Finite Group Databasebeta

← #33949806

Subgroups — #33949806

Order 18688.

2038 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623130C211yesmaximal, characteristic
2#22618599C213yesmaximal, complemented
3#22618596C213yesmaximal, complemented
4#22618588C213yesmaximal, complemented
5#22618588C213yesmaximal, complemented
6#22618581C213yesmaximal, complemented
7#22618574C213yesmaximal, complemented
8#22618568C213yesmaximal, complemented
9C2×#17988647C213yesmaximal, complemented
10#22618499C211yesmaximal, characteristic, complemented
11#22618378C211yesmaximal, characteristic
12#22618378C211yesmaximal, characteristic
13#22618357C211yesmaximal, characteristic, complemented
14#131×Dic73C211yesmaximal, characteristic, complemented
15C73×#2906C211yesmaximal, characteristic, complemented
16C2×#41×D73C2211yescharacteristic
17C2×#14556598C2211yescharacteristic
18C2×#14556598C2211yescharacteristic
19#17989069C411yescharacteristic
20#17989069C411yescharacteristic
21#17989066C413yes—
22#17989066C413yes—
23#17989063C411yescharacteristic
24#17989063C411yescharacteristic
25#17989059C413yes—
26#17989059C413yes—
27#41×Dic73C2211yescharacteristic
28C4×#11924028C2213yes—
29#17989055C2213yes—
30C2×#14556548C2213yes—
31#117×D73C2213yes—
32#17988647C2211yescharacteristic
33#17988647C2213yes—
34#17988647C2213yes—
35#17988647C2213yes—
36#17988647C2216yes—
37#17988647C2213yescomplemented
38#17988647C2213yescomplemented
39#17988647C2213yescomplemented
40#17988647C2213yescomplemented
41#17988647C2216yescomplemented
42#17988647C2216yescomplemented
43#17988643C2216yescomplemented
44#17988643C2216yescomplemented
45#17988639C2216yescomplemented
46#17988639C2216yescomplemented
47#17988614C2213yescomplemented
48#17988614C2213yescomplemented
49#17988611C2213yescomplemented
50C2×C4⋊#10596831C2213yescomplemented
51#17988555C2213yes—
52#17988555C2213yes—
53#17988553C2213yes—
54#17988553C2213yes—
55#17988550C2213yes—
56#17988550C2213yes—
57C2×#14556503C2213yes—
58C2×#14556503C2213yes—
59#17988545C2213yescomplemented
60#17988545C2213yescomplemented
61#17988542C2213yescomplemented
62#17988542C2213yescomplemented
63M16×Dic73C2213yescomplemented
64M16×Dic73C2213yescomplemented
65C2×#14556501C2213yescomplemented
66C2×C8×Dic73C2213yescomplemented
67C2×#131×C73C2211yescharacteristic
68C2×#131×C73C2211yescharacteristic
69C4×#41×C73C2211yescharacteristic
70#424×C73C2213yescomplemented
71#424×C73C2213yescomplemented
72#423×C73C2213yescomplemented
73C2×C4⋊C8×C73C2213yescomplemented
74C2×#11924029C2×C411yescharacteristic
75C2×#11924028C2313yes—
76C2×#11924027C2×C413yes—
77#41×D73—24no—
78#41×D73—24no—
79C2×Q8×D73C2×C411yescharacteristic
