Finite Group Databasebeta

← #32978662

Subgroups — #32978662

Order 18688.

570 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22609911C211yesmaximal, characteristic
2#22609911C211yesmaximal, characteristic
3C2×#17988313C212yesmaximal
4#22607774C212yesmaximal
5C2×#387×C73C211yesmaximal, characteristic
6C2×C4⋊#10596831—21no—
7C2×C4⋊#10596831—21no—
8C2×C22⋊#10596831C2212yes—
9C2×C22⋊#10596831C2212yes—
10#17988342—21no—
11#17988342—21no—
12#17988313—24no—
13C22×C4⋊C4×C73C411yescharacteristic
14C22×C4⋊C4×C73C2211yescharacteristic
15C22×C42×C73C2211yescharacteristic
16#387×C73—21no—
17#387×C73—21no—
18#387×C73—21no—
19#387×C73—21no—
20C2×#95×C73C411yescharacteristic
21C2×#95×C73C411yescharacteristic
22C2×#95×C73C411yescharacteristic
23C2×#95×C73C2211yescharacteristic
24C22×#10596831—22no—
25C22×#10596831—22no—
26C4⋊#10596831—42no—
27C4⋊#10596831—42no—
28C22⋊#10596831—22no—
29C22⋊#10596831—22no—
30C22⋊#10596831—22no—
31C22⋊#10596831—22no—
32C23×C4×C73C2×C411yescharacteristic
33C23×C4×C73C2×C411yescharacteristic
34C23×C4×C73C2×C411yescharacteristic
35C23×C4×C73C2×C411yescharacteristic
36C23×C4×C73C2×C411yescharacteristic
37C23×C4×C73C2×C411yescharacteristic
38C23×C4×C73C2311yescharacteristic
39C2×C4⋊C4×C73—21no—
40C2×C4⋊C4×C73—21no—
41C2×C4⋊C4×C73—21no—
42C2×C4⋊C4×C73—21no—
43C2×C4⋊C4×C73—21no—
44C2×C4⋊C4×C73—21no—
45C2×C4⋊C4×C73—42no—
46C2×C4⋊C4×C73D412yes—
47C2×C4⋊C4×C73Q812yes—
48C2×C42×C73—42no—
49C2×C42×C73D411yescharacteristic
50C2×C42×C73D411yescharacteristic
51C2×C42×C73D411yescharacteristic
52C2×C42×C73D411yescharacteristic
53#95×C73—21no—
54#95×C73—21no—
55#95×C73—21no—
56#95×C73—21no—
57#95×C73—21no—
58#95×C73—21no—
59#95×C73—21no—
60#95×C73—21no—
61C2×#10596831—42no—
62C2×#10596831—42no—
63C2×#10596831—42no—
64C2×#10596831—42no—
65C2×#10596831—42no—
66C2×#10596831—42no—
67C24×C73C22×C411yescharacteristic
68C22×C4×C73—21no—
69C22×C4×C73—21no—
70C22×C4×C73—21no—
71C22×C4×C73—21no—
72C22×C4×C73—22no—
73C22×C4×C73—22no—
74C22×C4×C73—22no—
75C22×C4×C73—22no—
76C22×C4×C73—22no—
77C22×C4×C73—22no—
78C22×C4×C73—21no—
79C22×C4×C73—21no—
80C22×C4×C73—22no—
81C22×C4×C73—22no—
82C22×C4×C73—41no—
83C22×C4×C73—41no—
84C22×C4×C73—41no—
85C22×C4×C73—41no—
86C22×C4×C73—41no—
87C22×C4×C73—41no—
88C22×C4×C73—41no—
89C22×C4×C73—41no—
90C22×C4×C73—41no—
91C22×C4×C73—41no—
92C22×C4×C73C22⋊C411yescharacteristic
93C22×C4×C73C22⋊C411yescharacteristic
94C22×C4×C73C22⋊C411yescharacteristic
95C22×C4×C73C22⋊C411yescharacteristic
96C22×C4×C73C4⋊C412yes—
97C22×C4×C73C4⋊C412yes—
98C22×C4×C73C2×D411yescharacteristic
99C22×C4×C73C2×D411yescharacteristic
100C22×C4×C73C2×D411yescharacteristic
101C22×C4×C73C2×Q811yescharacteristic
102C22×C4×C73#4111yescharacteristic
103C22×C4×C73#4111yescharacteristic
104C4⋊C4×C73—22no—
105C4⋊C4×C73—22no—
106C4⋊C4×C73—22no—
107C4⋊C4×C73—22no—
108C4⋊C4×C73—42no—
109C4⋊C4×C73—42no—
110C42×C73—22no—
111C42×C73—22no—
