Finite Group Databasebeta

← #32982165

Subgroups — #32982165

Order 18688.

678 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988782C211yesmaximal, characteristic
2#22610737C211yesmaximal, characteristic, complemented
3#22609931C211yesmaximal, characteristic, complemented
4C2×#17988330C211yesmaximal, characteristic, complemented
5#22607815C211yesmaximal, characteristic, complemented
6#22607766C211yesmaximal, characteristic, complemented
7C2×C8×D4×C73C211yesmaximal, characteristic, complemented
8C22×#11924013—21no—
9C2×#14556588C2211yescharacteristic
10#17988782—22no—
11#17988782C414yescomplemented
12C2×C4⋊#10596831C2211yescharacteristic
13C2×C4⋊#10596831C2211yescharacteristic
14C2×#14556513—21no—
15C2×#14556513—21no—
16C2×#14556512—21no—
17C2×#14556511—21no—
18#17988457C2211yescharacteristic
19#17988349—21no—
20#17988330—22no—
21C23×C8×C73—21no—
22C2×C4×D4×C73C2211yescharacteristic
23C8×D4×C73—22no—
24C8×D4×C73—22no—
25C2×C4⋊C8×C73C2211yescharacteristic
26C2×C22⋊C8×C73—21no—
27C2×C4×C8×C73C2211yescharacteristic
28C22×D292—21no—
29C22×D292—21no—
30C22×D292—21no—
31C2×#11924013—24no—
32C2×#11924013—42no—
33C2×#11924013—42no—
34C22×#10596831—21no—
35C22×#10596831—21no—
36#14556588—21no—
37#14556588—21no—
38#14556588—21no—
39#14556588C2×C412yes—
40C2×C4⋊Dic73—21no—
41C2×C4⋊Dic73—21no—
42C2×C4⋊Dic73—21no—
43C4⋊#10596831—21no—
44C4⋊#10596831—21no—
45C4⋊#10596831—21no—
46C4⋊#10596831C2×C412yes—
47#14556513—42no—
48#14556513—42no—
49#14556512—42no—
50#14556511—24no—
51C22×D4×C73D411yescharacteristic
52C23×C4×C73—21no—
53C22×C8×C73—24no—
54C22×C8×C73—21no—
55C22×C8×C73—42no—
56C22×C8×C73—42no—
57C22×C8×C73D411yescharacteristic
58C22×C8×C73D411yescharacteristic
59C4×D4×C73—21no—
60C4×D4×C73—21no—
61C4×D4×C73C2×C412yes—
62C4×D4×C73D412yes—
63C2×C4⋊C4×C73D411yescharacteristic
64C2×C22⋊C4×C73—21no—
65C2×C42×C73C2311yescharacteristic
66C4⋊C8×C73—21no—
67C4⋊C8×C73D412yes—
68C22⋊C8×C73—24no—
69C4×C8×C73—21no—
70C4×C8×C73—21no—
71C23×D73—41no—
72C2×D292—22no—
73C2×D292—22no—
74C2×D292—22no—
75C2×D292—41no—
76C2×D292—41no—
77C2×D292—41no—
78C2×D292—41no—
79C2×D292—41no—
80C2×D292—41no—
81C2×D292—41no—
82C2×D292—41no—
83C2×D292—41no—
84C2×D292—41no—
85C2×D292—41no—
86C2×D292—81no—
87C2×D292—81no—
88C22×Dic73—41no—
89#11924013—48no—
90C2×#10596831—22no—
91C2×#10596831—41no—
92C2×#10596831—41no—
93C2×#10596831—41no—
94C2×#10596831—41no—
95C2×#10596831—41no—
96C4⋊Dic73—41no—
97C4⋊Dic73—41no—
98C4⋊Dic73—41no—
99C4⋊Dic73—41no—
100C4⋊Dic73—81no—
101C24×C73—21no—
102C2×D4×C73—21no—
103C2×D4×C73—21no—
104C2×D4×C73—21no—
105C2×D4×C73C22⋊C412yes—
106C2×D4×C73D812yes—
107C2×D4×C73SD1612yes—
108C22×C4×C73—21no—
109C22×C4×C73—22no—
110C22×C4×C73—22no—
111C22×C4×C73—41no—
112C22×C4×C73—41no—
113C22×C4×C73—41no—
114C22×C4×C73—41no—
115C22×C4×C73C2×D411yescharacteristic
116C22×C4×C73C2×D411yescharacteristic
