Finite Group Databasebeta

← #34001420

Subgroups — #34001420

Order 18688.

566 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 110 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#22625823C211yesmaximal, characteristic
2#22625823C211yesmaximal, characteristic
3#22624750C212yesmaximal, complemented
4#22624749C212yesmaximal, complemented
5#389×D73C211yesmaximal, characteristic
6C2×#14556648—21no—
7C2×#14556648—21no—
8#17989453—21no—
9#17989453—21no—
10#17989453C2212yes—
11#17989453C2212yes—
12C2×C4⋊C4×D73—21no—
13C2×C4⋊C4×D73C411yescharacteristic
14C2×C4⋊C4×D73C411yescharacteristic
15C2×C42×D73C2211yescharacteristic
16#17988486C2211yescharacteristic
17#17988485C411yescharacteristic
18#17988484—21no—
19#17988483C2211yescharacteristic
20#17988482—21no—
21#95×D73—21no—
22#389×C73C411yescharacteristic
23C22×#10596833—22no—
24C22×#10596833—22no—
25#14556648—42no—
26#14556648—42no—
27C22×C4×D73—21no—
28C22×C4×D73—21no—
29C22×C4×D73C2×C411yescharacteristic
30C22×C4×D73D411yescharacteristic
31C22×C4×D73D411yescharacteristic
32C2×C4⋊Dic73—21no—
33C2×C4⋊Dic73C2×C411yescharacteristic
34C2×C4⋊Dic73C2×C411yescharacteristic
35C2×#11924007—21no—
36C2×#11924007—21no—
37C2×#11924007—21no—
38C2×#11924007—21no—
39C4⋊C4×D73—22no—
40C4⋊C4×D73—44no—
41C4⋊C4×D73—42no—
42C4⋊C4×D73C814yescomplemented
43C2×C4×Dic73D411yescharacteristic
44C2×C4×Dic73D411yescharacteristic
45C2×C4×Dic73C2311yescharacteristic
46C42×D73—42no—
47#14556498—21no—
48#14556498—21no—
49#14556498—21no—
50C2×C4⋊C4×C73—21no—
51C2×C4⋊C4×C73C2×C411yescharacteristic
52C2×C4⋊C4×C73C2×C411yescharacteristic
53C2×C42×C73C2×C411yescharacteristic
54#95×C73—21no—
55C2×#10596833—42no—
56C2×#10596833—42no—
57C2×#10596833—42no—
58C2×#10596833—42no—
59C2×#10596833—42no—
60C2×#10596833—42no—
61C23×D73C22⋊C411yescharacteristic
62C22×Dic73—21no—
63C22×Dic73—21no—
64C22×Dic73C22⋊C411yescharacteristic
65C22×Dic73C2×D411yescharacteristic
66C22×Dic73C2×D411yescharacteristic
67C2×C4×D73—22no—
68C2×C4×D73—22no—
69C2×C4×D73—24no—
70C2×C4×D73—22no—
71C2×C4×D73—22no—
72C2×C4×D73—22no—
73C2×C4×D73—22no—
74C2×C4×D73—41no—
75C2×C4×D73—41no—
76C2×C4×D73—42no—
77C2×C4×D73—42no—
78C2×C4×D73—42no—
79C2×C4×D73—42no—
80C2×C4×D73—42no—
81C2×C4×D73C2×C812yes—
82C2×C4×D73M1612yes—
83C4⋊Dic73—21no—
84C4⋊Dic73—42no—
85C4⋊Dic73—41no—
86C4⋊Dic73C2×C812yes—
87#11924007—24no—
88#11924007—42no—
89#11924007—42no—
90#11924007—42no—
91C4×Dic73—41no—
92C4×Dic73—41no—
93C4×Dic73—41no—
94C22×C4×C73—21no—
95C22×C4×C73—21no—
96C22×C4×C73C22⋊C411yescharacteristic
97C22×C4×C73C22⋊C411yescharacteristic
98C22×C4×C73C22×C411yescharacteristic
99C4⋊C4×C73—21no—
100C4⋊C4×C73—41no—
101C4⋊C4×C73—42no—
102C4⋊C4×C73C2×C812yes—
103C42×C73—41no—
104C23×C73C2×C22⋊C411yescharacteristic
105C22×D73—21no—
106C22×D73—21no—
107C22×D73—21no—
108C22×D73—21no—
109C22×D73C22⋊C812yes—
110C22×D73#9912yes—
111C22×D73#10112yes—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—22no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—41no—
122C2×C4×C73—41no—
123C2×C4×C73—41no—
124C2×C4×C73—41no—
125C2×C4×C73—41no—
126C2×C4×C73C22×C811yescharacteristic
127C2×C4×C73C2×M1611yescharacteristic
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—22no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140C2×Dic73C22⋊C812yes—
141C2×Dic73AGL(1,ℤ/8)12yes—
142C2×Dic73#13712yes—
143C4×D73—24no—
144C4×D73—24no—
145C4×D73—44no—
146C4×D73—44no—
147C4×D73—48no—
148C4×D73—84no—
149#10596833—82no—
150#10596833—82no—
151C22×C73C2×C22⋊C811yescharacteristic
152C22×C73C2×#9911yescharacteristic
153C22×C73C2×#10111yescharacteristic
154C22×C73#41811yescharacteristic
155C22×C73#41911yescharacteristic
156C22×C73#42111yescharacteristic
157C22×C73#42111yescharacteristic
158C2×D73—22no—
159C2×D73—22no—
160C2×D73—22no—
161C2×D73—22no—
162C2×D73—22no—
163C2×D73—22no—
164C2×D73#32414yes—
165C4×C73—21no—
166C4×C73—21no—
167C4×C73—42no—
168C4×C73—41no—
169C4×C73—41no—
170C4×C73—81no—
171Dic73—22no—
172Dic73—22no—
173Dic73—22no—
174Dic73—42no—
175Dic73—81no—
176#7593—731nomaximal, Sylow
177C2×C73C2×#32411yescharacteristic
