Finite Group Databasebeta

← #33055939

Subgroups — #33055939

Order 18688.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619951C211yesmaximal, characteristic
2#22618900C211yesmaximal, characteristic, complemented
3#22618887C211yesmaximal, characteristic, complemented
4#22608808C211yesmaximal, characteristic, complemented
5#22608801C211yesmaximal, characteristic, complemented
6#22608794C211yesmaximal, characteristic, complemented
7#22608787C211yesmaximal, characteristic, complemented
8#22608754C211yesmaximal, characteristic, complemented
9#22608749C211yesmaximal, characteristic, complemented
10#22608742C211yesmaximal, characteristic, complemented
11#22608742C211yesmaximal, characteristic, complemented
12#22608363C211yesmaximal, characteristic, complemented
13#22608337C211yesmaximal, characteristic, complemented
14#22608224C211yesmaximal, characteristic, complemented
15C73×#1572C211yesmaximal, characteristic, complemented
16#17989121C2211yescharacteristic
17C4×#11924028C2211yescharacteristic
18#17988929C411yescharacteristic
19#17988912C411yescharacteristic
20#17988895C411yescharacteristic
21#17988888C411yescharacteristic
22#17988810C411yescharacteristic
23#17988803C411yescharacteristic
24#17988751C411yescharacteristic
25#17988734C411yescharacteristic
26#17988714C2211yescharacteristic
27#17988711C2211yescharacteristic
28#17988711C2211yescharacteristic
29#17988711C2211yescharacteristic
30C4×Dic292C2211yescharacteristic
31C4×#11924017C2211yescharacteristic
32C4×#11924017C2211yescharacteristic
33C4×D584C2211yescharacteristic
34#17988664C2211yescharacteristic
35#17988655—21no—
36#17988652C2211yescharacteristic
37#17988652C2211yescharacteristic
38#17988652C2211yescharacteristic
39#17988650—21no—
40#17988650—21no—
41#17988650—21no—
42#17988649—21no—
43#17988640C2211yescharacteristic
44#17988638—21no—
45#17988544—21no—
46C2×C4×#10596831C2211yescharacteristic
47C4×C8×D73—21no—
48#17988317C2211yescharacteristic
49#17988317C2211yescharacteristic
50#17988317C2211yescharacteristic
51#17988317C2211yescharacteristic
52#17988314C2211yescharacteristic
53#17988314C2211yescharacteristic
54#17988314C2211yescharacteristic
55#17988314C2211yescharacteristic
56#17988309C2211yescharacteristic
57#17988309C2211yescharacteristic
58#17988308C2211yescharacteristic
59#17988308C2211yescharacteristic
60#432×C73C2211yescharacteristic
61#431×C73C2211yescharacteristic
62#431×C73C2211yescharacteristic
63#335×C73C2211yescharacteristic
64#335×C73C2211yescharacteristic
65#334×C73C2211yescharacteristic
66#334×C73C2211yescharacteristic
67C2×#11924028C2×C411yescharacteristic
68C2×Dic292C2×C411yescharacteristic
69C2×#11924017C2×C411yescharacteristic
70C2×#11924017C2×C411yescharacteristic
71C2×D584C2×C411yescharacteristic
72C2×#11924011—21no—
73C22×#10596831D411yescharacteristic
74C22×#10596831D411yescharacteristic
75C2×C8×D73—21no—
