Finite Group Databasebeta

← #33949946

Subgroups — #33949946

Order 18688.

2814 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556598C211yesmaximal, characteristic, complemented
2C2×#131×D73C211yesmaximal, characteristic, complemented
3#41×C22⋊D73C211yesmaximal, characteristic
4#22618671C213yesmaximal, complemented
5#22618663C213yesmaximal, complemented
6#22618661C213yesmaximal, complemented
7#22618652C213yesmaximal, complemented
8#22618639C213yesmaximal, complemented
9#22618628C213yesmaximal, complemented
10#22618621C213yesmaximal, complemented
11C2×#17988650C213yesmaximal, complemented
12#22618497C211yesmaximal, characteristic, complemented
13#22618378C211yesmaximal, characteristic, complemented
14#131×Dic73C211yesmaximal, characteristic, complemented
15C73×#2880C211yesmaximal, characteristic, complemented
16C2×#41×D73C2211yescharacteristic
17C2×#14556599C2213yescomplemented
18C2×#14556598—28no—
19C2×#14556598C2211yescharacteristic
20C2×#14556598C2211yescharacteristic
21C2×#14556598C2213yescomplemented
22C2×#14556598C2213yescomplemented
23C2×#14556597C2213yescomplemented
24#131×D73—28no—
25C22×#11924012C2213yescomplemented
26C2×M16×D73C2213yescomplemented
27C23×#10596831C2213yescomplemented
28C22×C8×D73C2213yescomplemented
29#17989256C411yescharacteristic
30Q8×C22⋊D73C411yescharacteristic
31#17989248C411yescharacteristic
32#17989244C411yescharacteristic
33#17989236C413yes—
34#17989231C413yes—
35#17989225C413yes—
36D4×C22⋊D73C413yes—
37#17989133C2213yes—
38#17989098C2213yes—
39#17989094C2213yes—
40#41×Dic73C2211yescharacteristic
41C2×C4×C22⋊D73C2213yes—
42#17988662C2216yescomplemented
43#17988662C2216yescomplemented
44#17988661C2216yescomplemented
45#17988661C2216yescomplemented
46#17988655C2216yescomplemented
47#17988655C2216yescomplemented
48#17988650C2213yes—
49#17988650C2211yescharacteristic
50#17988650C2213yescomplemented
51#17988650C2216yescomplemented
52#17988650C2213yescomplemented
53#17988650C2213yescomplemented
54#17988650C2213yescomplemented
55#17988650C2213yescomplemented
56#17988650C2213yescomplemented
57#17988615C2213yescomplemented
58#17988613C2213yescomplemented
59#17988610C2213yescomplemented
60C2×#14556520C2213yescomplemented
61#17988555C2213yescomplemented
62#17988553C2213yescomplemented
63#17988550C2213yescomplemented
64C2×#14556503C2213yescomplemented
65#17988545C2213yescomplemented
66#17988542C2213yescomplemented
67M16×Dic73C2213yescomplemented
68C2×C8×Dic73C2213yescomplemented
69C22×#41×C73C2211yescharacteristic
70C2×#131×C73C2211yescharacteristic
71C2×#131×C73C2211yescharacteristic
72#408×C73C2213yescomplemented
73#408×C73C2213yescomplemented
74#407×C73C2213yescomplemented
