Finite Group Databasebeta

← C73×#11033 #32920437

Subgroups — C73×#11033 #32920437

Order 18688.

1264 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C73C211yesmaximal, characteristic
2C2×#421×C73C211yesmaximal, characteristic, complemented
3C73×#2896C211yesmaximal, characteristic, complemented
4C2×#410×C73C211yesmaximal, characteristic, complemented
5C2×#410×C73C211yesmaximal, characteristic, complemented
6C73×#1742C211yesmaximal, characteristic, complemented
7C73×#1733C211yesmaximal, characteristic, complemented
8C22×#41×C73C2211yescharacteristic
9C22×#41×C73C2211yescharacteristic
10#575×C73—22no—
11#575×C73—22no—
12#575×C73—22no—
13#575×C73—22no—
14C2×#137×C73—21no—
15C2×#137×C73C412yescomplemented
16C2×AGL(1,ℤ/8)×C73—21no—
17C2×AGL(1,ℤ/8)×C73C412yescomplemented
18C2×#135×C73—22no—
19C22×M16×C73C2211yescharacteristic
20C22×M16×C73C2211yescharacteristic
21C2×#117×C73C2211yescharacteristic
22C2×#117×C73C2211yescharacteristic
23C2×#117×C73C2211yescharacteristic
24#421×C73—22no—
25#421×C73—22no—
26C2×#104×C73—22no—
27#419×C73—21no—
28#418×C73—21no—
29#417×C73—22no—
30#416×C73—22no—
31#410×C73—22no—
32#410×C73—22no—
33#410×C73—22no—
34#410×C73—22no—
35C2×#99×C73—22no—
36C2×#99×C73—22no—
37#343×C73—22no—
38#339×C73—22no—
39C2×#41×C73—21no—
40C2×#41×C73—21no—
41C2×#41×C73—21no—
42C2×#41×C73—21no—
43C2×#41×C73—21no—
44C2×#41×C73—21no—
45C2×#41×C73—21no—
46C2×#41×C73—21no—
47C2×#41×C73—21no—
48C2×#41×C73—21no—
49C2×#41×C73—21no—
50C2×#41×C73—21no—
51C2×#41×C73—21no—
52C2×#41×C73—21no—
53C2×#41×C73—21no—
54C2×#41×C73—21no—
55C2×#41×C73—21no—
56C2×#41×C73—21no—
57C2×#41×C73—21no—
58C2×#41×C73—21no—
59C2×#41×C73C2×C412yes—
60C2×#41×C73D412yes—
61C2×#41×C73D412yes—
62C2×#41×C73D412yes—
63C22×Q8×C73C2×C411yescharacteristic
64C22×Q8×C73D411yescharacteristic
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73C2×C411yescharacteristic
68C22×D4×C73D411yescharacteristic
69C23×C4×C73—21no—
70C23×C4×C73—21no—
71C23×C4×C73C2311yescharacteristic
72#137×C73—24no—
73#137×C73—24no—
74#137×C73—24no—
75#137×C73—24no—
76AGL(1,ℤ/8)×C73—24no—
77AGL(1,ℤ/8)×C73—24no—
78AGL(1,ℤ/8)×C73—24no—
79AGL(1,ℤ/8)×C73—24no—
80#135×C73—28no—
81#135×C73—28no—
82C2×Q16×C73—22no—
83C2×SD16×C73—22no—
84C2×SD16×C73—22no—
85C2×D8×C73—22no—
86C2×M16×C73—21no—
87C2×M16×C73—21no—
88C2×M16×C73—21no—
89C2×M16×C73—21no—
90C2×M16×C73—21no—
91C2×M16×C73—21no—
92C2×M16×C73—21no—
93C2×M16×C73—21no—
94C2×M16×C73C2×C412yes—
95C2×M16×C73D412yes—
96C2×M16×C73D412yes—
97C2×M16×C73D412yes—
98C22×C8×C73—21no—
99C22×C8×C73—21no—
100#117×C73—21no—
101#117×C73—21no—
102#117×C73—21no—
103#117×C73—21no—
104#117×C73—21no—
105#117×C73—21no—
106#117×C73—21no—
107#117×C73—21no—
108#117×C73—21no—
109#117×C73—21no—
110#117×C73D412yes—
111#117×C73D412yes—
112C2×C4⋊C4×C73—21no—
113C2×C4⋊C4×C73—21no—
114C2×C4⋊C4×C73—21no—
115C2×C22⋊C4×C73—21no—
116C2×C22⋊C4×C73—21no—
117C2×C22⋊C4×C73D412yes—
118C2×C42×C73—21no—
119C2×C42×C73—21no—
120C2×C42×C73—21no—
121#104×C73—28no—
122#103×C73—24no—
123#102×C73—24no—
124#99×C73—28no—
125#99×C73—28no—
126C24×C73—21no—
127C24×C73—21no—
128C24×C73C2×D411yescharacteristic
129#41×C73—22no—
130#41×C73—22no—
131#41×C73—22no—
