Finite Group Databasebeta

← #33241107

Subgroups — #33241107

Order 18688.

558 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620581C211yesmaximal, characteristic, complemented
2#22612116C211yesmaximal, characteristic, complemented
3#22612111C211yesmaximal, characteristic, complemented
4#22612095C211yesmaximal, characteristic, complemented
5#22612088C211yesmaximal, characteristic, complemented
6#22611971C211yesmaximal, characteristic, complemented
7#22611966C211yesmaximal, characteristic, complemented
8#22611854C211yesmaximal, characteristic, complemented
9#22611854C211yesmaximal, characteristic, complemented
10#22611805C211yesmaximal, characteristic, complemented
11#22611793C211yesmaximal, characteristic, complemented
12C4×#14556534C211yesmaximal, characteristic, complemented
13C4×#14556532C211yesmaximal, characteristic, complemented
14#22611738C211yesmaximal, characteristic, complemented
15C73×#2951C211yesmaximal, characteristic, complemented
16#17989192—21no—
17C2×#14556534C2211yescharacteristic
18C2×#14556534C2211yescharacteristic
19C2×#14556532C2211yescharacteristic
20C2×#14556532C2211yescharacteristic
21#17988989C2211yescharacteristic
22#17988964C2211yescharacteristic
23#17988952—21no—
24#17988840—21no—
25#17988823C2211yescharacteristic
26#17988823C2211yescharacteristic
27#17988700—21no—
28C4×D584C2211yescharacteristic
29C4×D584C2211yescharacteristic
30#17988414C2211yescharacteristic
31#17988414C2211yescharacteristic
32#17988412C2211yescharacteristic
33#17988412C2211yescharacteristic
34C4⋊#11924003C2211yescharacteristic
35C4⋊#11924003C2211yescharacteristic
36#17988391C2211yescharacteristic
37#17988391C2211yescharacteristic
38#17988388C2211yescharacteristic
39#17988388C2211yescharacteristic
40#17988387C2211yescharacteristic
41#17988387C2211yescharacteristic
42#17988387C2211yescharacteristic
43#17988387C2211yescharacteristic
44C22⋊#11924003C2211yescharacteristic
45C22⋊#11924003C2211yescharacteristic
46#17988363C2211yescharacteristic
47C4×#11924003C2211yescharacteristic
48C2×#135×C73C2211yescharacteristic
49#520×C73—21no—
50#440×C73—21no—
51#440×C73—21no—
52C4×Q16×C73C2211yescharacteristic
53C4×Q16×C73C2211yescharacteristic
54C4×D8×C73C2211yescharacteristic
55C4×D8×C73C2211yescharacteristic
56C2×#107×C73C2211yescharacteristic
57#417×C73—21no—
58#405×C73C2211yescharacteristic
59C2×D584—21no—
60C2×D584C2311yescharacteristic
61C2×D584C2311yescharacteristic
62#14556588—21no—
63#14556583—21no—
64#14556576—41no—
65#14556576—41no—
66#14556565—21no—
67#14556565—21no—
68#14556564—41no—
69#14556564—41no—
70C4×D292—21no—
71C4×D292—21no—
72#14556534—22no—
73#14556534—22no—
74#14556532—22no—
75#14556532—22no—
76C2×#11924003C2311yescharacteristic
77C2×#11924003C2311yescharacteristic
78C2×#11924003C2311yescharacteristic
79C2×#11924003C2311yescharacteristic
80#14556525C2311yescharacteristic
81#14556525C2311yescharacteristic
82#14556523—21no—
83#14556513—21no—
84#14556513—21no—
85#14556513—21no—
86#14556513—21no—
87C2×#41×C73—21no—
88#135×C73—22no—
89#135×C73—22no—
90C2×Q16×C73C2311yescharacteristic
