Finite Group Databasebeta

← #33068741

Subgroups — #33068741

Order 18688.

598 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620517C211yesmaximal, characteristic, complemented
2#22620002C212yesmaximal
3#22609485C212yesmaximal, complemented
4#22609478C212yesmaximal, complemented
5#22609449C211yesmaximal, characteristic, complemented
6#22609444C211yesmaximal, characteristic, complemented
7#22609425C211yesmaximal, characteristic, complemented
8#22609420C211yesmaximal, characteristic, complemented
9#22608679C211yesmaximal, characteristic, complemented
10#22608595C212yesmaximal, complemented
11C73×#2965C211yesmaximal, characteristic
12#17989144C2212yes—
13#17988992C2211yescharacteristic
14#17988967C2211yescharacteristic
15#17988938C2212yes—
16#17988928—22no—
17#17988872C2212yes—
18#17988867C2212yes—
19#17988828—21no—
20#17988828—21no—
21#17988797C2212yes—
22#17988792C2212yes—
23#17988749—22no—
24C4×Dic292—21no—
25C4×Dic292—21no—
26C4×#11924018—22no—
27C4×#11924016—22no—
28#17988640C2212yes—
29#17988340C2212yes—
30#17988338C2211yescharacteristic
31#17988338C2211yescharacteristic
32#17988334C2212yes—
33#17988334C2212yes—
34#17988332C2212yes—
35#17988332C2212yes—
36C4×#41×C73C2211yescharacteristic
37#446×C73C2211yescharacteristic
38#446×C73C2211yescharacteristic
39#436×C73C2211yescharacteristic
40#436×C73C2211yescharacteristic
41#435×C73—21no—
42#435×C73—21no—
43#431×C73—21no—
44#431×C73C2211yescharacteristic
45C4×M16×C73—21no—
46C2×C4×C8×C73C2211yescharacteristic
47C2×Dic292—21no—
48C2×Dic292—21no—
49C2×#11924018—22no—
50C2×#11924016—22no—
51#14556591C2312yes—
52#14556591C2312yes—
53#14556583—22no—
54#14556570—22no—
55#14556570—22no—
56C4×Dic146—22no—
57C4×Dic146—22no—
58#14556550—22no—
59#14556525—21no—
60#14556525—21no—
61#14556524—22no—
62#14556522—22no—
63C4⋊#10596831C2312yes—
64C4⋊#10596831C2312yes—
65#14556516—22no—
66#14556516—22no—
67#14556515—22no—
68#14556514—22no—
69#14556514—22no—
70#14556512—22no—
71C22⋊#10596831—22no—
72C4×#10596831—22no—
73C2×#41×C73D411yescharacteristic
74C2×M16×C73—21no—
75C2×M16×C73—21no—
76C22×C8×C73D411yescharacteristic
77C22×C8×C73D411yescharacteristic
78C4×Q8×C73D411yescharacteristic
79C4×Q8×C73C2311yescharacteristic
80C4×D4×C73—21no—
81C4×D4×C73—21no—
82C4×D4×C73D411yescharacteristic
83C4×D4×C73C2311yescharacteristic
84#117×C73—21no—
85#117×C73D411yescharacteristic
86C2×C42×C73—21no—
87C2×C42×C73C2311yescharacteristic
88C4⋊C8×C73—21no—
89C4⋊C8×C73—21no—
90C4⋊C8×C73C2311yescharacteristic
91C4⋊C8×C73C2311yescharacteristic
92C22⋊C8×C73—21no—
93C22⋊C8×C73—21no—
94C22⋊C8×C73—21no—
95#97×C73—21no—
96#97×C73—21no—
97C4×C8×C73—21no—
98C4×C8×C73D411yescharacteristic
99C4×C8×C73D411yescharacteristic
100C4×C8×C73C2311yescharacteristic
101C4×C8×C73C2311yescharacteristic
102C2×Dic146—22no—
103C2×Dic146—22no—
104Dic292—42no—
105Dic292—42no—
106#11924018—44no—
107#11924016—44no—
108C2×#10596831—22no—
109C2×#10596831—22no—
110C4⋊Dic73—22no—
111C4⋊Dic73—22no—
112C4⋊Dic73—22no—
113C4⋊Dic73—22no—
114#11924007—42no—
115#11924007—42no—
116C22⋊Dic73—42no—
117C4×Dic73—42no—
118#41×C73—42no—
119C2×Q8×C73C2×D411yescharacteristic
120C2×D4×C73—21no—
121C2×D4×C73C2×D411yescharacteristic
122C22×C4×C73—21no—
123C22×C4×C73—21no—
124C22×C4×C73—21no—
125C22×C4×C73C2×D411yescharacteristic
126C22×C4×C73C2×D411yescharacteristic
127C22×C4×C73#4111yescharacteristic
128M16×C73—42no—
129M16×C73—42no—
130C2×C8×C73—22no—
131C2×C8×C73—21no—
