Finite Group Databasebeta

← #33051918

Subgroups — #33051918

Order 18688.

1174 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989067C211yesmaximal, characteristic
2#22619015C212yesmaximal, complemented
3#22608271C212yesmaximal, complemented
4#22608270C212yesmaximal, complemented
5#22608265C211yesmaximal, characteristic, complemented
6#22608264C212yesmaximal, complemented
7#22608250C212yesmaximal, complemented
8#22608244C212yesmaximal, complemented
9C73×#1464C211yesmaximal, characteristic, complemented
10C22×#11924028C411yescharacteristic
11#17989067—24no—
12#17989067—24no—
13C2×C4×Dic146C411yescharacteristic
14C2×C4×Dic146C2211yescharacteristic
15C2×C4×D292C411yescharacteristic
16C2×C4×D292C2211yescharacteristic
17C2×#14556551C411yescharacteristic
18C2×#14556551C411yescharacteristic
19C2×#14556551C2211yescharacteristic
20C2×#14556551C2211yescharacteristic
21C2×#14556549C2211yescharacteristic
22C2×#14556549C2211yescharacteristic
23C22×C4⋊Dic73C411yescharacteristic
24C2×C4⋊C4×D73C411yescharacteristic
25C2×C4⋊C4×D73C411yescharacteristic
26#17988716—24no—
27#17988715—24no—
28#17988644C2212yes—
29#17988641C2214yes—
30#17988637C2214yes—
31#17988313C2212yes—
32#17988311C2212yes—
33#17988310C2214yes—
34#17988310C2214yes—
35C2×#117×C73C2211yescharacteristic
36#432×C73C2212yes—
37#324×C73C2212yes—
38#323×C73C2212yes—
39C2×#11924028—22no—
40C2×#11924028—22no—
41C2×#11924028—24no—
42C2×#11924028—24no—
43C22×Dic146C2×C411yescharacteristic
44C22×D292C2×C411yescharacteristic
45C22×C22⋊D73C2×C411yescharacteristic
46C22×C22⋊D73C2×C411yescharacteristic
47C23×Dic73C2×C411yescharacteristic
48C23×Dic73C2×C411yescharacteristic
49C22×C4×D73C2×C411yescharacteristic
50C22×C4×D73C2×C411yescharacteristic
51C22×C4×D73C2×C411yescharacteristic
52C22×C4×D73C2×C411yescharacteristic
53C22×C4×D73C2×C411yescharacteristic
54C22×C4×D73C2×C411yescharacteristic
55C4×Dic146—22no—
56C4×Dic146—22no—
57C4×Dic146D414yes—
58C4×Dic146D414yes—
59C4×D292—22no—
60C4×D292—22no—
61C4×D292—22no—
62C4×D292—22no—
63#14556551—24no—
64#14556551—24no—
65#14556551—24no—
66#14556551—24no—
67#14556549—24no—
68#14556549—24no—
69C2×C4⋊Dic73—22no—
70C2×C4⋊Dic73—22no—
71C2×C4⋊Dic73C2×C411yescharacteristic
72C2×C4⋊Dic73C2×C411yescharacteristic
73C2×C4⋊Dic73C2×C411yescharacteristic
74C2×C4⋊Dic73C2×C411yescharacteristic
75C2×#11924007C2×C411yescharacteristic
76C2×#11924007C2×C411yescharacteristic
77C2×#11924007C2×C411yescharacteristic
78C2×#11924007C2×C411yescharacteristic
79C4⋊C4×D73—24no—
80C4⋊C4×D73—24no—
81C2×#11924005C2×C411yescharacteristic
82C2×#11924005C2×C411yescharacteristic
83C2×#11924005C2311yescharacteristic
