Finite Group Databasebeta

← #33241531

Subgroups — #33241531

Order 18688.

526 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620501C211yesmaximal, characteristic, complemented
2#22612207C211yesmaximal, characteristic, complemented
3#22612190C211yesmaximal, characteristic, complemented
4#22612165C211yesmaximal, characteristic, complemented
5#22612162C211yesmaximal, characteristic, complemented
6#22612029C211yesmaximal, characteristic, complemented
7#22612025C211yesmaximal, characteristic, complemented
8#22612020C211yesmaximal, characteristic, complemented
9#22612015C211yesmaximal, characteristic
10C4×#14556537C211yesmaximal, characteristic, complemented
11C4×#14556534C211yesmaximal, characteristic, complemented
12C4×#14556535C211yesmaximal, characteristic, complemented
13C4×#14556532C211yesmaximal, characteristic, complemented
14C2×C4×#11924003C211yesmaximal, characteristic, complemented
15C73×#3168C211yesmaximal, characteristic, complemented
16#17989121—21no—
17C2×#14556537C2211yescharacteristic
18C2×#14556535C2211yescharacteristic
19C2×#14556534C2211yescharacteristic
20C2×#14556532C2211yescharacteristic
21C22×#11924003C2211yescharacteristic
22C22×#11924003C2211yescharacteristic
23#17988989C2211yescharacteristic
24#17988971C2211yescharacteristic
25#17988942—21no—
26#17988828C2211yescharacteristic
27#17988823C2211yescharacteristic
28#17988816—21no—
29C4×Dic292C2211yescharacteristic
30C4×#11924017—21no—
31C4×D584C2211yescharacteristic
32#17988414C2211yescharacteristic
33#17988414C2211yescharacteristic
34#17988412C2211yescharacteristic
35#17988412C2211yescharacteristic
36#17988391C2211yescharacteristic
37#17988391C2211yescharacteristic
38#17988390C2211yescharacteristic
39#17988390C2211yescharacteristic
40#17988388C2211yescharacteristic
41#17988388C2211yescharacteristic
42#17988387C2211yescharacteristic
43#17988387C2211yescharacteristic
44C4×#11924003C2211yescharacteristic
45C4×#11924003C2211yescharacteristic
46C4×#11924003C2211yescharacteristic
47C4×#11924003C2211yescharacteristic
48#529×C73—21no—
49#499×C73C2211yescharacteristic
50#495×C73C2211yescharacteristic
51#488×C73—21no—
52#467×C73C2211yescharacteristic
53#466×C73C2211yescharacteristic
54#465×C73—21no—
55C4×Q16×C73C2211yescharacteristic
56C4×SD16×C73—21no—
57C4×D8×C73C2211yescharacteristic
58C2×C4×C8×C73C2211yescharacteristic
59C2×Dic292C2311yescharacteristic
60C2×#11924017—21no—
61C2×D584C2311yescharacteristic
62#14556585—41no—
63#14556583—21no—
64#14556579—21no—
65#14556574—41no—
66#14556570—21no—
67#14556565—21no—
68C4×Dic146—21no—
69C4×D292—21no—
70C4×C22⋊D73—41no—
71#14556548—41no—
72#14556537—22no—
73#14556535—22no—
74#14556534—22no—
75#14556532—22no—
76C2×#11924003—22no—
77C2×#11924003—22no—
78C2×#11924003C2311yescharacteristic
79C2×#11924003C2311yescharacteristic
80C2×#11924003C2311yescharacteristic
81C2×#11924003C2311yescharacteristic
82#14556525C2311yescharacteristic
83#14556525C2311yescharacteristic
84#14556523—21no—
85#14556516—21no—
86#14556516—21no—
