Finite Group Databasebeta

← C73×#25144 #32934548

Subgroups — C73×#25144 #32934548

Order 18688.

1114 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#471×C73C211yesmaximal, characteristic, complemented
2C73×#3056C211yesmaximal, characteristic, complemented
3C73×#3003C211yesmaximal, characteristic
4C2×#450×C73C211yesmaximal, characteristic, complemented
5C73×#2933C211yesmaximal, characteristic, complemented
6C22×#100×C73C211yesmaximal, characteristic, complemented
7C73×#2063C211yesmaximal, characteristic, complemented
8C73×#2051C211yesmaximal, characteristic, complemented
9C73×#2046C211yesmaximal, characteristic, complemented
10C73×#2019C211yesmaximal, characteristic, complemented
11C73×#1977C211yesmaximal, characteristic, complemented
12C73×#1931C211yesmaximal, characteristic, complemented
13C73×#1907C211yesmaximal, characteristic, complemented
14C73×#1901C211yesmaximal, characteristic, complemented
15C73×#1855C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C2×#137×C73C2211yescharacteristic, complemented
18C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
20C22×SD16×C73C2211yescharacteristic
21C22×SD16×C73C2211yescharacteristic
22C2×#131×C73C2211yescharacteristic, complemented
23C22×M16×C73C2211yescharacteristic
24C22×M16×C73C2211yescharacteristic
25#525×C73C2211yescharacteristic
26C2×C22⋊Q8×C73C2211yescharacteristic
27#471×C73—24no—
28#470×C73—21no—
29#468×C73—21no—
30#467×C73—21no—
31#465×C73—21no—
32#450×C73—21no—
33#450×C73—21no—
34#450×C73—21no—
35#450×C73—21no—
36#450×C73—21no—
37#450×C73—21no—
38#447×C73—21no—
39#447×C73—21no—
40#436×C73—21no—
41#435×C73—21no—
42#435×C73—21no—
43C8×D4×C73—21no—
44C2×#108×C73C2211yescharacteristic, complemented
45C2×#108×C73C2211yescharacteristic, complemented
46#428×C73C2211yescharacteristic, complemented
47#424×C73C2211yescharacteristic, complemented
48#419×C73C2211yescharacteristic, complemented
49#418×C73C2211yescharacteristic
50#418×C73C2211yescharacteristic
51#417×C73C2211yescharacteristic, complemented
52C2×#102×C73C2211yescharacteristic
53C2×#102×C73C2211yescharacteristic
54C2×#101×C73C2211yescharacteristic, complemented
55C2×#101×C73C2211yescharacteristic, complemented
56C2×#100×C73—24no—
57C2×#100×C73C2211yescharacteristic
58C2×#100×C73C2211yescharacteristic
59C2×#100×C73C2211yescharacteristic
60C2×#100×C73C2211yescharacteristic
61#408×C73C2211yescharacteristic, complemented
62#407×C73C2211yescharacteristic
63C2×C22⋊C8×C73C2211yescharacteristic
64#405×C73C2211yescharacteristic, complemented
65#343×C73C2211yescharacteristic, complemented
66#343×C73C2211yescharacteristic, complemented
67#341×C73C2211yescharacteristic, complemented
68#341×C73C2211yescharacteristic, complemented
69C25×C73—21no—
70C2×#41×C73C2311yescharacteristic
71C22×Q8×C73C2311yescharacteristic
72C22×D4×C73—22no—
73C22×D4×C73—22no—
74C22×D4×C73—21no—
75C22×D4×C73—21no—