84C2×#11924005C2311yescharacteristic
85C2×C4×Dic73C2×C411yescharacteristic
86C2×C4×Dic73C2×C411yescharacteristic
87C2×C4×Dic73C2311yescharacteristic
88C2×C4×Dic73C2311yescharacteristic
89C4⋊#10596831—22no—
90#14556520—24no—
91#14556520—24no—
92C22⋊#10596831C2314yes—
93#14556502—22no—
94#14556501—24no—
95C8×Dic73—24no—
96C23×C4×C73C2×C411yescharacteristic
97#117×C73—22no—
98#117×C73—22no—
99C2×C4⋊C4×C73C2×C411yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C22⋊C4×C73C2×C411yescharacteristic
102C2×C22⋊C4×C73C2311yescharacteristic
103C2×C42×C73C2×C411yescharacteristic
104C2×C42×C73C2311yescharacteristic
105C4⋊C8×C73—22no—
106C22⋊C8×C73C2314yes—
107#97×C73—22no—
108C23×D73C22×C411yescharacteristic
109C23×D73C22×C411yescharacteristic
110#11924028—216no—
111#11924028—216no—
112C2×Dic146—22no—
113C2×Dic146—22no—
114C2×Dic146C22⋊C412yes—
115C2×Dic146C22⋊C412yes—
116C2×D292—22no—
117C2×D292—22no—
118C2×D292—21no—
119C2×D292—21no—
120C2×C22⋊D73—22no—
121C2×C22⋊D73—22no—
122C2×C22⋊D73—22no—
123C2×C22⋊D73—22no—
124C2×C22⋊D73—22no—
125C2×C22⋊D73M1614yes—
126C22×Dic73—22no—
127C22×Dic73—22no—
128C22×Dic73—81no—
129C22×Dic73—81no—
130C22×Dic73C22×C411yescharacteristic
131C22×Dic73C22×C411yescharacteristic
132C22×Dic73C22×C411yescharacteristic
133C22×Dic73C22×C411yescharacteristic
134C22×Dic73C22×C411yescharacteristic
135C22×Dic73C22×C411yescharacteristic
136C2×C4×D73—22no—
137C2×C4×D73—22no—
138C2×C4×D73—22no—
139C2×C4×D73—22no—
140C2×C4×D73—22no—
141C2×C4×D73—22no—
142C2×C4×D73—22no—
143C2×C4×D73—22no—
144C2×C4×D73—22no—
145C2×C4×D73—81no—
146C2×C4×D73—81no—
147C2×C4×D73—81no—
148C2×C4×D73—81no—
149C2×C4×D73M1614yes—
150C2×#10596831—24no—
151C4⋊Dic73—21no—
152C4⋊Dic73—21no—
153C4⋊Dic73—22no—
154C4⋊Dic73—22no—
155C4⋊Dic73C22⋊C412yes—
156C4⋊Dic73C22⋊C412yes—
157#11924007—22no—
158#11924007—22no—
159#11924007C22⋊C414yes—
160#11924007C22⋊C414yes—
161#11924005—22no—
162#11924005—22no—
163#11924005—22no—
164#11924005—22no—
165C4×Dic73—22no—
166C4×Dic73—22no—
167C4×Dic73C2×D414yes—
168C4×Dic73C2×D414yes—
169C24×C73C22×C411yescharacteristic
170C22×C4×C73—22no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—22no—
174C22×C4×C73C22×C411yescharacteristic
175C22×C4×C73C22×C411yescharacteristic
176C22×C4×C73C22×C411yescharacteristic
177C22×C4×C73C22×C411yescharacteristic
178C22×C4×C73C22×C411yescharacteristic
179C22×C4×C73C2411yescharacteristic
180C2×C8×C73—24no—
181C4⋊C4×C73—22no—
182C4⋊C4×C73—22no—
183C22⋊C4×C73—22no—
184C22⋊C4×C73—22no—
185C42×C73—21no—
186C42×C73—21no—
187C42×C73C2×D412yes—
188C42×C73C2×D412yes—
189C23×C73—21no—
190C23×C73—21no—
191C23×C73—41no—
192C23×C73—41no—
193C23×C73C2×M1612yes—
