Finite Group Databasebeta

← #2237×D73 #33240758

Subgroups — #2237×D73 #33240758

Order 18688.

586 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#467×D73C211yesmaximal, characteristic
2#427×D73C211yesmaximal, characteristic
3#22612142C211yesmaximal, characteristic, complemented
4#22612141C211yesmaximal, characteristic, complemented
5#22612140C211yesmaximal, characteristic, complemented
6#22612139C211yesmaximal, characteristic, complemented
7#22612138C211yesmaximal, characteristic, complemented
8#22612137C211yesmaximal, characteristic, complemented
9#22612136C211yesmaximal, characteristic, complemented
10#367×D73C211yesmaximal, characteristic, complemented
11#366×D73C211yesmaximal, characteristic, complemented
12#358×D73C211yesmaximal, characteristic, complemented
13#358×D73C211yesmaximal, characteristic, complemented
14C22⋊C16×D73C211yesmaximal, characteristic
15C73×#2237C211yesmaximal, characteristic, complemented
16C2×Q16×D73C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C22⋊Q8×D73—21no—
19#117×D73—21no—
20C2×C16×D73C2211yescharacteristic
21C2×C16×D73C2211yescharacteristic
22#17988829C2211yescharacteristic
23#17988828C2211yescharacteristic
24#17988827—21no—
25#17988826—21no—
26#17988825C2211yescharacteristic
27#17988625C2211yescharacteristic
28#17988624C2211yescharacteristic
29#17988624C2211yescharacteristic
30#17988623—21no—
31#17988622—21no—
32#107×D73C2211yescharacteristic
33#107×D73C2211yescharacteristic
34#107×D73C2211yescharacteristic
35#106×D73—21no—
36#103×D73—21no—
37#17988415C2211yescharacteristic, complemented
38#17988414C2211yescharacteristic, complemented
39#17988414C2211yescharacteristic, complemented
40#17988413C2211yescharacteristic, complemented
41#17988412C2211yescharacteristic, complemented
42#17988412C2211yescharacteristic, complemented
43#17988392C2211yescharacteristic, complemented
44#17988392C2211yescharacteristic, complemented
45#17988391C2211yescharacteristic, complemented
46#17988391C2211yescharacteristic, complemented
47#17988390C2211yescharacteristic, complemented
48#17988390C2211yescharacteristic, complemented
49C22⋊#11924003C2211yescharacteristic
50#17988366C2211yescharacteristic
51#17988366C2211yescharacteristic
52#467×C73C2211yescharacteristic
53#427×C73C2211yescharacteristic
54#367×C73C2211yescharacteristic, complemented
55#366×C73C2211yescharacteristic, complemented
56#358×C73C2211yescharacteristic, complemented
57#358×C73C2211yescharacteristic, complemented
58C22⋊C16×C73C2211yescharacteristic
59C2×Q8×D73—21no—
60C22×C4×D73D411yescharacteristic
61C2×Dic292C2311yescharacteristic
62C2×#11924018—21no—
63Q16×D73—22no—
64Q16×D73—22no—
65C22×#10596831D411yescharacteristic
66C2×C8×D73—22no—
67C2×C8×D73—22no—
68C2×C8×D73D411yescharacteristic
69C2×C8×D73D411yescharacteristic
70C2×C8×D73C2311yescharacteristic
71C2×C8×D73C2311yescharacteristic
72#14556571—21no—
73#14556570—21no—
74#14556569—41no—
75#14556568—41no—
76#14556567—21no—
77#14556550—21no—
78#14556549—21no—
79#14556549—21no—
80#14556548—41no—
81#14556547—41no—
82C4⋊C4×D73—21no—
83C4⋊C4×D73—21no—
84C4⋊C4×D73—21no—
85C4⋊C4×D73—41no—
86C22⋊C4×D73—41no—
87C22⋊C4×D73—41no—
88C42×D73—41no—
89C2×#11924003C2311yescharacteristic
90C2×#11924003C2311yescharacteristic
91C16×D73—22no—
92C16×D73—22no—
93#14556525C2311yescharacteristic
94#14556525C2311yescharacteristic
95#14556525C2311yescharacteristic
96#14556524—21no—
97#14556524—21no—
98#14556524—21no—
99#14556523—21no—
100#14556522—21no—
101#14556522—21no—
102#14556516—21no—
103#14556515—21no—
104#14556514—21no—
105C2×Q16×C73C2311yescharacteristic
106C22×C8×C73C2311yescharacteristic
107C22⋊Q8×C73—21no—
108#117×C73—21no—
109C2×C16×C73C2311yescharacteristic
110C2×C16×C73C2311yescharacteristic
111#107×C73C2311yescharacteristic
112#107×C73C2311yescharacteristic
113#107×C73C2311yescharacteristic
114#106×C73—21no—
115#103×C73—21no—
116C23×D73D811yescharacteristic
117C2×Dic146—21no—