76C22×D4×C73—21no—
77C22×D4×C73—21no—
78C22×D4×C73—21no—
79C22×D4×C73—41no—
80C22×D4×C73—41no—
81C22×D4×C73C2311yescharacteristic
82C22×D4×C73C2311yescharacteristic
83C23×C4×C73C2311yescharacteristic
84#137×C73—22no—
85#137×C73—41no—
86AGL(1,ℤ/8)×C73—22no—
87AGL(1,ℤ/8)×C73—22no—
88AGL(1,ℤ/8)×C73—41no—
89AGL(1,ℤ/8)×C73—41no—
90C2×Q16×C73—21no—
91C2×SD16×C73—21no—
92C2×SD16×C73—21no—
93C2×SD16×C73—21no—
94C2×SD16×C73—22no—
95C2×SD16×C73—22no—
96C2×SD16×C73—21no—
97C2×SD16×C73—21no—
98C2×SD16×C73—21no—
99C2×SD16×C73—21no—
100C2×SD16×C73—41no—
101C2×SD16×C73—41no—
102C2×D8×C73—21no—
103C2×D8×C73—21no—
104#131×C73—22no—
105#131×C73—41no—
106C2×M16×C73—21no—
107C2×M16×C73—21no—
108C2×M16×C73—21no—
109C2×M16×C73—22no—
110C2×M16×C73—22no—
111C2×M16×C73—41no—
112C2×M16×C73—41no—
113C2×M16×C73C2311yescharacteristic
114C2×M16×C73C2311yescharacteristic
115C2×M16×C73C2311yescharacteristic
116C2×M16×C73C2311yescharacteristic
117C2×M16×C73C2311yescharacteristic
118C2×M16×C73C2311yescharacteristic
119C22×C8×C73—21no—
120C22×C8×C73—21no—
121C22×C8×C73—21no—
122C22×C8×C73C2311yescharacteristic
123C22×C8×C73C2311yescharacteristic
124#123×C73—21no—
125C22⋊Q8×C73—21no—
126C22⋊Q8×C73—21no—
127C22⋊Q8×C73—21no—
128C22⋊Q8×C73—21no—
129C22⋊Q8×C73D411yescharacteristic
130C22⋊Q8×C73D411yescharacteristic
131#121×C73D411yescharacteristic
132#121×C73D411yescharacteristic
133#120×C73—21no—
134C4×D4×C73—21no—
135C4×D4×C73—21no—
136#117×C73C2311yescharacteristic
137C2×C4⋊C4×C73—21no—
138C2×C4⋊C4×C73C2311yescharacteristic
139C2×C22⋊C4×C73—21no—
140#108×C73—22no—
141#108×C73—41no—
142#107×C73—21no—
143#106×C73—21no—
144C4⋊C8×C73—21no—
145C4⋊C8×C73—21no—
146#103×C73—21no—
147#103×C73—21no—
148#103×C73—21no—
149#102×C73—21no—
150#102×C73—21no—
151#102×C73—21no—
152#102×C73—21no—
153#102×C73—21no—
154#102×C73—21no—
155#102×C73—21no—
156#102×C73—21no—
157#102×C73—21no—
158#101×C73—22no—
159#101×C73—41no—
160#100×C73—22no—
161#100×C73—22no—
162#100×C73—22no—
163#100×C73D414yescomplemented
164C22⋊C8×C73—21no—
165C22⋊C8×C73—21no—
166C22⋊C8×C73—21no—
167C22⋊C8×C73—21no—
168C22⋊C8×C73D411yescharacteristic
169C22⋊C8×C73D411yescharacteristic
170C22⋊C8×C73D411yescharacteristic
171C22⋊C8×C73D411yescharacteristic
172#97×C73—21no—
173C4×C8×C73—21no—
174C24×C73—24no—
175C24×C73—21no—
176C24×C73—21no—
177C24×C73—42no—
178C24×C73—41no—
179C24×C73—41no—
180C24×C73—82no—
181C24×C73—82no—
182C24×C73#4111yescharacteristic
183#41×C73—21no—
184#41×C73—21no—
185#41×C73—21no—
186#41×C73—21no—
187C2×Q8×C73—21no—
188C2×Q8×C73—21no—
189C2×Q8×C73—21no—
190C2×Q8×C73—21no—
191C2×Q8×C73—21no—
192C2×Q8×C73—21no—
193C2×Q8×C73C2×D411yescharacteristic
194C2×D4×C73—24no—
195C2×D4×C73—21no—
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—21no—
201C2×D4×C73—21no—
202C2×D4×C73—21no—
203C2×D4×C73—21no—
204C2×D4×C73—21no—
205C2×D4×C73—21no—
206C2×D4×C73—21no—
207C2×D4×C73—21no—
208C2×D4×C73—42no—
