Finite Group Databasebeta

← #33002865

Subgroups — #33002865

Order 18688.

488 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623033C211yesmaximal, characteristic, complemented
2#22618625C211yesmaximal, characteristic
3#22611551C211yesmaximal, characteristic, complemented
4#22611542C211yesmaximal, characteristic, complemented
5#22608018C211yesmaximal, characteristic, complemented
6#22608016C211yesmaximal, characteristic, complemented
7C73×#2112C211yesmaximal, characteristic, complemented
8C2×#14556597C2211yescharacteristic
9#17989098C411yescharacteristic
10#17989005—22no—
11#17989003—22no—
12C2×#14556531C2211yescharacteristic
13C2×#14556531C2211yescharacteristic
14M32×D73—22no—
15#17988658—22no—
16C8×C22⋊D73—22no—
17#17988613C411yescharacteristic
18#17988553C411yescharacteristic
19#17988551C411yescharacteristic
20#17988542C2211yescharacteristic
21#17988368—22no—
22C22⋊#11924003—22no—
23C23×C8×C73C2211yescharacteristic
24C2×M32×C73C2211yescharacteristic
25C2×M32×C73C2211yescharacteristic
26C22⋊C16×C73—22no—
27C2×#11924028C2×C411yescharacteristic
28#14556597—21no—
29#14556597—21no—
30#14556597—21no—
31#14556597—21no—
32C2×#11924012C2×C411yescharacteristic
33C2×#11924012C2×C411yescharacteristic
34C2×#11924011D412yes—
35C2×C8×D73D412yes—
36#14556574C812yes—
37#14556570—21no—
38#14556565—21no—
39#14556560C812yes—
40C4×C22⋊D73—22no—
41#14556550C2×C411yescharacteristic
42#14556531—21no—
43#14556531—21no—
44#14556531—21no—
45#14556531—21no—
46#14556530—24no—
47C2×#11924003—21no—
48C2×#11924003D412yescomplemented
49C16×D73—24no—
50#14556520—22no—
51C22⋊#10596831—22no—
52#14556503—22no—
53#14556501—21no—
54C8×Dic73—21no—
55C23×C4×C73C2×C411yescharacteristic
56C22×C8×C73—21no—
57C22×C8×C73—21no—
58C22×C8×C73—21no—
59C22×C8×C73—21no—
60C22×C8×C73—21no—
61C22×C8×C73—21no—
62C22×C8×C73C2×C411yescharacteristic
63C22×C8×C73C2311yescharacteristic
64M32×C73—21no—
65M32×C73—21no—
66M32×C73—21no—
67M32×C73—21no—
68C2×C16×C73—21no—
69C2×C16×C73D412yescomplemented
70#11924028—21no—
71#11924028—21no—
72#11924028—21no—
73#11924028—21no—
74C2×Dic146M1611yescharacteristic
75C2×D292M1611yescharacteristic
76C2×C22⋊D73—22no—
77C2×C22⋊D73C2×C812yes—
78C2×C4×D73C22⋊C412yes—
79#11924012—21no—
80#11924012—21no—
81#11924012—21no—
82#11924012—21no—
83#11924011—22no—
84#11924011—22no—
85C2×#10596831—21no—
86C2×#10596831C22⋊C412yes—
87C8×D73—22no—
88C8×D73—22no—
89C4⋊Dic73—21no—
90#11924007—22no—
91C22⋊Dic73—22no—
92C22⋊Dic73C2×C812yes—
93#11924005—22no—
94C4×Dic73—21no—
95#11924003—22no—
96#11924003—41no—
97C24×C73C2×C811yescharacteristic
98C22×C4×C73—21no—
99C22×C4×C73—21no—
100C22×C4×C73—21no—
101C22×C4×C73—21no—
102C22×C4×C73—21no—
103C22×C4×C73—21no—
104C22×C4×C73C2×C811yescharacteristic
105C22×C4×C73C22×C411yescharacteristic
106C2×C8×C73—21no—
107C2×C8×C73—21no—
108C2×C8×C73—21no—
109C2×C8×C73—41no—
110C2×C8×C73—41no—
