Finite Group Databasebeta

← #131×C22⋊D73 #33949948

Subgroups — #131×C22⋊D73 #33949948

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
1C2×#131×D73C211yesmaximal, characteristic, complemented
2#41×C22⋊D73C211yesmaximal, characteristic
3#22618673C213yesmaximal, complemented
4M16×C22⋊D73C213yesmaximal, complemented
5#22618656C213yesmaximal, complemented
6#22618653C213yesmaximal, complemented
7#22618641C213yesmaximal, complemented
8#22618625C213yesmaximal, complemented
9#22618623C213yesmaximal, complemented
10C2×C8×C22⋊D73C213yesmaximal, complemented
11#22618497C211yesmaximal, characteristic, complemented
12#22618380C211yesmaximal, characteristic, complemented
13#22618378C211yesmaximal, characteristic, complemented
14#131×Dic73C211yesmaximal, characteristic, complemented
15C22×#131×C73C211yesmaximal, characteristic, complemented
16C2×#41×D73C2211yescharacteristic
17C2×#14556599C2213yescomplemented
18C2×#14556598C2211yescharacteristic
19C2×#14556598C2211yescharacteristic
20C2×#14556597C2213yescomplemented
21#131×D73—28no—
22C2×M16×D73C2213yescomplemented
23C22×C8×D73C2213yescomplemented
24#17989256C411yescharacteristic
25Q8×C22⋊D73C411yescharacteristic
26#17989248C411yescharacteristic
27#17989244C411yescharacteristic
28#17989236C413yes—
29#17989231C413yes—
30#17989225C413yes—
31D4×C22⋊D73C413yes—
32#17989133C2213yes—
33#17989098C2213yes—
34#17989094C2213yes—
35#41×Dic73C2211yescharacteristic
36C2×C4×C22⋊D73C2213yes—
37#17988663C2216yescomplemented
38#17988663C2216yescomplemented
39#17988658C2216yescomplemented
40#17988658C2216yescomplemented
41#17988656C2216yescomplemented
42#17988656C2216yescomplemented
43C8×C22⋊D73C2213yes—
44C8×C22⋊D73C2211yescharacteristic
45C8×C22⋊D73C2213yescomplemented
46C8×C22⋊D73C2216yescomplemented
47C8×C22⋊D73C2213yescomplemented
48C8×C22⋊D73C2213yescomplemented
49C8×C22⋊D73C2213yescomplemented
50C8×C22⋊D73C2213yescomplemented
51C8×C22⋊D73C2213yescomplemented
52#17988615C2213yescomplemented
53#17988613C2213yescomplemented
54#17988610C2213yescomplemented
55C2×#14556520C2213yescomplemented
56#17988555C2213yescomplemented
57#17988554C2213yescomplemented
58#17988554C2213yescomplemented
59#17988553C2213yescomplemented
60#17988551C2213yescomplemented
61#17988550C2213yescomplemented
62C2×C22⋊#10596831C2213yescomplemented
63C2×#14556503C2213yescomplemented
64#17988545C2213yescomplemented
65#17988542C2213yescomplemented
66M16×Dic73C2213yescomplemented
67C2×C8×Dic73C2213yescomplemented
68C22×#41×C73C2211yescharacteristic
69C2×#131×C73—28no—
70C2×#131×C73C2211yescharacteristic
71C2×#131×C73C2211yescharacteristic
72C2×#131×C73C2213yescomplemented
73C2×#131×C73C2213yescomplemented
74C22×M16×C73C2213yescomplemented
75C23×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—24no—
87#14556598—24no—
88#14556597—212no—
89C2×#11924012C2313yes—
90C2×#11924012C2313yes—
91C2×#11924011C2316yes—
92M16×D73—212no—
93C22×#10596831C2313yes—
94C22×#10596831C2313yes—
95C2×C8×D73—212no—
96C2×C8×D73C2311yescharacteristic
97C2×C8×D73C2313yes—
98C2×C8×D73C2313yes—
99C2×C8×D73C2313yes—
100#14556589C2×C413yes—
101#14556587C2×C413yes—
102#14556580C2×C413yes—
103#14556578C2×C413yes—
104#14556574C2×C416yes—