112C42×C73—41no—
113C42×C73—41no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73—21no—
118C23×C73C2×C22⋊C411yescharacteristic
119C23×C73C2×C4⋊C411yescharacteristic
120C23×C73#11711yescharacteristic
121C23×C73#13112yes—
122C23×C73#13112yes—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—22no—
132C2×C4×C73—22no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—21no—
139C2×C4×C73—24no—
140C2×C4×C73—41no—
141C2×C4×C73—41no—
142C2×C4×C73—41no—
143C2×C4×C73—41no—
144C2×C4×C73—44no—
145C2×C4×C73—44no—
146C2×C4×C73—42no—
147C2×C4×C73—41no—
148C2×C4×C73—41no—
149C2×C4×C73—41no—
150C2×C4×C73—41no—
151C2×C4×C73—42no—
152C2×C4×C73—42no—
153C2×C4×C73—41no—
154C2×C4×C73—41no—
155C2×C4×C73—41no—
156C2×C4×C73—41no—
157C2×C4×C73—41no—
158C2×C4×C73—41no—
159C2×C4×C73—82no—
160C2×C4×C73—82no—
161C2×C4×C73#9912yes—
162C2×C4×C73#10112yes—
163C2×C4×C73#12111yescharacteristic
164C2×C4×C73#12111yescharacteristic
165C2×C4×C73C22⋊Q811yescharacteristic
166C2×C4×C73C22⋊Q811yescharacteristic
167#10596831—82no—
168#10596831—82no—
169C22×C73—21no—
170C22×C73—21no—
171C22×C73—21no—
172C22×C73—21no—
173C22×C73—22no—
174C22×C73—22no—
175C22×C73—22no—
176C22×C73—22no—
177C22×C73#38011yescharacteristic
178C22×C73#40811yescharacteristic
179C22×C73#40811yescharacteristic
180C22×C73C2×#9911yescharacteristic
181C22×C73#41011yescharacteristic
182C22×C73C2×#10111yescharacteristic
183C22×C73#41311yescharacteristic
184C22×C73#42412yes—
185C22×C73#43312yes—
186C4×C73—21no—
187C4×C73—21no—
188C4×C73—21no—
189C4×C73—21no—
190C4×C73—22no—
191C4×C73—22no—
192C4×C73—42no—
193C4×C73—42no—
194C4×C73—41no—
195C4×C73—41no—
196C4×C73—81no—
197C4×C73—81no—
198#8562—731nomaximal, Sylow
199C2×C73—22no—
200C2×C73—22no—
201C2×C73#146811yescharacteristic
202C2×C73#147011yescharacteristic
203C2×C73#147211yescharacteristic
204C2×C73#147311yescharacteristic
205C2×C73#179811yescharacteristic
206C2×C73#179911yescharacteristic
207C2×C73#180111yescharacteristic
208C2×#387D7311yescharacteristic
209#1797—731no—
210#1797—731no—
211C2×#324—732no—
212#1280—732no—
213C73#856211yescharacteristic, complemented, Sylow
214C22×C4⋊C4Dic7311yescharacteristic
215C22×C4⋊C4C2×D7311yescharacteristic
216C22×C42C2×D7311yescharacteristic
217C2×C4⋊C8—1461no—
218C2×C4⋊C8—1461no—
219C2×C22⋊C8—732no—
220C2×C22⋊C8—732no—
221#387—21no—
222#387—21no—
223#387—21no—
224#387—21no—
225C2×#95Dic7311yescharacteristic
226C2×#95Dic7311yescharacteristic
227C2×#95Dic7311yescharacteristic
228C2×#95C2×D7311yescharacteristic
229#336—1461no—
230#336—1461no—
231#324—1464no—
232C23×C4C2×Dic7311yescharacteristic
233C23×C4C2×Dic7311yescharacteristic
234C23×C4C2×Dic7311yescharacteristic
235C23×C4C2×Dic7311yescharacteristic
236C23×C4C2×Dic7311yescharacteristic
237C23×C4C2×Dic7311yescharacteristic
238C23×C4C22×D7311yescharacteristic
239C22×C8—1462no—
240C22×C8—1462no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—42no—