75C2×C22⋊C8×C73C2213yescomplemented
76C2×#11924029C2×C411yescharacteristic
77C2×#11924028C2313yes—
78C2×#11924027C2×C413yes—
79#41×D73—24no—
80#41×D73—24no—
81C2×Q8×D73C2×C411yescharacteristic
82C22×C22⋊D73C2×C413yes—
83C2×D4×D73C2×C413yes—
84C22×C4×D73C2313yes—
85#14556599—212no—
86#14556598—212no—
87#14556598—212no—
88#14556598—24no—
89#14556598D418yescomplemented
90#14556597—212no—
91C2×#11924012—212no—
92C2×#11924012C2313yes—
93C2×#11924012C2316yes—
94C2×#11924012C2313yes—
95C2×#11924011C2316yes—
96M16×D73—212no—
97C22×#10596831—212no—
98C22×#10596831C2313yes—
99C22×#10596831C2311yescharacteristic
100C22×#10596831C2313yes—
101C22×#10596831C2313yes—
102C22×#10596831C2313yes—
103C22×#10596831C2313yes—
104C2×C8×D73—212no—
105C2×C8×D73C2311yescharacteristic
106C2×C8×D73C2313yes—
107C2×C8×D73C2313yes—
108C2×C8×D73C2313yes—
109#14556589C2×C413yes—
110#14556587C2×C413yes—
111#14556580C2×C413yes—
112#14556578C2×C413yes—
113#14556574C2×C416yes—
114#14556572C2×C416yes—
115#14556570C2×C413yes—
116#14556570C2×C413yes—
117#14556567C2×C413yes—
118#14556567C2×C413yes—
119#14556565C2×C413yes—
120#14556565C2×C413yes—
121#14556563C2×C416yes—
122#14556563C2×C416yes—
123#14556562C2×C413yes—
124#14556562C2×C413yes—
125#14556560C2×C416yes—
126#14556559C2×C416yes—
127Q8×Dic73C2×C411yescharacteristic
128Q8×Dic73C2×C411yescharacteristic
129D4×Dic73C2×C413yes—
130D4×Dic73C2×C413yes—
131C4×C22⋊D73C2×C413yes—
132C4×C22⋊D73C2×C413yes—
133C4×C22⋊D73C2×C413yes—
134C4×C22⋊D73C2×C413yes—
135C4×C22⋊D73C2313yes—
136C4×C22⋊D73C2316yes—
137C4×C22⋊D73C2311yescharacteristic
138C4×C22⋊D73C2313yes—
139C4×C22⋊D73C2313yes—
140#14556550C2313yes—
141C2×#11924007C2×C413yes—
142C2×C22⋊Dic73C2×C413yes—
143C2×#11924005C2×C413yes—
144C2×C4×Dic73C2313yes—
145#14556520C2313yes—
146#14556520C2316yes—
147#14556520C2313yes—
148#14556520C2313yes—
149#14556520C2311yescharacteristic
150#14556503C2311yescharacteristic
151#14556503C2313yes—
152#14556503C2313yes—
153#14556503C2313yes—
154#14556503C2316yes—
155#14556501C2316yes—
156C8×Dic73C2311yescharacteristic
157C8×Dic73C2313yes—
158C8×Dic73C2313yes—
159C8×Dic73C2313yes—
160C2×#41×C73—24no—
161C2×#41×C73—24no—
162C2×#41×C73C2×C413yes—
163C2×#41×C73C2×C411yescharacteristic
164C2×#41×C73C2313yes—
165C2×#41×C73C2311yescharacteristic
166C22×Q8×C73C2×C411yescharacteristic
167C22×D4×C73C2×C413yes—
168C23×C4×C73C2313yes—
169#131×C73—24no—
170#131×C73—24no—
171C2×M16×C73C2313yes—
172C2×M16×C73C2313yes—
173C22×C8×C73C2313yes—
174C22×C8×C73C2313yes—
175C22⋊C8×C73C2311yescharacteristic
176C22⋊C8×C73C2313yes—
177C22⋊C8×C73C2313yes—
178C22⋊C8×C73C2313yes—
179C22⋊C8×C73C2316yes—
180C23×D73C22×C413yes—
181#11924029—24no—
182#11924028—26no—
183#11924028—26no—
