Finite Group Databasebeta

← #33105439

Subgroups — #33105439

Order 18688.

752 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#22618597C211yesmaximal, characteristic, complemented
3#22618500C211yesmaximal, characteristic, complemented
4#22610632C212yesmaximal, complemented
5#22610528C212yesmaximal, complemented
6#22610255C212yesmaximal
7#22610068C211yesmaximal, characteristic, complemented
8#22609952C211yesmaximal, characteristic, complemented
9C4⋊C4×#10596831C211yesmaximal, characteristic, complemented
10#22609765C212yesmaximal, complemented
11C73×#1806C211yesmaximal, characteristic, complemented
12C2×#14556611C2211yescharacteristic
13C2×#14556599C2212yes—
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#17988648—22no—
24#17988644—21no—
25#17988640—21no—
26#17988623C2211yescharacteristic
27#17988615C2212yes—
28#17988612—22no—
29#17988611C2211yescharacteristic
30#17988609—21no—
31C2×C4⋊#10596831C2211yescharacteristic
32C4⋊C8×D73—21no—
33C2×#14556519C2212yes—
34#17988583C2211yescharacteristic
35#17988581C2211yescharacteristic
36#17988554C2212yes—
37#17988543C2212yes—
38C2×C4×#10596831C2212yes—
39C2×C4×#10596831C2211yescharacteristic
40#17988351C2212yes—
41#17988351C2212yes—
42#17988347C2212yes—
43#17988342C2212yes—
44C4×#41×C73C2211yescharacteristic
45#423×C73C2211yescharacteristic
46C2×#104×C73C2212yes—
47C4×C4⋊C4×C73C2211yescharacteristic
48#339×C73C2212yes—
49C2×#11924028C2311yescharacteristic
50#14556611—22no—
51#14556611—22no—
52C2×#11924018C2×C411yescharacteristic
53C2×#11924016C2×C411yescharacteristic
54C2×#11924015C2×C411yescharacteristic
55C2×#11924013C2×C411yescharacteristic
56#14556599—24no—
57#14556599—42no—
58C2×#11924012C2312yes—
59C2×#11924011—22no—
60C22×#10596831C2311yescharacteristic
61C22×#10596831C2311yescharacteristic
62C22×#10596831C2312yes—
63C2×C8×D73—22no—
64C4×Dic146C2×C411yescharacteristic
65C4×Dic146C2×C411yescharacteristic
66C4×D292C2×C411yescharacteristic
67C4×D292C2×C411yescharacteristic
68C4×C22⋊D73—21no—
69C4×C22⋊D73—21no—
70#14556550C2311yescharacteristic
71#14556548—21no—
72C42×D73—21no—
73#14556524C2×C411yescharacteristic
74#14556524C2×C411yescharacteristic
75#14556522C2×C411yescharacteristic
76#14556522C2×C411yescharacteristic
77C4⋊#10596831—21no—
78C4⋊#10596831—21no—
79C4⋊#10596831D411yescharacteristic
80C4⋊#10596831D412yes—
81C4⋊#10596831D411yescharacteristic
82#14556520—22no—
83#14556520—22no—
84#14556519—24no—
85#14556515C2×C411yescharacteristic
86#14556515C2×C411yescharacteristic
87#14556514C2×C411yescharacteristic
88#14556514C2×C411yescharacteristic
89#14556512C2×C411yescharacteristic
90#14556512C2×C411yescharacteristic
91#14556511C2×C411yescharacteristic
92#14556511C2×C411yescharacteristic
93C22⋊#10596831—22no—
94C22⋊#10596831—22no—
95#14556502—22no—
96C4×#10596831—22no—
97C4×#10596831—42no—
98C4×#10596831C2×C411yescharacteristic
99C4×#10596831C2×C411yescharacteristic
100C4×#10596831C2×C411yescharacteristic
101C4×#10596831C2×C411yescharacteristic
102C2×#41×C73C2311yescharacteristic
103C2×M16×C73C2312yes—
104C4×Q8×C73C2×C411yescharacteristic
105C4×Q8×C73C2×C411yescharacteristic
106C4×D4×C73—21no—
107C4×D4×C73—21no—
108C4×D4×C73C2×C411yescharacteristic
109C4×D4×C73C2×C411yescharacteristic
110#117×C73—21no—
111#117×C73C2311yescharacteristic
112C2×C4⋊C4×C73—21no—
113C2×C42×C73—21no—
114C2×C42×C73C2312yes—
115C2×C42×C73C2311yescharacteristic
116C4⋊C8×C73—21no—
117C4⋊C8×C73—21no—
118#104×C73—42no—
119#95×C73—21no—
120#11924028—21no—
121#11924028—21no—
122#11924028#4112yes—
123#11924028#4112yes—
124C2×Dic146C22×C411yescharacteristic
125C2×D292C22×C411yescharacteristic
126C2×C22⋊D73—21no—
127C2×C4×D73—21no—
