Finite Group Databasebeta

← #21450890

Subgroups — #21450890

Order 7808.

696 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×#14519766C211yesmaximal, characteristic, complemented
2C2×#14519750C211yesmaximal, characteristic, complemented
3C2×#14519749C211yesmaximal, characteristic, complemented
4#16839681C211yesmaximal, characteristic, complemented
5#16839677C211yesmaximal, characteristic, complemented
6#16839671C211yesmaximal, characteristic, complemented
7#16839670C211yesmaximal, characteristic, complemented
8#16839662C211yesmaximal, characteristic, complemented
9#16839656C211yesmaximal, characteristic, complemented
10#16839653C211yesmaximal, characteristic, complemented
11#16839639C211yesmaximal, characteristic, complemented
12#16839638C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
14C4×#11758198C211yesmaximal, characteristic, complemented
15C2×#124×C61C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C22×C22⋊D61C2211yescharacteristic
20C22×C22⋊D61C2211yescharacteristic
21C23×Dic61C2211yescharacteristic
22C22×C4×D61C2211yescharacteristic
23#14519766—24no—
24#14519750—24no—
25#14519749—24no—
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×C4×Dic61C2211yescharacteristic
40C2×C4×Dic61C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47C22×Q8×C61C2211yescharacteristic
48C22×D4×C61C2211yescharacteristic
49#124×C61—24no—
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
54C2×C42×C61C2211yescharacteristic
55C24×C61C2311yescharacteristic
56C24×C61C2311yescharacteristic
57C23×D61C2311yescharacteristic
58C23×D61C2311yescharacteristic
59C2×Q8×C61—22no—
60C2×Q8×C61—22no—
61C2×Q8×C61—41no—
62C2×D4×C61—22no—
63C2×D4×C61—22no—
64C2×D4×C61—41no—
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C22×C4×C61C2311yescharacteristic
69C22×C4×C61C2311yescharacteristic
70C2×C22⋊D61—22no—
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—41no—
78C2×C22⋊D61—41no—
79C2×C22⋊D61—41no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C22×Dic61—22no—
83C22×Dic61—22no—
84C22×Dic61—41no—
85C22×Dic61C2311yescharacteristic
86C22×Dic61C2311yescharacteristic
87C22×Dic61C2311yescharacteristic
88C22×Dic61C2311yescharacteristic
89C22×Dic61C2311yescharacteristic
90C22×Dic61C2311yescharacteristic
91C2×D244—22no—
92C2×D244—22no—
93C2×D244—41no—
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61—41no—
97C22⋊C4×C61—22no—
98C22⋊C4×C61—22no—
99C22⋊C4×C61—22no—
100C22⋊C4×C61D414yescomplemented
101C42×C61—22no—
102C22⋊Dic61—22no—
103C22⋊Dic61—22no—
104C22⋊Dic61—22no—
105#11758198—22no—
106#11758198—22no—
107#11758198—22no—
108#11758198—22no—
109#11758198—22no—
110#11758198—22no—
111#11758198D414yescomplemented
112#11758196—22no—
113#11758196—22no—
114#11758196—41no—
115C4×Dic61—22no—
116C4×Dic61—41no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61—21no—
129C23×C61—21no—
130C23×C61C2×D412yes—
131C23×C61C2411yescharacteristic
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—21no—
143C22×D61—21no—
144C22×D61—21no—
145C22×D61C2×D412yes—
146Q8×C61—44no—
147D4×C61—44no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61C2×D412yes—
161C2×C4×C61C2×D412yes—
