Finite Group Databasebeta

← #16822832

Subgroups — #16822832

Order 3712.

908 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#90807C211yesmaximal, characteristic, complemented
2C2×#11745258C211yesmaximal, characteristic, complemented
3C2×#11745246C211yesmaximal, characteristic, complemented
4C2×#11745243C211yesmaximal, characteristic, complemented
5#14271078C211yesmaximal, characteristic, complemented
6#14271072C211yesmaximal, characteristic, complemented
7#14271071C211yesmaximal, characteristic, complemented
8#14271067C211yesmaximal, characteristic, complemented
9#14271063C211yesmaximal, characteristic, complemented
10#14271041C211yesmaximal, characteristic, complemented
11#14271040C211yesmaximal, characteristic, complemented
12#14271035C211yesmaximal, characteristic, complemented
13#14271034C211yesmaximal, characteristic, complemented
14#14271021C211yesmaximal, characteristic, complemented
15C29×#394C211yesmaximal, characteristic, complemented
16C22×D4×C29C2211yescharacteristic
17C22×C22⋊D29C2211yescharacteristic
18C22×C22⋊D29C2211yescharacteristic
19C22×C22⋊D29C2211yescharacteristic
20C22×C22⋊D29C2211yescharacteristic
21C23×Dic29C2211yescharacteristic
22C23×Dic29C2211yescharacteristic
23C2×#90807—24no—
24C2×#90807—24no—
25C2×#90807—24no—
26C22×D116C2211yescharacteristic
27C22×C4×D29C2211yescharacteristic
28C22×C4×D29C2211yescharacteristic
29C22×Dic58C2211yescharacteristic
30C2×C4⋊C4×C29C2211yescharacteristic
31C2×C22⋊C4×C29C2211yescharacteristic
32C2×C22⋊C4×C29C2211yescharacteristic
33C2×C22⋊C4×C29C2211yescharacteristic
34C2×C22⋊C4×C29C2211yescharacteristic
35C2×C22⋊Dic29C2211yescharacteristic
36C2×C22⋊Dic29C2211yescharacteristic
37C2×#90781C2211yescharacteristic
38C2×#90781C2211yescharacteristic
39C2×#90781C2211yescharacteristic
40C2×#90781C2211yescharacteristic
41C2×#90781C2211yescharacteristic
42C2×#90781C2211yescharacteristic
43C2×#90779C2211yescharacteristic
44C2×#90779C2211yescharacteristic
45C2×#90779C2211yescharacteristic
46C2×#90779C2211yescharacteristic
47C2×C4×Dic29C2211yescharacteristic
48#11745258—24no—
49#11745246—24no—
50#11745243—24no—
51C29×#95C2211yescharacteristic
52#11745179C2211yescharacteristic
53#11745179C2211yescharacteristic
54#11745179C2211yescharacteristic
55#11745179C2211yescharacteristic
56#11745179C2211yescharacteristic
57C24×C29C2311yescharacteristic
58C24×C29C2311yescharacteristic
59C23×D29C2311yescharacteristic
60C23×D29C2311yescharacteristic
61C2×D4×C29—22no—
62C2×D4×C29—22no—
63C2×D4×C29—22no—
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⋊D29—22no—
75C2×C22⋊D29—22no—
76C2×C22⋊D29—22no—
77C2×C22⋊D29—22no—
78C2×C22⋊D29—22no—
79C2×C22⋊D29—41no—
80C2×C22⋊D29D414yescomplemented
81C22×Dic29—22no—
82C22×Dic29—22no—
83C22×Dic29—22no—
84C22×Dic29—22no—
85C22×Dic29—22no—
86C22×Dic29D414yescomplemented
87C22×Dic29C2311yescharacteristic