248C2×C4⋊C4Dic14612yes—
249C2×C4⋊C4D29212yes—
250C2×C42—42no—
251C2×C42C22⋊D7311yescharacteristic
252C2×C42C22⋊D7311yescharacteristic
253C2×C42C22⋊D7311yescharacteristic
254C2×C42C22⋊D7311yescharacteristic
255C4⋊C8—2922no—
256C4⋊C8—2922no—
257C22⋊C8—1462no—
258C22⋊C8—1462no—
259C22⋊C8—1462no—
260C22⋊C8—1462no—
261#95—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—21no—
267#95—21no—
268#95—21no—
269C24C22×Dic7311yescharacteristic
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4C22⋊Dic7311yescharacteristic
295C22×C4C22⋊Dic7311yescharacteristic
296C22×C4C22⋊Dic7311yescharacteristic
297C22×C4C22⋊Dic7311yescharacteristic
298C22×C4C4⋊Dic7312yes—
299C22×C4C4⋊Dic7312yes—
300C22×C4C2×C22⋊D7311yescharacteristic
301C22×C4C2×C22⋊D7311yescharacteristic
302C22×C4C2×D29211yescharacteristic
303C22×C4C2×Dic14611yescharacteristic
304C22×C4#1192402811yescharacteristic
305C22×C4#1192402811yescharacteristic
306C2×C8—2922no—
307C2×C8—2922no—
308C2×C8—2922no—
309C2×C8—2922no—
310C2×C8—2922no—
311C2×C8—2922no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—42no—
317C4⋊C4—42no—
318C42—22no—
319C42—22no—
320C42—41no—
321C42—41no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23C2×C22⋊Dic7311yescharacteristic
327C23C2×C4⋊Dic7311yescharacteristic
328C23#1455655011yescharacteristic
329C23#1455659812yes—
330C23#1455659812yes—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—24no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4#1455650612yes—
370C2×C4#1455651012yes—
371C2×C4#1455656511yescharacteristic
372C2×C4#1455656511yescharacteristic
373C2×C4#1455657011yescharacteristic
374C2×C4#1455657011yescharacteristic
375C8—5842no—
376C8—5842no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—22no—
381C22—22no—
382C22—22no—
383C22—21no—
384C22—21no—
385C22#1798844711yescharacteristic
386C22#1798855411yescharacteristic
387C22#1798855411yescharacteristic
388C22C2×#1455650611yescharacteristic
389C22#1798856111yescharacteristic
390C22C2×#1455651011yescharacteristic
391C22#1798857111yescharacteristic
392C22#1798861412yes—
393C22#1798864812yes—
394C4—22no—
395C4—22no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—42no—
403C4—42no—
404C4—81no—
405C4—81no—
406C2—22no—
407C2—22no—
408C2#2260827911yescharacteristic
409C2#2260828711yescharacteristic
410C2#2260829511yescharacteristic
411C2#2260830011yescharacteristic
412C2#2260991511yescharacteristic
413C2#2260991911yescharacteristic
414C2#2260992711yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic73
commutator, prime radicalC24×C73C22×C4
FrattiniC23×C4C22×D73
FittingC2×#387×C73C2
socleC23×C73C2×C22⋊C4
cosocleC23×C4×C73C23
hypercenterC2×#387D73
hypocenterC73#8562
LCSG ▷ C24×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
213. C73#8562semidirect

Maximal subgroups

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

subgroupindex
#226099112
C2×#179883132
#226077742
C2×#387×C732
#856273