Finite Group Databasebeta

← #15763163

Subgroups — #15763163

Order 3328.

672 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718695C211yesmaximal, characteristic
2#13120580C211yesmaximal, characteristic
3C2×#11718320C211yesmaximal, characteristic, complemented
4#13114927C211yesmaximal, characteristic, complemented
5C2×#11718061C211yesmaximal, characteristic, complemented
6#13112715C211yesmaximal, characteristic, complemented
7C2×C13×#327C211yesmaximal, characteristic
8C2×C13×#121C2211yescharacteristic
9C2×#88189—21no—
10C22×C4⋊Dic13C2211yescharacteristic
11C22×#6101C2211yescharacteristic
12C2×C13×C22⋊C8C2211yescharacteristic
13C2×C13×#95C2211yescharacteristic
14#11718883—21no—
15#11718881—21no—
16C2×#88072—21no—
17#11718873C2211yescharacteristic
18C2×#88071—21no—
19C2×#88071—21no—
20C2×C22⋊#1055C2211yescharacteristic
21#11718695—22no—
22#11718695—22no—
23#11718641—21no—
24C2×#88048—21no—
25#11718609—22no—
26#11718320—22no—
27#11718320—22no—
28C13×#327—22no—
29#11718143—22no—
30#11718061—22no—
31C22×D4×C13—21no—
32C22×D4×C13D411yescharacteristic
33C23×C4×C13—21no—
34C23×C4×C13C2311yescharacteristic
35C23×Dic13—21no—
36C23×Dic13D411yescharacteristic
37C23×Dic13D411yescharacteristic
38C22×C8×C13—21no—
39C13×#121—21no—
40C13×#121—21no—
41C13×#121—21no—
42C13×#121—21no—
43C2×C13×C4⋊C4D411yescharacteristic
44C2×C13×C22⋊C4—21no—
45C2×C22⋊Dic13—22no—
46C2×C22⋊Dic13—21no—
47C2×C22⋊Dic13—22no—
48#88189—42no—
49#88189—42no—
50C2×C4⋊Dic13—21no—
51C2×C4⋊Dic13—21no—
52C2×C4⋊Dic13—21no—
53C2×C4⋊Dic13—21no—
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13D412yes—
56C2×C4⋊Dic13D412yes—
57C2×#6101—22no—
58C2×#6101—21no—
59C2×#6101—21no—
60C2×#6101—21no—
61C2×#6101—21no—
62C2×#6101—21no—
63C2×#6101—21no—
64C22×#1055—21no—
65C13×C22⋊C8—21no—
66C13×C22⋊C8—21no—
67C13×#95—21no—
68C13×#95D412yes—
69#88072—24no—
70#88071—24no—
71#88071—24no—
72#88071—22no—
73#88071—21no—
74C22⋊#1055—21no—
75C22⋊#1055D412yes—
76#88048—24no—
77#9921—131nomaximal, Sylow
78C24×C13—21no—
79C24×C13C2×D411yescharacteristic
80C2×D4×C13—21no—
81C2×D4×C13—21no—
82C2×D4×C13—42no—
83C2×D4×C13—41no—
84C2×D4×C13—41no—
85C2×D4×C13—41no—
86C2×D4×C13—41no—
87C2×D4×C13—41no—
88C2×D4×C13—41no—
89C22×C4×C13—22no—
90C22×C4×C13—21no—
91C22×C4×C13—42no—
92C22×C4×C13—42no—
93C22×C4×C13—42no—
94C22×C4×C13—41no—
95C22×C4×C13—41no—
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13#4111yescharacteristic
102C22×Dic13—21no—
103C22×Dic13—21no—
104C22×Dic13—21no—
105C22×Dic13—21no—
106C22×Dic13—21no—
107C22×Dic13—21no—
108C22×Dic13—21no—
109C22×Dic13—22no—
110C22×Dic13—21no—
111C22×Dic13—22no—
112C22×Dic13—21no—
113C22×Dic13—42no—
114C22×Dic13—44no—
115C22×Dic13—41no—
116C22×Dic13—41no—
117C22×Dic13SD1612yes—
118C2×C8×C13—42no—
119C2×C8×C13—41no—
120C13×C4⋊C4—21no—
121C13×C4⋊C4—21no—
122C13×C22⋊C4—41no—
123C13×C22⋊C4—41no—
124C22⋊Dic13—44no—
125C22⋊Dic13—41no—
126C22⋊Dic13—41no—
127C22⋊Dic13—82no—
128C4⋊Dic13—22no—
129C4⋊Dic13—22no—
130C4⋊Dic13—41no—
131C4⋊Dic13—41no—
132C4⋊Dic13—42no—
133#6101—44no—
134#6101—41no—
135#6101—41no—
136#6101—41no—
137#6101—41no—
138C2×#1055—22no—
139C2×#1055—42no—
140C2×#481—131no—
141#2618—131no—
142C2×#400—131no—
143#1824—131no—
144C2×#327D1311yescharacteristic
145C2×#324—131no—
146#1294—131no—
147C23×C13—22no—
148C23×C13—22no—
149C23×C13—41no—
