Finite Group Databasebeta

← #33096551

Subgroups — #33096551

Order 18688.

830 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988641C211yesmaximal, characteristic
2#22612334C211yesmaximal, characteristic
3#22612333C211yesmaximal, characteristic
4#22610693C211yesmaximal, characteristic, complemented
5#22610691C211yesmaximal, characteristic, complemented
6#22610688C211yesmaximal, characteristic, complemented
7#22610686C211yesmaximal, characteristic, complemented
8#22610132C211yesmaximal, characteristic
9#22610130C211yesmaximal, characteristic
10#22610128C211yesmaximal, characteristic
11#22610098C211yesmaximal, characteristic, complemented
12#22610096C211yesmaximal, characteristic, complemented
13#22610063C211yesmaximal, characteristic, complemented
14#22610063C211yesmaximal, characteristic, complemented
15C73×#1854C211yesmaximal, characteristic
16C2×#14556550C2211yescharacteristic
17C2×#14556547—21no—
18C22×C4×Dic73C2211yescharacteristic
19#17988641C418yescomplemented
20C2×#14556525C2211yescharacteristic
21C2×#14556524C2211yescharacteristic
22C2×#14556524C2211yescharacteristic
23C2×#14556523C2211yescharacteristic
24C2×#14556522C2211yescharacteristic
25C2×#14556522C2211yescharacteristic
26C2×#14556520C2211yescharacteristic
27C2×#14556520C2211yescharacteristic
28C2×C22⋊#10596831C2211yescharacteristic
29C2×#14556501C2211yescharacteristic
30C2×#14556501C2211yescharacteristic
31#17988456C2211yescharacteristic
32#17988456C2211yescharacteristic
33#17988456C2211yescharacteristic
34#17988456C2211yescharacteristic
35#17988452C2211yescharacteristic
36#17988452C2211yescharacteristic
37#17988451—21no—
38#17988447C2211yescharacteristic
39#17988445—21no—
40#17988445—21no—
41#17988445—21no—
42C4⋊C4×Dic73C2211yescharacteristic
43C4⋊C4×Dic73C2211yescharacteristic
44C4×#11924007—21no—
45C4×#11924007—21no—
46#17988438—21no—
47#17988350C2211yescharacteristic
48#17988350C2211yescharacteristic
49#17988349C2211yescharacteristic
50#17988349C2211yescharacteristic
51#17988349C2211yescharacteristic
52#17988349C2211yescharacteristic
53C2×#117×C73C2211yescharacteristic
54C2×#107×C73C2211yescharacteristic
55C2×#106×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60C23×Dic73D411yescharacteristic
61C23×Dic73D411yescharacteristic
62C22×#10596831C2311yescharacteristic
63C22×#10596831C2311yescharacteristic
64#14556550—41no—
65#14556550—41no—
66#14556547—44no—
67C2×C4⋊Dic73C2311yescharacteristic
68C2×C4⋊Dic73C2311yescharacteristic
69C2×C4⋊Dic73C2311yescharacteristic
70C2×C4⋊Dic73C2311yescharacteristic
71C2×#11924007—21no—
72C2×#11924007—21no—
73C2×#11924007—21no—
74C2×#11924007—21no—
75C2×#11924007—21no—
76C2×#11924007—21no—
77C2×#11924007—21no—
78C2×#11924007—21no—
79C2×C22⋊Dic73—21no—
80C2×C22⋊Dic73—21no—
81C2×C4×Dic73—21no—
82C2×C4×Dic73—21no—
83C2×C4×Dic73—21no—
84C2×C4×Dic73C2×C414yes—
85C2×C4×Dic73D411yescharacteristic
86C2×C4×Dic73D411yescharacteristic
87C2×C4×Dic73Q814yes—
88C2×C4×Dic73C2311yescharacteristic
89C2×C4×Dic73C2311yescharacteristic
90#14556525—41no—
91#14556524—41no—
92#14556524—41no—
93#14556523—41no—
94#14556522—41no—
95#14556522—41no—
96#14556520C2×C414yes—
97#14556520C2×C414yes—
98C22⋊#10596831C2×C414yes—
99#14556501C2×C414yes—
100#14556501C2×C414yes—
101#14556498—21no—