117C22×C4×C73#4111yescharacteristic
118C2×C8×C73—21no—
119C2×C8×C73—21no—
120C2×C8×C73—21no—
121C2×C8×C73—22no—
122C2×C8×C73—21no—
123C2×C8×C73—21no—
124C2×C8×C73—48no—
125C2×C8×C73—41no—
126C2×C8×C73—41no—
127C2×C8×C73D812yescomplemented
128C4⋊C4×C73—21no—
129C4⋊C4×C73C22⋊C412yes—
130C22⋊C4×C73—22no—
131C22⋊C4×C73—22no—
132C42×C73C22×C411yescharacteristic
133C42×C73C2×D411yescharacteristic
134C42×C73C2×D411yescharacteristic
135C42×C73#4111yescharacteristic
136C23×C73—22no—
137C23×C73—22no—
138C23×C73—22no—
139C23×C73—41no—
140C23×C73—41no—
141C23×C73—41no—
142C23×C73—41no—
143C23×C73#12111yescharacteristic
144C22×D73—42no—
145C22×D73—81no—
146C22×D73—81no—
147C22×D73—81no—
148C22×D73—81no—
149C22×D73—81no—
150C22×D73—81no—
151D4×C73—22no—
152D4×C73—22no—
153D4×C73—22no—
154D4×C73#10214yescomplemented
155C2×C4×C73—21no—
156C2×C4×C73—21no—
157C2×C4×C73—22no—
158C2×C4×C73—41no—
159C2×C4×C73—41no—
160C2×C4×C73—42no—
161C2×C4×C73—42no—
162C2×C4×C73—42no—
163C2×C4×C73—42no—
164C2×C4×C73C2×C22⋊C411yescharacteristic
165C2×C4×C73C4×D411yescharacteristic
166C2×C4×C73C4×D411yescharacteristic
167C2×C4×C73#12011yescharacteristic
168C2×C4×C73#12111yescharacteristic
169C2×C4×C73#12311yescharacteristic
170C2×C4×C73C2×D811yescharacteristic
171C2×C4×C73C2×D811yescharacteristic
172C2×C4×C73C2×SD1611yescharacteristic
173C2×C4×C73#13511yescharacteristic
174C2×C4×C73#13511yescharacteristic
175C2×C4×C73#13511yescharacteristic
176C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
178C2×Dic73—81no—
179C2×Dic73—81no—
180C2×Dic73—81no—
181D292—42no—
182D292—42no—
183D292—42no—
184D292—42no—
185D292—82no—
186D292—82no—
187D292—81no—
188D292—81no—
189D292—81no—
190D292—81no—
191C8×C73—22no—
192C8×C73—42no—
193C8×C73—41no—
194#10596831—42no—
195#10596831—81no—
196C22×C73—24no—
197C22×C73—42no—
198C22×C73—42no—
199C22×C73—42no—
200C22×C73—42no—
201C22×C73—42no—
202C22×C73—42no—
203C22×C73#38611yescharacteristic
204C22×C73#45911yescharacteristic
205C22×C73#46311yescharacteristic
206C22×C73#46511yescharacteristic
207C22×C73#46611yescharacteristic
208C22×C73#47111yescharacteristic
209C22×C73#47211yescharacteristic
210C2×D73—82no—
211C2×D73—82no—
212C2×D73—82no—
213C2×D73—161no—
214C2×D73—161no—
215C2×D73—161no—
216C2×D73—161no—
217C4×C73—21no—
218C4×C73—21no—
219C4×C73—42no—
220C4×C73C2×#10211yescharacteristic
221C4×C73#41611yescharacteristic
222C4×C73C4×D811yescharacteristic
223C4×C73#44211yescharacteristic
224C4×C73#44711yescharacteristic
225C4×C73#44911yescharacteristic
226C4×C73#46511yescharacteristic
227C4×C73#46611yescharacteristic
228Dic73—161no—
229#9221—731nomaximal, Sylow
230C2×C73—44no—
231C2×C73#166511yescharacteristic
232C2×C73#166711yescharacteristic
233C2×C73#167711yescharacteristic
234C2×C73#168111yescharacteristic
235C2×C73#187911yescharacteristic
236C2×C73#189311yescharacteristic