91C2×SD16×C73—21no—
92C2×D8×C73C2311yescharacteristic
93C2×M16×C73D411yescharacteristic
94C22×C8×C73C2311yescharacteristic
95C4×Q8×C73—21no—
96C4×Q8×C73—21no—
97C4×D4×C73—21no—
98C4×D4×C73—21no—
99C4×D4×C73—41no—
100C4×D4×C73—41no—
101#117×C73—41no—
102#117×C73D411yescharacteristic
103C2×C4⋊C4×C73—21no—
104C2×C4⋊C4×C73—41no—
105#107×C73—21no—
106#107×C73C2311yescharacteristic
107#107×C73C2311yescharacteristic
108#103×C73—21no—
109#103×C73—21no—
110#102×C73—21no—
111#102×C73—21no—
112#97×C73D411yescharacteristic
113#97×C73D411yescharacteristic
114C4×C8×C73C2311yescharacteristic
115C4×C8×C73C2311yescharacteristic
116C2×D292—21no—
117C2×D292—21no—
118C2×D292—41no—
119C2×D292—41no—
120C2×C22⋊D73—41no—
121C2×C22⋊D73—41no—
122C2×C4×D73—41no—
123C2×C4×D73—41no—
124D584—21no—
125D584—21no—
126D584—21no—
127D584—21no—
128D584—42no—
129C4⋊Dic73—21no—
130C4⋊Dic73—21no—
131#11924007—41no—
132#11924007—41no—
133#11924005—41no—
134#11924005—41no—
135#11924005—41no—
136#11924005—41no—
137#11924003—21no—
138#11924003—21no—
139#11924003—21no—
140#11924003—21no—
141#41×C73—24no—
142#41×C73—42no—
143C2×Q8×C73—21no—
144C2×D4×C73—21no—
145C2×D4×C73—41no—
146C22×C4×C73—41no—
147C22×C4×C73—41no—
148C22×C4×C73—41no—
149C22×C4×C73—41no—
150C22×C4×C73C2×D411yescharacteristic
151Q16×C73—21no—
152Q16×C73#4112yes—
153SD16×C73—24no—
154D8×C73—21no—
155D8×C73#4112yes—
156M16×C73—41no—
157C2×C8×C73—21no—
158C2×C8×C73—21no—
159C2×C8×C73C2×D411yescharacteristic
160C2×C8×C73C2×D411yescharacteristic
161C2×C8×C73C2×D411yescharacteristic
162C2×C8×C73C2411yescharacteristic
163C4⋊C4×C73—21no—
164C4⋊C4×C73—21no—
165C4⋊C4×C73—41no—
166C4⋊C4×C73—41no—
167C4⋊C4×C73—41no—
168C4⋊C4×C73D811yescharacteristic
169C4⋊C4×C73D811yescharacteristic
170C22⋊C4×C73—41no—
171C22⋊C4×C73—41no—
172C22⋊C4×C73D811yescharacteristic
173C22⋊C4×C73D811yescharacteristic
174C42×C73—41no—
175C42×C73—41no—
176C42×C73C2×D411yescharacteristic
177C42×C73C2×D411yescharacteristic
178C23×C73—41no—
179C23×C73C2×D811yescharacteristic
180C22×D73—41no—
181C22×D73—41no—
182Q8×C73—22no—
183Q8×C73—41no—
184D4×C73—22no—
185D4×C73—44no—
186D4×C73—41no—
187C2×C4×C73—21no—
188C2×C4×C73—21no—
189C2×C4×C73—44no—
190C2×C4×C73—41no—
191C2×C4×C73—41no—
192C2×C4×C73—41no—
193C2×C4×C73—161no—
194C2×C4×C73—161no—
195C2×C4×C73—161no—
196C2×C4×C73C2×D811yescharacteristic
197C2×C4×C73C2×D811yescharacteristic
198C2×C4×C73C2×D811yescharacteristic
199C2×C4×C73C2×D811yescharacteristic
200C2×C4×C73C2×D811yescharacteristic
201C2×C4×C73C22×D411yescharacteristic
202C22⋊D73—161no—
203C22⋊D73—161no—
204C2×Dic73—41no—
205C2×Dic73—41no—
206D292—41no—
207D292—41no—
208D292—41no—
209D292—41no—
210D292—161no—
211D292—161no—
212C4×D73—161no—
213C4×D73—161no—
214C8×C73—21no—
215C8×C73—21no—
216C8×C73—21no—
217C8×C73C2×#4111yescharacteristic
218C8×C73C2×#4111yescharacteristic
219C22×C73—21no—
220C22×C73—21no—
221C22×C73—21no—
222C22×C73—42no—
223C22×C73—81no—
224C22×C73—81no—
225C22×C73C22×D811yescharacteristic
226C2×D73—81no—
227C2×D73—81no—
228C2×D73—81no—
229C2×D73—81no—
230C2×D73—81no—