87#14556513—21no—
88#14556513—21no—
89C2×Q16×C73C2311yescharacteristic
90C2×SD16×C73—21no—
91C2×D8×C73C2311yescharacteristic
92C22×C8×C73D411yescharacteristic
93C22×C8×C73C2311yescharacteristic
94#126×C73—41no—
95#125×C73—21no—
96#124×C73—21no—
97#123×C73—41no—
98C22⋊Q8×C73—21no—
99#121×C73—21no—
100C4×Q8×C73—21no—
101C4×D4×C73—21no—
102C4×D4×C73—41no—
103#117×C73—41no—
104C2×C42×C73D411yescharacteristic
105#107×C73C2311yescharacteristic
106#107×C73C2311yescharacteristic
107#106×C73—21no—
108#103×C73—21no—
109#103×C73—21no—
110#102×C73—21no—
111#102×C73—21no—
112C4×C8×C73D411yescharacteristic
113C4×C8×C73D411yescharacteristic
114C4×C8×C73C2311yescharacteristic
115C4×C8×C73C2311yescharacteristic
116C2×Dic146—21no—
117C2×D292—21no—
118C2×C22⋊D73—41no—
119C2×C4×D73—41no—
120Dic292—21no—
121Dic292—21no—
122#11924017—42no—
123D584—21no—
124D584—21no—
125C4⋊Dic73—21no—
126C4⋊Dic73—21no—
127#11924007—41no—
128#11924007—41no—
129#11924007—41no—
130#11924007—41no—
131C22⋊Dic73—41no—
132#11924005—41no—
133#11924005—41no—
134#11924005—41no—
135#11924005—41no—
136C4×Dic73—41no—
137#11924003—21no—
138#11924003—21no—
139#11924003#4112yes—
140#11924003#4112yes—
141C2×Q8×C73—21no—
142C2×D4×C73—21no—
143C2×D4×C73—41no—
144C22×C4×C73—41no—
145C22×C4×C73D811yescharacteristic
146C22×C4×C73D811yescharacteristic
147C22×C4×C73C2×D411yescharacteristic
148Q16×C73—21no—
149Q16×C73—21no—
150SD16×C73—42no—
151D8×C73—21no—
152D8×C73—21no—
153C2×C8×C73—22no—
154C2×C8×C73—21no—
155C2×C8×C73—21no—
156C2×C8×C73C2×D411yescharacteristic
157C2×C8×C73C2×D411yescharacteristic
158C2×C8×C73C2×D411yescharacteristic
159C2×C8×C73C2411yescharacteristic
160C4⋊C4×C73—21no—
161C4⋊C4×C73—21no—
162C4⋊C4×C73—41no—
163C4⋊C4×C73—41no—
164C4⋊C4×C73—41no—
165C4⋊C4×C73—41no—
166C22⋊C4×C73—41no—
167C22⋊C4×C73—41no—
168C22⋊C4×C73—41no—
169C22⋊C4×C73—41no—
170C22⋊C4×C73—41no—
171C42×C73—41no—
172C42×C73D811yescharacteristic
173C42×C73D811yescharacteristic
174C42×C73C2×D411yescharacteristic
175C42×C73C2×D411yescharacteristic
176C23×C73—41no—
177C23×C73C2×D811yescharacteristic
178C22×D73—41no—
179Q8×C73—41no—
180Q8×C73—41no—
181D4×C73—41no—
182D4×C73—41no—
183D4×C73—82no—
184C2×C4×C73—22no—
185C2×C4×C73—21no—
186C2×C4×C73—21no—
187C2×C4×C73—22no—
188C2×C4×C73—41no—
189C2×C4×C73—41no—
190C2×C4×C73—41no—
191C2×C4×C73—82no—
192C2×C4×C73C2×D811yescharacteristic
193C2×C4×C73C2×D811yescharacteristic
194C2×C4×C73C2×D811yescharacteristic
195C2×C4×C73C2×D811yescharacteristic
196C2×C4×C73C2×D811yescharacteristic
197C2×C4×C73C22×D411yescharacteristic
198C22⋊D73—82no—
199C2×Dic73—41no—
200C2×Dic73—41no—
201C2×Dic73—41no—
202D292—41no—
203D292—41no—
204C4×D73—82no—
205Dic146—41no—
206Dic146—41no—
207C8×C73—21no—
208C8×C73—21no—
209C8×C73#13512yes—
210C8×C73C2×#4111yescharacteristic
211C8×C73C2×#4111yescharacteristic
212C22×C73—21no—
213C22×C73—21no—
214C22×C73—81no—
215C22×C73—81no—
216C22×C73—81no—
217C22×C73#50812yes—
218C22×C73C22×D811yescharacteristic
219C2×D73—81no—
220C2×D73—81no—