178C2×C73#147811yescharacteristic
179C2×C73#147911yescharacteristic
180C2×C73#151011yescharacteristic
181C2×C73#151111yescharacteristic
182C2×C73#153411yescharacteristic
183C2×C73#155611yescharacteristic
184D73—24no—
185C2×#389—731no—
186#1817—731no—
187#1817—731no—
188#1271—732no—
189#1271—732no—
190C73#759311yescharacteristic, complemented, Sylow
191C22×C4⋊C4—731no—
192C22×C4⋊C4—731no—
193C22×C4⋊C4—1461no—
194C22×C42—731no—
195C2×C22⋊C8—1461no—
196C2×C22⋊C8—1461no—
197#389—731no—
198#389—731no—
199#389—731no—
200#389—1461no—
201#389—1461no—
202#389#6440811yescharacteristic
203C2×#95—1461no—
204#336—732no—
205#336—732no—
206#336—1461no—
207#336—1461no—
208C23×C4—731no—
209C23×C4—731no—
210C23×C4—731no—
211C23×C4—1461no—
212C23×C4—1461no—
213C22×C8—1462no—
214C22×C8—1462no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—2924no—
217C2×C4⋊C4—2922no—
218C2×C4⋊C4—731no—
219C2×C4⋊C4—731no—
220C2×C4⋊C4—734no—
221C2×C4⋊C4—1462no—
222C2×C4⋊C4—1461no—
223C2×C4⋊C4—1461no—
224C2×C4⋊C4—1461no—
225C2×C4⋊C4—1461no—
226C2×C4⋊C4—1461no—
227C2×C4⋊C4C2×#6440811yescharacteristic
228C2×C4⋊C4C2×#6440811yescharacteristic
229C2×C42—2922no—
230C2×C42—731no—
231C2×C42—731no—
232C2×C42—731no—
233C2×C42C2×#6440811yescharacteristic
234C22⋊C8—2922no—
235C22⋊C8—2922no—
236#95—21no—
237#95—1461no—
238#95—1461no—
239#95—1461no—
240C24—731no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—2921no—
244C22×C4—2921no—
245C22×C4—2922no—
246C22×C4—2922no—
247C22×C4—2922no—
248C22×C4—2922no—
249C22×C4—2922no—
250C22×C4—731no—
251C22×C4—731no—
252C22×C4—731no—
253C22×C4—732no—
254C22×C4—732no—
255C22×C4—1462no—
256C22×C4—1462no—
257C22×C4—1462no—
258C22×C4—1462no—
259C22×C4—1464no—
260C22×C4—1462no—
261C22×C4—1462no—
262C22×C4—1461no—
263C22×C4—1461no—
264C22×C4C22⋊#6440811yescharacteristic
265C22×C4C22⋊#6440811yescharacteristic
266C22×C4C22×#6440811yescharacteristic
267C2×C8—2922no—
268C2×C8—2922no—
269C2×C8—2922no—
270C2×C8—2922no—
271C2×C8—2922no—
272C2×C8—2922no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—2921no—
277C4⋊C4—2922no—
278C4⋊C4—2922no—
279C4⋊C4—2922no—
280C4⋊C4—2922no—
281C4⋊C4—732no—
282C4⋊C4—1464no—
283C4⋊C4—1461no—
284C4⋊C4#1192403612yes—
285C42—41no—
286C42—2921no—
287C42—2921no—
288C42—2921no—
289C23—732no—
290C23—732no—
291C23—732no—
292C23—1461no—
293C23—1461no—
294C23—1461no—
295C23—1461no—
296C23C2×C22⋊#6440811yescharacteristic
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—2928no—
312C2×C4—2924no—
313C2×C4—2924no—
314C2×C4—2921no—
315C2×C4—2921no—
316C2×C4—2921no—
317C2×C4—2921no—
318C2×C4—2921no—
319C2×C4—5844no—
320C2×C4—732no—
321C2×C4—732no—
322C2×C4—732no—
323C2×C4—1464no—
324C2×C4—1464no—
325C2×C4—1462no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4C2×#1192403611yescharacteristic
333C2×C4D73⋊M1611yescharacteristic
334C8—5842no—
335C8—5842no—
336C22—734no—
337C22—1462no—
338C22—1462no—
339C22—1462no—
340C22—1462no—
341C22—1462no—
342C22—1462no—
343C22#1798955511yescharacteristic
344C22D73⋊#9911yescharacteristic
345C22D73⋊#10111yescharacteristic
346C22#1798957911yescharacteristic
347C22#1798958011yescharacteristic
348C22#1798958411yescharacteristic
349C22#1798958411yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—42no—
355C4—81no—
356C4—2922no—
357C4—5841no—
358C4—1462no—
359C4—1462no—
360C4—1462no—
361C2—1464no—
362C2#2262516011yescharacteristic
363C2#2262523111yescharacteristic
364C2#2262523411yescharacteristic
365C2#2262533711yescharacteristic
366C2#2262534011yescharacteristic
367C2#2262541411yescharacteristic
368C2#2262546111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
Fitting#389×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC23×D73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#389#64408
hypocenterC73#7593
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
3. #22624750C2semidirect
4. #22624749C2semidirect
42. C4⋊C4×D73C8semidirect
190. C73#7593semidirect

Maximal subgroups

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

subgroupindex
#226258232
#226247502
#226247492
#389×D732
#759373