102#14556498—21no—
103#14556498—21no—
104#14556498—21no—
105#14556498—21no—
106#14556498—21no—
107#14556498—21no—
108C23×C4×C73C2311yescharacteristic
109C22×C8×C73C2311yescharacteristic
110C22×C8×C73C2311yescharacteristic
111#117×C73—41no—
112#117×C73—41no—
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C22⋊C4×C73—21no—
118C2×C22⋊C4×C73—21no—
119C2×C42×C73—21no—
120#107×C73—41no—
121#106×C73—41no—
122C22⋊C8×C73C2×C414yes—
123#95×C73—21no—
124C22×Dic73—22no—
125C22×Dic73—22no—
126C22×Dic73—21no—
127C22×Dic73—21no—
128C22×Dic73—21no—
129C22×Dic73—21no—
130C22×Dic73—41no—
131C22×Dic73—41no—
132C22×Dic73C4⋊C414yes—
133C22×Dic73C4⋊C414yes—
134C22×Dic73C2×D411yescharacteristic
135C22×Dic73C2×D411yescharacteristic
136C22×Dic73C2×D411yescharacteristic
137C22×Dic73C2×D411yescharacteristic
138C2×#10596831—21no—
139C2×#10596831—21no—
140C2×#10596831—21no—
141C2×#10596831—21no—
142C2×#10596831C22×C412yes—
143C2×#10596831C22×C412yes—
144C4⋊Dic73—21no—
145C4⋊Dic73—21no—
146C4⋊Dic73—21no—
147C4⋊Dic73—21no—
148C4⋊Dic73—21no—
149C4⋊Dic73—21no—
150C4⋊Dic73—21no—
151C4⋊Dic73—21no—
152#11924007—42no—
153#11924007—42no—
154#11924007—42no—
155#11924007—42no—
156#11924007—42no—
157#11924007—42no—
158#11924007—42no—
159#11924007—42no—
160C22⋊Dic73—42no—
161C22⋊Dic73—42no—
162C4×Dic73—42no—
163C4×Dic73—42no—
164C4×Dic73—42no—
165C4×Dic73C4⋊C414yes—
166C4×Dic73C4⋊C414yes—
167C4×Dic73C22×C412yes—
168C4×Dic73C22×C412yes—
169C4×Dic73C2×Q812yes—
170C4×Dic73C2×Q812yes—
171C24×C73C2×D411yescharacteristic
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73C22×C412yes—
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×Q812yes—
183C22×C4×C73C2411yescharacteristic
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73C22×C412yes—
189C2×C8×C73C22×C412yes—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C22⋊C4×C73—42no—
199C22⋊C4×C73—42no—
200C42×C73—42no—
201C23×C73—21no—
202C23×C73—21no—
203C23×C73—21no—
204C23×C73—21no—
205C23×C73—21no—
206C23×C73—21no—
207C23×C73C2×C4⋊C412yes—
208C23×C73C22×D411yescharacteristic
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—22no—
212C2×C4×C73—22no—
213C2×C4×C73—22no—
214C2×C4×C73—22no—
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×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73—41no—
227C2×C4×C73C2×C4⋊C412yes—
228C2×C4×C73C23×C411yescharacteristic
229C2×C4×C73C22×Q811yescharacteristic
230C2×C4×C73H(5,𝔽2)11yescharacteristic
231C2×C4×C73H(5,𝔽2)11yescharacteristic
232C2×C4×C732−1+411yescharacteristic
233C2×C4×C732−1+411yescharacteristic
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—28no—
241C2×Dic73—44no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—41no—
247C2×Dic73—41no—
248C2×Dic73—41no—
249C2×Dic73—41no—
250C2×Dic73—41no—
251C2×Dic73—41no—
252C2×Dic73—41no—
253C2×Dic73—41no—
254C2×Dic73C2×C4⋊C412yes—
255C2×Dic73C2×C4⋊C412yes—
256C2×Dic73C2×C4⋊C412yes—
257C2×Dic73C2×C4⋊C412yes—
258C2×Dic73AGL(1,ℤ/8)12yes—
259C2×Dic73#13712yes—
260C8×C73—22no—
261C8×C73—22no—
262#10596831—22no—
263#10596831—22no—
264C22×C73—22no—
265C22×C73—22no—
266C22×C73—22no—
267C22×C73—41no—
268C22×C73—41no—
269C22×C73—41no—
270C22×C73—41no—
271C22×C73C22×C4⋊C411yescharacteristic
272C22×C73#53511yescharacteristic
