Finite Group Databasebeta

← #33002870

Subgroups — #33002870

Order 18688.

474 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
1#22623033C211yesmaximal, characteristic, complemented
2#22618641C211yesmaximal, characteristic
3#22611559C211yesmaximal, characteristic, complemented
4#22611551C211yesmaximal, characteristic, complemented
5#22608012C211yesmaximal, characteristic, complemented
6#22608012C211yesmaximal, characteristic, complemented
7C73×#2117C211yesmaximal, characteristic, complemented
8C2×#14556597C2211yescharacteristic
9#17989133C411yescharacteristic
10#17989005—22no—
11#17989003—22no—
12C2×#14556531C2211yescharacteristic
13C2×#14556531C2211yescharacteristic
14M32×D73—22no—
15#17988663—22no—
16C8×C22⋊D73—22no—
17#17988610C411yescharacteristic
18#17988555C411yescharacteristic
19#17988554C411yescharacteristic
20C2×C8×Dic73C2211yescharacteristic
21#17988371—22no—
22#17988368—22no—
23C2×#131×C73C2211yescharacteristic
24C2×M32×C73C2211yescharacteristic
25C2×M32×C73C2211yescharacteristic
26#350×C73—22no—
27C2×#11924028C2×C411yescharacteristic
28#14556597—21no—
29#14556597—21no—
30#14556597—21no—
31#14556597—21no—
32C2×#11924012C2×C411yescharacteristic
33C2×#11924011D412yes—
34C22×#10596831C2×C411yescharacteristic
35C2×C8×D73D412yes—
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—
45#14556531—21no—
46#14556531D412yescomplemented
47#14556530—24no—
48C2×#11924003—21no—
49C2×#11924003—21no—
50C16×D73—24no—
51#14556520—22no—
52C22⋊#10596831—22no—
53#14556503—22no—
54C8×Dic73—21no—
55C8×Dic73—21no—
56C2×#41×C73C2×C411yescharacteristic
57#131×C73—21no—
58#131×C73—21no—
59#131×C73—21no—
60#131×C73—21no—
61C2×M16×C73—21no—
62C2×M16×C73C2×C411yescharacteristic
63C22×C8×C73—21no—
64C22×C8×C73C2311yescharacteristic
65M32×C73—21no—
66M32×C73—21no—
67M32×C73—21no—
68M32×C73D412yescomplemented
69C2×C16×C73—21no—
70C2×C16×C73—21no—
71#11924028—21no—
72#11924028—21no—
73#11924028—21no—
74#11924028—21no—
75C2×Dic146C2×C811yescharacteristic
76C2×D292C2×C811yescharacteristic
77C2×C22⋊D73—22no—
78C2×C22⋊D73M1612yes—
79C22×Dic73—21no—
80C2×C4×D73C22⋊C412yes—
81#11924012—21no—
82#11924012—21no—
83#11924011—22no—
84#11924011—22no—
85C2×#10596831—21no—
86C2×#10596831—21no—
87C2×#10596831—21no—
88C2×#10596831C22⋊C412yes—
89C8×D73—22no—
90C8×D73—22no—
91#11924007—22no—
92C22⋊Dic73—22no—
93#11924005—22no—
94C4×Dic73—21no—
95C4×Dic73C2×C811yescharacteristic
96C4×Dic73C2×C811yescharacteristic
97#11924003—22no—
98#11924003—41no—
99#41×C73—21no—
100#41×C73—21no—
101#41×C73—21no—
102#41×C73—21no—
103C2×Q8×C73C2×C811yescharacteristic
104C2×D4×C73—21no—
105C2×D4×C73C2×C811yescharacteristic
106C22×C4×C73—21no—
107C22×C4×C73C22×C411yescharacteristic
108M16×C73—21no—
109M16×C73—21no—
110M16×C73—41no—
111M16×C73—41no—
112C2×C8×C73—21no—
113C2×C8×C73—41no—
114C2×C8×C73—41no—
115C2×C8×C73C2×D411yescharacteristic
116C2×C8×C73C2×D411yescharacteristic
