Finite Group Databasebeta

← #32996805

Subgroups — #32996805

Order 18688.

450 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 87 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#22609923C211yesmaximal, characteristic, complemented
2#22608269C211yesmaximal, characteristic, complemented
3#22607958C212yesmaximal, complemented
4#22607934C212yesmaximal, complemented
5C73×#2635C211yesmaximal, characteristic
6#17988611—21no—
7C2×#14556508—21no—
8#17988551—21no—
9#17988356C2212yes—
10#17988313C2212yes—
11#17988311—21no—
12C2×#121×C73C411yescharacteristic
13C2×C4×D4×C73C2211yescharacteristic
14#400×C73C2211yescharacteristic
15#399×C73C411yescharacteristic
16#394×C73—21no—
17#394×C73C2211yescharacteristic
18#392×C73—21no—
19#392×C73C411yescharacteristic
20#388×C73—21no—
21#386×C73—21no—
22#381×C73C411yescharacteristic
23C2×#11924012—22no—
24C2×#11924012—41no—
25C4⋊#10596831—41no—
26C4⋊#10596831—41no—
27#14556508—42no—
28C22⋊#10596831—22no—
29C22⋊#10596831—41no—
30C22×D4×C73—21no—
31C22×D4×C73—21no—
32C22×D4×C73C2×C411yescharacteristic
33C22×D4×C73D411yescharacteristic
34C23×C4×C73C2×C411yescharacteristic
35C23×C4×C73D411yescharacteristic
36#121×C73—41no—
37#121×C73—41no—
38C4×D4×C73—41no—
39C4×D4×C73—41no—
40C2×C4⋊C4×C73—21no—
41C2×C4⋊C4×C73C2×C411yescharacteristic
42C2×C4⋊C4×C73C2311yescharacteristic
43C2×C22⋊C4×C73—21no—
44C2×C22⋊C4×C73—21no—
45C2×C22⋊C4×C73—21no—
46C2×C22⋊C4×C73—21no—
47C2×C22⋊C4×C73—21no—
48C2×C22⋊C4×C73—21no—
49C2×C22⋊C4×C73C2×C411yescharacteristic
50C2×C22⋊C4×C73D411yescharacteristic
51C2×C42×C73D411yescharacteristic
52#95×C73—21no—
53#95×C73—21no—
54#95×C73—21no—
55#95×C73C2×C411yescharacteristic
56#95×C73C2×C411yescharacteristic
57#11924012—42no—
58#11924012—42no—
59#11924012—82no—
60C2×#10596831—42no—
61C2×#10596831—42no—
62C24×C73—21no—
63C24×C73C22⋊C411yescharacteristic
64C24×C73C22⋊C411yescharacteristic
65C2×D4×C73—21no—
66C2×D4×C73—21no—
67C2×D4×C73—41no—
68C2×D4×C73—41no—
69C2×D4×C73—41no—
70C2×D4×C73—42no—
71C2×D4×C73—42no—
72C2×D4×C73—81no—
73C2×D4×C73—81no—
74C2×D4×C73—81no—
75C2×D4×C73—81no—
76C2×D4×C73—81no—
77C22×C4×C73—21no—
78C22×C4×C73—21no—
79C22×C4×C73—21no—
80C22×C4×C73—21no—
81C22×C4×C73—21no—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73—81no—
85C22×C4×C73—81no—
86C22×C4×C73C22⋊C411yescharacteristic
87C22×C4×C73C22⋊C411yescharacteristic
88C22×C4×C73C22×C411yescharacteristic
89C22×C4×C73C2×D411yescharacteristic
90C22×C4×C73C2×D411yescharacteristic
91C4⋊C4×C73—41no—
92C4⋊C4×C73—41no—
93C4⋊C4×C73—81no—
94C22⋊C4×C73—41no—
95C22⋊C4×C73—41no—
96C22⋊C4×C73—41no—
97C22⋊C4×C73—41no—
98C22⋊C4×C73—41no—
99C22⋊C4×C73—41no—
100C22⋊C4×C73—81no—
101C22⋊C4×C73—81no—
102C22⋊C4×C73—81no—
103C22⋊C4×C73—81no—
104C42×C73—21no—
105C42×C73—21no—
106C23×C73—21no—
107C23×C73—21no—
108C23×C73—21no—
109C23×C73—21no—
110C23×C73—21no—
111C23×C73—21no—
112C23×C73—41no—
113C23×C73—41no—
114C23×C73—41no—
115C23×C73—41no—
116C23×C73—41no—
117C23×C73—41no—
118C23×C73—41no—
119C23×C73—41no—
120C23×C73—41no—
121C23×C73—41no—
122C23×C73—41no—
123C23×C73C2×C22⋊C411yescharacteristic
124D4×C73—42no—
125D4×C73—42no—
126D4×C73—82no—
127D4×C73—84no—
128D4×C73—84no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—41no—
135C2×C4×C73—42no—
136C2×C4×C73—41no—
137C2×C4×C73—41no—
138C2×C4×C73—41no—
139C2×C4×C73—41no—
140C2×C4×C73—41no—
141C2×C4×C73—41no—
142C2×C4×C73—41no—
143C2×C4×C73—41no—
144C2×C4×C73—41no—
145C2×C4×C73—41no—
146C2×C4×C73—41no—
147C2×C4×C73—41no—
148C2×C4×C73—81no—
149C2×C4×C73—81no—
150C2×C4×C73—81no—
151C2×C4×C73#9911yescharacteristic
152C2×C4×C73#9911yescharacteristic
153C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C73#13711yescharacteristic
155#10596831—82no—
156#10596831—82no—
157C22×C73—21no—
158C22×C73—21no—
159C22×C73—42no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—81no—
167C22×C73—81no—
168C22×C73—81no—
169C22×C73—81no—
170C22×C73—81no—
171C22×C73—81no—
172C22×C73—81no—
173C22×C73—81no—
174C22×C73—81no—
