Finite Group Databasebeta

← #21452082

Subgroups — #21452082

Order 7808.

734 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519773C211yesmaximal, characteristic, complemented
2C2×#14519759C211yesmaximal, characteristic, complemented
3C2×#14519751C211yesmaximal, characteristic, complemented
4C2×#14519750C211yesmaximal, characteristic, complemented
5#16839677C211yesmaximal, characteristic, complemented
6#16839677C211yesmaximal, characteristic, complemented
7#16839672C211yesmaximal, characteristic, complemented
8#16839671C211yesmaximal, characteristic, complemented
9#16839671C211yesmaximal, characteristic, complemented
10#16839670C211yesmaximal, characteristic, complemented
11#16839651C211yesmaximal, characteristic, complemented
12#16839645C211yesmaximal, characteristic, complemented
13#16839641C211yesmaximal, characteristic, complemented
14#16839640C211yesmaximal, characteristic, complemented
15C61×#386C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C22×C22⋊D61C2211yescharacteristic
22C22×C22⋊D61C2211yescharacteristic
23C22×C22⋊D61C2211yescharacteristic
24C22×C22⋊D61C2211yescharacteristic
25C22×C4×D61C2211yescharacteristic
26#14519773—24no—
27#14519759—24no—
28#14519751—24no—
29#14519750—24no—
30C2×C4⋊Dic61C2211yescharacteristic
31C2×#11758196C2211yescharacteristic
32C2×#11758196C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C2×C4×Dic61C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48C22×D4×C61C2211yescharacteristic
49C23×C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic
53#95×C61C2211yescharacteristic
54#95×C61C2211yescharacteristic
55C24×C61C2311yescharacteristic
56C24×C61C2311yescharacteristic
57C23×D61C2311yescharacteristic
58C23×D61C2311yescharacteristic
59C23×D61C2311yescharacteristic
60C2×D4×C61—22no—
61C2×D4×C61—22no—
62C2×D4×C61—41no—
63C22×C4×C61—22no—
64C22×C4×C61—41no—
65C22×C4×C61—41no—
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C22×C4×C61C2311yescharacteristic
71C2×C22⋊D61—22no—
72C2×C22⋊D61—22no—
73C2×C22⋊D61—22no—
74C2×C22⋊D61—22no—
75C2×C22⋊D61—22no—
76C2×C22⋊D61—22no—
77C2×C22⋊D61—22no—
78C2×C22⋊D61—41no—
79C2×C22⋊D61—41no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C2×C22⋊D61—41no—
83C2×C22⋊D61—41no—
84C2×C22⋊D61—41no—
85C2×C22⋊D61—41no—
86C2×C22⋊D61—41no—
87C2×C22⋊D61—41no—
88C2×C22⋊D61D414yescomplemented
89C22×Dic61C2311yescharacteristic
90C22×Dic61C2311yescharacteristic
91C22×Dic61C2311yescharacteristic
92C22×Dic61C2311yescharacteristic
93C22×Dic61C2311yescharacteristic
94C2×D244—22no—
95C2×D244—22no—
96C2×D244—22no—
97C2×D244—22no—
98C2×D244—41no—
99C2×D244—41no—
100C2×D244—41no—
101C2×D244—41no—
102C2×D244—41no—
103C2×C4×D61—22no—
104C2×C4×D61—22no—
105C2×C4×D61—41no—
106C22⋊C4×C61—22no—
107C22⋊C4×C61—22no—
108C22⋊C4×C61—41no—
109C22⋊Dic61—22no—
110C22⋊Dic61—41no—
111#11758198—22no—
112#11758198—22no—
113#11758198—22no—
114#11758198—22no—
115#11758198—22no—
116#11758198—41no—
117#11758198—41no—
118#11758198—41no—
119C4⋊Dic61D414yescomplemented
120#11758196—22no—
121#11758196—22no—
122C4×Dic61—22no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—21no—
132C23×C61—21no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61C2×D412yes—
137C23×C61C2411yescharacteristic
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—21no—
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—21no—
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—21no—
