Finite Group Databasebeta

← #21449256

Subgroups — #21449256

Order 7808.

788 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519749C211yesmaximal, characteristic, complemented
2C2×#14519749C211yesmaximal, characteristic, complemented
3C2×#14519749C211yesmaximal, characteristic, complemented
4C2×D4×Dic61C211yesmaximal, characteristic, complemented
5C22×#11758196C211yesmaximal, characteristic, complemented
6#16839685C211yesmaximal, characteristic, complemented
7#16839684C211yesmaximal, characteristic, complemented
8#16839677C211yesmaximal, characteristic, complemented
9#16839676C211yesmaximal, characteristic, complemented
10#16839662C211yesmaximal, characteristic, complemented
11#16839657C211yesmaximal, characteristic, complemented
12#16839642C211yesmaximal, characteristic, complemented
13#16839641C211yesmaximal, characteristic, complemented
14#16839620C211yesmaximal, characteristic, complemented
15C2×#121×C61C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20C23×Dic61C2211yescharacteristic
21C23×Dic61C2211yescharacteristic
22#14519749—24no—
23#14519749—24no—
24#14519749—24no—
25D4×Dic61—24no—
26C2×C4⋊Dic61C2211yescharacteristic
27C2×#11758196—24no—
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×#11758196C2211yescharacteristic
31C2×#11758196C2211yescharacteristic
32C2×#11758196C2211yescharacteristic
33C2×#11758196C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×C22⋊Dic61C2211yescharacteristic
37C2×C22⋊Dic61C2211yescharacteristic
38C2×C22⋊Dic61C2211yescharacteristic
39C2×C22⋊Dic61C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C2×#11758198C2211yescharacteristic
44C2×C4×Dic61C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48#14519684C2211yescharacteristic
49C22×D4×C61C2211yescharacteristic
50C22×D4×C61C2211yescharacteristic
51C22×D4×C61C2211yescharacteristic
52C23×C4×C61C2211yescharacteristic
53#121×C61—24no—
54C2×C4⋊C4×C61C2211yescharacteristic
55C2×C22⋊C4×C61C2211yescharacteristic
56C2×C22⋊C4×C61C2211yescharacteristic
57C24×C61C2311yescharacteristic
58C24×C61C2311yescharacteristic
59C24×C61C2311yescharacteristic
60C23×D61C2311yescharacteristic
61C2×D4×C61—22no—
62C2×D4×C61—22no—
63C2×D4×C61—22no—
64C2×D4×C61—22no—
65C2×D4×C61—22no—
66C2×D4×C61—22no—
67C2×D4×C61—22no—
68C2×D4×C61—41no—
69C2×D4×C61D414yescomplemented
70C22×C4×C61—22no—
71C22×C4×C61—22no—
72C22×C4×C61—41no—
73C22×C4×C61C2311yescharacteristic
74C22×C4×C61C2311yescharacteristic
75C22×C4×C61C2311yescharacteristic
76C22×C4×C61C2311yescharacteristic
77C2×C22⋊D61—22no—
78C2×C22⋊D61—22no—
79C2×C22⋊D61—22no—
80C2×C22⋊D61—22no—
81C2×C22⋊D61—22no—
82C2×C22⋊D61—22no—
83C2×C22⋊D61—22no—
84C2×C22⋊D61—22no—
85C2×C22⋊D61—41no—
86C22×Dic61—22no—
87C22×Dic61—22no—
88C22×Dic61—22no—
89C22×Dic61—22no—
90C22×Dic61—22no—
91C22×Dic61—22no—
92C22×Dic61—22no—
93C22×Dic61—41no—
94C22×Dic61D414yescomplemented
95C22×Dic61C2311yescharacteristic
96C22×Dic61C2311yescharacteristic
97C22×Dic61C2311yescharacteristic
98C22×Dic61C2311yescharacteristic
99C22×Dic61C2311yescharacteristic
100C22×Dic61C2311yescharacteristic
101C22×Dic61C2311yescharacteristic
102C4⋊C4×C61—22no—
103C22⋊C4×C61—22no—
104C22⋊C4×C61—22no—
105C22⋊Dic61—22no—
106C22⋊Dic61—22no—
107C22⋊Dic61—22no—
108C22⋊Dic61—22no—
109C22⋊Dic61—22no—
110C22⋊Dic61—41no—
111#11758198—22no—
112#11758198—22no—
113#11758198—22no—
114#11758198—41no—
115C4⋊Dic61—22no—
116#11758196—22no—
117#11758196—22no—
118#11758196—22no—
119#11758196—22no—
120#11758196—22no—
121#11758196D414yescomplemented
