Finite Group Databasebeta

← #32976503

Subgroups — #32976503

Order 18688.

602 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988471C211yesmaximal, characteristic
2#22609693C211yesmaximal, characteristic
3C2×#17988312C212yesmaximal
4#22607773C212yesmaximal
5C4×C22⋊C8×C73C211yesmaximal, characteristic
6C22×#11924007C411yescharacteristic
7C22×#11924007C2211yescharacteristic
8C2×C22⋊#10596831C2212yes—
9C2×#14556502—21no—
10#17988471—21no—
11#17988471—21no—
12#17988471—21no—
13#17988471—21no—
14C2×#14556498C411yescharacteristic
15C2×#14556498C411yescharacteristic
16C2×#14556498C411yescharacteristic
17C2×#14556498C2211yescharacteristic
18#17988342—21no—
19#17988312C418yescomplemented
20C22×C42×C73C2211yescharacteristic
21C2×C22⋊C8×C73C2212yes—
22C2×C4×C8×C73—21no—
23#336×C73—21no—
24C23×Dic73C2×C411yescharacteristic
25C23×Dic73C2×C411yescharacteristic
26C23×Dic73C2×C411yescharacteristic
27C23×Dic73C2×C411yescharacteristic
28C22×#10596831—22no—
29C2×#11924007—21no—
30C2×#11924007—21no—
31C2×#11924007—21no—
32C2×#11924007—21no—
33C2×#11924007—22no—
34C2×#11924007—42no—
35C2×#11924007C2×C414yes—
36C22⋊#10596831—22no—
37C22⋊#10596831C2×C414yes—
38#14556502—42no—
39#14556498—21no—
40#14556498—21no—
41#14556498—21no—
42#14556498—21no—
43#14556498—21no—
44#14556498—21no—
45#14556498—21no—
46#14556498—21no—
47C23×C4×C73C2×C411yescharacteristic
48C23×C4×C73C2×C411yescharacteristic
49C23×C4×C73C2311yescharacteristic
50C22×C8×C73—22no—
51C2×C42×C73—42no—
52C2×C42×C73D411yescharacteristic
53C2×C42×C73D411yescharacteristic
54C2×C42×C73D411yescharacteristic
55C2×C42×C73D411yescharacteristic
56C22⋊C8×C73—22no—
57C22⋊C8×C73C2×C414yes—
58C4×C8×C73—42no—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—21no—
62C22×Dic73—21no—
63C22×Dic73—22no—
64C22×Dic73—22no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73—22no—
68C22×Dic73—22no—
69C22×Dic73—41no—
70C22×Dic73—41no—
71C22×Dic73—41no—
72C22×Dic73—41no—
73C22×Dic73—41no—
74C22×Dic73—41no—
75C22×Dic73C4212yes—
76C22×Dic73C4212yes—
77C2×#10596831—24no—
78C2×#10596831—42no—
79C2×#10596831—42no—
80#11924007—24no—
81#11924007—24no—
82#11924007—42no—
83#11924007—42no—
84C24×C73C22×C411yescharacteristic
85C22×C4×C73—22no—
86C22×C4×C73—22no—
87C22×C4×C73—22no—
88C22×C4×C73—22no—
89C22×C4×C73—41no—
90C22×C4×C73—41no—
91C22×C4×C73—41no—
92C22×C4×C73—41no—
93C22×C4×C73C22⋊C411yescharacteristic
94C22×C4×C73C22⋊C411yescharacteristic
95C22×C4×C73C22⋊C411yescharacteristic
96C22×C4×C73C22⋊C411yescharacteristic
97C22×C4×C73C22×C412yes—
98C22×C4×C73C2×D411yescharacteristic
99C22×C4×C73C2×D411yescharacteristic
100C22×C4×C73#4112yes—
101C2×C8×C73—24no—
102C2×C8×C73—42no—
103C2×C8×C73—42no—
104C42×C73—22no—
105C42×C73—22no—
106C42×C73—41no—
107C42×C73—41no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73—21no—
112C23×C73C2×C4211yescharacteristic