194C23×C73C23×C411yescharacteristic
195C22×D73—21no—
196C22×D73—21no—
197C22×D73—21no—
198C22×D73—21no—
199C22×D73—41no—
200C22×D73—41no—
201C22×D73—41no—
202C22×D73—41no—
203C22×D73C2×M1612yes—
204C22×D73C2×M1612yes—
205C2×C4×C73—24no—
206C2×C4×C73—24no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—41no—
214C2×C4×C73—41no—
215C2×C4×C73—41no—
216C2×C4×C73—41no—
217C2×C4×C73C2×C22⋊C411yescharacteristic
218C2×C4×C73C2×C22⋊C411yescharacteristic
219C2×C4×C73C2×C22⋊C412yes—
220C2×C4×C73C2×M1612yes—
221C2×C4×C73C22×D412yes—
222C22⋊D73—28no—
223C22⋊D73—28no—
224C2×Dic73—21no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—41no—
229C2×Dic73—41no—
230C2×Dic73—41no—
231C2×Dic73—41no—
232C2×Dic73—82no—
233C2×Dic73—82no—
234C2×Dic73C2×C22⋊C412yes—
235C2×Dic73C2×C22⋊C412yes—
236C2×Dic73C2×C22⋊C412yes—
237C2×Dic73C2×C22⋊C412yes—
238C2×Dic73C2×M1612yes—
239C2×Dic73C2×M1612yes—
240D292—24no—
241D292—24no—
242C4×D73—28no—
243C4×D73—28no—
244C4×D73—82no—
245C4×D73—82no—
246C4×D73—82no—
247C4×D73—82no—
248Dic146—24no—
249Dic146—24no—
250C8×C73—44no—
251#10596831—44no—
252C22×C73—21no—
253C22×C73—21no—
254C22×C73—22no—
255C22×C73—42no—
256C22×C73—42no—
257C22×C73—41no—
258C22×C73—41no—
259C22×C73C22×C22⋊C411yescharacteristic
260C22×C73C22×M1611yescharacteristic
261C22×C73C22×M1611yescharacteristic
262C2×D73—22no—
263C2×D73—22no—
264C2×D73—42no—
265C2×D73—42no—
266C2×D73—41no—
267C2×D73—41no—
268C2×D73—41no—
269C2×D73—41no—
270C2×D73—42no—
271C2×D73—42no—
272C4×C73—21no—
273C4×C73—21no—
274C4×C73—22no—
275C4×C73—22no—
276C4×C73—22no—
277C4×C73—41no—
278C4×C73—41no—
279Dic73—22no—
280Dic73—22no—
281Dic73—22no—
282Dic73—41no—
283Dic73—41no—
284Dic73#40714yes—
285#17372—731nomaximal, Sylow
286C2×C73—21no—
287C2×C73—21no—
288C2×C73—42no—
289C2×C73C2×#40711yescharacteristic
290C2×C73#288411yescharacteristic
291C2×C73#288811yescharacteristic
292D73—42no—
293D73—42no—
294C2×#520—731no—
295#2983—732no—
296#1466—732no—
297#1466—732no—
298#1464—732no—
299#1464—731no—
300#1464D7311yescharacteristic, complemented
301#1460—732no—
302#1458—732no—
303C73#1737211yescharacteristic, complemented, Sylow
304C22×#41—731no—
305#520—1464no—
306#520—1464no—
307C2×C4×Q8—731no—
308C2×C4×Q8—731no—
309C2×C4×D4—731no—
310C2×C4×D4—731no—
311C2×C4×D4—731no—
312C2×C4×D4—731no—
313C2×C4×D4—731no—
314C2×C4×D4—731no—
315C2×#117—731no—
316C2×#117—731no—
317C2×#117C2×D7311yescharacteristic
318C22×C4⋊C4—731no—
319C22×C4⋊C4—731no—
320C22×C4⋊C4—731no—
321#446—1464no—
322#446—1464no—
323#432—732no—
324#432—734no—
325#432C2×D7312yes—
326#431—734no—
327#324—732no—
328#324C2×D7312yes—
329#323—732no—
330#323—734no—
331#323—734no—
332#323C2×D7312yes—