184#11924027—212no—
185C2×Dic146C22×C413yes—
186Q8×D73—24no—
187C2×D292C22×C413yes—
188C2×C22⋊D73—212no—
189C2×C22⋊D73C22×C413yes—
190C2×C22⋊D73C22×C413yes—
191C2×C22⋊D73C22×C413yes—
192C2×C22⋊D73C22×C416yes—
193C2×C22⋊D73C22×C416yes—
194C2×C22⋊D73C22×C411yescharacteristic
195D4×D73—212no—
196C22×Dic73C22×C413yes—
197C22×Dic73C22×C413yes—
198C22×Dic73C22×C413yes—
199C2×C4×D73—26no—
200C2×C4×D73—26no—
201C2×C4×D73C22×C413yes—
202C2×C4×D73C22×C413yes—
203C2×C4×D73C2411yescharacteristic
204C2×C4×D73C2413yes—
205#11924012—26no—
206#11924012—212no—
207#11924012C2×D4112yescomplemented
208#11924011—212no—
209C2×#10596831—26no—
210C2×#10596831—22no—
211C2×#10596831—26no—
212C2×#10596831—26no—
213C2×#10596831—26no—
214C2×#10596831C2×D4112yescomplemented
215C2×#10596831C2411yescharacteristic
216C2×#10596831C2413yes—
217C2×#10596831C2411yescharacteristic
218C2×#10596831C2413yes—
219C8×D73—22no—
220C8×D73—26no—
221C8×D73—26no—
222C8×D73—26no—
223C4⋊Dic73C22×C413yes—
224C4⋊Dic73C22×C413yes—
225#11924007C22×C411yescharacteristic
226#11924007C22×C413yes—
227#11924007C22×C413yes—
228#11924007C22×C413yes—
229#11924007C22×C416yes—
230C22⋊Dic73C22×C411yescharacteristic
231C22⋊Dic73C22×C413yes—
232C22⋊Dic73C22×C413yes—
233C22⋊Dic73C22×C413yes—
234C22⋊Dic73C22×C416yes—
235C22⋊Dic73C22×C416yes—
236#11924005C22×C411yescharacteristic
237#11924005C22×C413yes—
238#11924005C22×C413yes—
239#11924005C22×C413yes—
240#11924005C22×C416yes—
241C4×Dic73C22×C413yes—
242C4×Dic73C22×C413yes—
243C4×Dic73C2411yescharacteristic
244C4×Dic73C2413yes—
245C24×C73C22×C413yes—
246#41×C73—24no—
247#41×C73—212no—
248#41×C73—26no—
249#41×C73—26no—
250#41×C73C2×D414yes—
251#41×C73#4114yes—
252C2×Q8×C73—24no—
253C2×Q8×C73C22×C413yes—
254C2×Q8×C73C22×C411yescharacteristic
255C2×D4×C73—212no—
256C2×D4×C73C22×C416yes—
257C2×D4×C73C22×C413yes—
258C2×D4×C73C22×C413yes—
259C22×C4×C73—26no—
260C22×C4×C73—26no—
261C22×C4×C73C22×C413yes—
262C22×C4×C73C22×C413yes—
263C22×C4×C73C22×C413yes—
264C22×C4×C73C2411yescharacteristic
265C22×C4×C73C2413yes—
266C22×C4×C73C2413yes—
267M16×C73—26no—
268M16×C73—26no—
269C2×C8×C73—26no—
270C2×C8×C73—26no—
271C2×C8×C73C2411yescharacteristic
272C2×C8×C73C2411yescharacteristic
273C2×C8×C73C2413yes—
274C2×C8×C73C2413yes—
275C23×C73—26no—
276C23×C73—26no—
277C23×C73—43no—
278C23×C73C23×C413yes—
279C23×C73C23×C413yes—
280C23×C73C23×C411yescharacteristic
281C22×D73—26no—
282C22×D73—26no—
283C22×D73—43no—
284C22×D73C23×C413yes—
285C22×D73C23×C411yescharacteristic
286Q8×C73—26no—
287Q8×C73C4×D414yes—
288D4×C73—212no—
289D4×C73—26no—
290D4×C73C4×D4112yes—
291C2×C4×C73—26no—
292C2×C4×C73—26no—
293C2×C4×C73—26no—
294C2×C4×C73—21no—
295C2×C4×C73—23no—
