Finite Group Databasebeta

← #33096419

Subgroups — #33096419

Order 18688.

662 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618568C211yesmaximal, characteristic
2#22618567C211yesmaximal, characteristic
3C2×#17988612C211yesmaximal, characteristic
4#22610707C211yesmaximal, characteristic, complemented
5#22610706C211yesmaximal, characteristic, complemented
6#22610705C211yesmaximal, characteristic, complemented
7#22610705C211yesmaximal, characteristic, complemented
8#22610704C211yesmaximal, characteristic, complemented
9#22610703C211yesmaximal, characteristic, complemented
10#22610703C211yesmaximal, characteristic, complemented
11#22609972C211yesmaximal, characteristic
12#22609970C211yesmaximal, characteristic
13#22609968C211yesmaximal, characteristic
14#22609966C211yesmaximal, characteristic
15C73×#1950C211yesmaximal, characteristic, complemented
16C22×#11924011C2211yescharacteristic
17C22×C8×D73C2211yescharacteristic
18C2×#14556548C2211yescharacteristic
19#17988649—21no—
20#17988649—21no—
21#17988647—21no—
22#17988647—21no—
23#17988647—21no—
24#17988647—21no—
25#17988646—21no—
26#17988646—21no—
27C2×#14556527C2211yescharacteristic
28C2×#14556527C2211yescharacteristic
29C2×#14556526C2211yescharacteristic
30C2×#14556526C2211yescharacteristic
31C2×#14556526C2211yescharacteristic
32C2×#14556526C2211yescharacteristic
33#17988612C412yes—
34#17988612C412yes—
35#17988612C412yes—
36#17988612C412yes—
37#17988611C2211yescharacteristic
38#17988610C2211yescharacteristic
39#17988610C2211yescharacteristic
40C2×C4⋊#10596831C2211yescharacteristic
41C2×#14556520C2211yescharacteristic
42C2×#14556520C2211yescharacteristic
43#17988550C2211yescharacteristic
44#17988550C2211yescharacteristic
45#17988550C2211yescharacteristic
46#17988550C2211yescharacteristic
47C4×#11924012C2211yescharacteristic
48M16×Dic73C2211yescharacteristic
49M16×Dic73C2211yescharacteristic
50#17988352C2211yescharacteristic
51#17988352C2211yescharacteristic
52#17988351C2211yescharacteristic
53#17988351C2211yescharacteristic
54#17988351C2211yescharacteristic
55#17988351C2211yescharacteristic
56C2×#108×C73C2211yescharacteristic
57C2×#108×C73C2211yescharacteristic
58#423×C73C2211yescharacteristic
59C2×C4⋊C8×C73C2211yescharacteristic
60C4×M16×C73C2211yescharacteristic
61#341×C73C2211yescharacteristic
62#341×C73C2211yescharacteristic
63C22×C4×D73C2311yescharacteristic
64C2×#11924012C2311yescharacteristic
65C2×#11924012C2311yescharacteristic
66C2×#11924012C2311yescharacteristic
67C2×#11924012C2311yescharacteristic
68C2×#11924011—41no—
69C2×#11924011—41no—
70C2×#11924011C2×C412yes—
71C2×#11924011C2×C412yes—
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C2×C8×D73—41no—
75C2×C8×D73—41no—
76C2×C8×D73C2×C412yes—
77C2×C8×D73C2×C412yes—
78#14556548C2×C411yescharacteristic
79#14556548C2×C411yescharacteristic
80#14556548C2×C411yescharacteristic
81#14556548C2×C411yescharacteristic
