Finite Group Databasebeta

← #29731791

Subgroups — #29731791

Order 15616.

812 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840172C211yesmaximal, characteristic, complemented
2C2×#16840059C211yesmaximal, characteristic
3#21450768C211yesmaximal, characteristic
4#21447295C211yesmaximal, characteristic, complemented
5#21447290C211yesmaximal, characteristic, complemented
6#21447204C211yesmaximal, characteristic
7#21447190C211yesmaximal, characteristic
8#21446767C211yesmaximal, characteristic, complemented
9#21446582C211yesmaximal, characteristic, complemented
10#21446577C211yesmaximal, characteristic, complemented
11#21446543C211yesmaximal, characteristic, complemented
12#21446446C211yesmaximal, characteristic
13#21446439C211yesmaximal, characteristic
14#21445647C211yesmaximal, characteristic
15C61×#2370C211yesmaximal, characteristic, complemented
16C2×#14519777C2211yescharacteristic
17C2×#14519757—21no—
18C2×#14519757—21no—
19C2×C4×D244C2211yescharacteristic
20#16840172—24no—
21#16840059—24no—
22C2×#14519710C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519710C2211yescharacteristic
25C2×#14519708C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×#14519708C2211yescharacteristic
28C2×C4⋊#92418C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519688C2211yescharacteristic
36#16839699—21no—
37#16839699—21no—
38#16839664C2211yescharacteristic
39#16839664C2211yescharacteristic
40#16839632C2211yescharacteristic
41#16839632C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C2×#125×C61C2211yescharacteristic
51C61×#389—21no—
52C61×#389C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#387—21no—
55C61×#387—21no—
56C4×C4⋊C4×C61—21no—
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C4×C4⋊C4×C61C2211yescharacteristic
60C4×C4⋊C4×C61C2211yescharacteristic
61C22×Dic122—21no—
62C22×D244C2311yescharacteristic
63C22×C4×D61—21no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519777—22no—
69#14519777—22no—
70#14519757—44no—
71#14519757—44no—
72C4×D244—22no—
73C4×D244—22no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61—21no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87#14519710—22no—
88#14519710—22no—
89#14519710—22no—
90#14519708—22no—
91#14519708—22no—
92#14519708—22no—
93C4⋊#92418—22no—
94C4⋊#92418—22no—
95C4⋊#92418—22no—
96#14519697—22no—
97#14519697—22no—
98#14519697—22no—
99#14519697Q814yescomplemented
100#14519688—22no—
101#125×C61—22no—
102#125×C61D414yes—
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61D411yescharacteristic
108C2×C4⋊C4×C61D411yescharacteristic
109C2×C4⋊C4×C61C2311yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C42×C61—21no—
114C2×C42×C61—21no—
115C2×C42×C61—21no—
116C2×C42×C61C2311yescharacteristic
117C2×C42×C61C2311yescharacteristic
118C2×C42×C61C2311yescharacteristic
119#95×C61—21no—
120#95×C61—21no—
121#95×C61—21no—
122#95×C61—21no—
123#95×C61—21no—
124#95×C61D411yescharacteristic
125#95×C61D411yescharacteristic
126C23×D61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244C2×Q812yes—
147C2×C4×D61—42no—
148C2×C4×D61—42no—
149C2×C4×D61—42no—
150C2×Dic122—42no—
151C2×Dic122—42no—
152C2×Dic122—42no—
153C4⋊C4×C61—24no—
154C4⋊C4×C61—24no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—22no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—42no—
163C4⋊C4×C61—81no—
164C4⋊C4×C61C2×D412yes—
165C4⋊C4×C61C2×D412yes—
166C4⋊C4×C61C2×Q812yes—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—21no—
171C42×C61—42no—
172C42×C61—81no—
173C42×C61—81no—
174C42×C61C2×D412yes—
175C42×C61#4112yes—
176#11758198—42no—
177#11758198—42no—
178#11758198—42no—
179#11758198—42no—
180#11758198—42no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—42no—
188C4⋊Dic61—42no—
189C4⋊Dic61—42no—
190C4⋊Dic61—42no—
191C4⋊Dic61—42no—
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×#92418C2×Q812yes—
203C2×#92418#4112yes—
204C23×C61C22×D411yescharacteristic