80C2×D4×D73C2×C413yes—
81C22×C4×D73C2313yes—
82#14556598—24no—
83#14556598—24no—
84C2×#11924012C2313yes—
85C2×#11924012C2313yes—
86C22×#10596831C2313yes—
87C22×#10596831C2313yes—
88Q8×Dic73C2×C411yescharacteristic
89Q8×Dic73C2×C411yescharacteristic
90C4×Dic146C2×C413yes—
91C4×Dic146C2×C413yes—
92#14556556C2×C413yes—
93#14556556C2×C413yes—
94C4×D292C2×C413yes—
95C4×D292C2×C413yes—
96D4×Dic73C2×C413yes—
97D4×Dic73C2×C413yes—
98#14556553C2×C413yes—
99#14556553C2×C413yes—
100C4×C22⋊D73C2×C416yes—
101C4×C22⋊D73C2×C416yes—
102#14556551C2×C416yes—
103#14556551C2×C416yes—
104#14556550C2313yes—
105#14556549C2×C413yes—
106#14556549C2×C413yes—
107#14556548C2×C413yes—
108#14556548C2×C413yes—
109#14556548C2×C413yes—
110#14556548C2×C413yes—
111#14556548C2313yes—
112#14556548C2311yescharacteristic
113#14556548C2313yes—
114#14556548C2313yes—
115#14556547C2×C416yes—
116C2×#11924007C2×C413yes—
117C2×#11924007C2×C413yes—
118C4⋊C4×D73C2×C413yes—
119C4⋊C4×D73C2×C413yes—
120C2×#11924005C2×C413yes—
121C2×#11924005C2×C413yes—
122C22⋊C4×D73C2×C416yes—
123C2×C4×Dic73C2313yes—
124C42×D73C2316yes—
125C4⋊#10596831C2311yescharacteristic
126C4⋊#10596831C2313yes—
127C4⋊#10596831C2313yes—
128C4⋊#10596831C2313yes—
129C4⋊#10596831C2316yes—
130#14556503C2313yes—
131#14556503C2313yes—
132#14556503C2316yes—
133#14556503C2316yes—
134#14556503C2313yes—
135#14556503C2313yes—
136#14556503C2311yescharacteristic
137#14556503C2311yescharacteristic
138#14556503C2313yes—
139#14556503C2313yes—
140#14556501C2313yes—
141#14556501C2313yes—
142#14556501C2316yes—
143#14556501C2311yescharacteristic
144#14556501C2313yes—
145C8×Dic73C2313yes—
146C8×Dic73C2313yes—
147C8×Dic73C2316yes—
148C8×Dic73C2311yescharacteristic
149C8×Dic73C2313yes—
150C2×#41×C73C2311yescharacteristic
151#131×C73—24no—
152#131×C73—24no—
153C2×M16×C73C2313yes—
154C2×M16×C73C2313yes—
155C22×C8×C73C2313yes—
156C22×C8×C73C2313yes—
157C4×Q8×C73C2×C411yescharacteristic
158C4×Q8×C73C2×C411yescharacteristic
159C4×D4×C73C2×C413yes—
160C4×D4×C73C2×C413yes—
161#117×C73C2313yes—
162C2×C42×C73C2313yes—
163C4⋊C8×C73C2313yes—
164C4⋊C8×C73C2316yes—
165C4⋊C8×C73C2313yes—
166C4⋊C8×C73C2311yescharacteristic
167C4⋊C8×C73C2313yes—
168C23×D73C22×C413yes—
169#11924029—24no—
170#11924028—26no—
171#11924028—26no—
172#11924027—212no—
173C2×Dic146C22×C413yes—
174Q8×D73—24no—
175C2×D292C22×C413yes—
176C2×C22⋊D73C22×C416yes—
177D4×D73—212no—
178C22×Dic73C22×C413yes—
179C22×Dic73C22×C413yes—
180C22×Dic73C22×C413yes—
181C2×C4×D73—26no—
182C2×C4×D73—26no—
183C2×C4×D73C22×C413yes—
184C2×C4×D73C22×C413yes—
185C2×C4×D73C22×C416yes—
186C2×C4×D73C22×C416yes—
187C2×C4×D73C2413yes—