105#14556572C2×C416yes—
106#14556570C2×C413yes—
107#14556570C2×C413yes—
108#14556567C2×C413yes—
109#14556567C2×C413yes—
110#14556565C2×C413yes—
111#14556565C2×C413yes—
112#14556563C2×C416yes—
113#14556563C2×C416yes—
114#14556562C2×C413yes—
115#14556562C2×C413yes—
116#14556560C2×C416yes—
117#14556559C2×C416yes—
118Q8×Dic73C2×C411yescharacteristic
119Q8×Dic73C2×C411yescharacteristic
120D4×Dic73C2×C413yes—
121D4×Dic73C2×C413yes—
122C4×C22⋊D73C2×C413yes—
123C4×C22⋊D73C2×C413yes—
124C4×C22⋊D73C2×C413yes—
125C4×C22⋊D73C2×C413yes—
126C4×C22⋊D73C2313yes—
127C4×C22⋊D73C2316yes—
128C4×C22⋊D73C2311yescharacteristic
129C4×C22⋊D73C2313yes—
130C4×C22⋊D73C2313yes—
131#14556550C2313yes—
132C2×#11924007C2×C413yes—
133C2×C22⋊Dic73C2×C413yes—
134C2×#11924005C2×C413yes—
135C2×C4×Dic73C2313yes—
136#14556520C2313yes—
137#14556520C2316yes—
138#14556520C2313yes—
139#14556520C2313yes—
140#14556520C2311yescharacteristic
141C22⋊#10596831C2311yescharacteristic
142C22⋊#10596831C2313yes—
143C22⋊#10596831C2313yes—
144C22⋊#10596831C2313yes—
145C22⋊#10596831C2316yes—
146#14556503C2311yescharacteristic
147#14556503C2313yes—
148#14556503C2313yes—
149#14556503C2313yes—
150#14556503C2316yes—
151#14556501C2316yes—
152C8×Dic73C2311yescharacteristic
153C8×Dic73C2313yes—
154C8×Dic73C2313yes—
155C8×Dic73C2313yes—
156C2×#41×C73—24no—
157C2×#41×C73—24no—
158C2×#41×C73C2×C413yes—
159C2×#41×C73C2×C411yescharacteristic
160C2×#41×C73C2313yes—
161C2×#41×C73C2311yescharacteristic
162C22×Q8×C73C2×C411yescharacteristic
163C22×D4×C73C2×C413yes—
164C23×C4×C73C2313yes—
165#131×C73—24no—
166#131×C73—212no—
167#131×C73—212no—
168#131×C73D418yescomplemented
169C2×M16×C73—212no—
170C2×M16×C73C2313yes—
171C2×M16×C73C2316yes—
172C2×M16×C73C2313yes—
173C22×C8×C73—212no—
174C22×C8×C73C2313yes—
175C22×C8×C73C2311yescharacteristic
176C22×C8×C73C2313yes—
177C22×C8×C73C2313yes—
178C22×C8×C73C2313yes—
179C22×C8×C73C2313yes—
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—26no—
207#11924011—212no—
208C2×#10596831—26no—
209C2×#10596831—26no—
210C2×#10596831C2411yescharacteristic
211C2×#10596831C2413yes—
212C2×#10596831C2411yescharacteristic
213C2×#10596831C2413yes—
214C8×D73—22no—
215C8×D73—26no—
216C8×D73—26no—
217C8×D73—26no—
218C4⋊Dic73C22×C413yes—
219C4⋊Dic73C22×C413yes—
220#11924007C22×C411yescharacteristic
221#11924007C22×C413yes—
222#11924007C22×C413yes—
223#11924007C22×C413yes—
224#11924007C22×C416yes—
225C22⋊Dic73C22×C411yescharacteristic
226C22⋊Dic73C22×C413yes—
227C22⋊Dic73C22×C413yes—
228C22⋊Dic73C22×C413yes—
229C22⋊Dic73C22×C416yes—
230C22⋊Dic73C22×C416yes—
231#11924005C22×C411yescharacteristic
232#11924005C22×C413yes—
233#11924005C22×C413yes—
234#11924005C22×C413yes—
235#11924005C22×C416yes—
236C4×Dic73C22×C413yes—
237C4×Dic73C22×C413yes—
238C4×Dic73C2411yescharacteristic
239C4×Dic73C2413yes—
240C24×C73C22×C413yes—
241#41×C73—24no—
242#41×C73—212no—
243#41×C73—26no—
244#41×C73—26no—
245#41×C73C2×D414yes—
246#41×C73#4114yes—
247C2×Q8×C73—24no—
248C2×Q8×C73C22×C413yes—
249C2×Q8×C73C22×C411yescharacteristic
250C2×D4×C73—212no—
251C2×D4×C73C22×C416yes—
252C2×D4×C73C22×C413yes—
253C2×D4×C73C22×C413yes—
254C22×C4×C73—26no—
255C22×C4×C73—26no—
256C22×C4×C73C22×C413yes—