132#41×C73—22no—
133#41×C73—22no—
134#41×C73—22no—
135#41×C73—22no—
136#41×C73—22no—
137#41×C73—22no—
138#41×C73—22no—
139#41×C73—22no—
140#41×C73—22no—
141#41×C73—22no—
142#41×C73—22no—
143#41×C73—22no—
144#41×C73—22no—
145#41×C73—41no—
146#41×C73—41no—
147#41×C73—41no—
148#41×C73—41no—
149#41×C73—41no—
150#41×C73—41no—
151#41×C73—41no—
152#41×C73—41no—
153#41×C73—41no—
154#41×C73—41no—
155#41×C73—41no—
156#41×C73—41no—
157#41×C73—41no—
158#41×C73—41no—
159#41×C73—41no—
160#41×C73—41no—
161C2×Q8×C73—21no—
162C2×Q8×C73—21no—
163C2×Q8×C73—21no—
164C2×Q8×C73—21no—
165C2×Q8×C73—21no—
166C2×Q8×C73—21no—
167C2×Q8×C73—21no—
168C2×Q8×C73—21no—
169C2×Q8×C73—21no—
170C2×Q8×C73—21no—
171C2×Q8×C73C22⋊C412yes—
172C2×Q8×C73C22⋊C412yes—
173C2×D4×C73—22no—
174C2×D4×C73—22no—
175C2×D4×C73—22no—
176C2×D4×C73—22no—
177C2×D4×C73—21no—
178C2×D4×C73—21no—
179C2×D4×C73—21no—
180C2×D4×C73—21no—
181C2×D4×C73—21no—
182C2×D4×C73—21no—
183C2×D4×C73—21no—
184C2×D4×C73—21no—
185C2×D4×C73—21no—
186C2×D4×C73—21no—
187C2×D4×C73—41no—
188C2×D4×C73—41no—
189C2×D4×C73—41no—
190C2×D4×C73—41no—
191C2×D4×C73—41no—
192C2×D4×C73—41no—
193C2×D4×C73—41no—
194C2×D4×C73—41no—
195C2×D4×C73C22⋊C412yes—
196C2×D4×C73C22⋊C412yes—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—22no—
200C22×C4×C73—22no—
201C22×C4×C73—22no—
202C22×C4×C73—22no—
203C22×C4×C73—22no—
204C22×C4×C73—41no—
205C22×C4×C73—41no—
206C22×C4×C73—41no—
207C22×C4×C73—41no—
208C22×C4×C73—41no—
209C22×C4×C73—41no—
210C22×C4×C73—41no—
211C22×C4×C73—41no—
212C22×C4×C73—41no—
213C22×C4×C73—41no—
214C22×C4×C73C22×C411yescharacteristic
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2×D411yescharacteristic
219C22×C4×C73C2×D411yescharacteristic
220C22×C4×C73C2×D411yescharacteristic
221C22×C4×C73C2×D411yescharacteristic
222C22×C4×C73C2×D411yescharacteristic
223C22×C4×C73C2×D411yescharacteristic
224C22×C4×C73#4111yescharacteristic
225C22×C4×C73#4111yescharacteristic
226C22×C4×C73#4111yescharacteristic
227C22×C4×C73#4111yescharacteristic
228Q16×C73—28no—
229SD16×C73—28no—
230SD16×C73—28no—
231D8×C73—28no—
232M16×C73—22no—
233M16×C73—22no—
234M16×C73—22no—
235M16×C73—22no—
236M16×C73—22no—
237M16×C73—41no—
238M16×C73—41no—
239M16×C73C22⋊C414yes—
240C2×C8×C73—22no—
241C2×C8×C73—22no—
242C2×C8×C73—22no—
243C2×C8×C73—22no—
244C2×C8×C73—41no—
245C2×C8×C73—41no—
246C4⋊C4×C73—22no—
247C4⋊C4×C73—22no—
248C4⋊C4×C73—41no—
249C4⋊C4×C73—41no—
250C4⋊C4×C73—41no—
251C4⋊C4×C73—41no—
252C22⋊C4×C73—22no—
253C22⋊C4×C73—22no—
254C22⋊C4×C73—22no—
255C22⋊C4×C73—22no—
256C22⋊C4×C73—41no—
257C22⋊C4×C73—41no—
258C42×C73—22no—
259C42×C73—22no—
260C42×C73—41no—
261C42×C73—41no—
262C42×C73—41no—
263C42×C73—41no—
264C23×C73—22no—
265C23×C73—22no—
266C23×C73—41no—
267C23×C73—41no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73—81no—
271C23×C73—82no—
272C23×C73—82no—
273C23×C73C4×D411yescharacteristic
274C23×C73#12011yescharacteristic
275C23×C73#12011yescharacteristic
276C23×C73#12111yescharacteristic
277C23×C73#12111yescharacteristic
278C23×C73#12111yescharacteristic
279C23×C73#12711yescharacteristic
280Q8×C73—22no—
281Q8×C73—22no—
282Q8×C73—22no—
283Q8×C73—22no—
284Q8×C73—41no—
285Q8×C73—41no—