117C2×C8×C73C2×D411yescharacteristic
118C2×C8×C73C2×D411yescharacteristic
119C2×C8×C73#4111yescharacteristic
120C2×C8×C73#4111yescharacteristic
121C16×C73—22no—
122C16×C73—41no—
123C23×C73—21no—
124C23×C73C2×M1611yescharacteristic
125C22×D73C22⋊C812yes—
126Q8×C73—21no—
127Q8×C73—21no—
128D4×C73—21no—
129D4×C73—21no—
130D4×C73—41no—
131D4×C73—41no—
132C2×C4×C73—21no—
133C2×C4×C73—41no—
134C2×C4×C73—41no—
135C2×C4×C73C2×C22⋊C411yescharacteristic
136C2×C4×C73C4×D411yescharacteristic
137C2×C4×C73C4×D411yescharacteristic
138C2×C4×C73C22×C811yescharacteristic
139C2×C4×C73#13111yescharacteristic
140C2×C4×C73#13111yescharacteristic
141C22⋊D73—22no—
142C22⋊D73—22no—
143C22⋊D73—44no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—42no—
147C2×Dic73C22⋊C812yes—
148D292—21no—
149D292—21no—
150C4×D73—22no—
151C4×D73—22no—
152Dic146—21no—
153Dic146—21no—
154C8×C73—41no—
155C8×C73#12011yescharacteristic
156C8×C73#12111yescharacteristic
157C8×C73#12111yescharacteristic
158C8×C73#12311yescharacteristic
159#10596831—22no—
160#10596831—41no—
161C22×C73—41no—
162C22×C73—42no—
163C22×C73—41no—
164C22×C73C2×C22⋊C811yescharacteristic
165C22×C73#43511yescharacteristic
166C22×C73#43511yescharacteristic
167C2×D73—22no—
168C2×D73—42no—
169C4×C73—41no—
170C4×C73#38611yescharacteristic
171C4×C73#40811yescharacteristic
172C4×C73C8×D411yescharacteristic
173C4×C73C8×D411yescharacteristic
174Dic73—22no—
175Dic73—22no—
176Dic73—41no—
177#12982—731nomaximal, Sylow
178C2×C73—21no—
179C2×C73—21no—
180C2×C73—21no—
181C2×C73—81no—
182C2×C73#186911yescharacteristic
183D73—42no—
184#3407—731no—
185#2931—731no—
186#2117—731no—
187#2117D7311yescharacteristic, complemented
188#2115—731no—
189#1376—731no—
190#1376—731no—
191C73#1298211yescharacteristic, complemented, Sylow
192C2×#131—731no—
193C2×#131C2×D7311yescharacteristic
194#532—731no—
195#504—1462no—
196#504—1462no—
197C2×M32—731no—
198C2×M32—731no—
199C2×M32—1462no—
200C2×M32C2×D7311yescharacteristic
201C2×M32C2×D7311yescharacteristic
202#436—1462no—
203C8×D4—1462no—
204#423—731no—
205#408—731no—
206#408—731no—
207C2×C4×C8—731no—
208#350—22no—
209#350—1462no—
210#349—1462no—
211C2×#41—731no—
212C2×#41C4×D7311yescharacteristic
213#131—21no—
214#131—21no—
215#131—21no—
216#131—21no—
217#131—1461no—
218#131—1461no—
219#131—1461no—
220#131—1461no—
221C2×M16—21no—
222C2×M16—731no—
223C2×M16—732no—
224C2×M16C4×D7311yescharacteristic
225C22×C8—21no—
226C22×C8—732no—
227C22×C8—731no—
228C22×C8C22×D7311yescharacteristic
229C4⋊Q8—731no—
230#127—731no—
231#124—731no—
232#124—731no—
233#121—1462no—
234C4×D4—1462no—
235C2×C42—731no—
236M32—21no—
237M32—21no—
238M32—21no—
239M32—732no—
240M32—1464no—
241M32—1461no—
242M32—1461no—
243M32—1461no—
244M32C22⋊D7312yescomplemented
245C2×C16—21no—
246C2×C16—21no—
247C2×C16—1464no—
248C2×C16—1461no—
249C2×C16—1461no—
250C4⋊C8—1462no—
251C22⋊C8—1462no—
252C22⋊C8—1462no—
253C4×C8—1461no—
254C4×C8—1461no—
255#41—21no—