188C2×C4×D73C2411yescharacteristic
189#11924012—26no—
190#11924012—26no—
191C2×#10596831—26no—
192C2×#10596831—26no—
193C2×#10596831C2411yescharacteristic
194C2×#10596831C2413yes—
195C2×#10596831C2413yes—
196C2×#10596831C2411yescharacteristic
197C4⋊Dic73C22×C413yes—
198C4⋊Dic73C22×C413yes—
199#11924007C22×C413yes—
200#11924007C22×C413yes—
201#11924007C22×C411yescharacteristic
202#11924007C22×C411yescharacteristic
203#11924007C22×C413yes—
204#11924007C22×C413yes—
205#11924007C22×C413yes—
206#11924007C22×C413yes—
207C22⋊Dic73C22×C416yes—
208#11924005C22×C413yes—
209#11924005C22×C413yes—
210#11924005C22×C411yescharacteristic
211#11924005C22×C411yescharacteristic
212#11924005C22×C413yes—
213#11924005C22×C413yes—
214#11924005C22×C413yes—
215#11924005C22×C413yes—
216C4×Dic73C22×C416yes—
217C4×Dic73C22×C416yes—
218C4×Dic73C22×C413yes—
219C4×Dic73C22×C413yes—
220C4×Dic73C2413yes—
221C4×Dic73C2411yescharacteristic
222#41×C73#4114yes—
223#41×C73#4114yes—
224C2×Q8×C73C22×C411yescharacteristic
225C2×D4×C73C22×C413yes—
226C22×C4×C73C22×C413yes—
227C22×C4×C73C22×C413yes—
228C22×C4×C73C2413yes—
229M16×C73—26no—
230M16×C73—26no—
231C2×C8×C73—26no—
232C2×C8×C73—26no—
233C2×C8×C73C2411yescharacteristic
234C2×C8×C73C2411yescharacteristic
235C2×C8×C73C2413yes—
236C2×C8×C73C2413yes—
237C4⋊C4×C73C22×C413yes—
238C4⋊C4×C73C22×C413yes—
239C22⋊C4×C73C22×C416yes—
240C42×C73C22×C413yes—
241C42×C73C22×C413yes—
242C42×C73C2411yescharacteristic
243C42×C73C2413yes—
244C23×C73C23×C413yes—
245C22×D73—26no—
246C22×D73—43no—
247C22×D73—43no—
248C22×D73C23×C411yescharacteristic
249C22×D73C23×C413yes—
250Q8×C73#11714yes—
251D4×C73#117112yes—
252C2×C4×C73—43no—
253C2×C4×C73—43no—
254C2×C4×C73C23×C411yescharacteristic
255C2×C4×C73C23×C411yescharacteristic
256C2×C4×C73C23×C413yes—
257C2×C4×C73C23×C413yes—
258C2×C4×C73C23×C413yes—
259C2×C4×C73C2×#4116yes—
260C2×C4×C73C2×#4116yes—
261C2×C4×C73C2511yescharacteristic
262C22⋊D73—212no—
263C2×Dic73—26no—
264C2×Dic73—43no—
265C2×Dic73—43no—
266C2×Dic73C23×C413yes—
267C2×Dic73C23×C411yescharacteristic
268C2×Dic73C23×C411yescharacteristic
269C2×Dic73C23×C413yes—
270C2×Dic73C23×C413yes—
271C2×Dic73C23×C411yescharacteristic
272D292—26no—
273C4×D73—26no—
274C4×D73—26no—
275C4×D73—21no—
276C4×D73—21no—
277C4×D73—23no—
278C4×D73—23no—
279C4×D73—46no—
280C4×D73—46no—
281Dic146—26no—
282C8×C73—21no—
283C8×C73—21no—
284C8×C73—23no—
285C8×C73—23no—
286#10596831—21no—
287#10596831—21no—
288#10596831—23no—
289#10596831—23no—
290C22×C73—23no—
291C22×C73—23no—
292C22×C73C2×#11716yes—
293C22×C73C24×C411yescharacteristic
294C2×D73—21no—
295C2×D73—23no—
296C2×D73—23no—
297C2×D73—23no—
298C2×D73—21no—
299C2×D73—21no—