132C2×C8×C73—21no—
133C2×C8×C73—41no—
134C2×C8×C73C2×D411yescharacteristic
135C2×C8×C73C2×D411yescharacteristic
136C2×C8×C73C2×D411yescharacteristic
137C2×C8×C73C2×D411yescharacteristic
138C4⋊C4×C73—21no—
139C4⋊C4×C73—21no—
140C4⋊C4×C73C2×D411yescharacteristic
141C4⋊C4×C73C2×D411yescharacteristic
142C22⋊C4×C73—21no—
143C22⋊C4×C73—21no—
144C22⋊C4×C73—21no—
145C42×C73—21no—
146C42×C73—21no—
147C42×C73—21no—
148C42×C73C2×D411yescharacteristic
149C42×C73C2×D411yescharacteristic
150C42×C73#4111yescharacteristic
151C42×C73C2411yescharacteristic
152C23×C73—21no—
153C23×C73#12111yescharacteristic
154Q8×C73—22no—
155D4×C73—22no—
156D4×C73—42no—
157C2×C4×C73—21no—
158C2×C4×C73—21no—
159C2×C4×C73—22no—
160C2×C4×C73—22no—
161C2×C4×C73—21no—
162C2×C4×C73—21no—
163C2×C4×C73—21no—
164C2×C4×C73—42no—
165C2×C4×C73—41no—
166C2×C4×C73—41no—
167C2×C4×C73—42no—
168C2×C4×C73#12111yescharacteristic
169C2×C4×C73#12111yescharacteristic
170C2×C4×C73#12111yescharacteristic
171C2×C4×C73C22×D411yescharacteristic
172C2×C4×C73C22×D411yescharacteristic
173C2×C4×C73C2×#4111yescharacteristic
174C2×Dic73—42no—
175C2×Dic73—42no—
176Dic146—42no—
177Dic146—42no—
178Dic146—42no—
179Dic146—42no—
180C8×C73—21no—
181C8×C73—21no—
182C8×C73—21no—
183C8×C73—41no—
184C8×C73—41no—
185C8×C73#13512yes—
186#10596831—42no—
187#10596831—42no—
188C22×C73—21no—
189C22×C73—21no—
190C22×C73—21no—
191C22×C73—41no—
192C22×C73—41no—
193C22×C73—41no—
194C22×C73C2×#12111yescharacteristic
195C4×C73—21no—
196C4×C73—21no—
197C4×C73—21no—
198C4×C73—41no—
199C4×C73—41no—
200C4×C73—41no—
201C4×C73#47312yes—
202C4×C73C2×#13511yescharacteristic
203C4×C73#57511yescharacteristic
204C4×C73#57512yes—
205Dic73—82no—
206Dic73—82no—
207#19161—731nomaximal, Sylow
208C2×C73—41no—
209C2×C73—81no—
210C2×C73#303511yescharacteristic
211C2×C73#305411yescharacteristic
212C2×C73C2×#47311yescharacteristic
213#3170—731no—
214#3107—732no—
215#2965D7311yescharacteristic
216#1700—732no—
217#1699—732no—
218#1694—731no—
219#1693—731no—
220#1690—731no—
221#1689—731no—
222#1564—731no—
223#1544—732no—
224C73#1916111yescharacteristic, complemented, Sylow
225#533—732no—
226C4×#41C2×D7311yescharacteristic
227#500—731no—
228#494—731no—
229#487—732no—
230#485—1462no—
231#475—732no—
232#474—732no—
233#467—1461no—
234#467—1461no—
235#462—732no—
236#461—732no—
237#452—1462no—
238#446C2×D7311yescharacteristic
239#446C2×D7311yescharacteristic
240C4×Q16—1462no—
241C4×Q16—1461no—
242C4×Q16—1461no—
243C4×SD16—1462no—
244#436C2×D7311yescharacteristic
245#436C2×D7311yescharacteristic
246#435—21no—
247#435—21no—
248#431—21no—
249#431—732no—
250#431C2×D7311yescharacteristic
251C4×M16—21no—
252C2×C4×C8C2×D7311yescharacteristic
253#335—732no—
254#334—731no—
255#334—731no—
256#332—732no—
257#332—732no—
258#332—732no—
259#332—732no—
260C2×#41D29211yescharacteristic
261C2×Q16—1462no—
262C2×Q16—1461no—
263C2×Q16—1461no—
264C2×SD16—1462no—
265C2×M16—21no—
266C2×M16—21no—
267C22×C8C22⋊D7311yescharacteristic
268C22×C8C22⋊D7311yescharacteristic
269C4⋊Q8—732no—
270C4⋊Q8—732no—
271#125—1462no—
272C22⋊Q8—1462no—
273C22⋊Q8—1462no—
274C4×Q8—1462no—
275C4×Q8—1462no—
276C4×Q8D29211yescharacteristic
277C4×Q8C22×D7311yescharacteristic
278C4×D4—21no—
279C4×D4—21no—
280C4×D4D29211yescharacteristic
281C4×D4C22×D7311yescharacteristic
282#117—21no—
283#117—1462no—
284#117D29211yescharacteristic
285C2×C42—21no—
286C2×C42C22×D7311yescharacteristic
287#107—1461no—
288#107—1461no—