111C2×C8×C73—41no—
112C2×C8×C73—41no—
113C2×C8×C73C2×D411yescharacteristic
114C2×C8×C73C2×D411yescharacteristic
115C2×C8×C73C2×D411yescharacteristic
116C2×C8×C73C2×D411yescharacteristic
117C2×C8×C73#4111yescharacteristic
118C2×C8×C73#4111yescharacteristic
119C16×C73—22no—
120C16×C73—41no—
121C23×C73—21no—
122C23×C73—21no—
123C23×C73—21no—
124C23×C73—42no—
125C23×C73C22×C811yescharacteristic
126C22×D73C22⋊C812yes—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73—41no—
134C2×C4×C73C2×C22⋊C411yescharacteristic
135C2×C4×C73C4×D411yescharacteristic
136C2×C4×C73C4×D411yescharacteristic
137C2×C4×C73C2×M1611yescharacteristic
138C2×C4×C73#13111yescharacteristic
139C2×C4×C73#13111yescharacteristic
140C22⋊D73—22no—
141C22⋊D73—22no—
142C22⋊D73—44no—
143C2×Dic73—22no—
144C2×Dic73C22⋊C812yes—
145D292—21no—
146D292—21no—
147C4×D73—22no—
148C4×D73—22no—
149Dic146—21no—
150Dic146—21no—
151C8×C73—41no—
152C8×C73#12011yescharacteristic
153C8×C73#12111yescharacteristic
154C8×C73#12111yescharacteristic
155C8×C73#12311yescharacteristic
156#10596831—22no—
157#10596831—41no—
158C22×C73—22no—
159C22×C73—22no—
160C22×C73—22no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73C2×C22⋊C811yescharacteristic
167C22×C73C8×D411yescharacteristic
168C22×C73C8×D411yescharacteristic
169C2×D73—22no—
170C2×D73—42no—
171C4×C73—41no—
172C4×C73#38611yescharacteristic
173C4×C73#40811yescharacteristic
174C4×C73#43511yescharacteristic
175C4×C73#43511yescharacteristic
176Dic73—22no—
177Dic73—42no—
178#12981—731nomaximal, Sylow
179C2×C73—21no—
180C2×C73—21no—
181C2×C73—21no—
182C2×C73—42no—
183C2×C73#186911yescharacteristic
184D73—42no—
185#3407—731no—
186#2929—731no—
187#2115—731no—
188#2112—731no—
189#2112D7311yescharacteristic, complemented
190#1378—731no—
191#1378—731no—
192C73#1298111yescharacteristic, complemented, Sylow
193C2×#131—731no—
194C23×C8C2×D7311yescharacteristic
195#525—731no—
196#504—1462no—
197#504—1462no—
198C2×M32—731no—
199C2×M32—731no—
200C2×M32—1462no—
201C2×M32C2×D7311yescharacteristic
202C2×M32C2×D7311yescharacteristic
203#435—1462no—
204C8×D4—1462no—
205#424—731no—
206#408—731no—
207#407—731no—
208#405—731no—
209#349—1462no—
210C22⋊C16—22no—
211C22⋊C16—1462no—
212C2×#41—731no—
213C23×C4C4×D7311yescharacteristic
214#131—1461no—
215#131—1461no—
216#131—1461no—
217#131—1461no—
218C2×M16—731no—
219C2×M16—732no—
220C2×M16—731no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—732no—
228C22×C8C4×D7311yescharacteristic
229C22×C8C22×D7311yescharacteristic
230#123—732no—
231C22⋊Q8—1461no—
232#121—1461no—
233#120—732no—
234C4×D4—1462no—
235#117—731no—
236M32—21no—
237M32—21no—
238M32—21no—
239M32—21no—
240M32—1464no—
241M32—1461no—
242M32—1461no—
243M32—1461no—
244M32—1461no—
245C2×C16—21no—
246C2×C16—732no—
247C2×C16—1464no—
248C2×C16—1461no—
249C2×C16C22⋊D7312yescomplemented
250C4⋊C8—1462no—
251C22⋊C8—1462no—