300C2×D73—86no—
301C4×C73—23no—
302C4×C73—23no—
303C4×C73—21no—
304C4×C73—21no—
305C4×C73C2×#11716yes—
306C4×C73C22×#4111yescharacteristic
307C4×C73C22×#4111yescharacteristic
308Dic73—23no—
309Dic73—21no—
310Dic73—23no—
311Dic73—23no—
312Dic73—21no—
313Dic73—21no—
314#60129—731nomaximal, Sylow
315C2×C73—26no—
316C2×C73C22×#11711yescharacteristic
317C2×C73#357311yescharacteristic
318C2×C73#357311yescharacteristic
319D73—43no—
320D73—41no—
321#3428—731no—
322#2925—733no—
323#2925—733no—
324#2924—733no—
325#2924—733no—
326#2923—733no—
327#2922—733no—
328#2921—733no—
329C2×#433—733no—
330#2906—731no—
331#2906D7311yescharacteristic, complemented
332#2880—731no—
333#2880—731no—
334#2875—731no—
335C4×#131—731no—
336C73#6012911yescharacteristic, complemented, Sylow
337C22×#41—731no—
338C2×#131—731no—
339C2×#131—731no—
340C2×#131C2×D7311yescharacteristic
341C2×#131C2×D7311yescharacteristic
342#520—731no—
343#520—731no—
344#520—733no—
345#520—733no—
346#519—731no—
347#519—731no—
348#518—733no—
349#518—733no—
350C4×#41—731no—
351C4×#41—733no—
352C4×#41—733no—
353C4×#41C2×D7311yescharacteristic
354C2×#117—733no—
355C2×#117—733no—
356#433—731no—
357#433—733no—
358#433—733no—
359#433—733no—
360#433—736no—
361#433—733no—
362#433—733no—
363#433—733no—
364#433—733no—
365#433—736no—
366#433—736no—
367#432—736no—
368#432—736no—
369#431—736no—
370#431—736no—
371#424—733no—
372#424—733no—
373#424C2×D7313yescomplemented
374#424C2×D7313yescomplemented
375#423—733no—
376#423C2×D7313yescomplemented
377C2×C4⋊C8—733no—
378C2×C4⋊C8C2×D7313yescomplemented
379#408—733no—
380#408—733no—
381#408—733no—
382#408—733no—
383#407—733no—
384#407—733no—
385C2×C22⋊C8—733no—
386C2×C22⋊C8—733no—
387#405—733no—
388#405—733no—
389#405—733no—
390#405—733no—
391C4×M16—733no—
392C4×M16—733no—
393C2×#97—733no—
394C2×C4×C8—733no—
395C2×#41—731no—
396C2×#41—733no—
397C2×#41—733no—
398C2×#41—1464no—
399C2×#41—1464no—
400C2×#41C22×D7311yescharacteristic
401C22×Q8—731no—
402C22×D4—733no—
403C23×C4—733no—
404#131—24no—
405#131—24no—
406#131—1464no—
407#131—1464no—
408C2×M16—733no—
409C2×M16—733no—
410C2×M16C22×D7313yes—
411C2×M16C22×D7313yes—
412C22×C8—733no—
413C22×C8—733no—
414C22×C8C22×D7313yes—
415C22×C8C22×D7313yes—
416C4×Q8—731no—
417C4×Q8—731no—
418C4×Q8—733no—
419C4×Q8—733no—
420C4×Q8—733no—
421C4×Q8—733no—
422C4×Q8C4×D7311yescharacteristic
423C4×Q8C4×D7311yescharacteristic
424C4×D4—733no—
425C4×D4—733no—
426C4×D4—736no—
427C4×D4—736no—
428C4×D4—733no—
429C4×D4—733no—
430C4×D4—736no—
431C4×D4—736no—
432C4×D4—733no—
433C4×D4—733no—
434C4×D4C4×D7313yes—
435C4×D4C4×D7313yes—
436#117—733no—
437#117—733no—
438#117—733no—
