Finite Group Databasebeta

← #32980672

Subgroups — #32980672

Order 18688.

626 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
1#22618955C211yesmaximal, characteristic
2C4×#14556572C211yesmaximal, characteristic
3#22609997C212yesmaximal, complemented
4#22607777C212yesmaximal, complemented
5C73×#1459C211yesmaximal, characteristic
6C2×#14556572C411yescharacteristic
7C22×C4×Dic73C2211yescharacteristic
8D4×#10596831—24no—
9#17988640—21no—
10C2×C22⋊#10596831—21no—
11C2×C22⋊#10596831C2212yes—
12#17988475—21no—
13#17988468—21no—
14#17988467C411yescharacteristic
15#17988459C411yescharacteristic
16#17988448C411yescharacteristic
17C4×#11924007—21no—
18C4×C22⋊Dic73—21no—
19C4×C22⋊Dic73C2211yescharacteristic
20#17988341—24no—
21C2×C4×D4×C73C2211yescharacteristic
22C2×C22⋊C8×C73C2212yes—
23#324×C73—21no—
24#323×C73—21no—
25C23×Dic73C2×C411yescharacteristic
26C23×Dic73C2×C411yescharacteristic
27C22×#10596831—22no—
28C22×#10596831D414yes—
29#14556572—22no—
30#14556572C814yescomplemented
31C2×#11924007—21no—
32C2×#11924007—21no—
33C2×C22⋊Dic73—21no—
34C2×C22⋊Dic73—21no—
35C2×C22⋊Dic73C2×C411yescharacteristic
36C2×C22⋊Dic73C2×C411yescharacteristic
37C2×C4×Dic73—21no—
38C2×C4×Dic73—21no—
39C2×C4×Dic73—21no—
40C2×C4×Dic73—22no—
41C2×C4×Dic73—22no—
42C4⋊#10596831—22no—
43C22⋊#10596831—22no—
44C22⋊#10596831—22no—
45C22⋊#10596831—22no—
46C4×#10596831—22no—
47#14556498—21no—
48#14556498—21no—
49#14556498—21no—
50#14556498—21no—
51#14556498—21no—
52C22×D4×C73C2×C411yescharacteristic
53C23×C4×C73D411yescharacteristic
54C23×C4×C73C2311yescharacteristic
55C22×C8×C73—22no—
56C4×D4×C73—22no—
57C4×D4×C73—22no—
58C2×C4⋊C4×C73D411yescharacteristic
59C2×C22⋊C4×C73C2×C411yescharacteristic
60C2×C22⋊C4×C73D411yescharacteristic
61C2×C42×C73D411yescharacteristic
62C22⋊C8×C73—22no—
63C22⋊C8×C73—22no—
64C22×Dic73—21no—
65C22×Dic73—21no—
66C22×Dic73—21no—
67C22×Dic73—22no—
68C22×Dic73—22no—
69C22×Dic73—21no—
70C22×Dic73—22no—
71C22×Dic73—21no—
72C22×Dic73—42no—
73C22×Dic73C2×C812yescomplemented
74C2×#10596831—24no—
75C2×#10596831—44no—
76C2×#10596831—82no—
77#11924007—24no—
78#11924007—42no—
79C22⋊Dic73—24no—
80C22⋊Dic73—21no—
81C22⋊Dic73—22no—
82C22⋊Dic73—42no—
83C22⋊Dic73C2×C812yescomplemented
84C4×Dic73—42no—
85C4×Dic73—41no—
86C4×Dic73—42no—
87C4×Dic73—41no—
88C24×C73C22⋊C411yescharacteristic
89C24×C73C22×C411yescharacteristic
90C2×D4×C73—22no—
91C2×D4×C73—22no—
92C2×D4×C73C2×C812yes—
93C2×D4×C73M1612yes—
94C22×C4×C73—21no—
95C22×C4×C73—21no—
96C22×C4×C73—42no—
97C22×C4×C73—42no—
98C22×C4×C73C22⋊C411yescharacteristic
99C22×C4×C73C22⋊C411yescharacteristic
100C22×C4×C73C22⋊C411yescharacteristic
101C22×C4×C73C2×D412yes—
102C22×C4×C73C2×D411yescharacteristic
103C22×C4×C73C2×D411yescharacteristic
104C22×C4×C73#4112yes—
105C2×C8×C73—44no—
106C2×C8×C73—42no—
107C4⋊C4×C73—22no—
108C22⋊C4×C73—22no—
109C22⋊C4×C73—22no—
110C42×C73—21no—
111C42×C73—21no—
112C23×C73—21no—
113C23×C73—21no—