296C2×C4×C73—21no—
297C2×C4×C73—23no—
298C2×C4×C73C23×C411yescharacteristic
299C2×C4×C73C23×C413yes—
300C2×C4×C73C23×C413yes—
301C2×C4×C73C22×D416yes—
302C2×C4×C73C2×#4116yes—
303C2×C4×C73C2511yescharacteristic
304C22⋊D73—212no—
305C22⋊D73—26no—
306C22⋊D73—26no—
307C22⋊D73—26no—
308C22⋊D73—46no—
309C22⋊D73#13114yescomplemented
310C2×Dic73—26no—
311C2×Dic73—26no—
312C2×Dic73—43no—
313C2×Dic73C23×C411yescharacteristic
314C2×Dic73C23×C413yes—
315C2×Dic73C23×C413yes—
316C2×Dic73C23×C411yescharacteristic
317C2×Dic73C23×C413yes—
318C2×Dic73C23×C411yescharacteristic
319D292—26no—
320C4×D73—26no—
321C4×D73—26no—
322C4×D73—21no—
323C4×D73—23no—
324C4×D73—21no—
325C4×D73—23no—
326Dic146—26no—
327C8×C73—21no—
328C8×C73—23no—
329C8×C73—21no—
330C8×C73—23no—
331#10596831—21no—
332#10596831—23no—
333#10596831C22×D412yes—
334#10596831C22×D416yes—
335C22×C73—21no—
336C22×C73—23no—
337C22×C73—23no—
338C22×C73—21no—
339C22×C73—23no—
340C22×C73—23no—
341C22×C73—23no—
342C22×C73—412no—
343C22×C73C2×C4×D416yes—
344C22×C73C2×#13112yescomplemented
345C22×C73C24×C411yescharacteristic
346C2×D73—21no—
347C2×D73—21no—
348C2×D73—23no—
349C2×D73—23no—
350C2×D73—23no—
351C2×D73—412no—
352C2×D73C2×#13112yescomplemented
353C4×C73—21no—
354C4×C73—23no—
355C4×C73C2×C4×D416yes—
356C4×C73C23×D411yescharacteristic
357C4×C73C22×#4111yescharacteristic
358Dic73—23no—
359Dic73—21no—
360Dic73—23no—
361Dic73—21no—
362Dic73—23no—
363Dic73C2×#13112yescomplemented
364D4×#131—731nomaximal, Sylow
365C2×C73—26no—
366C2×C73—22no—
367C2×C73—43no—
368C2×C73C22×C4×D411yescharacteristic
369C2×C73C22×#13111yescharacteristic
370C2×C73#357311yescharacteristic
371D73—22no—
372D73—43no—
373C22×#131—731no—
374C22×#131—731no—
375D4×#41—731no—
376#2935—733no—
377D4×M16—733no—
378#2933—733no—
379#2933—733no—
380#2931—733no—
381#2929—733no—
382#2929—733no—
383C2×C8×D4—733no—
384#2906—731no—
385#2880—731no—
386#2880D7311yescharacteristic, complemented
387C4×#131—731no—
388C73D4×#13111yescharacteristic, complemented, Sylow
389C22×#41—731no—
390C22×#41C2×D7311yescharacteristic
391C2×#131—731no—
392C2×#131—731no—
393C2×#131—733no—
394C2×#131—733no—
395C2×#131—733no—
396C2×#131—733no—
397C2×#131—1468no—
398C2×#131—1468no—
399C2×#131C2×D7311yescharacteristic
400C2×#131C2×D7311yescharacteristic
401C22×M16—733no—
402C22×M16—733no—
403C23×C8—733no—
404C23×C8—733no—
405#550—731no—
406D4×Q8—731no—
407#548—731no—
408#548—731no—
409#547—733no—
410#546—733no—
411#546—733no—
412D42—733no—
413#532—733no—
414#525—733no—
415#525—733no—
416C4×#41—731no—
417C2×C4×D4—733no—
418#436—736no—
419#436—736no—
420#435—736no—
421#435—736no—
422#435—736no—
423#435—736no—
424C8×D4—731no—
425C8×D4—733no—
