Finite Group Databasebeta

← #15763213

Subgroups — #15763213

Order 3328.

778 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718631C211yesmaximal, characteristic, complemented
2#13120641C211yesmaximal, characteristic
3#13114926C211yesmaximal, characteristic, complemented
4C2×#11718044C211yesmaximal, characteristic, complemented
5C2×#11718117C211yesmaximal, characteristic
6#13112715C211yesmaximal, characteristic, complemented
7C2×C13×#399C211yesmaximal, characteristic
8C22×C13×C4⋊C4—21no—
9C22×C13×C4⋊C4C2211yescharacteristic
10C22×C13×C22⋊C4—21no—
11C22×C13×C22⋊C4C2211yescharacteristic
12C2×#88178C2211yescharacteristic
13C13×#399—22no—
14C13×#399—22no—
15C2×C13×#95C2211yescharacteristic
16#11718908—21no—
17#11718873C2211yescharacteristic
18#11718871—21no—
19C2×C22⋊#1055C2211yescharacteristic
20C2×C22⋊#1055C2211yescharacteristic
21#11718631—22no—
22#11718631—22no—
23C2×#88050—21no—
24C2×#88047—21no—
25#11718610—21no—
26#11718609—22no—
27#11718608—21no—
28#11718121—22no—
29#11718117—22no—
30#11718044—22no—
31C25×C13D411yescharacteristic
32C23×C4×C13—21no—
33C23×C4×C13—21no—
34C23×C4×C13D411yescharacteristic
35C23×C4×C13C2311yescharacteristic
36C22×Dic26D411yescharacteristic
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—24no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—44no—
44C2×C13×C4⋊C4D412yes—
45C2×C13×C22⋊C4—24no—
46C2×C13×C22⋊C4—21no—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—44no—
53C2×C22⋊Dic13—21no—
54C2×C22⋊Dic13—21no—
55C2×C22⋊Dic13—22no—
56C2×C22⋊Dic13—22no—
57C2×C4⋊Dic13D411yescharacteristic
58C2×C4⋊Dic13D412yes—
59#88178—21no—
60#88178—21no—
61#88178—21no—
62#88178—21no—
63C2×#6101—21no—
64C2×#6101—22no—
65C22×#1055—21no—
66C22×#1055—21no—
67C13×#95—21no—
68C13×#95D412yes—
69#88071—22no—
70#88071—21no—
71C22⋊#1055—21no—
72C22⋊#1055—21no—
73C22⋊#1055—21no—
74C22⋊#1055D412yes—
75#88050—24no—
76#88047—24no—
77#9928—131nomaximal, Sylow
78C24×C13—21no—
79C24×C13—21no—
80C24×C13—21no—
81C24×C13—21no—
82C24×C13—21no—
83C24×C13—21no—
84C24×C13—42no—
85C24×C13—42no—
86C24×C13Q1612yes—
87C24×C13C2×D411yescharacteristic
88C22×C4×C13—24no—
89C22×C4×C13—22no—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13—22no—
93C22×C4×C13—21no—
94C22×C4×C13—42no—
95C22×C4×C13—42no—
96C22×C4×C13—41no—
97C22×C4×C13—41no—
98C22×C4×C13—42no—
99C22×C4×C13—42no—
100C22×C4×C13—42no—
101C22×C4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13#4111yescharacteristic
109C22×Dic13—22no—
110C22×Dic13—21no—
111C22×Dic13—21no—
112C2×Dic26—21no—
113C2×Dic26—21no—
114C2×Dic26—42no—
115C13×C4⋊C4—22no—
116C13×C4⋊C4—22no—
117C13×C4⋊C4—48no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C22⋊C4—48no—
121C13×C22⋊C4—41no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—41no—
124C13×C22⋊C4—41no—
125C22⋊Dic13—41no—
126C22⋊Dic13—41no—
127C22⋊Dic13—41no—
128C22⋊Dic13—41no—
129C22⋊Dic13—82no—
130C22⋊Dic13—82no—
131C4⋊Dic13—21no—
132C4⋊Dic13—21no—
133C4⋊Dic13—42no—
134#6101—41no—
135#6101—41no—
136#6101—82no—
137C2×#1055—22no—
138C2×#1055—42no—
139C2×#1055—42no—
140C2×#1055—41no—
141C2×#484—131no—
142#2626—131no—
143C2×#399D1311yescharacteristic
144#1824—131no—
145C2×#328—131no—
146C2×#323—131no—
147#1294—131no—
148C23×C13—22no—
149C23×C13—22no—
150C23×C13—22no—
