Finite Group Databasebeta

← D73⋊#2935 #34031360

Subgroups — D73⋊#2935 #34031360

Order 18688.

2850 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D73⋊#131C212yesmaximal, complemented
2#22626677C212yesmaximal, complemented
3#22626676C214yesmaximal, complemented
4#22626675C214yesmaximal, complemented
5#22626674C212yesmaximal, complemented
6#22626673C214yesmaximal, complemented
7D73⋊#436C212yesmaximal, complemented
8D73⋊#435C214yesmaximal, complemented
9D4×#11924036C212yesmaximal, complemented
10C2×#17989588C211yesmaximal, characteristic, complemented
11D73⋊#408C212yesmaximal, complemented
12C4×D73⋊M16C211yesmaximal, characteristic, complemented
13#532×D73C211yesmaximal, characteristic
14C2×#14556679C2214yescomplemented
15D73⋊#131—216no—
16C2×#14556678C2218yescomplemented
17C2×#14556678C2214yescomplemented
18C2×D73⋊M16C2214yes—
19C2×D73⋊M16C2211yescharacteristic
20C2×D73⋊M16C2211yescharacteristic
21C22×#11924036C2212yes—
22C22×#11924036C2214yes—
23#17989622C2214yescomplemented
24#17989621C2214yescomplemented
25#17989620C2218yescomplemented
26#17989619C2218yescomplemented
27#17989618C2218yescomplemented
28#17989617C2218yescomplemented
29#17989616C2218yescomplemented
30#17989615C2214yescomplemented
31#17989614C2218yescomplemented
32D4×#10596833C2214yescomplemented
33C2×#14556658C2212yescomplemented
34#17989588C2211yescharacteristic
35#17989588C2212yes—
36#17989588C2211yescharacteristic
37#17989588C2212yescomplemented
38#17989588C2212yescomplemented
39C2×C4⋊#10596833C2212yescomplemented
40#17989562C2214yescomplemented
41#17989561C2214yescomplemented
42#17989560C2218yescomplemented
43#17989555C2214yes—
44#17989555C2214yes—
45C4×#11924038C2212yescomplemented
46C4×#11924038C2212yescomplemented
47C4×#11924037C2212yescomplemented
48C4×#11924037C2212yescomplemented
49#17989546C2212yes—
50C4×#11924036C2212yes—
51C2×#41×D73C2212yes—
52#17989138C2211yescharacteristic
53#17989137C411yescharacteristic
54#17989136C2212yes—
55#17989135C2211yescharacteristic
56#17989134C412yes—
57#17989134C412yes—
58#17989133C412yes—
59#17989132C2212yes—
60#17989132C2212yes—
61C4⋊Q8×D73C411yescharacteristic
62#127×D73C411yescharacteristic
63#124×D73C412yes—
64#121×D73C412yes—
65#121×D73C412yes—
66C4×D4×D73C2212yes—
67C4×D4×D73C2212yes—
68C2×C42×D73C2211yescharacteristic
69#532×C73C411yescharacteristic
70#14556679—216no—
71#14556678—216no—
72#14556678—232no—
73C2×#11924038C2318yes—
74C2×#11924038C2312yes—
75C2×#11924038C2312yes—
76D73⋊M16—216no—
77D73⋊M16—24no—
78D73⋊M16D418yescomplemented
79C2×#11924037C2318yes—
80C2×#11924037C2312yes—
81C2×#11924037C2312yes—
82C2×#11924036—216no—
83C2×#11924036—28no—
84C2×#11924036C2312yes—
85C2×#11924036C2312yes—
86C2×#11924036C2314yes—
87C2×#11924036C2318yes—
88C2×#11924036C2312yes—
89C2×#11924036C2312yes—
90C22×#10596833C2314yes—