426C8×D4—733no—
427C8×D4—733no—
428C8×D4—733no—
429C8×D4—733no—
430C8×D4—733no—
431C8×D4—733no—
432C8×D4—736no—
433#424—733no—
434#424—733no—
435#423—733no—
436C2×C4⋊C8—733no—
437#408—733no—
438#408—733no—
439#408C2×D7313yescomplemented
440#408C2×D7313yescomplemented
441#407—733no—
442#407C2×D7313yescomplemented
443C2×C22⋊C8—733no—
444C2×C22⋊C8C2×D7313yescomplemented
445#405—733no—
446#405—733no—
447C4×M16—733no—
448C2×C4×C8—733no—
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—731no—
452C2×#41—733no—
453C2×#41—733no—
454C2×#41—1464no—
455C2×#41—1464no—
456C2×#41C4×D7313yes—
457C2×#41C4×D7311yescharacteristic
458C2×#41C22×D7313yes—
459C2×#41C22×D7311yescharacteristic
460C22×Q8—731no—
461C22×Q8C4×D7311yescharacteristic
462C22×D4—733no—
463C22×D4—733no—
464C22×D4C4×D7313yes—
465C23×C4—733no—
466C23×C4C22×D7313yes—
467#131—24no—
468#131—24no—
469#131—738no—
470#131—14612no—
471#131—14612no—
472#131—14612no—
473#131—14612no—
474#131—1464no—
475C2×M16—733no—
476C2×M16—733no—
477C2×M16—736no—
478C2×M16—736no—
479C2×M16—14612no—
480C2×M16—14612no—
481C2×M16C22×D7313yes—
482C2×M16C22×D7313yes—
483C22×C8—733no—
484C22×C8—731no—
485C22×C8—733no—
486C22×C8—733no—
487C22×C8—733no—
488C22×C8—733no—
489C22×C8—731no—
490C22×C8—733no—
491C22×C8—733no—
492C22×C8—733no—
493C22×C8—14612no—
494C22×C8—14612no—
495C22×C8C22×D7313yes—
496C22×C8C22×D7313yes—
497C4⋊Q8—733no—
498#127—733no—
499#124—733no—
500#124—733no—
501#123—736no—
502#123—736no—
503C22⋊Q8—733no—
504C22⋊Q8—733no—
505C22⋊Q8—733no—
506C22⋊Q8—733no—
507#121—733no—
508#121—733no—
509#121—736no—
510#121—736no—
511#121—733no—
512#121—733no—
513#120—736no—
514#120—736no—
515C4×Q8—731no—
516C4×Q8—731no—
517C4×D4—733no—
518C4×D4—733no—
519C4×D4—733no—
520C4×D4—733no—
521C4×D4—733no—
522C4×D4—733no—
523C4×D4—731no—
524C4×D4—733no—
525C4×D4—733no—
526C4×D4—733no—
527C4×D4—736no—
528#117—733no—
529C2×C4⋊C4—733no—
530C2×C22⋊C4—733no—
531C2×C22⋊C4—733no—
532C2×C42—733no—
533C4⋊C8—731no—
534C4⋊C8—733no—
535C4⋊C8—733no—
536C4⋊C8—733no—
537C4⋊C8—736no—
538C22⋊C8—731no—
539C22⋊C8—733no—
540C22⋊C8—733no—
541C22⋊C8—733no—
542C22⋊C8—736no—
543C22⋊C8C22×D7311yescharacteristic
544C22⋊C8C22×D7313yes—
545C22⋊C8C22×D7313yes—
546C22⋊C8C22×D7313yes—
547C22⋊C8C22×D7316yes—
548#97—736no—
549C4×C8—731no—
550C4×C8—733no—
551C4×C8—733no—
552C4×C8—733no—
553C24—733no—
554C24C2×C4×D7313yes—
555#41—24no—
556#41—212no—
557#41—26no—
558#41—26no—
559#41—1464no—
560#41—14612no—
561#41—1466no—
562#41—1466no—
563#41D4×D7314yes—
564#41#1192402714yes—
565C2×Q8—24no—
566C2×Q8—733no—
567C2×Q8—1464no—
568C2×Q8C2×C4×D7313yes—
569C2×Q8C2×C4×D7311yescharacteristic
570C2×D4—212no—
571C2×D4—736no—
572C2×D4—731no—
573C2×D4—733no—
