Finite Group Databasebeta

← #15914697

Subgroups — #15914697

Order 3328.

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×#11718726C211yesmaximal, characteristic, complemented
2C2×#11718727C211yesmaximal, characteristic
3#13119785C211yesmaximal, characteristic
4#13116312C211yesmaximal, characteristic, complemented
5#13116307C211yesmaximal, characteristic, complemented
6#13116221C211yesmaximal, characteristic
7#13116207C211yesmaximal, characteristic
8#13115784C211yesmaximal, characteristic, complemented
9#13115599C211yesmaximal, characteristic, complemented
10#13115594C211yesmaximal, characteristic, complemented
11#13115560C211yesmaximal, characteristic, complemented
12#13115463C211yesmaximal, characteristic
13#13115456C211yesmaximal, characteristic
14#13114664C211yesmaximal, characteristic
15C13×#2370C211yesmaximal, characteristic, complemented
16C2×C13×#125C2211yescharacteristic
17C2×#88151—21no—
18C2×#88151—21no—
19C2×C4×D52C2211yescharacteristic
20C2×#88123C2211yescharacteristic
21C13×#389—21no—
22C13×#389C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#387—21no—
25C13×#387—21no—
26C4×C13×C4⋊C4—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30C4×C13×C4⋊C4C2211yescharacteristic
31#11718727—24no—
32#11718726—24no—
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43#11718600C2211yescharacteristic
44#11718600C2211yescharacteristic
45#11718596C2211yescharacteristic
46#11718596C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51#11718338—21no—
52#11718338—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D52C2311yescharacteristic
62C22×C4×D13—21no—
63C22×Dic26—21no—
64C13×#125—22no—
65C13×#125D414yes—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4D411yescharacteristic
71C2×C13×C4⋊C4D411yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C42×C13—21no—
77C2×C42×C13—21no—
78C2×C42×C13—21no—
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×#6103—21no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99#88151—44no—
100#88151—44no—
101C4×D52—22no—
102C4×D52—22no—
103#88123—22no—
104#88123—22no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95D411yescharacteristic
111C13×#95D411yescharacteristic
112#88049—22no—
113#88049—22no—
114#88049—22no—
115#88049Q814yescomplemented
116#88048—22no—
117#88048—22no—
118#88048—22no—
119#88047—22no—
120#88047—22no—
121#88047—22no—
122C4⋊#1055—22no—
123C4⋊#1055—22no—
124C4⋊#1055—22no—
125#88043—22no—
126#25465—131nomaximal, Sylow
127C23×D13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2411yescharacteristic
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C2×D52—21no—
143C2×D52—21no—
144C2×D52—21no—
145C2×D52—21no—
146C2×D52—21no—
147C2×D52C2×Q812yes—
148C2×C4×D13—42no—
149C2×C4×D13—42no—
150C2×C4×D13—42no—
151C2×Dic26—42no—
152C2×Dic26—42no—
153C2×Dic26—42no—
154C13×C4⋊C4—24no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—42no—
164C13×C4⋊C4—81no—
165C13×C4⋊C4C2×D412yes—
166C13×C4⋊C4C2×D412yes—
167C13×C4⋊C4C2×Q812yes—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—42no—
173C42×C13—81no—
174C42×C13—81no—
175C42×C13C2×D412yes—
176C42×C13#4112yes—
177#6103—42no—
178#6103—42no—
179#6103—42no—
180#6103—42no—
181#6103—42no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—42no—
189C4⋊Dic13—42no—
190C4⋊Dic13—42no—
191C4⋊Dic13—42no—
192C4⋊Dic13—42no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055C2×Q812yes—
204C2×#1055#4112yes—
205C2×#501—131no—
206C2×#478—131no—
207#2542—131no—
208#2370D1311yescharacteristic, complemented
209#2084—131no—
210#2083—131no—
211#2067—131no—
212#2065—131no—
213#1987—131no—
214#1948—131no—