91C22×#10596833C2318yes—
92#14556658C2312yes—
93#14556658C2314yes—
94#14556658C2312yes—
95C4⋊#10596833C2312yes—
96C4⋊#10596833C2314yes—
97C4⋊#10596833C2312yes—
98#14556648C2318yes—
99#14556648C2318yes—
100C22⋊#10596833C2318yes—
101C22⋊#10596833C2318yes—
102#14556646C2314yes—
103#14556646C2314yes—
104C4×#10596833C2314yes—
105C4×#10596833C2314yes—
106C2×#11924029C2312yes—
107C2×#11924028C2×C412yes—
108C2×#11924028C2×C414yes—
109C2×#11924027C2314yes—
110C2×#11924027C2312yes—
111#41×D73—28no—
112#41×D73—28no—
113C2×Q8×D73C2×C412yes—
114C2×D4×D73C2×C412yes—
115C2×D4×D73C2×C412yes—
116C2×D4×D73C2×C414yes—
117C2×D4×D73C2×C412yes—
118C22×C4×D73C2×C411yescharacteristic
119C22×C4×D73C2×C411yescharacteristic
120C22×C4×D73C2314yes—
121C22×C4×D73C2311yescharacteristic
122#14556591C2×C411yescharacteristic
123#14556590C2×C412yes—
124#14556590C2×C412yes—
125#14556589C2×C412yes—
126#14556588C2×C411yescharacteristic
127#14556587C2×C412yes—
128#14556587C2×C412yes—
129#14556587C2×C412yes—
130#14556580C2×C412yes—
131#14556579C2×C412yes—
132#14556578C2×C412yes—
133#14556577C2×C414yes—
134#14556577C2×C414yes—
135#14556566C2×C412yes—
136#14556566C2×C412yes—
137#14556565C2×C412yes—
138#14556565C2×C412yes—
139#14556564C2×C414yes—
140#14556564C2×C414yes—
141#14556563C2×C414yes—
142#14556563C2×C414yes—
143#14556562C2×C412yes—
144#14556562C2×C412yes—
145C4×D292C2×C412yes—
146C4×D292C2×C412yes—
147D4×Dic73C2312yes—
148D4×Dic73C2312yes—
149#14556553C2312yes—
150#14556553C2312yes—
151C4×C22⋊D73C2×C414yes—
152C4×C22⋊D73C2×C414yes—
153#14556551C2314yes—
154#14556551C2314yes—
155C4⋊C4×D73C2×C412yes—
156C4⋊C4×D73C2×C412yes—
157C22⋊C4×D73C2×C414yes—
158C22⋊C4×D73C2×C414yes—
159C2×C4×Dic73C2×C411yescharacteristic
160C2×C4×Dic73C2311yescharacteristic
161C2×C4×Dic73C2311yescharacteristic
162C42×D73C2×C411yescharacteristic
163C42×D73C2×C411yescharacteristic
164C42×D73C2×C411yescharacteristic
165C42×D73C2×C411yescharacteristic
166C42×D73C2311yescharacteristic
167C42×D73C2311yescharacteristic
168C42×D73C2311yescharacteristic
169C42×D73C2311yescharacteristic
170C2×#41×C73C2×C412yes—
171C4⋊Q8×C73C2×C411yescharacteristic
172#127×C73C2×C411yescharacteristic
173#124×C73C2×C412yes—
174#121×C73C2×C412yes—
175#121×C73C2×C412yes—
176C4×D4×C73C2×C412yes—
177C4×D4×C73C2×C412yes—
178C2×C42×C73C2×C411yescharacteristic
179#11924038—24no—
180#11924038—216no—
181#11924038C2×D418yescomplemented
182#11924037—24no—
183#11924037—216no—
184#11924037C2×D418yescomplemented
185#11924036—24no—
186#11924036—24no—
187#11924036—28no—
188#11924036—24no—
189#11924036—216no—
190#11924036C2×D418yes—
191C2×#10596833—28no—
192C2×#10596833—216no—
193C2×#10596833C2414yes—
194C2×#10596833C2414yes—
195C2×#10596833C2414yes—
196C2×#10596833C2414yes—
197C23×D73C22×C414yes—
198C23×D73C22×C411yescharacteristic
