Finite Group Databasebeta

← #33096378

Subgroups — #33096378

Order 18688.

830 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988609C211yesmaximal, characteristic
2#22612335C211yesmaximal, characteristic
3#22612324C211yesmaximal, characteristic
4#22610701C211yesmaximal, characteristic, complemented
5#22610699C211yesmaximal, characteristic, complemented
6#22610697C211yesmaximal, characteristic, complemented
7#22610693C211yesmaximal, characteristic, complemented
8#22610691C211yesmaximal, characteristic, complemented
9#22610688C211yesmaximal, characteristic, complemented
10#22610686C211yesmaximal, characteristic, complemented
11#22609965C211yesmaximal, characteristic
12#22609963C211yesmaximal, characteristic
13#22609963C211yesmaximal, characteristic
14#22609961C211yesmaximal, characteristic
15C73×#1949C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C22×#11924011C2211yescharacteristic
18C2×#14556548—21no—
19C2×C42×D73C2211yescharacteristic
20C2×#14556525C2211yescharacteristic
21C2×#14556524C2211yescharacteristic
22C2×#14556524C2211yescharacteristic
23C2×#14556523C2211yescharacteristic
24C2×#14556522C2211yescharacteristic
25C2×#14556522C2211yescharacteristic
26#17988609C418yescomplemented
27C2×C4⋊#10596831C2211yescharacteristic
28C2×#14556520C2211yescharacteristic
29C2×#14556520C2211yescharacteristic
30#17988456C2211yescharacteristic
31#17988456C2211yescharacteristic
32#17988454—21no—
33#17988453C2211yescharacteristic
34#17988451—21no—
35#17988449—21no—
36#17988446—21no—
37#17988444C2211yescharacteristic
38#17988444C2211yescharacteristic
39#17988444C2211yescharacteristic
40#17988444C2211yescharacteristic
41C4⋊C4×Dic73C2211yescharacteristic
42C4⋊C4×Dic73C2211yescharacteristic
43C4×#11924007—21no—
44C4×C4⋊Dic73C2211yescharacteristic
45#17988434—21no—
46#17988432—21no—
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53C2×#107×C73C2211yescharacteristic
54C2×#106×C73C2211yescharacteristic
55C2×C4⋊C8×C73C2211yescharacteristic
56#382×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60C22×C4×D73D411yescharacteristic
61C22×C4×D73D411yescharacteristic
62C22×C4×D73C2311yescharacteristic
63C2×#11924011—41no—
64C2×#11924011—41no—
65C2×#11924011—41no—
66C2×#11924011—41no—
67C2×#11924011C2×C414yes—
68C2×#11924011C2×C414yes—
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71#14556548—44no—
72C2×C4⋊Dic73C2311yescharacteristic
73C2×C4⋊Dic73C2311yescharacteristic
74C2×C4⋊Dic73C2311yescharacteristic
75C2×C4⋊Dic73C2311yescharacteristic
76C2×#11924007—21no—
77C2×#11924007—21no—
78C2×#11924007—21no—
79C2×#11924007—21no—
80C2×#11924005—21no—
81C2×#11924005—21no—
82C2×#11924005—21no—
83C2×#11924005—21no—
84C2×C4×Dic73—21no—
85C2×C4×Dic73—21no—
86C2×C4×Dic73—21no—
87C2×C4×Dic73D411yescharacteristic
88C2×C4×Dic73D411yescharacteristic
89C2×C4×Dic73C2311yescharacteristic
90C42×D73C2×C414yes—
91C42×D73Q814yes—
92#14556525—41no—
93#14556524—41no—
94#14556524—41no—
95#14556523—41no—
96#14556522—41no—
97#14556522—41no—
98C4⋊#10596831C2×C414yes—
99#14556520C2×C414yes—
100#14556520C2×C414yes—
101#14556498—21no—
102#14556498—21no—
103#14556498—21no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107#14556498—21no—
108#14556498—21no—
109#14556498—21no—
110C22×C8×C73C2311yescharacteristic
111C22×C8×C73C2311yescharacteristic
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C42×C73—21no—