151C23×C13—22no—
152C23×C13—22no—
153C23×C13—44no—
154C23×C13—42no—
155C23×C13—44no—
156C23×C13—42no—
157C23×C13—41no—
158C23×C13—41no—
159C23×C13—41no—
160C23×C13—42no—
161C23×C13—42no—
162C23×C13—41no—
163C23×C13—82no—
164C23×C13—82no—
165C23×C13—81no—
166C23×C13—81no—
167C23×C13#12011yescharacteristic
168C23×C13#12011yescharacteristic
169C23×C13#12111yescharacteristic
170C23×C13C2×Q1611yescharacteristic
171C23×C13#13511yescharacteristic
172C23×C13#13711yescharacteristic
173C23×C13#13711yescharacteristic
174C2×C4×C13—22no—
175C2×C4×C13—22no—
176C2×C4×C13—24no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—44no—
182C2×C4×C13—44no—
183C2×C4×C13—42no—
184C2×C4×C13—42no—
185C2×C4×C13—42no—
186C2×C4×C13—42no—
187C2×C4×C13—42no—
188C2×C4×C13—41no—
189C2×C4×C13—42no—
190C2×C4×C13—42no—
191C2×C4×C13—82no—
192C2×C4×C13—82no—
193C2×C4×C13—81no—
194C2×C4×C13#12011yescharacteristic
195C2×C4×C13#12111yescharacteristic
196C2×C4×C13#12111yescharacteristic
197C2×C4×C13#12711yescharacteristic
198C2×Dic13—41no—
199C2×Dic13—41no—
200C2×Dic13—42no—
201C2×Dic13—42no—
202C2×Dic13—42no—
203C2×Dic13—42no—
204C2×Dic13—42no—
205Dic26—42no—
206Dic26—81no—
207#1055—42no—
208#1055—81no—
209C2×C22⋊Q8—131no—
210C22×C4⋊C4—21no—
211C22×C4⋊C4C2×D1311yescharacteristic
212C22×C22⋊C4—21no—
213C22×C22⋊C4C2×D1311yescharacteristic
214#484—262no—
215#484—262no—
216C2×#107—261no—
217C2×#103—261no—
218C2×C22⋊C8—131no—
219C2×C22⋊C8—131no—
220#399—22no—
221#399—22no—
222#399—261no—
223#396—262no—
224#393—261no—
225#385—261no—
226#380—131no—
227#379—261no—
228C2×#95C2×D1311yescharacteristic
229#340—262no—
230#328—262no—
231#323—262no—
232C22×C13—22no—
233C22×C13—22no—
234C22×C13—22no—
235C22×C13—22no—
236C22×C13—21no—
237C22×C13—21no—
238C22×C13—21no—
239C22×C13—21no—
240C22×C13—44no—
241C22×C13—44no—
242C22×C13—42no—
243C22×C13—82no—
244C22×C13—82no—
245C22×C13—82no—
246C22×C13—82no—
247C22×C13—81no—
248C22×C13—81no—
249C22×C13#39211yescharacteristic
250C22×C13#45111yescharacteristic
251C22×C13#45111yescharacteristic
252C22×C13#45211yescharacteristic
253C22×C13#45211yescharacteristic
254C22×C13#45312yes—
255C22×C13#45812yes—
256C22×C13#46711yescharacteristic
257C22×C13#47011yescharacteristic
258C4×C13—21no—
259C4×C13—21no—
260C4×C13—21no—
261C4×C13—21no—
262C4×C13—44no—
263C4×C13—81no—
264C4×C13—82no—
265Dic13—82no—
266Dic13—81no—
267Dic13—81no—
268C25C22⋊D1311yescharacteristic
269C22×Q8—131no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4C22⋊D1311yescharacteristic
273C23×C4C22×D1311yescharacteristic
274C22×C8—261no—
275C22×C8—261no—
276C22⋊Q8—261no—
277C22⋊Q8—261no—
278C22⋊Q8—261no—
279C22⋊Q8—261no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—131no—
288C2×C4⋊C4—132no—
289C2×C4⋊C4—261no—
290C2×C4⋊C4—262no—
291C2×C4⋊C4C22⋊D1312yes—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4—21no—
297C2×C22⋊C4—21no—
298C2×C22⋊C4—21no—
299C2×C22⋊C4—44no—
300C2×C22⋊C4—261no—
301C2×C22⋊C4—261no—
302C2×C22⋊C4—262no—
303C2×C22⋊C4—262no—
304#107—264no—
305#103—264no—
306C22⋊C8—132no—
307C22⋊C8—261no—
308C22⋊C8—261no—
309C22⋊C8—261no—
310#95—21no—
311#95—262no—
312#95—261no—
313#95C22⋊D1312yes—
314C2×C13—21no—
315C2×C13—21no—
316C2×C13—21no—
317C2×C13—21no—
318C2×C13—82no—
319C2×C13#161412yes—
320C2×C13#161812yes—