199#11924029—24no—
200#11924029—24no—
201#11924028—28no—
202#11924028—216no—
203#11924027—28no—
204#11924027—28no—
205#11924027—24no—
206#11924027—24no—
207C2×Dic146C22×C414yes—
208C2×Dic146C22×C412yes—
209Q8×D73—28no—
210C2×D292C22×C412yes—
211C2×D292C22×C414yes—
212C2×D292C22×C412yes—
213C2×D292C22×C412yes—
214C2×C22⋊D73C22×C414yes—
215C2×C22⋊D73C22×C414yes—
216C2×C22⋊D73C22×C414yes—
217C2×C22⋊D73C22×C414yes—
218C2×C22⋊D73C22×C414yes—
219D4×D73—216no—
220D4×D73—28no—
221D4×D73—28no—
222D4×D73—44no—
223C22×Dic73C22×C411yescharacteristic
224C22×Dic73C22×C411yescharacteristic
225C22×Dic73C2414yes—
226C22×Dic73C2411yescharacteristic
227C2×C4×D73—24no—
228C2×C4×D73—28no—
229C2×C4×D73—28no—
230C2×C4×D73—42no—
231C2×C4×D73C22×C411yescharacteristic
232C2×C4×D73C22×C411yescharacteristic
233C2×C4×D73C22×C411yescharacteristic
234C2×C4×D73C22×C411yescharacteristic
235C2×C4×D73C22×C411yescharacteristic
236C2×C4×D73C22×C414yes—
237C2×C4×D73C22×C414yes—
238C2×C4×D73C22×C411yescharacteristic
239C2×C4×D73C22×C411yescharacteristic
240C2×C4×D73C22×C411yescharacteristic
241C2×C4×D73C22×C411yescharacteristic
242C2×C4×D73C22×C411yescharacteristic
243C2×C4×D73C2×D414yes—
244C2×C4×D73#4114yes—
245C2×C4×D73C2414yes—
246C2×C4×D73C2411yescharacteristic
247C2×C4×D73C2411yescharacteristic
248C4⋊Dic73C22×C412yes—
249C4⋊Dic73C22×C412yes—
250#11924007C22×C414yes—
251#11924007C22×C414yes—
252C22⋊Dic73C22×C414yes—
253C22⋊Dic73C22×C414yes—
254#11924005C22×C414yes—
255#11924005C22×C414yes—
256#11924005C22×C414yes—
257#11924005C22×C414yes—
258C4×Dic73C22×C411yescharacteristic
259C4×Dic73C22×C411yescharacteristic
260C4×Dic73C22×C411yescharacteristic
261C4×Dic73C22×C411yescharacteristic
262C4×Dic73C22×C411yescharacteristic
263C4×Dic73C22×C411yescharacteristic
264C4×Dic73C22×C411yescharacteristic
265C4×Dic73C22×C411yescharacteristic
266C4×Dic73C2411yescharacteristic
267C4×Dic73C2411yescharacteristic
268C4×Dic73C2411yescharacteristic
269C4×Dic73C2411yescharacteristic
270#41×C73—28no—
271C2×Q8×C73C22×C412yes—
272C2×D4×C73C22×C412yes—
273C2×D4×C73C22×C414yes—
274C2×D4×C73C22×C412yes—
275C2×D4×C73C22×C412yes—
276C22×C4×C73C22×C411yescharacteristic
277C22×C4×C73C22×C414yes—
278C22×C4×C73C22×C411yescharacteristic
279C22×C4×C73C22×C411yescharacteristic
280C4⋊C4×C73C22×C412yes—
281C4⋊C4×C73C22×C412yes—
282C22⋊C4×C73C22×C414yes—
283C22⋊C4×C73C22×C414yes—
284C42×C73C22×C411yescharacteristic
285C42×C73C22×C411yescharacteristic
286C42×C73C22×C411yescharacteristic
287C42×C73C22×C411yescharacteristic
288C23×C73C23×C414yes—
289C23×C73C23×C411yescharacteristic
290C22×D73—22no—
291C22×D73—22no—
292C22×D73—28no—
293C22×D73—28no—
294C22×D73—28no—
295C22×D73C4×D414yes—
296C22×D73C23×C414yes—
297C22×D73C23×C411yescharacteristic
298C22×D73C23×C411yescharacteristic
299Q8×C73—24no—
300D4×C73—28no—