118C2×Dic146—41no—
119Q8×D73—42no—
120Q8×D73—42no—
121C22×Dic73D811yescharacteristic
122C2×C4×D73—22no—
123C2×C4×D73—22no—
124C2×C4×D73—41no—
125C2×C4×D73—41no—
126C2×C4×D73—41no—
127C2×C4×D73—41no—
128C2×C4×D73D811yescharacteristic
129C2×C4×D73D811yescharacteristic
130C2×C4×D73C2×D411yescharacteristic
131C2×C4×D73C2×D411yescharacteristic
132Dic292—21no—
133Dic292—21no—
134#11924018—42no—
135C2×#10596831—22no—
136C2×#10596831C2×D411yescharacteristic
137C2×#10596831C2×D411yescharacteristic
138C8×D73—22no—
139C8×D73—21no—
140C8×D73—21no—
141C8×D73—22no—
142C8×D73#4112yes—
143C8×D73#4112yes—
144C4⋊Dic73—21no—
145C4⋊Dic73—21no—
146C4⋊Dic73—21no—
147C4⋊Dic73—41no—
148#11924007—41no—
149#11924007—41no—
150#11924007—41no—
151#11924007—41no—
152#11924007—41no—
153C22⋊Dic73—41no—
154C22⋊Dic73—41no—
155#11924005—41no—
156#11924005—41no—
157#11924005—41no—
158#11924005—41no—
159C4×Dic73—41no—
160C4×Dic73—41no—
161C4×Dic73—41no—
162#11924003—21no—
163#11924003—21no—
164C2×Q8×C73—21no—
165C22×C4×C73C2×D411yescharacteristic
166Q16×C73—21no—
167Q16×C73—21no—
168C2×C8×C73—21no—
169C2×C8×C73—21no—
170C2×C8×C73C2×D411yescharacteristic
171C2×C8×C73C2411yescharacteristic
172C4⋊C4×C73—21no—
173C4⋊C4×C73—21no—
174C4⋊C4×C73—21no—
175C4⋊C4×C73—41no—
176C22⋊C4×C73—41no—
177C22⋊C4×C73—41no—
178C42×C73—41no—
179C16×C73—21no—
180C16×C73—21no—
181C23×C73C2×D811yescharacteristic
182C22×D73—22no—
183C22×D73—22no—
184C22×D73—22no—
185C22×D73C2×D811yescharacteristic
186C22×D73C2×D811yescharacteristic
187Q8×C73—41no—
188Q8×C73—41no—
189C2×C4×C73—21no—
190C2×C4×C73—21no—
191C2×C4×C73—41no—
192C2×C4×C73—41no—
193C2×C4×C73—41no—
194C2×C4×C73—41no—
195C2×C4×C73C2×D811yescharacteristic
196C2×C4×C73C22×D411yescharacteristic
197C2×Dic73—22no—
198C2×Dic73—41no—
199C2×Dic73—41no—
200C2×Dic73—41no—
201C2×Dic73—41no—
202C2×Dic73C2×D811yescharacteristic
203C2×Dic73C2×D811yescharacteristic
204C4×D73—22no—
205C4×D73—21no—
206C4×D73—21no—
207C4×D73—22no—
208C4×D73—82no—
209C4×D73—82no—
210C4×D73—82no—
211C4×D73—82no—
212C4×D73#12312yes—
213C4×D73#13712yes—
214Dic146—41no—
215Dic146—41no—
216Dic146—82no—
217C8×C73—21no—
218C8×C73C2×#4111yescharacteristic
219C8×C73C2×#4111yescharacteristic
220#10596831—21no—
221#10596831#12312yes—
222C22×C73—21no—
223C22×C73—21no—
224C22×C73—21no—
225C22×C73C22×D811yescharacteristic
226C2×D73—21no—
227C2×D73—21no—
228C2×D73—21no—
229C2×D73—44no—
230C2×D73#48012yes—
231C2×D73#50812yes—
232C2×D73#51012yes—
233C4×C73—21no—
234C4×C73—81no—
235C4×C73—81no—
236C4×C73—81no—
237C4×C73—81no—
238C4×C73C2×#12311yescharacteristic
239C4×C73C2×#13711yescharacteristic
240Dic73—21no—
241Dic73—81no—
242Dic73—81no—
243Dic73—81no—
244Dic73—81no—
245Dic73#48012yes—
246C2×#2237—731nomaximal, Sylow
247C2×C73—41no—
248C2×C73C2×#48011yescharacteristic
249C2×C73C2×#50811yescharacteristic
250C2×C73C2×#51011yescharacteristic
251D73—41no—
252D73#223714yesdirect product factor
253C2×#467—731no—
254C2×#427—731no—
255#2237—731no—
256#2237—731no—
257#2237—731no—
258#2237—731no—
259#2237—731no—
260#2237—731no—
261#2237—731no—
262#2237D7311yescharacteristic, direct product factor
263C2×#367—731no—
264C2×#366—731no—
265C2×#358—731no—
266C2×#358—731no—
267C2×C22⋊C16—731no—
268C73C2×#223711yescharacteristic, complemented, Sylow
269C22×Q16—731no—
270C23×C8—731no—
271C2×C22⋊Q8—1461no—
272C2×#117—1461no—
273C22×C16—731no—
274C22×C16—731no—
275#467—731no—
276#467—731no—
277#467—731no—
278#467—1461no—
279#467—1461no—
280#467C2×D7311yescharacteristic
281#427—731no—
282#427—731no—
283#427—731no—
284#427—1461no—
285#427—1461no—
286#427C2×D7311yescharacteristic
287C2×#107—731no—
288C2×#107—731no—
289C2×#107—731no—
290C2×#106—1461no—
291C2×#103—1461no—
292#367—731no—
293#367—731no—
294#367—731no—
295#367C2×D7311yescharacteristic, complemented
296#366—731no—
297#366—731no—
298#366—731no—
299#366C2×D7311yescharacteristic, complemented
300#358—731no—
301#358—731no—
302#358—731no—
303#358—731no—