209C2×D4×C73—42no—
210C2×D4×C73—42no—
211C2×D4×C73—42no—
212C2×D4×C73—42no—
213C2×D4×C73—42no—
214C2×D4×C73—42no—
215C2×D4×C73—42no—
216C2×D4×C73—42no—
217C2×D4×C73—41no—
218C2×D4×C73—41no—
219C2×D4×C73C2×D412yes—
220C2×D4×C73C2×D411yescharacteristic
221C2×D4×C73#4112yes—
222C22×C4×C73—21no—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73C2×D411yescharacteristic
230C22×C4×C73C2×D411yescharacteristic
231C22×C4×C73C2×D411yescharacteristic
232C22×C4×C73C2×D411yescharacteristic
233C22×C4×C73#4111yescharacteristic
234C22×C4×C73C2411yescharacteristic
235Q16×C73—42no—
236SD16×C73—42no—
237SD16×C73—42no—
238SD16×C73—42no—
239SD16×C73—42no—
240SD16×C73—42no—
241SD16×C73—42no—
242SD16×C73—42no—
243D8×C73—42no—
244D8×C73—42no—
245M16×C73—21no—
246M16×C73—21no—
247M16×C73—21no—
248M16×C73—21no—
249M16×C73—21no—
250M16×C73—21no—
251M16×C73—21no—
252M16×C73—21no—
253M16×C73—21no—
254M16×C73—21no—
255M16×C73—42no—
256M16×C73—42no—
257M16×C73—42no—
258M16×C73C2×D412yes—
259M16×C73C2×D412yes—
260C2×C8×C73—21no—
261C2×C8×C73—21no—
262C2×C8×C73—21no—
263C2×C8×C73—21no—
264C2×C8×C73—21no—
265C2×C8×C73—21no—
266C2×C8×C73—21no—
267C2×C8×C73—21no—
268C2×C8×C73—21no—
269C2×C8×C73—21no—
270C2×C8×C73—42no—
271C2×C8×C73—42no—
272C2×C8×C73—42no—
273C2×C8×C73C2×D411yescharacteristic
274C2×C8×C73C2×D411yescharacteristic
275C2×C8×C73C2×D411yescharacteristic
276C2×C8×C73C2×D411yescharacteristic
277C4⋊C4×C73—21no—
278C4⋊C4×C73—21no—
279C4⋊C4×C73—21no—
280C4⋊C4×C73—21no—
281C4⋊C4×C73—41no—
282C4⋊C4×C73—41no—
283C4⋊C4×C73C2×D411yescharacteristic
284C4⋊C4×C73C2×D411yescharacteristic
285C22⋊C4×C73—21no—
286C22⋊C4×C73—21no—
287C22⋊C4×C73—21no—
288C22⋊C4×C73—21no—
289C22⋊C4×C73—21no—
290C22⋊C4×C73—41no—
291C22⋊C4×C73—41no—
292C42×C73—21no—
293C23×C73—21no—
294C23×C73—21no—
295C23×C73—22no—
296C23×C73—21no—
297C23×C73—22no—
298C23×C73—22no—
299C23×C73—41no—
300C23×C73—44no—
301C23×C73—44no—
302C23×C73—41no—
303C23×C73—41no—
304C23×C73—41no—
305C23×C73—41no—
306C23×C73—81no—
307C23×C73—81no—
308C23×C73—81no—
309C23×C73—81no—
310C23×C73—82no—
311C23×C73—82no—
312C23×C73—82no—
313C23×C73—88no—
314C23×C73—88no—
315C23×C73—82no—
316C23×C73#12111yescharacteristic
317C23×C73#12111yescharacteristic
318C23×C73C2×#4111yescharacteristic
319Q8×C73—21no—
320Q8×C73—21no—
321Q8×C73—41no—
322Q8×C73—41no—
323Q8×C73—41no—
324Q8×C73—41no—
325D4×C73—21no—
326D4×C73—22no—
327D4×C73—22no—
328D4×C73—21no—
329D4×C73—22no—
330D4×C73—22no—
331D4×C73—44no—
332D4×C73—44no—
333D4×C73—41no—
334D4×C73—41no—
335D4×C73—42no—
336D4×C73—41no—
337D4×C73—41no—
338D4×C73—41no—
339D4×C73—41no—
340D4×C73—81no—
341C2×C4×C73—21no—
342C2×C4×C73—21no—
343C2×C4×C73—21no—
344C2×C4×C73—21no—
345C2×C4×C73—21no—
346C2×C4×C73—21no—
347C2×C4×C73—21no—
348C2×C4×C73—21no—
349C2×C4×C73—21no—
350C2×C4×C73—21no—
351C2×C4×C73—21no—
352C2×C4×C73—21no—
353C2×C4×C73—21no—
354C2×C4×C73—41no—
