Finite Group Databasebeta

← #32979878

Subgroups — #32979878

Order 18688.

440 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619044C211yesmaximal, characteristic
2#22610082C211yesmaximal, characteristic, complemented
3C4×#14556517C211yesmaximal, characteristic
4#22608316C211yesmaximal, characteristic
5#22607782C211yesmaximal, characteristic, complemented
6#22607763C211yesmaximal, characteristic, complemented
7C73×#1565C211yesmaximal, characteristic, complemented
8C4×#11924028C2211yescharacteristic
9#17988717—21no—
10#17988666—21no—
11#17988655—22no—
12#17988643—21no—
13#17988640C2211yescharacteristic
14#17988609—21no—
15C2×C4⋊#10596831C2211yescharacteristic
16C2×#14556520—22no—
17C2×#14556517C411yescharacteristic
18C2×#14556517C411yescharacteristic
19C42×Dic73C2211yescharacteristic
20#17988348C411yescharacteristic
21#17988348C411yescharacteristic
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
30C2×#11924011—22no—
31C22×#10596831D412yes—
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#14556520—44no—
50#14556517—22no—
51#14556517—22no—
52C22⋊#10596831—21no—
53#14556503—22no—
54#14556501—22no—
55C4×#10596831—21no—
56C2×M16×C73C2×C411yescharacteristic
57C2×M16×C73C2×C411yescharacteristic
58C22×C8×C73—21no—
59C2×C42×C73C2311yescharacteristic
60C4⋊C8×C73—21no—
61C4⋊C8×C73—21no—
62C4⋊C8×C73D411yescharacteristic
63C4⋊C8×C73D411yescharacteristic
64C22⋊C8×C73—21no—
65#97×C73—21no—
66C4×C8×C73—21no—
67C4×C8×C73—21no—
68#11924028—21no—
69#11924028—21no—
70#11924028—21no—
71#11924028—21no—
72C2×Dic146C4⋊C411yescharacteristic
73C2×D292C4⋊C411yescharacteristic
74C2×C22⋊D73—21no—
75C22×Dic73—21no—
76C22×Dic73—21no—
77C2×C4×D73—21no—
78C2×C4×D73—21no—
79C2×C4×D73—21no—
80#11924011—82no—
81C2×#10596831—22no—
82C2×#10596831—42no—
83C2×#10596831—41no—
84C4⋊Dic73C4⋊C411yescharacteristic
85C4⋊Dic73C4⋊C411yescharacteristic
86#11924007—21no—
87#11924007—21no—
88C22⋊Dic73—21no—
89#11924005—21no—
90#11924005—21no—
91C4×Dic73—22no—
92C4×Dic73—22no—
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73—21no—
97C4×Dic73—21no—
98C4×Dic73—21no—
99C4×Dic73—42no—
100C4×Dic73M1612yescomplemented
101C22×C4×C73C22×C411yescharacteristic
102C22×C4×C73C2×D411yescharacteristic
103C22×C4×C73#4111yescharacteristic
104M16×C73—21no—
105M16×C73—21no—
106M16×C73—21no—
107M16×C73M1612yescomplemented
108C2×C8×C73—21no—
109C2×C8×C73—21no—
110C2×C8×C73—21no—
111C2×C8×C73—21no—
112C2×C8×C73—42no—
113C2×C8×C73—41no—
114C42×C73C2×D411yescharacteristic
115C42×C73C2×D411yescharacteristic
116C42×C73C2×Q811yescharacteristic
117C42×C73#4111yescharacteristic
118C23×C73C4×D411yescharacteristic
119C22×D73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—41no—
123C2×C4×C73C2×C4⋊C411yescharacteristic
124C2×C4×C73C4×D411yescharacteristic
125C2×C4×C73#12011yescharacteristic
126C2×C4×C73C22⋊Q811yescharacteristic
127C2×C4×C73C22⋊Q811yescharacteristic