117C2×C42×C73C2311yescharacteristic
118#107×C73—41no—
119#106×C73—41no—
120C4⋊C8×C73C2×C414yes—
121#95×C73—21no—
122#95×C73—21no—
123#95×C73—21no—
124C23×D73C2×D411yescharacteristic
125C22×Dic73—21no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73C2×D411yescharacteristic
130C22×Dic73C2×D411yescharacteristic
131C22×Dic73C2×D411yescharacteristic
132C2×C4×D73—21no—
133C2×C4×D73—21no—
134C2×C4×D73—21no—
135C2×C4×D73—21no—
136C2×C4×D73—22no—
137C2×C4×D73—22no—
138C2×C4×D73—41no—
139C2×C4×D73—41no—
140C2×C4×D73C4⋊C414yes—
141C2×C4×D73C4⋊C414yes—
142C2×C4×D73C22×C412yes—
143C2×C4×D73C2×Q812yes—
144#11924011—44no—
145#11924011—44no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831C22×C412yes—
151C2×#10596831C22×C412yes—
152C4⋊Dic73—21no—
153C4⋊Dic73—21no—
154C4⋊Dic73—21no—
155C4⋊Dic73—21no—
156C4⋊Dic73—21no—
157C4⋊Dic73—21no—
158C4⋊Dic73—21no—
159C4⋊Dic73—21no—
160#11924007—42no—
161#11924007—42no—
162#11924007—42no—
163#11924007—42no—
164#11924005—42no—
165#11924005—42no—
166#11924005—42no—
167#11924005—42no—
168C4×Dic73—42no—
169C4×Dic73—42no—
170C4×Dic73—42no—
171C4×Dic73C4⋊C414yes—
172C4×Dic73C4⋊C414yes—
173C4×Dic73C22×C412yes—
174C4×Dic73C2×Q812yes—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2411yescharacteristic
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73C22×C412yes—
187C2×C8×C73C22×C412yes—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C42×C73—42no—
197C42×C73C22×C412yes—
198C42×C73C2×Q812yes—
199C23×C73C22×D411yescharacteristic
200C22×D73—21no—
201C22×D73—21no—
202C22×D73—21no—
203C22×D73—21no—
204C22×D73—21no—
205C22×D73—21no—
206C22×D73C2×C4⋊C412yes—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—41no—
212C2×C4×C73—41no—
213C2×C4×C73—41no—
214C2×C4×C73—41no—
215C2×C4×C73—41no—
216C2×C4×C73—41no—
217C2×C4×C73—41no—
218C2×C4×C73—41no—
219C2×C4×C73—41no—
220C2×C4×C73—41no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73C2×C4⋊C412yes—
224C2×C4×C73C2×C4⋊C412yes—
225C2×C4×C73C23×C411yescharacteristic
226C2×C4×C73C22×Q811yescharacteristic
227C2×C4×C73H(5,𝔽2)11yescharacteristic
228C2×C4×C73H(5,𝔽2)11yescharacteristic
229C2×C4×C732−1+411yescharacteristic
230C2×C4×C732−1+411yescharacteristic
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—21no—
235C2×Dic73—41no—
236C2×Dic73—41no—
237C2×Dic73—41no—
238C2×Dic73—41no—
239C2×Dic73—41no—
240C2×Dic73—41no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73C2×C4⋊C412yes—
248C2×Dic73C2×C4⋊C412yes—
249C2×Dic73C2×C4⋊C412yes—
250C2×Dic73AGL(1,ℤ/8)12yes—
251C2×Dic73#13712yes—
252C4×D73—22no—
253C4×D73—22no—
254C4×D73—22no—
255C4×D73—22no—
256C4×D73—28no—
257C4×D73—44no—
258C8×C73—22no—
259C8×C73—22no—
260#10596831—22no—
261#10596831—22no—
262C22×C73C22×C4⋊C411yescharacteristic
263C22×C73#53711yescharacteristic
264C22×C73#53711yescharacteristic
265C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C73C2×#13711yescharacteristic
267C22×C73#57511yescharacteristic
268C22×C73#57511yescharacteristic
269C2×D73—22no—
270C2×D73—22no—
271C2×D73—22no—
272C2×D73—41no—
273C2×D73—41no—
274C2×D73—41no—
275C2×D73—41no—
276C4×C73—22no—
277C4×C73—22no—
278C4×C73—81no—
279C4×C73—81no—
280C4×C73—81no—
281C4×C73—81no—
282C4×C73#51811yescharacteristic
283C4×C73#51911yescharacteristic
284C4×C73#54411yescharacteristic
285C4×C73#54411yescharacteristic
286Dic73—22no—