355C2×C4×C73—41no—
356C2×C4×C73—41no—
357C2×C4×C73—41no—
358C2×C4×C73—41no—
359C2×C4×C73—41no—
360C2×C4×C73—81no—
361C2×C4×C73#12111yescharacteristic
362C2×C4×C73#12111yescharacteristic
363C2×C4×C73C22×D411yescharacteristic
364C2×C4×C73C22×D411yescharacteristic
365C2×C4×C73C22×D411yescharacteristic
366C2×C4×C73C2×#4111yescharacteristic
367C2×C4×C73H(5,𝔽2)11yescharacteristic
368C2×C4×C73H(5,𝔽2)11yescharacteristic
369C8×C73—21no—
370C8×C73—21no—
371C8×C73—22no—
372C8×C73—22no—
373C8×C73—21no—
374C8×C73—21no—
375C8×C73—41no—
376C8×C73—41no—
377C8×C73—41no—
378C8×C73—41no—
379C22×C73—21no—
380C22×C73—21no—
381C22×C73—21no—
382C22×C73—21no—
383C22×C73—21no—
384C22×C73—21no—
385C22×C73—21no—
386C22×C73—42no—
387C22×C73—42no—
388C22×C73—41no—
389C22×C73—42no—
390C22×C73—42no—
391C22×C73—41no—
392C22×C73—41no—
393C22×C73—82no—
394C22×C73—82no—
395C22×C73—88no—
396C22×C73—82no—
397C22×C73—82no—
398C22×C73—88no—
399C22×C73—81no—
400C22×C73—81no—
401C22×C73—81no—
402C22×C73—81no—
403C22×C73#47112yescomplemented
404C22×C73C2×#12111yescharacteristic
405C22×C73#52511yescharacteristic
406C22×C73#53811yescharacteristic
407C4×C73—21no—
408C4×C73—21no—
409C4×C73—41no—
410C4×C73—41no—
411C4×C73—41no—
412C4×C73—81no—
413C4×C73—81no—
414C4×C73D4211yescharacteristic
415C4×C73D4211yescharacteristic
416C4×C73#54611yescharacteristic
417C4×C73#54611yescharacteristic
418#25144C7311yesmaximal, characteristic, direct product factor, Sylow
419C2×C73—21no—
420C2×C73—21no—
421C2×C73—22no—
422C2×C73—41no—
423C2×C73—81no—
424C2×C73—82no—
425C2×C73—82no—
426C2×C73#242411yescharacteristic
427C2×C73C2×#47111yescharacteristic
428C2×C73#306811yescharacteristic
429C2×#471C2×C7311yescharacteristic, complemented
430#3056C2×C7311yescharacteristic, complemented
431#3003C2×C7311yescharacteristic
432C2×#450C2×C7311yescharacteristic, complemented
433#2933C2×C7311yescharacteristic, complemented
434C22×#100C2×C7311yescharacteristic, complemented
435#2063C2×C7311yescharacteristic, complemented
436#2051C2×C7311yescharacteristic, complemented
437#2046C2×C7311yescharacteristic, complemented
438#2019C2×C7311yescharacteristic, complemented
439#1977C2×C7311yescharacteristic, complemented
440#1931C2×C7311yescharacteristic, complemented
441#1907C2×C7311yescharacteristic, complemented
442#1901C2×C7311yescharacteristic, complemented
443#1855C2×C7311yescharacteristic, complemented
444C73#2514411yescharacteristic, direct product factor, Sylow
445C23×D4C22×C7311yescharacteristic
446C2×#137C22×C7311yescharacteristic, complemented
447C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
448C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
449C22×SD16C22×C7311yescharacteristic
450C22×SD16C22×C7311yescharacteristic
451C2×#131C22×C7311yescharacteristic, complemented
452C22×M16C22×C7311yescharacteristic
453C22×M16C22×C7311yescharacteristic
454#525C22×C7311yescharacteristic