114C23×C73—41no—
115C23×C73—41no—
116C23×C73—41no—
117C23×C73—41no—
118C23×C73C22⋊C812yes—
119C23×C73C2×C22⋊C411yescharacteristic
120C23×C73C4×D412yes—
121C23×C73C22×C811yescharacteristic
122C23×C73C2×M1611yescharacteristic
123C23×C73#13112yes—
124D4×C73—24no—
125D4×C73—24no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—24no—
129C2×C4×C73—22no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—41no—
133C2×C4×C73—42no—
134C2×C4×C73—42no—
135C2×C4×C73—41no—
136C2×C4×C73—41no—
137C2×C4×C73—81no—
138C2×C4×C73C22⋊C812yes—
139C2×C4×C73#12011yescharacteristic
140C2×C4×C73#12112yes—
141C2×C4×C73#12311yescharacteristic
142C2×Dic73—22no—
143C2×Dic73—24no—
144C2×Dic73—22no—
145C2×Dic73—22no—
146C2×Dic73—24no—
147C2×Dic73—41no—
148C2×Dic73—41no—
149C2×Dic73—41no—
150C2×Dic73—42no—
151C2×Dic73—41no—
152C2×Dic73—41no—
153C2×Dic73—41no—
154C2×Dic73—42no—
155C2×Dic73—41no—
156C2×Dic73—41no—
157C2×Dic73—41no—
158C8×C73—82no—
159#10596831—44no—
160C22×C73—21no—
161C22×C73—22no—
162C22×C73—21no—
163C22×C73—22no—
164C22×C73—22no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73—42no—
168C22×C73—42no—
169C22×C73—41no—
170C22×C73—41no—
171C22×C73—81no—
172C22×C73#38611yescharacteristic
173C22×C73C2×C22⋊C811yescharacteristic
174C22×C73#40811yescharacteristic
175C22×C73C8×D412yes—
176C22×C73#43512yes—
177C4×C73—22no—
178C4×C73—22no—
179C4×C73—21no—
180C4×C73—41no—
181C4×C73—41no—
182C4×C73#45812yes—
183Dic73—42no—
184Dic73—42no—
185Dic73—42no—
186Dic73—81no—
187#8966—731nomaximal, Sylow
188C2×C73—21no—
189C2×C73—21no—
190C2×C73—22no—
191C2×C73—22no—
192C2×C73—42no—
193C2×C73#186911yescharacteristic
194C2×C73#189011yescharacteristic
195C2×C73#189111yescharacteristic
196#2972—731no—
197C4×#123—731no—
198#1817—732no—
199#1459D7311yescharacteristic
200#1282—732no—
201C73#896611yescharacteristic, complemented, Sylow
202C2×#123—731no—
203C2×C4×D4C2×D7311yescharacteristic
204C22×C42—731no—
205C8×D4—1464no—
206#431—1461no—
207C2×C22⋊C8—732no—
208C2×C22⋊C8—1461no—
209C2×C22⋊C8C2×D7312yes—
210#388—1461no—
211#387—1461no—
212#386—731no—
213#385—731no—
214#381—731no—
215C4×C4⋊C4—1461no—
216C4×C22⋊C4—731no—
217C4×C22⋊C4—1461no—
218#336—1464no—
219#324—21no—
220#323—21no—
221C22×D4C4×D7311yescharacteristic
222C23×C4—731no—
223C23×C4—731no—
224C23×C4D29211yescharacteristic
225C23×C4C22×D7311yescharacteristic
226C22×C8—22no—
227C22×C8—734no—
228C22×C8—1462no—
229#123—734no—
230#123—1462no—
231C4×D4—22no—
232C4×D4—22no—
233C2×C4⋊C4—1461no—
234C2×C4⋊C4—1461no—
235C2×C4⋊C4C22⋊D7311yescharacteristic
236C2×C22⋊C4—731no—
237C2×C22⋊C4—731no—
238C2×C22⋊C4—1461no—
239C2×C22⋊C4—1461no—
240C2×C22⋊C4C4×D7311yescharacteristic
241C2×C22⋊C4C22⋊D7311yescharacteristic
242C2×C42—1462no—
243C2×C42—1461no—
244C2×C42—1461no—
245C2×C42—1461no—
246C2×C42—1462no—
247C2×C42D29211yescharacteristic
248C4⋊C8—1462no—
249C22⋊C8—22no—
250C22⋊C8—22no—
251C22⋊C8—1462no—
252C22⋊C8—1462no—
253C22⋊C8—1462no—