82#14556548D411yescharacteristic
83#14556548D411yescharacteristic
84#14556548D411yescharacteristic
85#14556548D411yescharacteristic
86C2×#11924007Q811yescharacteristic
87C2×#11924007Q811yescharacteristic
88C2×#11924005Q811yescharacteristic
89C2×#11924005Q811yescharacteristic
90C2×C4×Dic73C2311yescharacteristic
91#14556527—41no—
92#14556527—41no—
93#14556526—41no—
94#14556526—41no—
95#14556526—41no—
96#14556526—41no—
97C4⋊#10596831—21no—
98C4⋊#10596831—21no—
99C4⋊#10596831C2×C412yes—
100C4⋊#10596831C2×C412yes—
101#14556520—21no—
102#14556520—21no—
103#14556520—21no—
104#14556520—21no—
105#14556520C2×C412yes—
106#14556520C2×C412yes—
107#14556520C2×C412yes—
108#14556520C2×C412yes—
109#14556503—21no—
110#14556503—21no—
111#14556503—21no—
112#14556503—21no—
113#14556503—21no—
114#14556503—21no—
115#14556503—21no—
116#14556503—21no—
117#14556502—21no—
118#14556501—21no—
119#14556501—21no—
120C4×#10596831—21no—
121C8×Dic73—21no—
122C8×Dic73—21no—
123C2×M16×C73C2311yescharacteristic
124C2×M16×C73C2311yescharacteristic
125C2×M16×C73C2311yescharacteristic
126C2×M16×C73C2311yescharacteristic
127C22×C8×C73C2311yescharacteristic
128C22×C8×C73C2311yescharacteristic
129C2×C42×C73C2311yescharacteristic
130#108×C73—41no—
131#108×C73—41no—
132C4⋊C8×C73—21no—
133C4⋊C8×C73—21no—
134C4⋊C8×C73C2×C412yes—
135C4⋊C8×C73C2×C412yes—
136#97×C73—21no—
137C4×C8×C73—21no—
138C23×D73C2×Q811yescharacteristic
139C22×Dic73C2×Q811yescharacteristic
140C22×Dic73C2×Q811yescharacteristic
141C22×Dic73C2×Q811yescharacteristic
142C2×C4×D73—21no—
143C2×C4×D73—21no—
144C2×C4×D73—21no—
145C2×C4×D73—21no—
146C2×C4×D73C22×C411yescharacteristic
147C2×C4×D73C22×C411yescharacteristic
148C2×C4×D73C2×D411yescharacteristic
149C2×C4×D73C2×D411yescharacteristic
150#11924012—21no—
151#11924012—21no—
152#11924012—21no—
153#11924012—21no—
154#11924012—21no—
155#11924012—21no—
156#11924012—21no—
157#11924012—21no—
158#11924011—42no—
159#11924011—42no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—21no—
165C2×#10596831—21no—
166C2×#10596831—21no—
167C2×#10596831—21no—
168C2×#10596831C22×C412yes—
169C2×#10596831C22×C412yes—
170C8×D73—42no—
171C8×D73—42no—
172#11924007C4⋊C411yescharacteristic
173#11924007C4⋊C411yescharacteristic
174#11924007C4⋊C411yescharacteristic
175#11924007C4⋊C411yescharacteristic
176#11924007C4⋊C411yescharacteristic
177#11924007C4⋊C411yescharacteristic
178#11924007C4⋊C411yescharacteristic
179#11924007C4⋊C411yescharacteristic
180#11924005C4⋊C411yescharacteristic
181#11924005C4⋊C411yescharacteristic
182#11924005C4⋊C411yescharacteristic
183#11924005C4⋊C411yescharacteristic
184#11924005C4⋊C411yescharacteristic
185#11924005C4⋊C411yescharacteristic
186#11924005C4⋊C411yescharacteristic
187#11924005C4⋊C411yescharacteristic
188C4×Dic73C22×C411yescharacteristic
189C4×Dic73C22×C411yescharacteristic
190C4×Dic73C2×D411yescharacteristic
191C4×Dic73C2×D411yescharacteristic
192C22×C4×C73C2×Q811yescharacteristic
