Finite Group Databasebeta

← #15763148

Subgroups — #15763148

Order 3328.

716 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718694C211yesmaximal, characteristic
2C2×#11718644C211yesmaximal, characteristic, complemented
3#13114920C211yesmaximal, characteristic, complemented
4C2×#11718129C211yesmaximal, characteristic
5C2×#11718120C211yesmaximal, characteristic, complemented
6#13112714C211yesmaximal, characteristic, complemented
7C13×#2618C211yesmaximal, characteristic
8C2×C13×#123—21no—
9C2×C13×#121C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic13C2211yescharacteristic
12C22×#6101—21no—
13C13×#398—21no—
14C13×#396—22no—
15C13×#394—21no—
16C13×#386—21no—
17C13×#380C2211yescharacteristic
18C2×#88072—21no—
19C2×#88071—21no—
20C2×#88071C2211yescharacteristic
21C2×C22⋊#1055C2211yescharacteristic
22C2×C22⋊#1055C2211yescharacteristic
23#11718694—22no—
24#11718694—22no—
25#11718644—22no—
26#11718644—22no—
27C2×#88047—21no—
28#11718129—22no—
29#11718121—22no—
30#11718120—22no—
31C22×D4×C13—21no—
32C22×D4×C13D411yescharacteristic
33C23×C4×C13D411yescharacteristic
34C23×C4×C13D411yescharacteristic
35C23×C4×C13C2311yescharacteristic
36C23×Dic13—21no—
37C23×Dic13—21no—
38C13×#123—42no—
39C13×#123—42no—
40C13×#121—21no—
41C13×#121—21no—
42C13×#121—21no—
43C13×#121—21no—
44C2×C13×C4⋊C4—22no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4D411yescharacteristic
52C2×C13×C4⋊C4D412yes—
53C2×C13×C22⋊C4—22no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—22no—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13—21no—
61C2×C4⋊Dic13—21no—
62C2×C4⋊Dic13D412yes—
63C2×#6101—24no—
64C2×#6101—42no—
65C2×#6101—42no—
66C22×#1055—21no—
67C22×#1055—21no—
68C13×#95—22no—
69C13×#95—21no—
70#88072—24no—
71#88071—24no—
72#88071—21no—
73#88071D412yes—
74C22⋊#1055—21no—
75C22⋊#1055—21no—
76C22⋊#1055—21no—
77C22⋊#1055D412yes—
78#88047—24no—
79#9919—131nomaximal, Sylow
80C24×C13—21no—
81C24×C13C2×D411yescharacteristic
82C2×D4×C13—21no—
83C2×D4×C13—21no—
84C2×D4×C13—42no—
85C2×D4×C13—41no—
86C2×D4×C13—41no—
87C2×D4×C13—41no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—22no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—21no—
102C22×C4×C13—42no—
103C22×C4×C13—42no—
104C22×C4×C13D812yes—
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×D411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13#4111yescharacteristic
111C22×Dic13—24no—
112C22×Dic13—22no—
113C22×Dic13—22no—
114C22×Dic13—42no—
115C22×Dic13—41no—
116C22×Dic13—41no—
117C22×Dic13—41no—
118C22×Dic13—41no—
119C22×Dic13—41no—
120C22×Dic13—41no—
121C22×Dic13—41no—
122C22×Dic13—41no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—21no—
125C13×C4⋊C4—42no—
126C13×C4⋊C4—44no—
127C13×C4⋊C4—41no—
128C13×C4⋊C4—41no—
129C13×C4⋊C4—41no—
130C13×C4⋊C4—41no—
131C13×C22⋊C4—44no—
132C13×C22⋊C4—41no—
133C13×C22⋊C4—41no—
134C13×C22⋊C4—41no—
135C13×C22⋊C4—41no—
136C13×C22⋊C4—82no—
137C4⋊Dic13—22no—
138C4⋊Dic13—22no—
139C4⋊Dic13—41no—
140C4⋊Dic13—41no—
141#6101—48no—
142C2×#1055—22no—
143C2×#1055—42no—
144C2×#1055—42no—
145C2×#1055—41no—
146C2×#480—131no—
147#2618D1311yescharacteristic
148C2×#398—131no—
149#1823—131no—
150C2×#327—131no—
151C2×#324—131no—
152#1294—131no—
153C23×C13—22no—
154C23×C13—22no—
155C23×C13—41no—
