Finite Group Databasebeta

← #33004149

Subgroups — #33004149

Order 18688.

442 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618641C211yesmaximal, characteristic
2#22611686C211yesmaximal, characteristic, complemented
3C2×#17988372C211yesmaximal, characteristic, complemented
4C2×#17988371C211yesmaximal, characteristic, complemented
5C2×#17988370C211yesmaximal, characteristic, complemented
6C2×#17988362C211yesmaximal, characteristic, complemented
7C2×#350×C73C211yesmaximal, characteristic, complemented
8C2×#14556597C2211yescharacteristic
9#17989133C411yescharacteristic
10C2×#14556531C2211yescharacteristic
11C22×#11924003C2211yescharacteristic
12#17988663—22no—
13C8×C22⋊D73—22no—
14#17988610C411yescharacteristic
15#17988555C411yescharacteristic
16#17988554C411yescharacteristic
17C2×C8×Dic73C2211yescharacteristic
18#17988405—22no—
19#17988372—22no—
20#17988371—22no—
21#17988370—22no—
22#17988362—22no—
23C2×#131×C73C2211yescharacteristic
24C2×M32×C73C2211yescharacteristic
25C22×C16×C73C2211yescharacteristic
26#350×C73—22no—
27C2×#11924028C2×C411yescharacteristic
28#14556597—21no—
29#14556597—21no—
30#14556597—21no—
31#14556597—21no—
32C2×#11924012C2×C411yescharacteristic
33C2×#11924011—21no—
34C22×#10596831C2×C411yescharacteristic
35C2×C8×D73—21no—
36#14556589C811yescharacteristic
37#14556587C811yescharacteristic
38#14556580C811yescharacteristic
39#14556578C811yescharacteristic
40#14556563—22no—
41C4×C22⋊D73—22no—
42C2×C4×Dic73C2×C411yescharacteristic
43#14556531—21no—
44#14556531—21no—
45C2×#11924003—21no—
46C2×#11924003—21no—
47C2×#11924003—21no—
48C2×#11924003D412yescomplemented
49#14556520—22no—
50C22⋊#10596831—22no—
51#14556503—22no—
52C8×Dic73D412yes—
53C8×Dic73D412yes—
54C2×#41×C73C2×C411yescharacteristic
55#131×C73—21no—
56#131×C73—21no—
57#131×C73—21no—
58#131×C73—21no—
59C2×M16×C73—21no—
60C2×M16×C73C2×C411yescharacteristic
61C22×C8×C73—21no—
62C22×C8×C73C2311yescharacteristic
63M32×C73—21no—
64M32×C73—21no—
65C2×C16×C73—21no—
66C2×C16×C73—21no—
67C2×C16×C73—21no—
68C2×C16×C73D412yescomplemented
69#11924028—21no—
70#11924028—21no—
71#11924028—21no—
72#11924028—21no—
73C2×Dic146C2×C811yescharacteristic
74C2×D292C2×C811yescharacteristic
75C2×C22⋊D73—21no—
76C2×C22⋊D73—22no—
77C22×Dic73M1612yes—
78C2×C4×D73—21no—
79#11924012—21no—
80#11924012—21no—
81#11924011—41no—
82#11924011—41no—
83C2×#10596831—21no—
84C2×#10596831—21no—
85C2×#10596831—21no—
86C2×#10596831C22⋊C412yes—
87C8×D73—41no—
88C8×D73—41no—
89#11924007—22no—
90C22⋊Dic73—22no—
91#11924005—22no—
92C4×Dic73C22⋊C412yes—
93C4×Dic73C2×C811yescharacteristic
94C4×Dic73C2×C811yescharacteristic
95#11924003—22no—
96#11924003—41no—
97#41×C73—21no—
98#41×C73—21no—
99#41×C73—21no—
100#41×C73—21no—
101C2×Q8×C73C2×C811yescharacteristic
102C2×D4×C73—21no—
103C2×D4×C73C2×C811yescharacteristic
104C22×C4×C73—21no—
105C22×C4×C73C22×C411yescharacteristic
106M16×C73—21no—