193C22×C4×C73C2×Q811yescharacteristic
194C22×C4×C73C2411yescharacteristic
195M16×C73—21no—
196M16×C73—21no—
197M16×C73—21no—
198M16×C73—21no—
199M16×C73—21no—
200M16×C73—21no—
201M16×C73—21no—
202M16×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73C22×C412yes—
212C2×C8×C73C22×C412yes—
213C42×C73C22×C411yescharacteristic
214C42×C73C22×C411yescharacteristic
215C42×C73C2×D411yescharacteristic
216C42×C73C2×D411yescharacteristic
217C23×C73C22×Q811yescharacteristic
218C22×D73—21no—
219C22×D73—21no—
220C22×D73—41no—
221C22×D73—41no—
222C22×D73C2×C4⋊C411yescharacteristic
223C22×D73C2×C4⋊C411yescharacteristic
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73C2×C4⋊C411yescharacteristic
227C2×C4×C73C2×C4⋊C411yescharacteristic
228C2×C4×C73C2×C4⋊C411yescharacteristic
229C2×C4×C73C2×C4⋊C411yescharacteristic
230C2×C4×C73C23×C411yescharacteristic
231C2×C4×C73C22×D411yescharacteristic
232C2×C4×C73H(5,𝔽2)11yescharacteristic
233C2×C4×C73H(5,𝔽2)11yescharacteristic
234C2×C4×C732−1+411yescharacteristic
235C2×C4×C732−1+411yescharacteristic
236C2×Dic73—21no—
237C2×Dic73—21no—
238C2×Dic73—41no—
239C2×Dic73—41no—
240C2×Dic73C2×C4⋊C411yescharacteristic
241C2×Dic73C2×C4⋊C411yescharacteristic
242C2×Dic73C2×C4⋊C411yescharacteristic
243C2×Dic73C2×C4⋊C411yescharacteristic
244C2×Dic73C2×C4⋊C411yescharacteristic
245C2×Dic73C2×C4⋊C411yescharacteristic
246C4×D73—21no—
247C4×D73—21no—
248C4×D73—21no—
249C4×D73—21no—
250C4×D73—21no—
251C4×D73—21no—
252C4×D73—21no—
253C4×D73—21no—
254C8×C73—22no—
255C8×C73—22no—
256C8×C73—41no—
257C8×C73—41no—
258C8×C73—41no—
259C8×C73—41no—
260#10596831—22no—
261#10596831—22no—
262#10596831—41no—
263#10596831—41no—
264#10596831—41no—
265#10596831—41no—
266C22×C73—21no—
267C22×C73—21no—
268C22×C73C22×C4⋊C411yescharacteristic
269C22×C73#54411yescharacteristic
270C22×C73#54411yescharacteristic
271C2×D73—21no—
272C2×D73—21no—
273C2×D73—21no—
274C2×D73—21no—
275C2×D73—21no—
276C2×D73—21no—
277C2×D73—42no—
278C2×D73—42no—
279C4×C73—21no—
280C4×C73—21no—
281C4×C73—21no—
282C4×C73—21no—
283C4×C73#51811yescharacteristic
284C4×C73#51911yescharacteristic
285C4×C73#53711yescharacteristic
286C4×C73#53711yescharacteristic
287Dic73—21no—
288Dic73—21no—
289Dic73—21no—
290Dic73—21no—
291Dic73—21no—
292Dic73—21no—
293#21971—731nomaximal, Sylow
294C2×C73—21no—
295C2×C73—21no—
296C2×C73#231611yescharacteristic
297C2×C73#291611yescharacteristic
298C2×C73#291611yescharacteristic
299D73—41no—
300D73—41no—
301#2921—731no—
302#2921—731no—
303C2×#424—731no—
304#1950—731no—
305#1950—731no—
306#1950—731no—
307#1950—731no—
308#1950—731no—
309#1950—731no—
310#1950—731no—
311#1950D7311yescharacteristic, complemented
312#1811—731no—
313#1811—731no—
314#1810—731no—
315#1810—731no—
316C73#2197111yescharacteristic, complemented, Sylow
317C22×M16—731no—
318C23×C8—731no—
319C2×#117—731no—
320#433—1461no—
321#433—1461no—
322#433—1461no—
323#433—1461no—
324#433—1461no—