215#1947—131no—
216#1940—131no—
217#1926—131no—
218#1925—131no—
219#1762—131no—
220C23×C13C22×D411yescharacteristic
221C22×D13—22no—
222C22×D13—41no—
223C22×D13—41no—
224C22×D13—41no—
225C22×D13—41no—
226C22×D13—41no—
227C22×D13—41no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—22no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13#12112yes—
255C2×C4×C13#12112yes—
256C2×C4×C13AGL(1,ℤ/8)12yes—
257C2×C4×C13AGL(1,ℤ/8)12yes—
258C2×C4×C13C22×D411yescharacteristic
259C2×C4×C13C22×Q811yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C2×C4×C13C2×#4111yescharacteristic
262C2×C4×C132−1+411yescharacteristic
263C2×C4×C132−1+411yescharacteristic
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273D52—22no—
274D52—22no—
275D52—41no—
276D52—41no—
277C4×D13—84no—
278Dic26—84no—
279#1055—22no—
280#1055—22no—
281#1055—41no—
282#1055—41no—
283C2×C4⋊Q8—131no—
284C2×#125C2×D1311yescharacteristic
285C2×C22⋊Q8—261no—
286C2×C22⋊Q8—261no—
287C2×C4×D4—131no—
288#501—264no—
289#478—264no—
290C2×#107—131no—
291C2×#107—131no—
292C2×#107—131no—
293C2×#106—131no—
294C2×#106—131no—
295C2×#106—131no—
296C2×C4⋊C8—131no—
297C2×C4⋊C8—131no—
298C2×C4⋊C8—131no—
299C2×#102—131no—
300C2×#102—131no—
301C2×#102—131no—
302C2×#102—131no—
303C2×#97—131no—
304#399—261no—
305#399—261no—
306#390—131no—
307#390—131no—
308#389—21no—
309#389C2×D1311yescharacteristic
310#389C2×D1311yescharacteristic
311#387—21no—
312#387—21no—
313#384—131no—
314#384—131no—
315C4×C4⋊C4—21no—
316C4×C4⋊C4C2×D1311yescharacteristic
317C4×C4⋊C4C2×D1311yescharacteristic
318C4×C4⋊C4C2×D1311yescharacteristic
319C4×C4⋊C4C2×D1311yescharacteristic
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#336—131no—
327#336—131no—
328C22×C13C2×#12111yescharacteristic
329C22×C13#54711yescharacteristic
330C22×C13D4×Q811yescharacteristic
331C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C13#57711yescharacteristic
334C22×C13#57811yescharacteristic
335C2×D13—42no—
336C2×D13—42no—
337C2×D13—42no—
338C2×D13—81no—
339C2×D13—81no—
340C2×D13—81no—
341C2×D13—81no—
342C4×C13—22no—
343C4×C13—22no—
344C4×C13—22no—
345C4×C13—22no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13—42no—
349C4×C13—42no—
350C4×C13—42no—
351C4×C13—81no—
352C4×C13#53311yescharacteristic
353C4×C13#54111yescharacteristic
354C4×C13#54811yescharacteristic
355C4×C13D4×Q811yescharacteristic
356Dic13—81no—
357Dic13—81no—
358Dic13—81no—
359C22×Q8—261no—
360C22×D4—131no—
361C23×C4—261no—
362C22×C8—131no—
363C22×C8—131no—
364C22×C8—131no—
365C22×C8—131no—
366C4⋊Q8—262no—
367C4⋊Q8—262no—
368#125—22no—
369#125D5214yes—
370C22⋊Q8—524no—
371C22⋊Q8—524no—
372C4×D4—262no—
373C4×D4—262no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4C22⋊D1311yescharacteristic
387C2×C4⋊C4C22⋊D1311yescharacteristic
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C4⋊C4C22×D1311yescharacteristic
390C2×C4⋊C4C22×D1311yescharacteristic
391C2×C4⋊C4C22×D1311yescharacteristic
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C22⋊C4—261no—
395C2×C22⋊C4—261no—
396C2×C22⋊C4—261no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42C22×D1311yescharacteristic
401C2×C42C22×D1311yescharacteristic
402C2×C42C22×D1311yescharacteristic
403#107—262no—
404#107—262no—
405#107—262no—
406#106—262no—
407#106—262no—
408#106—262no—
409C4⋊C8—262no—
410C4⋊C8—262no—
411C4⋊C8—262no—
412#102—134no—
413#102—262no—
414#102—262no—
415#102—262no—
416#97—262no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95C22⋊D1311yescharacteristic
423#95C22⋊D1311yescharacteristic
424C2×C13#242911yescharacteristic
425C2×C13#303811yescharacteristic
426C2×C13#304611yescharacteristic