286Q8×C73—41no—
287Q8×C73—41no—
288D4×C73—22no—
289D4×C73—22no—
290D4×C73—22no—
291D4×C73—22no—
292D4×C73—42no—
293D4×C73—42no—
294D4×C73—42no—
295D4×C73—42no—
296D4×C73—42no—
297D4×C73—42no—
298D4×C73—42no—
299D4×C73—42no—
300D4×C73—41no—
301D4×C73—41no—
302D4×C73—41no—
303D4×C73—41no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
310C2×C4×C73—42no—
311C2×C4×C73—42no—
312C2×C4×C73—42no—
313C2×C4×C73—42no—
314C2×C4×C73—42no—
315C2×C4×C73—42no—
316C2×C4×C73—42no—
317C2×C4×C73—42no—
318C2×C4×C73—42no—
319C2×C4×C73—42no—
320C2×C4×C73—42no—
321C2×C4×C73—82no—
322C2×C4×C73—82no—
323C2×C4×C73—82no—
324C2×C4×C73C2×C22⋊C411yescharacteristic
325C2×C4×C73C2×C22⋊C411yescharacteristic
326C2×C4×C73C2×C22⋊C411yescharacteristic
327C2×C4×C73C4×D411yescharacteristic
328C2×C4×C73C4×D411yescharacteristic
329C2×C4×C73C4×D411yescharacteristic
330C2×C4×C73#12011yescharacteristic
331C2×C4×C73#12011yescharacteristic
332C2×C4×C73#12011yescharacteristic
333C2×C4×C73#12011yescharacteristic
334C2×C4×C73#12011yescharacteristic
335C2×C4×C73#12011yescharacteristic
336C2×C4×C73#12111yescharacteristic
337C2×C4×C73#12111yescharacteristic
338C2×C4×C73#12111yescharacteristic
339C2×C4×C73#12111yescharacteristic
340C2×C4×C73#12111yescharacteristic
341C2×C4×C73#12111yescharacteristic
342C2×C4×C73#12111yescharacteristic
343C2×C4×C73#12111yescharacteristic
344C2×C4×C73#12111yescharacteristic
345C2×C4×C73#12311yescharacteristic
346C2×C4×C73#12311yescharacteristic
347C2×C4×C73#12311yescharacteristic
348C2×C4×C73#12311yescharacteristic
349C2×C4×C73#12411yescharacteristic
350C2×C4×C73#12411yescharacteristic
351C2×C4×C73#12711yescharacteristic
352C8×C73—24no—
353C8×C73—42no—
354C22×C73—41no—
355C22×C73—41no—
356C22×C73—41no—
357C22×C73—41no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—41no—
361C22×C73—42no—
362C22×C73—42no—
363C22×C73—82no—
364C22×C73—82no—
365C22×C73—82no—
366C22×C73—82no—
367C22×C73—82no—
368C22×C73—82no—
369C22×C73#38611yescharacteristic
370C22×C73#38611yescharacteristic
371C22×C73#39011yescharacteristic
372C22×C73#39211yescharacteristic
373C22×C73#39211yescharacteristic
374C22×C73#39211yescharacteristic
375C22×C73#39411yescharacteristic
376C4×C73—42no—
377C4×C73—42no—
378C4×C73—82no—
379C4×C73—82no—
380C4×C73—82no—
381C4×C73#37911yescharacteristic
382C4×C73#38611yescharacteristic
383C4×C73#38611yescharacteristic
384C4×C73#39011yescharacteristic
385C4×C73#39211yescharacteristic
386C4×C73#39411yescharacteristic
387C4×C73#39411yescharacteristic
388C4×C73#39411yescharacteristic
389#11033C7311yesmaximal, characteristic, direct product factor, Sylow
390C2×C73—21no—
391C2×C73—21no—
392C2×C73—21no—
393C2×C73—21no—
394C2×C73—21no—
395C2×C73—21no—
396C2×C73—21no—
397C2×C73—82no—
398C2×C73—82no—
399C2×C73#143811yescharacteristic
400C2×#575C2×C7311yescharacteristic
401C2×#421C2×C7311yescharacteristic, complemented
402#2896C2×C7311yescharacteristic, complemented
403C2×#410C2×C7311yescharacteristic, complemented
404C2×#410C2×C7311yescharacteristic, complemented
405#1742C2×C7311yescharacteristic, complemented
406#1733C2×C7311yescharacteristic, complemented
407C73#1103311yescharacteristic, direct product factor, Sylow