113C23×C73C2×C22⋊C411yescharacteristic
114C23×C73#11711yescharacteristic
115C23×C73#13112yes—
116C23×C73#13112yes—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—21no—
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—42no—
132C2×C4×C73—42no—
133C2×C4×C73—44no—
134C2×C4×C73—44no—
135C2×C4×C73#9912yes—
136C2×C4×C73#10112yes—
137C2×C4×C73C4×D412yes—
138C2×C4×C73C4×D412yes—
139C2×Dic73—22no—
140C2×Dic73—22no—
141C2×Dic73—24no—
142C2×Dic73—42no—
143C2×Dic73—41no—
144C2×Dic73—41no—
145C2×Dic73—41no—
146C2×Dic73—41no—
147C2×Dic73—42no—
148C2×Dic73—42no—
149C2×Dic73—41no—
150C2×Dic73—41no—
151C2×Dic73—41no—
152C2×Dic73—41no—
153C2×Dic73—41no—
154C2×Dic73—41no—
155C2×Dic73—82no—
156C2×Dic73—82no—
157C8×C73—44no—
158#10596831—44no—
159C22×C73—22no—
160C22×C73—22no—
161C22×C73—22no—
162C22×C73—22no—
163C22×C73—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73—21no—
167C22×C73C4×C22⋊C411yescharacteristic
168C22×C73#40512yes—
169C22×C73#40811yescharacteristic
170C22×C73#40811yescharacteristic
171C22×C73C2×#9911yescharacteristic
172C22×C73#41011yescharacteristic
173C22×C73C2×#10111yescharacteristic
174C22×C73#41311yescharacteristic
175C22×C73#43312yes—
176C4×C73—22no—
177C4×C73—22no—
178C4×C73—22no—
179C4×C73—22no—
180C4×C73—41no—
181C4×C73—41no—
182Dic73—42no—
183Dic73—42no—
184Dic73—81no—
185Dic73—81no—
186#8154—731nomaximal, Sylow
187C2×C73—22no—
188C2×C73—22no—
189C2×C73#146811yescharacteristic
190C2×C73#147011yescharacteristic
191C2×C73#147211yescharacteristic
192C2×C73#147311yescharacteristic
193C2×C73#175011yescharacteristic
194C2×C73C4×#9911yescharacteristic
195C2×C73C4×#10111yescharacteristic
196C2×#387—731no—
197#1749—731no—
198C4×C22⋊C8D7311yescharacteristic
199C2×#324—732no—
200#1280—732no—
201C73#815411yescharacteristic, complemented, Sylow
202C22×C4⋊C4—731no—
203C22×C4⋊C4—731no—
204C22×C42C2×D7311yescharacteristic
205C2×C22⋊C8—732no—
206C2×C22⋊C8C2×D7312yes—
207C2×#97—1461no—
208C2×C4×C8—21no—
209#387—1461no—
210#387—1461no—
211#387—1461no—
212#387—1461no—
213C2×#95—731no—
214C2×#95—731no—
215C2×#95—731no—
216C2×#95—731no—
217#336—21no—
218#336—1461no—
219#324—738no—
220C23×C4—731no—
221C23×C4—731no—
222C23×C4—731no—
223C23×C4—731no—
224C23×C4C4×D7311yescharacteristic
225C23×C4C4×D7311yescharacteristic
226C23×C4C22×D7311yescharacteristic
227C22×C8—22no—
228C22×C8—1462no—
229C2×C4⋊C4—2922no—
230C2×C4⋊C4—734no—
231C2×C4⋊C4—1461no—
232C2×C4⋊C4—1461no—
233C2×C4⋊C4—1461no—
234C2×C4⋊C4—1461no—
235C2×C4⋊C4—1462no—
236C2×C42—42no—
237C2×C42D29211yescharacteristic
238C2×C42D29211yescharacteristic
239C2×C42C22⋊D7311yescharacteristic
240C2×C42C22⋊D7311yescharacteristic
241C22⋊C8—22no—
242C22⋊C8—734no—
243C22⋊C8—1462no—
244C22⋊C8C4×D7314yes—
245#97—2922no—
246C4×C8—42no—
247#95—1461no—
248#95—1461no—
249#95—1461no—
250#95—1461no—
251#95—1461no—
252#95—1461no—
253#95—1461no—