455C2×C22⋊Q8C22×C7311yescharacteristic
456#471—24no—
457#470—21no—
458#468—21no—
459#467—21no—
460#465—21no—
461#450—21no—
462#450—21no—
463#450—21no—
464#450—21no—
465#450—21no—
466#450—21no—
467#447—21no—
468#447—21no—
469#436—21no—
470#435—21no—
471#435—21no—
472C8×D4—21no—
473C2×#108C22×C7311yescharacteristic, complemented
474C2×#108C22×C7311yescharacteristic, complemented
475#428C22×C7311yescharacteristic, complemented
476#424C22×C7311yescharacteristic, complemented
477#419C22×C7311yescharacteristic, complemented
478#418C22×C7311yescharacteristic
479#418C22×C7311yescharacteristic
480#417C22×C7311yescharacteristic, complemented
481C2×#102C22×C7311yescharacteristic
482C2×#102C22×C7311yescharacteristic
483C2×#101C22×C7311yescharacteristic, complemented
484C2×#101C22×C7311yescharacteristic, complemented
485C2×#100—24no—
486C2×#100C22×C7311yescharacteristic
487C2×#100C22×C7311yescharacteristic
488C2×#100C22×C7311yescharacteristic
489C2×#100C22×C7311yescharacteristic
490#408C22×C7311yescharacteristic, complemented
491#407C22×C7311yescharacteristic
492C2×C22⋊C8C22×C7311yescharacteristic
493#405C22×C7311yescharacteristic, complemented
494#343C22×C7311yescharacteristic, complemented
495#343C22×C7311yescharacteristic, complemented
496#341C22×C7311yescharacteristic, complemented
497#341C22×C7311yescharacteristic, complemented
498C25—21no—
499C2×#41C23×C7311yescharacteristic
500C22×Q8C23×C7311yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C23×C7311yescharacteristic
511C22×D4C23×C7311yescharacteristic
512C23×C4C23×C7311yescharacteristic
513#137—22no—
514#137—41no—
515AGL(1,ℤ/8)—22no—
516AGL(1,ℤ/8)—22no—
517AGL(1,ℤ/8)—41no—
518AGL(1,ℤ/8)—41no—
519C2×Q16—21no—
520C2×SD16—21no—
521C2×SD16—21no—
522C2×SD16—22no—
523C2×SD16—21no—
524C2×SD16—22no—
525C2×SD16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×D8—21no—
532C2×D8—21no—
533#131—22no—
534#131—41no—
535C2×M16—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16C23×C7311yescharacteristic
543C2×M16C23×C7311yescharacteristic
544C2×M16C23×C7311yescharacteristic
545C2×M16C23×C7311yescharacteristic
546C2×M16C23×C7311yescharacteristic
547C2×M16C23×C7311yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—21no—
551C22×C8C23×C7311yescharacteristic
552C22×C8C23×C7311yescharacteristic
553#123—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8D4×C7311yescharacteristic
559C22⋊Q8D4×C7311yescharacteristic
560#121D4×C7311yescharacteristic
561#121D4×C7311yescharacteristic
562#120—21no—
563C4×D4—21no—
564C4×D4—21no—
565#117C23×C7311yescharacteristic
566C2×C4⋊C4—21no—
567C2×C4⋊C4C23×C7311yescharacteristic
568C2×C22⋊C4—21no—
569#108—22no—
570#108—41no—
571#107—21no—
572#106—21no—
573C4⋊C8—21no—
574C4⋊C8—21no—
575#103—21no—
576#103—21no—
577#103—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581#102—21no—
582#102—21no—
583#102—21no—
584#102—21no—
585#102—21no—