325#433—1461no—
326#433—1461no—
327#433—1461no—
328C2×#108—731no—
329C2×#108—731no—
330C2×#108—731no—
331C2×#108—731no—
332C2×#108—731no—
333C2×#108—731no—
334C2×#108C2×D7311yescharacteristic
335C2×#108C2×D7311yescharacteristic
336#424—732no—
337#424—732no—
338#424—732no—
339#424—732no—
340#423—731no—
341#423—731no—
342#423—731no—
343#423C2×D7311yescharacteristic
344C2×C4⋊C8—731no—
345C2×C4⋊C8—731no—
346C2×C4⋊C8—731no—
347C2×C4⋊C8C2×D7311yescharacteristic
348#407—731no—
349#407—731no—
350#407—731no—
351#407—731no—
352C4×M16—731no—
353C4×M16—731no—
354C4×M16—731no—
355C4×M16C2×D7311yescharacteristic
356#341—731no—
357#341—731no—
358#341—731no—
359#341—731no—
360#341—731no—
361#341—731no—
362#341C2×D7311yescharacteristic
363#341C2×D7311yescharacteristic
364C23×C4—731no—
365C2×M16—2921no—
366C2×M16—2921no—
367C2×M16—732no—
368C2×M16—732no—
369C2×M16—731no—
370C2×M16—731no—
371C2×M16—731no—
372C2×M16—731no—
373C2×M16C22×D7311yescharacteristic
374C2×M16C22×D7311yescharacteristic
375C2×M16C22×D7311yescharacteristic
376C2×M16C22×D7311yescharacteristic
377C22×C8—2921no—
378C22×C8—2921no—
379C22×C8—732no—
380C22×C8—732no—
381C22×C8—731no—
382C22×C8—731no—
383C22×C8C22×D7311yescharacteristic
384C22×C8C22×D7311yescharacteristic
385#117—731no—
386#117—731no—
387#117—731no—
388#117—731no—
389#117—731no—
390#117—731no—
391#117—731no—
392#117—731no—
393C2×C4⋊C4—731no—
394C2×C4⋊C4—731no—
395C2×C22⋊C4—731no—
396C2×C22⋊C4—731no—
397C2×C42—731no—
398C2×C42C22×D7311yescharacteristic
399#108—41no—
400#108—41no—
401#108—2921no—
402#108—2921no—
403#108—2921no—
404#108—2921no—
405#108—2921no—
406#108—2921no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8—732no—
410C4⋊C8—732no—
411C4⋊C8—732no—
412C4⋊C8—732no—
413C4⋊C8—732no—
414C4⋊C8—732no—
415C4⋊C8—1461no—
416C4⋊C8—1461no—
417C4⋊C8—1461no—
418C4⋊C8—1461no—
419C4⋊C8—1461no—
420C4⋊C8—1461no—
421C4⋊C8C4×D7312yes—
422C4⋊C8C4×D7312yes—
423C22⋊C8—1461no—
424C22⋊C8—1461no—
425C22⋊C8—1461no—
426C22⋊C8—1461no—
427C22⋊C8—1461no—
428C22⋊C8—1461no—
429C22⋊C8—1461no—
430C22⋊C8—1461no—
431#97—21no—
432#97—1461no—
433#97—1461no—
434#97—1461no—
435C4×C8—21no—
436C4×C8—1461no—
437C4×C8—1461no—
438C4×C8—1461no—
439C24—731no—
440C22×C4—731no—
441C22×C4—731no—
442C22×C4—731no—
443C22×C4—731no—
444C22×C4—731no—
445C22×C4—731no—
446C22×C4—731no—
447C22×C4—1461no—
448C22×C4—1461no—
449C22×C4—1461no—
450C22×C4—1461no—
451C22×C4Q8×D7311yescharacteristic
452C22×C4Q8×D7311yescharacteristic
453C22×C4C23×D7311yescharacteristic
454M16—21no—
455M16—21no—
456M16—21no—
457M16—21no—
458M16—21no—
459M16—21no—
460M16—21no—
461M16—21no—
462M16—2922no—
463M16—2922no—
464M16—1461no—
465M16—1461no—
466M16—1461no—
467M16—1461no—
468M16—1461no—
469M16—1461no—
470M16—1461no—
471M16—1461no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—2922no—
481C2×C8—2922no—
482C2×C8—732no—
483C2×C8—732no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8—1461no—