287Dic73—22no—
288Dic73—81no—
289Dic73—81no—
290Dic73—81no—
291Dic73—81no—
292Dic73#42814yes—
293#21963—731nomaximal, Sylow
294C2×C73#231611yescharacteristic
295C2×C73C2×#42811yescharacteristic
296C2×C73#291111yescharacteristic
297C2×C73#325111yescharacteristic
298C2×C73#325111yescharacteristic
299C2×C73#325211yescharacteristic
300C2×C73#325211yescharacteristic
301D73—42no—
302C2×#423—731no—
303#2285—731no—
304#2283—731no—
305#1949—731no—
306#1949—731no—
307#1949—731no—
308#1949D7311yescharacteristic, complemented
309#1948—731no—
310#1948—731no—
311#1947—731no—
312#1947—731no—
313#1809—731no—
314#1809—731no—
315#1809—731no—
316#1809—731no—
317C73#2196311yescharacteristic, complemented, Sylow
318C22×M16—731no—
319C22×M16—731no—
320C2×#117—1461no—
321C22×C42—731no—
322C2×#107—731no—
323C2×#107—731no—
324C2×#107—731no—
325C2×#107C2×D7311yescharacteristic
326C2×#106—731no—
327C2×#106—731no—
328C2×#106—731no—
329C2×#106C2×D7311yescharacteristic
330#423—738no—
331C2×C4⋊C8—731no—
332C2×C4⋊C8—731no—
333C2×C4⋊C8—731no—
334C2×C4⋊C8C2×D7311yescharacteristic
335#384—731no—
336#384—731no—
337#383—1461no—
338#382—731no—
339#382—1461no—
340#382C2×D7311yescharacteristic
341#381—1461no—
342#380—731no—
343#380—731no—
344#380—731no—
345#380—731no—
346#380—1461no—
347C4×C4⋊C4—731no—
348C4×C4⋊C4—731no—
349C4×C4⋊C4—731no—
350C4×C4⋊C4—1461no—
351C4×C4⋊C4C2×D7311yescharacteristic
352C4×C22⋊C4—1461no—
353#376—1461no—
354#340—731no—
355#340—731no—
356#340—731no—
357#340—731no—
358#340—731no—
359#340—731no—
360#340C2×D7311yescharacteristic
361#340C2×D7311yescharacteristic
362C23×C4—731no—
363C23×C4—731no—
364C23×C4—731no—
365C2×M16—2921no—
366C2×M16—2921no—
367C2×M16—2921no—
368C2×M16—2921no—
369C2×M16—734no—
370C2×M16—734no—
371C22×C8—731no—
372C22×C8—731no—
373C22×C8C22×D7311yescharacteristic
374C22×C8C22×D7311yescharacteristic
375#117—2924no—
376C2×C4⋊C4—731no—
377C2×C4⋊C4—731no—
378C2×C4⋊C4—731no—
379C2×C4⋊C4—731no—
380C2×C4⋊C4—1461no—
381C2×C4⋊C4—1461no—
382C2×C4⋊C4—1461no—
383C2×C4⋊C4—1461no—
384C2×C4⋊C4C22×D7311yescharacteristic
385C2×C4⋊C4C22×D7311yescharacteristic
386C2×C4⋊C4C22×D7311yescharacteristic
387C2×C4⋊C4C22×D7311yescharacteristic
388C2×C22⋊C4—1461no—
389C2×C22⋊C4—1461no—
390C2×C22⋊C4—1461no—
391C2×C22⋊C4—1461no—
392C2×C42—21no—
393C2×C42—731no—
394C2×C42—731no—
395C2×C42—731no—
396C2×C42—734no—
397C2×C42—734no—
398C2×C42—1461no—
399C2×C42—1461no—
400C2×C42—1461no—
401C2×C42C22×D7311yescharacteristic
402#107—41no—
403#107—2921no—
404#107—2921no—
405#107—2921no—
406#106—41no—
407#106—2921no—
408#106—2921no—
409#106—2921no—
410C4⋊C8—734no—
411C4⋊C8—734no—
412C4⋊C8—734no—
413C4⋊C8C4×D7314yes—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—1461no—
418#95—1461no—
419#95—1461no—
420#95—1461no—
421#95—1461no—
422#95—1461no—
423#95—1461no—
424#95—1461no—
425#95—1461no—
426C24—731no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—2921no—
432C22×C4—2921no—
433C22×C4—734no—
434C22×C4—731no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—734no—
438C22×C4—732no—
439C22×C4—732no—
440C22×C4—1462no—
441C22×C4—1462no—
442C22×C4—1461no—
443C22×C4—1461no—
444C22×C4—1461no—
445C22×C4—1461no—
446C22×C4—1461no—
447C22×C4—1461no—
448C22×C4—1461no—
449C22×C4—1461no—
450C22×C4D4×D7311yescharacteristic
451C22×C4D4×D7311yescharacteristic
452C22×C4C23×D7311yescharacteristic