231C2×D73—81no—
232C4×C73—21no—
233C4×C73—21no—
234C4×C73—21no—
235C4×C73—21no—
236C4×C73—21no—
237C4×C73—42no—
238C4×C73—81no—
239C4×C73—81no—
240C4×C73#52511yescharacteristic
241C4×C73#57511yescharacteristic
242Dic73—81no—
243Dic73—81no—
244#33679—731nomaximal, Sylow
245C2×C73—41no—
246C2×C73—82no—
247C2×C73#310011yescharacteristic
248C2×C73#341511yescharacteristic
249C2×C73#341611yescharacteristic
250D73—161no—
251D73—161no—
252#3176—731no—
253#2951D7311yescharacteristic, complemented
254#2233—731no—
255#2232—731no—
256#2229—731no—
257#2228—731no—
258#2207—731no—
259#2206—731no—
260#2186—731no—
261#2186—731no—
262#2177—731no—
263#2175—731no—
264C4×SD32—731no—
265C4×D16—731no—
266#2164—731no—
267C73#3367911yescharacteristic, complemented, Sylow
268C2×#135C2×D7311yescharacteristic
269#540—1461no—
270#520—21no—
271C2×SD32—731no—
272C2×SD32—731no—
273C2×D16—731no—
274C2×D16—731no—
275#499—731no—
276#493—731no—
277#490—1461no—
278#469—1461no—
279#466—731no—
280#466—731no—
281#442—1461no—
282#440—21no—
283#440—21no—
284C4×Q16C2×D7311yescharacteristic
285C4×Q16C2×D7311yescharacteristic
286C4×D8—731no—
287C4×D8—731no—
288C4×D8C2×D7311yescharacteristic
289C4×D8C2×D7311yescharacteristic
290C2×#107C2×D7311yescharacteristic
291#417—21no—
292#405C2×D7311yescharacteristic
293#367—731no—
294#367—731no—
295#366—731no—
296#366—731no—
297C4⋊C16—731no—
298C4⋊C16—731no—
299#358—731no—
300#358—731no—
301#357—731no—
302#357—731no—
303#357—731no—
304#357—731no—
305#357—731no—
306#357—731no—
307C22⋊C16—731no—
308C22⋊C16—731no—
309#346—731no—
310C4×C16—731no—
311C2×#41—21no—
312#135—22no—
313#135—22no—
314C2×Q16C22×D7311yescharacteristic
315C2×SD16—21no—
316C2×D8—731no—
317C2×D8—731no—
318C2×D8—1461no—
319C2×D8C22×D7311yescharacteristic
320C2×M16C22⋊D7311yescharacteristic
321C22×C8C22×D7311yescharacteristic
322#127—1461no—
323#125—1461no—
324#123—2921no—
325#123—2921no—
326#121—2921no—
327#121—2921no—
328#121—1461no—
329#121—1461no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—41no—
335C4×D4—41no—
336C4×D4—1461no—
337C4×D4—1461no—
338#117—41no—
339#117C22⋊D7311yescharacteristic
340C2×C4⋊C4—21no—
341C2×C4⋊C4—41no—
342SD32—1462no—
343SD32—1462no—
344D16—1462no—
345D16—1462no—
346C2×C16—731no—
347C2×C16—731no—
348C2×C16—731no—
349C2×C16—731no—
350#107—21no—
351#107—731no—
352#107—731no—
353#107C22×D7311yescharacteristic
354#107C22×D7311yescharacteristic
355#106—1461no—
356#103—21no—
357#103—21no—
358#102—21no—
359#102—21no—
360#102—1461no—
361#102—1461no—
362#102—1461no—
363#102—1461no—
364#97C22⋊D7311yescharacteristic
365#97C22⋊D7311yescharacteristic
366C4×C8C22×D7311yescharacteristic
367C4×C8C22×D7311yescharacteristic
368#41—24no—
369#41—42no—
370C2×Q8—21no—
371C2×D4—21no—
372C2×D4—41no—
373C2×D4—2921no—
374C2×D4—2921no—
375C2×D4—2921no—
376C2×D4—2921no—
377C2×D4—1461no—
378C2×D4—1461no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—2921no—
384C22×C4—2921no—
385C22×C4C2×C22⋊D7311yescharacteristic
386Q16—21no—
387Q16#1192402812yes—
388SD16—24no—
389D8—21no—
390D8—2922no—
391D8—1461no—
392D8—1461no—