427C2×C13#334311yescharacteristic
428C2×C13#334511yescharacteristic
429C2×C13#338411yescharacteristic
430C2×C13#338611yescharacteristic
431D13—82no—
432C24—261no—
433C2×Q8—522no—
434C2×Q8—522no—
435C2×Q8—522no—
436C2×D4—132no—
437C2×D4—261no—
438C2×D4—261no—
439C2×D4—261no—
440C2×D4—261no—
441C2×D4—261no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—522no—
450C22×C4—522no—
451C22×C4—522no—
452C22×C4C2×C22⋊D1311yescharacteristic
453C22×C4C2×C22⋊D1311yescharacteristic
454C22×C4C2×C22⋊D1311yescharacteristic
455C22×C4C2×C22⋊D1311yescharacteristic
456C22×C4C2×C22⋊D1311yescharacteristic
457C22×C4C2×C22⋊D1311yescharacteristic
458C22×C4C23×D1311yescharacteristic
459C2×C8—132no—
460C2×C8—132no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—81no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—522no—
489C4⋊C4—522no—
490C4⋊C4—522no—
491C4⋊C4—522no—
492C4⋊C4—522no—
493C4⋊C4C2×D5212yes—
494C4⋊C4C2×D5212yes—
495C4⋊C4Q8×D1312yes—
496C22⋊C4—522no—
497C22⋊C4—522no—
498C22⋊C4—522no—
499C22⋊C4—522no—
500C22⋊C4—522no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—42no—
506C42—81no—
507C42—81no—
508C42C2×D5212yes—
509C42#612712yes—
510C13#2546511yescharacteristic, complemented, Sylow
511C23—262no—
512C23—521no—
513C23—521no—
514C23—521no—
515C23—521no—
516C23—521no—
517C23—521no—
518C23C22×C22⋊D1311yescharacteristic
519Q8—1044no—
520D4—262no—
521D4—262no—
522D4—521no—
523D4—521no—
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—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
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—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—1044no—
560C2×C4#8818412yes—
561C2×C4#8818412yes—
562C2×C4#8820312yes—
563C2×C4#8820312yes—
564C2×C4C22×D5211yescharacteristic
565C2×C4C2×#612711yescharacteristic
566C2×C4C2×Q8×D1311yescharacteristic
567C2×C4#8825411yescharacteristic
568C2×C4#41×D1311yescharacteristic
569C2×C4#8825711yescharacteristic
570C8—262no—
571C8—262no—
572C8—521no—
573C8—521no—
574C22—522no—
575C22—522no—
576C22—522no—
577C22—1041no—
578C22—1041no—
579C22—1041no—
580C22—1041no—
581C22C2×#8818411yescharacteristic
582C22Q8×C22⋊D1311yescharacteristic
583C22C2×#8820311yescharacteristic
584C22C2×#8820311yescharacteristic
585C22#1171952911yescharacteristic
586C22#1171954111yescharacteristic
587C22#1171954311yescharacteristic
588C4—22no—
589C4—22no—
590C4—22no—
591C4—22no—
592C4—42no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—1041no—
599C4—1041no—
600C4—1041no—
601C4Q8×D5211yescharacteristic
602C4#1171928111yescharacteristic
603C4#1171928311yescharacteristic
604C4#1171928811yescharacteristic
605C2—1042no—
606C2#1311842911yescharacteristic
607C2#1312431611yescharacteristic
608C2#1312438611yescharacteristic
609C2#1312727611yescharacteristic
610C2#1312730011yescharacteristic
611C2#1312773511yescharacteristic
612C2#1312775311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2370C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2370D13
hypocenterC13#25465
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
1. C2×#11718726C2semidirect
4. #13116312C2semidirect
5. #13116307C2semidirect
8. #13115784C2semidirect
9. #13115599C2semidirect
10. #13115594C2semidirect
11. #13115560C2semidirect
15. C13×#2370C2semidirect
115. #88049Q8semidirect
208. #2370D13semidirect
510. C13#25465semidirect

Maximal subgroups

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

subgroupindex
C2×#117187262
C2×#117187272
#131197852
#131163122
#131163072
#131162212
#131162072
#131157842
#131155992
#131155942
#131155602
#131154632
#131154562
#131146642
C13×#23702
#2546513