Finite Group Databasebeta

← #34012453

Subgroups — #34012453

Order 18688.

420 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989643C211yesmaximal, characteristic
2C2×#17989478C211yesmaximal, characteristic, complemented
3C2×#17989477C211yesmaximal, characteristic, complemented
4#22625667C211yesmaximal, characteristic
5#22624971C211yesmaximal, characteristic, complemented
6#22624971C211yesmaximal, characteristic, complemented
7#22611540C211yesmaximal, characteristic
8C2×#14556666C2211yescharacteristic
9C2×#14556666C2211yescharacteristic
10#17989643—22no—
11#17989643—22no—
12C2×#14556665C412yescomplemented
13C2×#14556664C412yescomplemented
14#17989555C411yescharacteristic
15C2×#14556645C2211yescharacteristic
16C2×#14556645C2211yescharacteristic
17C4×C22⋊#64408C411yescharacteristic
18#17989478—22no—
19#17989477—22no—
20#17989452C411yescharacteristic
21#17989452C411yescharacteristic
22C22×C8×D73C2211yescharacteristic
23C2×#14556530C2211yescharacteristic
24C2×#14556530C2211yescharacteristic
25C22⋊#11924003C411yescharacteristic, complemented
26#17988366C411yescharacteristic, complemented
27#17988366C411yescharacteristic, complemented
28C22⋊C16×C73C411yescharacteristic, complemented
29C2×#11924036C2×C411yescharacteristic
30C2×#11924036C2×C411yescharacteristic
31C2×C22⋊#64408—21no—
32C2×C4×#64408C2×C411yescharacteristic
33C2×C4×#64408C2×C411yescharacteristic
34#14556666—21no—
35#14556666—21no—
36#14556666D412yes—
37#14556666D412yes—
38#14556665—24no—
39#14556664—24no—
40C2×#11924031C2×C412yes—
41C2×#11924031C2×C412yes—
42#14556648—21no—
43C22⋊#10596833—21no—
44#14556645—21no—
45#14556645—21no—
46#14556645—21no—
47#14556645—21no—
48(C2×#64408)⋊C4—21no—
49C22×C4×D73C2×C411yescharacteristic
50C22×#10596831C2×C411yescharacteristic
51C2×C8×D73—21no—
52C2×C8×D73—21no—
53C2×C8×D73—21no—
54C2×C8×D73—21no—
55C2×C8×D73C2×C411yescharacteristic
56C2×C8×D73C2×C411yescharacteristic
57C2×C8×D73C2×C411yescharacteristic
58C2×C8×D73C2311yescharacteristic
59#14556530—21no—
60#14556530—21no—
61#14556530—21no—
62#14556530—21no—
63C2×#11924003C2×C411yescharacteristic
64C2×#11924003C2×C411yescharacteristic
65C22×C8×C73C2×C411yescharacteristic
66C2×C16×C73C2×C411yescharacteristic
67C2×C16×C73C2×C411yescharacteristic
68C22×#64408—21no—
69C22×#64408—21no—
70#11924036—21no—
71#11924036—21no—
72#11924036—21no—
73#11924036—21no—
74C2×#10596833—21no—
75C2×#10596833—21no—
76C22⋊#64408—42no—
77C4×#64408—21no—
78C4×#64408—21no—
79C4×#64408—21no—
80C4×#64408—21no—
81#11924031—22no—
82#11924031C22⋊C414yescomplemented
83C23×D73M1611yescharacteristic
84C22×Dic73M1611yescharacteristic
85C2×C4×D73—21no—
86C2×C4×D73—21no—
87C2×C4×D73—21no—
88C2×C4×D73—21no—
89C2×C4×D73C4211yescharacteristic
90C2×C4×D73M1611yescharacteristic
91C2×C4×D73M1611yescharacteristic
92C2×C4×D73C22×C411yescharacteristic
93C2×#10596831—21no—
94C2×#10596831—21no—
95C2×#10596831C4211yescharacteristic
96C2×#10596831C22×C411yescharacteristic
97C8×D73—21no—
98C8×D73—21no—
99C8×D73—21no—
100C8×D73—21no—
101C8×D73—21no—
102C8×D73—21no—
103C8×D73C2×D411yescharacteristic
104C8×D73C2×D411yescharacteristic