162C2×C4×C61C2×D412yes—
163C22⋊D61—44no—
164C22⋊D61—44no—
165C22⋊D61—44no—
166C22⋊D61—44no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—44no—
182C2×Dic61C2×D412yes—
183C2×Dic61#4112yes—
184C2×Dic61#4112yes—
185C2×Dic61#4112yes—
186D244—44no—
187C4×D61—44no—
188C22×C61—22no—
189C22×C61—22no—
190C22×C61—22no—
191C22×C61—41no—
192C22×C61—41no—
193C22×C61—41no—
194C22×C61—41no—
195C22×C61—41no—
196C22×C61—41no—
197C22×C61—41no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61—41no—
201C22×C61—41no—
202C22×C61C22×D411yescharacteristic
203C22×C61C22×D411yescharacteristic
204C22×C61C2×#4111yescharacteristic
205C22×C61C2×#4111yescharacteristic
206C22×C61C2×#4111yescharacteristic
207C22×C61H(5,𝔽2)11yescharacteristic
208C22×C61H(5,𝔽2)11yescharacteristic
209C2×D61—22no—
210C2×D61—22no—
211C2×D61—22no—
212C2×D61—41no—
213C2×D61—41no—
214C2×D61—41no—
215C2×D61—41no—
216C2×D61—41no—
217C2×D61—41no—
218C2×D61—41no—
219C2×D61—41no—
220C2×D61—41no—
221C2×D61—41no—
222C2×D61—41no—
223C4×C61—22no—
224C4×C61—22no—
225C4×C61—22no—
226C4×C61—41no—
227C4×C61—41no—
228Dic61—22no—
229Dic61—22no—
230Dic61—22no—
231Dic61—22no—
232Dic61—41no—
233Dic61—41no—
234#2555—611nomaximal, Sylow
235C2×C61—42no—
236C2×C61—81no—
237C2×C61#53211yescharacteristic
238C2×C61#53211yescharacteristic
239C2×C61#53811yescharacteristic
240C2×C61D4211yescharacteristic
241C2×C61#54611yescharacteristic
242C2×C61#54611yescharacteristic
243C2×C61#55511yescharacteristic
244D61—42no—
245D61—81no—
246C2×#124—611no—
247C2×#124D6111yescharacteristic, complemented
248C2×#121—611no—
249C2×#121—611no—
250#395—611no—
251#394—611no—
252#392—611no—
253#392—611no—
254#390—611no—
255#388—611no—
256#388—611no—
257#386—611no—
258#386—611no—
259C4×C22⋊C4—611no—
260C4×C22⋊C4—611no—
261C61#255511yescharacteristic, complemented, Sylow
262C22×Q8C2×D6111yescharacteristic
263C22×D4—611no—
264C22×D4—611no—
265C22×D4—611no—
266C22×D4—611no—
267C22×D4—611no—
268C22×D4C2×D6111yescharacteristic
269C23×C4—611no—
270C23×C4—611no—
271#124—24no—
272#124—1224no—
273#121—1224no—
274#121—1224no—
275C2×C4⋊C4—611no—
276C2×C4⋊C4—611no—
277C2×C4⋊C4—611no—
278C2×C22⋊C4—611no—
279C2×C22⋊C4—611no—
280C2×C22⋊C4—611no—
281C2×C22⋊C4—611no—
282C2×C22⋊C4—611no—
283C2×C22⋊C4—611no—
284C2×C22⋊C4—611no—
285C2×C22⋊C4—611no—
286C2×C22⋊C4—611no—
287C2×C22⋊C4—611no—
288C2×C22⋊C4C2×D6111yescharacteristic
289C2×C22⋊C4C2×D6111yescharacteristic
290C2×C22⋊C4C2×D6111yescharacteristic
291C2×C22⋊C4C2×D6111yescharacteristic
292C2×C42—611no—
293C2×C42—611no—
294C2×C42C2×D6111yescharacteristic
295#95—611no—
296#95—611no—
297#95—611no—
298#95—611no—
299#95—611no—
300#95—611no—
301C24—611no—
302C24—611no—
303C24C22×D6111yescharacteristic
304C24C22×D6111yescharacteristic
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—41no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—41no—
311C2×D4—1222no—
312C2×D4—1222no—
313C2×D4—1222no—
314C2×D4—1222no—
315C2×D4—1222no—
316C2×D4—1222no—
317C2×D4—1222no—
318C2×D4—1222no—
319C2×D4—1222no—
320C2×D4—2441no—
321C2×D4—2441no—
322C2×D4—2441no—
323C2×D4—2441no—
324C2×D4—2441no—
325C2×D4—2441no—
326C22×C4—611no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—611no—