491C2×C8—1461no—
492C2×C8C2×C4×D7312yes—
493C2×C8C2×C4×D7312yes—
494C4⋊C4—731no—
495C4⋊C4—731no—
496C4⋊C4—731no—
497C4⋊C4—731no—
498C4⋊C4—731no—
499C4⋊C4—731no—
500C4⋊C4—731no—
501C4⋊C4—731no—
502C22⋊C4—731no—
503C22⋊C4—731no—
504C22⋊C4—731no—
505C22⋊C4—731no—
506C22⋊C4—731no—
507C22⋊C4—731no—
508C22⋊C4—731no—
509C22⋊C4—731no—
510C42—731no—
511C42—731no—
512C42—731no—
513C42—731no—
514C42C2×C4×D7311yescharacteristic
515C42C2×C4×D7311yescharacteristic
516C42D4×D7311yescharacteristic
517C42D4×D7311yescharacteristic
518C23—2921no—
519C23—2921no—
520C23—731no—
521C23—731no—
522C23—1461no—
523C23—1461no—
524C23C2×Q8×D7311yescharacteristic
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—2921no—
528C2×C4—2921no—
529C2×C4—731no—
530C2×C4—731no—
531C2×C4—731no—
532C2×C4—731no—
533C2×C4—731no—
534C2×C4—731no—
535C2×C4—1461no—
536C2×C4—1461no—
537C2×C4—1461no—
538C2×C4—1461no—
539C2×C4—1461no—
540C2×C4—1461no—
541C2×C4—1461no—
542C2×C4—1461no—
543C2×C4—1461no—
544C2×C4—1461no—
545C2×C4C4⋊C4×D7311yescharacteristic
546C2×C4C4⋊C4×D7311yescharacteristic
547C2×C4C4⋊C4×D7311yescharacteristic
548C2×C4C4⋊C4×D7311yescharacteristic
549C2×C4C22×C4×D7311yescharacteristic
550C2×C4C2×D4×D7311yescharacteristic
551C2×C4#1455663611yescharacteristic
552C2×C4#1455663711yescharacteristic
553C2×C4#1455663811yescharacteristic
554C2×C4#1455663911yescharacteristic
555C8—22no—
556C8—22no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—2921no—
562C8—2921no—
563C8—2921no—
564C8—2921no—
565C8—1462no—
566C8—1462no—
567C22—21no—
568C22—21no—
569C22—2922no—
570C22—2922no—
571C22—1461no—
572C22—1461no—
573C22—1461no—
574C22—1461no—
575C22—1461no—
576C22—1461no—
577C22C2×C4⋊C4×D7311yescharacteristic
578C22#1798921411yescharacteristic
579C22#1798921711yescharacteristic
580C4—21no—
581C4—21no—
582C4—21no—
583C4—21no—
584C4—1461no—
585C4—1461no—
586C4—1461no—
587C4—1461no—
588C4—1461no—
589C4—1461no—
590C4#1798905911yescharacteristic
591C4#1798906311yescharacteristic
592C4#1798916611yescharacteristic
593C4#1798916711yescharacteristic
594C2—21no—
595C2—21no—
596C2—2921no—
597C2—2921no—
598C2#2261254611yescharacteristic
599C2#2261853911yescharacteristic
600C2#2261854111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1950C2
socleC22×C73C22×C4⋊C4
prime radicalC23×D73C2×Q8
cosocleC22×C4×C73C24
hypercenter#1950D73
hypocenterC73#21971
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
4. #22610707C2semidirect
5. #22610706C2semidirect
6. #22610705C2semidirect
7. #22610705C2semidirect
8. #22610704C2semidirect
9. #22610703C2semidirect
10. #22610703C2semidirect
15. C73×#1950C2semidirect
311. #1950D73semidirect
316. C73#21971semidirect

Maximal subgroups

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

subgroupindex
#226185682
#226185672
C2×#179886122
#226107072
#226107062
#226107052
#226107042
#226107032
#226099722
#226099702
#226099682
#226099662
C73×#19502
#2197173