301D4×C73—24no—
302D4×C73—24no—
303D4×C73—42no—
304C2×C4×C73—28no—
305C2×C4×C73—22no—
306C2×C4×C73—41no—
307C2×C4×C73C4×D414yes—
308C2×C4×C73C23×C411yescharacteristic
309C2×C4×C73C23×C411yescharacteristic
310C2×C4×C73C23×C411yescharacteristic
311C2×C4×C73C23×C414yes—
312C2×C4×C73C23×C411yescharacteristic
313C2×C4×C73C23×C411yescharacteristic
314C2×C4×C73C23×C411yescharacteristic
315C22⋊D73—28no—
316C22⋊D73—28no—
317C22⋊D73—28no—
318C22⋊D73—28no—
319C22⋊D73—44no—
320C2×Dic73—22no—
321C2×Dic73—24no—
322C2×Dic73—24no—
323C2×Dic73—41no—
324C2×Dic73C23×C411yescharacteristic
325C2×Dic73C23×C411yescharacteristic
326C2×Dic73C23×C411yescharacteristic
327C2×Dic73C23×C414yes—
328C2×Dic73C23×C411yescharacteristic
329C2×Dic73C23×C411yescharacteristic
330C2×Dic73C22×D412yes—
331C2×Dic73C2×#4112yes—
332C2×Dic73C2511yescharacteristic
333D292—28no—
334D292—24no—
335D292—24no—
336D292—42no—
337C4×D73—28no—
338C4×D73—22no—
339C4×D73—22no—
340C4×D73—22no—
341C4×D73—28no—
342C4×D73—22no—
343C4×D73—22no—
344C4×D73—24no—
345C4×D73—24no—
346C4×D73—41no—
347C4×D73—41no—
348C4×D73C4×D414yes—
349C4×D73C4×D414yes—
350C4×D73#13114yescomplemented
351C4×D73C22×D412yes—
352C4×D73C22×D412yes—
353C4×D73C2×#4112yes—
354C4×D73C2×#4112yes—
355Dic146—24no—
356Dic146—28no—
357#10596833—24no—
358#10596833—24no—
359#10596833—24no—
360#10596833C22×D418yes—
361C22×C73—21no—
362C22×C73—21no—
363C22×C73—24no—
364C22×C73—24no—
365C22×C73—24no—
366C22×C73C2×C4×D412yes—
367C22×C73C24×C411yescharacteristic
368C2×D73—21no—
369C2×D73—21no—
370C2×D73—28no—
371C2×D73—24no—
372C2×D73—24no—
373C2×D73—24no—
374C2×D73—416no—
375C2×D73C2×C4×D412yes—
376C2×D73C2×C4×D412yes—
377C2×D73C2×#13112yes—
378C2×D73#56812yes—
379C4×C73—24no—
380C4×C73—21no—
381C4×C73—21no—
382C4×C73—21no—
383C4×C73C2×C4×D412yes—
384C4×C73C2×C4×D412yes—
385C4×C73C2×#13112yescomplemented
386Dic73—24no—
387Dic73—21no—
388Dic73—21no—
389Dic73—21no—
390Dic73C2×C4×D412yes—
391Dic73C2×#13112yescomplemented
392Dic73C23×D411yescharacteristic
393Dic73C22×#4111yescharacteristic
394C2×#2935—731nomaximal, Sylow
395C2×C73—22no—
396C2×C73—44no—
397C2×C73C22×C4×D411yescharacteristic
398C2×C73C22×#13111yescharacteristic
399C2×C73C2×#56811yescharacteristic
400D73—22no—
401D73—44no—
402D73#293514yescomplemented
403C22×#131—732no—
404C2×#532—731no—
405#2935—734no—
406#2935—732no—
407#2935—734no—
408#2935—734no—
409#2935—732no—
410C2×#436—732no—
411C2×#435—734no—
412C2×C8×D4—732no—
413C22×C4⋊C8—731no—
414C2×#408—732no—
415C2×C4×M16—731no—
416C73C2×#293511yescharacteristic, complemented, Sylow
417C22×#41—732no—
418C2×#131—738no—
419C2×#131—734no—
420C2×#131—734no—
421C2×#131—14616no—
422C22×M16—731no—
423C22×M16—731no—
424C22×M16—734no—
425C23×C8—732no—
426C23×C8—734no—
427#532—732no—
428#532—731no—
429#532—731no—
430#532—732no—
