Finite Group Databasebeta

← #15763423

Subgroups — #15763423

Order 3328.

594 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 101 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
1#13125593C211yesmaximal, characteristic
2C2×#11718631C211yesmaximal, characteristic, complemented
3#13115821C211yesmaximal, characteristic, complemented
4#13114926C211yesmaximal, characteristic, complemented
5#13113404C211yesmaximal, characteristic
6#13112684C211yesmaximal, characteristic, complemented
7C13×#2504C211yesmaximal, characteristic
8C2×C13×#121C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C2×#88178C2211yescharacteristic
11C13×#397—22no—
12C13×#390—21no—
13C13×#386—22no—
14C13×#382—21no—
15C4×C13×C22⋊C4C2211yescharacteristic
16#11718879—21no—
17#11718873C2211yescharacteristic
18C2×C22⋊#1055C2211yescharacteristic
19C2×C22⋊#1055C2211yescharacteristic
20#11718702—22no—
21#11718701—21no—
22#11718695—21no—
23#11718632—21no—
24#11718631—22no—
25#11718631—22no—
26C2×#88050—21no—
27C2×#88047—21no—
28#11718129—22no—
29#11718121—22no—
30#11718119—22no—
31C22×D4×C13—21no—
32C22×D4×C13D411yescharacteristic
33C23×C4×C13—21no—
34C23×C4×C13C2311yescharacteristic
35C22×Dic26D411yescharacteristic
36C13×#121—21no—
37C13×#121—21no—
38C13×#121—21no—
39C13×#121—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4D411yescharacteristic
46C2×C13×C4⋊C4D412yes—
47C2×C13×C22⋊C4—21no—
48C2×C13×C22⋊C4—24no—
49C2×C13×C22⋊C4D412yes—
50C2×C42×C13—21no—
51C2×C22⋊Dic13—21no—
52C2×C22⋊Dic13—21no—
53C2×#6105—22no—
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13D411yescharacteristic
56#88178—21no—
57#88178—21no—
58#88178—21no—
59#88178—21no—
60C2×#6101—21no—
61C22×#1055—21no—
62C22×#1055D412yes—
63C13×#95—24no—
64C13×#95—21no—
65#88072—22no—
66#88071—21no—
67C22⋊#1055—21no—
68C22⋊#1055—21no—
69C22⋊#1055—21no—
70C22⋊#1055D412yes—
71#88050—22no—
72#88050—24no—
73#88048—22no—
74#88047—24no—
75#9958—131nomaximal, Sylow
76C24×C13—21no—
77C24×C13C2×D411yescharacteristic
78C2×D4×C13—21no—
79C2×D4×C13—21no—
80C2×D4×C13—42no—
81C2×D4×C13—41no—
82C2×D4×C13—41no—
83C2×D4×C13—42no—
84C2×D4×C13—42no—
85C22×C4×C13—21no—
86C22×C4×C13—22no—
87C22×C4×C13—22no—
88C22×C4×C13—42no—
89C22×C4×C13—41no—
90C22×C4×C13—41no—
91C22×C4×C13—82no—
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13#4111yescharacteristic
98C22×Dic13—21no—
99C22×Dic13—21no—
100C22×Dic13—41no—
101C2×Dic26—21no—
102C2×Dic26—21no—
103C2×Dic26—42no—
104C13×C4⋊C4—22no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—22no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C22⋊C4—22no—
111C13×C22⋊C4—22no—
112C13×C22⋊C4—41no—
113C13×C22⋊C4—41no—
114C13×C22⋊C4—84no—
115C42×C13—42no—
116C22⋊Dic13—41no—
117C22⋊Dic13—41no—
118C22⋊Dic13—42no—
119#6105—82no—
120C4⋊Dic13—21no—
121C4⋊Dic13—21no—
122C4⋊Dic13—42no—
123#6101—41no—
124#6101—41no—
125C2×#1055—22no—
126C2×#1055—22no—
127C2×#1055—42no—
128C2×#1055—42no—
129#3187—131no—
130C2×#484—131no—
131#2504D1311yescharacteristic
132#1996—131no—
133#1824—131no—
134#1519—131no—
135#1282—131no—
136C23×C13—41no—
137C23×C13—41no—
138C23×C13—42no—
139C23×C13—42no—
140C23×C13—41no—
141C23×C13—42no—
142C23×C13#12011yescharacteristic
143C23×C13#12111yescharacteristic
144C23×C13#12711yescharacteristic
145C23×C13#13512yes—
146C23×C13#13712yes—
147D4×C13—42no—
148D4×C13—81no—
149D4×C13—82no—
150D4×C13—81no—
151D4×C13—81no—
152C2×C4×C13—22no—
153C2×C4×C13—22no—
154C2×C4×C13—22no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13—44no—
161C2×C4×C13—41no—
162C2×C4×C13—42no—
163C2×C4×C13—42no—
164C2×C4×C13—42no—
165C2×C4×C13—82no—
166C2×C4×C13—82no—
167C2×C4×C13#12011yescharacteristic
168C2×C4×C13#12011yescharacteristic
169C2×C4×C13#12111yescharacteristic
170C2×C4×C13#12111yescharacteristic
171C2×Dic13—41no—
172C2×Dic13—41no—
173C2×Dic13—81no—
174C2×Dic13—81no—
175C2×Dic13—81no—
176C2×Dic13—81no—
177C2×Dic13—81no—
178Dic26—42no—
179Dic26—42no—
180#1055—42no—
181#1055—42no—
182C2×C22⋊Q8—131no—
183C2×#121C2×D1311yescharacteristic
184C22×C4⋊C4C2×D1311yescharacteristic
185#484—262no—
186#484—262no—
187#483—261no—
188#481—261no—
189#465—262no—
190#450—261no—
191#448—261no—
192C2×#107—261no—
193C2×#103—261no—
194C2×C22⋊C8—131no—
195C2×C22⋊C8—131no—
196#397—22no—
197#390—21no—
198#386—22no—
199#382—21no—
200#380—131no—
201C4×C22⋊C4C2×D1311yescharacteristic
202#342—262no—
203#340—262no—
