Finite Group Databasebeta

← #33105436

Subgroups — #33105436

Order 18688.

740 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556611C211yesmaximal, characteristic
2#22618496C211yesmaximal, characteristic, complemented
3#22610645C212yesmaximal, complemented
4#22610530C212yesmaximal, complemented
5#22610261C212yesmaximal
6#22610068C211yesmaximal, characteristic, complemented
7#22609951C211yesmaximal, characteristic, complemented
8#22609948C211yesmaximal, characteristic, complemented
9#22609801C211yesmaximal, characteristic, complemented
10#22609777C212yesmaximal, complemented
11C73×#2925C211yesmaximal, characteristic, complemented
12C2×#14556611C2211yescharacteristic
13C2×#14556597C2212yes—
14C4×#11924028C2211yescharacteristic
15C4×#11924018C411yescharacteristic, complemented
16C4×#11924018C411yescharacteristic, complemented
17C4×#11924015C411yescharacteristic, complemented
18C4×#11924015C411yescharacteristic, complemented
19C4×#11924016C411yescharacteristic, complemented
20C4×#11924016C411yescharacteristic, complemented
21C4×#11924013C411yescharacteristic, complemented
22C4×#11924013C411yescharacteristic, complemented
23#17988623C2211yescharacteristic
24#17988613C2212yes—
25#17988612—22no—
26#17988611C2211yescharacteristic
27#17988609—21no—
28C4⋊C8×D73—21no—
29C2×#14556518C2212yes—
30C2×#14556517C2212yes—
31#17988583C2211yescharacteristic
32#17988581C2211yescharacteristic
33C2×#14556501C2212yes—
34C2×C4×#10596831C2211yescharacteristic
35C4×C4⋊Dic73C2211yescharacteristic
36#17988351C2212yes—
37#17988351C2212yes—
38#17988348C2212yes—
39#17988346C2212yes—
40#17988341C2212yes—
41C4×#41×C73C2211yescharacteristic
42#433×C73—22no—
43#432×C73—21no—
44#431×C73—21no—
45#423×C73C2211yescharacteristic
46C2×C4⋊C8×C73C2211yescharacteristic
47#408×C73C2212yes—
48#405×C73C2212yes—
49C2×#11924028C2311yescharacteristic
50#14556611—22no—
51#14556611—22no—
52C2×#11924018C2×C411yescharacteristic
53C2×#11924016C2×C411yescharacteristic
54C2×#11924015C2×C411yescharacteristic
55C2×#11924013C2×C411yescharacteristic
56#14556597—24no—
57#14556597—42no—
58C2×#11924012C2312yes—
59C2×#11924011—22no—
60C22×#10596831C2311yescharacteristic
61C22×#10596831C2311yescharacteristic
62C2×C8×D73—22no—
63C4×Dic146C2×C411yescharacteristic
64C4×Dic146C2×C411yescharacteristic
65C4×D292C2×C411yescharacteristic
66C4×D292C2×C411yescharacteristic
67C4×C22⋊D73—21no—
68C4×C22⋊D73—21no—
69#14556550C2311yescharacteristic
70#14556548—21no—
71C2×C4⋊Dic73—21no—
72C2×C4×Dic73C2312yes—
73C42×D73—21no—
74#14556524C2×C411yescharacteristic
75#14556524C2×C411yescharacteristic
76#14556522C2×C411yescharacteristic
77#14556522C2×C411yescharacteristic
78C4⋊#10596831—21no—
79C4⋊#10596831—21no—
80#14556520—22no—
81#14556520—22no—
82#14556518—42no—
83#14556517—24no—
84#14556515C2×C411yescharacteristic
85#14556515C2×C411yescharacteristic
86#14556514C2×C411yescharacteristic
87#14556514C2×C411yescharacteristic
88#14556512C2×C411yescharacteristic
89#14556512C2×C411yescharacteristic
90#14556511C2×C411yescharacteristic
91#14556511C2×C411yescharacteristic
92#14556501—42no—
93C4×#10596831C2×C411yescharacteristic
94C4×#10596831C2×C411yescharacteristic
95C4×#10596831C2×C411yescharacteristic
96C4×#10596831C2×C411yescharacteristic
97#14556498—21no—
98C2×#41×C73C2311yescharacteristic
99C2×M16×C73C2312yes—
100C22×C8×C73C2312yes—
101C4×Q8×C73C2×C411yescharacteristic
102C4×Q8×C73C2×C411yescharacteristic
