Finite Group Databasebeta

← #33004191

Subgroups — #33004191

Order 18688.

420 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618632C211yesmaximal, characteristic
2#22611696C211yesmaximal, characteristic, complemented
3#22611559C211yesmaximal, characteristic, complemented
4C2×#17988368C211yesmaximal, characteristic, complemented
5C2×#17988368C211yesmaximal, characteristic, complemented
6#22611535C211yesmaximal, characteristic, complemented
7C73×#2117C211yesmaximal, characteristic, complemented
8C22×#11924011C2211yescharacteristic
9#17989094C411yescharacteristic
10C2×#14556531C2211yescharacteristic
11C2×#14556531C2211yescharacteristic
12#17988663—22no—
13#17988658—22no—
14#17988615C411yescharacteristic
15#17988554C411yescharacteristic
16#17988550C411yescharacteristic
17#17988542C2211yescharacteristic
18#17988407—22no—
19#17988371—22no—
20#17988368—22no—
21#17988368—22no—
22#17988364—22no—
23C2×#131×C73C2211yescharacteristic
24C2×M32×C73C2211yescharacteristic
25C2×M32×C73C2211yescharacteristic
26#350×C73—22no—
27C22×C4×D73C2×C411yescharacteristic
28C2×#11924012C2×C411yescharacteristic
29C2×#11924011—21no—
30C2×#11924011—21no—
31C2×#11924011—21no—
32C2×#11924011—21no—
33C2×#11924011—21no—
34C2×#11924011—21no—
35C22×#10596831C2×C411yescharacteristic
36#14556572—21no—
37#14556567—21no—
38#14556562—21no—
39#14556559—21no—
40C4×C22⋊D73—22no—
41#14556550C2×C411yescharacteristic
42#14556531—21no—
43#14556531—21no—
44#14556531—21no—
45#14556531D412yescomplemented
46C2×#11924003—21no—
47C2×#11924003—21no—
48#14556520—22no—
49C22⋊#10596831—22no—
50#14556503—22no—
51#14556501D412yes—
52C8×Dic73D412yes—
53C2×#41×C73C2×C411yescharacteristic
54#131×C73—21no—
55#131×C73—21no—
56#131×C73—21no—
57#131×C73—21no—
58C2×M16×C73—21no—
59C2×M16×C73C2×C411yescharacteristic
60C22×C8×C73—21no—
61C22×C8×C73C2311yescharacteristic
62M32×C73—21no—
63M32×C73—21no—
64M32×C73—21no—
65M32×C73D412yescomplemented
66C2×C16×C73—21no—
67C2×C16×C73—21no—
68C23×D73M1611yescharacteristic
69C2×C22⋊D73—22no—
70C22×Dic73M1611yescharacteristic
71C2×C4×D73—21no—
72C2×C4×D73—21no—
73C2×C4×D73—21no—
74C2×C4×D73—21no—
75C2×C4×D73—21no—
76C2×C4×D73—21no—
77#11924012—21no—
78#11924012—21no—
79#11924011—41no—
80#11924011—41no—
81#11924011—41no—
82#11924011—41no—
83C2×#10596831—21no—
84C2×#10596831—21no—
85C2×#10596831—21no—
86C2×#10596831C22⋊C412yes—
87C4⋊Dic73—21no—
88#11924007—22no—
89C22⋊Dic73—22no—
90C22⋊Dic73—21no—
91#11924005—22no—
92C4×Dic73C22⋊C412yes—
93#11924003—22no—
94#11924003—41no—
95#41×C73—21no—
96#41×C73—21no—
97#41×C73—21no—
98#41×C73—21no—
99C2×Q8×C73M1611yescharacteristic
100C2×D4×C73—21no—
101C2×D4×C73M1611yescharacteristic
102C22×C4×C73—21no—
103C22×C4×C73C22×C411yescharacteristic
104M16×C73—21no—
105M16×C73—21no—
106M16×C73—41no—
107M16×C73—41no—
108C2×C8×C73—21no—
109C2×C8×C73—41no—
