Finite Group Databasebeta

← #32980080

Subgroups — #32980080

Order 18688.

702 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22612634C211yesmaximal, characteristic
2#22610248C211yesmaximal, characteristic
3#22610124C211yesmaximal, characteristic, complemented
4C2×#17988320C211yesmaximal, characteristic
5#22607810C211yesmaximal, characteristic, complemented
6#22607774C211yesmaximal, characteristic, complemented
7C73×#1444C211yesmaximal, characteristic, complemented
8C2×#14556565C2211yescharacteristic
9C2×C4×C22⋊D73—21no—
10C2×#14556522—21no—
11C2×#14556511—21no—
12C2×C22⋊#10596831C2211yescharacteristic
13C2×C22⋊#10596831C2211yescharacteristic
14#17988479—21no—
15#17988472—21no—
16#17988466—21no—
17#17988465—21no—
18#17988461—21no—
19#17988447C2211yescharacteristic
20#17988349—21no—
21#17988349—21no—
22#17988320C414yescomplemented
23C22×C4⋊C4×C73—21no—
24C22×C4⋊C4×C73C2211yescharacteristic
25C2×#95×C73—21no—
26C2×#95×C73C2211yescharacteristic
27C2×#95×C73C2211yescharacteristic
28C22×D292D411yescharacteristic
29C22×C22⋊D73—21no—
30C22×C4×D73—21no—
31C22×#10596831—21no—
32C22×#10596831—21no—
33#14556565—21no—
34#14556565—21no—
35#14556565C2×C412yes—
36#14556565Q812yes—
37C4×C22⋊D73—42no—
38C4×C22⋊D73—42no—
39C2×C4⋊Dic73D411yescharacteristic
40C2×C4⋊Dic73D411yescharacteristic
41C2×C4⋊Dic73D411yescharacteristic
42C2×#11924007—21no—
43C2×C22⋊Dic73—21no—
44C2×#11924005—21no—
45C2×#11924005—21no—
46C2×#11924005—21no—
47C2×#11924005—21no—
48C2×C4×Dic73—21no—
49#14556522—42no—
50#14556511—42no—
51C22⋊#10596831—21no—
52C22⋊#10596831—21no—
53C22⋊#10596831—21no—
54C22⋊#10596831C2×C412yescomplemented
55#14556498—21no—
56#14556498—21no—
57#14556498—21no—
58C23×C4×C73—21no—
59C23×C4×C73—21no—
60C23×C4×C73D411yescharacteristic
61C23×C4×C73D411yescharacteristic
62C23×C4×C73C2311yescharacteristic
63C2×C4⋊C4×C73—21no—
64C2×C4⋊C4×C73—21no—
65C2×C4⋊C4×C73—42no—
66C2×C4⋊C4×C73—42no—
67C2×C4⋊C4×C73—42no—
68C2×C4⋊C4×C73—42no—
69#95×C73—21no—
70#95×C73—21no—
71#95×C73—21no—
72#95×C73—42no—
73#95×C73C2×C412yescomplemented
74C23×D73—21no—
75C2×D292—21no—
76C2×D292—41no—
77C2×D292—41no—
78C2×D292C4⋊C412yescomplemented
79C2×C22⋊D73—22no—
80C2×C22⋊D73—22no—
81C2×C22⋊D73—41no—
82C2×C22⋊D73—41no—
83C2×C22⋊D73—41no—
84C2×C22⋊D73—41no—
85C22×Dic73—21no—
86C22×Dic73—21no—
87C22×Dic73—21no—
88C2×C4×D73—42no—
89C2×C4×D73—81no—
90C2×C4×D73—81no—
91C2×#10596831—22no—
92C2×#10596831—41no—
93C2×#10596831—41no—
94C2×#10596831—41no—
95C2×#10596831—41no—
96C2×#10596831—41no—
97C4⋊Dic73—21no—
98C4⋊Dic73—41no—
99C4⋊Dic73—41no—
100C4⋊Dic73C4⋊C412yescomplemented
101#11924007—42no—
102C22⋊Dic73—41no—
103C22⋊Dic73—41no—
104#11924005—22no—
105#11924005—22no—
106#11924005—42no—
107#11924005—81no—
108#11924005—81no—
109C4×Dic73—42no—
110C24×C73C2×D411yescharacteristic
111C22×C4×C73—22no—
112C22×C4×C73—22no—
113C22×C4×C73—22no—
114C22×C4×C73—21no—
115C22×C4×C73—21no—
116C22×C4×C73—22no—