103C4×D4×C73—21no—
104C4×D4×C73—21no—
105C4×D4×C73C2×C411yescharacteristic
106C4×D4×C73C2×C411yescharacteristic
107#117×C73—21no—
108#117×C73C2311yescharacteristic
109C2×C42×C73—21no—
110C2×C42×C73C2311yescharacteristic
111C4⋊C8×C73—21no—
112C4⋊C8×C73—21no—
113C4⋊C8×C73D411yescharacteristic
114C4⋊C8×C73D412yes—
115C4⋊C8×C73D411yescharacteristic
116C22⋊C8×C73—22no—
117C22⋊C8×C73—22no—
118#97×C73—22no—
119C4×C8×C73—22no—
120#11924028—21no—
121#11924028—21no—
122#11924028#4112yes—
123#11924028#4112yes—
124C2×Dic146C22×C411yescharacteristic
125C2×D292C22×C411yescharacteristic
126C2×C22⋊D73—21no—
127C22×Dic73—22no—
128C2×C4×D73—21no—
129C2×C4×D73—21no—
130C2×C4×D73—21no—
131#11924018—22no—
132#11924016—22no—
133#11924015—22no—
134#11924013—22no—
135#11924012—22no—
136#11924012—22no—
137#11924011—44no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831—22no—
143C2×#10596831C22×C411yescharacteristic
144C2×#10596831C22×C411yescharacteristic
145C2×#10596831C22×C411yescharacteristic
146C2×#10596831C22×C411yescharacteristic
147C8×D73—44no—
148C4⋊Dic73—42no—
149C4⋊Dic73C22×C411yescharacteristic
150C4⋊Dic73C22×C411yescharacteristic
151#11924007—21no—
152#11924007—21no—
153C22⋊Dic73—21no—
154#11924005—21no—
155#11924005—21no—
156C4×Dic73—21no—
157C4×Dic73—21no—
158C4×Dic73—21no—
159C4×Dic73—22no—
160C4×Dic73—22no—
161#41×C73—21no—
162#41×C73—21no—
163#41×C73—21no—
164#41×C73—21no—
165C2×Q8×C73C22×C411yescharacteristic
166C2×D4×C73—21no—
167C2×D4×C73C22×C411yescharacteristic
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73#4111yescharacteristic
172C22×C4×C73#4111yescharacteristic
173C22×C4×C73C2411yescharacteristic
174M16×C73—22no—
175M16×C73—22no—
176C2×C8×C73—22no—
177C2×C8×C73—22no—
178C2×C8×C73—22no—
179C2×C8×C73C2×D412yes—
180C2×C8×C73C2×D412yes—
181C4⋊C4×C73—21no—
182C4⋊C4×C73—21no—
183C4⋊C4×C73C22×C411yescharacteristic
184C4⋊C4×C73C22×C411yescharacteristic
185C22⋊C4×C73—21no—
186C22⋊C4×C73—21no—
187C22⋊C4×C73—21no—
188C42×C73—21no—
189C42×C73—21no—
190C42×C73—21no—
191C42×C73C22×C411yescharacteristic
192C42×C73C22×C411yescharacteristic
193C42×C73C2×D411yescharacteristic
194C42×C73C2×D411yescharacteristic
195C23×C73—21no—
196C23×C73C2×#4111yescharacteristic
197C22×D73—21no—
198Q8×C73—21no—
199Q8×C73—21no—
200D4×C73—21no—
201D4×C73—21no—
202D4×C73—41no—
203D4×C73—41no—
204C2×C4×C73—22no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—41no—
209C2×C4×C73—41no—
210C2×C4×C73—41no—
211C2×C4×C73—42no—
212C2×C4×C73—81no—
213C2×C4×C73C4×D411yescharacteristic
214C2×C4×C73C4×D411yescharacteristic
215C2×C4×C73C4×D411yescharacteristic
216C2×C4×C73C4×D411yescharacteristic
217C2×C4×C73C23×C411yescharacteristic
218C2×C4×C73C22×D411yescharacteristic
219C2×C4×C73C2×#4111yescharacteristic
220C2×C4×C73C2×#4111yescharacteristic
221C2×C4×C73H(5,𝔽2)11yescharacteristic
222C2×C4×C732−1+411yescharacteristic
223C22⋊D73—22no—
224C22⋊D73—22no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—42no—
229C2×Dic73—42no—
230C2×Dic73—42no—
231D292—21no—
232D292#11712yes—
233C4×D73—22no—
234C4×D73—22no—
235C4×D73—42no—
236C4×D73—81no—
237Dic146—21no—
238Dic146#11712yes—
239C8×C73—22no—
240C8×C73—22no—
241C8×C73—42no—
242#10596831—21no—
243#10596831—21no—
244#10596831—21no—
245#10596831—21no—
246#10596831—42no—
247C22×C73—21no—
248C22×C73—21no—
249C22×C73—41no—
250C22×C73—41no—
251C22×C73—41no—
252C22×C73C2×C4×D411yescharacteristic