105C8×D73#4111yescharacteristic
106C8×D73#4111yescharacteristic
107#11924003—21no—
108#11924003—21no—
109C22×C4×C73C4211yescharacteristic
110C2×C8×C73—21no—
111C2×C8×C73—21no—
112C2×C8×C73C4211yescharacteristic
113C2×C8×C73C22×C411yescharacteristic
114C16×C73—21no—
115C16×C73—21no—
116C23×C73#9711yescharacteristic
117C22×D73—22no—
118C22×D73—21no—
119C22×D73—21no—
120C22×D73—41no—
121C22×D73#9711yescharacteristic
122C22×D73C2×M1611yescharacteristic
123C2×#64408—41no—
124C2×#64408—41no—
125C2×#64408—41no—
126C2×#64408—41no—
127C2×#64408—41no—
128C2×#64408—41no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73#9711yescharacteristic
132C2×C4×C73C2×C4211yescharacteristic
133C2×Dic73—21no—
134C2×Dic73—21no—
135C2×Dic73#9711yescharacteristic
136C2×Dic73C2×M1611yescharacteristic
137C4×D73—21no—
138C4×D73—21no—
139C4×D73—21no—
140C4×D73—21no—
141C4×D73—21no—
142C4×D73—21no—
143C4×D73C4×D411yescharacteristic
144C4×D73C4×D411yescharacteristic
145C4×D73#13111yescharacteristic
146C4×D73#13111yescharacteristic
147#10596833—41no—
148#10596833—41no—
149C8×C73—21no—
150C8×C73C4×D411yescharacteristic
151C8×C73C4×D411yescharacteristic
152#10596831—21no—
153#10596831C2×C22⋊C411yescharacteristic
154#10596831#11711yescharacteristic
155C22×C73—21no—
156C22×C73—21no—
157C22×C73—21no—
158C22×C73C2×#9711yescharacteristic
159C2×D73—21no—
160C2×D73—21no—
161C2×D73—21no—
162C2×D73—21no—
163C2×D73—42no—
164C2×D73—42no—
165C2×D73#34712yescomplemented
166C2×D73#43511yescharacteristic
167C2×D73#43511yescharacteristic
168#64408—81no—
169#64408—81no—
170C4×C73—21no—
171C4×C73C4×C22⋊C411yescharacteristic
172C4×C73#40511yescharacteristic
173Dic73—21no—
174Dic73#43511yescharacteristic
175Dic73#43511yescharacteristic
176#12616—731nomaximal, Sylow
177C2×C73—41no—
178C2×C73#175211yescharacteristic
179C2×C73C2×#34711yescharacteristic
180C2×C73#211011yescharacteristic
181D73—21no—
182D73—21no—
183D73—22no—
184C22×M32—731no—
185#2112—731no—
186C2×#347—731no—
187C2×#347—731no—
188#1752—731no—
189#1375—731no—
190#1375—731no—
191C73#1261611yescharacteristic, complemented, Sylow
192C23×C8—731no—
193C2×M32—731no—
194C2×M32—732no—
195C2×M32—731no—
196C2×M32—731no—
197C2×M32—731no—
198C2×M32—1462no—
199C2×M32—1462no—
200C22×C16—732no—
201C2×C22⋊C8—731no—
202C2×#97—731no—
203C2×#97—731no—
204C4×C22⋊C4—731no—
205C22⋊C16—731no—
206C22⋊C16—731no—
207C22⋊C16—731no—
208C22⋊C16#6440811yescharacteristic, complemented
209#347—1462no—
210#347—1462no—
211#336—731no—
212#336—731no—
213C23×C4—731no—
214C22×C8—731no—
215C22×C8—731no—
216C22×C8—731no—
217C22×C8—731no—
218C22×C8—731no—
219C22×C8—731no—
220C22×C8—731no—
221C22×C8—1461no—
222C22×C8—1461no—
223C22×C8—1461no—
224C22×C8—1461no—
225C22×C8C2×#6440811yescharacteristic
226C2×C22⋊C4—1461no—
227C2×C42—731no—
228C2×C42—731no—
229M32—732no—
230M32—732no—
231M32—1461no—
232M32—1461no—
233M32—1461no—
234M32—1461no—
235M32—1464no—
236M32—1461no—
237M32—1461no—
238C2×C16—732no—
239C2×C16—732no—
240C2×C16—731no—
241C2×C16—731no—
242C2×C16—1464no—
243C2×C16C2×#6440811yescharacteristic
244C2×C16C2×#6440811yescharacteristic