453M16—2924no—
454M16—2924no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—732no—
460C2×C8—732no—
461C2×C8—1461no—
462C2×C8—1461no—
463C2×C8—1461no—
464C2×C8—1461no—
465C2×C8C2×C4×D7312yes—
466C2×C8C2×C4×D7312yes—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—2922no—
476C4⋊C4—2922no—
477C4⋊C4—2922no—
478C4⋊C4—2922no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
481C4⋊C4—1461no—
482C4⋊C4—1461no—
483C4⋊C4—1461no—
484C4⋊C4—1461no—
485C4⋊C4—1461no—
486C4⋊C4—1461no—
487C22⋊C4—2922no—
488C22⋊C4—2922no—
489C22⋊C4—2922no—
490C22⋊C4—2922no—
491C42—42no—
492C42—2922no—
493C42—2922no—
494C42—2922no—
495C42—734no—
496C42—734no—
497C42—732no—
498C42—732no—
499C42C2×C4×D7312yes—
500C42Q8×D7312yes—
501C23—732no—
502C23—1461no—
503C23—1461no—
504C23—1461no—
505C23—1461no—
506C23—1461no—
507C23—1461no—
508C23C2×D4×D7311yescharacteristic
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—2924no—
526C2×C4—2921no—
527C2×C4—2921no—
528C2×C4—2921no—
529C2×C4—2921no—
530C2×C4—2921no—
531C2×C4—2921no—
532C2×C4—2921no—
533C2×C4—2921no—
534C2×C4—2921no—
535C2×C4—2921no—
536C2×C4—2921no—
537C2×C4—2921no—
538C2×C4—732no—
539C2×C4—732no—
540C2×C4—732no—
541C2×C4—732no—
542C2×C4—732no—
543C2×C4—1468no—
544C2×C4—1461no—
545C2×C4—1461no—
546C2×C4—1461no—
547C2×C4—1461no—
548C2×C4—1462no—
549C2×C4—1462no—
550C2×C4—1462no—
551C2×C4—1462no—
552C2×C4C4⋊C4×D7312yes—
553C2×C4C4⋊C4×D7312yes—
554C2×C4C22×C4×D7311yescharacteristic
555C2×C4C2×Q8×D7311yescharacteristic
556C2×C4#1455663611yescharacteristic
557C2×C4#1455663711yescharacteristic
558C2×C4#1455663811yescharacteristic
559C2×C4#1455663911yescharacteristic
560C8—22no—
561C8—22no—
562C8—1462no—
563C8—1462no—
564C22—2921no—
565C22—2921no—
566C22—2921no—
567C22—2921no—
568C22—1462no—
569C22—1462no—
570C22—1462no—
571C22C2×C4⋊C4×D7311yescharacteristic
572C22#1798916611yescharacteristic
573C22#1798916711yescharacteristic
574C22AGL(1,ℤ/8)×D7311yescharacteristic
575C22#137×D7311yescharacteristic
576C22#1798938411yescharacteristic
577C22#1798938411yescharacteristic
578C4—22no—
579C4—22no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—5841no—
585C4—5841no—
586C4—5841no—
587C4—5841no—
588C4—734no—
589C4—1462no—
590C4—1462no—
591C4#1798905911yescharacteristic
592C4#1798906311yescharacteristic
593C4#1798921411yescharacteristic
594C4#1798921711yescharacteristic
595C2—2922no—
596C2#2261254611yescharacteristic
597C2#428×D7311yescharacteristic
598C2#2261851911yescharacteristic
599C2#2262129011yescharacteristic
600C2#2262129211yescharacteristic
601C2#2262130111yescharacteristic
602C2#2262130311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1949C2
socleC23×C73C22×D4
prime radicalC23×D73C2×D4
cosocleC22×C4×C73C24
hypercenter#1949D73
hypocenterC73#21963
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #22610701C2semidirect
5. #22610699C2semidirect
6. #22610697C2semidirect
7. #22610693C2semidirect
8. #22610691C2semidirect
9. #22610688C2semidirect
10. #22610686C2semidirect
15. C73×#1949C2semidirect
26. #17988609C4semidirect
308. #1949D73semidirect
317. C73#21963semidirect

Maximal subgroups

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

subgroupindex
C2×#179886092
#226123352
#226123242
#226107012
#226106992
#226106972
#226106932
#226106912
#226106882
#226106862
#226099652
#226099632
#226099612
C73×#19492
#2196373