439#117—736no—
440#117—733no—
441#117—733no—
442#117—733no—
443#117—733no—
444#117—733no—
445#117—731no—
446#117—733no—
447#117—733no—
448#117C22×D7313yes—
449C2×C4⋊C4—733no—
450C2×C4⋊C4—733no—
451C2×C4⋊C4—733no—
452C2×C4⋊C4—733no—
453C2×C22⋊C4—733no—
454C2×C22⋊C4—733no—
455C2×C22⋊C4—736no—
456C2×C42—733no—
457C2×C42—736no—
458C2×C42C22×D7313yes—
459C4⋊C8—731no—
460C4⋊C8—733no—
461C4⋊C8—733no—
462C4⋊C8—733no—
463C4⋊C8—736no—
464C4⋊C8C22×D7311yescharacteristic
465C4⋊C8C22×D7313yes—
466C4⋊C8C22×D7313yes—
467C4⋊C8C22×D7313yes—
468C4⋊C8C22×D7316yes—
469C22⋊C8—731no—
470C22⋊C8—731no—
471C22⋊C8—733no—
472C22⋊C8—733no—
473C22⋊C8—733no—
474C22⋊C8—733no—
475C22⋊C8—733no—
476C22⋊C8—733no—
477C22⋊C8—736no—
478C22⋊C8—736no—
479#97—731no—
480#97—733no—
481#97—733no—
482#97—733no—
483#97—736no—
484C4×C8—731no—
485C4×C8—733no—
486C4×C8—733no—
487C4×C8—733no—
488C4×C8—736no—
489C24—733no—
490#41—1464no—
491#41—14612no—
492#41—1466no—
493#41—1466no—
494#41#1192402714yes—
495#41#1192402914yes—
496C2×Q8—733no—
497C2×Q8—1464no—
498C2×Q8C2×C4×D7311yescharacteristic
499C2×D4—736no—
500C2×D4—733no—
501C2×D4—14612no—
502C2×D4C2×C4×D7313yes—
503C22×C4—733no—
504C22×C4—733no—
505C22×C4—736no—
506C22×C4—736no—
507C22×C4—733no—
508C22×C4—733no—
509C22×C4—733no—
510C22×C4—733no—
511C22×C4—731no—
512C22×C4—1466no—
513C22×C4—1466no—
514C22×C4C2×C4×D7313yes—
515C22×C4C2×C4×D7313yes—
516C22×C4C23×D7313yes—
517M16—26no—
518M16—26no—
519M16—1466no—
520M16—1466no—
521C2×C8—26no—
522C2×C8—26no—
523C2×C8—731no—
524C2×C8—733no—
525C2×C8—733no—
526C2×C8—731no—
527C2×C8—1466no—
528C2×C8—1466no—
529C2×C8C23×D7311yescharacteristic
530C2×C8C23×D7313yes—
531C2×C8C23×D7313yes—
532C2×C8C23×D7311yescharacteristic
533C4⋊C4—733no—
534C4⋊C4—733no—
535C4⋊C4—731no—
536C4⋊C4—731no—
537C4⋊C4—733no—
538C4⋊C4—733no—
539C4⋊C4—733no—
540C4⋊C4—733no—
541C4⋊C4—733no—
542C4⋊C4—733no—
543C4⋊C4C2×C4×D7313yes—
544C4⋊C4C2×C4×D7313yes—
545C22⋊C4—736no—
546C22⋊C4—733no—
547C22⋊C4—733no—
548C22⋊C4—731no—
549C22⋊C4—731no—
550C22⋊C4—733no—
551C22⋊C4—733no—
552C22⋊C4—733no—
553C22⋊C4—733no—
554C22⋊C4C2×C4×D7316yes—
555C42—733no—
556C42—733no—
557C42—736no—
558C42—736no—
559C42—733no—
560C42—731no—
561C42C2×C4×D7313yes—
562C42C2×C4×D7313yes—
563C42C23×D7313yes—
564C42C23×D7311yescharacteristic
565C23—2923no—
566C23—2923no—
567C23—731no—
568C23—733no—
569C23—1466no—
570C23C22×C4×D7313yes—
571Q8—1466no—
572Q8#1455654914yes—
573D4—14612no—
574D4—1466no—
575D4#14556549112yes—
576C2×C4—43no—
577C2×C4—43no—
578C2×C4—2926no—
579C2×C4—2926no—
580C2×C4—2923no—
581C2×C4—2923no—
582C2×C4—733no—
583C2×C4—731no—
584C2×C4—733no—
585C2×C4—731no—
586C2×C4—733no—
587C2×C4—731no—