586#102—21no—
587#101—22no—
588#101—41no—
589#100—22no—
590#100—22no—
591#100—22no—
592#100D4×C7314yescomplemented
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—21no—
596C22⋊C8—21no—
597C22⋊C8D4×C7311yescharacteristic
598C22⋊C8D4×C7311yescharacteristic
599C22⋊C8D4×C7311yescharacteristic
600C22⋊C8D4×C7311yescharacteristic
601#97—21no—
602C4×C8—21no—
603C24—24no—
604C24—21no—
605C24—21no—
606C24—42no—
607C24—41no—
608C24—41no—
609C24—82no—
610C24—82no—
611C24#41×C7311yescharacteristic
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8C2×D4×C7311yescharacteristic
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—41no—
647C2×D4—41no—
648C2×D4C2×D4×C7312yes—
649C2×D4C2×D4×C7311yescharacteristic
650C2×D4#41×C7312yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4C2×D4×C7311yescharacteristic
659C22×C4C2×D4×C7311yescharacteristic
660C22×C4C2×D4×C7311yescharacteristic
661C22×C4C2×D4×C7311yescharacteristic
662C22×C4#41×C7311yescharacteristic
663C22×C4C24×C7311yescharacteristic
664Q16—42no—
665SD16—42no—
666SD16—42no—
667SD16—42no—
668SD16—42no—
669SD16—42no—
670SD16—42no—
671SD16—42no—
672D8—42no—
673D8—42no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—42no—
685M16—42no—
686M16—42no—
687M16C2×D4×C7312yes—
688M16C2×D4×C7312yes—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—42no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8C2×D4×C7311yescharacteristic
703C2×C8C2×D4×C7311yescharacteristic
704C2×C8C2×D4×C7311yescharacteristic
705C2×C8C2×D4×C7311yescharacteristic
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—41no—
711C4⋊C4—41no—
712C4⋊C4C2×D4×C7311yescharacteristic
713C4⋊C4C2×D4×C7311yescharacteristic
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—41no—
720C22⋊C4—41no—
721C42—21no—
722C23—22no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—22no—
727C23—22no—
728C23—41no—
729C23—44no—
730C23—44no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—81no—
736C23—81no—
737C23—81no—
738C23—81no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—88no—
743C23—88no—
744C23—82no—
745C23#121×C7311yescharacteristic
746C23#121×C7311yescharacteristic
747C23C2×#41×C7311yescharacteristic
748Q8—21no—
749Q8—21no—
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754D4—21no—
755D4—22no—
756D4—22no—
757D4—21no—
758D4—22no—
759D4—22no—
760D4—44no—
761D4—44no—
762D4—42no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—81no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—81no—
790C2×C4#121×C7311yescharacteristic
791C2×C4#121×C7311yescharacteristic
792C2×C4C22×D4×C7311yescharacteristic
793C2×C4C22×D4×C7311yescharacteristic
794C2×C4C22×D4×C7311yescharacteristic
795C2×C4C2×#41×C7311yescharacteristic
796C2×C4H(5,𝔽2)×C7311yescharacteristic
797C2×C4H(5,𝔽2)×C7311yescharacteristic
798C8—21no—
799C8—21no—
800C8—22no—
801C8—22no—
802C8—21no—
803C8—21no—
804C8—41no—
805C8—41no—