431#532—732no—
432#532—732no—
433#532—732no—
434#532—732no—
435#532—731no—
436#532#6440811yescharacteristic
437C2×C4⋊Q8—731no—
438C2×#127—731no—
439C2×#124—732no—
440C2×#121—732no—
441C2×#121—732no—
442C2×C4×D4—732no—
443C2×C4×D4—732no—
444C22×C42—731no—
445#436—738no—
446#436—734no—
447#436—734no—
448#435—738no—
449#435—738no—
450#435—738no—
451#435—738no—
452C8×D4—734no—
453C8×D4—738no—
454C8×D4—734no—
455C2×C4⋊C8—731no—
456C2×C4⋊C8—732no—
457C2×C4⋊C8—731no—
458C2×C4⋊C8—732no—
459C2×C4⋊C8—732no—
460C2×C4⋊C8—732no—
461C2×C4⋊C8—732no—
462#408—738no—
463#408—734no—
464#408—734no—
465C2×C22⋊C8—734no—
466C2×C22⋊C8—734no—
467C4×M16—732no—
468C4×M16—732no—
469C4×M16—732no—
470C4×M16—732no—
471C2×#97—732no—
472C2×C4×C8—732no—
473C2×#41—732no—
474C2×#41—734no—
475C2×#41—732no—
476C2×#41—734no—
477C2×#41—732no—
478C2×#41—1468no—
479C2×#41—1468no—
480C2×#41C2×#6440812yes—
481C22×Q8—732no—
482C22×D4—732no—
483C22×D4—732no—
484C22×D4—734no—
485C22×D4—732no—
486C23×C4—731no—
487C23×C4—731no—
488C23×C4—734no—
489C23×C4—731no—
490#131—14616no—
491#131—14632no—
492#131—14616no—
493C2×M16—732no—
494C2×M16—738no—
495C2×M16—732no—
496C2×M16—738no—
497C2×M16—732no—
498C2×M16—738no—
499C2×M16—732no—
500C2×M16—14616no—
501C2×M16—1464no—
502C22×C8—732no—
503C22×C8—734no—
504C22×C8—738no—
505C22×C8—732no—
506C22×C8—732no—
507C22×C8—734no—
508C22×C8—738no—
509C22×C8—732no—
510C22×C8—14616no—
511C22×C8—1468no—
512C4⋊Q8—732no—
513C4⋊Q8—732no—
514C4⋊Q8—732no—
515C4⋊Q8—731no—
516C4⋊Q8C2×#6440811yescharacteristic
517#127—732no—
518#127—732no—
519#127—732no—
520#127—731no—
521#127C2×#6440811yescharacteristic
522#124—732no—
523#124—732no—
524#124—734no—
525#124—734no—
526#124—732no—
527#124C2×#6440812yes—
528#121—732no—
529#121—732no—
530#121—734no—
531#121—734no—
532#121—732no—
533#121—732no—
534#121—732no—
535#121—732no—
536#121—734no—
537#121—734no—
538#121C2×#6440812yes—
539#121C2×#6440812yes—
540C4×D4—732no—
541C4×D4—732no—
542C4×D4—734no—
543C4×D4—734no—
544C4×D4—732no—
545C4×D4—732no—
546C4×D4—734no—
547C4×D4—734no—
548C4×D4—732no—
549C4×D4—732no—
550C4×D4C2×#6440812yes—
551C4×D4C2×#6440812yes—
552C2×C4⋊C4—732no—
553C2×C4⋊C4—732no—
554C2×C22⋊C4—734no—
555C2×C22⋊C4—734no—
556C2×C42—731no—
557C2×C42—731no—
558C2×C42—731no—
559C2×C42—731no—
560C2×C42—731no—
561C2×C42—731no—
562C2×C42—731no—
563C2×C42—731no—
564C2×C42—731no—
565C2×C42—731no—
566C2×C42—731no—
567C2×C42C2×#6440811yescharacteristic
568C4⋊C8—732no—
569C4⋊C8—732no—
570C4⋊C8—734no—
571C4⋊C8—734no—
572C4⋊C8—732no—
573C4⋊C8—732no—
574C22⋊C8—738no—
575C22⋊C8—738no—
576C22⋊C8—738no—
577C22⋊C8—738no—
578#97—734no—
579#97—734no—
580C4×C8—734no—
581C4×C8—734no—
582C24—731no—
583C24—734no—
584#41—28no—
585#41—14616no—
586#41—1468no—
587#41—1464no—
588#41—1468no—
589#41—1464no—
590#41—1464no—
591#41—1464no—
