Finite Group Databasebeta

← #32989372

Subgroups — #32989372

Order 18688.

516 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22615100C211yesmaximal, characteristic
2#22610732C211yesmaximal, characteristic, complemented
3#22609928C211yesmaximal, characteristic
4C2×#17988335C211yesmaximal, characteristic, complemented
5C2×#17988314C211yesmaximal, characteristic
6#22607772C211yesmaximal, characteristic, complemented
7C73×#1948C211yesmaximal, characteristic, complemented
8C2×#14556591C2211yescharacteristic
9C2×C4×D292C2211yescharacteristic
10C2×C4⋊#10596831C2211yescharacteristic
11C2×#14556514—22no—
12C2×#14556511—21no—
13C2×C4×#10596831C2211yescharacteristic
14#17988500—22no—
15#17988489—21no—
16#17988453—21no—
17#17988444—21no—
18#17988444—21no—
19#17988349—21no—
20#17988335—22no—
21#17988314—22no—
22C2×#106×C73—21no—
23C2×C4⋊C8×C73C2211yescharacteristic
24#384×C73C2211yescharacteristic
25C4×C4⋊C4×C73C2211yescharacteristic
26#340×C73—21no—
27C22×Dic146D412yes—
28C22×D292D411yescharacteristic
29C22×C4×D73—21no—
30C22×#10596831—21no—
31C22×#10596831—21no—
32#14556591—21no—
33#14556591—21no—
34#14556591—21no—
35#14556591—21no—
36C4×D292—21no—
37C4×D292—21no—
38C4×D292—21no—
39C4×D292—21no—
40C2×C4⋊Dic73—21no—
41C2×C4⋊Dic73—21no—
42C2×C4⋊Dic73D411yescharacteristic
43C2×#11924005—22no—
44C2×#11924005—22no—
45C2×#11924005—21no—
46C4⋊#10596831—21no—
47C4⋊#10596831—21no—
48#14556514—44no—
49#14556511—42no—
50C4×#10596831—21no—
51C4×#10596831—21no—
52#14556498—22no—
53#14556498—22no—
54C22×C8×C73—21no—
55C2×C4⋊C4×C73—21no—
56C2×C4⋊C4×C73—21no—
57C2×C4⋊C4×C73—21no—
58C2×C4⋊C4×C73D411yescharacteristic
59C2×C4⋊C4×C73D411yescharacteristic
60C2×C42×C73—21no—
61C2×C42×C73C2311yescharacteristic
62#106×C73—42no—
63C4⋊C8×C73—21no—
64C4⋊C8×C73D412yes—
65#95×C73—21no—
66C23×D73—21no—
67C2×Dic146—22no—
68C2×Dic146—22no—
69C2×Dic146—42no—
70C2×Dic146—42no—
71C2×D292—21no—
72C2×D292—21no—
73C2×D292—21no—
74C2×D292—21no—
75C2×D292—21no—
76C2×D292SD1612yes—
77C22×Dic73—21no—
78C22×Dic73—22no—
79C2×C4×D73—41no—
80C2×C4×D73—41no—
81C2×C4×D73—41no—
82C2×C4×D73—41no—
83C2×C4×D73—41no—
84C2×C4×D73—41no—
85C2×#10596831—22no—
86C2×#10596831—41no—
87C2×#10596831—41no—
88C2×#10596831—41no—
89C2×#10596831—41no—
90C2×#10596831—41no—
91C4⋊Dic73—21no—
92C4⋊Dic73—21no—
93C4⋊Dic73—41no—
94C4⋊Dic73—41no—
95C4⋊Dic73—41no—
96C4⋊Dic73—41no—
97#11924005—41no—
98#11924005—41no—
99#11924005—82no—
100#11924005—82no—
101C22×C4×C73—21no—
102C22×C4×C73—21no—
103C22×C4×C73—41no—
104C22×C4×C73C2×D411yescharacteristic
105C22×C4×C73C2×D411yescharacteristic
106C22×C4×C73C2×D411yescharacteristic
107C2×C8×C73—22no—
108C2×C8×C73—41no—
109C2×C8×C73—41no—
110C4⋊C4×C73—21no—
111C4⋊C4×C73—21no—
112C4⋊C4×C73—21no—
113C4⋊C4×C73—21no—
114C4⋊C4×C73—42no—
115C4⋊C4×C73—41no—
116C4⋊C4×C73—41no—
117C4⋊C4×C73—41no—
118C4⋊C4×C73—41no—
119C42×C73—41no—
120C42×C73—41no—
121C42×C73C2×D411yescharacteristic
122C42×C73#4111yescharacteristic
123C42×C73#4111yescharacteristic
124C42×C73#4111yescharacteristic
125C23×C73#12011yescharacteristic
126C22×D73—22no—
127C22×D73—41no—
128C22×D73—41no—
129C22×D73—41no—
130C22×D73—41no—
131C22×D73—41no—
132C22×D73—41no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—41no—
136C2×C4×C73—41no—
137C2×C4×C73—41no—
138C2×C4×C73—41no—
139C2×C4×C73—41no—
140C2×C4×C73—41no—
141C2×C4×C73—81no—
142C2×C4×C73—81no—
143C2×C4×C73—81no—