588C2×C4—1466no—
589C2×C4—1461no—
590C2×C4—1463no—
591C2×C4—1461no—
592C2×C4—1463no—
593C2×C4—1466no—
594C2×C4—1466no—
595C2×C4C22×C4×D7313yes—
596C2×C4C22×C4×D7313yes—
597C2×C4C22×C4×D7311yescharacteristic
598C2×C4C22×C4×D7311yescharacteristic
599C2×C4C22×C4×D7313yes—
600C2×C4C2×#1192402716yes—
601C2×C4C2×#1192402916yes—
602C2×C4C24×D7311yescharacteristic
603C8—21no—
604C8—21no—
605C8—23no—
606C8—23no—
607C8—1461no—
608C8—1461no—
609C8—1463no—
610C8—1463no—
611C22—23no—
612C22—23no—
613C22—5846no—
614C22—1461no—
615C22—1463no—
616C22—1463no—
617C22—1461no—
618C22—1463no—
619C22—1461no—
620C22C2×#1455654916yes—
621C22C23×C4×D7311yescharacteristic
622C4—21no—
623C4—23no—
624C4—21no—
625C4—23no—
626C4—1461no—
627C4—1463no—
628C4—1463no—
629C4—1461no—
630C4—1463no—
631C4—1461no—
632C4C2×#1455654916yes—
633C4C22×#1192402711yescharacteristic
634C4C22×#1192402911yescharacteristic
635C2—26no—
636C2—2921no—
637C2—2923no—
638C2C22×#1455654911yescharacteristic
639C2#2262464211yescharacteristic
640C2#2262464411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D73
commutator, socleC22×C73C24×C4
FittingC73×#2906C2
prime radicalC2×#41×D73C22
cosocleC2×C4×C73C25
hypercenter#2906D73
hypocenterC73#60129
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #22618599C2semidirect
3. #22618596C2semidirect
4. #22618588C2semidirect
5. #22618588C2semidirect
6. #22618581C2semidirect
7. #22618574C2semidirect
8. #22618568C2semidirect
9. C2×#17988647C2semidirect
10. #22618499C2semidirect
13. #22618357C2semidirect
14. #131×Dic73C2semidirect
15. C73×#2906C2semidirect
37. #17988647C22semidirect
38. #17988647C22semidirect
39. #17988647C22semidirect
40. #17988647C22semidirect
41. #17988647C22semidirect
42. #17988647C22semidirect
43. #17988643C22semidirect
44. #17988643C22semidirect
45. #17988639C22semidirect
46. #17988639C22semidirect
47. #17988614C22semidirect
48. #17988614C22semidirect
49. #17988611C22semidirect
50. C2×C4⋊#10596831C22semidirect
59. #17988545C22semidirect
60. #17988545C22semidirect
61. #17988542C22semidirect
62. #17988542C22semidirect
63. M16×Dic73C22semidirect
64. M16×Dic73C22semidirect
65. C2×#14556501C22semidirect
66. C2×C8×Dic73C22semidirect
70. #424×C73C22semidirect
71. #424×C73C22semidirect
72. #423×C73C22semidirect
73. C2×C4⋊C8×C73C22semidirect
331. #2906D73semidirect
336. C73#60129semidirect
373. #424C2×D73semidirect
374. #424C2×D73semidirect
376. #423C2×D73semidirect
378. C2×C4⋊C8C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226231302
#226185992
#226185962
#226185882
#226185812
#226185742
#226185682
C2×#179886472
#226184992
#226183782
#226183572
#131×Dic732
C73×#29062
#6012973