592#41—1468no—
593C2×Q8—734no—
594C2×Q8—732no—
595C2×Q8—1468no—
596C2×Q8C22×#6440812yes—
597C2×D4—2924no—
598C2×D4—734no—
599C2×D4—734no—
600C2×D4—734no—
601C2×D4—734no—
602C2×D4—734no—
603C2×D4—732no—
604C2×D4—732no—
605C2×D4—734no—
606C2×D4—732no—
607C2×D4—1468no—
608C2×D4—1468no—
609C2×D4—14616no—
610C2×D4C22×#6440812yes—
611C2×D4C22×#6440814yes—
612C2×D4C22×#6440812yes—
613C2×D4C22×#6440812yes—
614C22×C4—2922no—
615C22×C4—731no—
616C22×C4—731no—
617C22×C4—731no—
618C22×C4—731no—
619C22×C4—731no—
620C22×C4—731no—
621C22×C4—731no—
622C22×C4—731no—
623C22×C4—731no—
624C22×C4—734no—
625C22×C4—734no—
626C22×C4—731no—
627C22×C4—734no—
628C22×C4—731no—
629C22×C4—731no—
630C22×C4—731no—
631C22×C4—731no—
632C22×C4—731no—
633C22×C4—734no—
634C22×C4—734no—
635C22×C4—734no—
636C22×C4—1468no—
637C22×C4—1464no—
638C22×C4—1468no—
639C22×C4C22×#6440811yescharacteristic
640C22×C4C22×#6440814yes—
641C22×C4C22×#6440811yescharacteristic
642C22×C4C22×#6440811yescharacteristic
643M16—738no—
644M16—738no—
645M16—14616no—
646M16—14616no—
647M16—1464no—
648M16—1464no—
649C2×C8—734no—
650C2×C8—738no—
651C2×C8—734no—
652C2×C8—734no—
653C2×C8—734no—
654C2×C8—14616no—
655C2×C8—14616no—
656C2×C8—1468no—
657C2×C8—1464no—
658C2×C8—1464no—
659C2×C8—1468no—
660C2×C8—1464no—
661C4⋊C4—734no—
662C4⋊C4—734no—
663C4⋊C4—732no—
664C4⋊C4—732no—
665C4⋊C4C22×#6440812yes—
666C4⋊C4C22×#6440812yes—
667C22⋊C4—734no—
668C22⋊C4—734no—
669C22⋊C4—734no—
670C22⋊C4—734no—
671C22⋊C4—734no—
672C22⋊C4—734no—
673C22⋊C4C22×#6440814yes—
674C22⋊C4C22×#6440814yes—
675C42—731no—
676C42—731no—
677C42—731no—
678C42—731no—
679C42—731no—
680C42—731no—
681C42—731no—
682C42—731no—
683C42—731no—
684C42—731no—
685C42—731no—
686C42—731no—
687C42C22×#6440811yescharacteristic
688C42C22×#6440811yescharacteristic
689C42C22×#6440811yescharacteristic
690C42C22×#6440811yescharacteristic
691C23—731no—
692C23—734no—
693C23—731no—
694C23—734no—
695C23—1468no—
696C23—1468no—
697C23—1468no—
698C23—1462no—
699C23—1462no—
700C23C23×#6440814yes—
701C23C23×#6440811yescharacteristic
702Q8—24no—
703Q8—1468no—
704Q8—1464no—
705D4—28no—
706D4—24no—
707D4—24no—
708D4—42no—
709D4—2922no—
710D4—2924no—
711D4—1468no—
712D4—1468no—
713D4—1468no—
714D4—1468no—
715D4—1468no—
716D4—1464no—
717D4—1464no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—41no—
721C2×C4—2921no—
722C2×C4—2921no—
723C2×C4—2921no—
724C2×C4—732no—
725C2×C4—732no—
726C2×C4—731no—
727C2×C4—731no—
728C2×C4—731no—
729C2×C4—732no—
730C2×C4—732no—
731C2×C4—732no—
732C2×C4—732no—
733C2×C4—734no—
734C2×C4—734no—
735C2×C4—734no—
736C2×C4—731no—
737C2×C4—731no—
738C2×C4—731no—
739C2×C4—734no—
740C2×C4—1464no—
741C2×C4—1464no—
742C2×C4—1462no—
743C2×C4—1462no—
744C2×C4—1462no—
745C2×C4—1468no—
746C2×C4—1462no—
747C2×C4—1464no—
748C2×C4—1464no—
749C2×C4—1462no—
