Finite Group Databasebeta

← #32979871

Subgroups — #32979871

Order 18688.

446 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619039C211yesmaximal, characteristic
2#22610047C211yesmaximal, characteristic, complemented
3C4×#14556517C211yesmaximal, characteristic
4#22608316C211yesmaximal, characteristic
5#22607782C211yesmaximal, characteristic, complemented
6#22607763C211yesmaximal, characteristic, complemented
7C73×#1565C211yesmaximal, characteristic, complemented
8C4×#11924028C2211yescharacteristic
9C8×Dic146—21no—
10C8×D292—21no—
11#17988650—22no—
12#17988640C2211yescharacteristic
13#17988639—21no—
14C2×C4⋊#10596831C2211yescharacteristic
15C4⋊C8×D73—21no—
16C2×#14556517C411yescharacteristic
17C2×#14556517C411yescharacteristic
18C42×Dic73C2211yescharacteristic
19#17988348C411yescharacteristic
20#17988348C411yescharacteristic
21#17988341—22no—
22#17988317—21no—
23#17988314—21no—
24#431×C73C2211yescharacteristic
25C2×C4⋊C8×C73C2211yescharacteristic
26C4×M16×C73C2211yescharacteristic
27#335×C73—21no—
28#334×C73—21no—
29C2×#11924028C2×C411yescharacteristic
30C22×#10596831D412yes—
31C2×C8×D73—22no—
32C4×Dic146D411yescharacteristic
33C4×Dic146Q811yescharacteristic
34C4×D292D411yescharacteristic
35C4×D292Q811yescharacteristic
36C4×C22⋊D73—21no—
37C4×C22⋊D73—21no—
38#14556550C2×C411yescharacteristic
39#14556548—21no—
40C2×C4×Dic73—21no—
41C2×C4×Dic73—21no—
42C2×C4×Dic73C2×C411yescharacteristic
43C2×C4×Dic73C2×C411yescharacteristic
44C42×D73—21no—
45C4⋊#10596831—21no—
46C4⋊#10596831—21no—
47C4⋊#10596831—21no—
48#14556520—22no—
49#14556517—22no—
50#14556517C814yescomplemented
51C22⋊#10596831—21no—
52#14556503—22no—
53C4×#10596831—21no—
54C8×Dic73—22no—
55C2×M16×C73C2×C411yescharacteristic
56C2×M16×C73C2×C411yescharacteristic
57C22×C8×C73—21no—
58C2×C42×C73C2311yescharacteristic
59C4⋊C8×C73—21no—
60C4⋊C8×C73—21no—
61C4⋊C8×C73D411yescharacteristic
62C4⋊C8×C73D411yescharacteristic
63C22⋊C8×C73—21no—
64#97×C73—21no—
65C4×C8×C73—21no—
66C4×C8×C73—21no—
67#11924028—21no—
68#11924028—21no—
69#11924028C2×C812yes—
70#11924028M1612yes—
71C2×Dic146C4⋊C411yescharacteristic
72C2×D292C4⋊C411yescharacteristic
73C2×C22⋊D73—21no—
74C22×Dic73—21no—
75C22×Dic73—21no—
76C2×C4×D73—21no—
77C2×C4×D73—21no—
78C2×C4×D73—21no—
79C2×#10596831—22no—
80C2×#10596831—42no—
81C2×#10596831—41no—
82C8×D73—82no—
83C4⋊Dic73C4⋊C411yescharacteristic
84C4⋊Dic73C4⋊C411yescharacteristic
85#11924007—21no—
86#11924007—21no—
87C22⋊Dic73—21no—
88#11924005—21no—
89#11924005—21no—
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73—42no—
97C4×Dic73—41no—
98C4×Dic73—41no—
99C4×Dic73C2×C812yescomplemented
100C22×C4×C73C22×C411yescharacteristic
101C22×C4×C73C2×D411yescharacteristic
102C22×C4×C73#4111yescharacteristic
103M16×C73—21no—
104M16×C73—21no—
105M16×C73—21no—
106M16×C73C2×C812yescomplemented
107C2×C8×C73—21no—
108C2×C8×C73—21no—
109C2×C8×C73—21no—
110C2×C8×C73—21no—
111C2×C8×C73—42no—
112C2×C8×C73—41no—
113C42×C73C2×D411yescharacteristic
114C42×C73C2×D411yescharacteristic
115C42×C73C2×Q811yescharacteristic
116C42×C73#4111yescharacteristic