304#358—731no—
305#358—731no—
306#358C2×D7311yescharacteristic, complemented
307#358C2×D7311yescharacteristic, complemented
308C22⋊C16—731no—
309C22⋊C16—731no—
310C22⋊C16—731no—
311C22⋊C16C2×D7311yescharacteristic
312C22×Q8—1461no—
313C23×C4—731no—
314C2×Q16—731no—
315C2×Q16—1462no—
316C2×Q16—1462no—
317C2×Q16—1461no—
318C2×Q16C22×D7311yescharacteristic
319C22×C8—731no—
320C22×C8—731no—
321C22×C8—731no—
322C22×C8—731no—
323C22×C8—731no—
324C22×C8—1462no—
325C22×C8—1462no—
326C22×C8C22×D7311yescharacteristic
327C22⋊Q8—21no—
328C22⋊Q8—2921no—
329C22⋊Q8—2921no—
330C22⋊Q8—1461no—
331C22⋊Q8—1461no—
332C22⋊Q8—1461no—
333#117—21no—
334#117—2921no—
335#117—2921no—
336#117—1461no—
337#117—1461no—
338#117—1461no—
339C2×C4⋊C4—2921no—
340C2×C4⋊C4—1461no—
341C2×C4⋊C4—1461no—
342C2×C4⋊C4—1461no—
343C2×C22⋊C4—2921no—
344C2×C22⋊C4—2921no—
345C2×C42—2921no—
346C2×C16—731no—
347C2×C16—731no—
348C2×C16—1462no—
349C2×C16—1462no—
350C2×C16C22×D7311yescharacteristic
351C2×C16C22×D7311yescharacteristic
352#107—731no—
353#107—731no—
354#107—731no—
355#107—1461no—
356#107—1461no—
357#107—1461no—
358#107C22×D7311yescharacteristic
359#107C22×D7311yescharacteristic
360#107C22×D7311yescharacteristic
361#106—21no—
362#106—1461no—
363#106—1461no—
364#106—1461no—
365#103—21no—
366#103—1461no—
367#103—1461no—
368#103—1461no—
369C24—731no—
370C2×Q8—21no—
371C2×Q8—2921no—
372C2×Q8—2922no—
373C2×Q8—2922no—
374C2×Q8—1461no—
375C22×C4—2921no—
376C22×C4—2921no—
377C22×C4—2921no—
378C22×C4—2921no—
379C22×C4—731no—
380C22×C4—731no—
381C22×C4—731no—
382C22×C4—731no—
383C22×C4—731no—
384C22×C4—1462no—
385C22×C4—1462no—
386C22×C4D4×D7311yescharacteristic
387Q16—21no—
388Q16—21no—
389Q16—2922no—
390Q16—1461no—
391Q16—1461no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—731no—
395C2×C8—732no—
396C2×C8—732no—
397C2×C8—731no—
398C2×C8—1462no—
399C2×C8—1462no—
400C2×C8—1462no—
401C2×C8—1461no—
402C2×C8—1461no—
403C2×C8D4×D7311yescharacteristic
404C2×C8C23×D7311yescharacteristic
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—41no—
409C4⋊C4—2921no—
410C4⋊C4—2921no—
411C4⋊C4—2921no—
412C4⋊C4—2921no—
413C4⋊C4—2921no—
414C4⋊C4—2921no—
415C4⋊C4—1461no—
416C4⋊C4—1461no—
417C4⋊C4—1461no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—2921no—
421C22⋊C4—2921no—
422C22⋊C4—2921no—
423C22⋊C4—2921no—
424C22⋊C4—2921no—
425C22⋊C4—2921no—
426C42—41no—
427C42—2921no—
428C42—2921no—
429C42—2921no—
430C16—21no—
431C16—21no—
432C16—1461no—
433C16—1461no—
434C23—731no—
435C23—731no—
436C23—1462no—
437C23—1462no—
438C23—1462no—
439C23D8×D7311yescharacteristic
440Q8—41no—
441Q8—41no—
442Q8—2921no—
443Q8—2921no—
444Q8—5842no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—2921no—
452C2×C4—2921no—
453C2×C4—2921no—
454C2×C4—2921no—
455C2×C4—5842no—
456C2×C4—5842no—
457C2×C4—5842no—
458C2×C4—5842no—
459C2×C4—731no—
460C2×C4—732no—
461C2×C4—732no—
462C2×C4—731no—
463C2×C4—1462no—
464C2×C4—1462no—
465C2×C4—1462no—
466C2×C4—1461no—
467C2×C4—1461no—
468C2×C4D8×D7311yescharacteristic
469C2×C4C2×D4×D7311yescharacteristic
470C8—21no—
471C8—732no—
472C8—1461no—
473C8#41×D7311yescharacteristic
474C8#41×D7311yescharacteristic
475C22—21no—
476C22—21no—
477C22—21no—
478C22—2924no—
479C22—732no—
480C22—732no—
481C22—732no—
482C22—1461no—
483C22—1461no—
484C22—1461no—
485C22C2×D8×D7311yescharacteristic
486C4—21no—
487C4—81no—
488C4—81no—
489C4—81no—
490C4—81no—
491C4—5841no—
492C4—5841no—
493C4—5841no—
494C4—5841no—
495C4—732no—
496C4—1461no—
497C4#123×D7311yescharacteristic
498C4#137×D7311yescharacteristic
499C2—41no—
500C2—2921no—
501C2—734no—
502C2#480×D7311yescharacteristic
503C2#508×D7311yescharacteristic
504C2#510×D7311yescharacteristic
subgroupG/H
centerC22C2×D8×D73
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC73×#2237C2
socleC22×C73C22×D8
prime radicalC23×D73D8
hypercenter#2237D73
hypocenterC73C2×#2237
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2237