110C2×C8×C73—41no—
111C2×C8×C73C2×D411yescharacteristic
112C2×C8×C73C2×D411yescharacteristic
113C2×C8×C73C2×D411yescharacteristic
114C2×C8×C73C2×D411yescharacteristic
115C2×C8×C73#4111yescharacteristic
116C2×C8×C73#4111yescharacteristic
117C16×C73—22no—
118C16×C73—41no—
119C23×C73—21no—
120C23×C73C2×M1611yescharacteristic
121C22×D73—21no—
122C22×D73—21no—
123C22×D73—21no—
124C22×D73—81no—
125Q8×C73—21no—
126Q8×C73—21no—
127D4×C73—21no—
128D4×C73—21no—
129D4×C73—41no—
130D4×C73—41no—
131C2×C4×C73—21no—
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—82no—
141C2×Dic73—22no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C4×D73—41no—
146C4×D73—41no—
147C4×D73—41no—
148C4×D73—41no—
149C8×C73—41no—
150C8×C73#12111yescharacteristic
151C8×C73#12111yescharacteristic
152C8×C73#12411yescharacteristic
153C8×C73#12711yescharacteristic
154#10596831—22no—
155#10596831—41no—
156C22×C73—41no—
157C22×C73—42no—
158C22×C73—41no—
159C22×C73#40711yescharacteristic
160C22×C73#43511yescharacteristic
161C22×C73#43511yescharacteristic
162C2×D73—41no—
163C2×D73—41no—
164C2×D73—41no—
165C2×D73—81no—
166C2×D73—81no—
167C4×C73—41no—
168C4×C73#39011yescharacteristic
169C4×C73#40811yescharacteristic
170C4×C73#43511yescharacteristic
171C4×C73#43511yescharacteristic
172Dic73—42no—
173Dic73—41no—
174#13201—731nomaximal, Sylow
175C2×C73—21no—
176C2×C73—21no—
177C2×C73—21no—
178C2×C73—81no—
179C2×C73#195511yescharacteristic
180D73—81no—
181#2930—731no—
182#2153—731no—
183#2117—731no—
184#2117D7311yescharacteristic, complemented
185C2×#349—731no—
186C2×#349—731no—
187#2110—731no—
188C73#1320111yescharacteristic, complemented, Sylow
189C2×#131C2×D7311yescharacteristic
190C22×M16—731no—
191#525—731no—
192C2×M32—731no—
193C2×M32—731no—
194C2×M32C2×D7311yescharacteristic
195C2×M32C2×D7311yescharacteristic
196#436—1462no—
197#435—1462no—
198#424—731no—
199#408—731no—
200#407—731no—
201#405—731no—
202#364—1462no—
203#350—22no—
204#350—1462no—
205#349—1462no—
206#349—1462no—
207#347—1462no—
208C2×#41C4×D7311yescharacteristic
209C23×C4—731no—
210#131—21no—
211#131—21no—
212#131—21no—
213#131—21no—
214C2×M16—21no—
215C2×M16—731no—
216C2×M16—1461no—
217C2×M16—1461no—
218C2×M16—1461no—
219C2×M16—1461no—
220C2×M16—1461no—
221C2×M16—1461no—
222C2×M16C4×D7311yescharacteristic
223C22×C8—21no—
224C22×C8—731no—
225C22×C8C22×D7311yescharacteristic
226#123—1461no—
227C22⋊Q8—1461no—
228#121—1461no—
229#120—1461no—
230C4×D4—1462no—
231#117—731no—
232M32—21no—
233M32—21no—
234M32—21no—
235M32—732no—
236M32—1461no—
237M32—1461no—
238M32—1461no—
239M32C22⋊D7312yescomplemented
240C2×C16—21no—
241C2×C16—21no—
242C2×C16—1461no—
243C2×C16—1461no—
244C4⋊C8—1462no—
245C22⋊C8—1462no—
246C22⋊C8—1462no—
247#97—732no—
248C4×C8—732no—
249C24—731no—
250#41—21no—
251#41—21no—
252#41—21no—
253#41—21no—
254C2×Q8#1192401111yescharacteristic