76C2×C8×D73—21no—
77C2×C8×D73—21no—
78#14556585—21no—
79#14556583C2×C411yescharacteristic
80#14556579C2×C411yescharacteristic
81#14556574—21no—
82#14556570C2×C411yescharacteristic
83#14556565C2×C411yescharacteristic
84C4×Dic146C2×C411yescharacteristic
85C4×Dic146C2311yescharacteristic
86C4×Dic146C2311yescharacteristic
87C4×D292C2×C411yescharacteristic
88C4×D292C2311yescharacteristic
89C4×D292C2311yescharacteristic
90C4×C22⋊D73—21no—
91C4×C22⋊D73—21no—
92C4×C22⋊D73—21no—
93#14556550C2×C411yescharacteristic
94#14556548—21no—
95#14556548—21no—
96C42×D73—21no—
97#14556525C2×C411yescharacteristic
98#14556525C2×C411yescharacteristic
99#14556523C2×C411yescharacteristic
100#14556523C2×C411yescharacteristic
101C4⋊#10596831—21no—
102#14556520—21no—
103#14556520—21no—
104#14556520—21no—
105#14556520—21no—
106#14556516C2×C411yescharacteristic
107#14556516C2×C411yescharacteristic
108#14556516C2×C411yescharacteristic
109#14556516C2×C411yescharacteristic
110#14556513C2×C411yescharacteristic
111#14556513C2×C411yescharacteristic
112#14556513C2×C411yescharacteristic
113#14556513C2×C411yescharacteristic
114C22⋊#10596831—21no—
115#14556503—21no—
116#14556503—21no—
117#14556503—21no—
118#14556503—21no—
119#14556501—21no—
120C4×#10596831D411yescharacteristic
121C4×#10596831D411yescharacteristic
122C4×#10596831C2311yescharacteristic
123C4×#10596831C2311yescharacteristic
124C4×#10596831C2311yescharacteristic
125C4×#10596831C2311yescharacteristic
126C8×Dic73—21no—
127C8×Dic73—21no—
128C8×Dic73—21no—
129C2×C42×C73C2311yescharacteristic
130C4⋊C8×C73C2×C411yescharacteristic
131C4⋊C8×C73C2×C411yescharacteristic
132C4⋊C8×C73C2311yescharacteristic
133C4⋊C8×C73C2311yescharacteristic
134C4⋊C8×C73C2311yescharacteristic
135C4⋊C8×C73C2311yescharacteristic
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138C22⋊C8×C73C2×C411yescharacteristic
139C22⋊C8×C73C2×C411yescharacteristic
140#97×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#11924028—22no—
145#11924028—22no—
146C2×Dic146C22×C411yescharacteristic
147C2×Dic146C22×C411yescharacteristic
148C2×D292C22×C411yescharacteristic
149C2×D292C22×C411yescharacteristic
150C2×C22⋊D73—21no—
151C2×C22⋊D73—21no—
152C2×C4×D73—21no—
153C2×C4×D73—21no—
154C2×C4×D73—21no—
155C2×C4×D73—21no—
156Dic292—22no—
157#11924017—22no—
158#11924017—22no—
159D584—22no—
160#11924011—42no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—41no—
164C2×#10596831—41no—
165C2×#10596831C2×D411yescharacteristic
166C2×#10596831C2×D411yescharacteristic
167C2×#10596831C2×D411yescharacteristic
168C2×#10596831C2×D411yescharacteristic
169C8×D73—42no—
170C8×D73—42no—
171C8×D73—42no—
172C4⋊Dic73C22×C411yescharacteristic
173C4⋊Dic73C22×C411yescharacteristic
174C4⋊Dic73C22×C411yescharacteristic
175C4⋊Dic73C22×C411yescharacteristic
176#11924007—21no—
177#11924007—21no—
178#11924007—21no—
179#11924007—21no—