117C23×C73C4×D411yescharacteristic
118C22×D73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—41no—
122C2×C4×C73C2×C4⋊C411yescharacteristic
123C2×C4×C73C4×D411yescharacteristic
124C2×C4×C73#12011yescharacteristic
125C2×C4×C73C22⋊Q811yescharacteristic
126C2×C4×C73C22⋊Q811yescharacteristic
127C2×C4×C73#12311yescharacteristic
128C2×C4×C73C22×C811yescharacteristic
129C2×C4×C73C2×M1611yescharacteristic
130C2×C4×C73#13111yescharacteristic
131C2×C4×C73#13111yescharacteristic
132C22⋊D73—22no—
133C22⋊D73—22no—
134C2×Dic73—21no—
135C2×Dic73—22no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—22no—
139C2×Dic73—41no—
140C2×Dic73—41no—
141C2×Dic73—41no—
142C2×Dic73—41no—
143D292—21no—
144D292C4⋊C812yes—
145C4×D73—22no—
146C4×D73—22no—
147C4×D73—41no—
148C4×D73—41no—
149C4×D73—81no—
150Dic146—21no—
151Dic146C4⋊C812yes—
152C8×C73—22no—
153C8×C73—41no—
154C8×C73—41no—
155C8×C73—41no—
156C8×C73—81no—
157#10596831—42no—
158#10596831—81no—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73#38511yescharacteristic
162C22×C73C8×D411yescharacteristic
163C22×C73#43511yescharacteristic
164C2×D73—22no—
165C2×D73—41no—
166C2×D73—41no—
167C4×C73—21no—
168C4×C73—21no—
169C4×C73—21no—
170C4×C73C2×C4⋊C811yescharacteristic
171C4×C73#42411yescharacteristic
172C4×C73C8×D411yescharacteristic
173C4×C73#43511yescharacteristic
174C4×C73#45411yescharacteristic
175C4×C73#45511yescharacteristic
176Dic73—22no—
177Dic73—42no—
178Dic73—42no—
179Dic73—41no—
180Dic73—41no—
181#8840—731nomaximal, Sylow
182C2×C73—21no—
183C2×C73—21no—
184C2×C73#185011yescharacteristic
185C2×C73#186011yescharacteristic
186C2×C73#186111yescharacteristic
187D73—42no—
188#2988—731no—
189#1831—731no—
190C4×#104—731no—
191#1565D7311yescharacteristic, complemented
192#1477—731no—
193#1283—731no—
194#1276—731no—
195C73#884011yescharacteristic, complemented, Sylow
196C4×#41—731no—
197C8×Q8—1461no—
198C8×D4—1461no—
199C8×D4—1462no—
200#431—731no—
201#431—1461no—
202#431C2×D7311yescharacteristic
203C2×C4⋊C8—731no—
204C2×C4⋊C8—1461no—
205C2×C4⋊C8C2×D7311yescharacteristic
206C2×#104—731no—
207C2×#104—731no—
208C4×M16C2×D7311yescharacteristic
209C43—731no—
210#339—731no—
211#339—731no—
212#336—1462no—
213#335—21no—
214#334—21no—
215Q8⋊C8—1461no—
216D4⋊C8—1461no—
217C2×#41—731no—
218C2×M16C4×D7311yescharacteristic
219C2×M16C4×D7311yescharacteristic
220C22×C8—21no—
221C22×C8—732no—
222C22×C8—1462no—
223C4×Q8—731no—
224C4×Q8—731no—
225C4×D4—731no—
226C4×D4—731no—
227C4×D4—1461no—
228C4×D4—1461no—
229#117—731no—
230#117—1461no—
231C2×C42—731no—
232C2×C42—731no—
233C2×C42—1461no—
234C2×C42—1461no—
235C2×C42—1461no—
236C2×C42C22×D7311yescharacteristic
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—1462no—
240C4⋊C8—1461no—
241C4⋊C8—1461no—
242C4⋊C8—1461no—
243C4⋊C8C22⋊D7311yescharacteristic
244C4⋊C8C22⋊D7311yescharacteristic
245#104—734no—
246#104—1462no—
247C22⋊C8—21no—
248C22⋊C8—1462no—
249C22⋊C8—1461no—
250#97—21no—
251C4×C8—21no—
252C4×C8—21no—
253C4×C8—1462no—
254C4×C8—1461no—
255#41—732no—
256#41—732no—
257#41—1461no—
258#41—1461no—
