Finite Group Databasebeta

← #34013366

Subgroups — #34013366

Order 18688.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989597C211yesmaximal, characteristic
2C2×#17989514C211yesmaximal, characteristic, complemented
3C2×#17989513C211yesmaximal, characteristic, complemented
4#22625808C211yesmaximal, characteristic
5#22624989C211yesmaximal, characteristic, complemented
6#22624989C211yesmaximal, characteristic, complemented
7C22⋊C16×D73C211yesmaximal, characteristic
8C2×#14556670—21no—
9#17989597—22no—
10#17989597—22no—
11C2×#14556660C2211yescharacteristic
12C2×#14556660C2211yescharacteristic
13C2×#14556660C2211yescharacteristic
14C2×#14556660C2211yescharacteristic
15C2×#14556659—21no—
16#17989529—21no—
17#17989514—22no—
18#17989513—22no—
19#17989461—21no—
20C22×C8×D73C2211yescharacteristic
21C2×C16×D73C2211yescharacteristic
22C2×C16×D73C2211yescharacteristic
23C22⋊#11924003C411yescharacteristic, complemented
24#17988366C411yescharacteristic, complemented
25#17988366C411yescharacteristic, complemented
26C22⋊C16×C73C411yescharacteristic, complemented
27#14556670—24no—
28#14556670—42no—
29C2×C4⋊#64408—21no—
30C2×C4⋊#64408—21no—
31C2×C4⋊#64408—21no—
32C2×C4⋊#64408—21no—
33C2×C22⋊#64408—41no—
34C2×C22⋊#64408—41no—
35C2×C4×#64408—41no—
36#14556660—21no—
37#14556660—21no—
38#14556660—21no—
39#14556660—21no—
40#14556660—21no—
41#14556660—21no—
42#14556660D412yes—
43#14556660D412yes—
44#14556659—24no—
45(C2×#64408)⋊C4—41no—
46C22×C4×D73D411yescharacteristic
47C22×#10596831Q811yescharacteristic
48C2×C8×D73—21no—
49C2×C8×D73—21no—
50C2×C8×D73—21no—
51C2×C8×D73—21no—
52C2×C8×D73C2×C411yescharacteristic
53C2×C8×D73D411yescharacteristic
54C2×C8×D73Q811yescharacteristic
55C2×C8×D73C2311yescharacteristic
56C2×#11924003C2×C411yescharacteristic
57C2×#11924003C2×C411yescharacteristic
58C16×D73—21no—
59C16×D73—21no—
60C16×D73—21no—
61C16×D73—21no—
62C22×C8×C73C2×C411yescharacteristic
63C2×C16×C73C2×C411yescharacteristic
64C2×C16×C73C2×C411yescharacteristic
65C22×#64408—41no—
66C22×#64408—41no—
67C22×#64408—41no—
68C22×#64408—41no—
69C4⋊#64408—22no—
70C4⋊#64408—22no—
71C4⋊#64408—41no—
72C4⋊#64408—41no—
73C4⋊#64408—41no—
74C4⋊#64408—41no—
75C4⋊#64408—41no—
76C4⋊#64408—41no—
77C22⋊#64408—44no—
78C22⋊#64408—82no—
79C4×#64408—44no—
80C23×D73D811yescharacteristic
81C22×Dic73Q1611yescharacteristic
82C2×C4×D73—21no—
83C2×C4×D73—21no—
84C2×C4×D73—21no—
85C2×C4×D73—21no—
86C2×C4×D73C4⋊C411yescharacteristic
87C2×C4×D73D811yescharacteristic
88C2×C4×D73Q1611yescharacteristic
89C2×C4×D73C2×D411yescharacteristic
90C2×#10596831—21no—
91C2×#10596831—21no—
92C2×#10596831C4⋊C411yescharacteristic
93C2×#10596831C2×Q811yescharacteristic
94C8×D73—21no—
95C8×D73—21no—
96C8×D73—21no—
97C8×D73—21no—
98C8×D73—21no—
99C8×D73—21no—
100C8×D73C2×D411yescharacteristic
101C8×D73C2×D411yescharacteristic
102C8×D73#4111yescharacteristic
103C8×D73#4111yescharacteristic
104#11924003—21no—
105#11924003—21no—
106C22×C4×C73C4⋊C411yescharacteristic
107C2×C8×C73—21no—
108C2×C8×C73—21no—
109C2×C8×C73C4⋊C411yescharacteristic
110C2×C8×C73C22×C411yescharacteristic
111C16×C73—21no—
112C16×C73—21no—
113C23×C73#10711yescharacteristic