88C22×Dic29C2311yescharacteristic
89C22×Dic29C2311yescharacteristic
90C22×Dic29C2311yescharacteristic
91C22×Dic29C2311yescharacteristic
92C22×Dic29C2311yescharacteristic
93#90807—232no—
94C2×D116—22no—
95C2×D116—22no—
96C2×D116—41no—
97C2×C4×D29—22no—
98C2×C4×D29—22no—
99C2×C4×D29—22no—
100C2×C4×D29—22no—
101C2×C4×D29—22no—
102C2×C4×D29—22no—
103C2×Dic58—22no—
104C2×Dic58—22no—
105C2×Dic58D414yescomplemented
106C4⋊C4×C29—22no—
107C22⋊C4×C29—22no—
108C22⋊C4×C29—22no—
109C22⋊C4×C29—41no—
110C22⋊C4×C29—41no—
111C22⋊Dic29—22no—
112C22⋊Dic29—41no—
113#90781—22no—
114#90781—22no—
115#90781—22no—
116#90781—22no—
117#90781—22no—
118#90781—41no—
119#90779—22no—
120#90779—22no—
121#90779—22no—
122#90779—22no—
123C4×Dic29—22no—
124C23×C29—21no—
125C23×C29—21no—
126C23×C29—21no—
127C23×C29—21no—
128C23×C29—21no—
129C23×C29—21no—
130C23×C29—21no—
131C23×C29—21no—
132C23×C29—21no—
133C23×C29—21no—
134C23×C29—21no—
135C23×C29—21no—
136C23×C29C2×D412yes—
137C23×C29C2×D412yes—
138C23×C29C2411yescharacteristic
139C22×D29—21no—
140C22×D29—21no—
141C22×D29—21no—
142C22×D29—21no—
143C22×D29—21no—
144C22×D29—21no—
145C22×D29—21no—
146C22×D29—21no—
147C22×D29—21no—
148C22×D29—21no—
149C22×D29—21no—
150C22×D29—21no—
151C22×D29C2×D412yes—
152C22×D29#4112yescomplemented
153D4×C29—28no—
154C2×C4×C29—21no—
155C2×C4×C29—21no—
156C2×C4×C29—21no—
157C2×C4×C29—21no—
158C2×C4×C29—21no—
159C2×C4×C29—21no—
160C2×C4×C29—21no—
161C2×C4×C29—21no—
162C2×C4×C29—21no—
163C2×C4×C29—21no—
164C2×C4×C29—21no—
165C2×C4×C29—21no—
166C2×C4×C29—21no—
167C2×C4×C29—21no—
168C2×C4×C29C2×D412yes—
169C22⋊D29—28no—
170C22⋊D29—28no—
171C22⋊D29—28no—
172C22⋊D29—44no—
173C2×Dic29—28no—
174C2×Dic29—21no—
175C2×Dic29—21no—
176C2×Dic29—21no—
177C2×Dic29—21no—
178C2×Dic29—21no—
179C2×Dic29—21no—
180C2×Dic29—28no—
181C2×Dic29—21no—
182C2×Dic29—21no—
183C2×Dic29—21no—
184C2×Dic29—21no—
185C2×Dic29—21no—
186C2×Dic29—21no—
187C2×Dic29C2×D412yes—
188C2×Dic29C2×D412yes—
189C2×Dic29C2×D412yes—
190C2×Dic29C2×D412yes—
191C2×Dic29C2×D412yes—
192C2×Dic29#4112yescomplemented
193D116—44no—
194C4×D29—28no—
195C4×D29—44no—
196Dic58—28no—
197#2407—291nomaximal, Sylow
198C22×C29—22no—
199C22×C29—22no—
200C22×C29—22no—
201C22×C29—22no—
202C22×C29—22no—
203C22×C29—22no—
204C22×C29—41no—
205C22×C29—41no—
206C22×C29—41no—
207C22×C29—41no—
208C22×C29—41no—
209C22×C29—41no—
210C22×C29—41no—
211C22×C29—41no—
212C22×C29C22×D411yescharacteristic
213C22×C29C22×D411yescharacteristic
214C22×C29C22×D411yescharacteristic
215C22×C29C2×#4111yescharacteristic
216C22×C29C2×#4111yescharacteristic
217C22×C29H(5,𝔽2)11yescharacteristic
218C22×C292−1+411yescharacteristic
219C2×D29—22no—
220C2×D29—22no—
221C2×D29—22no—
222C2×D29—22no—
223C2×D29—22no—
224C2×D29—22no—
225C2×D29—41no—
226C2×D29—41no—
227C2×D29—41no—
228C2×D29—41no—
229C2×D29—41no—
230C2×D29—41no—
231C2×D29—41no—