144C2×C4×C73#12111yescharacteristic
145C2×C4×C73#12111yescharacteristic
146C2×C4×C73#12111yescharacteristic
147C2×C4×C73#12311yescharacteristic
148C2×C4×C73#12311yescharacteristic
149C2×C4×C73#12411yescharacteristic
150C2×C4×C73C2×SD1611yescharacteristic
151C2×C4×C73#13511yescharacteristic
152C2×C4×C73#13511yescharacteristic
153C2×C4×C73#13511yescharacteristic
154C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C73#13711yescharacteristic
156C2×C4×C73#13711yescharacteristic
157C2×C4×C73#13711yescharacteristic
158C2×Dic73—41no—
159C2×Dic73—42no—
160C2×Dic73—41no—
161C2×Dic73—41no—
162C2×Dic73—42no—
163C2×Dic73—42no—
164D292—22no—
165D292—22no—
166D292—41no—
167D292—41no—
168C4×D73—81no—
169C4×D73—81no—
170C4×D73—81no—
171C4×D73—81no—
172Dic146—44no—
173Dic146—82no—
174C8×C73—42no—
175#10596831—42no—
176#10596831—81no—
177C22×C73#39411yescharacteristic
178C22×C73#44811yescharacteristic
179C22×C73#44911yescharacteristic
180C22×C73#45211yescharacteristic
181C22×C73#45211yescharacteristic
182C22×C73#45311yescharacteristic
183C22×C73#45511yescharacteristic
184C2×D73—42no—
185C2×D73—42no—
186C2×D73—42no—
187C2×D73—81no—
188C2×D73—81no—
189C2×D73—81no—
190C2×D73—81no—
191C4×C73—21no—
192C4×C73—21no—
193C4×C73—81no—
194C4×C73—81no—
195C4×C73—161no—
196C4×C73#46311yescharacteristic
197C4×C73#46411yescharacteristic
198C4×C73#46511yescharacteristic
199C4×C73#47011yescharacteristic
200C4×C73#48311yescharacteristic
201C4×C73#48511yescharacteristic
202C4×C73#48811yescharacteristic
203C4×C73#48911yescharacteristic
204Dic73—82no—
205Dic73—81no—
206#10412—731nomaximal, Sylow
207C2×C73#162211yescharacteristic
208C2×C73#163411yescharacteristic
209C2×C73#164311yescharacteristic
210C2×C73#164611yescharacteristic
211C2×C73#203511yescharacteristic
212C2×C73#203711yescharacteristic
213C2×C73#204211yescharacteristic
214D73—82no—
215#2563—731no—
216#1956—731no—
217#1948D7311yescharacteristic, complemented
218#1802—731no—
219C2×#333—731no—
220C2×D4⋊C8—731no—
221#1279—731no—
222C73#1041211yescharacteristic, complemented, Sylow
223C2×C4⋊Q8—731no—
224C2×C4×D4—731no—
225C2×#106—21no—
226C2×C4⋊C8—731no—
227C2×C4⋊C8C2×D7311yescharacteristic
228C2×#103—1462no—
229C2×#102—1461no—
230C2×C4×C8—731no—
231#393—1462no—
232#390—1461no—
233#384C2×D7311yescharacteristic
234#382—1461no—
235#380—1461no—
236#380—1461no—
237C4×C4⋊C4C2×D7311yescharacteristic
238#340—21no—
239#340—1461no—
240#333—1462no—
241D4⋊C8—1462no—
242C22×Q8—732no—
243C22×D4—731no—
244C23×C4—1461no—
245C22×C8—21no—
246C22×C8—1461no—
247C22×C8—1461no—
248C4⋊Q8—1461no—
249C4⋊Q8—1461no—
250C4⋊Q8—1461no—
251C4⋊Q8—1461no—
252C4×D4—1461no—
253C4×D4—1461no—
254C4×D4—1461no—
255C4×D4—1461no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—731no—
260C2×C4⋊C4—1461no—
261C2×C4⋊C4—1461no—
262C2×C4⋊C4C22⋊D7311yescharacteristic
263C2×C4⋊C4C22⋊D7311yescharacteristic
264C2×C22⋊C4—1461no—
265C2×C22⋊C4—1462no—
266C2×C22⋊C4—1462no—
267C2×C42—21no—
268C2×C42C22×D7311yescharacteristic
269#106—42no—
270C4⋊C8—21no—
271C4⋊C8—1461no—
272C4⋊C8—1461no—
273C4⋊C8D29212yes—
274#103—2924no—
275#102—2922no—
276C4×C8—1461no—
277C4×C8—1461no—
278#95—21no—
279#95—1462no—
280#95—1462no—
281C24—1461no—
282C2×Q8—2922no—
283C2×Q8—2922no—
284C2×Q8—1462no—
285C2×Q8—1462no—
286C2×D4—732no—
287C2×D4—1461no—
288C2×D4—1461no—
289C2×D4—1461no—
290C2×D4—1461no—
291C2×D4—1461no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—41no—