806C8—41no—
807C8—41no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—42no—
821C22—42no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—88no—
827C22—88no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22#471×C7312yescomplemented
833C22C2×#121×C7311yescharacteristic
834C22#525×C7311yescharacteristic
835C22#538×C7311yescharacteristic
836C4—21no—
837C4—21no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—81no—
842C4—81no—
843C4D42×C7311yescharacteristic
844C4D42×C7311yescharacteristic
845C4#546×C7311yescharacteristic
846C4#546×C7311yescharacteristic
847C2—22no—
848C2—21no—
849C2—21no—
850C2—41no—
851C2—81no—
852C2—82no—
853C2—82no—
854C2C73×#242411yescharacteristic
855C2C2×#471×C7311yescharacteristic
856C2C73×#306811yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#3003C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#471×C73C2semidirect
2. C73×#3056C2semidirect
4. C2×#450×C73C2semidirect
5. C73×#2933C2semidirect
6. C22×#100×C73C2semidirect
7. C73×#2063C2semidirect
8. C73×#2051C2semidirect
9. C73×#2046C2semidirect
10. C73×#2019C2semidirect
11. C73×#1977C2semidirect
12. C73×#1931C2semidirect
13. C73×#1907C2semidirect
14. C73×#1901C2semidirect
15. C73×#1855C2semidirect
17. C2×#137×C73C22semidirect
22. C2×#131×C73C22semidirect
44. C2×#108×C73C22semidirect
45. C2×#108×C73C22semidirect
46. #428×C73C22semidirect
47. #424×C73C22semidirect
48. #419×C73C22semidirect
51. #417×C73C22semidirect
54. C2×#101×C73C22semidirect
55. C2×#101×C73C22semidirect
61. #408×C73C22semidirect
64. #405×C73C22semidirect
65. #343×C73C22semidirect
66. #343×C73C22semidirect
67. #341×C73C22semidirect
68. #341×C73C22semidirect
163. #100×C73D4semidirect
403. C22×C73#471semidirect
418. #25144C73direct (N × H)
429. C2×#471C2×C73semidirect
430. #3056C2×C73semidirect
432. C2×#450C2×C73semidirect
433. #2933C2×C73semidirect
434. C22×#100C2×C73semidirect
435. #2063C2×C73semidirect
436. #2051C2×C73semidirect
437. #2046C2×C73semidirect
438. #2019C2×C73semidirect
439. #1977C2×C73semidirect
440. #1931C2×C73semidirect
441. #1907C2×C73semidirect
442. #1901C2×C73semidirect
443. #1855C2×C73semidirect
444. C73#25144direct (N × H)
446. C2×#137C22×C73semidirect
451. C2×#131C22×C73semidirect
473. C2×#108C22×C73semidirect
474. C2×#108C22×C73semidirect
475. #428C22×C73semidirect
476. #424C22×C73semidirect
477. #419C22×C73semidirect
480. #417C22×C73semidirect
483. C2×#101C22×C73semidirect
484. C2×#101C22×C73semidirect
490. #408C22×C73semidirect
493. #405C22×C73semidirect
494. #343C22×C73semidirect
495. #343C22×C73semidirect
496. #341C22×C73semidirect
497. #341C22×C73semidirect
592. #100D4×C73semidirect
832. C22#471×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#471×C732
C73×#30562
C73×#30032
C2×#450×C732
C73×#29332
C22×#100×C732
C73×#20632
C73×#20512
C73×#20462
C73×#20192
C73×#19772
C73×#19312
C73×#19072
C73×#19012
C73×#18552
#2514473