273C22×C73#53611yescharacteristic
274C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C73C2×#13711yescharacteristic
276C22×C73#57511yescharacteristic
277C22×C73#57511yescharacteristic
278C4×C73—22no—
279C4×C73—81no—
280C4×C73—81no—
281C4×C73—81no—
282C4×C73—81no—
283C4×C73#52011yescharacteristic
284C4×C73#52011yescharacteristic
285C4×C73#54411yescharacteristic
286C4×C73#54411yescharacteristic
287Dic73—22no—
288Dic73—22no—
289Dic73—22no—
290Dic73—81no—
291Dic73—81no—
292Dic73—81no—
293Dic73—81no—
294Dic73#42814yes—
295#21988—731nomaximal, Sylow
296C2×C73—42no—
297C2×C73#231711yescharacteristic
298C2×C73C2×#42811yescharacteristic
299C2×C73#291111yescharacteristic
300C2×C73#321411yescharacteristic
301C2×C73#321611yescharacteristic
302C2×C73#323511yescharacteristic
303C2×C73#323711yescharacteristic
304C2×#432—731no—
305#2285—731no—
306#2285—731no—
307#1948—731no—
308#1948—731no—
309#1947—731no—
310#1947—731no—
311#1854—731no—
312#1854—731no—
313#1854—731no—
314#1854D7311yescharacteristic
315#1847—731no—
316#1847—731no—
317#1836—731no—
318#1836—731no—
319C73#2198811yescharacteristic, complemented, Sylow
320C2×#117—731no—
321C2×#117—1461no—
322C2×#117C2×D7311yescharacteristic
323C22×C42—731no—
324#432—738no—
325C2×#107—731no—
326C2×#107—731no—
327C2×#107—731no—
328C2×#107C2×D7311yescharacteristic
329C2×#106—731no—
330C2×#106—731no—
331C2×#106—731no—
332C2×#106C2×D7311yescharacteristic
333C2×C4⋊C8—731no—
334C2×C4⋊C8—731no—
335C2×C22⋊C8—731no—
336C2×C22⋊C8C2×D7311yescharacteristic
337C2×#97—731no—
338C2×#97—731no—
339#384—731no—
340#384—731no—
341#384—731no—
342#384—731no—
343#382—731no—
344#382—731no—
345#382—1461no—
346#380—731no—
347#380—1461no—
348#380—1461no—
349#380—1461no—
350#380C2×D7311yescharacteristic
351C4×C4⋊C4—731no—
352C4×C4⋊C4—731no—
353C4×C4⋊C4—1461no—
354C4×C4⋊C4—1461no—
355C4×C4⋊C4—1461no—
356#340—731no—
357#340—731no—
358#340—731no—
359#340—731no—
360#340—731no—
361#340—731no—
362#340C2×D7311yescharacteristic
363#340C2×D7311yescharacteristic
364C23×C4—731no—
365C23×C4—731no—
366C23×C4C22×D7311yescharacteristic
367C22×C8—731no—
368C22×C8—731no—
369C22×C8C22×D7311yescharacteristic
370C22×C8C22×D7311yescharacteristic
371#117—41no—
372#117—41no—
373#117—2924no—
374#117—2921no—
375#117—2921no—
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⋊C4—1461no—
385C2×C4⋊C4—1461no—
386C2×C4⋊C4—1461no—
387C2×C4⋊C4—1461no—
388C2×C4⋊C4C22×D7311yescharacteristic
389C2×C4⋊C4C22×D7311yescharacteristic
390C2×C4⋊C4C22×D7311yescharacteristic
391C2×C4⋊C4C22×D7311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—1461no—
395C2×C22⋊C4—1461no—
396C2×C42—21no—
397C2×C42—734no—
398C2×C42—731no—
399C2×C42—731no—
400C2×C42—734no—
401C2×C42—731no—
402C2×C42—731no—
403C2×C42—1461no—
404C2×C42—1461no—
405C2×C42—1461no—
406#107—41no—
407#107—2921no—
408#107—2921no—
409#107—2921no—
410#106—41no—
411#106—2921no—
412#106—2921no—
413#106—2921no—
414C4⋊C8—734no—
415C4⋊C8—734no—
416C22⋊C8—734no—
417C22⋊C8C4×D7314yes—
418#97—734no—
419#97—734no—
420#95—21no—
421#95—1461no—
422#95—1461no—
423#95—1461no—
424#95—1461no—
425#95—1461no—
426#95—1461no—
427#95—1461no—
428C24D4×D7311yescharacteristic
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—2921no—
438C22×C4—2921no—
439C22×C4—734no—