254#95—1461no—
255C24C2×C4×D7311yescharacteristic
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—2921no—
265C22×C4—2921no—
266C22×C4—2921no—
267C22×C4—2921no—
268C22×C4—2921no—
269C22×C4—2921no—
270C22×C4—732no—
271C22×C4—732no—
272C22×C4—1461no—
273C22×C4—1461no—
274C22×C4—1461no—
275C22×C4—1461no—
276C22×C4—1461no—
277C22×C4—1461no—
278C22×C4—1462no—
279C22×C4—1462no—
280C22×C4—1462no—
281C22×C4—1462no—
282C22×C4#1192400511yescharacteristic
283C22×C4#1192400511yescharacteristic
284C22×C4#1192400511yescharacteristic
285C22×C4#1192400511yescharacteristic
286C22×C4C2×C4×D7312yes—
287C22×C4C2×C22⋊D7311yescharacteristic
288C22×C4C2×D29211yescharacteristic
289C22×C4#1192402812yes—
290C2×C8—24no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—2922no—
294C2×C8—2922no—
295C2×C8—1464no—
296C4⋊C4—2922no—
297C4⋊C4—2922no—
298C4⋊C4—1464no—
299C4⋊C4—1464no—
300C42—22no—
301C42—22no—
302C42—41no—
303C42—41no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23C42×D7311yescharacteristic
309C23C2×#1192400511yescharacteristic
310C23#1455654811yescharacteristic
311C23#1455659712yes—
312C23#1455659712yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—2922no—
332C2×C4—2922no—
333C2×C4—2921no—
334C2×C4—2921no—
335C2×C4—2921no—
336C2×C4—2921no—
337C2×C4—2922no—
338C2×C4—2921no—
339C2×C4—2921no—
340C2×C4—2921no—
341C2×C4—2921no—
342C2×C4—2921no—
343C2×C4—2921no—
344C2×C4—5842no—
345C2×C4—5842no—
346C2×C4—1462no—
347C2×C4—1462no—
348C2×C4—1464no—
349C2×C4#1455650512yes—
350C2×C4#1455650912yes—
351C2×C4C4×C22⋊D7312yes—
352C2×C4C4×D29212yes—
353C8—44no—
354C8—2924no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22C4×#1192400511yescharacteristic
364C22#1798854112yes—
365C22#1798855311yescharacteristic
366C22#1798855311yescharacteristic
367C22C2×#1455650511yescharacteristic
368C22#1798856011yescharacteristic
369C22C2×#1455650911yescharacteristic
370C22#1798856911yescharacteristic
371C22#1798864612yes—
372C4—22no—
373C4—22no—
374C4—22no—
375C4—22no—
376C4—41no—
377C4—41no—
378C4—2922no—
379C4—2922no—
380C4—5841no—
381C4—5841no—
382C2—22no—
383C2—22no—
384C2#2260827711yescharacteristic
385C2#2260828611yescharacteristic
386C2#2260829411yescharacteristic
387C2#2260829811yescharacteristic
388C2#2260969811yescharacteristic
389C2C4×#1455650511yescharacteristic
390C2C4×#1455650911yescharacteristic
subgroupG/H
centerC23C2×#11924005
commutatorC23×C73C2×C42
FrattiniC23×C4C22×D73
FittingC4×C22⋊C8×C73C2
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22×C4
cosocleC23×C4×C73C23
hypercenterC4×C22⋊C8D73
hypocenterC73#8154
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
19. #17988312C4semidirect
201. C73#8154semidirect

Maximal subgroups

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

subgroupindex
C2×#179884712
#226096932
C2×#179883122
#226077732
C4×C22⋊C8×C732
#815473