254C4×C8—1462no—
255#95—1461no—
256#95—1461no—
257#95—1461no—
258#95—1461no—
259#95—1461no—
260C24#1192400511yescharacteristic
261C24C2×C4×D7311yescharacteristic
262C2×D4—22no—
263C2×D4—22no—
264C2×D4C8×D7312yes—
265C2×D4#1192401112yes—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—2922no—
271C22×C4—732no—
272C22×C4—1461no—
273C22×C4—1461no—
274C22×C4—1461no—
275C22×C4—1461no—
276C22×C4—1462no—
277C22×C4—1462no—
278C22×C4—1461no—
279C22×C4—1462no—
280C22×C4#1192400511yescharacteristic
281C22×C4#1192400511yescharacteristic
282C22×C4#1192400511yescharacteristic
283C22×C4D4×D7312yes—
284C22×C4C2×C22⋊D7311yescharacteristic
285C22×C4C2×D29211yescharacteristic
286C22×C4#1192402712yes—
287C2×C8—44no—
288C2×C8—42no—
289C2×C8—2924no—
290C2×C8—5842no—
291C2×C8—1464no—
292C4⋊C4—22no—
293C4⋊C4—2922no—
294C4⋊C4—1464no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—2922no—
298C22⋊C4—732no—
299C22⋊C4—1462no—
300C22⋊C4—1464no—
301C22⋊C4—1461no—
302C42—21no—
303C42—21no—
304C42—2922no—
305C42—2921no—
306C42—2922no—
307C42—2921no—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23#1455650312yes—
315C23C2×#1192400511yescharacteristic
316C23#1455655112yes—
317C23C2×C8×D7311yescharacteristic
318C23C2×#1192401111yescharacteristic
319C23#1455659912yes—
320D4—24no—
321D4—24no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—2921no—
335C2×C4—2921no—
336C2×C4—2921no—
337C2×C4—2922no—
338C2×C4—2922no—
339C2×C4—2921no—
340C2×C4—2921no—
341C2×C4—2921no—
342C2×C4—2921no—
343C2×C4—2921no—
344C2×C4—2921no—
345C2×C4—1462no—
346C2×C4—1464no—
347C2×C4—1464no—
348C2×C4—1462no—
349C2×C4—1462no—
350C2×C4#1455650312yes—
351C2×C4#1455656111yescharacteristic
352C2×C4#1455656312yes—
353C2×C4#1455657511yescharacteristic
354C8—82no—
355C8—2924no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—42no—
364C22—42no—
365C22—41no—
366C22—41no—
367C22—81no—
368C22#1798846411yescharacteristic
369C22C2×#1455650311yescharacteristic
370C22#1798855511yescharacteristic
371C22#1798865012yes—
372C22#1798865512yes—
373C4—22no—
374C4—22no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—2922no—
379C4—2922no—
380C4—2922no—
381C4—5841no—
382C4#1798877812yes—
383C2—21no—
384C2—21no—
385C2—22no—
386C2—22no—
387C2—42no—
388C2#2261022111yescharacteristic
389C2#2261034211yescharacteristic
390C2#2261034711yescharacteristic
subgroupG/H
centerC2×C4#14556561
commutatorC23×C73C22×C8
FrattiniC23×C4C22×D73
FittingC73×#1459C2
socleC22×C73#386
prime radicalC22×D4×C73C2×C4
cosocleC23×C4×C73C23
hypercenter#1459D73
hypocenterC73#8966
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #22609997C2semidirect
4. #22607777C2semidirect
30. #14556572C8semidirect
73. C22×Dic73C2×C8semidirect
83. C22⋊Dic73C2×C8semidirect
201. C73#8966semidirect

Maximal subgroups

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

subgroupindex
#226189552
C4×#145565722
#226099972
#226077772
C73×#14592
#896673