117C22×C4×C73—21no—
118C22×C4×C73—21no—
119C22×C4×C73—21no—
120C22×C4×C73—41no—
121C22×C4×C73—41no—
122C22×C4×C73—41no—
123C22×C4×C73—41no—
124C22×C4×C73—41no—
125C22×C4×C73—41no—
126C22×C4×C73—41no—
127C22×C4×C73—41no—
128C22×C4×C73—41no—
129C22×C4×C73—41no—
130C22×C4×C73—41no—
131C22×C4×C73—41no—
132C22×C4×C73—41no—
133C22×C4×C73—41no—
134C22×C4×C73—41no—
135C22×C4×C73—41no—
136C22×C4×C73SD1612yes—
137C22×C4×C73C22×C411yescharacteristic
138C22×C4×C73C2×D411yescharacteristic
139C22×C4×C73C2×D411yescharacteristic
140C22×C4×C73C2×Q811yescharacteristic
141C22×C4×C73#4111yescharacteristic
142C22×C4×C73#4111yescharacteristic
143C4⋊C4×C73—22no—
144C4⋊C4×C73—22no—
145C4⋊C4×C73—41no—
146C4⋊C4×C73—41no—
147C4⋊C4×C73—48no—
148C23×C73—21no—
149C23×C73—21no—
150C23×C73—21no—
151C23×C73—21no—
152C23×C73C4×D411yescharacteristic
153C23×C73#12011yescharacteristic
154C23×C73C22⋊Q811yescharacteristic
155C23×C73C2×SD1611yescharacteristic
156C23×C73#13511yescharacteristic
157C23×C73AGL(1,ℤ/8)11yescharacteristic
158C23×C73AGL(1,ℤ/8)11yescharacteristic
159C22×D73—22no—
160C22×D73—41no—
161C22×D73—41no—
162C22×D73—41no—
163C22×D73—41no—
164C22×D73—41no—
165C22×D73—41no—
166C2×C4×C73—21no—
167C2×C4×C73—21no—
168C2×C4×C73—21no—
169C2×C4×C73—21no—
170C2×C4×C73—24no—
171C2×C4×C73—22no—
172C2×C4×C73—41no—
173C2×C4×C73—41no—
174C2×C4×C73—41no—
175C2×C4×C73—41no—
176C2×C4×C73—42no—
177C2×C4×C73—42no—
178C2×C4×C73—42no—
179C2×C4×C73—42no—
180C2×C4×C73—42no—
181C2×C4×C73—42no—
182C2×C4×C73—41no—
183C2×C4×C73—41no—
184C2×C4×C73—42no—
185C2×C4×C73—42no—
186C2×C4×C73—42no—
187C2×C4×C73—42no—
188C2×C4×C73—41no—
189C2×C4×C73—41no—
190C2×C4×C73—42no—
191C2×C4×C73—41no—
192C2×C4×C73—81no—
193C2×C4×C73—81no—
194C2×C4×C73—81no—
195C2×C4×C73—81no—
196C2×C4×C73—81no—
197C2×C4×C73—81no—
198C2×C4×C73C2×C4⋊C411yescharacteristic
199C2×C4×C73C4×D411yescharacteristic
200C2×C4×C73C22⋊Q811yescharacteristic
201C2×C4×C73#12311yescharacteristic
202C22⋊D73—42no—
203C22⋊D73—42no—
204C22⋊D73—42no—
205C22⋊D73—42no—
206C2×Dic73—22no—
207C2×Dic73—41no—
208C2×Dic73—41no—
209C2×Dic73—41no—
210C2×Dic73—41no—
211C2×Dic73—41no—
212C2×Dic73—41no—
213C2×Dic73—41no—
214C2×Dic73—41no—
215D292—42no—
216D292—81no—
217C4×D73—84no—
218#10596831—42no—
219#10596831—81no—
220C22×C73—21no—
221C22×C73—21no—
222C22×C73—21no—
223C22×C73—21no—
224C22×C73—21no—
225C22×C73—21no—
226C22×C73—21no—
227C22×C73—21no—
228C22×C73—21no—
229C22×C73—21no—
230C22×C73—21no—
231C22×C73—21no—
232C22×C73#38511yescharacteristic
233C22×C73C4×SD1611yescharacteristic
234C22×C73#44211yescharacteristic
235C22×C73#44911yescharacteristic
236C22×C73#45011yescharacteristic
237C22×C73#45311yescharacteristic
238C22×C73#45611yescharacteristic
239C22×C73B(4,𝔽2)11yescharacteristic
240C22×C73#45811yescharacteristic
241C22×C73#47611yescharacteristic
242C22×C73#47811yescharacteristic
243C2×D73—42no—
244C2×D73—42no—
245C2×D73—42no—
246C2×D73—81no—
247C2×D73—81no—
