Finite Group Databasebeta

← #29690516

Subgroups — #29690516

Order 15616.

774 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839823C211yesmaximal, characteristic
2C2×#16839789C211yesmaximal, characteristic
3#21446543C211yesmaximal, characteristic, complemented
4#21446543C211yesmaximal, characteristic, complemented
5#21446538C211yesmaximal, characteristic, complemented
6#21446538C211yesmaximal, characteristic, complemented
7#21446004C211yesmaximal, characteristic
8#21446004C211yesmaximal, characteristic
9#21445999C211yesmaximal, characteristic
10#21445999C211yesmaximal, characteristic
11#21445973C211yesmaximal, characteristic, complemented
12#21445971C211yesmaximal, characteristic, complemented
13#21445939C211yesmaximal, characteristic, complemented
14#21445936C211yesmaximal, characteristic, complemented
15C61×#2298C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18#16839823—24no—
19#16839789—24no—
20C2×C4⋊#92418C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C2×C4⋊#92418C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×C4⋊#92418C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×C4⋊#92418C2211yescharacteristic
33C2×C4⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×#14519688C2211yescharacteristic
37C2×C4×#92418C2211yescharacteristic
38#16839517C2211yescharacteristic
39#16839517C2211yescharacteristic
40#16839517C2211yescharacteristic
41#16839517C2211yescharacteristic
42#16839517C2211yescharacteristic
43#16839517C2211yescharacteristic
44#16839517C2211yescharacteristic
45#16839517C2211yescharacteristic
46C2×#117×C61C2211yescharacteristic
47C61×#388C411yescharacteristic
48C61×#388C411yescharacteristic
49C61×#388C411yescharacteristic
50C61×#388C411yescharacteristic
51C61×#387C411yescharacteristic
52C61×#387C411yescharacteristic
53C61×#387C411yescharacteristic
54C61×#387C411yescharacteristic
55C4×C4⋊C4×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C4×C22⋊C4×C61C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#376C2211yescharacteristic
60C43×C61C2211yescharacteristic
61C2×#11758194—22no—
62C2×#11758194—41no—
63C2×#11758194—41no—
64C22×#92418—22no—
65C22×#92418—41no—
66C22×#92418—41no—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C4⋊#92418—22no—
76C4⋊#92418—22no—
77C4⋊#92418—22no—
78C4⋊#92418—22no—
79C4⋊#92418—22no—
80C4⋊#92418—22no—
81C4⋊#92418—41no—
82C4⋊#92418—41no—
83C4⋊#92418—41no—
84C4⋊#92418—41no—
85C4⋊#92418—41no—
86C4⋊#92418—41no—
87C4⋊#92418—41no—
88C4⋊#92418—41no—
89C22⋊#92418—22no—
90C22⋊#92418—22no—
91#14519688—22no—
92C4×#92418—22no—
93C23×C4×C61C2311yescharacteristic
94#117×C61D414yes—
95#117×C61Q814yes—
96C2×C4⋊C4×C61C2×C411yescharacteristic
97C2×C4⋊C4×C61C2×C411yescharacteristic
98C2×C4⋊C4×C61C2×C411yescharacteristic
99C2×C4⋊C4×C61C2×C411yescharacteristic
100C2×C4⋊C4×C61C2×C411yescharacteristic
101C2×C4⋊C4×C61C2×C411yescharacteristic
102C2×C22⋊C4×C61C2×C411yescharacteristic
103C2×C22⋊C4×C61C2×C411yescharacteristic
104C2×C22⋊C4×C61C2×C411yescharacteristic
105C2×C22⋊C4×C61C2×C411yescharacteristic
106C2×C22⋊C4×C61C2×C411yescharacteristic
107C2×C22⋊C4×C61C2×C411yescharacteristic
108C2×C42×C61C2×C411yescharacteristic
109C2×C42×C61C2×C411yescharacteristic
110C2×C42×C61C2×C411yescharacteristic
111C2×C42×C61C2×C411yescharacteristic