259C2×Q8—731no—
260C2×D4—731no—
261C2×D4—1461no—
262C22×C4—1461no—
263C22×C4—1461no—
264C22×C4—1461no—
265C22×C4—1461no—
266C22×C4—1461no—
267C22×C4C2×C4×D7311yescharacteristic
268C22×C4D4×D7311yescharacteristic
269C22×C4#1192402911yescharacteristic
270M16—21no—
271M16—21no—
272M16—21no—
273M16C8×D7312yescomplemented
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—42no—
279C2×C8—41no—
280C2×C8—2922no—
281C2×C8—2921no—
282C2×C8—5842no—
283C2×C8—1462no—
284C4⋊C4—731no—
285C4⋊C4—731no—
286C4⋊C4—1461no—
287C4⋊C4—1461no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C42—2921no—
292C42—2921no—
293C42—2922no—
294C42—732no—
295C42—1461no—
296C42—1461no—
297C42—1461no—
298C42—1461no—
299C42—1461no—
300C42—1461no—
301C42D4×D7311yescharacteristic
302C42C2×C22⋊D7311yescharacteristic
303C42Q8×D7311yescharacteristic
304C42#1192402811yescharacteristic
305C23—1461no—
306C23#1455655311yescharacteristic
307Q8—732no—
308Q8—1461no—
309D4—732no—
310D4—1462no—
311D4—1462no—
312D4—1461no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—2921no—
317C2×C4—2921no—
318C2×C4—2921no—
319C2×C4—2921no—
320C2×C4—2921no—
321C2×C4—2921no—
322C2×C4—5841no—
323C2×C4—1462no—
324C2×C4—1462no—
325C2×C4—1461no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1462no—
329C2×C4—1462no—
330C2×C4C4⋊C4×D7311yescharacteristic
331C2×C4C4×C22⋊D7311yescharacteristic
332C2×C4#1455655911yescharacteristic
333C2×C4#1455656711yescharacteristic
334C2×C4#1455656911yescharacteristic
335C2×C4#1455657611yescharacteristic
336C2×C4C2×C8×D7311yescharacteristic
337C2×C4M16×D7311yescharacteristic
338C2×C4#1455659711yescharacteristic
339C2×C4#1455659911yescharacteristic
340C8—22no—
341C8—41no—
342C8—41no—
343C8—41no—
344C8—81no—
345C8—2922no—
346C8—5841no—
347C22—21no—
348C22—21no—
349C22—2921no—
350C22—2921no—
351C22—1462no—
352C22#1798845811yescharacteristic
353C22#1798865211yescharacteristic
354C22#1798865711yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—2922no—
359C4—2922no—
360C4—2921no—
361C4—2921no—
362C4—1462no—
363C4C4⋊C8×D7311yescharacteristic
364C4#1798861211yescharacteristic
365C4C8×C22⋊D7311yescharacteristic
366C4#1798865611yescharacteristic
367C4#1798875811yescharacteristic
368C4#1798876311yescharacteristic
369C2—21no—
370C2—21no—
371C2—2922no—
372C2#2261010711yescharacteristic
373C2#2261016111yescharacteristic
374C2#2261016811yescharacteristic
subgroupG/H
centerC2×C4#14556559
commutatorC2×C4×C73C22×C8
FrattiniC2×C42C22×D73
FittingC73×#1565C2
socleC22×C73#385
prime radicalC2×#11924028C2×C4
cosocleC2×C42×C73C23
hypercenter#1565D73
hypocenterC73#8840
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
2. #22610047C2semidirect
5. #22607782C2semidirect
6. #22607763C2semidirect
7. C73×#1565C2semidirect
50. #14556517C8semidirect
99. C4×Dic73C2×C8semidirect
106. M16×C73C2×C8semidirect
191. #1565D73semidirect
195. C73#8840semidirect
273. M16C8×D73semidirect

Maximal subgroups

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

subgroupindex
#226190392
#226100472
C4×#145565172
#226083162
#226077822
#226077632
C73×#15652
#884073