Finite Group Databasebeta

← C73×#33553 #32942957

Subgroups — C73×#33553 #32942957

Order 18688.

1252 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3537C211yesmaximal, characteristic, complemented
2C73×#3027C211yesmaximal, characteristic, complemented
3C73×#3025C211yesmaximal, characteristic, complemented
4C73×#3021C211yesmaximal, characteristic, complemented
5C73×#2200C214yesmaximal, complemented
6C73×#2196C214yesmaximal, complemented
7C73×#2128C211yesmaximal, characteristic, complemented
8C73×#2122C211yesmaximal, characteristic, complemented
9C73×#2120C211yesmaximal, characteristic, complemented
10#585×C73C2211yescharacteristic, complemented
11C2×AGL(1,ℤ/8)×C73—21no—
12#560×C73—21no—
13#560×C73C2212yescomplemented
14#553×C73—21no—
15#553×C73—21no—
16D42×C73—21no—
17D42×C73—21no—
18D42×C73—21no—
19D42×C73C2212yescomplemented
20#540×C73—21no—
21#538×C73—22no—
22#535×C73—21no—
23#535×C73C2211yescharacteristic
24#535×C73C2211yescharacteristic
25#534×C73—22no—
26#525×C73—21no—
27#525×C73C2211yescharacteristic
28C2×#121×C73—21no—
29#458×C73—21no—
30#458×C73C2212yescomplemented
31B(4,𝔽2)×C73—21no—
32B(4,𝔽2)×C73—22no—
33B(4,𝔽2)×C73C2212yescomplemented
34B(4,𝔽2)×C73C2214yescomplemented
35#454×C73—22no—
36#453×C73C2214yescomplemented
37#421×C73—21no—
38#413×C73C2211yescharacteristic, complemented
39#410×C73—21no—
40#410×C73—21no—
41#410×C73C2211yescharacteristic, complemented
42#410×C73C2211yescharacteristic, complemented
43#353×C73C2214yescomplemented
44#352×C73C2212yescomplemented
45AΣL(1,𝔽16)×C73C2212yescomplemented
46AΣL(1,𝔽16)×C73C2214yescomplemented
472−1+4×C73—21no—
482−1+4×C73—41no—
49H(5,𝔽2)×C73—21no—
50H(5,𝔽2)×C73—21no—
51H(5,𝔽2)×C73—41no—
52H(5,𝔽2)×C73C2312yes—
53C2×#41×C73—21no—
54C2×#41×C73—21no—
55C2×#41×C73—21no—
56C2×#41×C73—42no—
57C2×#41×C73C2311yescharacteristic
58C22×D4×C73—21no—
59C22×D4×C73—22no—
60C22×D4×C73—22no—
61C22×D4×C73—22no—
62C22×D4×C73D411yescharacteristic, complemented
63C22×D4×C73D411yescharacteristic, complemented
64C23×C4×C73D411yescharacteristic, complemented
65AGL(1,ℤ/8)×C73—24no—
66AGL(1,ℤ/8)×C73—42no—
67C2×SD16×C73—41no—
68C2×D8×C73—41no—
69C2×M16×C73—21no—
70#127×C73—21no—
71#127×C73—21no—
72#127×C73—41no—
73#127×C73C2312yes—
74#126×C73—22no—
75#126×C73—22no—
76#125×C73—21no—
77#124×C73—21no—
78#124×C73—41no—
79#124×C73D412yescomplemented
80#123×C73—22no—
81#123×C73—22no—
82#123×C73—22no—
83#123×C73—22no—
84#123×C73—22no—
85#123×C73D411yescharacteristic, complemented
86#123×C73C2311yescharacteristic
87C22⋊Q8×C73—21no—
88C22⋊Q8×C73—41no—
89#121×C73—22no—
90#121×C73—21no—
91#121×C73—21no—
92#121×C73—22no—
93#121×C73—22no—
94#121×C73—21no—
95#121×C73—22no—
96#121×C73—21no—
97#121×C73—21no—
98#121×C73—22no—
99#121×C73—21no—
100#121×C73—21no—
101#121×C73—22no—