112C2×C42×C61C2311yescharacteristic
113C2×C42×C61C2311yescharacteristic
114C2×C42×C61C2311yescharacteristic
115C2×C42×C61C2311yescharacteristic
116C2×C42×C61C2311yescharacteristic
117C2×C42×C61C2311yescharacteristic
118#95×C61C2×C411yescharacteristic
119#95×C61C2×C411yescharacteristic
120#95×C61C2×C411yescharacteristic
121#95×C61C2×C411yescharacteristic
122#95×C61C2×C411yescharacteristic
123#95×C61C2×C411yescharacteristic
124#95×C61C2×C411yescharacteristic
125#95×C61C2×C411yescharacteristic
126#95×C61C2×C411yescharacteristic
127#95×C61C2×C411yescharacteristic
128#95×C61C2×C411yescharacteristic
129#95×C61C2×C411yescharacteristic
130C24×C61C22×C411yescharacteristic
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C22×C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C2×D412yes—
149C22×C4×C61C2×Q812yes—
150C22×C4×C61C2411yescharacteristic
151C4⋊C4×C61—22no—
152C4⋊C4×C61—22no—
153C4⋊C4×C61—41no—
154C4⋊C4×C61—41no—
155C4⋊C4×C61C4⋊C414yes—
156C4⋊C4×C61C4⋊C414yes—
157C22⋊C4×C61—22no—
158C22⋊C4×C61—22no—
159C22⋊C4×C61—41no—
160C22⋊C4×C61—41no—
161C22⋊C4×C61C4⋊C414yes—
162C22⋊C4×C61C4⋊C414yes—
163C42×C61—22no—
164C42×C61—22no—
165C42×C61—21no—
166C42×C61—21no—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—21no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61—41no—
174C42×C61—41no—
175C42×C61C2×D412yes—
176C42×C61C2×D412yes—
177C42×C61C2×Q812yes—
178C42×C61C2×Q812yes—
179#11758194—44no—
180C2×#92418—21no—
181C2×#92418—21no—
182C2×#92418—21no—
183C2×#92418—21no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—44no—
205C23×C61—21no—
206C23×C61—21no—
207C23×C61—21no—
208C23×C61—21no—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61C2×C4⋊C412yes—
212C23×C61C23×C411yescharacteristic
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61C2×C4⋊C412yes—
250C2×C4×C61C2×C4⋊C412yes—
251C2×C4×C61C2×C4⋊C412yes—
252C2×C4×C61C2×C4⋊C412yes—
253C2×C4×C61C2×C4⋊C412yes—
254C2×C4×C61#13112yes—
255C2×C4×C61#13112yes—
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61C22×Q811yescharacteristic
258C2×C4×C61H(5,𝔽2)11yescharacteristic
259C2×C4×C61H(5,𝔽2)11yescharacteristic
260C2×C4×C612−1+411yescharacteristic
261C2×C4×C612−1+411yescharacteristic
262#92418—41no—
263#92418—41no—
264#92418—41no—
265#92418—41no—
266#92418—41no—
267#92418—41no—
268#92418—41no—
269#92418—41no—
270#21980—611nomaximal, Sylow
271C22×C61—22no—
272C22×C61—22no—
273C22×C61—22no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61C22×C4⋊C411yescharacteristic
279C22×C61#52011yescharacteristic
280C22×C61#52011yescharacteristic
281C22×C61C2×#13111yescharacteristic
282C22×C61C2×#13111yescharacteristic
283C22×C61#56811yescharacteristic
284C22×C61#56811yescharacteristic
285C4×C61—22no—
286C4×C61—22no—
287C4×C61—22no—
288C4×C61—22no—
289C4×C61—22no—
290C4×C61—22no—
291C4×C61—22no—
292C4×C61—41no—
293C4×C61—41no—
294C4×C61—41no—
295C4×C61—41no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61#53511yescharacteristic
299C4×C61#53611yescharacteristic
300C4×C61#54411yescharacteristic
301C4×C61#54411yescharacteristic
302C2×#433—611no—
303C2×#424—611no—
304#2298D6111yescharacteristic
305#1940—611no—
306#1940—611no—
307#1939—611no—
308#1939—611no—
309#1851—611no—
310#1851—611no—
311#1850—611no—
312#1850—611no—
313#1843—611no—
314#1842—611no—