180#11924007—21no—
181#11924007—21no—
182C22⋊Dic73—21no—
183C22⋊Dic73—21no—
184#11924005—21no—
185#11924005—21no—
186#11924005—21no—
187#11924005—21no—
188#11924005—21no—
189#11924005—21no—
190C4×Dic73—21no—
191C4×Dic73—21no—
192C4×Dic73—21no—
193C4×Dic73—21no—
194C22×C4×C73C22×C411yescharacteristic
195C22×C4×C73C2×D411yescharacteristic
196C22×C4×C73#4111yescharacteristic
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73C22×C411yescharacteristic
202C2×C8×C73C22×C411yescharacteristic
203C2×C8×C73C22×C411yescharacteristic
204C2×C8×C73C22×C411yescharacteristic
205C42×C73C22×C411yescharacteristic
206C42×C73C2×D411yescharacteristic
207C42×C73#4111yescharacteristic
208C42×C73C2411yescharacteristic
209C23×C73C4×D411yescharacteristic
210C22×D73—21no—
211C22×D73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—41no—
217C2×C4×C73C4×D411yescharacteristic
218C2×C4×C73C4×D411yescharacteristic
219C2×C4×C73C4×D411yescharacteristic
220C2×C4×C73C23×C411yescharacteristic
221C2×C4×C73C22×D411yescharacteristic
222C2×C4×C73C2×#4111yescharacteristic
223C22⋊D73—24no—
224C22⋊D73—42no—
225C2×Dic73—21no—
226C2×Dic73—21no—
227C2×Dic73—21no—
228C2×Dic73—21no—
229C2×Dic73—21no—
230C2×Dic73—21no—
231D292—21no—
232D292—21no—
233D292—21no—
234D292#13112yes—
235C4×D73—24no—
236C4×D73—42no—
237C4×D73—41no—
238C4×D73—41no—
239C4×D73—41no—
240C4×D73—41no—
241Dic146—21no—
242Dic146—21no—
243Dic146—21no—
244Dic146#13112yes—
245C8×C73—21no—
246C8×C73—21no—
247C8×C73—21no—
248C8×C73—21no—
249C8×C73—41no—
250C8×C73—41no—
251C8×C73—41no—
252C8×C73—41no—
253#10596831—21no—
254#10596831—21no—
255#10596831—21no—
256#10596831—21no—
257#10596831—41no—
258#10596831—41no—
259C22×C73—21no—
260C22×C73—21no—
261C22×C73—21no—
262C22×C73C2×C4×D411yescharacteristic
263C2×D73—22no—
264C2×D73—41no—
265C2×D73—41no—
266C2×D73—41no—
267C2×D73—41no—
268C2×D73—41no—
269C4×C73—21no—
270C4×C73—21no—
271C4×C73—21no—
272C4×C73—21no—
273C4×C73C2×#13111yescharacteristic
274C4×C73C2×#13111yescharacteristic
275C4×C73#57511yescharacteristic
276C4×C73#57511yescharacteristic
277Dic73—22no—
278Dic73—41no—
279Dic73—41no—
280Dic73—41no—
281Dic73—41no—
282Dic73—41no—
283#17909—731nomaximal, Sylow
284C2×C73—41no—
285C2×C73#292911yescharacteristic
286C2×C73#294311yescharacteristic
287C2×C73#295511yescharacteristic
288D73—42no—
289D73—81no—
290#3102—731no—
291#2966—731no—
292C8×#41—731no—
293#1588—731no—
294#1587—731no—
295#1586—731no—
296#1585—731no—
297#1580—731no—
298#1579—731no—
299SD16⋊C8—731no—
300SD16⋊C8—731no—
301#1572D7311yescharacteristic, complemented
302#1488—731no—
303#1482—731no—
304#1452—731no—
305C73#1790911yescharacteristic, complemented, Sylow
306#529—731no—
307C4×#41—731no—
308#485—731no—
309#482—731no—
310#479—731no—
311#478—731no—
312#464—731no—
313#463—731no—
314#452—731no—
315#449—731no—
316#446—731no—
317C8×Q8—731no—
318C8×Q8—731no—