128C2×C4×C73#12311yescharacteristic
129C2×C4×C73C2×M1611yescharacteristic
130C2×C4×C73C2×M1611yescharacteristic
131C2×C4×C73#13111yescharacteristic
132C2×C4×C73#13111yescharacteristic
133C22⋊D73—41no—
134C22⋊D73—41no—
135C2×Dic73—22no—
136C2×Dic73—22no—
137C2×Dic73—22no—
138C2×Dic73—22no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73—21no—
142C2×Dic73—41no—
143C2×Dic73—41no—
144D292—21no—
145D292—21no—
146C4×D73—41no—
147C4×D73—41no—
148C4×D73—41no—
149C4×D73—41no—
150C4×D73—81no—
151Dic146—21no—
152Dic146—21no—
153C8×C73—22no—
154C8×C73—41no—
155C8×C73—41no—
156C8×C73—41no—
157C8×C73—81no—
158#10596831—42no—
159#10596831—81no—
160C22×C73—21no—
161C22×C73—21no—
162C22×C73#38511yescharacteristic
163C22×C73#43511yescharacteristic
164C22×C73#43611yescharacteristic
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—41no—
168C4×C73—21no—
169C4×C73—21no—
170C4×C73—21no—
171C4×C73#42311yescharacteristic
172C4×C73#42411yescharacteristic
173C4×C73#43511yescharacteristic
174C4×C73#43611yescharacteristic
175C4×C73#45311yescharacteristic
176C4×C73#45611yescharacteristic
177Dic73—24no—
178Dic73—42no—
179Dic73—41no—
180Dic73—41no—
181Dic73—41no—
182#8841—731nomaximal, Sylow
183C2×C73—21no—
184C2×C73—21no—
185C2×C73#185111yescharacteristic
186C2×C73#185911yescharacteristic
187C2×C73#186111yescharacteristic
188D73—81no—
189#2989—731no—
190#1842—731no—
191C4×#104—731no—
192#1565D7311yescharacteristic, complemented
193#1477—731no—
194#1283—731no—
195#1276—731no—
196C73#884111yescharacteristic, complemented, Sylow
197C4×#41—731no—
198#446—1461no—
199#436—1461no—
200#435—1462no—
201#432—1461no—
202#431—731no—
203#431C2×D7311yescharacteristic
204#423—1461no—
205C2×C4⋊C8—731no—
206C2×C4⋊C8—1462no—
207C2×C4⋊C8C2×D7311yescharacteristic
208C2×#104—731no—
209C2×#104—731no—
210C4×M16C2×D7311yescharacteristic
211C43—731no—
212#339—731no—
213#339—731no—
214#335—21no—
215#334—21no—
216Q8⋊C8—1461no—
217D4⋊C8—1461no—
218C2×#41—731no—
219C2×M16—1462no—
220C2×M16C4×D7311yescharacteristic
221C2×M16C4×D7311yescharacteristic
222C22×C8—21no—
223C22×C8—732no—
224C4×Q8—731no—
225C4×Q8—731no—
226C4×D4—731no—
227C4×D4—731no—
228C4×D4—1461no—
229C4×D4—1461no—
230#117—731no—
231#117—1461no—
232C2×C42—731no—
233C2×C42—731no—
234C2×C42—1461no—
235C2×C42—1461no—
236C2×C42—1461no—
237C2×C42C22×D7311yescharacteristic
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—2924no—
241C4⋊C8—1462no—
242C4⋊C8—1461no—
243C4⋊C8—1461no—
244C4⋊C8—1461no—
245C4⋊C8C22⋊D7311yescharacteristic
246C4⋊C8C22⋊D7311yescharacteristic
247#104—1462no—
248#104—1462no—
249C22⋊C8—21no—
250C22⋊C8—1462no—
251C22⋊C8—1461no—
252#97—21no—
253#97—1462no—
254C4×C8—21no—
255C4×C8—21no—
256C4×C8—1461no—
257#41—1461no—
258#41—1461no—
259#41—1461no—
260#41—1461no—
261C2×Q8—731no—
262C2×D4—731no—
263C2×D4—1461no—
264C22×C4—1461no—
265C22×C4—1461no—
266C22×C4—1461no—
267C22×C4—1461no—
268C22×C4—1461no—