128C2×C4×D73—21no—
129C2×C4×D73—21no—
130#11924018—22no—
131#11924016—22no—
132#11924015—22no—
133#11924013—22no—
134#11924012—22no—
135#11924012—22no—
136#11924011—44no—
137C2×#10596831—22no—
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—22no—
142C2×#10596831—21no—
143C2×#10596831—22no—
144C2×#10596831C22×C411yescharacteristic
145C2×#10596831C22×C411yescharacteristic
146C2×#10596831C22×C411yescharacteristic
147C2×#10596831C22×C411yescharacteristic
148C2×#10596831C2×D412yes—
149C2×#10596831C2×D412yes—
150C8×D73—44no—
151C4⋊Dic73C22×C411yescharacteristic
152C4⋊Dic73C22×C411yescharacteristic
153#11924007—21no—
154#11924007—21no—
155C22⋊Dic73—21no—
156#11924005—21no—
157#11924005—21no—
158C4×Dic73—21no—
159C4×Dic73—21no—
160C4×Dic73—21no—
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—22no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73#4111yescharacteristic
173C22×C4×C73#4111yescharacteristic
174C22×C4×C73C2411yescharacteristic
175M16×C73—22no—
176M16×C73—22no—
177C2×C8×C73—22no—
178C4⋊C4×C73—24no—
179C4⋊C4×C73—21no—
180C4⋊C4×C73—21no—
181C4⋊C4×C73C22×C411yescharacteristic
182C4⋊C4×C73C22×C411yescharacteristic
183C22⋊C4×C73—21no—
184C22⋊C4×C73—21no—
185C22⋊C4×C73—21no—
186C42×C73—21no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73—22no—
190C42×C73—22no—
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—24no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—41no—
210C2×C4×C73—42no—
211C2×C4×C73—42no—
212C2×C4×C73—41no—
213C2×C4×C73—41no—
214C2×C4×C73—42no—
215C2×C4×C73—81no—
216C2×C4×C73C4×D411yescharacteristic
217C2×C4×C73C4×D411yescharacteristic
218C2×C4×C73C4×D411yescharacteristic
219C2×C4×C73C4×D411yescharacteristic
220C2×C4×C73C23×C411yescharacteristic
221C2×C4×C73C22×D411yescharacteristic
222C2×C4×C73C2×#4111yescharacteristic
223C2×C4×C73C2×#4111yescharacteristic
224C2×C4×C73H(5,𝔽2)11yescharacteristic
225C2×C4×C732−1+411yescharacteristic
226C22⋊D73—22no—
227C22⋊D73—22no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231D292—21no—
232D292#11712yes—
233C4×D73—22no—
234C4×D73—22no—
235C4×D73—42no—
236C4×D73—81no—
237Dic146—21no—
238Dic146#11712yes—
239C8×C73—42no—
240#10596831—21no—
241#10596831—21no—
242#10596831—21no—
243#10596831—21no—
244#10596831—22no—
245#10596831—22no—
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—44no—
262C4×C73—41no—
263C4×C73—41no—
264C4×C73—41no—
265C4×C73#44312yes—
266C4×C73C2×#11711yescharacteristic
267C4×C73#52011yescharacteristic
268C4×C73#54611yescharacteristic
269C4×C73#54811yescharacteristic
270Dic73—22no—
271Dic73—41no—
272Dic73—41no—
273#22783—731nomaximal, Sylow
274C2×C73—21no—
275C2×C73—21no—
276C2×C73—81no—
277C2×C73#235211yescharacteristic
278C2×C73C2×#44311yescharacteristic
279C2×C73#295711yescharacteristic
280D73—42no—
281C4×#135—731no—
282#2925—731no—
283#2906—731no—
284#1937—732no—
285#1922—732no—
286#1876—732no—
287#1837—731no—
288#1806—731no—
289#1806D7311yescharacteristic, complemented
290C8×C4⋊C4—731no—
291#1764—732no—
292C73#2278311yescharacteristic, 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—1462no—
306#432—1461no—
307#431—1461no—
308#427—731no—
309#424—732no—
310#424—1462no—
311#423—731no—
312#423—1461no—
313#423C2×D7311yescharacteristic
314C2×C4⋊C8—731no—
315C2×C4⋊C8—1461no—
316C2×#104—732no—
317C2×#104C2×D7312yes—
318#416—731no—
319#416—731no—
320#408—732no—
321#405—732no—
322C2×C4×C8—732no—
323C2×C4×C8—731no—
324C4×C4⋊C4C2×D7311yescharacteristic
325#341—732no—
326#341—732no—
327#339—732no—
328#339C2×D7312yes—
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—732no—
344C22×C8—731no—
345C22×C8—731no—
346C22×C8—1462no—