248C2×D73—81no—
249C2×D73—81no—
250C4×C73—21no—
251C4×C73—21no—
252C4×C73—21no—
253C4×C73—21no—
254C4×C73—44no—
255C4×C73—42no—
256C4×C73—81no—
257C4×C73—82no—
258Dic73—42no—
259Dic73—81no—
260Dic73—81no—
261#8873—731nomaximal, Sylow
262C2×C73—21no—
263C2×C73—21no—
264C2×C73—21no—
265C2×C73—21no—
266C2×C73#160011yescharacteristic
267C2×C73#160411yescharacteristic
268C2×C73#160911yescharacteristic
269C2×C73#161311yescharacteristic
270C2×C73#185911yescharacteristic
271C2×C73#186411yescharacteristic
272C2×C73#186711yescharacteristic
273D73—82no—
274#2325—731no—
275#1874—731no—
276#1853—731no—
277C2×#327—731no—
278#1444D7311yescharacteristic, complemented
279#1294—731no—
280#1280—731no—
281C73#887311yescharacteristic, complemented, Sylow
282C2×#121—731no—
283C2×C4×D4—1461no—
284C22×C4⋊C4—21no—
285C22×C4⋊C4C2×D7311yescharacteristic
286C2×#106—1461no—
287C2×#102—1461no—
288C2×C22⋊C8—731no—
289C2×C22⋊C8—731no—
290#388—1461no—
291#387—1461no—
292#386—1461no—
293#386—1461no—
294#385—1461no—
295#380—731no—
296C2×#95—21no—
297C2×#95C2×D7311yescharacteristic
298C2×#95C2×D7311yescharacteristic
299#340—1461no—
300#340—1461no—
301#327—734no—
302C22×D4—731no—
303C22×D4—1461no—
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—1461no—
307C23×C4C22⋊D7311yescharacteristic
308C23×C4C22⋊D7311yescharacteristic
309C23×C4C22×D7311yescharacteristic
310C22×C8—1461no—
311C22×C8—1461no—
312#121—732no—
313#121—732no—
314#121—1461no—
315#121—1461no—
316C4×D4—2922no—
317C4×D4—2922no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—731no—
325C2×C4⋊C4—731no—
326C2×C4⋊C4—731no—
327C2×C4⋊C4—1461no—
328C2×C22⋊C4—1461no—
329C2×C22⋊C4—1461no—
330C2×C22⋊C4—1461no—
331C2×C22⋊C4—1461no—
332C2×C22⋊C4—1461no—
333C2×C42—1461no—
334#106—2922no—
335#102—2922no—
336C22⋊C8—732no—
337C22⋊C8—1461no—
338C22⋊C8—1461no—
339C22⋊C8—1461no—
340#95—21no—
341#95—21no—
342#95—21no—
343#95—42no—
344#95—1461no—
345#95—1461no—
346#95—1461no—
347#95C4×D7312yescomplemented
348C24—1461no—
349C24C2×C22⋊D7311yescharacteristic
350C2×D4—2921no—
351C2×D4—2921no—
352C2×D4—2921no—
353C2×D4—2921no—
354C2×D4—2921no—
355C2×D4—2921no—
356C2×D4—732no—
357C2×D4—1462no—
358C2×D4—1462no—
359C2×D4—1461no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—2922no—
386C22×C4—5841no—
387C22×C4—5841no—
388C22×C4—1461no—
389C22×C4—1461no—
390C22×C4—1461no—
391C22×C4#1192401512yes—
392C22×C4C2×C4×D7311yescharacteristic
393C22×C4D4×D7311yescharacteristic
394C22×C4D4×D7311yescharacteristic
395C22×C4Q8×D7311yescharacteristic
396C22×C4#1192402811yescharacteristic
397C22×C4#1192402911yescharacteristic
398C2×C8—2921no—
399C2×C8—2921no—
400C2×C8—2921no—
401C2×C8—2921no—
402C2×C8—2921no—
403C2×C8—1462no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—48no—
409C4⋊C4—2921no—
410C4⋊C4—2921no—
411C4⋊C4—2922no—
412C4⋊C4—732no—
413C4⋊C4—1461no—
414C22⋊C4—2922no—
415C22⋊C4—2921no—
416C22⋊C4—2921no—
417C22⋊C4—5841no—