157C22×D61—21no—
158C22×D61C2×D412yes—
159D4×C61—44no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—44no—
174C2×C4×C61C2×D412yes—
175C2×C4×C61#4112yes—
176C22⋊D61—44no—
177C22⋊D61—44no—
178C22⋊D61—44no—
179C22⋊D61—44no—
180C22⋊D61—44no—
181C22⋊D61—44no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—21no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61C2×D412yes—
195C2×Dic61C2×D412yes—
196C2×Dic61C2×D412yes—
197D244—44no—
198D244—44no—
199D244—44no—
200C4×D61—44no—
201C22×C61—22no—
202C22×C61—22no—
203C22×C61—22no—
204C22×C61—41no—
205C22×C61—41no—
206C22×C61—41no—
207C22×C61—41no—
208C22×C61—41no—
209C22×C61—41no—
210C22×C61—41no—
211C22×C61—41no—
212C22×C61—41no—
213C22×C61—41no—
214C22×C61—41no—
215C22×C61C22×D411yescharacteristic
216C22×C61C22×D411yescharacteristic
217C22×C61C2×#4111yescharacteristic
218C22×C61H(5,𝔽2)11yescharacteristic
219C22×C61H(5,𝔽2)11yescharacteristic
220C22×C61H(5,𝔽2)11yescharacteristic
221C22×C61H(5,𝔽2)11yescharacteristic
222C2×D61—22no—
223C2×D61—22no—
224C2×D61—22no—
225C2×D61—41no—
226C2×D61—41no—
227C2×D61—41no—
228C2×D61—41no—
229C2×D61—41no—
230C2×D61—41no—
231C2×D61—41no—
232C2×D61—41no—
233C2×D61—41no—
234C2×D61—41no—
235C2×D61—41no—
236C2×D61—41no—
237C2×D61—41no—
238C2×D61—41no—
239C2×D61—41no—
240C2×D61—41no—
241C2×D61—41no—
242C2×D61—41no—
243C4×C61—22no—
244C4×C61—22no—
245C4×C61—41no—
246C4×C61—41no—
247C4×C61—41no—
248Dic61—22no—
249Dic61—22no—
250Dic61—22no—
251Dic61—41no—
252Dic61—41no—
253#2673—611nomaximal, Sylow
254C2×C61—42no—
255C2×C61—81no—
256C2×C61#53411yescharacteristic
257C2×C61#53511yescharacteristic
258C2×C61#54011yescharacteristic
259C2×C61D4211yescharacteristic
260C2×C61#54611yescharacteristic
261C2×C61#55011yescharacteristic
262C2×C61#56011yescharacteristic
263D61—42no—
264D61—81no—
265D61—81no—
266C2×#127—611no—
267C2×#123—611no—
268C2×#121—611no—
269C2×#121—611no—
270#394—611no—
271#394—611no—
272#392—611no—
273#392—611no—
274#392—611no—
275#392—611no—
276#388—611no—
277#387—611no—
278#386—611no—
279#386—611no—
280#386D6111yescharacteristic, complemented
281C61#267311yescharacteristic, complemented, Sylow
282C22×D4—611no—
283C22×D4—611no—
284C22×D4—611no—
285C22×D4—611no—
286C22×D4—611no—
287C22×D4—611no—
288C22×D4—611no—
289C22×D4—611no—
290C22×D4—611no—
291C22×D4C2×D6111yescharacteristic
292C23×C4—611no—
293C23×C4C2×D6111yescharacteristic
294#127—1224no—
295#123—1224no—
296#121—1224no—
297#121—1224no—
298C2×C4⋊C4—611no—
299C2×C4⋊C4—611no—
300C2×C4⋊C4—611no—
301C2×C22⋊C4—611no—
302C2×C22⋊C4—611no—
303C2×C22⋊C4—611no—
304C2×C22⋊C4—611no—
305C2×C22⋊C4—611no—
306C2×C22⋊C4—611no—
307C2×C22⋊C4—611no—
308C2×C22⋊C4—611no—
309C2×C22⋊C4—611no—
310C2×C22⋊C4—611no—
311C2×C22⋊C4C2×D6111yescharacteristic
312C2×C22⋊C4C2×D6111yescharacteristic
313C2×C22⋊C4C2×D6111yescharacteristic
314C2×C42—611no—
315#95—611no—
316#95—611no—
317#95—611no—
318#95—611no—
319#95C2×D6111yescharacteristic
320#95C2×D6111yescharacteristic
321C24—611no—
322C24—611no—
323C24—611no—
324C24C22×D6111yescharacteristic
325C24C22×D6111yescharacteristic
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—41no—
329C2×D4—614no—
330C2×D4—1222no—
331C2×D4—1222no—
332C2×D4—1222no—
333C2×D4—1222no—
334C2×D4—1222no—
335C2×D4—1222no—
336C2×D4—1222no—
337C2×D4—1222no—
338C2×D4—1222no—
339C2×D4—1222no—
340C2×D4—1222no—
341C2×D4—2441no—
342C2×D4—2441no—
343C2×D4—2441no—
344C2×D4—2441no—