257C22×C4×C73C22×C413yes—
258C22×C4×C73C22×C413yes—
259C22×C4×C73C2411yescharacteristic
260C22×C4×C73C2413yes—
261C22×C4×C73C2413yes—
262M16×C73—26no—
263M16×C73—212no—
264M16×C73C2×D4112yescomplemented
265C2×C8×C73—26no—
266C2×C8×C73—22no—
267C2×C8×C73—26no—
268C2×C8×C73—26no—
269C2×C8×C73—26no—
270C2×C8×C73C2×D4112yescomplemented
271C2×C8×C73C2411yescharacteristic
272C2×C8×C73C2413yes—
273C2×C8×C73C2413yes—
274C2×C8×C73C2411yescharacteristic
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#13114yesdirect product factor
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×C73C22×D412yes—
330C8×C73C22×D416yes—
331#10596831—21no—
332#10596831—23no—
333#10596831—21no—
334#10596831—23no—
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×#131D7311yescharacteristic, complemented
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#2880—731no—
387C4×#131—731no—
388C73D4×#13111yescharacteristic, complemented, Sylow
389C22×#41—731no—
390C22×#41C2×D7311yescharacteristic
391C2×#131—28no—
392C2×#131—731no—
393C2×#131—731no—
394C2×#131—733no—
395C2×#131—733no—
396C2×#131—1468no—
397C2×#131C2×D7311yescharacteristic
398C2×#131C2×D7311yescharacteristic
399C2×#131C2×D7313yescomplemented
400C2×#131C2×D7313yescomplemented
401C22×M16—733no—
402C22×M16C2×D7313yescomplemented
403C23×C8—733no—
404C23×C8C2×D7313yescomplemented
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#408—733no—
440#408—733no—
441#407—733no—
442#407—733no—
443C2×C22⋊C8—733no—
444C2×C22⋊C8—733no—
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—212no—
469#131—212no—
470#131—1464no—
471#131—1464no—
472#131—14612no—
473#131—14612no—
474#131C22⋊D7318yesdirect product factor
475C2×M16—212no—
476C2×M16—733no—
477C2×M16—733no—
478C2×M16—736no—
479C2×M16—14612no—
480C2×M16C22×D7313yes—
481C2×M16C22×D7316yes—
482C2×M16C22×D7313yes—
483C22×C8—212no—
484C22×C8—733no—
485C22×C8—733no—
486C22×C8—733no—
487C22×C8—733no—
488C22×C8—731no—
489C22×C8—733no—
490C22×C8—14612no—
491C22×C8C22×D7313yes—
492C22×C8C22×D7313yes—
493C22×C8C22×D7313yes—
494C22×C8C22×D7311yescharacteristic
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⋊C8—731no—
544C22⋊C8—733no—
545C22⋊C8—733no—
546C22⋊C8—733no—
547C22⋊C8—736no—
548#97—736no—
549C4×C8—733no—
550C4×C8—733no—
551C4×C8—731no—
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#41C2×C22⋊D7314yes—
564#41#1192402814yes—
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—212no—
602M16—1466no—
603M16—1466no—
604M16—14612no—
605M16C2×C22⋊D73112yescomplemented
606C2×C8—26no—
607C2×C8—22no—
608C2×C8—26no—
609C2×C8—26no—
610C2×C8—26no—
611C2×C8—731no—
612C2×C8—733no—
613C2×C8—731no—
614C2×C8—733no—
615C2×C8—1466no—
616C2×C8—1466no—
617C2×C8—1462no—
618C2×C8—1466no—
619C2×C8—1466no—
620C2×C8—1466no—
621C2×C8C2×C22⋊D73112yescomplemented
622C2×C8C23×D7311yescharacteristic
623C2×C8C23×D7313yes—
624C2×C8C23×D7313yes—
625C2×C8C23×D7311yescharacteristic
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—
661Q8C4×C22⋊D7314yes—
662D4—212no—
663D4—26no—
664D4—2926no—
665D4—734no—
666D4—1466no—
667D4—1466no—
668D4—14612no—
669D4—1466no—
670D4—1466no—
671D4C4×C22⋊D73112yes—
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×C4C22×C22⋊D7316yes—