232C2×D29—41no—
233C4×C29—22no—
234C4×C29—41no—
235C4×C29—41no—
236C4×C29—41no—
237C4×C29—41no—
238Dic29—22no—
239Dic29—22no—
240Dic29—22no—
241Dic29—41no—
242Dic29—41no—
243Dic29#12014yes—
244C22×#41—291no—
245C2×C22⋊Q8—291no—
246C2×#121—291no—
247C2×C4×D4—291no—
248#394—291no—
249#394D2911yescharacteristic, complemented
250#392—291no—
251#392—291no—
252#391—291no—
253#390—291no—
254#386—291no—
255#386—291no—
256#385—291no—
257#385—291no—
258#380—291no—
259C2×C29—42no—
260C2×C29—42no—
261C2×C29C2×#12011yescharacteristic
262C2×C29#52511yescharacteristic
263C2×C29#53711yescharacteristic
264C2×C29#54611yescharacteristic
265C2×C29#54711yescharacteristic
266C2×C29#54811yescharacteristic
267C2×C29#55011yescharacteristic
268D29—42no—
269D29—42no—
270C2×#41—584no—
271C2×#41—584no—
272C2×#41—584no—
273C22×Q8—291no—
274C22×D4—291no—
275C22×D4—291no—
276C22×D4—291no—
277C22×D4—291no—
278C22×D4—291no—
279C22×D4C2×D2911yescharacteristic
280C23×C4—291no—
281C23×C4—291no—
282C23×C4—291no—
283C23×C4—291no—
284C22⋊Q8—584no—
285#121—584no—
286C4×D4—584no—
287C2×C4⋊C4—291no—
288C2×C4⋊C4—291no—
289C2×C4⋊C4—291no—
290C2×C4⋊C4—291no—
291C2×C4⋊C4C2×D2911yescharacteristic
292C2×C22⋊C4—291no—
293C2×C22⋊C4—291no—
294C2×C22⋊C4—291no—
295C2×C22⋊C4—291no—
296C2×C22⋊C4—291no—
297C2×C22⋊C4—291no—
298C2×C22⋊C4—291no—
299C2×C22⋊C4—291no—
300C2×C22⋊C4C2×D2911yescharacteristic
301C2×C22⋊C4C2×D2911yescharacteristic
302C2×C22⋊C4C2×D2911yescharacteristic
303C2×C22⋊C4C2×D2911yescharacteristic
304C2×C42—291no—
305#95—291no—
306#95—291no—
307#95—291no—
308#95—291no—
309#95—291no—
310#95C2×D2911yescharacteristic
311C29#240711yescharacteristic, complemented, Sylow
312C24—291no—
313C24—291no—
314C24C22×D2911yescharacteristic
315C24C22×D2911yescharacteristic
316#41—5832no—
317C2×Q8—294no—
318C2×Q8—582no—
319C2×Q8—582no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—294no—
324C2×D4—582no—
325C2×D4—582no—
326C2×D4—582no—
327C2×D4—582no—
328C2×D4—582no—
329C2×D4—582no—
330C2×D4—582no—
331C2×D4—582no—
332C2×D4—582no—
333C2×D4—582no—
334C2×D4—582no—
335C2×D4—582no—
336C2×D4—1161no—
337C2×D4—1161no—
338C22×C4—291no—
339C22×C4—294no—
340C22×C4—291no—
341C22×C4—291no—
342C22×C4—291no—
343C22×C4—291no—
344C22×C4—291no—
345C22×C4—582no—
346C22×C4—582no—
347C22×C4—582no—
348C22×C4—582no—
349C22×C4—582no—
350C22×C4—582no—
351C22×C4—582no—
352C22×C4—582no—
353C22×C4—582no—
354C22×C4—582no—
355C22×C4—582no—
356C22×C4C22×D2911yescharacteristic
357C22×C4C22×D2911yescharacteristic
358C22×C4C22×D2911yescharacteristic
359C22×C4C22×D2911yescharacteristic
360C22×C4C22×D2911yescharacteristic
361C4⋊C4—22no—
362C4⋊C4—582no—
363C4⋊C4—582no—
364C4⋊C4—582no—
365C4⋊C4—582no—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—582no—
371C22⋊C4—582no—
372C22⋊C4—582no—
373C22⋊C4—582no—
374C22⋊C4—582no—
375C22⋊C4—582no—
376C22⋊C4—1161no—
377C22⋊C4—1161no—