102#121×C73—22no—
103#121×C73—22no—
104#121×C73—42no—
105#121×C73—41no—
106#120×C73—22no—
107#120×C73—22no—
108#120×C73—22no—
109#120×C73—21no—
110#120×C73—21no—
111#120×C73—22no—
112#120×C73—22no—
113#120×C73—24no—
114#120×C73D411yescharacteristic, complemented
115#120×C73D412yescomplemented
116#120×C73C2311yescharacteristic
117#120×C73C2312yes—
118C4×D4×C73—22no—
119C4×D4×C73—21no—
120C4×D4×C73—21no—
121C4×D4×C73—21no—
122C4×D4×C73—21no—
123C4×D4×C73—22no—
124C4×D4×C73—42no—
125#117×C73—21no—
126#117×C73—21no—
127#117×C73D411yescharacteristic, complemented
128#117×C73D411yescharacteristic, complemented
129#117×C73D411yescharacteristic, complemented
130C2×C4⋊C4×C73—21no—
131C2×C22⋊C4×C73—22no—
132#104×C73—24no—
133#101×C73—21no—
134#100×C73C2312yes—
135#99×C73—21no—
136#99×C73—21no—
137#99×C73—24no—
138#99×C73—22no—
139#99×C73—22no—
140#99×C73C2312yes—
141#99×C73C2312yes—
142C24×C73—22no—
143C24×C73—21no—
144C24×C73C2×D411yescharacteristic
145C24×C73C2×D412yes—
146#41×C73—22no—
147#41×C73—22no—
148#41×C73—41no—
149#41×C73—41no—
150#41×C73—42no—
151#41×C73—41no—
152#41×C73—41no—
153#41×C73—41no—
154#41×C73—41no—
155#41×C73—41no—
156#41×C73—42no—
157#41×C73—42no—
158#41×C73—42no—
159#41×C73—41no—
160#41×C73—41no—
161#41×C73—41no—
162C2×Q8×C73—21no—
163C2×Q8×C73—21no—
164C2×Q8×C73—21no—
165C2×Q8×C73—42no—
166C2×Q8×C73C2×D411yescharacteristic
167C2×D4×C73—21no—
168C2×D4×C73—22no—
169C2×D4×C73—22no—
170C2×D4×C73—21no—
171C2×D4×C73—21no—
172C2×D4×C73—21no—
173C2×D4×C73—22no—
174C2×D4×C73—22no—
175C2×D4×C73—21no—
176C2×D4×C73—22no—
177C2×D4×C73—22no—
178C2×D4×C73—22no—
179C2×D4×C73—22no—
180C2×D4×C73—22no—
181C2×D4×C73—22no—
182C2×D4×C73—22no—
183C2×D4×C73—21no—
184C2×D4×C73—21no—
185C2×D4×C73—21no—
186C2×D4×C73—41no—
187C2×D4×C73—41no—
188C2×D4×C73—41no—
189C2×D4×C73—41no—
190C2×D4×C73—42no—
191C2×D4×C73—42no—
192C2×D4×C73—42no—
193C2×D4×C73—41no—
194C2×D4×C73—42no—
195C2×D4×C73—44no—
196C2×D4×C73—81no—
197C2×D4×C73—81no—
198C2×D4×C73—84no—
199C2×D4×C73—84no—
200C2×D4×C73—84no—
201C2×D4×C73C2×D411yescharacteristic
202C2×D4×C73C2×D411yescharacteristic
203C2×D4×C73C2×D412yes—
204C2×D4×C73C2411yescharacteristic
205C22×C4×C73—22no—
206C22×C4×C73—22no—
207C22×C4×C73—22no—
208C22×C4×C73—22no—
209C22×C4×C73—22no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—41no—
213C22×C4×C73—41no—
214C22×C4×C73—41no—
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2×D411yescharacteristic
219SD16×C73—44no—
220D8×C73—44no—
221M16×C73—22no—
222M16×C73—41no—
223C2×C8×C73—41no—
224C4⋊C4×C73—22no—
225C4⋊C4×C73—22no—
226C4⋊C4×C73—22no—
227C4⋊C4×C73—21no—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—21no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—41no—
233C4⋊C4×C73—41no—
234C4⋊C4×C73—42no—
235C22⋊C4×C73—22no—