221C2×D73—81no—
222C4×C73—21no—
223C4×C73—21no—
224C4×C73—21no—
225C4×C73—21no—
226C4×C73—81no—
227C4×C73—81no—
228C4×C73—81no—
229C4×C73#50812yes—
230C4×C73#53211yescharacteristic
231C4×C73C2×#13511yescharacteristic
232Dic73—81no—
233Dic73—81no—
234Dic73—81no—
235#33735—731nomaximal, Sylow
236C2×C73—22no—
237C2×C73—161no—
238C2×C73#316911yescharacteristic
239C2×C73C2×#50811yescharacteristic
240C2×C73C2×#50811yescharacteristic
241D73—161no—
242#3168—731no—
243#3168D7311yescharacteristic, complemented
244#2253—731no—
245#2249—731no—
246#2242—731no—
247#2242—731no—
248#2217—731no—
249#2217—731no—
250#2216—731no—
251#2215—731no—
252C4×Q32—731no—
253C4×SD32—731no—
254C4×SD32—731no—
255C4×D16—731no—
256C2×C4×C16—731no—
257C73#3373511yescharacteristic, complemented, Sylow
258#529—21no—
259#529—1461no—
260C2×Q32—731no—
261C2×SD32—731no—
262C2×SD32—731no—
263C2×D16—731no—
264C22×C16—731no—
265C22×C16—731no—
266#499—731no—
267#499C2×D7311yescharacteristic
268#495—731no—
269#495C2×D7311yescharacteristic
270#488—21no—
271#488—1461no—
272#467—731no—
273#467C2×D7311yescharacteristic
274#466—731no—
275#466C2×D7311yescharacteristic
276#465—21no—
277#465—1461no—
278C4×Q16—731no—
279C4×Q16C2×D7311yescharacteristic
280C4×SD16—21no—
281C4×SD16—1461no—
282C4×D8—731no—
283C4×D8C2×D7311yescharacteristic
284C2×C4×C8C2×D7311yescharacteristic
285#367—731no—
286#367—731no—
287#366—731no—
288#366—731no—
289#358—731no—
290#358—731no—
291#358—731no—
292#358—731no—
293#357—731no—
294#357—731no—
295#357—731no—
296#357—731no—
297C4×C16—731no—
298C4×C16—731no—
299C4×C16—731no—
300C4×C16—731no—
301C2×Q16—731no—
302C2×Q16C22×D7311yescharacteristic
303C2×SD16—21no—
304C2×SD16—1461no—
305C2×D8—731no—
306C2×D8C22×D7311yescharacteristic
307C22×C8C22⋊D7311yescharacteristic
308C22×C8C22×D7311yescharacteristic
309#126—41no—
310#126—2921no—
311#125—21no—
312#125—1461no—
313#124—21no—
314#124—1461no—
315#123—41no—
316#123—2921no—
317C22⋊Q8—21no—
318C22⋊Q8—1461no—
319#121—21no—
320#121—1461no—
321C4×Q8—21no—
322C4×Q8—1461no—
323C4×D4—21no—
324C4×D4—41no—
325C4×D4—2921no—
326C4×D4—1461no—
327#117—41no—
328#117—2921no—
329C2×C42C22⋊D7311yescharacteristic
330Q32—1462no—
331SD32—1462no—
332SD32—1462no—
333D16—1462no—
334C2×C16—731no—
335C2×C16—731no—
336C2×C16—731no—
337C2×C16—731no—
338C2×C16—1462no—
339C2×C16—1462no—
340#107—731no—
341#107—731no—
342#107C22×D7311yescharacteristic
343#107C22×D7311yescharacteristic
344#106—21no—
345#106—1461no—
346#103—21no—
347#103—21no—
348#103—1461no—
349#103—1461no—
350#102—21no—
351#102—21no—
352#102—1461no—
353#102—1461no—
354C4×C8C22⋊D7311yescharacteristic
355C4×C8C22⋊D7311yescharacteristic
356C4×C8C22×D7311yescharacteristic
357C4×C8C22×D7311yescharacteristic
358C2×Q8—21no—
359C2×Q8—1461no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—2921no—
363C2×D4—1461no—
364C22×C4—41no—
365C22×C4—2921no—
366C22×C4#1192401311yescharacteristic
367C22×C4#1192401311yescharacteristic
368C22×C4C2×C22⋊D7311yescharacteristic
369Q16—21no—