332C22×C4—1222no—
333C22×C4—1222no—
334C22×C4—1222no—
335C22×C4—1222no—
336C22×C4—2441no—
337C22×C4—2441no—
338C22×C4C22×D6111yescharacteristic
339C22×C4C22×D6111yescharacteristic
340C22×C4C22×D6111yescharacteristic
341C22×C4C22×D6111yescharacteristic
342C22×C4C22×D6111yescharacteristic
343C4⋊C4—1222no—
344C4⋊C4—1222no—
345C4⋊C4—2441no—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—614no—
350C22⋊C4—1222no—
351C22⋊C4—1222no—
352C22⋊C4—1222no—
353C22⋊C4—1222no—
354C22⋊C4—1222no—
355C22⋊C4—1222no—
356C22⋊C4—1222no—
357C22⋊C4—1222no—
358C22⋊C4—1222no—
359C22⋊C4C22⋊D6114yescomplemented
360C42—22no—
361C42—1222no—
362C42—2441no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—612no—
377C23—1221no—
378C23—1221no—
379C23—1221no—
380C23—1221no—
381C23—1221no—
382C23—1221no—
383C23—1221no—
384C23—1221no—
385C23—1221no—
386C23—1221no—
387C23—1221no—
388C23—1221no—
389C23—1221no—
390C23C2×C22⋊D6112yes—
391C23C23×D6111yescharacteristic
392Q8—44no—
393D4—44no—
394D4—2444no—
395D4—2444no—
396D4—2444no—
397D4—2444no—
398D4—2444no—
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—21no—
411C2×C4—612no—
412C2×C4—612no—
413C2×C4—612no—
414C2×C4—612no—
415C2×C4—1221no—
416C2×C4—1221no—
417C2×C4—1221no—
418C2×C4—1221no—
419C2×C4—1221no—
420C2×C4—1221no—
421C2×C4—1221no—
422C2×C4—1221no—
423C2×C4—1221no—
424C2×C4—1221no—
425C2×C4—1221no—
426C2×C4—1221no—
427C2×C4—1221no—
428C2×C4—1221no—
429C2×C4—2444no—
430C2×C4—2444no—
431C2×C4D4×D6112yes—
432C2×C4C2×C22⋊D6112yes—
433C2×C4C2×C22⋊D6112yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—1222no—
449C22—1222no—
450C22—1222no—
451C22—2441no—
452C22—2441no—
453C22—2441no—
454C22—2441no—
455C22—2441no—
456C22—2441no—
457C22—2441no—
458C22—2441no—
459C22—2441no—
460C22—2441no—
461C22—2441no—
462C22C2×D4×D6111yescharacteristic
463C22C22×C22⋊D6111yescharacteristic
464C22#41×D6111yescharacteristic
465C22#41×D6111yescharacteristic
466C22#41×D6111yescharacteristic
467C22#1451982211yescharacteristic
468C22#1451982311yescharacteristic
469C4—22no—
470C4—22no—
471C4—22no—
472C4—41no—
473C4—41no—
474C4—1222no—
475C4—1222no—
476C4—1222no—
477C4—1222no—
478C4—2441no—
479C4—2441no—
480C2—42no—
481C2—81no—
482C2—4881no—
483C2—2442no—
484C2#1684030811yescharacteristic
485C2#1684031111yescharacteristic
486C2#1684034611yescharacteristic
487C2D4×C22⋊D6111yescharacteristic
488C2#1684040011yescharacteristic
489C2#1684040511yescharacteristic
490C2#1684047411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#124×C61C2
hypercenterC2×#124D61
hypocenterC61#2555
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#14519766C2semidirect
2. C2×#14519750C2semidirect
3. C2×#14519749C2semidirect
4. #16839681C2semidirect
5. #16839677C2semidirect
6. #16839671C2semidirect
7. #16839670C2semidirect
8. #16839662C2semidirect
9. #16839656C2semidirect
10. #16839653C2semidirect
11. #16839639C2semidirect
12. #16839638C2semidirect
13. C22⋊C4×Dic61C2semidirect
14. C4×#11758198C2semidirect
15. C2×#124×C61C2semidirect
100. C22⋊C4×C61D4semidirect
111. #11758198D4semidirect
247. C2×#124D61semidirect
261. C61#2555semidirect
359. C22⋊C4C22⋊D61semidirect