236C22⋊C4×C73—22no—
237C22⋊C4×C73—22no—
238C22⋊C4×C73—22no—
239C22⋊C4×C73—21no—
240C22⋊C4×C73—21no—
241C22⋊C4×C73—21no—
242C22⋊C4×C73—22no—
243C22⋊C4×C73—22no—
244C22⋊C4×C73—21no—
245C22⋊C4×C73—22no—
246C22⋊C4×C73—21no—
247C22⋊C4×C73—22no—
248C22⋊C4×C73—22no—
249C22⋊C4×C73—22no—
250C22⋊C4×C73—42no—
251C22⋊C4×C73—44no—
252C22⋊C4×C73—42no—
253C22⋊C4×C73C2×D412yes—
254C22⋊C4×C73C2×D411yescharacteristic
255C22⋊C4×C73C2×D411yescharacteristic
256C42×C73—21no—
257C42×C73—21no—
258C42×C73—41no—
259C42×C73—41no—
260C42×C73C2×D412yes—
261C23×C73—21no—
262C23×C73—22no—
263C23×C73—22no—
264C23×C73—22no—
265C23×C73—22no—
266C23×C73—41no—
267C23×C73—42no—
268C23×C73—41no—
269C23×C73—44no—
270C23×C73—42no—
271C23×C73—81no—
272C23×C73—82no—
273C23×C73—82no—
274C23×C73—82no—
275C23×C73—82no—
276C23×C73#12011yescharacteristic
277C23×C73C22×D411yescharacteristic
278C23×C73C22×D411yescharacteristic
279Q8×C73—22no—
280Q8×C73—41no—
281Q8×C73—41no—
282Q8×C73—41no—
283Q8×C73—41no—
284D4×C73—22no—
285D4×C73—41no—
286D4×C73—41no—
287D4×C73—41no—
288D4×C73—42no—
289D4×C73—41no—
290D4×C73—41no—
291D4×C73—42no—
292D4×C73—42no—
293D4×C73—42no—
294D4×C73—42no—
295D4×C73—44no—
296D4×C73—44no—
297D4×C73—42no—
298D4×C73—42no—
299D4×C73—41no—
300D4×C73—41no—
301D4×C73—41no—
302D4×C73—41no—
303D4×C73—41no—
304D4×C73—81no—
305D4×C73—82no—
306D4×C73—82no—
307D4×C73—82no—
308D4×C73—82no—
309D4×C73—82no—
310D4×C73—82no—
311D4×C73—82no—
312D4×C73—84no—
313D4×C73—164no—
314C2×C4×C73—21no—
315C2×C4×C73—21no—
316C2×C4×C73—21no—
317C2×C4×C73—21no—
318C2×C4×C73—21no—
319C2×C4×C73—21no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—22no—
326C2×C4×C73—21no—
327C2×C4×C73—42no—
328C2×C4×C73—42no—
329C2×C4×C73—42no—
330C2×C4×C73—41no—
331C2×C4×C73—42no—
332C2×C4×C73—41no—
333C2×C4×C73—41no—
334C2×C4×C73—41no—
335C2×C4×C73—42no—
336C2×C4×C73—42no—
337C2×C4×C73—81no—
338C2×C4×C73—82no—
339C2×C4×C73—82no—
340C2×C4×C73—82no—
341C2×C4×C73#12011yescharacteristic
342C2×C4×C73#12011yescharacteristic
343C2×C4×C73#12011yescharacteristic
344C2×C4×C73C22×D411yescharacteristic
345C8×C73—42no—
346C22×C73—22no—
347C22×C73—21no—
348C22×C73—21no—
349C22×C73—21no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73—41no—
354C22×C73—42no—
355C22×C73—42no—
356C22×C73—42no—
357C22×C73—42no—
358C22×C73—42no—
359C22×C73—41no—
360C22×C73—42no—
361C22×C73—42no—
362C22×C73—42no—
363C22×C73—81no—
364C22×C73—82no—
365C22×C73—82no—
366C22×C73—84no—
367C22×C73—161no—
368C22×C73—164no—
369C22×C73—162no—
370C22×C73C2×#12011yescharacteristic
371C4×C73—21no—
372C4×C73—21no—
373C4×C73—21no—
374C4×C73—42no—
375C4×C73—41no—
376C4×C73—41no—
377C4×C73—42no—
378C4×C73—42no—
379C4×C73—41no—
380C4×C73—82no—
381C4×C73—82no—
382C4×C73B(4,𝔽2)11yescharacteristic
383C4×C73B(4,𝔽2)11yescharacteristic