253C22×C73#55211yescharacteristic
254C22×C73#55311yescharacteristic
255C2×D73—22no—
256C2×D73—41no—
257C2×D73—41no—
258C4×C73—21no—
259C4×C73—21no—
260C4×C73—21no—
261C4×C73—41no—
262C4×C73—41no—
263C4×C73—41no—
264C4×C73#44412yes—
265C4×C73C2×#11711yescharacteristic
266C4×C73#52011yescharacteristic
267C4×C73#54611yescharacteristic
268C4×C73#54811yescharacteristic
269Dic73—22no—
270Dic73—41no—
271Dic73—41no—
272Dic73—82no—
273#22782—731nomaximal, Sylow
274C2×C73—21no—
275C2×C73—21no—
276C2×C73—81no—
277C2×C73#235211yescharacteristic
278C2×C73C2×#44411yescharacteristic
279C2×C73#295711yescharacteristic
280D73—42no—
281C4×#135—731no—
282#2925D7311yescharacteristic, complemented
283#2906—731no—
284#1938—732no—
285#1922—732no—
286#1876—732no—
287#1837—731no—
288#1806—731no—
289#1806—731no—
290#1770—731no—
291#1765—732no—
292C73#2278211yescharacteristic, complemented, Sylow
293C2×#135—731no—
294C2×#131—732no—
295C4×#41—731no—
296C4×#41C2×D7311yescharacteristic
297C4×Q16—731no—
298C4×Q16—731no—
299C4×SD16—731no—
300C4×SD16—731no—
301C4×SD16—731no—
302C4×SD16—731no—
303C4×D8—731no—
304C4×D8—731no—
305#433—22no—
306#432—21no—
307#431—21no—
308#427—731no—
309#424—732no—
310#424—1462no—
311#423—731no—
312#423—1461no—
313#423C2×D7311yescharacteristic
314C2×C4⋊C8—1461no—
315C2×C4⋊C8C2×D7311yescharacteristic
316C2×#104—732no—
317C2×#104—732no—
318#416—731no—
319#416—731no—
320#408C2×D7312yes—
321#405C2×D7312yes—
322C2×#97—732no—
323C2×C4×C8—731no—
324C4×C4⋊C4—731no—
325#341—732no—
326#341—732no—
327#339—732no—
328#339—732no—
329#336—732no—
330C2×#41—731no—
331C2×#41C22×D7311yescharacteristic
332#135—1462no—
333#135—1462no—
334C2×Q16—731no—
335C2×SD16—731no—
336C2×SD16—731no—
337C2×D8—731no—
338#131—2922no—
339#131—1464no—
340C2×M16—732no—
341C2×M16—1462no—
342C2×M16C22×D7312yes—
343C22×C8—731no—
344C22×C8—731no—
345C22×C8—1462no—
346C22×C8C22×D7312yes—
347C4×Q8—731no—
348C4×Q8—731no—
349C4×Q8C4×D7311yescharacteristic
350C4×Q8C4×D7311yescharacteristic
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—731no—
354C4×D4—731no—
355C4×D4—1461no—
356C4×D4—1461no—
357C4×D4C4×D7311yescharacteristic
358C4×D4C4×D7311yescharacteristic
359#117—21no—
360#117—731no—
361#117—1461no—
362#117C22×D7311yescharacteristic
363C2×C4⋊C4—1461no—
364C2×C42—21no—
365C2×C42—732no—
366C2×C42—1461no—
367C2×C42C22×D7311yescharacteristic
368#107—731no—
369#107—731no—
370#106—731no—
371#106—731no—
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8—1462no—
375C4⋊C8—1462no—
376C4⋊C8—1461no—
377C4⋊C8—1461no—
378C4⋊C8C22⋊D7311yescharacteristic
379C4⋊C8C22⋊D7311yescharacteristic
380C4⋊C8C22⋊D7312yes—
381#104—2922no—
382#104—1464no—
383#103—731no—
384#103—731no—
385#103—731no—
386#103—731no—
387#102—731no—
388#102—731no—
389#102—731no—
390#102—731no—
391C22⋊C8—22no—
392C22⋊C8—22no—
393#97—22no—
394#97—2922no—
395C4×C8—22no—
396C4×C8—731no—
397C4×C8—731no—
398C4×C8—731no—
399C4×C8—731no—
400#95—1461no—
401#41—21no—
402#41—21no—
403#41—21no—
404#41—21no—
405#41—732no—
406#41—732no—
407#41—1461no—
408#41—1461no—
409C2×Q8—731no—
410C2×Q8C2×C4×D7311yescharacteristic
411C2×D4—21no—
412C2×D4—731no—
413C2×D4—1461no—
414C2×D4C2×C4×D7311yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—1462no—
419C22×C4—1461no—
420C22×C4—1461no—
421C22×C4—1461no—
422C22×C4#1192402811yescharacteristic
423C22×C4#1192402811yescharacteristic
424C22×C4C23×D7311yescharacteristic
425Q16—1462no—