245C22⋊C8—1461no—
246C22⋊C8—1461no—
247#97—1461no—
248#97—1461no—
249#97—1461no—
250#97—1461no—
251#95—1461no—
252C24—731no—
253C22×C4—731no—
254C22×C4—731no—
255C22×C4—731no—
256C22×C4—731no—
257C22×C4—731no—
258C22×C4—1461no—
259C22×C4—1461no—
260C22×C4—1461no—
261C22×C4—1461no—
262C22×C4—1461no—
263C22×C4—1461no—
264C22×C4C4×#6440811yescharacteristic
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—731no—
268C2×C8—731no—
269C2×C8—731no—
270C2×C8—731no—
271C2×C8—731no—
272C2×C8—731no—
273C2×C8—1461no—
274C2×C8—1461no—
275C2×C8—1461no—
276C2×C8—1461no—
277C2×C8—1461no—
278C2×C8—1461no—
279C2×C8—1461no—
280C2×C8—1461no—
281C2×C8—1461no—
282C2×C8—1461no—
283C2×C8—1461no—
284C2×C8—1461no—
285C2×C8—1461no—
286C2×C8—1461no—
287C2×C8C4×#6440811yescharacteristic
288C2×C8C22×#6440811yescharacteristic
289C22⋊C4—2922no—
290C42—1461no—
291C42—1461no—
292C42—1461no—
293C42—1461no—
294C16—21no—
295C16—21no—
296C16—734no—
297C16—1462no—
298C16—1461no—
299C16—1461no—
300C23—2921no—
301C23—731no—
302C23—731no—
303C23—1462no—
304C23—1461no—
305C23—1461no—
306C23#1455664511yescharacteristic
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—2921no—
310C2×C4—2921no—
311C2×C4—2921no—
312C2×C4—2921no—
313C2×C4—2921no—
314C2×C4—2921no—
315C2×C4—731no—
316C2×C4—731no—
317C2×C4—731no—
318C2×C4—731no—
319C2×C4—731no—
320C2×C4—731no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4—1461no—
324C2×C4—1461no—
325C2×C4—1461no—
326C2×C4—1461no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4#1455664511yescharacteristic
330C2×C4C2×C4×#6440811yescharacteristic
331C8—21no—
332C8—2921no—
333C8—2921no—
334C8—731no—
335C8—731no—
336C8—1461no—
337C8D4×#6440811yescharacteristic
338C8D4×#6440811yescharacteristic
339C22—21no—
340C22—21no—
341C22—21no—
342C22—2922no—
343C22—2922no—
344C22—732no—
345C22—731no—
346C22—731no—
347C22—1461no—
348C22—1461no—
349C22—1461no—
350C22—1461no—
351C22C2×#1455664511yescharacteristic
352C4—21no—
353C4—5841no—
354C4—5841no—
355C4—731no—
356C4—731no—
357C4—1461no—
358C4C22⋊C4×#6440811yescharacteristic
359C4#1798955311yescharacteristic
360C2—41no—
361C2—1461no—
362C2—1461no—
363C2—1462no—
364C2#2262567011yescharacteristic
365C2#2262614611yescharacteristic
366C2#2262615011yescharacteristic
subgroupG/H
centerC2×C4C2×C4×#64408
commutatorC2×C4×C73C2×C42
FrattiniC2×C8C22×#64408
FittingC22⋊C16×C73C4
socleC22×C73C2×#97
prime radicalC23×D73M16
cosocleC2×C8×D73C23
hypercenterC22⋊C16#64408
hypocenterC73#12616
LCSG ▷ C2×C4×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
2. C2×#17989478C2semidirect
3. C2×#17989477C2semidirect
5. #22624971C2semidirect
6. #22624971C2semidirect
12. C2×#14556665C4semidirect
13. C2×#14556664C4semidirect
25. C22⋊#11924003C4semidirect
26. #17988366C4semidirect
27. #17988366C4semidirect
28. C22⋊C16×C73C4semidirect
82. #11924031C22⋊C4semidirect
165. C2×D73#347semidirect
191. C73#12616semidirect
208. C22⋊C16#64408semidirect

Maximal subgroups

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

subgroupindex
C2×#179896432
C2×#179894782
C2×#179894772
#226256672
#226249712
#226115402
#1261673