114C22×D73—21no—
115C22×D73—21no—
116C22×D73—21no—
117C22×D73—21no—
118C22×D73—21no—
119C22×D73—21no—
120C22×D73#10711yescharacteristic
121C22×D73C2×D811yescharacteristic
122C2×#64408—42no—
123C2×#64408—42no—
124C2×#64408—81no—
125C2×#64408—81no—
126C2×#64408—81no—
127C2×#64408—81no—
128C2×#64408—81no—
129C2×#64408—81no—
130C2×#64408—81no—
131C2×#64408—81no—
132C2×#64408—81no—
133C2×#64408—81no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73#10711yescharacteristic
137C2×C4×C73C2×C4⋊C411yescharacteristic
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73#10711yescharacteristic
141C2×Dic73C2×Q1611yescharacteristic
142C4×D73—21no—
143C4×D73—21no—
144C4×D73—21no—
145C4×D73—21no—
146C4×D73—21no—
147C4×D73—21no—
148C4×D73#12011yescharacteristic
149C4×D73#12311yescharacteristic
150C4×D73AGL(1,ℤ/8)11yescharacteristic
151C4×D73#13711yescharacteristic
152C8×C73—21no—
153C8×C73C4×D411yescharacteristic
154C8×C73C4×D411yescharacteristic
155#10596831—21no—
156#10596831C22⋊Q811yescharacteristic
157#10596831C22⋊Q811yescharacteristic
158C22×C73—21no—
159C22×C73—21no—
160C22×C73—21no—
161C22×C73C2×#10711yescharacteristic
162C2×D73—21no—
163C2×D73—21no—
164C2×D73—21no—
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—41no—
168C2×D73—41no—
169C2×D73#44711yescharacteristic
170C2×D73#48011yescharacteristic
171C2×D73#50811yescharacteristic
172C2×D73#50811yescharacteristic
173C2×D73#50911yescharacteristic
174C2×D73#51011yescharacteristic
175#64408—82no—
176#64408—82no—
177#64408—161no—
178#64408—161no—
179C4×C73—21no—
180C4×C73#38511yescharacteristic
181C4×C73#42811yescharacteristic
182Dic73—21no—
183Dic73#45111yescharacteristic
184Dic73#48411yescharacteristic
185#12921—731nomaximal, Sylow
186C2×C73—41no—
187C2×C73#185211yescharacteristic
188C2×C73#215811yescharacteristic
189C2×C73#215911yescharacteristic
190D73—41no—
191D73#218611yescharacteristic
192D73#218911yescharacteristic
193D73#223411yescharacteristic
194D73#223711yescharacteristic
195C2×#427—731no—
196C2×#367—731no—
197C2×#366—731no—
198C2×C22⋊C16—731no—
199#1808—731no—
200#1380—731no—
201#1380—731no—
202C73#1292111yescharacteristic, complemented, Sylow
203C23×C8—731no—
204C2×#117—1461no—
205C22×C16—731no—
206C22×C16—731no—
207#427—1462no—
208#427—1462no—
209C2×#107—731no—
210C2×#107—731no—
211C2×#107—731no—
212C2×#107—731no—
213C2×#106—1461no—
214#380—1461no—
215#367—1462no—
216#366—1462no—
217C22⋊C16—731no—
218C22⋊C16—731no—
219C22⋊C16—731no—
220C22⋊C16#6440811yescharacteristic, complemented
221#340—1461no—
222C23×C4—731no—
223C22×C8—731no—
224C22×C8—731no—
225C22×C8—731no—
226C22×C8—731no—
227C22×C8—731no—
228C22×C8—1461no—
229C22×C8—1461no—
230C22×C8—1461no—
231C22×C8—1461no—
232C22×C8C2×#6440811yescharacteristic
233#117—2922no—
234#117—1464no—
235C2×C4⋊C4—1461no—
236C2×C4⋊C4—1461no—
237C2×C4⋊C4—1461no—
238C2×C4⋊C4—1461no—
239C2×C22⋊C4—2921no—
240C2×C22⋊C4—2921no—
241C2×C42—2921no—
242C2×C16—731no—
243C2×C16—731no—
244C2×C16—1461no—
245C2×C16—1461no—
246C2×C16—1461no—
247C2×C16—1461no—
248C2×C16C2×#6440811yescharacteristic
249C2×C16C2×#6440811yescharacteristic
250#107—732no—
251#107—732no—
252#107—1461no—