Complements

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

NH ≅ G/Ntype
3. #22612142C2semidirect
4. #22612141C2semidirect
5. #22612140C2semidirect
6. #22612139C2semidirect
7. #22612138C2semidirect
8. #22612137C2semidirect
9. #22612136C2semidirect
10. #367×D73C2semidirect
11. #366×D73C2semidirect
12. #358×D73C2semidirect
13. #358×D73C2semidirect
15. C73×#2237C2semidirect
37. #17988415C22semidirect
38. #17988414C22semidirect
39. #17988414C22semidirect
40. #17988413C22semidirect
41. #17988412C22semidirect
42. #17988412C22semidirect
43. #17988392C22semidirect
44. #17988392C22semidirect
45. #17988391C22semidirect
46. #17988391C22semidirect
47. #17988390C22semidirect
48. #17988390C22semidirect
54. #367×C73C22semidirect
55. #366×C73C22semidirect
56. #358×C73C22semidirect
57. #358×C73C22semidirect
252. D73#2237direct (N × H)
262. #2237D73direct (N × H)
268. C73C2×#2237semidirect
295. #367C2×D73semidirect
299. #366C2×D73semidirect
306. #358C2×D73semidirect
307. #358C2×D73semidirect

Maximal subgroups

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

subgroupindex
#467×D732
#427×D732
#226121422
#226121412
#226121402
#226121392
#226121382
#226121372
#226121362
#367×D732
#366×D732
#358×D732
C22⋊C16×D732
C73×#22372
C2×#223773