370Q16—21no—
371Q16—1461no—
372Q16—1461no—
373SD16—42no—
374SD16—2922no—
375D8—21no—
376D8—21no—
377D8—1461no—
378D8—1461no—
379C2×C8—22no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8C2×C22⋊D7311yescharacteristic
383C2×C8C2×C22⋊D7311yescharacteristic
384C2×C8C2×C22⋊D7311yescharacteristic
385C2×C8C23×D7311yescharacteristic
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—2921no—
393C4⋊C4—2921no—
394C4⋊C4—2921no—
395C4⋊C4—2921no—
396C4⋊C4—1461no—
397C4⋊C4—1461no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—2921no—
404C22⋊C4—2921no—
405C22⋊C4—2921no—
406C22⋊C4—2921no—
407C22⋊C4—2921no—
408C42—41no—
409C42—2921no—
410C42#1192401311yescharacteristic
411C42#1192401311yescharacteristic
412C42C2×C22⋊D7311yescharacteristic
413C42C2×C22⋊D7311yescharacteristic
414C16—732no—
415C16—732no—
416C16—1461no—
417C16—1461no—
418C23—41no—
419C23—2921no—
420C23C2×#1192401311yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—2921no—
424Q8—2921no—
425D4—41no—
426D4—41no—
427D4—82no—
428D4—2921no—
429D4—2921no—
430D4—5842no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—82no—
439C2×C4—2921no—
440C2×C4—2921no—
441C2×C4—2921no—
442C2×C4—5842no—
443C2×C4C2×#1192401311yescharacteristic
444C2×C4C2×#1192401311yescharacteristic
445C2×C4C2×#1192401311yescharacteristic
446C2×C4C2×#1192401311yescharacteristic
447C2×C4C2×#1192401311yescharacteristic
448C2×C4C22×C22⋊D7311yescharacteristic
449C8—21no—
450C8—21no—
451C8#1455661112yes—
452C8#41×D7311yescharacteristic
453C8#41×D7311yescharacteristic
454C22—21no—
455C22—21no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—5841no—
460C22—5841no—
461C22—5841no—
462C22#1798901712yes—
463C22C22×#1192401311yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—81no—
469C4—81no—
470C4—81no—
471C4—5841no—
472C4—5841no—
473C4—5841no—
474C4#1798901712yes—
475C4#1798913311yescharacteristic
476C4C2×#1455661111yescharacteristic
477C2—22no—
478C2—161no—
479C2—11681no—
480C2#2262050611yescharacteristic
481C2C2×#1798901711yescharacteristic
482C2C2×#1798901711yescharacteristic
subgroupG/H
centerC2×C4C2×#11924013
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC73×#3168C2
socleC22×C73C22×D8
prime radical#22612015C2
hypercenter#3168D73
hypocenterC73#33735
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #22620501C2semidirect
2. #22612207C2semidirect
3. #22612190C2semidirect
4. #22612165C2semidirect
5. #22612162C2semidirect
6. #22612029C2semidirect
7. #22612025C2semidirect
8. #22612020C2semidirect
10. C4×#14556537C2semidirect
11. C4×#14556534C2semidirect
12. C4×#14556535C2semidirect
13. C4×#14556532C2semidirect
14. C2×C4×#11924003C2semidirect
15. C73×#3168C2semidirect
243. #3168D73semidirect
257. C73#33735semidirect

Maximal subgroups

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

subgroupindex
#226205012
#226122072
#226121902
#226121652
#226121622
#226120292
#226120252
#226120202
#226120152
C4×#145565372
C4×#145565342
C4×#145565352
C4×#145565322
C2×C4×#119240032
C73×#31682
#3373573