2×C4—588no—
402C2×C4—581no—
403C2×C4—581no—
404C2×C4—581no—
405C2×C4—581no—
406C2×C4—581no—
407C2×C4—581no—
408C2×C4—581no—
409C2×C4—581no—
410C2×C4—581no—
411C2×C4—581no—
412C2×C4—581no—
413C2×C4—581no—
414C2×C4—581no—
415C2×C4—581no—
416C2×C4—581no—
417C2×C4—1164no—
418C2×C4#9080512yescomplemented
419C2×C4D4×D2912yes—
420C2×C4D4×D2912yes—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—294no—
429C22—582no—
430C22—582no—
431C22—582no—
432C22—582no—
433C22—582no—
434C22—582no—
435C22—582no—
436C22—582no—
437C22—582no—
438C22—1161no—
439C22—1161no—
440C22—1161no—
441C22—1161no—
442C22C2×#9080511yescharacteristic
443C22C2×D4×D2911yescharacteristic
444C22C2×D4×D2911yescharacteristic
445C22C2×D4×D2911yescharacteristic
446C22#1174536211yescharacteristic
447C22#41×D2911yescharacteristic
448C22#1174536511yescharacteristic
449C4—22no—
450C4—22no—
451C4—22no—
452C4—41no—
453C4—41no—
454C4—41no—
455C4—582no—
456C4—582no—
457C4—582no—
458C4—1161no—
459C4—1161no—
460C4—1161no—
461C2—42no—
462C2—584no—
463C2—1162no—
464C2#120×D2911yescharacteristic
465C2#1427167211yescharacteristic
466C2#1427173611yescharacteristic
467C2#1427181111yescharacteristic
468C2#1427181411yescharacteristic
469C2#1427181511yescharacteristic
470C2#1427181811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutator, socle, cosocleC23×C29C24
FittingC29×#385C2
prime radicalC22×#90805C2
hypercenter#385D29
hypocenterC29#2406
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#11745256C2semidirect
3. C2×#11745245C2semidirect
4. C2×C4⋊C4×D29C2semidirect
5. #14271084C2semidirect
6. #14271083C2semidirect
7. #14271079C2semidirect
8. #14271078C2semidirect
9. #14271041C2semidirect
10. #14271039C2semidirect
11. #14271037C2semidirect
12. #14271036C2semidirect
13. #14271034C2semidirect
14. #14271025C2semidirect
15. C29×#385C2semidirect
158. C2×C4×C29#41semidirect
178. C2×Dic29#41semidirect
239. #385D29semidirect
292. C29#2406semidirect
418. C2×C4#90805semidirect

Maximal subgroups

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

subgroupindex
C22×#908052
C2×#117452562
C2×#117452452
C2×C4⋊C4×D292
#142710842
#142710832
#142710792
#142710782
#142710412
#142710392
#142710372
#142710362
#142710342
#142710252
C29×#3852
#240629