Finite Group Databasebeta

← #29699130

Subgroups — #29699130

Order 15616.

854 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839820C211yesmaximal, characteristic, complemented
2C2×#16839784C211yesmaximal, characteristic, complemented
3#21448265C211yesmaximal, characteristic
4#21446427C211yesmaximal, characteristic, complemented
5#21446386C211yesmaximal, characteristic, complemented
6#21446373C211yesmaximal, characteristic, complemented
7#21446113C211yesmaximal, characteristic
8#21446113C211yesmaximal, characteristic
9#21445937C211yesmaximal, characteristic, complemented
10#21445801C211yesmaximal, characteristic, complemented
11#21445798C211yesmaximal, characteristic, complemented
12#21445679C211yesmaximal, characteristic, complemented
13#21445604C211yesmaximal, characteristic, complemented
14#21445599C211yesmaximal, characteristic, complemented
15C61×#1924C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C2×C4×C22⋊D61C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20C2×C42×D61C2211yescharacteristic
21#16839820—24no—
22#16839784—24no—
23C2×C4⋊#92418C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519687C2211yescharacteristic
33C2×C4×#92418C2211yescharacteristic
34C2×C8×Dic61C2211yescharacteristic
35#16839656C411yescharacteristic
36#16839656C411yescharacteristic
37#16839649C411yescharacteristic
38#16839649C411yescharacteristic
39#16839638C411yescharacteristic
40#16839638C411yescharacteristic
41#16839636C411yescharacteristic
42#16839636C411yescharacteristic
43C4×#11758196C2211yescharacteristic
44C4×#11758198C2211yescharacteristic
45#16839608C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×C4⋊C8×C61C2211yescharacteristic
55C2×C22⋊C8×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C61×#336C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C22×C22⋊D61C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2311yescharacteristic
65C2×#11758189—22no—
66C2×#11758189—22no—
67C2×#11758189—22no—
68C2×#11758189—22no—
69C2×#11758189—41no—
70C2×#11758189—41no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C4×C22⋊D61—22no—
76C4×C22⋊D61—22no—
77#14519736—22no—
78#14519736—22no—
79C2×C4⋊Dic61C2×C411yescharacteristic
80C2×C4⋊Dic61C2×C411yescharacteristic
81C2×#11758196C2×C411yescharacteristic
82C2×#11758196C2×C411yescharacteristic
83C2×#11758196C2×C411yescharacteristic
84C2×C22⋊Dic61C2×C411yescharacteristic
85C2×C22⋊Dic61C2×C411yescharacteristic
86C2×C22⋊Dic61C2×C411yescharacteristic
87C2×#11758198C2×C411yescharacteristic
88C2×#11758198C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×C4×Dic61C2×C411yescharacteristic
91C2×C4×Dic61C2×C411yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93C2×C4×Dic61C2311yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95C42×D61—22no—
96C42×D61—22no—
97C4⋊#92418—22no—
98#14519706—22no—
99#14519706—22no—
100#14519706—22no—
101#14519706D414yescomplemented
102C22⋊#92418—22no—
103C22⋊#92418—41no—
104#14519689—22no—
105#14519689—22no—
106#14519687—22no—
107C4×#92418—41no—
108C8×Dic61—22no—
109#14519684C2×C411yescharacteristic
110#14519684C2×C411yescharacteristic
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117C23×C4×C61C2311yescharacteristic
118C22×C8×C61C2311yescharacteristic
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C2×C22⋊C4×C61C2×C411yescharacteristic