408C22×#41C22×C7311yescharacteristic
409C22×#41C22×C7311yescharacteristic
410#575—22no—
411#575—22no—
412#575—22no—
413#575—22no—
414C2×#137—21no—
415C2×#137C4×C7312yescomplemented
416C2×AGL(1,ℤ/8)—21no—
417C2×AGL(1,ℤ/8)C4×C7312yescomplemented
418C2×#135—22no—
419C22×M16C22×C7311yescharacteristic
420C22×M16C22×C7311yescharacteristic
421C2×#117C22×C7311yescharacteristic
422C2×#117C22×C7311yescharacteristic
423C2×#117C22×C7311yescharacteristic
424#421—22no—
425#421—22no—
426C2×#104—22no—
427#419—21no—
428#418—21no—
429#417—22no—
430#416—22no—
431#410—22no—
432#410—22no—
433#410—22no—
434#410—22no—
435C2×#99—22no—
436C2×#99—22no—
437#343—22no—
438#339—22no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41C2×C4×C7312yes—
460C2×#41D4×C7312yes—
461C2×#41D4×C7312yes—
462C2×#41D4×C7312yes—
463C22×Q8C2×C4×C7311yescharacteristic
464C22×Q8D4×C7311yescharacteristic
465C22×D4—21no—
466C22×D4—21no—
467C22×D4C2×C4×C7311yescharacteristic
468C22×D4D4×C7311yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4C23×C7311yescharacteristic
472#137—24no—
473#137—24no—
474#137—24no—
475#137—24no—
476AGL(1,ℤ/8)—24no—
477AGL(1,ℤ/8)—24no—
478AGL(1,ℤ/8)—24no—
479AGL(1,ℤ/8)—24no—
480#135—28no—
481#135—28no—
482C2×Q16—22no—
483C2×SD16—22no—
484C2×SD16—22no—
485C2×D8—22no—
486C2×M16—21no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—21no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16C2×C4×C7312yes—
495C2×M16D4×C7312yes—
496C2×M16D4×C7312yes—
497C2×M16D4×C7312yes—
498C22×C8—21no—
499C22×C8—21no—
500#117—21no—
501#117—21no—
502#117—21no—
503#117—21no—
504#117—21no—
505#117—21no—
506#117—21no—
507#117—21no—
508#117—21no—
509#117—21no—
510#117D4×C7312yes—
511#117D4×C7312yes—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4D4×C7312yes—
518C2×C42—21no—
519C2×C42—21no—
520C2×C42—21no—
521#104—28no—
522#103—24no—
523#102—24no—
524#99—28no—
525#99—28no—
526C24—21no—
527C24—21no—
528C24C2×D4×C7311yescharacteristic
529#41—22no—
530#41—22no—
531#41—22no—
532#41—22no—
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8C22⋊C4×C7312yes—
572C2×Q8C22⋊C4×C7312yes—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4C22⋊C4×C7312yes—
596C2×D4C22⋊C4×C7312yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4C22×C4×C7311yescharacteristic
615C22×C4C2×D4×C7311yescharacteristic
616C22×C4C2×D4×C7311yescharacteristic
617C22×C4C2×D4×C7311yescharacteristic
618C22×C4C2×D4×C7311yescharacteristic
619C22×C4C2×D4×C7311yescharacteristic
620C22×C4C2×D4×C7311yescharacteristic
621C22×C4C2×D4×C7311yescharacteristic
622C22×C4C2×D4×C7311yescharacteristic
623C22×C4C2×D4×C7311yescharacteristic
624C22×C4#41×C7311yescharacteristic
625C22×C4#41×C7311yescharacteristic
626C22×C4#41×C7311yescharacteristic
627C22×C4#41×C7311yescharacteristic
628Q16—28no—
629SD16—28no—
630SD16—28no—
631D8—28no—
632M16—22no—
633M16—22no—
634M16—22no—
635M16—22no—
636M16—22no—
637M16—41no—
638M16—41no—
639M16C22⋊C4×C7314yes—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—41no—
645C2×C8—41no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—41no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C4⋊C4—41no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—41no—