252C22⋊C8—1462no—
253#97—1461no—
254C4×C8—1461no—
255C24C8×D7311yescharacteristic
256#41—1461no—
257#41—1461no—
258#41—1461no—
259#41—1461no—
260C2×Q8—731no—
261C2×D4—732no—
262C2×D4—731no—
263C2×D4—1462no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—732no—
271C22×C4C8×D7311yescharacteristic
272C22×C4C2×C4×D7311yescharacteristic
273M16—1461no—
274M16—1461no—
275M16—1461no—
276M16—1461no—
277M16—1462no—
278M16—1462no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—732no—
287C2×C8—1461no—
288C2×C8—1462no—
289C2×C8—1462no—
290C2×C8D4×D7311yescharacteristic
291C2×C8D4×D7311yescharacteristic
292C2×C8D4×D7311yescharacteristic
293C2×C8C2×C22⋊D7311yescharacteristic
294C2×C8#1192402711yescharacteristic
295C2×C8#1192402811yescharacteristic
296C4⋊C4—1462no—
297C4⋊C4—1461no—
298C22⋊C4—732no—
299C22⋊C4—1462no—
300C22⋊C4—1462no—
301C42—1461no—
302C16—22no—
303C16—41no—
304C16—2921no—
305C16—1462no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—42no—
310C23—732no—
311C23C2×C8×D7311yescharacteristic
312Q8—1461no—
313Q8—1461no—
314D4—2924no—
315D4—1462no—
316D4—1462no—
317D4—1461no—
318D4—1461no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—732no—
327C2×C4—1462no—
328C2×C4—1462no—
329C2×C4—1462no—
330C2×C4C22⋊C4×D7311yescharacteristic
331C2×C4#1455655111yescharacteristic
332C2×C4C4×C22⋊D7311yescharacteristic
333C2×C4M16×D7311yescharacteristic
334C2×C4#1455659711yescharacteristic
335C2×C4#1455659911yescharacteristic
336C8—41no—
337C8—2921no—
338C8—1462no—
339C8#1455655911yescharacteristic
340C8#1455656211yescharacteristic
341C8#1455656411yescharacteristic
342C8#1455657311yescharacteristic
343C22—22no—
344C22—22no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—2922no—
352C22—1462no—
353C22C22⋊C8×D7311yescharacteristic
354C22#1798865011yescharacteristic
355C22C8×C22⋊D7311yescharacteristic
356C4—41no—
357C4—2922no—
358C4—1462no—
359C4#1798846311yescharacteristic
360C4#1798855211yescharacteristic
361C4#1798865611yescharacteristic
362C4#1798866111yescharacteristic
363C2—21no—
364C2—21no—
365C2—21no—
366C2—42no—
367C2—2922no—
368C2#2261022011yescharacteristic
subgroupG/H
centerC8#14556559
commutatorC23×C73C22×C8
FrattiniC22×C8C22×D73
FittingC73×#2112C2
socleC2×C73#1869
prime radical#17989098C4
cosocleC22×C8×C73C23
hypercenter#2112D73
hypocenterC73#12981
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2112

Complements

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

NH ≅ G/Ntype
1. #22623033C2semidirect
3. #22611551C2semidirect
4. #22611542C2semidirect
5. #22608018C2semidirect
6. #22608016C2semidirect
7. C73×#2112C2semidirect
48. C2×#11924003D4semidirect
69. C2×C16×C73D4semidirect
189. #2112D73semidirect
192. C73#12981semidirect
249. C2×C16C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
#226230332
#226186252
#226115512
#226115422
#226080182
#226080162
C73×#21122
#1298173