256#41—21no—
257#41—21no—
258#41—21no—
259#41—1461no—
260#41—1461no—
261#41—1461no—
262#41—1461no—
263C2×Q8—731no—
264C2×Q8C8×D7311yescharacteristic
265C2×D4—21no—
266C2×D4—732no—
267C2×D4—731no—
268C2×D4—1462no—
269C2×D4C8×D7311yescharacteristic
270C22×C4—21no—
271C22×C4—732no—
272C22×C4—1461no—
273C22×C4C2×C4×D7311yescharacteristic
274M16—21no—
275M16—21no—
276M16—41no—
277M16—41no—
278M16—1461no—
279M16—1461no—
280M16—1462no—
281M16—1462no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—732no—
286C2×C8—1461no—
287C2×C8—1461no—
288C2×C8—1461no—
289C2×C8—1462no—
290C2×C8—1462no—
291C2×C8D4×D7311yescharacteristic
292C2×C8D4×D7311yescharacteristic
293C2×C8D4×D7311yescharacteristic
294C2×C8C2×C22⋊D7311yescharacteristic
295C2×C8#1192402711yescharacteristic
296C2×C8#1192402811yescharacteristic
297C4⋊C4—1462no—
298C22⋊C4—1462no—
299C22⋊C4—1462no—
300C42—731no—
301C42—731no—
302C42—1461no—
303C16—22no—
304C16—41no—
305C16—2921no—
306C16—1462no—
307C23—21no—
308C23—732no—
309C23M16×D7311yescharacteristic
310Q8—21no—
311Q8—21no—
312Q8—1461no—
313Q8—1461no—
314D4—21no—
315D4—21no—
316D4—41no—
317D4—41no—
318D4—2924no—
319D4—1462no—
320D4—1462no—
321D4—1461no—
322D4—1461no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—2922no—
327C2×C4—732no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1462no—
331C2×C4—1462no—
332C2×C4C22⋊C4×D7311yescharacteristic
333C2×C4#1455655111yescharacteristic
334C2×C4C4×C22⋊D7311yescharacteristic
335C2×C4C2×C8×D7311yescharacteristic
336C2×C4#1455659711yescharacteristic
337C2×C4#1455659911yescharacteristic
338C8—41no—
339C8—2921no—
340C8—1462no—
341C8#1455655911yescharacteristic
342C8#1455656211yescharacteristic
343C8#1455656411yescharacteristic
344C8#1455657311yescharacteristic
345C22—41no—
346C22—42no—
347C22—41no—
348C22—2922no—
349C22—1462no—
350C22C22⋊C8×D7311yescharacteristic
351C22#1798865611yescharacteristic
352C22#1798866111yescharacteristic
353C4—41no—
354C4—2921no—
355C4—1462no—
356C4—1462no—
357C4#1798846311yescharacteristic
358C4#1798855211yescharacteristic
359C4#1798865011yescharacteristic
360C4C8×C22⋊D7311yescharacteristic
361C2—21no—
362C2—21no—
363C2—21no—
364C2—81no—
365C2—2922no—
366C2#2261022011yescharacteristic
subgroupG/H
centerC8#14556559
commutatorC2×C4×C73C22×C8
FrattiniC22×C8C22×D73
FittingC73×#2117C2
socleC2×C73#1869
prime radical#17989133C4
cosocleC22×C8×C73C23
hypercenter#2117D73
hypocenterC73#12982
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
1. #22623033C2semidirect
3. #22611559C2semidirect
4. #22611551C2semidirect
5. #22608012C2semidirect
6. #22608012C2semidirect
7. C73×#2117C2semidirect
46. #14556531D4semidirect
68. M32×C73D4semidirect
187. #2117D73semidirect
191. C73#12982semidirect
244. M32C22⋊D73semidirect

Maximal subgroups

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

subgroupindex
#226230332
#226186412
#226115592
#226115512
#226080122
C73×#21172
#1298273