Finite Group Databasebeta

← #16822213

Subgroups — #16822213

Order 3712.

740 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11745302C211yesmaximal, characteristic
2C2×C4×C22⋊D29C211yesmaximal, characteristic, complemented
3C2×#11745243C211yesmaximal, characteristic, complemented
4#14271063C211yesmaximal, characteristic, complemented
5#14271063C211yesmaximal, characteristic, complemented
6#14271043C211yesmaximal, characteristic, complemented
7#14271042C211yesmaximal, characteristic, complemented
8#14271041C211yesmaximal, characteristic, complemented
9#14271041C211yesmaximal, characteristic, complemented
10#14271040C211yesmaximal, characteristic, complemented
11#14271039C211yesmaximal, characteristic, complemented
12#14271039C211yesmaximal, characteristic, complemented
13#14271027C211yesmaximal, characteristic, complemented
14#14271008C211yesmaximal, characteristic, complemented
15C29×#386C211yesmaximal, characteristic, complemented
16C22×D4×C29C2211yescharacteristic
17C23×C4×C29C2211yescharacteristic
18C22×C22⋊D29C2211yescharacteristic
19C22×C22⋊D29C2211yescharacteristic
20C22×C22⋊D29C2211yescharacteristic
21C22×C22⋊D29C2211yescharacteristic
22C23×Dic29C2211yescharacteristic
23C22×D116C2211yescharacteristic
24C22×C4×D29C2211yescharacteristic
25C22×C4×D29C2211yescharacteristic
26C2×C22⋊C4×C29C2211yescharacteristic
27C2×C22⋊C4×C29C2211yescharacteristic
28C2×C22⋊C4×C29C2211yescharacteristic
29C2×C22⋊Dic29C2211yescharacteristic
30C2×C22⋊Dic29C2211yescharacteristic
31C2×C22⋊Dic29C2211yescharacteristic
32#11745302C418yescomplemented
33C4×C22⋊D29—24no—
34C2×#90781C2211yescharacteristic
35C2×#90781C2211yescharacteristic
36C2×#90781C2211yescharacteristic
37C2×#90781C2211yescharacteristic
38C2×#90781C2211yescharacteristic
39C2×#90781C2211yescharacteristic
40C2×#90779C2211yescharacteristic
41C2×#90779C2211yescharacteristic
42C2×C4×Dic29C2211yescharacteristic
43C2×C4×Dic29C2211yescharacteristic
44C2×C4×Dic29C2211yescharacteristic
45#11745243—24no—
46C29×#95C2211yescharacteristic
47C29×#95C2211yescharacteristic
48#11745179C2211yescharacteristic
49#11745179C2211yescharacteristic
50#11745179C2211yescharacteristic
51#11745179C2211yescharacteristic
52#11745179C2211yescharacteristic
53#11745179C2211yescharacteristic
54C24×C29C2311yescharacteristic
55C24×C29C2311yescharacteristic
56C23×D29C2311yescharacteristic
57C23×D29C2311yescharacteristic
58C2×D4×C29—41no—
59C2×D4×C29—41no—
60C2×D4×C29C2×C414yescomplemented
61C22×C4×C29—22no—
62C22×C4×C29—41no—
63C22×C4×C29—41no—
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—41no—
74C2×C22⋊D29—41no—
75C2×C22⋊D29—41no—
76C2×C22⋊D29—41no—
77C2×C22⋊D29C2×C414yescomplemented
78C2×C22⋊D29C2×C414yescomplemented
79C2×C22⋊D29C2×C414yescomplemented
80C2×C22⋊D29C2×C414yescomplemented
81C22×Dic29—22no—
82C22×Dic29—41no—
83C22×Dic29—41no—
84C22×Dic29C2311yescharacteristic
85C22×Dic29C2311yescharacteristic
86C22×Dic29C2311yescharacteristic
87C22×Dic29C2311yescharacteristic
88C22×Dic29C2311yescharacteristic
89C22×Dic29C2311yescharacteristic
90C2×D116—41no—
91C2×D116—41no—
92C2×D116C2×C414yescomplemented
93C2×C4×D29—22no—
94C2×C4×D29—22no—
95C2×C4×D29—41no—
96C2×C4×D29—41no—
97C2×C4×D29—41no—
98C2×C4×D29—41no—
99C22⋊C4×C29—22no—
100C22⋊C4×C29—41no—
101C22⋊C4×C29—41no—
102C22⋊Dic29—22no—
103C22⋊Dic29—41no—
104C22⋊Dic29—41no—
105#90781—22no—
106#90781—22no—
107#90781—41no—
108#90781—41no—
109#90781—41no—
110#90781—41no—
111#90779—22no—
112#90779—22no—
113C4×Dic29—22no—
114C4×Dic29C2×C414yescomplemented
115C4×Dic29D414yescomplemented
116C23×C29—21no—
117C23×C29—21no—
118C23×C29—21no—
119C23×C29—21no—
120C23×C29—21no—
121C23×C29—21no—