107M16×C73—21no—
108M16×C73—41no—
109M16×C73—41no—
110C2×C8×C73—21no—
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×C73C2×M1611yescharacteristic
123C22×D73—21no—
124Q8×C73—21no—
125Q8×C73—21no—
126D4×C73—21no—
127D4×C73—21no—
128D4×C73—41no—
129D4×C73—41no—
130C2×C4×C73—21no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73C2×C22⋊C411yescharacteristic
134C2×C4×C73C4×D411yescharacteristic
135C2×C4×C73C4×D411yescharacteristic
136C2×C4×C73C22×C811yescharacteristic
137C2×C4×C73#13111yescharacteristic
138C2×C4×C73#13111yescharacteristic
139C22⋊D73—44no—
140C22⋊D73—41no—
141C22⋊D73—41no—
142C2×Dic73—21no—
143C2×Dic73—42no—
144C2×Dic73C22⋊C812yes—
145C2×Dic73C22⋊C812yes—
146D292—21no—
147D292—21no—
148C4×D73—41no—
149C4×D73—41no—
150Dic146—21no—
151Dic146—21no—
152C8×C73—41no—
153C8×C73#12111yescharacteristic
154C8×C73#12111yescharacteristic
155C8×C73#12411yescharacteristic
156C8×C73#12711yescharacteristic
157#10596831—22no—
158#10596831—41no—
159C22×C73—22no—
160C22×C73—42no—
161C22×C73—41no—
162C22×C73C2×C22⋊C811yescharacteristic
163C22×C73#43611yescharacteristic
164C22×C73#43611yescharacteristic
165C2×D73—42no—
166C2×D73—41no—
167C4×C73—41no—
168C4×C73#39011yescharacteristic
169C4×C73#40811yescharacteristic
170C4×C73C8×D411yescharacteristic
171C4×C73C8×D411yescharacteristic
172Dic73—22no—
173Dic73—22no—
174Dic73—41no—
175#13192—731nomaximal, Sylow
176C2×C73—21no—
177C2×C73—21no—
178C2×C73—81no—
179C2×C73#195411yescharacteristic
180C2×C73#211712yes—
181D73—81no—
182#2931—731no—
183#2150—731no—
184C2×#350—731no—
185C2×#350—731no—
186C2×#350—731no—
187C2×#350D7311yescharacteristic, complemented
188C2×#346—731no—
189C73#1319211yescharacteristic, complemented, Sylow
190C2×#131—731no—
191C2×#131C2×D7311yescharacteristic
192#532—731no—
193C2×M32—731no—
194C2×M32C2×D7311yescharacteristic
195C22×C16—731no—
196C22×C16C2×D7311yescharacteristic
197#436—1462no—
198C8×D4—1462no—
199#423—731no—
200#408—731no—
201#408—731no—
202C2×C4×C8—731no—
203C4⋊C16—1462no—
204#350—22no—
205#350—1462no—
206#350—1462no—
207#350—1462no—
208#346—1462no—
209C2×#41—731no—
210C2×#41C4×D7311yescharacteristic
211#131—21no—
212#131—21no—
213#131—21no—
214#131—21no—
215#131—1461no—
216#131—1461no—
217#131—1461no—
218#131—1461no—
219C2×M16—21no—
220C2×M16—731no—
221C2×M16—1461no—
222C2×M16C4×D7311yescharacteristic
223C22×C8—21no—
224C22×C8—731no—
225C22×C8—1461no—
226C22×C8C22×D7311yescharacteristic
227C4⋊Q8—731no—
228#127—731no—
229#124—731no—
230#124—731no—
231#121—1462no—
232C4×D4—1462no—
233C2×C42—731no—
234M32—21no—
235M32—21no—
236M32—1461no—
237M32—1461no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—732no—
242C2×C16—1461no—
243C2×C16—1461no—
244C2×C16—1461no—
245C2×C16C22⋊D7312yescomplemented
246C4⋊C8—1462no—
247C22⋊C8—1462no—
248C22⋊C8—1462no—
249C4×C8—732no—
250C4×C8—732no—
251#41—21no—
252#41—21no—
253#41—21no—
254#41—21no—
255#41—1461no—