156C23×C13—41no—
157C23×C13—41no—
158C23×C13—42no—
159C23×C13—42no—
160C23×C13#12011yescharacteristic
161C23×C13#12011yescharacteristic
162C23×C13#12111yescharacteristic
163C23×C13C2×D811yescharacteristic
164C23×C13#13511yescharacteristic
165C23×C13AGL(1,ℤ/8)11yescharacteristic
166C23×C13AGL(1,ℤ/8)11yescharacteristic
167D4×C13—42no—
168D4×C13—81no—
169D4×C13—81no—
170D4×C13—81no—
171D4×C13—81no—
172D4×C13—81no—
173C2×C4×C13—22no—
174C2×C4×C13—22no—
175C2×C4×C13—22no—
176C2×C4×C13—22no—
177C2×C4×C13—22no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—42no—
187C2×C4×C13—41no—
188C2×C4×C13—41no—
189C2×C4×C13—42no—
190C2×C4×C13—41no—
191C2×C4×C13—41no—
192C2×C4×C13—42no—
193C2×C4×C13—42no—
194C2×C4×C13—42no—
195C2×C4×C13—81no—
196C2×C4×C13#12011yescharacteristic
197C2×C4×C13#12111yescharacteristic
198C2×C4×C13#12111yescharacteristic
199C2×C4×C13#12711yescharacteristic
200C2×Dic13—24no—
201C2×Dic13—44no—
202C2×Dic13—44no—
203C2×Dic13—42no—
204C2×Dic13—42no—
205C2×Dic13—42no—
206C2×Dic13—42no—
207C2×Dic13—42no—
208C2×Dic13—81no—
209C2×Dic13—81no—
210C2×Dic13—81no—
211C2×Dic13—81no—
212#1055—42no—
213#1055—81no—
214C2×#123—21no—
215C2×#121C2×D1311yescharacteristic
216C22×C4⋊C4—131no—
217C22×C4⋊C4—261no—
218C22×C4⋊C4C2×D1311yescharacteristic
219#480—262no—
220#480—262no—
221C2×#107—261no—
222C2×#102—261no—
223C2×C22⋊C8—131no—
224C2×C22⋊C8—131no—
225#398—21no—
226#398—262no—
227#398—262no—
228#396—22no—
229#394—21no—
230#386—21no—
231#380C2×D1311yescharacteristic
232C2×#95—131no—
233C2×#95—261no—
234#340—262no—
235#327—262no—
236#324—262no—
237C22×C13—22no—
238C22×C13—22no—
239C22×C13—22no—
240C22×C13—22no—
241C22×C13—21no—
242C22×C13—21no—
243C22×C13—21no—
244C22×C13—21no—
245C22×C13—82no—
246C22×C13—82no—
247C22×C13—81no—
248C22×C13—81no—
249C22×C13—81no—
250C22×C13#39211yescharacteristic
251C22×C13#44711yescharacteristic
252C22×C13#44711yescharacteristic
253C22×C13#44911yescharacteristic
254C22×C13#44911yescharacteristic
255C22×C13#45612yes—
256C22×C13#45812yes—
257C22×C13#46611yescharacteristic
258C22×C13#46911yescharacteristic
259C4×C13—21no—
260C4×C13—21no—
261C4×C13—21no—
262C4×C13—21no—
263C4×C13—42no—
264C4×C13—82no—
265C4×C13—81no—
266C4×C13—81no—
267Dic13—44no—
268Dic13—82no—
269C22×D4—21no—
270C22×D4C22⋊D1311yescharacteristic
271C23×C4—261no—
272C23×C4—261no—
273C23×C4C22⋊D1311yescharacteristic
274C23×C4C22⋊D1311yescharacteristic
275C23×C4C22×D1311yescharacteristic
276C22×C8—261no—
277C22×C8—261no—
278#123—42no—
279#123—42no—
280#121—21no—
281#121—21no—
282#121—21no—
283#121—21no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—132no—
292C2×C4⋊C4—261no—
293C2×C4⋊C4—261no—
294C2×C4⋊C4—261no—
295C2×C4⋊C4—261no—
296C2×C4⋊C4—264no—
297C2×C4⋊C4—261no—
298C2×C4⋊C4—522no—
299C2×C4⋊C4—522no—
300C2×C4⋊C4C22⋊D1311yescharacteristic
301C2×C4⋊C4C22⋊D1312yes—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—22no—
306#107—264no—
307#102—264no—
308C22⋊C8—132no—
309C22⋊C8—261no—
310C22⋊C8—261no—
311C22⋊C8—261no—
312#95—22no—
313#95—21no—
314#95—132no—
315#95—264no—
316#95—261no—
317C2×C13—21no—
318C2×C13—21no—
319C2×C13—21no—
320C2×C13—21no—
321C2×C13—161no—
322C2×C13#160912yes—
323C2×C13#161012yes—
324C2×C13#199911yescharacteristic
325C2×C13#200511yescharacteristic