319C8×Q8—731no—
320C4×Q16—731no—
321C4×SD16—731no—
322C4×SD16—731no—
323C4×D8—731no—
324#436—731no—
325#435—1461no—
326C8×D4—731no—
327C8×D4—731no—
328C8×D4—731no—
329C8×D4—1461no—
330C8×D4—1461no—
331C8×D4—1461no—
332#433—1461no—
333#432C2×D7311yescharacteristic
334#431—731no—
335#431—1461no—
336#431C2×D7311yescharacteristic
337#431C2×D7311yescharacteristic
338#405—1461no—
339C2×C4×C8—731no—
340C2×C4×C8—1461no—
341#335C2×D7311yescharacteristic
342#335C2×D7311yescharacteristic
343#334C2×D7311yescharacteristic
344#334C2×D7311yescharacteristic
345Q8⋊C8—731no—
346Q8⋊C8—731no—
347Q8⋊C8—731no—
348Q8⋊C8—731no—
349D4⋊C8—731no—
350D4⋊C8—731no—
351D4⋊C8—731no—
352D4⋊C8—731no—
353#322—731no—
354#322—731no—
355#322—731no—
356#322—731no—
357C2×#41—731no—
358C2×Q16—731no—
359C2×SD16—731no—
360C2×SD16—731no—
361C2×D8—731no—
362C2×M16—1461no—
363C22×C8—731no—
364C22×C8—731no—
365C22×C8—1461no—
366C22×C8—1461no—
367C22×C8—1461no—
368#126—1461no—
369#125—731no—
370#124—731no—
371#123—1461no—
372C22⋊Q8—731no—
373#121—731no—
374C4×Q8—731no—
375C4×Q8—731no—
376C4×Q8—731no—
377C4×D4—731no—
378C4×D4—731no—
379C4×D4—731no—
380C4×D4—1461no—
381C4×D4—1461no—
382C4×D4—1461no—
383#117—731no—
384#117—1461no—
385#117—1461no—
386C2×C42—1461no—
387C2×C42C22×D7311yescharacteristic
388#107—731no—
389#107—731no—
390#106—731no—
391#106—731no—
392C4⋊C8—1461no—
393C4⋊C8—1461no—
394C4⋊C8—1461no—
395C4⋊C8—1461no—
396C4⋊C8—1461no—
397C4⋊C8C4×D7311yescharacteristic
398C4⋊C8C4×D7311yescharacteristic
399C4⋊C8C22×D7311yescharacteristic
400C4⋊C8C22×D7311yescharacteristic
401C4⋊C8C22×D7311yescharacteristic
402C4⋊C8C22×D7311yescharacteristic
403#103—731no—
404#103—731no—
405#103—731no—
406#103—731no—
407#102—731no—
408#102—731no—
409#102—731no—
410#102—731no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—1461no—
414C22⋊C8—1461no—
415C22⋊C8—1461no—
416C22⋊C8—1461no—
417C22⋊C8—1461no—
418C22⋊C8C4×D7311yescharacteristic
419C22⋊C8C4×D7311yescharacteristic
420#97—21no—
421#97—1461no—
422C4×C8—21no—
423C4×C8—731no—
424C4×C8—731no—
425C4×C8—731no—
426C4×C8—731no—
427C4×C8—731no—
428C4×C8—731no—
429C4×C8—1461no—
430C4×C8—1461no—
431C4×C8—1461no—
432C4×C8C22×D7311yescharacteristic
433C4×C8C22×D7311yescharacteristic
434#41—1462no—
435#41—1462no—
436C2×Q8—731no—
437C2×Q8—731no—
438C2×D4—731no—
439C2×D4—731no—
440C2×D4—1461no—
441C2×D4—1461no—
442C22×C4—1461no—
443C22×C4—1461no—
444C22×C4—1461no—
445C22×C4—1461no—
446C22×C4C2×C4×D7311yescharacteristic
447C22×C4D4×D7311yescharacteristic
448C22×C4#1192402911yescharacteristic
449Q16—1462no—
450SD16—1462no—
451SD16—1462no—
452D8—1462no—
453M16—2922no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—2922no—
459C2×C8—2922no—
460C2×C8—2922no—
461C2×C8—2921no—
462C2×C8—2921no—
463C2×C8—731no—
464C2×C8—731no—
465C2×C8—731no—
466C2×C8—731no—
467C2×C8—1461no—
468C2×C8—1461no—
469C2×C8C2×C4×D7311yescharacteristic