123C2×C22⋊C4×C61C2×C411yescharacteristic
124C2×C42×C61C2311yescharacteristic
125C2×C42×C61C2311yescharacteristic
126C4⋊C8×C61—22no—
127C22⋊C8×C61—22no—
128C22⋊C8×C61—41no—
129#97×C61—41no—
130#95×C61C2×C411yescharacteristic
131#95×C61C2×C411yescharacteristic
132C24×C61C22×C411yescharacteristic
133C23×D61C22×C411yescharacteristic
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61C22×C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C2411yescharacteristic
146C2×C22⋊D61—22no—
147C2×C22⋊D61—41no—
148C2×C22⋊D61—41no—
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C411yescharacteristic
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—41no—
164C2×C4×D61—41no—
165C2×C4×D61—41no—
166C2×C4×D61#4112yes—
167C2×C4×D61#4112yes—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61C2×D412yes—
180C22⋊C4×C61—22no—
181C22⋊C4×C61—41no—
182C42×C61—21no—
183C42×C61—21no—
184C42×C61—21no—
185C42×C61—21no—
186C22⋊Dic61—22no—
187C22⋊Dic61—22no—
188C22⋊Dic61—22no—
189#11758198—22no—
190#11758198—41no—
191#11758198—41no—
192C4⋊Dic61—22no—
193C4⋊Dic61—22no—
194#11758196—22no—
195#11758196—22no—
196#11758196—41no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—22no—
202C4×Dic61—22no—
203C4×Dic61C2×D412yes—
204C4×Dic61#4112yes—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418C2×D412yes—
217#11758189—44no—
218#11758189—44no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61C23×C411yescharacteristic
227C22×D61—21no—
228C22×D61—21no—
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—21no—
232C22×D61—21no—
233C22×D61#11712yes—
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—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61#13112yes—
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C2×#4111yescharacteristic
255C2×C4×C61C2×#4111yescharacteristic
256C2×C4×C61C2×#4111yescharacteristic
257C2×C4×C61H(5,𝔽2)11yescharacteristic
258C2×C4×C612−1+411yescharacteristic
259C22⋊D61—44no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61#11712yes—
279C2×Dic61C4×D412yes—
280C2×Dic61C4×D412yes—
281C4×D61—22no—
282C4×D61—22no—
283C4×D61—22no—
284C4×D61—22no—
285C4×D61—44no—
286C4×D61—44no—
287C8×C61—22no—
288C8×C61—41no—
289C8×C61—41no—
290C8×C61—41no—
291#92418—22no—
292#92418—41no—
293#92418—41no—
294#92418—41no—
295#22755—611nomaximal, Sylow
296C22×C61—41no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61—41no—
303C22×C61C2×#11711yescharacteristic
304C22×C61C2×C4×D411yescharacteristic
305C22×C61#52011yescharacteristic
306C22×C61C2×#13111yescharacteristic
307C22×C61#56811yescharacteristic
308C22×C61#56811yescharacteristic
309C22×C61#56811yescharacteristic
310C2×D61—22no—
311C2×D61—22no—
312C2×D61—22no—
313C2×D61—41no—
314C2×D61—41no—
315C2×D61—41no—
316C2×D61—41no—
317C4×C61—22no—
318C4×C61—41no—
319C4×C61—41no—
320C4×C61—41no—
321C4×C61—41no—
322C4×C61#54611yescharacteristic
323C4×C61#54811yescharacteristic
324C4×C61#55211yescharacteristic
325C4×C61#55311yescharacteristic
326Dic61—22no—
327Dic61—22no—
328Dic61—22no—
329Dic61—41no—
330Dic61—41no—
331Dic61—41no—
332Dic61—41no—
333C2×#433—611no—
334C2×#423—611no—
335#2290—611no—
336#1924D6111yescharacteristic, complemented
337#1923—611no—
338#1917—611no—
339#1916—611no—
340#1870—611no—
341#1870—611no—
342#1832—611no—