384#33553C7311yesmaximal, characteristic, direct product factor, Sylow
385C2×C73—21no—
386C2×C73—41no—
387C2×C73—41no—
388C2×C73—42no—
389C2×C73—41no—
390C2×C73—82no—
391C2×C73—82no—
392C2×C73—82no—
393C2×C73C2×B(4,𝔽2)11yescharacteristic
394#3537C2×C7311yescharacteristic, complemented
395#3027C2×C7311yescharacteristic, complemented
396#3025C2×C7311yescharacteristic, complemented
397#3021C2×C7311yescharacteristic, complemented
398#2200C2×C7314yescomplemented
399#2196C2×C7314yescomplemented
400#2128C2×C7311yescharacteristic, complemented
401#2122C2×C7311yescharacteristic, complemented
402#2120C2×C7311yescharacteristic, complemented
403C73#3355311yescharacteristic, direct product factor, Sylow
404#585C22×C7311yescharacteristic, complemented
405C2×AGL(1,ℤ/8)—21no—
406#560—21no—
407#560C22×C7312yescomplemented
408#553—21no—
409#553—21no—
410D42—21no—
411D42—21no—
412D42—21no—
413D42C22×C7312yescomplemented
414#540—21no—
415#538—22no—
416#535—21no—
417#535C22×C7311yescharacteristic
418#535C22×C7311yescharacteristic
419#534—22no—
420#525—21no—
421#525C22×C7311yescharacteristic
422C2×#121—21no—
423#458—21no—
424#458C22×C7312yescomplemented
425B(4,𝔽2)—21no—
426B(4,𝔽2)—22no—
427B(4,𝔽2)C22×C7312yescomplemented
428B(4,𝔽2)C22×C7314yescomplemented
429#454—22no—
430#453C22×C7314yescomplemented
431#421—21no—
432#413C22×C7311yescharacteristic, complemented
433#410—21no—
434#410—21no—
435#410C22×C7311yescharacteristic, complemented
436#410C22×C7311yescharacteristic, complemented
437#353C22×C7314yescomplemented
438#352C22×C7312yescomplemented
439AΣL(1,𝔽16)C22×C7312yescomplemented
440AΣL(1,𝔽16)C22×C7314yescomplemented
4412−1+4—21no—
4422−1+4—41no—
443H(5,𝔽2)—21no—
444H(5,𝔽2)—21no—
445H(5,𝔽2)—41no—
446H(5,𝔽2)C23×C7312yes—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—42no—
451C2×#41C23×C7311yescharacteristic
452C22×D4—21no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4D4×C7311yescharacteristic, complemented
457C22×D4D4×C7311yescharacteristic, complemented
458C23×C4D4×C7311yescharacteristic, complemented
459AGL(1,ℤ/8)—24no—
460AGL(1,ℤ/8)—42no—
461C2×SD16—41no—
462C2×D8—41no—
463C2×M16—21no—
464#127—21no—
465#127—21no—
466#127—41no—
467#127C23×C7312yes—
468#126—22no—
469#126—22no—
470#125—21no—
471#124—21no—
472#124—41no—
473#124D4×C7312yescomplemented
474#123—22no—
475#123—22no—
476#123—22no—
477#123—22no—
478#123—22no—
479#123D4×C7311yescharacteristic, complemented
480#123C23×C7311yescharacteristic
481C22⋊Q8—21no—
482C22⋊Q8—41no—
483#121—22no—
484#121—21no—
485#121—21no—
486#121—22no—
487#121—22no—
488#121—21no—
489#121—22no—
490#121—21no—
491#121—21no—
492#121—22no—
493#121—21no—
494#121—21no—
495#121—22no—
496#121—22no—
497#121—22no—
498#121—42no—
499#121—41no—
500#120—22no—
501#120—22no—
502#120—22no—