698C2×C4C2×#1192402816yes—
699C2×C4C24×D7311yescharacteristic
700C8—21no—
701C8—23no—
702C8—1461no—
703C8—1463no—
704C8—1461no—
705C8—1463no—
706C8C22×C22⋊D7312yes—
707C8C22×C22⋊D7316yes—
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×C4×C22⋊D7316yes—
724C22#131×D7312yescomplemented
725C22C23×C4×D7311yescharacteristic
726C4—21no—
727C4—23no—
728C4—732no—
729C4—1463no—
730C4—1461no—
731C4—1463no—
732C4—1461no—
733C4—1463no—
734C4C2×C4×C22⋊D7316yes—
735C4C23×C22⋊D7311yescharacteristic
736C4C22×#1192402811yescharacteristic
737C2—22no—
738C2—26no—
739C2—43no—
740C2—2923no—
741C2—1462no—
742C2C22×C4×C22⋊D7311yescharacteristic
743C2C2×#131×D7311yescharacteristic
744C2#2262464211yescharacteristic
subgroupG/H
centerC2×C8C23×D73
commutator, socleC22×C73C24×C4
FrattiniC2×C4C24×D73
FittingC22×#131×C73C2
prime radical#41×C22⋊D73C2
cosocleC2×C4×C73C25
hypercenterC22×#131D73
hypocenterC73D4×#131
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C8 ◁ C22×#131

Complements

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

NH ≅ G/Ntype
1. C2×#131×D73C2semidirect
3. #22618673C2semidirect
4. M16×C22⋊D73C2semidirect
5. #22618656C2semidirect
6. #22618653C2semidirect
7. #22618641C2semidirect
8. #22618625C2semidirect
9. #22618623C2semidirect
10. C2×C8×C22⋊D73C2semidirect
11. #22618497C2semidirect
12. #22618380C2semidirect
13. #22618378C2semidirect
14. #131×Dic73C2semidirect
15. C22×#131×C73C2semidirect
17. C2×#14556599C22semidirect
20. C2×#14556597C22semidirect
22. C2×M16×D73C22semidirect
23. C22×C8×D73C22semidirect
37. #17988663C22semidirect
38. #17988663C22semidirect
39. #17988658C22semidirect
40. #17988658C22semidirect
41. #17988656C22semidirect
42. #17988656C22semidirect
45. C8×C22⋊D73C22semidirect
46. C8×C22⋊D73C22semidirect
47. C8×C22⋊D73C22semidirect
48. C8×C22⋊D73C22semidirect
49. C8×C22⋊D73C22semidirect
50. C8×C22⋊D73C22semidirect
51. C8×C22⋊D73C22semidirect
52. #17988615C22semidirect
53. #17988613C22semidirect
54. #17988610C22semidirect
55. C2×#14556520C22semidirect
56. #17988555C22semidirect
57. #17988554C22semidirect
58. #17988554C22semidirect
59. #17988553C22semidirect
60. #17988551C22semidirect
61. #17988550C22semidirect
62. C2×C22⋊#10596831C22semidirect
63. C2×#14556503C22semidirect
64. #17988545C22semidirect
65. #17988542C22semidirect
66. M16×Dic73C22semidirect
67. C2×C8×Dic73C22semidirect
72. C2×#131×C73C22semidirect
73. C2×#131×C73C22semidirect
74. C22×M16×C73C22semidirect
75. C23×C8×C73C22semidirect
168. #131×C73D4semidirect
264. M16×C73C2×D4semidirect
270. C2×C8×C73C2×D4semidirect
309. C22⋊D73#131direct (N × H)
344. C22×C73C2×#131semidirect
352. C2×D73C2×#131semidirect
363. Dic73C2×#131semidirect
374. C22×#131D73semidirect
388. C73D4×#131semidirect
399. C2×#131C2×D73semidirect
400. C2×#131C2×D73semidirect
402. C22×M16C2×D73semidirect
404. C23×C8C2×D73semidirect
474. #131C22⋊D73direct (N × H)
605. M16C2×C22⋊D73semidirect
621. C2×C8C2×C22⋊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
C2×#131×D732
#41×C22⋊D732
#226186732
M16×C22⋊D732
#226186562
#226186532
#226186412
#226186252
#226186232
C2×C8×C22⋊D732
#226184972
#226183802
#226183782
#131×Dic732
C22×#131×C732
D4×#13173