269C22×C4C2×C4×D7311yescharacteristic
270C22×C4D4×D7311yescharacteristic
271C22×C4#1192402911yescharacteristic
272M16—21no—
273M16—21no—
274M16—21no—
275M16—5842no—
276M16#1192401112yescomplemented
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—42no—
282C2×C8—41no—
283C2×C8—2922no—
284C2×C8—2921no—
285C2×C8—1462no—
286C4⋊C4—731no—
287C4⋊C4—731no—
288C4⋊C4—1461no—
289C4⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C42—2922no—
294C42—732no—
295C42—1462no—
296C42—1462no—
297C42—1461no—
298C42—1461no—
299C42—1461no—
300C42—1461no—
301C42—1461no—
302C42—1461no—
303C42D4×D7311yescharacteristic
304C42C2×C22⋊D7311yescharacteristic
305C42Q8×D7311yescharacteristic
306C42#1192402811yescharacteristic
307C23—1461no—
308C23#1455655311yescharacteristic
309Q8—1461no—
310Q8—1461no—
311D4—2921no—
312D4—2921no—
313D4—1461no—
314D4—1461no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—2921no—
319C2×C4—2921no—
320C2×C4—2921no—
321C2×C4—2921no—
322C2×C4—2921no—
323C2×C4—2921no—
324C2×C4—5841no—
325C2×C4—1462no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4—1462no—
330C2×C4—1462no—
331C2×C4—1462no—
332C2×C4C4⋊C4×D7311yescharacteristic
333C2×C4C4×C22⋊D7311yescharacteristic
334C2×C4#1455655911yescharacteristic
335C2×C4#1455656711yescharacteristic
336C2×C4#1455656911yescharacteristic
337C2×C4#1455657611yescharacteristic
338C2×C4M16×D7311yescharacteristic
339C2×C4C2×#1192401111yescharacteristic
340C2×C4#1455659711yescharacteristic
341C2×C4#1455659911yescharacteristic
342C8—22no—
343C8—41no—
344C8—41no—
345C8—41no—
346C8—81no—
347C8—2922no—
348C8—5841no—
349C22—21no—
350C22—21no—
351C22—2921no—
352C22—2921no—
353C22—2921no—
354C22#1798845811yescharacteristic
355C22#1798865711yescharacteristic
356C22#1798866411yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—2922no—
361C4—2921no—
362C4—2921no—
363C4—2921no—
364C4—1464no—
365C4#1798860911yescharacteristic
366C4#1798861211yescharacteristic
367C4#1798865811yescharacteristic
368C4#1798866311yescharacteristic
369C4#1798875311yescharacteristic
370C4#1798876811yescharacteristic
371C2—21no—
372C2—21no—
373C2—5841no—
374C2#2261011211yescharacteristic
375C2#2261015411yescharacteristic
376C2#2261016811yescharacteristic
subgroupG/H
centerC2×C4#14556559
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1565C2
socleC22×C73#385
prime radicalC2×#11924028C2×C4
cosocleC2×C42×C73C23
hypercenter#1565D73
hypocenterC73#8841
LCSG ▷ C22×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. #22610082C2semidirect
5. #22607782C2semidirect
6. #22607763C2semidirect
7. C73×#1565C2semidirect
100. C4×Dic73M16semidirect
107. M16×C73M16semidirect
192. #1565D73semidirect
196. C73#8841semidirect
276. M16#11924011semidirect

Maximal subgroups

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

subgroupindex
#226190442
#226100822
C4×#145565172
#226083162
#226077822
#226077632
C73×#15652
#884173