204#327—262no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13—21no—
211C22×C13—42no—
212C22×C13—42no—
213C22×C13—84no—
214C22×C13—81no—
215C22×C13—81no—
216C22×C13—81no—
217C22×C13#39211yescharacteristic
218C22×C13#45212yes—
219C22×C13#46412yes—
220C22×C13#49511yescharacteristic
221C22×C13#49711yescharacteristic
222C4×C13—21no—
223C4×C13—21no—
224C4×C13—21no—
225C4×C13—82no—
226C4×C13—82no—
227C4×C13—81no—
228C4×C13#45812yes—
229Dic13—81no—
230Dic13—81no—
231Dic13—161no—
232C22×Q8—131no—
233C22×D4—21no—
234C22×D4C22⋊D1311yescharacteristic
235C23×C4—21no—
236C23×C4C22×D1311yescharacteristic
237C2×SD16—262no—
238C22×C8—132no—
239C22×C8—261no—
240C22⋊Q8—261no—
241C22⋊Q8—261no—
242C22⋊Q8—261no—
243C22⋊Q8—261no—
244#121—21no—
245#121—21no—
246#121—21no—
247#121—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—131no—
254C2×C4⋊C4—261no—
255C2×C4⋊C4—261no—
256C2×C4⋊C4C22⋊D1312yes—
257C2×C4⋊C4C22⋊D1311yescharacteristic
258C2×C22⋊C4—21no—
259C2×C22⋊C4—24no—
260C2×C22⋊C4—261no—
261C2×C22⋊C4—261no—
262C2×C22⋊C4C22⋊D1312yes—
263C2×C42—21no—
264#107—264no—
265#106—262no—
266#103—264no—
267#103—262no—
268#102—262no—
269C22⋊C8—132no—
270C22⋊C8—261no—
271C22⋊C8—261no—
272C22⋊C8—261no—
273#95—24no—
274#95—21no—
275#95—261no—
276C2×C13—21no—
277C2×C13—22no—
278C2×C13—22no—
279C2×C13—21no—
280C2×C13—161no—
281C2×C13#200811yescharacteristic
282C2×C13#201511yescharacteristic
283C2×C13#202211yescharacteristic
284C24—21no—
285C24C2×C22⋊D1311yescharacteristic
286C2×Q8—261no—
287C2×Q8—261no—
288C2×Q8—522no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—42no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—42no—
295C2×D4—42no—
296C22×C4—21no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—42no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—82no—
303C22×C4—261no—
304C22×C4—261no—
305C22×C4—521no—
306C22×C4D4×D1311yescharacteristic
307C22×C4D4×D1311yescharacteristic
308C22×C4D4×D1311yescharacteristic
309C22×C4#612911yescharacteristic
310C22×C4C2×C22⋊D1311yescharacteristic
311C22×C4C2×C22⋊D1311yescharacteristic
312SD16—1042no—
313C2×C8—262no—
314C2×C8—262no—
315C2×C8—522no—
316C2×C8—522no—
317C4⋊C4—21no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—261no—
324C4⋊C4—261no—
325C4⋊C4—522no—
326C4⋊C4—521no—
327C4⋊C4—521no—
328C22⋊C4—22no—
329C22⋊C4—22no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—84no—
333C22⋊C4—521no—
334C22⋊C4—521no—
335C22⋊C4—522no—
336C42—42no—
337C13#995811yescharacteristic, complemented, Sylow
338C23—41no—
339C23—41no—
340C23—42no—
341C23—42no—
342C23—41no—
343C23—42no—
344C23#8819211yescharacteristic
345C23#8819411yescharacteristic
346C23#8820412yes—
347C23#8820512yes—
348C23#8820711yescharacteristic
349Q8—522no—
350Q8—522no—
351D4—42no—
352D4—81no—
353D4—82no—
354D4—81no—
355D4—81no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—44no—
365C2×C4—41no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—521no—
372C2×C4—521no—
373C2×C4—1041no—
374C2×C4—1041no—
375C2×C4—1041no—
376C2×C4—1041no—
377C2×C4—1041no—
378C2×C4#8819111yescharacteristic
379C2×C4#8819111yescharacteristic
380C2×C4#8819311yescharacteristic
381C2×C4#8819311yescharacteristic
382C8—522no—
383C8—522no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—42no—
391C22—42no—
392C22—84no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22#1171871512yes—
397C22#1171872011yescharacteristic
398C22#1171872111yescharacteristic
399C22#1171888411yescharacteristic
400C22#1171890012yes—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—82no—
405C4—81no—
406C4—82no—
407C4—1041no—
408C4—1041no—
409C4—2081no—
410C4#1171871412yes—
411C2—22no—
412C2—21no—
413C2—22no—
414C2—21no—
415C2—161no—
416C2#1311588911yescharacteristic
417C2#1311593011yescharacteristic
418C2#1311596411yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#2504C2
socleC22×C13#392
prime radicalC2×C13×#121C22
hypercenter#2504D13
hypocenterC13#9958
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2504

Complements

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

NH ≅ G/Ntype
2. C2×#11718631C2semidirect
3. #13115821C2semidirect
4. #13114926C2semidirect
6. #13112684C2semidirect
337. C13#9958semidirect

Maximal subgroups

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

subgroupindex
#131255932
C2×#117186312
#131158212
#131149262
#131134042
#131126842
C13×#25042
#995813