503#120—21no—
504#120—21no—
505#120—22no—
506#120—22no—
507#120—24no—
508#120D4×C7311yescharacteristic, complemented
509#120D4×C7312yescomplemented
510#120C23×C7311yescharacteristic
511#120C23×C7312yes—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—22no—
518C4×D4—42no—
519#117—21no—
520#117—21no—
521#117D4×C7311yescharacteristic, complemented
522#117D4×C7311yescharacteristic, complemented
523#117D4×C7311yescharacteristic, complemented
524C2×C4⋊C4—21no—
525C2×C22⋊C4—22no—
526#104—24no—
527#101—21no—
528#100C23×C7312yes—
529#99—21no—
530#99—21no—
531#99—24no—
532#99—22no—
533#99—22no—
534#99C23×C7312yes—
535#99C23×C7312yes—
536C24—22no—
537C24—21no—
538C24C2×D4×C7311yescharacteristic
539C24C2×D4×C7312yes—
540#41—22no—
541#41—22no—
542#41—41no—
543#41—41no—
544#41—42no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—41no—
554#41—41no—
555#41—41no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—42no—
560C2×Q8C2×D4×C7311yescharacteristic
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—44no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—84no—
593C2×D4—84no—
594C2×D4—84no—
595C2×D4C2×D4×C7311yescharacteristic
596C2×D4C2×D4×C7311yescharacteristic
597C2×D4C2×D4×C7312yes—
598C2×D4C24×C7311yescharacteristic
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4C2×D4×C7311yescharacteristic
610C22×C4C2×D4×C7311yescharacteristic
611C22×C4C2×D4×C7311yescharacteristic
612C22×C4C2×D4×C7311yescharacteristic
613SD16—44no—
614D8—44no—
615M16—22no—
616M16—41no—
617C2×C8—41no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—41no—
627C4⋊C4—41no—
628C4⋊C4—42no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—42no—
645C22⋊C4—44no—
646C22⋊C4—42no—
647C22⋊C4C2×D4×C7312yes—
648C22⋊C4C2×D4×C7311yescharacteristic
649C22⋊C4C2×D4×C7311yescharacteristic
650C42—21no—
651C42—21no—
652C42—41no—
653C42—41no—
654C42C2×D4×C7312yes—
655C23—21no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—41no—
661C23—42no—
662C23—41no—
663C23—44no—
664C23—42no—
665C23—81no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23—82no—
670C23#120×C7311yescharacteristic
671C23C22×D4×C7311yescharacteristic
672C23C22×D4×C7311yescharacteristic
673Q8—22no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—41no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—42no—
683D4—41no—
684D4—41no—
685D4—42no—
686D4—42no—
687D4—42no—
688D4—42no—
689D4—44no—
690D4—44no—
691D4—42no—
692D4—42no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—81no—
699D4—82no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—82no—
705D4—82no—
706D4—84no—
707D4—164no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—82no—
733C2×C4—82no—
734C2×C4—82no—
735C2×C4#120×C7311yescharacteristic
736C2×C4#120×C7311yescharacteristic