122C23×C29—21no—
123C23×C29—21no—
124C23×C29—21no—
125C23×C29—21no—
126C23×C29—21no—
127C23×C29—21no—
128C23×C29C22×C412yes—
129C23×C29C22×C412yes—
130C23×C29C2411yescharacteristic
131C22×D29—21no—
132C22×D29—21no—
133C22×D29—21no—
134C22×D29—21no—
135C22×D29—21no—
136C22×D29—21no—
137C22×D29—21no—
138C22×D29—21no—
139C22×D29—21no—
140C22×D29—21no—
141C22×D29—21no—
142C22×D29—21no—
143C22×D29C22×C412yes—
144C22×D29C22×C412yes—
145D4×C29—44no—
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×C29—21no—
157C2×C4×C29—21no—
158C2×C4×C29—21no—
159C2×C4×C29—44no—
160C2×C4×C29C22×C412yes—
161C2×C4×C29C2×D412yes—
162C22⋊D29—28no—
163C22⋊D29—28no—
164C22⋊D29—44no—
165C22⋊D29—44no—
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×Dic29—21no—
177C2×Dic29—21no—
178C2×Dic29—21no—
179C2×Dic29—44no—
180C2×Dic29C22×C412yes—
181C2×Dic29C22×C412yes—
182C2×Dic29C2×D412yes—
183C2×Dic29C2×D412yes—
184C2×Dic29#4112yes—
185D116—44no—
186C4×D29—44no—
187C4×D29—44no—
188#2328—291nomaximal, Sylow
189C22×C29—22no—
190C22×C29—22no—
191C22×C29—22no—
192C22×C29—22no—
193C22×C29—22no—
194C22×C29—22no—
195C22×C29—41no—
196C22×C29—41no—
197C22×C29—41no—
198C22×C29—41no—
199C22×C29—41no—
200C22×C29—41no—
201C22×C29—41no—
202C22×C29—41no—
203C22×C29C23×C411yescharacteristic
204C22×C29C22×D411yescharacteristic
205C22×C29C2×#4111yescharacteristic
206C22×C29H(5,𝔽2)11yescharacteristic
207C22×C29H(5,𝔽2)11yescharacteristic
208C22×C29H(5,𝔽2)11yescharacteristic
209C22×C29H(5,𝔽2)11yescharacteristic
210C2×D29—22no—
211C2×D29—22no—
212C2×D29—22no—
213C2×D29—22no—
214C2×D29—22no—
215C2×D29—22no—
216C2×D29—41no—
217C2×D29—41no—
218C2×D29—41no—
219C2×D29—41no—
220C2×D29—41no—
221C2×D29—41no—
222C2×D29—41no—
223C2×D29—41no—
224C4×C29—22no—
225C4×C29—22no—
226C4×C29—41no—
227C4×C29—41no—
228C4×C29—41no—
229Dic29—22no—
230Dic29—22no—
231Dic29—41no—
232Dic29—41no—
233Dic29—41no—
234Dic29C4×D414yes—
235C2×#127—291no—
236C2×C4×D4—291no—
237C2×C4×D4—291no—
238#390—291no—
239#390—291no—
240#386—291no—
241#386—291no—
242#386—291no—
243#386—291no—
244#386—291no—
245#386—291no—
246#386—291no—
247#386D2911yescharacteristic, complemented
248#382—291no—
249#376—291no—
250C2×C29—42no—
251C2×C29—42no—
252C2×C29C2×C4×D411yescharacteristic
253C2×C29#51811yescharacteristic
254C2×C29#51811yescharacteristic
255C2×C29#53511yescharacteristic
256C2×C29#53511yescharacteristic
257C2×C29#54011yescharacteristic
258C2×C29#54011yescharacteristic
259D29—42no—
260D29—42no—
261C22×D4—291no—
262C22×D4—291no—
263C22×D4—291no—
264C22×D4—291no—
265C22×D4—291no—
266C22×D4C2×D2911yescharacteristic
267C23×C4—291no—
268C23×C4—291no—
269C23×C4—291no—
270C23×C4C2×D2911yescharacteristic
271#127—298no—
272C4×D4—584no—
273C4×D4—584no—
274C2×C4⋊C4—291no—
275C2×C4⋊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⋊C4—291no—
283C2×C22⋊C4—291no—
284C2×C22⋊C4—291no—
285C2×C22⋊C4C2×D2911yescharacteristic
286C2×C22⋊C4C2×D2911yescharacteristic
287C2×C22⋊C4C2×D2911yescharacteristic
288C2×C42—291no—
289C2×C42—291no—
290C2×C42—291no—
291#95—291no—
292#95—291no—
293#95—291no—
294#95—291no—
295#95—291no—
296#95—291no—
297#95C2×D2911yescharacteristic
298#95C2×D2911yescharacteristic
299C29#232811yescharacteristic, complemented, Sylow
300C24—291no—
301C24—291no—
302C24C22×D2911yescharacteristic
303C24C22×D2911yescharacteristic
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—294no—
307C2×D4—294no—
308C2×D4—294no—
309C2×D4—294no—
310C2×D4—294no—
311C2×D4—582no—
312C2×D4—582no—
313C2×D4—582no—
314C2×D4—582no—
315C2×D4—1161no—
316C2×D4—1161no—
317C2×D4—1161no—
318C2×D4—1161no—
319C2×D4—1161no—
320C2×D4—1161no—
321C2×D4C4×D2914yescomplemented
