Finite Group Databasebeta

← #33004679

Subgroups — #33004679

Order 18688.

670 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556532C211yesmaximal, characteristic, complemented
2C2×#17988823C211yesmaximal, characteristic, complemented
3C2×#17988388C211yesmaximal, characteristic, complemented
4C2×#17988387C211yesmaximal, characteristic, complemented
5C2×C22⋊#11924003C211yesmaximal, characteristic, complemented
6#22608022C211yesmaximal, characteristic, complemented
7C2×#466×C73C211yesmaximal, characteristic, complemented
8C22×D584C2211yescharacteristic
9C2×#14556565—21no—
10C2×#14556532—22no—
11C2×#14556532—22no—
12C2×#14556532—22no—
13C22×#11924003C2211yescharacteristic
14C22×#11924003C2211yescharacteristic
15#17988823—22no—
16#17988823—22no—
17C2×#14556525C2211yescharacteristic
18C2×#14556513—21no—
19#17988388—22no—
20#17988387—22no—
21C22⋊#11924003—22no—
22C22×D8×C73C2211yescharacteristic
23C23×C8×C73C2211yescharacteristic
24C2×#121×C73—21no—
25#466×C73—22no—
26#466×C73—22no—
27C2×#107×C73C2211yescharacteristic
28C2×#102×C73—21no—
29C22×D292—21no—
30C22×C22⋊D73—41no—
31C2×D584—21no—
32C2×D584—21no—
33C2×D584—21no—
34C2×D584—21no—
35C2×D584—21no—
36C2×D584D412yescomplemented
37#14556565—24no—
38#14556565—42no—
39C2×C4⋊Dic73—21no—
40C2×#11924005—41no—
41#14556532—28no—
42C2×#11924003—21no—
43C2×#11924003—21no—
44C2×#11924003—21no—
45C2×#11924003—21no—
46C2×#11924003—21no—
47C2×#11924003D412yescomplemented
48#14556525—21no—
49#14556525D412yescomplemented
50#14556513—24no—
51C22×D4×C73—21no—
52C22×D4×C73—41no—
53C23×C4×C73D411yescharacteristic
54C2×D8×C73—21no—
55C2×D8×C73—21no—
56C2×D8×C73—21no—
57C2×D8×C73—21no—
58C2×D8×C73—21no—
59C2×D8×C73D412yescomplemented
60C22×C8×C73—21no—
61C22×C8×C73—21no—
62C22×C8×C73—21no—
63C22×C8×C73—21no—
64C22×C8×C73—21no—
65C22×C8×C73—21no—
66C22×C8×C73D411yescharacteristic
67C22×C8×C73C2311yescharacteristic
68#121×C73—24no—
69#121×C73—42no—
70C2×C4⋊C4×C73—21no—
71C2×C22⋊C4×C73—41no—
72#107×C73—21no—
73#107×C73D412yescomplemented
74#102×C73—24no—
75C23×D73—41no—
76C2×D292—22no—
77C2×D292—41no—
78C2×D292—41no—
79C2×D292—41no—
80C2×D292—41no—
81C2×D292—41no—
82C2×C22⋊D73—44no—
83C2×C22⋊D73—82no—
84C2×C22⋊D73—82no—
85C22×Dic73—41no—
86D584—22no—
87D584—22no—
88D584—41no—
89D584—41no—
90C4⋊Dic73—22no—
91C4⋊Dic73—41no—
92#11924005—44no—
93#11924003—22no—
94#11924003—41no—
95C24×C73—41no—
96C24×C73D811yescharacteristic
97C2×D4×C73—22no—
98C2×D4×C73—44no—
99C2×D4×C73—41no—
100C2×D4×C73—41no—
101C2×D4×C73—41no—
102C2×D4×C73—41no—
103C2×D4×C73—41no—
104C2×D4×C73—82no—
105C2×D4×C73—82no—
106C22×C4×C73—21no—
107C22×C4×C73—21no—
108C22×C4×C73—21no—
109C22×C4×C73—21no—
110C22×C4×C73—21no—
111C22×C4×C73—21no—
112C22×C4×C73—41no—
113C22×C4×C73D811yescharacteristic
114C22×C4×C73C2×D411yescharacteristic
115D8×C73—22no—
116D8×C73—22no—
117D8×C73—41no—
118D8×C73—41no—
119C2×C8×C73—21no—
120C2×C8×C73—21no—
121C2×C8×C73—21no—
122C2×C8×C73—41no—
123C2×C8×C73—41no—
124C2×C8×C73—41no—
125C2×C8×C73—41no—
126C2×C8×C73C2×D411yescharacteristic
127C2×C8×C73C2×D411yescharacteristic
128C2×C8×C73C2×D411yescharacteristic
129C2×C8×C73C2×D411yescharacteristic
130C2×C8×C73C2×D411yescharacteristic
131C2×C8×C73#4111yescharacteristic
132C4⋊C4×C73—22no—
133C4⋊C4×C73—41no—
134C22⋊C4×C73—44no—
135C23×C73—21no—
136C23×C73—21no—
137C23×C73—21no—
138C23×C73—21no—
139C23×C73—21no—
140C23×C73—21no—
141C23×C73—42no—
142C23×C73—81no—
143C23×C73—81no—
144C23×C73—81no—
145C23×C73—81no—
146C23×C73—81no—
147C23×C73—81no—
148C23×C73D1612yescomplemented
149C23×C73C2×D811yescharacteristic
150C22×D73—42no—
151C22×D73—81no—