574C2×D4—733no—
575C2×D4—733no—
576C2×D4—736no—
577C2×D4—733no—
578C2×D4—14612no—
579C2×D4—14612no—
580C2×D4C2×C4×D7316yes—
581C2×D4C2×C4×D7313yes—
582C2×D4C2×C4×D7313yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—733no—
586C22×C4—733no—
587C22×C4—733no—
588C22×C4—733no—
589C22×C4—733no—
590C22×C4—731no—
591C22×C4—733no—
592C22×C4—1466no—
593C22×C4—1466no—
594C22×C4C2×C4×D7313yes—
595C22×C4C2×C4×D7313yes—
596C22×C4C2×C4×D7313yes—
597C22×C4C23×D7311yescharacteristic
598C22×C4C23×D7313yes—
599C22×C4C23×D7313yes—
600M16—26no—
601M16—26no—
602M16—7312no—
603M16—14612no—
604M16—14612no—
605M16—1466no—
606C2×C8—26no—
607C2×C8—26no—
608C2×C8—7312no—
609C2×C8—731no—
610C2×C8—733no—
611C2×C8—731no—
612C2×C8—733no—
613C2×C8—1462no—
614C2×C8—1466no—
615C2×C8—1466no—
616C2×C8—1466no—
617C2×C8—1462no—
618C2×C8—1466no—
619C2×C8—1466no—
620C2×C8—1466no—
621C2×C8—1466no—
622C2×C8C23×D7311yescharacteristic
623C2×C8C23×D7313yes—
624C2×C8C23×D7311yescharacteristic
625C2×C8C23×D7313yes—
626C4⋊C4—731no—
627C4⋊C4—733no—
628C4⋊C4—733no—
629C4⋊C4—733no—
630C4⋊C4—736no—
631C4⋊C4—733no—
632C4⋊C4—733no—
633C22⋊C4—731no—
634C22⋊C4—733no—
635C22⋊C4—733no—
636C22⋊C4—733no—
637C22⋊C4—736no—
638C22⋊C4—736no—
639C22⋊C4—731no—
640C22⋊C4—733no—
641C22⋊C4—733no—
642C22⋊C4—733no—
643C22⋊C4—736no—
644C42—733no—
645C42—733no—
646C42—731no—
647C42—733no—
648C23—26no—
649C23—26no—
650C23—43no—
651C23—2923no—
652C23—731no—
653C23—733no—
654C23—1466no—
655C23—1466no—
656C23C22×C4×D7313yes—
657C23C22×C4×D7313yes—
658C23C22×C4×D7311yescharacteristic
659Q8—26no—
660Q8—1466no—
661Q8#1455655114yes—
662D4—212no—
663D4—26no—
664D4—2926no—
665D4—734no—
666D4—1466no—
667D4—1466no—
668D4—14612no—
669D4—1466no—
670D4—1466no—
671D4#14556551112yes—
672C2×C4—26no—
673C2×C4—21no—
674C2×C4—23no—
675C2×C4—21no—
676C2×C4—23no—
677C2×C4—26no—
678C2×C4—26no—
679C2×C4—2923no—
680C2×C4—731no—
681C2×C4—731no—
682C2×C4—733no—
683C2×C4—733no—
684C2×C4—731no—
685C2×C4—733no—
686C2×C4—1466no—
687C2×C4—1466no—
688C2×C4—1461no—
689C2×C4—1463no—
690C2×C4—1461no—
691C2×C4—1463no—
692C2×C4—1466no—
693C2×C4—1466no—
694C2×C4C22×C4×D7311yescharacteristic
695C2×C4C22×C4×D7313yes—
696C2×C4C22×C4×D7313yes—
697C2×C4C2×D4×D7316yes—
698C2×C4C2×#1192402716yes—
699C2×C4C24×D7311yescharacteristic
700C8—21no—
701C8—23no—
702C8—21no—
703C8—23no—
704C8—732no—
705C8—736no—
706C8—1461no—
707C8—1463no—
708C22—23no—
709C22—21no—
710C22—23no—
711C22—21no—
712C22—23no—
713C22—23no—
714C22—23no—
715C22—412no—
716C22—29212no—
717C22—732no—
718C22—1463no—
719C22—1463no—
720C22—1463no—
721C22—1461no—
722C22—1461no—
723C22C2×#1455655116yes—
724C22#131×D7312yescomplemented
725C22C23×C4×D7311yescharacteristic