343#1798—611no—
344#1797—611no—
345#1768—611no—
346#1753—611no—
347#1753—611no—
348C2×C61—81no—
349C2×C61#235211yescharacteristic
350C2×C61#292111yescharacteristic
351C2×C61#292511yescharacteristic
352C2×C61#293011yescharacteristic
353C2×C61#293311yescharacteristic
354C2×C61#299311yescharacteristic
355C2×C61#299511yescharacteristic
356D61—42no—
357C22×M16—611no—
358C22×M16—611no—
359C2×C4×D4—611no—
360C2×#117—611no—
361C22×C42—611no—
362#433—1224no—
363#423—1224no—
364C2×C4⋊C8—611no—
365C2×C4⋊C8—611no—
366C2×C4⋊C8—611no—
367C2×C4⋊C8—611no—
368C2×C4⋊C8—611no—
369C2×C4⋊C8C2×D6111yescharacteristic
370C2×C22⋊C8—611no—
371C2×C22⋊C8—611no—
372C2×C22⋊C8—611no—
373C2×C22⋊C8—611no—
374C2×C22⋊C8C2×D6111yescharacteristic
375C2×C22⋊C8C2×D6111yescharacteristic
376C2×#97—611no—
377C2×#97C2×D6111yescharacteristic
378C2×C4×C8—611no—
379C2×C4×C8—611no—
380#388—611no—
381#388—611no—
382#387—611no—
383#387—611no—
384#386—611no—
385#386—611no—
386#385—611no—
387#385—611no—
388C4×C4⋊C4—611no—
389C4×C22⋊C4—611no—
390C4×C22⋊C4C2×D6111yescharacteristic
391#376—611no—
392#336—611no—
393#336—611no—
394#336—611no—
395#336—611no—
396#336—611no—
397#336—611no—
398#336—611no—
399#336—611no—
400#336C2×D6111yescharacteristic
401#336C2×D6111yescharacteristic
402C61#2275511yescharacteristic, complemented, Sylow
403C22×D4—611no—
404C23×C4—611no—
405C23×C4—611no—
406C23×C4—611no—
407C23×C4C22×D6111yescharacteristic
408C2×M16—1222no—
409C2×M16—1222no—
410C2×M16—1222no—
411C2×M16—1222no—
412C2×M16—2441no—
413C2×M16—2441no—
414C22×C8—611no—
415C22×C8—611no—
416C22×C8—611no—
417C22×C8—611no—
418C22×C8C22×D6111yescharacteristic
419C22×C8C22×D6111yescharacteristic
420C22×C8C22×D6111yescharacteristic
421C22×C8C22×D6111yescharacteristic
422C4×D4—1222no—
423C4×D4—1222no—
424#117—1222no—
425#117—1222no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C22⋊C4—611no—
432C2×C22⋊C4—611no—
433C2×C22⋊C4—611no—
434C2×C22⋊C4—611no—
435C2×C22⋊C4—611no—
436C2×C22⋊C4—611no—
437C2×C22⋊C4C4×D6111yescharacteristic
438C2×C22⋊C4C4×D6111yescharacteristic
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—1222no—
445C2×C42—1222no—
446C2×C42C22×D6111yescharacteristic
447C2×C42C22×D6111yescharacteristic
448C4⋊C8—22no—
449C4⋊C8—614no—
450C4⋊C8—1222no—
451C4⋊C8—1222no—
452C4⋊C8—1222no—
453C4⋊C8—1222no—
454C22⋊C8—22no—
455C22⋊C8—41no—
456C22⋊C8—1222no—
457C22⋊C8—1222no—
458C22⋊C8—1222no—
459C22⋊C8—2441no—
460#97—41no—
461#97—1222no—
462C4×C8—1222no—
463C4×C8—2441no—
464#95—611no—
465#95—611no—
466#95—611no—
467#95—611no—
468#95—611no—
469#95—611no—
470#95—611no—
471#95—611no—
472#95C4×D6111yescharacteristic
473#95C4×D6111yescharacteristic
474C24—611no—
475C24C2×C4×D6111yescharacteristic
476C2×D4—1222no—
477C2×D4—2441no—
478C2×D4—2441no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—612no—
489C22×C4—612no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4—1222no—
501C22×C4—2441no—
502C22×C4—2441no—
503C22×C4—2441no—
504C22×C4C2×C4×D6111yescharacteristic
505C22×C4C2×C4×D6111yescharacteristic
506C22×C4C2×C4×D6111yescharacteristic
507C22×C4C2×C4×D6111yescharacteristic
508C22×C4C2×C4×D6111yescharacteristic
509C22×C4C23×D6111yescharacteristic
510M16—2444no—
511M16—2444no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—612no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—1221no—