205C22×D61—22no—
206C22×D61—41no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—41no—
211C22×D61—41no—
212C2×C4×C61—21no—
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—22no—
221C2×C4×C61—22no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—22no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61#12112yes—
239C2×C4×C61#12112yes—
240C2×C4×C61AGL(1,ℤ/8)12yes—
241C2×C4×C61AGL(1,ℤ/8)12yes—
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C22×Q811yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C612−1+411yescharacteristic
247C2×C4×C612−1+411yescharacteristic
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257D244—22no—
258D244—22no—
259D244—41no—
260D244—41no—
261C4×D61—84no—
262Dic122—84no—
263#92418—22no—
264#92418—22no—
265#92418—41no—
266#92418—41no—
267#25465—611nomaximal, Sylow
268C22×C61C2×#12111yescharacteristic
269C22×C61#54711yescharacteristic
270C22×C61D4×Q811yescharacteristic
271C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
272C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
273C22×C61#57711yescharacteristic
274C22×C61#57811yescharacteristic
275C2×D61—42no—
276C2×D61—42no—
277C2×D61—42no—
278C2×D61—81no—
279C2×D61—81no—
280C2×D61—81no—
281C2×D61—81no—
282C4×C61—22no—
283C4×C61—22no—
284C4×C61—22no—
285C4×C61—22no—
286C4×C61—41no—
287C4×C61—41no—
288C4×C61—42no—
289C4×C61—42no—
290C4×C61—42no—
291C4×C61—81no—
292C4×C61#53311yescharacteristic
293C4×C61#54111yescharacteristic
294C4×C61#54811yescharacteristic
295C4×C61D4×Q811yescharacteristic
296Dic61—81no—
297Dic61—81no—
298Dic61—81no—
299C2×#501—611no—
300C2×#478—611no—
301#2542—611no—
302#2370D6111yescharacteristic, complemented
303#2084—611no—
304#2083—611no—
305#2067—611no—
306#2065—611no—
307#1987—611no—
308#1948—611no—
309#1947—611no—
310#1940—611no—
311#1926—611no—
312#1925—611no—
313#1762—611no—
314C2×C61#242911yescharacteristic
315C2×C61#303811yescharacteristic
316C2×C61#304611yescharacteristic
317C2×C61#334311yescharacteristic
318C2×C61#334511yescharacteristic
319C2×C61#338411yescharacteristic
320C2×C61#338611yescharacteristic
321D61—82no—
322C2×C4⋊Q8—611no—
323C2×#125C2×D6111yescharacteristic
324C2×C22⋊Q8—1221no—
325C2×C22⋊Q8—1221no—
326C2×C4×D4—611no—
327#501—1224no—
328#478—1224no—
329C2×#107—611no—
330C2×#107—611no—
331C2×#107—611no—
332C2×#106—611no—
333C2×#106—611no—
334C2×#106—611no—
335C2×C4⋊C8—611no—
336C2×C4⋊C8—611no—
337C2×C4⋊C8—611no—
338C2×#102—611no—
339C2×#102—611no—
340C2×#102—611no—
341C2×#102—611no—
342C2×#97—611no—
343#399—1221no—
344#399—1221no—
345#390—611no—
346#390—611no—
347#389—21no—
348#389C2×D6111yescharacteristic
349#389C2×D6111yescharacteristic
350#387—21no—
351#387—21no—
352#384—611no—
353#384—611no—
354C4×C4⋊C4—21no—
355C4×C4⋊C4C2×D6111yescharacteristic
356C4×C4⋊C4C2×D6111yescharacteristic
357C4×C4⋊C4C2×D6111yescharacteristic
358C4×C4⋊C4C2×D6111yescharacteristic
359#340—611no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340—611no—
364#340—611no—
365#336—611no—
366#336—611no—
367C61#2546511yescharacteristic, complemented, Sylow
368C22×Q8—1221no—
369C22×D4—611no—
370C23×C4—1221no—
371C22×C8—611no—
372C22×C8—611no—
373C22×C8—611no—
374C22×C8—611no—
375C4⋊Q8—1222no—
376C4⋊Q8—1222no—
377#125—22no—
378#125D24414yes—
379C22⋊Q8—2444no—
380C22⋊Q8—2444no—
381C4×D4—1222no—
382C4×D4—1222no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4C22⋊D6111yescharacteristic
396C2×C4⋊C4C22⋊D6111yescharacteristic
397C2×C4⋊C4C22×D6111yescharacteristic
398C2×C4⋊C4C22×D6111yescharacteristic
399C2×C4⋊C4C22×D6111yescharacteristic
400C2×C4⋊C4C22×D6111yescharacteristic
401C2×C22⋊C4—1221no—
402C2×C22⋊C4—1221no—
403C2×C22⋊C4—1221no—
404C2×C22⋊C4—1221no—
405C2×C22⋊C4—1221no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42C22×D6111yescharacteristic
410C2×C42C22×D6111yescharacteristic
411C2×C42C22×D6111yescharacteristic
412#107—1222no—
413#107—1222no—