737C2×C4#120×C7311yescharacteristic
738C2×C4C22×D4×C7311yescharacteristic
739C8—42no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—81no—
758C22—82no—
759C22—82no—
760C22—84no—
761C22—164no—
762C22—161no—
763C22—162no—
764C22C2×#120×C7311yescharacteristic
765C4—21no—
766C4—21no—
767C4—21no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—41no—
774C4—82no—
775C4—82no—
776C4B(4,𝔽2)×C7311yescharacteristic
777C4B(4,𝔽2)×C7311yescharacteristic
778C2—21no—
779C2—41no—
780C2—41no—
781C2—42no—
782C2—41no—
783C2—82no—
784C2—82no—
785C2—82no—
786C2C2×B(4,𝔽2)×C7311yescharacteristic
subgroupG/H
center, socleC2×C73C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C73
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C73 ◁ C2×C4×C73 ◁ C2×#41×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3537C2semidirect
2. C73×#3027C2semidirect
3. C73×#3025C2semidirect
4. C73×#3021C2semidirect
5. C73×#2200C2semidirect
6. C73×#2196C2semidirect
7. C73×#2128C2semidirect
8. C73×#2122C2semidirect
9. C73×#2120C2semidirect
10. #585×C73C22semidirect
13. #560×C73C22semidirect
19. D42×C73C22semidirect
30. #458×C73C22semidirect
33. B(4,𝔽2)×C73C22semidirect
34. B(4,𝔽2)×C73C22semidirect
36. #453×C73C22semidirect
38. #413×C73C22semidirect
41. #410×C73C22semidirect
42. #410×C73C22semidirect
43. #353×C73C22semidirect
44. #352×C73C22semidirect
45. AΣL(1,𝔽16)×C73C22semidirect
46. AΣL(1,𝔽16)×C73C22semidirect
62. C22×D4×C73D4semidirect
63. C22×D4×C73D4semidirect
64. C23×C4×C73D4semidirect
79. #124×C73D4semidirect
85. #123×C73D4semidirect
114. #120×C73D4semidirect
115. #120×C73D4semidirect
127. #117×C73D4semidirect
128. #117×C73D4semidirect
129. #117×C73D4semidirect
384. #33553C73direct (N × H)
394. #3537C2×C73semidirect
395. #3027C2×C73semidirect
396. #3025C2×C73semidirect
397. #3021C2×C73semidirect
398. #2200C2×C73semidirect
399. #2196C2×C73semidirect
400. #2128C2×C73semidirect
401. #2122C2×C73semidirect
402. #2120C2×C73semidirect
403. C73#33553direct (N × H)
404. #585C22×C73semidirect
407. #560C22×C73semidirect
413. D42C22×C73semidirect
424. #458C22×C73semidirect
427. B(4,𝔽2)C22×C73semidirect
428. B(4,𝔽2)C22×C73semidirect
430. #453C22×C73semidirect
432. #413C22×C73semidirect
435. #410C22×C73semidirect
436. #410C22×C73semidirect
437. #353C22×C73semidirect
438. #352C22×C73semidirect
439. AΣL(1,𝔽16)C22×C73semidirect
440. AΣL(1,𝔽16)C22×C73semidirect
456. C22×D4D4×C73semidirect
457. C22×D4D4×C73semidirect
458. C23×C4D4×C73semidirect
473. #124D4×C73semidirect
479. #123D4×C73semidirect
508. #120D4×C73semidirect
509. #120D4×C73semidirect
521. #117D4×C73semidirect
522. #117D4×C73semidirect
523. #117D4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35372
C73×#30272
C73×#30252
C73×#30212
C73×#22002
C73×#21962
C73×#21282
C73×#21222
C73×#21202
#3355373