393D8—1461no—
394D8—1461no—
395D8#1192402812yes—
396M16—41no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8C2×C22⋊D7311yescharacteristic
400C2×C8C2×C22⋊D7311yescharacteristic
401C2×C8C2×C22⋊D7311yescharacteristic
402C2×C8C23×D7311yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—2921no—
409C4⋊C4—2921no—
410C4⋊C4—1461no—
411C4⋊C4—1461no—
412C4⋊C4#1192401311yescharacteristic
413C4⋊C4#1192401311yescharacteristic
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—2921no—
417C22⋊C4—2921no—
418C22⋊C4—2921no—
419C22⋊C4—2921no—
420C22⋊C4#1192401311yescharacteristic
421C22⋊C4#1192401311yescharacteristic
422C42—41no—
423C42—41no—
424C42C2×C22⋊D7311yescharacteristic
425C42C2×C22⋊D7311yescharacteristic
426C16—1461no—
427C16—1461no—
428C16—1461no—
429C16—1461no—
430C23—41no—
431C23—2921no—
432C23—2921no—
433C23C2×#1192401311yescharacteristic
434Q8—22no—
435Q8—41no—
436D4—22no—
437D4—44no—
438D4—41no—
439D4—2921no—
440D4—2921no—
441D4—2921no—
442D4—2921no—
443D4—11681no—
444D4—11681no—
445D4—11681no—
446D4—11681no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—44no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—161no—
454C2×C4—161no—
455C2×C4—161no—
456C2×C4—2921no—
457C2×C4—2921no—
458C2×C4—11681no—
459C2×C4—11681no—
460C2×C4C2×#1192401311yescharacteristic
461C2×C4C2×#1192401311yescharacteristic
462C2×C4C2×#1192401311yescharacteristic
463C2×C4C2×#1192401311yescharacteristic
464C2×C4C2×#1192401311yescharacteristic
465C2×C4C22×C22⋊D7311yescharacteristic
466C8—21no—
467C8—21no—
468C8—21no—
469C8C2×#1192402811yescharacteristic
470C8C2×#1192402811yescharacteristic
471C22—21no—
472C22—21no—
473C22—21no—
474C22—42no—
475C22—81no—
476C22—81no—
477C22—5841no—
478C22—5841no—
479C22—5841no—
480C22—5841no—
481C22—5841no—
482C22—5841no—
483C22C22×#1192401311yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—42no—
490C4—81no—
491C4—81no—
492C4—5841no—
493C4—5841no—
494C4#1798909811yescharacteristic
495C4#1798938511yescharacteristic
496C2—41no—
497C2—82no—
498C2—11681no—
499C2—11681no—
500C2#2261993111yescharacteristic
501C2#2262307011yescharacteristic
502C2#2262307511yescharacteristic
subgroupG/H
centerC22C22×#11924013
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC73×#2951C2
socleC22×C73C22×D8
hypercenter#2951D73
hypocenterC73#33679
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
1. #22620581C2semidirect
2. #22612116C2semidirect
3. #22612111C2semidirect
4. #22612095C2semidirect
5. #22612088C2semidirect
6. #22611971C2semidirect
7. #22611966C2semidirect
8. #22611854C2semidirect
9. #22611854C2semidirect
10. #22611805C2semidirect
11. #22611793C2semidirect
12. C4×#14556534C2semidirect
13. C4×#14556532C2semidirect
14. #22611738C2semidirect
15. C73×#2951C2semidirect
253. #2951D73semidirect
267. C73#33679semidirect

Maximal subgroups

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

subgroupindex
#226205812
#226121162
#226121112
#226120952
#226120882
#226119712
#226119662
#226118542
#226118052
#226117932
C4×#145565342
C4×#145565322
#226117382
C73×#29512
#3367973