152C22×D73—81no—
153C22×D73—81no—
154C22×D73—81no—
155C22×D73—81no—
156C22×D73—81no—
157D4×C73—42no—
158D4×C73—42no—
159D4×C73—88no—
160D4×C73—81no—
161D4×C73—81no—
162C2×C4×C73—21no—
163C2×C4×C73—21no—
164C2×C4×C73—21no—
165C2×C4×C73—41no—
166C2×C4×C73—41no—
167C2×C4×C73—41no—
168C2×C4×C73—41no—
169C2×C4×C73—42no—
170C2×C4×C73—81no—
171C2×C4×C73—81no—
172C2×C4×C73#12011yescharacteristic
173C2×C4×C73#12011yescharacteristic
174C2×C4×C73#12111yescharacteristic
175C2×C4×C73#13511yescharacteristic
176C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
178C22⋊D73—88no—
179C2×Dic73—42no—
180C2×Dic73—81no—
181C2×Dic73—81no—
182D292—42no—
183D292—42no—
184D292—81no—
185D292—81no—
186C8×C73—41no—
187C8×C73#12011yescharacteristic
188C8×C73#12111yescharacteristic
189C8×C73#12111yescharacteristic
190C8×C73#12711yescharacteristic
191C22×C73—22no—
192C22×C73—22no—
193C22×C73—22no—
194C22×C73—41no—
195C22×C73—41no—
196C22×C73—41no—
197C22×C73—41no—
198C22×C73—82no—
199C22×C73—82no—
200C22×C73—82no—
201C22×C73—161no—
202C22×C73—161no—
203C22×C73—161no—
204C22×C73—161no—
205C22×C73#44711yescharacteristic
206C22×C73#44711yescharacteristic
207C22×C73#46611yescharacteristic
208C22×C73C2×D1611yescharacteristic
209C22×C73#50811yescharacteristic
210C22×C73#50911yescharacteristic
211C22×C73#50911yescharacteristic
212C2×D73—82no—
213C2×D73—82no—
214C2×D73—82no—
215C2×D73—161no—
216C2×D73—161no—
217C2×D73—161no—
218C2×D73—161no—
219C4×C73—41no—
220C4×C73—82no—
221C4×C73#39211yescharacteristic
222C4×C73#44911yescharacteristic
223C4×C73#44911yescharacteristic
224C4×C73#46911yescharacteristic
225Dic73—82no—
226#13304—731nomaximal, Sylow
227C2×C73—42no—
228C2×C73—162no—
229C2×C73#199911yescharacteristic
230C2×C73#218411yescharacteristic
231C2×C73#218411yescharacteristic
232C2×C73#218611yescharacteristic
233C2×C73#218611yescharacteristic
234C2×C73#221511yescharacteristic
235C2×C73#221811yescharacteristic
236D73—162no—
237C22×D16—731no—
238C2×#466—731no—
239C2×#466D7311yescharacteristic, complemented
240C2×#357—731no—
241C2×#357—731no—
242C2×C22⋊C16—731no—
243#1380—731no—
244C73#1330411yescharacteristic, complemented, Sylow
245C22×D8—731no—
246C22×D8C2×D7311yescharacteristic
247C23×C8C2×D7311yescharacteristic
248C2×#121—21no—
249C2×#121—1461no—
250C2×D16—1462no—
251C2×D16—1462no—
252C2×D16—1462no—
253C22×C16—731no—
254C22×C16—731no—
255#466—22no—
256#466—22no—
257#466—1462no—
258#466—1462no—
259C2×#107—731no—
260C2×#107C2×D7311yescharacteristic
261C2×#102—21no—
262C2×#102—1461no—
263#357—1462no—
264#357—1462no—
265C22⋊C16—1462no—
266C22×D4—21no—
267C22×D4—41no—
268C22×D4—2921no—
269C22×D4—1461no—
270C23×C4C22⋊D7311yescharacteristic
271C2×D8—21no—
272C2×D8—21no—
273C2×D8—21no—
274C2×D8—21no—
275C2×D8—21no—
276C2×D8—732no—
277C2×D8—1461no—
278C2×D8—1461no—
279C2×D8—1461no—
280C2×D8—1461no—
281C2×D8—1461no—
282C2×D8C22⋊D7312yescomplemented
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8C22⋊D7311yescharacteristic
290C22×C8C22×D7311yescharacteristic
291#121—24no—
292#121—42no—
293#121—2922no—
294#121—1464no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—1461no—
297C2×C22⋊C4—41no—
298C2×C22⋊C4—2921no—
299D16—1468no—
300C2×C16—732no—
301C2×C16—1461no—
302C2×C16—1461no—
303C2×C16—1461no—
304C2×C16—1461no—
305C2×C16—1461no—
306#107—21no—
307#107—732no—
308#107—1461no—
309#107C22⋊D7312yescomplemented
310#102—24no—
311#102—1464no—
312C24—41no—
313C24—2921no—
314C24#1192401311yescharacteristic
315C2×D4—22no—
316C2×D4—44no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—82no—
323C2×D4—82no—
324C2×D4—2924no—
325C2×D4—2921no—
326C2×D4—2921no—