750C2×C4—1468no—
751C2×C4—1462no—
752C2×C4D4×#6440814yes—
753C2×C4C23×#6440811yescharacteristic
754C2×C4C23×#6440811yescharacteristic
755C2×C4C23×#6440811yescharacteristic
756C2×C4C23×#6440814yes—
757C2×C4C23×#6440811yescharacteristic
758C2×C4C23×#6440811yescharacteristic
759C2×C4C23×#6440811yescharacteristic
760C8—738no—
761C8—1464no—
762C8—1464no—
763C8—1464no—
764C22—21no—
765C22—21no—
766C22—24no—
767C22—24no—
768C22—24no—
769C22—29216no—
770C22—732no—
771C22—732no—
772C22—732no—
773C22—732no—
774C22—1468no—
775C22—1464no—
776C22—1464no—
777C22—1464no—
778C22—1461no—
779C22—1461no—
780C22C2×D4×#6440812yes—
781C22C24×#6440811yescharacteristic
782C4—24no—
783C4—21no—
784C4—21no—
785C4—21no—
786C4—731no—
787C4—731no—
788C4—732no—
789C4—732no—
790C4—1464no—
791C4—1461no—
792C4—1461no—
793C4—1461no—
794C4C2×D4×#6440812yes—
795C4C2×D4×#6440812yes—
796C4D73⋊#13112yescomplemented
797C2—22no—
798C2—44no—
799C2—2924no—
800C2—734no—
801C2—1462no—
802C2C22×D4×#6440811yescharacteristic
803C2C2×D73⋊#13111yescharacteristic
804C2D73⋊#56811yescharacteristic
subgroupG/H
centerC2×C4C23×#64408
commutator, socleC22×C73C24×C4
FrattiniC22C24×#64408
Fitting#532×C73C4
prime radical#532×D73C2
cosocleC2×Dic73C25
hypercenter#532#64408
hypocenterC73C2×#2935
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×D73⋊#131C2semidirect
2. #22626677C2semidirect
3. #22626676C2semidirect
4. #22626675C2semidirect
5. #22626674C2semidirect
6. #22626673C2semidirect
7. D73⋊#436C2semidirect
8. D73⋊#435C2semidirect
9. D4×#11924036C2semidirect
10. C2×#17989588C2semidirect
11. D73⋊#408C2semidirect
12. C4×D73⋊M16C2semidirect
14. C2×#14556679C22semidirect
16. C2×#14556678C22semidirect
17. C2×#14556678C22semidirect
23. #17989622C22semidirect
24. #17989621C22semidirect
25. #17989620C22semidirect
26. #17989619C22semidirect
27. #17989618C22semidirect
28. #17989617C22semidirect
29. #17989616C22semidirect
30. #17989615C22semidirect
31. #17989614C22semidirect
32. D4×#10596833C22semidirect
33. C2×#14556658C22semidirect
37. #17989588C22semidirect
38. #17989588C22semidirect
39. C2×C4⋊#10596833C22semidirect
40. #17989562C22semidirect
41. #17989561C22semidirect
42. #17989560C22semidirect
45. C4×#11924038C22semidirect
46. C4×#11924038C22semidirect
47. C4×#11924037C22semidirect
48. C4×#11924037C22semidirect
78. D73⋊M16D4semidirect
181. #11924038C2×D4semidirect
184. #11924037C2×D4semidirect
350. C4×D73#131semidirect
385. C4×C73C2×#131semidirect
391. Dic73C2×#131semidirect
402. D73#2935semidirect
416. C73C2×#2935semidirect
796. C4D73⋊#131semidirect

Maximal subgroups

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

subgroupindex
C2×D73⋊#1312
#226266772
#226266762
#226266752
#226266742
#226266732
D73⋊#4362
D73⋊#4352
D4×#119240362
C2×#179895882
D73⋊#4082
C4×D73⋊M162
#532×D732
C2×#293573