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—21no—
364C2×C42—21no—
365C2×C42—1461no—
366C2×C42C22×D7312yes—
367C2×C42C22×D7311yescharacteristic
368#107—731no—
369#107—731no—
370#106—731no—
371#106—731no—
372C4⋊C8—21no—
373C4⋊C8—21no—
374C4⋊C8—731no—
375C4⋊C8—731no—
376C4⋊C8—732no—
377C4⋊C8—1462no—
378C4⋊C8—1462no—
379C4⋊C8—1461no—
380C4⋊C8—1461no—
381#104—42no—
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—1462no—
392C22⋊C8—1462no—
393#97—1462no—
394C4×C8—2922no—
395C4×C8—731no—
396C4×C8—731no—
397C4×C8—731no—
398C4×C8—731no—
399C4×C8—1462no—
400#95—21no—
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—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—1461no—
420C22×C4—1461no—
421C22×C4—1461no—
422C22×C4#1192402711yescharacteristic
423C22×C4#1192402711yescharacteristic
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—2924no—
436C2×C8—731no—
437C2×C8—731no—
438C2×C8—731no—
439C2×C8—731no—
440C2×C8—732no—
441C2×C8—732no—
442C2×C8—1462no—
443C2×C8—1462no—
444C2×C8—1461no—
445C2×C8—1461no—
446C2×C8—1461no—
447C2×C8—1462no—
448C2×C8—1461no—
449C4⋊C4—24no—
450C4⋊C4—21no—
451C4⋊C4—21no—
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—22no—
468C42—22no—
469C42—1461no—
470C42—1461no—
471C42—1461no—
472C42C2×C4×D7311yescharacteristic
473C42C2×C4×D7311yescharacteristic
474C42D4×D7311yescharacteristic
475C42D4×D7311yescharacteristic
476C23—21no—
477C23—1461no—
478C23C2×#1192402711yescharacteristic
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—24no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—81no—
503C2×C4—2922no—
504C2×C4—5841no—
505C2×C4—1461no—
506C2×C4—1461no—
507C2×C4—1461no—
508C2×C4—1462no—
509C2×C4—1462no—
510C2×C4#1455655111yescharacteristic
511C2×C4#1455655111yescharacteristic
512C2×C4#1455655111yescharacteristic
513C2×C4#1455655111yescharacteristic
514C2×C4C22×C4×D7311yescharacteristic
515C2×C4C2×D4×D7311yescharacteristic
516C2×C4#41×D7311yescharacteristic
517C2×C4#41×D7311yescharacteristic
518C2×C4#1455663611yescharacteristic
519C2×C4#1455663911yescharacteristic
520C8—42no—
521C8—2922no—
522C8—1462no—
523C8—1462no—
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×#1455655111yescharacteristic
537C22#1798927111yescharacteristic
538C22#1798928411yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—44no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—2921no—
547C4—2921no—
548C4—1462no—
549C4#1798870112yes—
550C4#117×D7311yescharacteristic
551C4#1798906811yescharacteristic
552C4#1798923411yescharacteristic
553C4#1798924711yescharacteristic
554C2—21no—
555C2—21no—
556C2—81no—
557C2—2922no—
558C2#2261285311yescharacteristic
559C2C2×#1798870111yescharacteristic
560C2#2261884411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1806C2
socleC22×C73C2×C4×D4
prime radicalC2×#14556611C22
cosocleC22×C4×C73C24
hypercenter#1806D73
hypocenterC73#22783
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #22618597C2semidirect
3. #22618500C2semidirect
4. #22610632C2semidirect
5. #22610528C2semidirect
7. #22610068C2semidirect
8. #22609952C2semidirect
9. C4⋊C4×#10596831C2semidirect
10. #22609765C2semidirect
11. C73×#1806C2semidirect
15. C4×#11924018C4semidirect
16. C4×#11924018C4semidirect
17. C4×#11924015C4semidirect
18. C4×#11924015C4semidirect
19. C4×#11924016C4semidirect
20. C4×#11924016C4semidirect
21. C4×#11924013C4semidirect
22. C4×#11924013C4semidirect
289. #1806D73semidirect
292. C73#22783semidirect

Maximal subgroups

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

subgroupindex
C4×#145566112
#226185972
#226185002
#226106322
#226105282
#226102552
#226100682
#226099522
C4⋊C4×#105968312
#226097652
C73×#18062
#2278373