414#107—1222no—
415#106—1222no—
416#106—1222no—
417#106—1222no—
418C4⋊C8—1222no—
419C4⋊C8—1222no—
420C4⋊C8—1222no—
421#102—614no—
422#102—1222no—
423#102—1222no—
424#102—1222no—
425#97—1222no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95C22⋊D6111yescharacteristic
432#95C22⋊D6111yescharacteristic
433C24—1221no—
434C2×Q8—2442no—
435C2×Q8—2442no—
436C2×Q8—2442no—
437C2×D4—612no—
438C2×D4—1221no—
439C2×D4—1221no—
440C2×D4—1221no—
441C2×D4—1221no—
442C2×D4—1221no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1221no—
450C22×C4—2442no—
451C22×C4—2442no—
452C22×C4—2442no—
453C22×C4C2×C22⋊D6111yescharacteristic
454C22×C4C2×C22⋊D6111yescharacteristic
455C22×C4C2×C22⋊D6111yescharacteristic
456C22×C4C2×C22⋊D6111yescharacteristic
457C22×C4C2×C22⋊D6111yescharacteristic
458C22×C4C2×C22⋊D6111yescharacteristic
459C22×C4C23×D6111yescharacteristic
460C2×C8—612no—
461C2×C8—612no—
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—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—24no—
476C4⋊C4—24no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—42no—
482C4⋊C4—81no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—2442no—
490C4⋊C4—2442no—
491C4⋊C4—2442no—
492C4⋊C4—2442no—
493C4⋊C4—2442no—
494C4⋊C4C2×D24412yes—
495C4⋊C4C2×D24412yes—
496C4⋊C4Q8×D6112yes—
497C22⋊C4—2442no—
498C22⋊C4—2442no—
499C22⋊C4—2442no—
500C22⋊C4—2442no—
501C22⋊C4—2442no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—42no—
507C42—81no—
508C42—81no—
509C42C2×D24412yes—
510C42#1175822212yes—
511C23—1222no—
512C23—2441no—
513C23—2441no—
514C23—2441no—
515C23—2441no—
516C23—2441no—
517C23—2441no—
518C23C22×C22⋊D6111yescharacteristic
519Q8—4884no—
520D4—1222no—
521D4—1222no—
522D4—2441no—
523D4—2441no—
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—22no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—4884no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4#1451975112yes—
561C2×C4#1451975112yes—
562C2×C4#1451980212yes—
563C2×C4#1451980212yes—
564C2×C4C22×D24411yescharacteristic
565C2×C4C2×Q8×D6111yescharacteristic
566C2×C4#41×D6111yescharacteristic
567C2×C4C2×#1175822211yescharacteristic
568C2×C4#1451982411yescharacteristic
569C2×C4#1451982511yescharacteristic
570C8—1222no—
571C8—1222no—
572C8—2441no—
573C8—2441no—
574C22—4881no—
575C22—4881no—
576C22—4881no—
577C22—4881no—
578C22—2442no—
579C22—2442no—
580C22—2442no—
581C22C2×#1451975111yescharacteristic
582C22#1684041111yescharacteristic
583C22Q8×C22⋊D6111yescharacteristic
584C22C2×#1451980211yescharacteristic
585C22C2×#1451980211yescharacteristic
586C22#1684057311yescharacteristic
587C22#1684057711yescharacteristic
588C4—22no—
589C4—22no—
590C4—22no—
591C4—22no—
592C4—42no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—4881no—
599C4—4881no—
600C4—4881no—
601C4#1684031611yescharacteristic
602C4#1684037011yescharacteristic
603C4#1684042411yescharacteristic
604C4Q8×D24411yescharacteristic
605C2—4882no—
606C2#2144941211yescharacteristic
607C2#2145529911yescharacteristic
608C2#2145536911yescharacteristic
609C2#2145825911yescharacteristic
610C2#2145828311yescharacteristic
611C2#2145871811yescharacteristic
612C2#2145873611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2370C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#2370D61
hypocenterC61#25465
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
1. C2×#16840172C2semidirect
4. #21447295C2semidirect
5. #21447290C2semidirect
8. #21446767C2semidirect
9. #21446582C2semidirect
10. #21446577C2semidirect
11. #21446543C2semidirect
15. C61×#2370C2semidirect
99. #14519697Q8semidirect
302. #2370D61semidirect
367. C61#25465semidirect

Maximal subgroups

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

subgroupindex
C2×#168401722
C2×#168400592
#214507682
#214472952
#214472902
#214472042
#214471902
#214467672
#214465822
#214465772
#214465432
#214464462
#214464392
#214456472
C61×#23702
#2546561