418C22⋊C4—5841no—
419C22⋊C4—1462no—
420C22⋊C4—1462no—
421C42—2922no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—2921no—
427C23—2921no—
428C23—2921no—
429C23—2921no—
430C23—2921no—
431C23—2921no—
432C23—1462no—
433C23C4×C22⋊D7311yescharacteristic
434C23#1455655911yescharacteristic
435C23#1455656711yescharacteristic
436C23C2×#1192401511yescharacteristic
437C23#1455661111yescharacteristic
438C23#1455661611yescharacteristic
439C23#1455661711yescharacteristic
440D4—2922no—
441D4—2922no—
442D4—2922no—
443D4—2922no—
444D4—2922no—
445D4—5841no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—24no—
451C2×C4—22no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—81no—
473C2×C4—81no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—2921no—
479C2×C4—2921no—
480C2×C4—2921no—
481C2×C4—2921no—
482C2×C4—2921no—
483C2×C4—2921no—
484C2×C4—2921no—
485C2×C4—2921no—
486C2×C4—5844no—
487C2×C4—1462no—
488C2×C4C4⋊C4×D7311yescharacteristic
489C2×C4#1455655311yescharacteristic
490C2×C4#1455656911yescharacteristic
491C2×C4#1455657611yescharacteristic
492C8—2922no—
493C8—5841no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—2922no—
507C22—2922no—
508C22—2922no—
509C22—5841no—
510C22—5841no—
511C22—5841no—
512C22—5841no—
513C22#1798845811yescharacteristic
514C22C4×#1192401511yescharacteristic
515C22#1798869711yescharacteristic
516C22#1798873011yescharacteristic
517C22#1798873711yescharacteristic
518C22#1798875411yescharacteristic
519C22#1798876911yescharacteristic
520C22#1798877311yescharacteristic
521C22#1798877611yescharacteristic
522C22#1798887411yescharacteristic
523C22#1798888411yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—44no—
529C4—42no—
530C4—81no—
531C4—82no—
532C4—2922no—
533C4—5841no—
534C4—5841no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—21no—
539C2—5842no—
540C2#2260887511yescharacteristic
541C2#2260889911yescharacteristic
542C2#2260892611yescharacteristic
543C2#2260895011yescharacteristic
544C2#2261015611yescharacteristic
545C2#2261019111yescharacteristic
546C2#2261021011yescharacteristic
subgroupG/H
centerC23#14556559
commutatorC22×C4×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#1444C2
socleC23×C73#120
prime radicalC2×#14556565C22
cosocleC23×C4×C73C23
hypercenter#1444D73
hypocenterC73#8873
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1444

Complements

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

NH ≅ G/Ntype
3. #22610124C2semidirect
5. #22607810C2semidirect
6. #22607774C2semidirect
7. C73×#1444C2semidirect
22. #17988320C4semidirect
54. C22⋊#10596831C2×C4semidirect
73. #95×C73C2×C4semidirect
78. C2×D292C4⋊C4semidirect
100. C4⋊Dic73C4⋊C4semidirect
278. #1444D73semidirect
281. C73#8873semidirect
347. #95C4×D73semidirect

Maximal subgroups

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

subgroupindex
#226126342
#226102482
#226101242
C2×#179883202
#226078102
#226077742
C73×#14442
#887373