295C22×C4—2921no—
296C22×C4—2921no—
297C22×C4—2921no—
298C22×C4—2921no—
299C22×C4—2921no—
300C22×C4—2921no—
301C22×C4—1461no—
302C22×C4—1462no—
303C22×C4D4×D7311yescharacteristic
304C22×C4D4×D7311yescharacteristic
305C22×C4C2×C22⋊D7311yescharacteristic
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—41no—
309C2×C8—2921no—
310C2×C8—2921no—
311C2×C8—2921no—
312C2×C8—2921no—
313C2×C8—2921no—
314C2×C8—1462no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—42no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—2921no—
325C4⋊C4—2921no—
326C4⋊C4—2921no—
327C4⋊C4—2921no—
328C4⋊C4—1461no—
329C4⋊C4—1461no—
330C22⋊C4—2921no—
331C22⋊C4—2921no—
332C22⋊C4—5842no—
333C22⋊C4—5842no—
334C42—41no—
335C42—41no—
336C42C2×D29211yescharacteristic
337C42#1192402811yescharacteristic
338C42#1192402911yescharacteristic
339C42#1192402911yescharacteristic
340C23—2921no—
341C23—2921no—
342C23—2921no—
343C23—2921no—
344C23—2921no—
345C23—2921no—
346C23—1462no—
347C23#1455655911yescharacteristic
348Q8—2924no—
349Q8—5842no—
350D4—2921no—
351D4—2921no—
352D4—1462no—
353D4—1462no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—2921no—
366C2×C4—2921no—
367C2×C4—2922no—
368C2×C4—2921no—
369C2×C4—2922no—
370C2×C4—2922no—
371C2×C4—5841no—
372C2×C4—5841no—
373C2×C4—5841no—
374C2×C4—5841no—
375C2×C4#1455656511yescharacteristic
376C2×C4#1455656611yescharacteristic
377C2×C4#1455656611yescharacteristic
378C2×C4#1455657611yescharacteristic
379C2×C4#1455657611yescharacteristic
380C2×C4#1455658011yescharacteristic
381C2×C4SD16×D7311yescharacteristic
382C2×C4#1455661111yescharacteristic
383C2×C4#1455661111yescharacteristic
384C2×C4#1455661211yescharacteristic
385C2×C4#1455661711yescharacteristic
386C2×C4#1455662011yescharacteristic
387C2×C4#1455662011yescharacteristic
388C2×C4#1455662211yescharacteristic
389C8—42no—
390C8—2922no—
391C8—5841no—
392C22—2922no—
393C22—2922no—
394C22—2922no—
395C22—5841no—
396C22—5841no—
397C22—5841no—
398C22—5841no—
399C22#1798850411yescharacteristic
400C22#1798872411yescharacteristic
401C22#1798873011yescharacteristic
402C22#1798874611yescharacteristic
403C22#1798874711yescharacteristic
404C22#1798875311yescharacteristic
405C22#1798876311yescharacteristic
406C4—21no—
407C4—21no—
408C4—81no—
409C4—81no—
410C4—161no—
411C4—5842no—
412C4—5841no—
413C4#1798880211yescharacteristic
414C4#1798880911yescharacteristic
415C4#1798881711yescharacteristic
416C4#1798884611yescharacteristic
417C4#1798891911yescharacteristic
418C4#1798893111yescharacteristic
419C4#1798894411yescharacteristic
420C4#1798894911yescharacteristic
421C2—5842no—
422C2#2260900211yescharacteristic
423C2#2260907511yescharacteristic
424C2#2260913711yescharacteristic
425C2#2260915711yescharacteristic
426C2#2261112911yescharacteristic
427C2#2261114311yescharacteristic
428C2#2261117211yescharacteristic
subgroupG/H
centerC23#14556559
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1948C2
socleC23×C73#120
prime radicalC22×D292D4
hypercenter#1948D73
hypocenterC73#10412
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
2. #22610732C2semidirect
4. C2×#17988335C2semidirect
6. #22607772C2semidirect
7. C73×#1948C2semidirect
217. #1948D73semidirect
222. C73#10412semidirect

Maximal subgroups

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

subgroupindex
#226151002
#226107322
#226099282
C2×#179883352
C2×#179883142
#226077722
C73×#19482
#1041273