315#1832—611no—
316#1831—611no—
317C2×C61—42no—
318C2×C61#231711yescharacteristic
319C2×C61#290611yescharacteristic
320C2×C61#290611yescharacteristic
321C2×C61#299211yescharacteristic
322C2×C61#299311yescharacteristic
323C2×C61#299411yescharacteristic
324C2×C61#299511yescharacteristic
325C22×M16—611no—
326C23×C8—611no—
327C2×#117C2×D6111yescharacteristic
328#433—1224no—
329#424—1224no—
330C2×C4⋊C8—611no—
331C2×C4⋊C8—611no—
332C2×C4⋊C8—611no—
333C2×C4⋊C8—611no—
334C2×C4⋊C8—611no—
335C2×C4⋊C8—611no—
336C2×C4⋊C8—611no—
337C2×C4⋊C8—611no—
338C2×C4⋊C8—611no—
339C2×C4⋊C8—611no—
340C2×C4⋊C8—611no—
341C2×C4⋊C8—611no—
342C2×C4⋊C8—611no—
343C2×C4⋊C8—611no—
344C2×C22⋊C8—611no—
345C2×C22⋊C8—611no—
346C2×#97—611no—
347C2×C4×C8—611no—
348#388Dic6111yescharacteristic
349#388Dic6111yescharacteristic
350#388Dic6111yescharacteristic
351#388Dic6111yescharacteristic
352#387Dic6111yescharacteristic
353#387Dic6111yescharacteristic
354#387Dic6111yescharacteristic
355#387Dic6111yescharacteristic
356C4×C4⋊C4C2×D6111yescharacteristic
357C4×C4⋊C4C2×D6111yescharacteristic
358C4×C22⋊C4C2×D6111yescharacteristic
359C4×C22⋊C4C2×D6111yescharacteristic
360#376C2×D6111yescharacteristic
361C43C2×D6111yescharacteristic
362#336—611no—
363#336—611no—
364#336—611no—
365#336—611no—
366#336—611no—
367#336—611no—
368#336—611no—
369#336—611no—
370C61#2198011yescharacteristic, complemented, Sylow
371C23×C4C22×D6111yescharacteristic
372C2×M16—1222no—
373C2×M16—2441no—
374C2×M16—2441no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8—611no—
379C22×C8—611no—
380C22×C8—611no—
381C22×C8—611no—
382C22×C8—611no—
383C22×C8—1222no—
384C22×C8—2441no—
385C22×C8—2441no—
386#117Dic12214yes—
387#117D24414yes—
388C2×C4⋊C4C2×Dic6111yescharacteristic
389C2×C4⋊C4C2×Dic6111yescharacteristic
390C2×C4⋊C4C2×Dic6111yescharacteristic
391C2×C4⋊C4C2×Dic6111yescharacteristic
392C2×C4⋊C4C2×Dic6111yescharacteristic
393C2×C4⋊C4C2×Dic6111yescharacteristic
394C2×C22⋊C4C2×Dic6111yescharacteristic
395C2×C22⋊C4C2×Dic6111yescharacteristic
396C2×C22⋊C4C2×Dic6111yescharacteristic
397C2×C22⋊C4C2×Dic6111yescharacteristic
398C2×C22⋊C4C2×Dic6111yescharacteristic
399C2×C22⋊C4C2×Dic6111yescharacteristic
400C2×C42C2×Dic6111yescharacteristic
401C2×C42C2×Dic6111yescharacteristic
402C2×C42C2×Dic6111yescharacteristic
403C2×C42C2×Dic6111yescharacteristic
404C2×C42C22×D6111yescharacteristic
405C2×C42C22×D6111yescharacteristic
406C2×C42C22×D6111yescharacteristic
407C2×C42C22×D6111yescharacteristic
408C2×C42C22×D6111yescharacteristic
409C2×C42C22×D6111yescharacteristic
410C4⋊C8—1222no—
411C4⋊C8—1222no—
412C4⋊C8—1222no—
413C4⋊C8—1222no—
414C4⋊C8—1222no—
415C4⋊C8—1222no—
416C4⋊C8—2441no—
417C4⋊C8—2441no—
418C4⋊C8—2441no—
419C4⋊C8—2441no—
420C4⋊C8—2441no—
421C4⋊C8—2441no—
422C4⋊C8—2441no—
423C4⋊C8—2441no—
424C22⋊C8—1222no—
425C22⋊C8—1222no—
426#97—1222no—
427C4×C8—1222no—
428#95C2×Dic6111yescharacteristic
429#95C2×Dic6111yescharacteristic
430#95C2×Dic6111yescharacteristic
431#95C2×Dic6111yescharacteristic
432#95C2×Dic6111yescharacteristic
433#95C2×Dic6111yescharacteristic
434#95C2×Dic6111yescharacteristic
435#95C2×Dic6111yescharacteristic
436#95C2×Dic6111yescharacteristic
437#95C2×Dic6111yescharacteristic
438#95C2×Dic6111yescharacteristic
439#95C2×Dic6111yescharacteristic
440C24C22×Dic6111yescharacteristic