657C22⋊C4—41no—
658C42—22no—
659C42—22no—
660C42—41no—
661C42—41no—
662C42—41no—
663C42—41no—
664C23—22no—
665C23—22no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—81no—
671C23—82no—
672C23—82no—
673C23C4×D4×C7311yescharacteristic
674C23#120×C7311yescharacteristic
675C23#120×C7311yescharacteristic
676C23#121×C7311yescharacteristic
677C23#121×C7311yescharacteristic
678C23#121×C7311yescharacteristic
679C23#127×C7311yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—82no—
722C2×C4—82no—
723C2×C4—82no—
724C2×C4C2×C22⋊C4×C7311yescharacteristic
725C2×C4C2×C22⋊C4×C7311yescharacteristic
726C2×C4C2×C22⋊C4×C7311yescharacteristic
727C2×C4C4×D4×C7311yescharacteristic
728C2×C4C4×D4×C7311yescharacteristic
729C2×C4C4×D4×C7311yescharacteristic
730C2×C4#120×C7311yescharacteristic
731C2×C4#120×C7311yescharacteristic
732C2×C4#120×C7311yescharacteristic
733C2×C4#120×C7311yescharacteristic
734C2×C4#120×C7311yescharacteristic
735C2×C4#120×C7311yescharacteristic
736C2×C4#121×C7311yescharacteristic
737C2×C4#121×C7311yescharacteristic
738C2×C4#121×C7311yescharacteristic
739C2×C4#121×C7311yescharacteristic
740C2×C4#121×C7311yescharacteristic
741C2×C4#121×C7311yescharacteristic
742C2×C4#121×C7311yescharacteristic
743C2×C4#121×C7311yescharacteristic
744C2×C4#121×C7311yescharacteristic
745C2×C4#123×C7311yescharacteristic
746C2×C4#123×C7311yescharacteristic
747C2×C4#123×C7311yescharacteristic
748C2×C4#123×C7311yescharacteristic
749C2×C4#124×C7311yescharacteristic
750C2×C4#124×C7311yescharacteristic
751C2×C4#127×C7311yescharacteristic
752C8—24no—
753C8—42no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22#386×C7311yescharacteristic
770C22#386×C7311yescharacteristic
771C22#390×C7311yescharacteristic
772C22#392×C7311yescharacteristic
773C22#392×C7311yescharacteristic
774C22#392×C7311yescharacteristic
775C22#394×C7311yescharacteristic
776C4—42no—
777C4—42no—
778C4—82no—
779C4—82no—
780C4—82no—
781C4#379×C7311yescharacteristic
782C4#386×C7311yescharacteristic
783C4#386×C7311yescharacteristic
784C4#390×C7311yescharacteristic
785C4#392×C7311yescharacteristic
786C4#394×C7311yescharacteristic
787C4#394×C7311yescharacteristic
788C4#394×C7311yescharacteristic
789C2—21no—
790C2—21no—
791C2—21no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—82no—
797C2—82no—
798C2C73×#143811yescharacteristic
subgroupG/H
centerC4×C73#394
commutatorC22×C4C22×C4×C73
Frattini, cosocleC23×C4C23×C73
socleC2×C73#1438
prime radicalC2×#575×C73C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#421×C73C2semidirect
3. C73×#2896C2semidirect
4. C2×#410×C73C2semidirect
5. C2×#410×C73C2semidirect
6. C73×#1742C2semidirect
7. C73×#1733C2semidirect
15. C2×#137×C73C4semidirect
17. C2×AGL(1,ℤ/8)×C73C4semidirect
389. #11033C73direct (N × H)
401. C2×#421C2×C73semidirect
402. #2896C2×C73semidirect
403. C2×#410C2×C73semidirect
404. C2×#410C2×C73semidirect
405. #1742C2×C73semidirect
406. #1733C2×C73semidirect
407. C73#11033direct (N × H)
415. C2×#137C4×C73semidirect
417. C2×AGL(1,ℤ/8)C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C732
C2×#421×C732
C73×#28962
C2×#410×C732
C73×#17422
C73×#17332
#1103373