326C2×C13#202211yescharacteristic
327C24—21no—
328C24C2×C22⋊D1311yescharacteristic
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—42no—
332C2×D4—41no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—41no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—264no—
352C22×C4—262no—
353C22×C4—262no—
354C22×C4—522no—
355C22×C4—521no—
356C22×C4—521no—
357C22×C4—521no—
358C22×C4—521no—
359C22×C4—521no—
360C22×C4—521no—
361C22×C4—521no—
362C22×C4—521no—
363C22×C4#610412yes—
364C22×C4D4×D1311yescharacteristic
365C22×C4D4×D1311yescharacteristic
366C22×C4D4×D1311yescharacteristic
367C22×C4#612911yescharacteristic
368C22×C4C2×C22⋊D1311yescharacteristic
369C22×C4C2×C22⋊D1311yescharacteristic
370C2×C8—262no—
371C2×C8—522no—
372C2×C8—522no—
373C2×C8—521no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—42no—
377C4⋊C4—44no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—262no—
383C4⋊C4—262no—
384C4⋊C4—528no—
385C4⋊C4—521no—
386C4⋊C4—521no—
387C22⋊C4—44no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—82no—
393C13#991911yescharacteristic, complemented, Sylow
394C23—22no—
395C23—22no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—42no—
400C23—42no—
401C23C2×#610411yescharacteristic
402C23#8818611yescharacteristic
403C23#8819111yescharacteristic
404C23#8819311yescharacteristic
405C23#8820311yescharacteristic
406C23#8820411yescharacteristic
407C23#8820711yescharacteristic
408D4—42no—
409D4—81no—
410D4—81no—
411D4—81no—
412D4—81no—
413D4—81no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—81no—
437C2×C4—264no—
438C2×C4—522no—
439C2×C4—524no—
440C2×C4—524no—
441C2×C4—522no—
442C2×C4—522no—
443C2×C4—522no—
444C2×C4—522no—
445C2×C4—1041no—
446C2×C4—1041no—
447C2×C4—1041no—
448C2×C4—1041no—
449C2×C4#8819111yescharacteristic
450C2×C4#8819211yescharacteristic
451C2×C4#8819311yescharacteristic
452C2×C4#8819411yescharacteristic
453C8—522no—
454C8—1041no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—81no—
464C22—81no—
465C22—81no—
466C22—82no—
467C22—82no—
468C22#1171869711yescharacteristic
469C22#1171869811yescharacteristic
470C22#1171869911yescharacteristic
471C22#1171870011yescharacteristic
472C22#1171887811yescharacteristic
473C22#1171888411yescharacteristic
474C22#1171889911yescharacteristic
475C22#1171890412yes—
476C22#1171890712yes—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—42no—
482C4—81no—
483C4—81no—
484C4—82no—
485C4—524no—
486C4—1042no—
487C2—21no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—161no—
492C2#1311383312yes—
493C2#1311383912yes—
494C2#1311583211yescharacteristic
495C2#1311587011yescharacteristic
496C2#1311596511yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#2618C2
socleC23×C13#120
prime radicalC2×C13×#121C22
hypercenter#2618D13
hypocenterC13#9919
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2618

Complements

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

NH ≅ G/Ntype
2. C2×#11718644C2semidirect
3. #13114920C2semidirect
5. C2×#11718120C2semidirect
6. #13112714C2semidirect
393. C13#9919semidirect

Maximal subgroups

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

subgroupindex
C2×#117186942
C2×#117186442
#131149202
C2×#117181292
C2×#117181202
#131127142
C13×#26182
#991913