378C42—582no—
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—292no—
392C23—292no—
393C23—581no—
394C23—581no—
395C23—581no—
396C23—581no—
397C23—581no—
398C23—581no—
399C23—581no—
400C23—581no—
401C23—581no—
402C23—581no—
403C23—581no—
404C23—581no—
405C23D4×D2912yes—
406C23D4×D2912yes—
407C23C23×D2911yescharacteristic
408Q8—588no—
409D4—28no—
410D4—588no—
411D4—588no—
412D4—588no—
413D4—1164no—
414D4—1164no—
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—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—292no—
430C2×C4—292no—
431C2×C4—292no—
432C2×C4—292no—
433C2×C4—292no—
434C2×C4—292no—
435C2×C4—588no—
436C2×C4—588no—
437C2×C4—588no—
438C2×C4—581no—
439C2×C4—581no—
440C2×C4—581no—
441C2×C4—581no—
442C2×C4—581no—
443C2×C4—581no—
444C2×C4—581no—
445C2×C4—581no—
446C2×C4—581no—
447C2×C4—581no—
448C2×C4—581no—
449C2×C4—581no—
450C2×C4—1164no—
451C2×C4D4×D2912yes—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—582no—
467C22—582no—
468C22—582no—
469C22—582no—
470C22—582no—
471C22—582no—
472C22—1161no—
473C22—1161no—
474C22—1161no—
475C22—1161no—
476C22—1161no—
477C22—1161no—
478C22—1161no—
479C22—1161no—
480C22C2×D4×D2911yescharacteristic
481C22C2×D4×D2911yescharacteristic
482C22C2×D4×D2911yescharacteristic
483C22#1174535911yescharacteristic
484C22#41×D2911yescharacteristic
485C22#41×D2911yescharacteristic
486C22#1174536511yescharacteristic
487C4—22no—
488C4—41no—
489C4—41no—
490C4—41no—
491C4—41no—
492C4—294no—
493C4—582no—
494C4—582no—
495C4—582no—
496C4—1161no—
497C4—1161no—
498C2—42no—
499C2—42no—
500C2—1162no—
501C2—1162no—
502C2#120×D2911yescharacteristic
503C2#1427167111yescharacteristic
504C2#1427174011yescharacteristic
505C2#1427180211yescharacteristic
506C2#1427181111yescharacteristic
507C2#1427182111yescharacteristic
508C2#1427183111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutator, socle, cosocleC23×C29C24
FittingC29×#394C2
hypercenter#394D29
hypocenterC29#2407
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C22×#90807C2semidirect
2. C2×#11745258C2semidirect
3. C2×#11745246C2semidirect
4. C2×#11745243C2semidirect
5. #14271078C2semidirect
6. #14271072C2semidirect
7. #14271071C2semidirect
8. #14271067C2semidirect
9. #14271063C2semidirect
10. #14271041C2semidirect
11. #14271040C2semidirect
12. #14271035C2semidirect
13. #14271034C2semidirect
14. #14271021C2semidirect
15. C29×#394C2semidirect
80. C2×C22⋊D29D4semidirect
86. C22×Dic29D4semidirect
105. C2×Dic58D4semidirect
152. C22×D29#41semidirect
192. C2×Dic29#41semidirect
249. #394D29semidirect
311. C29#2407semidirect

Maximal subgroups

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

subgroupindex
C22×#908072
C2×#117452582
C2×#117452462
C2×#117452432
#142710782
#142710722
#142710712
#142710672
#142710632
#142710412
#142710402
#142710352
#142710342
#142710212
C29×#3942
#240729