333C2×#41—1464no—
334C2×#41—1464no—
335C2×#41—1462no—
336C2×#41—1462no—
337C22×Q8—731no—
338C22×D4—731no—
339C22×D4—731no—
340C22×D4—731no—
341C23×C4—731no—
342C23×C4—731no—
343C23×C4—731no—
344C23×C4—731no—
345C23×C4—731no—
346C23×C4—731no—
347C23×C4—731no—
348C23×C4—731no—
349C23×C4C4×D7311yescharacteristic
350C4×Q8—734no—
351C4×Q8—734no—
352C4×Q8—1462no—
353C4×Q8—1462no—
354C4×D4—1462no—
355C4×D4—1462no—
356C4×D4—1464no—
357C4×D4—1464no—
358C4×D4—1464no—
359C4×D4—1464no—
360C4×D4—1462no—
361C4×D4—1462no—
362#117—22no—
363#117—22no—
364#117—1464no—
365#117—1464no—
366C2×C4⋊C4—731no—
367C2×C4⋊C4—731no—
368C2×C4⋊C4—731no—
369C2×C4⋊C4—731no—
370C2×C4⋊C4—731no—
371C2×C4⋊C4—731no—
372C2×C4⋊C4—731no—
373C2×C4⋊C4—731no—
374C2×C4⋊C4—1464no—
375C2×C4⋊C4—1464no—
376C2×C4⋊C4—1462no—
377C2×C4⋊C4—1462no—
378C2×C4⋊C4C4×D7311yescharacteristic
379C2×C4⋊C4C22×D7311yescharacteristic
380C2×C22⋊C4—731no—
381C2×C22⋊C4—731no—
382C2×C22⋊C4—731no—
383C2×C22⋊C4—731no—
384C2×C22⋊C4C4×D7311yescharacteristic
385C2×C22⋊C4C22×D7311yescharacteristic
386C2×C42—731no—
387C2×C42—731no—
388C2×C42—731no—
389C2×C42—731no—
390C2×C42C4×D7311yescharacteristic
391C2×C42C22×D7311yescharacteristic
392C4⋊C8—22no—
393C4⋊C8—1464no—
394C4⋊C8—1464no—
395C4⋊C8—1462no—
396C22⋊C8—734no—
397C22⋊C8C22×D7314yes—
398#97—22no—
399#97—1464no—
400#97—1462no—
401C4×C8—1464no—
402C24—731no—
403C24—731no—
404C24C2×C4×D7311yescharacteristic
405#41—14616no—
406#41—14616no—
407C2×Q8—732no—
408C2×Q8—732no—
409C2×Q8—1462no—
410C2×Q8—1462no—
411C2×D4—734no—
412C2×D4—1462no—
413C2×D4—1462no—
414C2×D4—1462no—
415C2×D4—1462no—
416C2×D4—1462no—
417C2×D4—1462no—
418C2×D4—1462no—
419C2×D4—1461no—
420C2×D4—1461no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—5841no—
426C22×C4—5841no—
427C22×C4—5841no—
428C22×C4—5841no—
429C22×C4—5841no—
430C22×C4—5841no—
431C22×C4—731no—
432C22×C4—731no—
433C22×C4—731no—
434C22×C4—731no—
435C22×C4—731no—
436C22×C4—731no—
437C22×C4—734no—
438C22×C4—1462no—
439C22×C4—1462no—
440C22×C4—1462no—
441C22×C4—1462no—
442C22×C4—1462no—
443C22×C4—1462no—
444C22×C4—1462no—
445C22×C4—1462no—
446C22×C4—1462no—
447C22×C4—1462no—
448C22×C4—1462no—
449C22×C4C2×C4×D7311yescharacteristic
450C22×C4C2×C4×D7311yescharacteristic
451C22×C4C2×C4×D7311yescharacteristic
452C22×C4C2×C4×D7311yescharacteristic
453C22×C4C2×C4×D7311yescharacteristic
454C22×C4C23×D7311yescharacteristic
455C2×C8—24no—
456C2×C8—1464no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—734no—
460C4⋊C4—734no—
461C4⋊C4—732no—
462C4⋊C4—732no—
463C4⋊C4—1462no—
464C4⋊C4—1462no—
465C4⋊C4—1462no—
466C4⋊C4—1462no—
467C4⋊C4—1461no—