327C2×D4—2921no—
328C2×D4—2921no—
329C2×D4—2921no—
330C2×D4—5842no—
331C2×D4—5842no—
332C2×D4—1462no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—41no—
340C22×C4—2921no—
341C22×C4#1192401311yescharacteristic
342C22×C4C2×C22⋊D7311yescharacteristic
343D8—22no—
344D8—22no—
345D8—41no—
346D8—41no—
347D8—2921no—
348D8—2921no—
349D8—1462no—
350D8—1462no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—41no—
358C2×C8D4×D7311yescharacteristic
359C2×C8D4×D7311yescharacteristic
360C2×C8D4×D7311yescharacteristic
361C2×C8C2×C22⋊D7311yescharacteristic
362C2×C8C2×C22⋊D7311yescharacteristic
363C2×C8#1192402711yescharacteristic
364C4⋊C4—22no—
365C4⋊C4—41no—
366C4⋊C4—2921no—
367C4⋊C4—1462no—
368C22⋊C4—44no—
369C22⋊C4—2924no—
370C16—2921no—
371C16—1462no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—42no—
379C23—81no—
380C23—81no—
381C23—81no—
382C23—81no—
383C23—81no—
384C23—81no—
385C23—2922no—
386C23—5841no—
387C23—5841no—
388C23—5841no—
389C23—5841no—
390C23—5841no—
391C23—5841no—
392C23#1455653212yescomplemented
393C23C2×#1192401311yescharacteristic
394D4—42no—
395D4—42no—
396D4—88no—
397D4—81no—
398D4—81no—
399D4—2922no—
400D4—2922no—
401D4—5848no—
402D4—5841no—
403D4—5841no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—2922no—
415C2×C4—5841no—
416C2×C4—5841no—
417C2×C4#1455655911yescharacteristic
418C2×C4#1455656011yescharacteristic
419C2×C4#1455656311yescharacteristic
420C2×C4#1455661111yescharacteristic
421C2×C4#1455661611yescharacteristic
422C2×C4#1455661711yescharacteristic
423C8—41no—
424C8#1455655911yescharacteristic
425C8#1455656211yescharacteristic
426C8#1455656311yescharacteristic
427C8#1455658711yescharacteristic
428C22—22no—
429C22—22no—
430C22—22no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—82no—
436C22—82no—
437C22—82no—
438C22—161no—
439C22—161no—
440C22—161no—
441C22—161no—
442C22—5842no—
443C22—5842no—
444C22—5842no—
445C22—11681no—
446C22—11681no—
447C22—11681no—
448C22—11681no—
449C22#1798872011yescharacteristic
450C22#1798872111yescharacteristic
451C22#1798882111yescharacteristic
452C22C2×#1455653211yescharacteristic
453C22#1798901711yescharacteristic
454C22#1798902211yescharacteristic
455C22#1798902311yescharacteristic
456C4—41no—
457C4—82no—
458C4—5842no—
459C4#1798849511yescharacteristic
460C4#1798873011yescharacteristic
461C4#1798873211yescharacteristic
462C4#1798883811yescharacteristic
463C2—42no—
464C2—162no—
465C2—11682no—
466C2#2261092711yescharacteristic
467C2#2261184211yescharacteristic
468C2#2261184311yescharacteristic
469C2#2261185211yescharacteristic
470C2#2261185411yescharacteristic
471C2#2261201511yescharacteristic
472C2#2261203211yescharacteristic
subgroupG/H
centerC23C2×#11924013
commutator, cosocleC22×C8×C73C23
FrattiniC22×C8C22×D73
FittingC2×#466×C73C2
socleC23×C73C2×D8
hypercenterC2×#466D73
hypocenterC73#13304
LCSG ▷ C22×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C22×#14556532C2semidirect
2. C2×#17988823C2semidirect
3. C2×#17988388C2semidirect
4. C2×#17988387C2semidirect
5. C2×C22⋊#11924003C2semidirect
6. #22608022C2semidirect
7. C2×#466×C73C2semidirect
36. C2×D584D4semidirect
47. C2×#11924003D4semidirect
49. #14556525D4semidirect
59. C2×D8×C73D4semidirect
73. #107×C73D4semidirect
148. C23×C73D16semidirect
239. C2×#466D73semidirect
244. C73#13304semidirect
282. C2×D8C22⋊D73semidirect
309. #107C22⋊D73semidirect
392. C23#14556532semidirect

Maximal subgroups

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

subgroupindex
C22×#145565322
C2×#179888232
C2×#179883882
C2×#179883872
C2×C22⋊#119240032
#226080222
C2×#466×C732
#1330473