253#107—1461no—
254#107—1461no—
255#107—1461no—
256#107—1461no—
257#107—1461no—
258#106—1464no—
259#95—2921no—
260C24—731no—
261C22×C4—2921no—
262C22×C4—2921no—
263C22×C4—2921no—
264C22×C4—2921no—
265C22×C4—731no—
266C22×C4—731no—
267C22×C4—731no—
268C22×C4—731no—
269C22×C4—731no—
270C22×C4—1461no—
271C22×C4—1461no—
272C22×C4—1461no—
273C22×C4—1461no—
274C22×C4C4⋊#6440811yescharacteristic
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—731no—
278C2×C8—731no—
279C2×C8—731no—
280C2×C8—731no—
281C2×C8—731no—
282C2×C8—731no—
283C2×C8—1461no—
284C2×C8—1461no—
285C2×C8—1461no—
286C2×C8—1461no—
287C2×C8—1461no—
288C2×C8—1461no—
289C2×C8—1461no—
290C2×C8—1461no—
291C2×C8C4⋊#6440811yescharacteristic
292C2×C8C22×#6440811yescharacteristic
293C4⋊C4—2921no—
294C4⋊C4—2921no—
295C4⋊C4—2921no—
296C4⋊C4—2921no—
297C4⋊C4—2921no—
298C4⋊C4—2921no—
299C4⋊C4—1462no—
300C4⋊C4—1462no—
301C22⋊C4—2924no—
302C22⋊C4—5842no—
303C42—2924no—
304C16—21no—
305C16—21no—
306C16—1461no—
307C16—1461no—
308C23—731no—
309C23—731no—
310C23—1461no—
311C23—1461no—
312C23—1461no—
313C23—1461no—
314C23—1461no—
315C23—1461no—
316C23#1455666011yescharacteristic
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—2922no—
320C2×C4—2922no—
321C2×C4—5841no—
322C2×C4—5841no—
323C2×C4—5841no—
324C2×C4—5841no—
325C2×C4—5841no—
326C2×C4—5841no—
327C2×C4—5841no—
328C2×C4—5841no—
329C2×C4—5841no—
330C2×C4—5841no—
331C2×C4—731no—
332C2×C4—731no—
333C2×C4—731no—
334C2×C4—731no—
335C2×C4—731no—
336C2×C4—731no—
337C2×C4—1461no—
338C2×C4—1461no—
339C2×C4—1461no—
340C2×C4—1461no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4#1455666011yescharacteristic
346C2×C4C2×C4⋊#6440811yescharacteristic
347C8—21no—
348C8—731no—
349C8—731no—
350C8—1461no—
351C8D4×#6440811yescharacteristic
352C8D4×#6440811yescharacteristic
353C22—21no—
354C22—21no—
355C22—21no—
356C22—2921no—
357C22—2921no—
358C22—2921no—
359C22—2921no—
360C22—731no—
361C22—731no—
362C22—731no—
363C22—731no—
364C22—731no—
365C22—731no—
366C22—1461no—
367C22—1461no—
368C22—1461no—
369C22C2×#1455666011yescharacteristic
370C4—21no—
371C4—5842no—
372C4—5842no—
373C4—731no—
374C4—731no—
375C4—11681no—
376C4—11681no—
377C4—1461no—
378C4#1798953411yescharacteristic
379C4#1798959811yescharacteristic
380C2—41no—
381C2—2921no—
382C2—731no—
383C2—731no—
384C2—731no—
385C2—731no—
386C2#2262588011yescharacteristic
387C2#2262628211yescharacteristic
388C2#2262628311yescharacteristic
subgroupG/H
centerC22C2×#14556660
commutatorC2×C8×C73C22×C4
FrattiniC2×C8C22×#64408
FittingC22⋊C16×C73C4
socleC22×C73C2×#107
prime radicalC23×D73D8
cosocleC2×C8×D73C23
hypercenterC22⋊C16#64408
hypocenterC73#12921
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
2. C2×#17989514C2semidirect
3. C2×#17989513C2semidirect
5. #22624989C2semidirect
6. #22624989C2semidirect
23. C22⋊#11924003C4semidirect
24. #17988366C4semidirect
25. #17988366C4semidirect
26. C22⋊C16×C73C4semidirect
202. C73#12921semidirect
220. C22⋊C16#64408semidirect

Maximal subgroups

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

subgroupindex
C2×#179895972
C2×#179895142
C2×#179895132
#226258082
#226249892
C22⋊C16×D732
#1292173