468C4⋊C4—1461no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—1462no—
472C22⋊C4—1462no—
473C22⋊C4—1462no—
474C22⋊C4—1462no—
475C42—21no—
476C42—21no—
477C42—734no—
478C42—734no—
479C42—1462no—
480C42—1462no—
481C42D4×D7312yes—
482C42D4×D7312yes—
483C23—21no—
484C23—21no—
485C23—41no—
486C23—41no—
487C23—2921no—
488C23—2921no—
489C23—2921no—
490C23—2921no—
491C23—732no—
492C23—732no—
493C23—1461no—
494C23—1461no—
495C23—1461no—
496C23—1461no—
497C23M16×D7312yes—
498C23C22×C4×D7311yescharacteristic
499Q8—1464no—
500Q8—1464no—
501D4—1464no—
502D4—1464no—
503D4—1468no—
504D4—1468no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—21no—
508C2×C4—21no—
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—2921no—
518C2×C4—2921no—
519C2×C4—2921no—
520C2×C4—2921no—
521C2×C4—5842no—
522C2×C4—5842no—
523C2×C4—5842no—
524C2×C4—5842no—
525C2×C4—5842no—
526C2×C4—5842no—
527C2×C4—732no—
528C2×C4—732no—
529C2×C4—732no—
530C2×C4—732no—
531C2×C4—732no—
532C2×C4—732no—
533C2×C4—1468no—
534C2×C4—1468no—
535C2×C4—1461no—
536C2×C4—1461no—
537C2×C4—1461no—
538C2×C4—1461no—
539C2×C4C22⋊C4×D7311yescharacteristic
540C2×C4C22⋊C4×D7311yescharacteristic
541C2×C4C22⋊C4×D7312yes—
542C2×C4M16×D7312yes—
543C2×C4C2×D4×D7312yes—
544C8—44no—
545C8—2924no—
546C22—21no—
547C22—21no—
548C22—22no—
549C22—42no—
550C22—42no—
551C22—41no—
552C22—41no—
553C22—2922no—
554C22—2922no—
555C22—2922no—
556C22—2922no—
557C22—2921no—
558C22—2921no—
559C22—2921no—
560C22—2921no—
561C22—1462no—
562C22—1462no—
563C22C2×C22⋊C4×D7311yescharacteristic
564C22C2×M16×D7311yescharacteristic
565C22C2×M16×D7311yescharacteristic
566C4—22no—
567C4—22no—
568C4—22no—
569C4—21no—
570C4—21no—
571C4—41no—
572C4—41no—
573C4—2921no—
574C4—2921no—
575C4—734no—
576C4—1462no—
577C4—1462no—
578C4—1462no—
579C2—21no—
580C2—21no—
581C2—42no—
582C2—2922no—
583C2—2922no—
584C2#407×D7311yescharacteristic
585C2#2261839311yescharacteristic
586C2#2261840811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D73
commutatorC23×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1464C2
socleC22×C73C22×C22⋊C4
prime radicalC22×#11924028C4
cosocleC22×C4×C73C24
hypercenter#1464D73
hypocenterC73#17372
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #22619015C2semidirect
3. #22608271C2semidirect
4. #22608270C2semidirect
5. #22608265C2semidirect
6. #22608264C2semidirect
7. #22608250C2semidirect
8. #22608244C2semidirect
9. C73×#1464C2semidirect
300. #1464D73semidirect
303. C73#17372semidirect

Maximal subgroups

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

subgroupindex
C2×#179890672
#226190152
#226082712
#226082702
#226082652
#226082642
#226082502
#226082442
C73×#14642
#1737273