255C2×D4—21no—
256C2×D4—1462no—
257C2×D4#1192401111yescharacteristic
258C22×C4—21no—
259C22×C4—731no—
260C22×C4—1461no—
261C22×C4—1461no—
262C22×C4—1461no—
263C22×C4—1461no—
264C22×C4—1461no—
265C22×C4—1461no—
266C22×C4C2×C4×D7311yescharacteristic
267M16—21no—
268M16—21no—
269M16—41no—
270M16—41no—
271M16—2921no—
272M16—2921no—
273M16—2921no—
274M16—2921no—
275M16—1461no—
276M16—1461no—
277C2×C8—21no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—732no—
281C2×C8—1461no—
282C2×C8—1461no—
283C2×C8—1461no—
284C2×C8D4×D7311yescharacteristic
285C2×C8D4×D7311yescharacteristic
286C2×C8D4×D7311yescharacteristic
287C2×C8C2×C22⋊D7311yescharacteristic
288C2×C8#1192402711yescharacteristic
289C2×C8#1192402811yescharacteristic
290C4⋊C4—1462no—
291C4⋊C4—1461no—
292C22⋊C4—1462no—
293C22⋊C4—1462no—
294C22⋊C4—1461no—
295C42—732no—
296C16—22no—
297C16—41no—
298C16—2921no—
299C16—1462no—
300C23—21no—
301C23—5841no—
302C23—1461no—
303C23—1461no—
304C23—1461no—
305C23M16×D7311yescharacteristic
306Q8—21no—
307Q8—21no—
308D4—21no—
309D4—21no—
310D4—41no—
311D4—41no—
312D4—5842no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—2921no—
317C2×C4—2921no—
318C2×C4—2921no—
319C2×C4—2921no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1462no—
323C2×C4—1461no—
324C2×C4C22⋊C4×D7311yescharacteristic
325C2×C4#1455655111yescharacteristic
326C2×C4C4×C22⋊D7311yescharacteristic
327C2×C4C2×#1192401111yescharacteristic
328C2×C4#1455659711yescharacteristic
329C2×C4#1455659911yescharacteristic
330C8—41no—
331C8—2921no—
332C8—1462no—
333C8#1455656311yescharacteristic
334C8#1455656411yescharacteristic
335C8#1455657711yescharacteristic
336C8#1455658711yescharacteristic
337C22—41no—
338C22—42no—
339C22—41no—
340C22—2921no—
341C22—2921no—
342C22—2921no—
343C22—5841no—
344C22—5841no—
345C22#1798854911yescharacteristic
346C22#1798865611yescharacteristic
347C22#1798866111yescharacteristic
348C4—41no—
349C4—2922no—
350C4—2921no—
351C4#1798848711yescharacteristic
352C4#1798855211yescharacteristic
353C4#1798865511yescharacteristic
354C4#1798865811yescharacteristic
355C2—21no—
356C2—21no—
357C2—21no—
358C2—81no—
359C2—5841no—
360C2#2261072711yescharacteristic
subgroupG/H
centerC4#17988487
commutatorC22×C4×C73C22×C4
FrattiniC22×C8C22×D73
FittingC73×#2117C2
socleC2×C73#1955
prime radical#17989094C4
cosocleC22×C8×C73C23
hypercenter#2117D73
hypocenterC73#13201
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
2. #22611696C2semidirect
3. #22611559C2semidirect
4. C2×#17988368C2semidirect
5. C2×#17988368C2semidirect
6. #22611535C2semidirect
7. C73×#2117C2semidirect
45. #14556531D4semidirect
65. M32×C73D4semidirect
184. #2117D73semidirect
188. C73#13201semidirect
239. M32C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
#226186322
#226116962
#226115592
C2×#179883682
#226115352
C73×#21172
#1320173