426SD16—1462no—
427SD16—1462no—
428D8—1462no—
429M16—22no—
430M16—22no—
431M16—2924no—
432M16—1462no—
433M16—1462no—
434C2×C8—22no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—2924no—
438C2×C8—731no—
439C2×C8—731no—
440C2×C8—731no—
441C2×C8—731no—
442C2×C8—1462no—
443C2×C8—1461no—
444C2×C8—1461no—
445C2×C8—1461no—
446C2×C8—1461no—
447C2×C8C2×C22⋊D7312yes—
448C2×C8C2×C22⋊D7312yes—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—2922no—
452C4⋊C4—731no—
453C4⋊C4—731no—
454C4⋊C4—1461no—
455C4⋊C4—1461no—
456C4⋊C4C2×C4×D7311yescharacteristic
457C4⋊C4C2×C4×D7311yescharacteristic
458C22⋊C4—21no—
459C22⋊C4—21no—
460C22⋊C4—21no—
461C22⋊C4—1461no—
462C22⋊C4—1461no—
463C22⋊C4—1461no—
464C42—21no—
465C42—21no—
466C42—21no—
467C42—1462no—
468C42—1462no—
469C42—1461no—
470C42—1461no—
471C42—1461no—
472C42C2×C4×D7311yescharacteristic
473C42C2×C4×D7311yescharacteristic
474C42C2×C22⋊D7311yescharacteristic
475C42C2×C22⋊D7311yescharacteristic
476C23—21no—
477C23—1461no—
478C23C2×#1192402811yescharacteristic
479Q8—21no—
480Q8—21no—
481Q8—732no—
482Q8—1461no—
483D4—21no—
484D4—21no—
485D4—41no—
486D4—41no—
487D4—732no—
488D4—1462no—
489D4—1462no—
490D4—1461no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—81no—
500C2×C4—2922no—
501C2×C4—2922no—
502C2×C4—2922no—
503C2×C4—2922no—
504C2×C4—5841no—
505C2×C4—1461no—
506C2×C4—1461no—
507C2×C4—1461no—
508C2×C4—1462no—
509C2×C4—1462no—
510C2×C4C4×C22⋊D7311yescharacteristic
511C2×C4C4×C22⋊D7311yescharacteristic
512C2×C4C4×C22⋊D7311yescharacteristic
513C2×C4C4×C22⋊D7311yescharacteristic
514C2×C4C22×C4×D7311yescharacteristic
515C2×C4C22×C22⋊D7311yescharacteristic
516C2×C4#41×D7311yescharacteristic
517C2×C4#41×D7311yescharacteristic
518C2×C4#1455663711yescharacteristic
519C2×C4#1455663811yescharacteristic
520C8—22no—
521C8—22no—
522C8—42no—
523C8—2922no—
524C8—1461no—
525C8—1461no—
526C8—1461no—
527C8—1461no—
528C22—21no—
529C22—21no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—2921no—
534C22—2921no—
535C22—1462no—
536C22C2×C4×C22⋊D7311yescharacteristic
537C22#1798927611yescharacteristic
538C22#1798928111yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—2921no—
546C4—2921no—
547C4—5842no—
548C4—1462no—
549C4#1798870712yes—
550C4#117×D7311yescharacteristic
551C4#1798906711yescharacteristic
552C4#1798922511yescharacteristic
553C4#1798924411yescharacteristic
554C2—21no—
555C2—21no—
556C2—81no—
557C2—2922no—
558C2#2261286111yescharacteristic
559C2C2×#1798870711yescharacteristic
560C2#2261884611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2925C2
socleC22×C73C2×C4×D4
prime radicalC2×#14556611C22
cosocleC22×C4×C73C24
hypercenter#2925D73
hypocenterC73#22782
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #22618496C2semidirect
3. #22610645C2semidirect
4. #22610530C2semidirect
6. #22610068C2semidirect
7. #22609951C2semidirect
8. #22609948C2semidirect
9. #22609801C2semidirect
10. #22609777C2semidirect
11. C73×#2925C2semidirect
15. C4×#11924018C4semidirect
16. C4×#11924018C4semidirect
17. C4×#11924015C4semidirect
18. C4×#11924015C4semidirect
19. C4×#11924016C4semidirect
20. C4×#11924016C4semidirect
21. C4×#11924013C4semidirect
22. C4×#11924013C4semidirect
282. #2925D73semidirect
292. C73#22782semidirect

Maximal subgroups

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

subgroupindex
C4×#145566112
#226184962
#226106452
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