256#41—1461no—
257#41—1461no—
258#41—1461no—
259C2×Q8—731no—
260C2×Q8C8×D7311yescharacteristic
261C2×D4—21no—
262C2×D4—731no—
263C2×D4—1462no—
264C2×D4—1461no—
265C2×D4C8×D7311yescharacteristic
266C22×C4—21no—
267C22×C4—732no—
268C22×C4—1461no—
269C22×C4C2×C4×D7311yescharacteristic
270M16—21no—
271M16—21no—
272M16—41no—
273M16—41no—
274M16—2921no—
275M16—2921no—
276M16—1461no—
277M16—1461no—
278C2×C8—21no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—2921no—
282C2×C8—2921no—
283C2×C8—732no—
284C2×C8—1461no—
285C2×C8—1461no—
286C2×C8—1461no—
287C2×C8D4×D7311yescharacteristic
288C2×C8D4×D7311yescharacteristic
289C2×C8D4×D7311yescharacteristic
290C2×C8C2×C22⋊D7311yescharacteristic
291C2×C8#1192402711yescharacteristic
292C2×C8#1192402811yescharacteristic
293C4⋊C4—1462no—
294C22⋊C4—1462no—
295C22⋊C4—1462no—
296C42—732no—
297C42—731no—
298C42—731no—
299C16—22no—
300C16—41no—
301C16—2921no—
302C16—1462no—
303C23—21no—
304C23—1461no—
305C23M16×D7311yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—1461no—
309Q8—1461no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—41no—
314D4—2921no—
315D4—2921no—
316D4—2924no—
317D4—1461no—
318D4—1461no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—2921no—
323C2×C4—2921no—
324C2×C4—2922no—
325C2×C4—732no—
326C2×C4—732no—
327C2×C4—1461no—
328C2×C4C22⋊C4×D7311yescharacteristic
329C2×C4#1455655111yescharacteristic
330C2×C4C4×C22⋊D7311yescharacteristic
331C2×C4C2×C8×D7311yescharacteristic
332C2×C4#1455659711yescharacteristic
333C2×C4#1455659911yescharacteristic
334C8—41no—
335C8—2921no—
336C8—1462no—
337C8#1455656311yescharacteristic
338C8#1455656411yescharacteristic
339C8#1455657711yescharacteristic
340C8#1455658711yescharacteristic
341C22—22no—
342C22—41no—
343C22—42no—
344C22—2921no—
345C22—2922no—
346C22C22⋊C8×D7311yescharacteristic
347C22#1798866211yescharacteristic
348C22#1798866311yescharacteristic
349C4—41no—
350C4—2921no—
351C4—1462no—
352C4—1462no—
353C4#1798848711yescharacteristic
354C4#1798855211yescharacteristic
355C4#1798865011yescharacteristic
356C4C8×C22⋊D7311yescharacteristic
357C2—21no—
358C2—21no—
359C2—81no—
360C2—5841no—
361C2#2261072311yescharacteristic
362C2#2261155712yes—
subgroupG/H
centerC2×C8D4×D73
commutatorC2×C4×C73C22×C8
FrattiniC22×C8C22×D73
FittingC2×#350×C73C2
socleC22×C73C2×C22⋊C8
prime radical#17989133C4
cosocleC22×C8×C73C23
hypercenterC2×#350D73
hypocenterC73#13192
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
2. #22611686C2semidirect
3. C2×#17988372C2semidirect
4. C2×#17988371C2semidirect
5. C2×#17988370C2semidirect
6. C2×#17988362C2semidirect
7. C2×#350×C73C2semidirect
48. C2×#11924003D4semidirect
68. C2×C16×C73D4semidirect
187. C2×#350D73semidirect
189. C73#13192semidirect
245. C2×C16C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
#226186412
#226116862
C2×#179883722
C2×#179883712
C2×#179883702
C2×#179883622
C2×#350×C732
#1319273