237C2×C73#190711yescharacteristic
238D73—162no—
239C2×#459—731no—
240C2×C8×D4D7311yescharacteristic, complemented
241#1957—731no—
242#1802—731no—
243C2×#331—731no—
244#1296—731no—
245#1277—731no—
246C73#922111yescharacteristic, complemented, Sylow
247C22×D8—1461no—
248C23×C8—21no—
249C2×#127—731no—
250C2×C4×D4C2×D7311yescharacteristic
251#459—734no—
252#459—1462no—
253C8×D4—22no—
254C8×D4—22no—
255C2×C4⋊C8—731no—
256C2×C4⋊C8—731no—
257C2×C4⋊C8C2×D7311yescharacteristic
258C2×#102—1461no—
259C2×#102—1461no—
260C2×#102—1461no—
261C2×#102—1461no—
262C2×C22⋊C8—21no—
263C2×C4×C8C2×D7311yescharacteristic
264#384—731no—
265#340—1461no—
266#331—1462no—
267C22×D4—1461no—
268C22×D4—1461no—
269C22×D4—1461no—
270C22×D4D29211yescharacteristic
271C23×C4—21no—
272C2×D8—2922no—
273C2×D8—2922no—
274C2×D8—1464no—
275C22×C8—24no—
276C22×C8—21no—
277C22×C8—42no—
278C22×C8—42no—
279C22×C8—1461no—
280C22×C8—1461no—
281C22×C8C22⋊D7311yescharacteristic
282C22×C8C22⋊D7311yescharacteristic
283#127—732no—
284#127—1461no—
285#127—1461no—
286#127—1461no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4C4×D7312yes—
290C4×D4C22⋊D7312yes—
291C2×C4⋊C4—1461no—
292C2×C4⋊C4—1461no—
293C2×C4⋊C4—1461no—
294C2×C4⋊C4D29211yescharacteristic
295C2×C22⋊C4—21no—
296C2×C42C22×D7311yescharacteristic
297C4⋊C8—21no—
298C4⋊C8—732no—
299C4⋊C8—1461no—
300C4⋊C8—1461no—
301C4⋊C8—1461no—
302C4⋊C8C22⋊D7312yes—
303#102—2922no—
304#102—2922no—
305#102—2922no—
306#102—1464no—
307C22⋊C8—24no—
308C4×C8—21no—
309C4×C8—21no—
310C24—21no—
311C24—2921no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—21no—
315C2×D4—2921no—
316C2×D4—2921no—
317C2×D4—2921no—
318C2×D4—2921no—
319C2×D4—2921no—
320C2×D4—2921no—
321C2×D4—2921no—
322C2×D4—2921no—
323C2×D4—2921no—
324C2×D4—2921no—
325C2×D4—2921no—
326C2×D4—5841no—
327C2×D4—5841no—
328C2×D4—1462no—
329C2×D4—1462no—
330C2×D4—1462no—
331C2×D4#1192400512yes—
332C2×D4D58412yes—
333C2×D4#1192401712yes—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—2921no—
342C22×C4C2×C22⋊D7311yescharacteristic
343C22×C4C2×D29211yescharacteristic
344C22×C4#1192402811yescharacteristic
345D8—2928no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—22no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—48no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—2921no—
356C2×C8—2921no—
357C2×C8—2921no—
358C2×C8—2921no—
359C2×C8—2921no—
360C2×C8—1462no—
361C2×C8#1192401312yescomplemented
362C4⋊C4—21no—
363C4⋊C4—2921no—
364C4⋊C4—2921no—
365C4⋊C4—2921no—
366C4⋊C4—2921no—
367C4⋊C4—5841no—
368C4⋊C4#1192400512yes—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C42C2×C4×D7311yescharacteristic
372C42C2×C22⋊D7311yescharacteristic
373C42C2×C22⋊D7311yescharacteristic
374C42#1192402811yescharacteristic
375C23—22no—
376C23—22no—
377C23—22no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—2922no—