150C23×C13—41no—
151C23×C13—41no—
152C23×C13—42no—
153C23×C13—42no—
154C23×C13#12011yescharacteristic
155C23×C13#12011yescharacteristic
156C23×C13#12111yescharacteristic
157C23×C13C2×SD1611yescharacteristic
158C23×C13#13511yescharacteristic
159C23×C13AGL(1,ℤ/8)11yescharacteristic
160C23×C13#13711yescharacteristic
161D4×C13—42no—
162D4×C13—81no—
163D4×C13—81no—
164D4×C13—81no—
165D4×C13—81no—
166D4×C13—81no—
167C2×C4×C13—22no—
168C2×C4×C13—22no—
169C2×C4×C13—41no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—42no—
174C2×C4×C13—42no—
175C2×C4×C13—41no—
176C2×C4×C13—42no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—82no—
180C2×C4×C13—82no—
181C2×C4×C13#12011yescharacteristic
182C2×C4×C13#12111yescharacteristic
183C2×C4×C13#12111yescharacteristic
184C2×C4×C13#12711yescharacteristic
185C2×Dic13—22no—
186C2×Dic13—22no—
187C2×Dic13—22no—
188C2×Dic13—41no—
189C2×Dic13—41no—
190C2×Dic13—41no—
191C2×Dic13—41no—
192C2×Dic13—44no—
193C2×Dic13—42no—
194C2×Dic13—41no—
195C2×Dic13—42no—
196C2×Dic13—42no—
197C2×Dic13—42no—
198C2×Dic13—42no—
199C2×Dic13—42no—
200C2×Dic13—82no—
201C2×Dic13—82no—
202C2×Dic13—81no—
203C8×C13—81no—
204#1055—42no—
205C2×#123—261no—
206C2×#121C2×D1311yescharacteristic
207C22×C4⋊C4—131no—
208C22×C4⋊C4—131no—
209#481—262no—
210#481—262no—
211C2×#106—261no—
212C2×#102—261no—
213C2×C22⋊C8—131no—
214C2×C22⋊C8C2×D1311yescharacteristic
215#400—262no—
216#400—262no—
217#398—261no—
218#396—262no—
219#394—261no—
220#386—261no—
221#380—131no—
222C2×#95—261no—
223C2×#95—261no—
224C2×#95C2×D1311yescharacteristic
225#340—262no—
226#327—22no—
227#324—262no—
228C22×C13—22no—
229C22×C13—22no—
230C22×C13—22no—
231C22×C13—22no—
232C22×C13—21no—
233C22×C13—21no—
234C22×C13—21no—
235C22×C13—21no—
236C22×C13—82no—
237C22×C13—82no—
238C22×C13—81no—
239C22×C13—81no—
240C22×C13—81no—
241C22×C13#39211yescharacteristic
242C22×C13#44811yescharacteristic
243C22×C13#44911yescharacteristic
244C22×C13#45011yescharacteristic
245C22×C13#45211yescharacteristic
246C22×C13#45412yes—
247C22×C13#45812yes—
248C22×C13#46511yescharacteristic
249C22×C13#46811yescharacteristic
250C4×C13—21no—
251C4×C13—21no—
252C4×C13—21no—
253C4×C13—21no—
254C4×C13—82no—
255C4×C13—81no—
256Dic13—42no—
257Dic13—82no—
258Dic13—82no—
259Dic13—81no—
260C22×D4—21no—
261C22×D4D5211yescharacteristic
262C23×C4—21no—
263C23×C4—131no—
264C23×C4—131no—
265C23×C4—261no—
266C23×C4C22×D1311yescharacteristic
267C22×C8—21no—
268C22×C8—261no—
269#123—522no—
270#123—522no—
271#121—21no—
272#121—21no—
273#121—21no—
274#121—21no—
275C2×C4⋊C4—132no—
276C2×C4⋊C4—132no—
277C2×C4⋊C4—261no—
278C2×C4⋊C4—261no—
279C2×C4⋊C4—261no—
280C2×C4⋊C4—261no—
281C2×C4⋊C4—262no—
282C2×C4⋊C4—261no—
283C2×C4⋊C4—261no—
284C2×C4⋊C4—261no—
285C2×C4⋊C4—261no—
286C2×C4⋊C4—261no—
287C2×C4⋊C4—261no—
288C2×C4⋊C4—261no—
289C2×C4⋊C4D5211yescharacteristic
290C2×C22⋊C4—21no—
291C2×C22⋊C4—262no—
292C2×C22⋊C4—261no—
293C2×C22⋊C4—262no—
294#106—264no—
295#102—264no—
296C22⋊C8—21no—
297C22⋊C8—21no—
298C22⋊C8—132no—
299C22⋊C8—261no—
300#95—21no—
301#95—264no—
302#95—264no—
303#95—262no—
304#95—261no—
305#95C22⋊D1312yes—
306C2×C13—21no—
307C2×C13—21no—
308C2×C13—21no—
309C2×C13—21no—
310C2×C13—161no—
311C2×C13#161512yes—
312C2×C13#161612yes—
313C2×C13#200011yescharacteristic
314C2×C13#200311yescharacteristic