345C2×D4—2441no—
346C2×D4—2441no—
347C2×D4—2441no—
348C2×D4—2441no—
349C2×D4—2441no—
350C2×D4—2441no—
351C2×D4—2441no—
352C2×D4—2441no—
353C2×D4—2441no—
354C2×D4—2441no—
355C2×D4—2441no—
356C22×C4—22no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—611no—
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—1222no—
365C22×C4—1222no—
366C22×C4—2441no—
367C22×C4C22×D6111yescharacteristic
368C22×C4C22×D6111yescharacteristic
369C22×C4C22×D6111yescharacteristic
370C22×C4C22×D6111yescharacteristic
371C22×C4C22×D6111yescharacteristic
372C4⋊C4—614no—
373C4⋊C4—1222no—
374C4⋊C4—1222no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—41no—
378C22⋊C4—1222no—
379C22⋊C4—1222no—
380C22⋊C4—1222no—
381C22⋊C4—1222no—
382C22⋊C4—1222no—
383C22⋊C4—1222no—
384C22⋊C4—2441no—
385C22⋊C4—2441no—
386C22⋊C4—2441no—
387C22⋊C4—2441no—
388C42—1222no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—612no—
403C23—1221no—
404C23—1221no—
405C23—1221no—
406C23—1221no—
407C23—1221no—
408C23—1221no—
409C23—1221no—
410C23—1221no—
411C23—1221no—
412C23—1221no—
413C23—1221no—
414C23—1221no—
415C23—1221no—
416C23—1221no—
417C23—1221no—
418C23—1221no—
419C23—1221no—
420C23—1221no—
421C23—1221no—
422C23—1221no—
423C23D4×D6112yes—
424C23C23×D6111yescharacteristic
425D4—44no—
426D4—2444no—
427D4—2444no—
428D4—2444no—
429D4—2444no—
430D4—2444no—
431D4—2444no—
432D4—2444no—
433D4—2444no—
434D4—2444no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—44no—
449C2×C4—612no—
450C2×C4—612no—
451C2×C4—612no—
452C2×C4—1221no—
453C2×C4—1221no—
454C2×C4—1221no—
455C2×C4—1221no—
456C2×C4—1221no—
457C2×C4—1221no—
458C2×C4—1221no—
459C2×C4—1221no—
460C2×C4—1221no—
461C2×C4—1221no—
462C2×C4—1221no—
463C2×C4—1221no—
464C2×C4—2444no—
465C2×C4#1175822212yes—
466C2×C4D4×D6112yes—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—1222no—
482C22—1222no—
483C22—1222no—
484C22—2441no—
485C22—2441no—
486C22—2441no—
487C22—2441no—
488C22—2441no—
489C22—2441no—
490C22—2441no—
491C22—2441no—
492C22—2441no—
493C22—2441no—
494C22—2441no—
495C22—2441no—
496C22—2441no—
497C22—2441no—
498C22—2441no—
499C22—2441no—
500C22—2441no—
501C22—2441no—
502C22C2×D4×D6111yescharacteristic
503C22C2×D4×D6111yescharacteristic
504C22C2×#1175822211yescharacteristic
505C22#1451982211yescharacteristic
506C22#1451982211yescharacteristic
507C22#1451982311yescharacteristic
508C22#1451982311yescharacteristic
509C4—22no—
510C4—22no—
511C4—41no—
512C4—41no—
513C4—41no—
514C4—1222no—
515C4—1222no—
516C4—1222no—
517C4—2441no—
518C4—2441no—
519C2—42no—
520C2—81no—
521C2—4881no—
522C2—4881no—
523C2—2442no—
524C2#1684032011yescharacteristic
525C2#1684032711yescharacteristic
526C2#1684036311yescharacteristic
527C2#1684039611yescharacteristic
528C2#1684040211yescharacteristic
529C2#1684043311yescharacteristic
530C2#1684050211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2673
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#14519773C2semidirect
2. C2×#14519759C2semidirect
3. C2×#14519751C2semidirect
4. C2×#14519750C2semidirect
5. #16839677C2semidirect
6. #16839677C2semidirect
7. #16839672C2semidirect
8. #16839671C2semidirect
9. #16839671C2semidirect
10. #16839670C2semidirect
11. #16839651C2semidirect
12. #16839645C2semidirect
13. #16839641C2semidirect
14. #16839640C2semidirect
15. C61×#386C2semidirect
88. C2×C22⋊D61D4semidirect
119. C4⋊Dic61D4semidirect
280. #386D61semidirect
281. C61#2673semidirect