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4C2×Dic12212yes—
446C22×C4C2×D24412yes—
447C22×C4C22×Dic6111yescharacteristic
448C22×C4C22×Dic6111yescharacteristic
449C22×C4C22×Dic6111yescharacteristic
450C22×C4C22×Dic6111yescharacteristic
451C22×C4C22×Dic6111yescharacteristic
452C22×C4C22×Dic6111yescharacteristic
453C22×C4C22×Dic6111yescharacteristic
454C22×C4C22×Dic6111yescharacteristic
455C22×C4C22×Dic6111yescharacteristic
456C22×C4C22×Dic6111yescharacteristic
457C22×C4C22×Dic6111yescharacteristic
458C22×C4C22×Dic6111yescharacteristic
459C22×C4C22×Dic6111yescharacteristic
460C22×C4C23×D6111yescharacteristic
461M16—2444no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—2444no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4C4⋊Dic6114yes—
492C4⋊C4C4⋊Dic6114yes—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4C4⋊Dic6114yes—
498C22⋊C4C4⋊Dic6114yes—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—22no—
508C42—22no—
509C42—41no—
510C42—41no—
511C42C2×Dic12212yes—
512C42C2×Dic12212yes—
513C42C2×D24412yes—
514C42C2×D24412yes—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23C2×C4⋊Dic6112yes—
522C23C23×Dic6111yescharacteristic
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4C2×C4⋊Dic6112yes—
560C2×C4C2×C4⋊Dic6112yes—
561C2×C4C2×C4⋊Dic6112yes—
562C2×C4C2×C4⋊Dic6112yes—
563C2×C4C2×C4⋊Dic6112yes—
564C2×C4#1451978412yes—
565C2×C4#1451978412yes—
566C2×C4C22×D24411yescharacteristic
567C2×C4C22×Dic12211yescharacteristic
568C2×C4#1451982311yescharacteristic
569C2×C4#1451982311yescharacteristic
570C2×C4#1451982411yescharacteristic
571C2×C4#1451982411yescharacteristic
572C8—2441no—
573C8—2441no—
574C8—2441no—
575C8—2441no—
576C8—2441no—
577C8—2441no—
578C8—2441no—
579C8—2441no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C22×C4⋊Dic6111yescharacteristic
588C22#1684024511yescharacteristic
589C22#1684024511yescharacteristic
590C22C2×#1451978411yescharacteristic
591C22C2×#1451978411yescharacteristic
592C22#1684052911yescharacteristic
593C22#1684052911yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—22no—
599C4—22no—
600C4—22no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4#1684033111yescharacteristic
608C4#1684033811yescharacteristic
609C4#1684039011yescharacteristic
610C4#1684039011yescharacteristic
611C2—42no—
612C2#2144844211yescharacteristic
613C2#2145438711yescharacteristic
614C2#2145438711yescharacteristic
615C2#2145495811yescharacteristic
616C2#2145496811yescharacteristic
617C2#2145497911yescharacteristic
618C2#2145498911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#2298C2
prime radicalC24×C61C22×C4
cosocleC22×C4×C61C24
hypercenter#2298D61
hypocenterC61#21980
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #2298

Complements

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

NH ≅ G/Ntype
3. #21446543C2semidirect
4. #21446543C2semidirect
5. #21446538C2semidirect
6. #21446538C2semidirect
11. #21445973C2semidirect
12. #21445971C2semidirect
13. #21445939C2semidirect
14. #21445936C2semidirect
370. C61#21980semidirect

Maximal subgroups

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

subgroupindex
C2×#168398232
C2×#168397892
#214465432
#214465382
#214460042
#214459992
#214459732
#214459712
#214459392
#214459362
C61×#22982
#2198061