383C23—5841no—
384C23—5841no—
385C23—5841no—
386C23—5841no—
387C23—5841no—
388C23—5841no—
389C23#1455656511yescharacteristic
390D4—22no—
391D4—22no—
392D4—22no—
393D4—2922no—
394D4—2922no—
395D4—2922no—
396D4—2922no—
397D4—5842no—
398D4—5842no—
399D4—5841no—
400D4—5841no—
401D4—5841no—
402D4—5841no—
403D4#1455651314yescomplemented
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—5841no—
414C2×C4—5841no—
415C2×C4—5841no—
416C2×C4C2×#1192400511yescharacteristic
417C2×C4C4×C22⋊D7311yescharacteristic
418C2×C4C4×C22⋊D7311yescharacteristic
419C2×C4#1455656011yescharacteristic
420C2×C4#1455656511yescharacteristic
421C2×C4#1455657411yescharacteristic
422C2×C4C2×#1192401311yescharacteristic
423C2×C4C2×D58411yescharacteristic
424C2×C4C2×#1192401711yescharacteristic
425C2×C4#1455661111yescharacteristic
426C2×C4#1455661311yescharacteristic
427C2×C4#1455661311yescharacteristic
428C2×C4#1455661611yescharacteristic
429C2×C4#1455661711yescharacteristic
430C8—22no—
431C8—42no—
432C8—41no—
433C8—2922no—
434C8—5841no—
435C22—24no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—42no—
442C22—5842no—
443C22—5842no—
444C22—5842no—
445C22—11681no—
446C22—11681no—
447C22—11681no—
448C22—11681no—
449C22#1798846611yescharacteristic
450C22#1798878211yescharacteristic
451C22#1798880211yescharacteristic
452C22#1798881611yescharacteristic
453C22#1798882311yescharacteristic
454C22#1798885011yescharacteristic
455C22#1798885711yescharacteristic
456C4—21no—
457C4—21no—
458C4—42no—
459C4—11681no—
460C4C2×#1455651311yescharacteristic
461C4#1798858411yescharacteristic
462C4C4×#1192401311yescharacteristic
463C4#1798869711yescharacteristic
464C4#1798872111yescharacteristic
465C4#1798873211yescharacteristic
466C4#1798881611yescharacteristic
467C4#1798882311yescharacteristic
468C2—44no—
469C2—11682no—
470C2#2260927211yescharacteristic
471C2#2260928611yescharacteristic
472C2#2260934011yescharacteristic
473C2#2260936811yescharacteristic
474C2#2261027911yescharacteristic
475C2#2261035911yescharacteristic
476C2#2261043911yescharacteristic
subgroupG/H
centerC23#14556565
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC2×C8×D4×C73C2
socleC23×C73#121
prime radicalC2×#17988782C2
cosocleC2×C42×C73C23
hypercenterC2×C8×D4D73
hypocenterC73#9221
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
2. #22610737C2semidirect
3. #22609931C2semidirect
4. C2×#17988330C2semidirect
5. #22607815C2semidirect
6. #22607766C2semidirect
7. C2×C8×D4×C73C2semidirect
11. #17988782C4semidirect
127. C2×C8×C73D8semidirect
154. D4×C73#102semidirect
240. C2×C8×D4D73semidirect
246. C73#9221semidirect
361. C2×C8#11924013semidirect
403. D4#14556513semidirect

Maximal subgroups

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

subgroupindex
C2×#179887822
#226107372
#226099312
C2×#179883302
#226078152
#226077662
C2×C8×D4×C732
#922173