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×C61—21no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—21no—
140C23×C61C2×D412yes—
141C23×C61C2×D412yes—
142C23×C61C2×D412yes—
143C23×C61#4112yes—
144C23×C61C2411yescharacteristic
145C22×D61—21no—
146C22×D61—21no—
147C22×D61—21no—
148C22×D61—21no—
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—21no—
152D4×C61—28no—
153D4×C61—44no—
154D4×C61—44no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—44no—
166C2×C4×C61C2×D412yes—
167C2×C4×C61C2×D412yes—
168C22⋊D61—44no—
169C22⋊D61—44no—
170C22⋊D61—44no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—28no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—21no—
181C2×Dic61—21no—
182C2×Dic61—21no—
183C2×Dic61—21no—
184C2×Dic61—21no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—44no—
189C2×Dic61—44no—
190C2×Dic61C2×D412yes—
191C2×Dic61C2×D412yes—
192C2×Dic61C2×D412yes—
193C2×Dic61C2×D412yes—
194C2×Dic61#4112yes—
195C22×C61—22no—
196C22×C61—22no—
197C22×C61—22no—
198C22×C61—22no—
199C22×C61—22no—
200C22×C61—22no—
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×C61#12114yescomplemented
216C22×C61C22×D411yescharacteristic
217C22×C61C22×D411yescharacteristic
218C22×C61C22×D411yescharacteristic
219C22×C61C2×#4111yescharacteristic
220C22×C61C2×#4111yescharacteristic
221C22×C61H(5,𝔽2)11yescharacteristic
222C22×C612−1+411yescharacteristic
223C2×D61—41no—
224C2×D61—41no—
225C2×D61—41no—
226C2×D61—41no—
227C2×D61—41no—
228C2×D61—41no—
229C2×D61—41no—
230C4×C61—22no—
231C4×C61—22no—
232C4×C61—41no—
233C4×C61—41no—
234Dic61—22no—
235Dic61—22no—
236Dic61—41no—
237Dic61—41no—
238Dic61—41no—
239Dic61—41no—
240Dic61#12114yescomplemented
241#2416—611nomaximal, Sylow
242C2×C61—24no—
243C2×C61—42no—
244C2×C61—81no—
245C2×C61C2×#12111yescharacteristic
246C2×C61C2×#12111yescharacteristic
247C2×C61#53711yescharacteristic
248C2×C61D4211yescharacteristic
249C2×C61#54711yescharacteristic
250C2×C61#54811yescharacteristic
251C2×C61#55311yescharacteristic
252D61—81no—
253C2×#121—611no—
254C2×#121—611no—
255C2×#121—611no—
256C2×#121D6111yescharacteristic, complemented
257C2×C4×D4—611no—
258C22×C4⋊C4—611no—
259#396—611no—
260#396—611no—
261#394—611no—
262#394—611no—
263#390—611no—
264#389—611no—
265#386—611no—
266#386—611no—
267#380—611no—
268C61#241611yescharacteristic, complemented, Sylow
269C22×D4—611no—
270C22×D4—611no—
271C22×D4—611no—
272C22×D4C2×D6111yescharacteristic
273C22×D4C2×D6111yescharacteristic
274C22×D4C2×D6111yescharacteristic
275C23×C4—611no—
276C23×C4—611no—
277C23×C4—611no—
278C23×C4C2×D6111yescharacteristic
279#121—24no—
280#121—1224no—
281#121—1224no—
282#121—1224no—
283C4×D4—1224no—
284C2×C4⋊C4—611no—
285C2×C4⋊C4—611no—
286C2×C4⋊C4—611no—
287C2×C4⋊C4—611no—
288C2×C4⋊C4—611no—
289C2×C4⋊C4—611no—
290C2×C4⋊C4—611no—
291C2×C4⋊C4—1224no—
292C2×C4⋊C4C2×D6111yescharacteristic
293C2×C22⋊C4—611no—
294C2×C22⋊C4—611no—
295C2×C22⋊C4—611no—
296C2×C22⋊C4—611no—
297C2×C22⋊C4—611no—
298C2×C22⋊C4—611no—
299C2×C22⋊C4—611no—
300C2×C22⋊C4—611no—
301C2×C22⋊C4—611no—
302C2×C22⋊C4—611no—
303C2×C22⋊C4C2×D6111yescharacteristic
304C2×C22⋊C4C2×D6111yescharacteristic
305C2×C42—611no—
306#95—611no—
307#95—611no—
308#95—611no—
309#95—611no—
310C24—611no—
311C24C22×D6111yescharacteristic
312C24C22×D6111yescharacteristic
313C24C22×D6111yescharacteristic
314C2×D4—22no—
315C2×D4—22no—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—41no—
322C2×D4—1222no—
323C2×D4—1222no—
324C2×D4—1222no—