315C2×C13#202211yescharacteristic
316C24—21no—
317C24D4×D1311yescharacteristic
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—42no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—132no—
335C22×C4—261no—
336C22×C4—261no—
337C22×C4—261no—
338C22×C4—261no—
339C22×C4—261no—
340C22×C4—261no—
341C22×C4—262no—
342C22×C4—261no—
343C22×C4—262no—
344C22×C4—261no—
345C22×C4—261no—
346C22×C4—522no—
347C22×C4—524no—
348C22×C4—521no—
349C22×C4—521no—
350C22×C4C2×D5211yescharacteristic
351C22×C4#612711yescharacteristic
352C22×C4D4×D1311yescharacteristic
353C22×C4D4×D1311yescharacteristic
354C22×C4D4×D1311yescharacteristic
355C22×C4C2×C22⋊D1311yescharacteristic
356C2×C8—42no—
357C2×C8—41no—
358C2×C8—262no—
359C2×C8—522no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—262no—
363C4⋊C4—262no—
364C4⋊C4—522no—
365C4⋊C4—524no—
366C4⋊C4—521no—
367C4⋊C4—521no—
368C4⋊C4—521no—
369C4⋊C4—521no—
370C4⋊C4—521no—
371C4⋊C4—521no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—524no—
375C22⋊C4—521no—
376C22⋊C4—521no—
377C22⋊C4—1042no—
378C13#992111yescharacteristic, complemented, Sylow
379C23—22no—
380C23—22no—
381C23—42no—
382C23—41no—
383C23—41no—
384C23—42no—
385C23—41no—
386C23#8813611yescharacteristic
387C23#8813811yescharacteristic
388C23#8816511yescharacteristic
389C23#8816611yescharacteristic
390C23SD16×D1311yescharacteristic
391C23#8816911yescharacteristic
392C23#8819111yescharacteristic
393D4—42no—
394D4—81no—
395D4—81no—
396D4—81no—
397D4—81no—
398D4—81no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4—262no—
414C2×C4—262no—
415C2×C4—262no—
416C2×C4—521no—
417C2×C4—521no—
418C2×C4—521no—
419C2×C4—521no—
420C2×C4—522no—
421C2×C4—524no—
422C2×C4—522no—
423C2×C4—522no—
424C2×C4—522no—
425C2×C4—522no—
426C2×C4—522no—
427C2×C4—521no—
428C2×C4—1042no—
429C2×C4—1042no—
430C2×C4—1041no—
431C2×C4#8813611yescharacteristic
432C2×C4#8813811yescharacteristic
433C2×C4#8818411yescharacteristic
434C2×C4#8819411yescharacteristic
435C8—81no—
436C8—522no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—22no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—82no—
446C22—82no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22#1171840312yes—
451C22#1171843711yescharacteristic
452C22#1171843911yescharacteristic
453C22#1171844111yescharacteristic
454C22#1171844411yescharacteristic
455C22#1171848812yes—
456C22#1171862111yescharacteristic
457C22#1171881911yescharacteristic
458C22#1171883111yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—21no—
463C4—82no—
464C4—81no—
465C4—522no—
466C4—1042no—
467C4—1041no—
468C4—1042no—
469C2—21no—
470C2—21no—
471C2—21no—
472C2—21no—
473C2—161no—
474C2#1311386812yes—
475C2#1311387412yes—
476C2#1311584011yescharacteristic
477C2#1311585711yescharacteristic
478C2#1311596611yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC2×C13×#327C2
socleC23×C13#120
prime radicalC2×C13×#121C22
hypercenterC2×#327D13
hypocenterC13#9921
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
3. C2×#11718320C2semidirect
4. #13114927C2semidirect
5. C2×#11718061C2semidirect
6. #13112715C2semidirect
378. C13#9921semidirect

Maximal subgroups

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

subgroupindex
C2×#117186952
#131205802
C2×#117183202
#131149272
C2×#117180612
#131127152
C2×C13×#3272
#992113