440C22×C4—731no—
441C22×C4—734no—
442C22×C4—731no—
443C22×C4—731no—
444C22×C4—731no—
445C22×C4—1461no—
446C22×C4—1461no—
447C22×C4—1461no—
448C22×C4—1461no—
449C22×C4—1462no—
450C22×C4—1462no—
451C22×C4C2×C4×D7312yes—
452C22×C4D4×D7311yescharacteristic
453C22×C4Q8×D7312yes—
454C22×C4C23×D7311yescharacteristic
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—2922no—
480C4⋊C4—2922no—
481C4⋊C4—2922no—
482C4⋊C4—2922no—
483C4⋊C4—1461no—
484C4⋊C4—1461no—
485C4⋊C4—1461no—
486C4⋊C4—1461no—
487C4⋊C4—1461no—
488C4⋊C4—1461no—
489C4⋊C4—1461no—
490C4⋊C4—1461no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—2922no—
494C22⋊C4—2922no—
495C42—42no—
496C42—2922no—
497C42—2922no—
498C42—2922no—
499C42—734no—
500C42—734no—
501C42—732no—
502C42—732no—
503C42—732no—
504C42—732no—
505C23—21no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23C4⋊C4×D7312yes—
512C23C2×D4×D7311yescharacteristic
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—2921no—
532C2×C4—2921no—
533C2×C4—2921no—
534C2×C4—2921no—
535C2×C4—2921no—
536C2×C4—2921no—
537C2×C4—2921no—
538C2×C4—2921no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—2924no—
544C2×C4—732no—
545C2×C4—732no—
546C2×C4—732no—
547C2×C4—732no—
548C2×C4—732no—
549C2×C4—732no—
550C2×C4—1468no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4—1461no—
554C2×C4—1461no—
555C2×C4—1461no—
556C2×C4—1461no—
557C2×C4C4⋊C4×D7312yes—
558C2×C4C22×C4×D7311yescharacteristic
559C2×C4C2×Q8×D7311yescharacteristic
560C2×C4#1455663611yescharacteristic
561C2×C4#1455663611yescharacteristic
562C2×C4#1455663811yescharacteristic
563C2×C4#1455663811yescharacteristic
564C8—22no—
565C8—22no—
566C8—1462no—
567C8—1462no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22C2×C4⋊C4×D7311yescharacteristic
576C22#1798915211yescharacteristic
577C22#1798915911yescharacteristic
578C22AGL(1,ℤ/8)×D7311yescharacteristic
579C22#137×D7311yescharacteristic
580C22#1798938411yescharacteristic
581C22#1798938411yescharacteristic
582C4—22no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—5841no—
588C4—5841no—
589C4—5841no—
590C4—5841no—
591C4—734no—
592C4—1462no—
593C4—1462no—
594C4—1462no—
595C4#1798906611yescharacteristic
596C4#1798906611yescharacteristic
597C4#1798921611yescharacteristic
598C4#1798921611yescharacteristic
599C2—42no—
600C2#2261255011yescharacteristic
601C2#428×D7311yescharacteristic
602C2#2261851911yescharacteristic
603C2#2262092311yescharacteristic
604C2#2262093911yescharacteristic
605C2#2262112611yescharacteristic
606C2#2262114211yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1854C2
socleC23×C73C22×D4
prime radicalC24×C73C2×D4
cosocleC22×C4×C73C24
hypercenter#1854D73
hypocenterC73#21988
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #22610693C2semidirect
5. #22610691C2semidirect
6. #22610688C2semidirect
7. #22610686C2semidirect
11. #22610098C2semidirect
12. #22610096C2semidirect
13. #22610063C2semidirect
14. #22610063C2semidirect
19. #17988641C4semidirect
319. C73#21988semidirect

Maximal subgroups

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

subgroupindex
C2×#179886412
#226123342
#226123332
#226106932
#226106912
#226106882
#226106862
#226101322
#226101302
#226101282
#226100982
#226100962
#226100632
C73×#18542
#2198873