175C22×C73—81no—
176C22×C73C2×#9911yescharacteristic
177C22×C73#41711yescharacteristic
178C22×C73#42111yescharacteristic
179C4×C73—21no—
180C4×C73—21no—
181C4×C73—21no—
182C4×C73—21no—
183C4×C73—41no—
184C4×C73—41no—
185C4×C73—41no—
186C4×C73—81no—
187C4×C73—81no—
188C4×C73—81no—
189#11832—731nomaximal, Sylow
190C2×C73—21no—
191C2×C73—21no—
192C2×C73—81no—
193C2×C73—81no—
194C2×C73—161no—
195C2×C73#151311yescharacteristic
196C2×C73#212111yescharacteristic
197C2×C73#213411yescharacteristic
198#2635D7311yescharacteristic
199#1800—731no—
200#1465—731no—
201#1353—732no—
202#1345—732no—
203C73#1183211yescharacteristic, complemented, Sylow
204C2×#121Dic7311yescharacteristic
205C2×C4×D4C2×D7311yescharacteristic
206#423—1461no—
207C2×#100—1461no—
208#407—1461no—
209#400C2×D7311yescharacteristic
210#399Dic7311yescharacteristic
211#394—21no—
212#394C2×D7311yescharacteristic
213#392—21no—
214#392Dic7311yescharacteristic
215#388—21no—
216#386—21no—
217#381Dic7311yescharacteristic
218#343—732no—
219#324—732no—
220#323—1461no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4C2×Dic7311yescharacteristic
224C22×D4C22⋊D7311yescharacteristic
225C23×C4C2×Dic7311yescharacteristic
226C23×C4C22⋊D7311yescharacteristic
227C2×M16—2921no—
228C2×M16—1462no—
229#121—41no—
230#121—41no—
231C4×D4—41no—
232C4×D4—41no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C2×Dic7311yescharacteristic
235C2×C4⋊C4C22×D7311yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4C2×Dic7311yescharacteristic
243C2×C22⋊C4C22⋊D7311yescharacteristic
244C2×C42C22⋊D7311yescharacteristic
245C4⋊C8—2921no—
246C4⋊C8—2921no—
247#100—2922no—
248C22⋊C8—2921no—
249C22⋊C8—1462no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95C2×Dic7311yescharacteristic
254#95C2×Dic7311yescharacteristic
255C24—21no—
256C24C22⋊Dic7311yescharacteristic
257C24C22⋊Dic7311yescharacteristic
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—81no—
266C2×D4—81no—
267C2×D4—81no—
268C2×D4—81no—
269C2×D4—81no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—81no—
278C22×C4—81no—
279C22×C4C22⋊Dic7311yescharacteristic
280C22×C4C22⋊Dic7311yescharacteristic
281C22×C4C22×Dic7311yescharacteristic
282C22×C4C2×C22⋊D7311yescharacteristic
283C22×C4C2×C22⋊D7311yescharacteristic
284M16—2922no—
285M16—2922no—
286M16—5842no—
287C2×C8—2922no—
288C2×C8—2922no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—81no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—81no—
299C22⋊C4—81no—
300C22⋊C4—81no—
301C22⋊C4—81no—
302C42—21no—
303C42—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23C2×C22⋊Dic7311yescharacteristic
322D4—42no—
323D4—42no—
324D4—82no—
325D4—84no—
326D4—84no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4#1455650611yescharacteristic
350C2×C4#1455650611yescharacteristic
351C2×C4#1455661611yescharacteristic
352C2×C4#1455662111yescharacteristic
353C8—5842no—
354C8—5842no—
355C22—21no—
356C22—21no—
357C22—42no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22C2×#1455650611yescharacteristic
375C22#1798858811yescharacteristic
376C22#1798860411yescharacteristic
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—81no—
385C4—81no—
386C4—81no—
387C2—21no—
388C2—21no—
389C2—81no—
390C2—81no—
391C2—161no—
392C2#2260847411yescharacteristic
393C2#2261157711yescharacteristic
394C2#2261162311yescharacteristic
subgroupG/H
centerC22C2×#14556506
commutatorC22×C4×C73C22×C4
FrattiniC2×C4⋊C4C22×D73
Fitting, prime radicalC73×#2635C2
socleC22×C73C2×#99
cosocleC2×C4⋊C4×C73C23
hypercenter#2635D73
hypocenterC73#11832
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2635

Complements

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

NH ≅ G/Ntype
1. #22609923C2semidirect
2. #22608269C2semidirect
3. #22607958C2semidirect
4. #22607934C2semidirect
203. C73#11832semidirect

Maximal subgroups

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

subgroupindex
#226099232
#226082692
#226079582
#226079342
C73×#26352
#1183273