470C2×C8C2×C4×D7311yescharacteristic
471C2×C8C2×C4×D7311yescharacteristic
472C2×C8C2×C4×D7311yescharacteristic
473C4⋊C4—731no—
474C4⋊C4—731no—
475C4⋊C4—731no—
476C4⋊C4—731no—
477C4⋊C4—1461no—
478C4⋊C4—1461no—
479C4⋊C4—1461no—
480C4⋊C4—1461no—
481C4⋊C4—1461no—
482C4⋊C4—1461no—
483C22⋊C4—1461no—
484C22⋊C4—1461no—
485C22⋊C4—1461no—
486C22⋊C4—1461no—
487C22⋊C4—1461no—
488C22⋊C4—1461no—
489C22⋊C4—1461no—
490C22⋊C4—1461no—
491C42—1461no—
492C42—1461no—
493C42—1461no—
494C42—1461no—
495C42C2×C4×D7311yescharacteristic
496C42D4×D7311yescharacteristic
497C42#1192402911yescharacteristic
498C42C23×D7311yescharacteristic
499C23—1461no—
500C23—1461no—
501C23#1455655311yescharacteristic
502Q8—732no—
503Q8—1461no—
504Q8—1461no—
505Q8—1461no—
506D4—2922no—
507D4—732no—
508D4—1464no—
509D4—1461no—
510D4—1461no—
511D4—1461no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—2922no—
518C2×C4—2921no—
519C2×C4—2921no—
520C2×C4—2921no—
521C2×C4—2921no—
522C2×C4—1464no—
523C2×C4—1461no—
524C2×C4—1461no—
525C2×C4—1461no—
526C2×C4—1461no—
527C2×C4—1461no—
528C2×C4—1461no—
529C2×C4#1455655311yescharacteristic
530C2×C4#1455655311yescharacteristic
531C2×C4#1455655311yescharacteristic
532C2×C4C22×C4×D7311yescharacteristic
533C2×C4C2×D4×D7311yescharacteristic
534C2×C4C2×#1192402911yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—2921no—
544C8—2921no—
545C8—1461no—
546C8—1461no—
547C8—1461no—
548C8—1461no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—2921no—
553C22—2921no—
554C22—2921no—
555C22—2921no—
556C22—2921no—
557C22—1462no—
558C22C2×#1455655311yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—2921no—
564C4—2921no—
565C4—2921no—
566C4—2921no—
567C4—2921no—
568C4—1462no—
569C4#131×D7311yescharacteristic
570C4#131×D7311yescharacteristic
571C4#1798938411yescharacteristic
572C4#1798938411yescharacteristic
573C2—41no—
574C2—2922no—
575C2—5841no—
576C2#2261862411yescharacteristic
577C2#2261873111yescharacteristic
578C2#2261883311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#1572C2
socleC22×C73C2×C4×D4
prime radical#17988734C4
cosocleC42×C73C24
hypercenter#1572D73
hypocenterC73#17909
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
2. #22618900C2semidirect
3. #22618887C2semidirect
4. #22608808C2semidirect
5. #22608801C2semidirect
6. #22608794C2semidirect
7. #22608787C2semidirect
8. #22608754C2semidirect
9. #22608749C2semidirect
10. #22608742C2semidirect
11. #22608742C2semidirect
12. #22608363C2semidirect
13. #22608337C2semidirect
14. #22608224C2semidirect
15. C73×#1572C2semidirect
301. #1572D73semidirect
305. C73#17909semidirect

Maximal subgroups

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

subgroupindex
#226199512
#226189002
#226188872
#226088082
#226088012
#226087942
#226087872
#226087542
#226087492
#226087422
#226083632
#226083372
#226082242
C73×#15722
#1790973