289#107—1462no—
290#106—1462no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8—732no—
294C4⋊C8—732no—
295C4⋊C8C22×D7311yescharacteristic
296C4⋊C8C22×D7311yescharacteristic
297#103—1462no—
298#103—1462no—
299#103—1462no—
300#103—1462no—
301#103—1462no—
302#102—1462no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—1462no—
307#97—21no—
308#97—21no—
309C4×C8—21no—
310C4×C8—1462no—
311C4×C8C22⋊D7311yescharacteristic
312C4×C8C22⋊D7311yescharacteristic
313C4×C8C22×D7311yescharacteristic
314C4×C8C22×D7311yescharacteristic
315#41—42no—
316C2×Q8—1462no—
317C2×Q8—1462no—
318C2×Q8C2×D29211yescharacteristic
319C2×D4—21no—
320C2×D4C2×D29211yescharacteristic
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4C2×C22⋊D7311yescharacteristic
325C22×C4C2×D29211yescharacteristic
326C22×C4#1192402811yescharacteristic
327Q16—2922no—
328Q16—2924no—
329Q16—2922no—
330SD16—2924no—
331M16—42no—
332M16—42no—
333C2×C8—22no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—41no—
337C2×C8—1462no—
338C2×C8—1462no—
339C2×C8C2×C22⋊D7311yescharacteristic
340C2×C8C2×C22⋊D7311yescharacteristic
341C2×C8C2×C22⋊D7311yescharacteristic
342C2×C8C2×C22⋊D7311yescharacteristic
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—2922no—
346C4⋊C4—2922no—
347C4⋊C4—1462no—
348C4⋊C4—1462no—
349C4⋊C4—1462no—
350C4⋊C4—1462no—
351C4⋊C4C2×D29211yescharacteristic
352C4⋊C4C2×D29211yescharacteristic
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—2922no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—2922no—
361C42C2×C22⋊D7311yescharacteristic
362C42C2×D29211yescharacteristic
363C42#1192402811yescharacteristic
364C42C23×D7311yescharacteristic
365C23—21no—
366C23#1455656511yescharacteristic
367Q8—22no—
368Q8—2922no—
369Q8—2922no—
370Q8—2922no—
371Q8—2922no—
372D4—22no—
373D4—42no—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—2922no—
386C2×C4—2922no—
387C2×C4#1455656511yescharacteristic
388C2×C4#1455656511yescharacteristic
389C2×C4#1455656511yescharacteristic
390C2×C4C22×C22⋊D7311yescharacteristic
391C2×C4C22×D29211yescharacteristic
392C2×C4C2×#1192402811yescharacteristic
393C8—21no—
394C8—21no—
395C8—21no—
396C8—41no—
397C8—41no—
398C8—2922no—
399C8—2922no—
400C8#1455661112yes—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22C2×#1455656511yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—41no—
412C4—41no—
413C4—41no—
414C4—5842no—
415C4—5842no—
416C4#1798886212yes—
417C4C2×#1455661111yescharacteristic
418C4#1798938511yescharacteristic
419C4#1798938712yes—
420C2—41no—
421C2—81no—
422C2#2261938611yescharacteristic
423C2#2261954011yescharacteristic
424C2C2×#1798886211yescharacteristic
subgroupG/H
centerC2×C4#14556565
commutator, cosocleC42×C73C24
FrattiniC42C23×D73
FittingC73×#2965C2
socleC22×C73C2×#121
prime radicalC2×#41×C73D4
hypercenter#2965D73
hypocenterC73#19161
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2965

Complements

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

NH ≅ G/Ntype
1. #22620517C2semidirect
3. #22609485C2semidirect
4. #22609478C2semidirect
5. #22609449C2semidirect
6. #22609444C2semidirect
7. #22609425C2semidirect
8. #22609420C2semidirect
9. #22608679C2semidirect
10. #22608595C2semidirect
224. C73#19161semidirect

Maximal subgroups

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

subgroupindex
#226205172
#226200022
#226094852
#226094782
#226094492
#226094442
#226094252
#226094202
#226086792
#226085952
C73×#29652
#1916173