322C22×C4—22no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—291no—
326C22×C4—291no—
327C22×C4—291no—
328C22×C4—291no—
329C22×C4—291no—
330C22×C4—291no—
331C22×C4—582no—
332C22×C4—582no—
333C22×C4—582no—
334C22×C4—1161no—
335C22×C4—1161no—
336C22×C4—1161no—
337C22×C4—1161no—
338C22×C4—1161no—
339C22×C4—1161no—
340C22×C4C22×D2911yescharacteristic
341C22×C4C22×D2911yescharacteristic
342C22×C4C22×D2911yescharacteristic
343C22×C4C22×D2911yescharacteristic
344C22×C4C22×D2911yescharacteristic
345C4⋊C4—582no—
346C4⋊C4—582no—
347C22⋊C4—22no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—582no—
351C22⋊C4—582no—
352C22⋊C4—582no—
353C22⋊C4—1161no—
354C22⋊C4—1161no—
355C22⋊C4—1161no—
356C22⋊C4—1161no—
357C22⋊C4—1161no—
358C22⋊C4—1161no—
359C42—294no—
360C42—294no—
361C42—582no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—292no—
375C23—292no—
376C23—581no—
377C23—581no—
378C23—581no—
379C23—581no—
380C23—581no—
381C23—581no—
382C23—581no—
383C23—581no—
384C23—581no—
385C23—581no—
386C23—581no—
387C23—581no—
388C23C2×C4×D2912yes—
389C23C2×C4×D2912yes—
390C23C23×D2911yescharacteristic
391D4—44no—
392D4—588no—
393D4—588no—
394D4—1164no—
395D4—1164no—
396D4—1164no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—44no—
411C2×C4—292no—
412C2×C4—292no—
413C2×C4—292no—
414C2×C4—292no—
415C2×C4—292no—
416C2×C4—581no—
417C2×C4—581no—
418C2×C4—581no—
419C2×C4—581no—
420C2×C4—581no—
421C2×C4—581no—
422C2×C4—581no—
423C2×C4—581no—
424C2×C4—581no—
425C2×C4—581no—
426C2×C4—581no—
427C2×C4—581no—
428C2×C4—581no—
429C2×C4—1164no—
430C2×C4—1164no—
431C2×C4—1164no—
432C2×C4C2×C4×D2912yes—
433C2×C4D4×D2912yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—582no—
449C22—582no—
450C22—582no—
451C22—582no—
452C22—582no—
453C22—582no—
454C22—1161no—
455C22—1161no—
456C22—1161no—
457C22—1161no—
458C22—1161no—
459C22—1161no—
460C22—1161no—
461C22—1161no—
462C22C22×C4×D2911yescharacteristic
463C22C2×D4×D2911yescharacteristic
464C22#1174535911yescharacteristic
465C22#1174535911yescharacteristic
466C22#1174535911yescharacteristic
467C22#41×D2911yescharacteristic
468C22#1174536411yescharacteristic
469C4—22no—
470C4—22no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—294no—
475C4—582no—
476C4—582no—
477C4—1161no—
478C4—1161no—
479C4—1161no—
480C2—42no—
481C2—42no—
482C2—1162no—
483C2—1162no—
484C2C4×D4×D2911yescharacteristic
485C2#1427163511yescharacteristic
486C2#1427163611yescharacteristic
487C2#1427172811yescharacteristic
488C2#1427172911yescharacteristic
489C2#1427176311yescharacteristic
490C2#1427176511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC29×#386C2
socle, cosocleC23×C29C24
prime radicalC2×#11745302C2
hypercenter#386D29
hypocenterC29#2328
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D29C2semidirect
3. C2×#11745243C2semidirect
4. #14271063C2semidirect
5. #14271063C2semidirect
6. #14271043C2semidirect
7. #14271042C2semidirect
8. #14271041C2semidirect
9. #14271041C2semidirect
10. #14271040C2semidirect
11. #14271039C2semidirect
12. #14271039C2semidirect
13. #14271027C2semidirect
14. #14271008C2semidirect
15. C29×#386C2semidirect
32. #11745302C4semidirect
60. C2×D4×C29C2×C4semidirect
77. C2×C22⋊D29C2×C4semidirect
78. C2×C22⋊D29C2×C4semidirect
79. C2×C22⋊D29C2×C4semidirect
80. C2×C22⋊D29C2×C4semidirect
92. C2×D116C2×C4semidirect
114. C4×Dic29C2×C4semidirect
115. C4×Dic29D4semidirect
247. #386D29semidirect
299. C29#2328semidirect
321. C2×D4C4×D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117453022
C2×C4×C22⋊D292
C2×#117452432
#142710632
#142710432
#142710422
#142710412
#142710402
#142710392
#142710272
#142710082
C29×#3862
#232829