321C2×C13#200111yescharacteristic
322C2×C13#200211yescharacteristic
323C2×C13#202211yescharacteristic
324C24—21no—
325C24—21no—
326C24—21no—
327C24—21no—
328C24—21no—
329C24—21no—
330C24—42no—
331C24—42no—
332C24#610712yes—
333C24C2×C22⋊D1311yescharacteristic
334C2×Q8—261no—
335C2×Q8—261no—
336C2×Q8—522no—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—262no—
353C22×C4—261no—
354C22×C4—261no—
355C22×C4D4×D1311yescharacteristic
356C22×C4D4×D1311yescharacteristic
357C22×C4D4×D1311yescharacteristic
358C22×C4#612911yescharacteristic
359C22×C4C2×C22⋊D1311yescharacteristic
360C22×C4C2×C22⋊D1311yescharacteristic
361C2×C8—262no—
362C2×C8—522no—
363C2×C8—522no—
364C2×C8—521no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—48no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—261no—
371C4⋊C4—261no—
372C4⋊C4—522no—
373C4⋊C4—521no—
374C4⋊C4—521no—
375C4⋊C4—1042no—
376C22⋊C4—48no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—521no—
382C22⋊C4—521no—
383C22⋊C4—521no—
384C22⋊C4—521no—
385C22⋊C4—1042no—
386C22⋊C4—1042no—
387C13#992811yescharacteristic, complemented, Sylow
388C23—22no—
389C23—22no—
390C23—22no—
391C23—22no—
392C23—22no—
393C23—44no—
394C23—42no—
395C23—44no—
396C23—42no—
397C23—41no—
398C23—41no—
399C23—42no—
400C23—42no—
401C23—41no—
402C23—41no—
403C23—82no—
404C23—82no—
405C23—81no—
406C23—81no—
407C23#8819111yescharacteristic
408C23#8819311yescharacteristic
409C23#8819611yescharacteristic
410C23C2×#610711yescharacteristic
411C23#8820411yescharacteristic
412C23#8820511yescharacteristic
413C23#8820711yescharacteristic
414Q8—522no—
415Q8—1041no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—82no—
434C2×C4—82no—
435C2×C4—81no—
436C2×C4—522no—
437C2×C4—522no—
438C2×C4—522no—
439C2×C4—522no—
440C2×C4—522no—
441C2×C4—521no—
442C2×C4—521no—
443C2×C4#8819111yescharacteristic
444C2×C4#8819211yescharacteristic
445C2×C4#8819311yescharacteristic
446C2×C4#8819411yescharacteristic
447C8—522no—
448C8—1041no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—44no—
458C22—44no—
459C22—42no—
460C22—82no—
461C22—82no—
462C22—82no—
463C22—82no—
464C22—81no—
465C22—81no—
466C22#1171870811yescharacteristic
467C22#1171871111yescharacteristic
468C22#1171871211yescharacteristic
469C22#1171871311yescharacteristic
470C22#1171871412yes—
471C22#1171873812yes—
472C22#1171888411yescharacteristic
473C22#1171888911yescharacteristic
474C22#1171890011yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—21no—
479C4—44no—
480C4—81no—
481C4—82no—
482C4—1042no—
483C4—1041no—
484C4—1041no—
485C2—21no—
486C2—21no—
487C2—21no—
488C2—21no—
489C2—82no—
490C2#1311386012yes—
491C2#1311388212yes—
492C2#1311584411yescharacteristic
493C2#1311585111yescharacteristic
494C2#1311596411yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC2×C13×#399C2
socleC23×C13#120
prime radicalC25×C13D4
hypercenterC2×#399D13
hypocenterC13#9928
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C2×#11718631C2semidirect
3. #13114926C2semidirect
4. C2×#11718044C2semidirect
6. #13112715C2semidirect
387. C13#9928semidirect

Maximal subgroups

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

subgroupindex
C2×#117186312
#131206412
#131149262
C2×#117180442
C2×#117181172
#131127152
C2×C13×#3992
#992813