530C2×C8—1221no—
531C2×C8—1221no—
532C2×C8—1221no—
533C2×C8—1221no—
534C2×C8—1221no—
535C2×C8D4×D6112yes—
536C4⋊C4—1222no—
537C4⋊C4—1222no—
538C4⋊C4—1222no—
539C4⋊C4—1222no—
540C4⋊C4—2441no—
541C22⋊C4—22no—
542C22⋊C4—41no—
543C22⋊C4—1222no—
544C22⋊C4—1222no—
545C22⋊C4—1222no—
546C22⋊C4—1222no—
547C22⋊C4—2441no—
548C22⋊C4—2441no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—612no—
554C42—612no—
555C42—1222no—
556C42—1222no—
557C42—1221no—
558C42—1221no—
559C42—1221no—
560C42—1221no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—612no—
569C23—1221no—
570C23—1221no—
571C23—1221no—
572C23—1221no—
573C23—1221no—
574C23—1221no—
575C23C22×C4×D6111yescharacteristic
576D4—2444no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—612no—
596C2×C4—612no—
597C2×C4—612no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1222no—
605C2×C4—1222no—
606C2×C4—1222no—
607C2×C4—1222no—
608C2×C4—1221no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—1221no—
613C2×C4—1221no—
614C2×C4—1221no—
615C2×C4—1221no—
616C2×C4—1221no—
617C2×C4—1221no—
618C2×C4—1221no—
619C2×C4—1221no—
620C2×C4—2444no—
621C2×C4—2444no—
622C2×C4#1451978512yes—
623C2×C4C2×D4×D6111yescharacteristic
624C2×C4#41×D6111yescharacteristic
625C2×C4#41×D6111yescharacteristic
626C2×C4#41×D6111yescharacteristic
627C2×C4#1451982211yescharacteristic
628C2×C4#1451982411yescharacteristic
629C8—22no—
630C8—41no—
631C8—41no—
632C8—41no—
633C8—1222no—
634C8—2441no—
635C8—2441no—
636C8—2441no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—1222no—
645C22—1222no—
646C22—1222no—
647C22—2441no—
648C22—2441no—
649C22—2441no—
650C22—2441no—
651C22#117×D6111yescharacteristic
652C22C4×D4×D6111yescharacteristic
653C22#1684024111yescharacteristic
654C22C2×#1451978511yescharacteristic
655C22#1684052711yescharacteristic
656C22#1684052711yescharacteristic
657C22#1684052811yescharacteristic
658C4—22no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—1222no—
664C4—1222no—
665C4—1222no—
666C4—2441no—
667C4—2441no—
668C4—2441no—
669C4—2441no—
670C4#1684040111yescharacteristic
671C4#1684042011yescharacteristic
672C4#1684044811yescharacteristic
673C4#1684045711yescharacteristic
674C2—81no—
675C2—2442no—
676C2#2144874711yescharacteristic
677C2#2145445311yescharacteristic
678C2#2145448611yescharacteristic
679C2#2145451711yescharacteristic
680C2#2145454511yescharacteristic
681C2#2145496311yescharacteristic
682C2#2145498511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1924C2
prime radicalC22×C22⋊D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1924D61
hypocenterC61#22755
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. C2×#16839820C2semidirect
2. C2×#16839784C2semidirect
4. #21446427C2semidirect
5. #21446386C2semidirect
6. #21446373C2semidirect
9. #21445937C2semidirect
10. #21445801C2semidirect
11. #21445798C2semidirect
12. #21445679C2semidirect
13. #21445604C2semidirect
14. #21445599C2semidirect
15. C61×#1924C2semidirect
101. #14519706D4semidirect
336. #1924D61semidirect
402. C61#22755semidirect

Maximal subgroups

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

subgroupindex
C2×#168398202
C2×#168397842
#214482652
#214464272
#214463862
#214463732
#214461132
#214459372
#214458012
#214457982
#214456792
#214456042
#214455992
C61×#19242
#2275561