726C4—21no—
727C4—23no—
728C4—732no—
729C4—1463no—
730C4—1461no—
731C4—1463no—
732C4—1461no—
733C4—1463no—
734C4C2×#1455655116yes—
735C4C22×D4×D7311yescharacteristic
736C4C22×#1192402711yescharacteristic
737C2—22no—
738C2—26no—
739C2—43no—
740C2—2923no—
741C2—1462no—
742C2C22×#1455655111yescharacteristic
743C2C2×#131×D7311yescharacteristic
744C2#2262464411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D73
commutator, socleC22×C73C24×C4
FittingC73×#2880C2
prime radical#41×C22⋊D73C2
cosocleC2×C4×C73C25
hypercenter#2880D73
hypocenterC73D4×#131
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
1. C22×#14556598C2semidirect
2. C2×#131×D73C2semidirect
4. #22618671C2semidirect
5. #22618663C2semidirect
6. #22618661C2semidirect
7. #22618652C2semidirect
8. #22618639C2semidirect
9. #22618628C2semidirect
10. #22618621C2semidirect
11. C2×#17988650C2semidirect
12. #22618497C2semidirect
13. #22618378C2semidirect
14. #131×Dic73C2semidirect
15. C73×#2880C2semidirect
17. C2×#14556599C22semidirect
21. C2×#14556598C22semidirect
22. C2×#14556598C22semidirect
23. C2×#14556597C22semidirect
25. C22×#11924012C22semidirect
26. C2×M16×D73C22semidirect
27. C23×#10596831C22semidirect
28. C22×C8×D73C22semidirect
42. #17988662C22semidirect
43. #17988662C22semidirect
44. #17988661C22semidirect
45. #17988661C22semidirect
46. #17988655C22semidirect
47. #17988655C22semidirect
50. #17988650C22semidirect
51. #17988650C22semidirect
52. #17988650C22semidirect
53. #17988650C22semidirect
54. #17988650C22semidirect
55. #17988650C22semidirect
56. #17988650C22semidirect
57. #17988615C22semidirect
58. #17988613C22semidirect
59. #17988610C22semidirect
60. C2×#14556520C22semidirect
61. #17988555C22semidirect
62. #17988553C22semidirect
63. #17988550C22semidirect
64. C2×#14556503C22semidirect
65. #17988545C22semidirect
66. #17988542C22semidirect
67. M16×Dic73C22semidirect
68. C2×C8×Dic73C22semidirect
72. #408×C73C22semidirect
73. #408×C73C22semidirect
74. #407×C73C22semidirect
75. C2×C22⋊C8×C73C22semidirect
89. #14556598D4semidirect
207. #11924012C2×D4semidirect
214. C2×#10596831C2×D4semidirect
309. C22⋊D73#131semidirect
344. C22×C73C2×#131semidirect
352. C2×D73C2×#131semidirect
363. Dic73C2×#131semidirect
386. #2880D73semidirect
388. C73D4×#131semidirect
439. #408C2×D73semidirect
440. #408C2×D73semidirect
442. #407C2×D73semidirect
444. C2×C22⋊C8C2×D73semidirect
724. C22#131×D73semidirect

Maximal subgroups

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

subgroupindex
C22×#145565982
C2×#131×D732
#41×C22⋊D732
#226186712
#226186632
#226186612
#226186522
#226186392
#226186282
#226186212
C2×#179886502
#226184972
#226183782
#131×Dic732
C73×#28802
D4×#13173