325C2×D4—1222no—
326C2×D4—1222no—
327C2×D4—1222no—
328C2×D4—1222no—
329C2×D4—1222no—
330C2×D4—2441no—
331C2×D4C22⋊D6114yescomplemented
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—41no—
335C22×C4—611no—
336C22×C4—614no—
337C22×C4—611no—
338C22×C4—611no—
339C22×C4—611no—
340C22×C4—611no—
341C22×C4—611no—
342C22×C4—611no—
343C22×C4—1222no—
344C22×C4—1222no—
345C22×C4—1222no—
346C22×C4—1222no—
347C22×C4—1222no—
348C22×C4—1222no—
349C22×C4—1222no—
350C22×C4—2441no—
351C22×C4C22×D6111yescharacteristic
352C22×C4C22×D6111yescharacteristic
353C22×C4C22×D6111yescharacteristic
354C22×C4C22×D6111yescharacteristic
355C4⋊C4—22no—
356C4⋊C4—614no—
357C4⋊C4—1222no—
358C4⋊C4—1222no—
359C4⋊C4—1222no—
360C4⋊C4—1222no—
361C4⋊C4—1222no—
362C4⋊C4—1222no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—1222no—
366C22⋊C4—1222no—
367C22⋊C4—1222no—
368C22⋊C4—1222no—
369C22⋊C4—1222no—
370C22⋊C4—1222no—
371C22⋊C4—1222no—
372C22⋊C4—1222no—
373C22⋊C4—2441no—
374C22⋊C4—2441no—
375C42—1222no—
376C23—21no—
377C23—21no—
378C23—21no—
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—21no—
392C23—21no—
393C23—1221no—
394C23—1221no—
395C23—1221no—
396C23—1221no—
397C23—1221no—
398C23—1221no—
399C23—1221no—
400C23D4×D6112yes—
401C23#1175822412yes—
402C23C2×C22⋊D6112yes—
403C23C2×C22⋊D6112yes—
404C23C23×D6111yescharacteristic
405D4—28no—
406D4—44no—
407D4—44no—
408D4—2444no—
409D4—2444no—
410D4—2444no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—44no—
422C2×C4—612no—
423C2×C4—612no—
424C2×C4—612no—
425C2×C4—612no—
426C2×C4—612no—
427C2×C4—1228no—
428C2×C4—1221no—
429C2×C4—1221no—
430C2×C4—1221no—
431C2×C4—1221no—
432C2×C4—1221no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—1221no—
442C2×C4—1221no—
443C2×C4—1221no—
444C2×C4—2444no—
445C2×C4—2444no—
446C2×C4D4×D6112yes—
447C2×C4C2×C22⋊D6112yes—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—2441no—
469C22—2441no—
470C22—2441no—
471C22—2441no—
472C22—2441no—
473C22—2441no—
474C22—2441no—
475C22#1451974914yescomplemented
476C22C2×D4×D6111yescharacteristic
477C22C2×D4×D6111yescharacteristic
478C22C22×C22⋊D6111yescharacteristic
479C22#41×D6111yescharacteristic
480C22C2×#1175822411yescharacteristic
481C22#1451982211yescharacteristic
482C22#1451982411yescharacteristic
483C4—22no—
484C4—22no—
485C4—41no—
486C4—41no—
487C4—614no—
488C4—1222no—
489C4—1222no—
490C4—2441no—
491C4—2441no—
492C4—2441no—
493C4—2441no—
494C2—24no—
495C2—42no—
496C2—81no—
497C2—4881no—
498C2#121×D6111yescharacteristic
499C2C2×#1451974911yescharacteristic
500C2#1684033911yescharacteristic
501C2D4×C22⋊D6111yescharacteristic
502C2#1684041111yescharacteristic
503C2#1684041811yescharacteristic
504C2#1684045511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#121×C61C2
hypercenterC2×#121D61
hypocenterC61#2416
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14519749C2semidirect
2. C2×#14519749C2semidirect
3. C2×#14519749C2semidirect
4. C2×D4×Dic61C2semidirect
5. C22×#11758196C2semidirect
6. #16839685C2semidirect
7. #16839684C2semidirect
8. #16839677C2semidirect
9. #16839676C2semidirect
10. #16839662C2semidirect
11. #16839657C2semidirect
12. #16839642C2semidirect
13. #16839641C2semidirect
14. #16839620C2semidirect
15. C2×#121×C61C2semidirect
69. C2×D4×C61D4semidirect
94. C22×Dic61D4semidirect
121. #11758196D4semidirect
215. C22×C61#121semidirect
240. Dic61#121semidirect
256. C2×#121D61semidirect
268. C61#2416semidirect
331. C2×D4C22⋊D61semidirect
475. C22#14519749semidirect