Finite Group Databasebeta

← C73×#26246 #32935650

Subgroups — C73×#26246 #32935650

Order 18688.

1006 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C73C211yesmaximal, characteristic, complemented
2C2×#482×C73C211yesmaximal, characteristic, complemented
3C73×#2541C211yesmaximal, characteristic
4C73×#2352C211yesmaximal, characteristic, complemented
5C73×#2034C211yesmaximal, characteristic, complemented
6C73×#2033C211yesmaximal, characteristic, complemented
7C73×#2033C211yesmaximal, characteristic, complemented
8C73×#2033C211yesmaximal, characteristic, complemented
9C73×#1982C211yesmaximal, characteristic, complemented
10C73×#1961C211yesmaximal, characteristic, complemented
11C73×#1955C211yesmaximal, characteristic, complemented
12C73×#1949C211yesmaximal, characteristic, complemented
13C73×#1875C211yesmaximal, characteristic, complemented
14C73×#1874C211yesmaximal, characteristic, complemented
15C73×#1776C211yesmaximal, characteristic, complemented
16C2×#127×C73—21no—
17C2×#127×C73C2211yescharacteristic
18C2×#121×C73C2211yescharacteristic
19C2×#121×C73C2211yescharacteristic
20C2×#121×C73C2211yescharacteristic
21C2×#121×C73C2211yescharacteristic
22C2×C4×D4×C73C2211yescharacteristic
23C2×#117×C73C2211yescharacteristic
24C22×C4⋊C4×C73C2211yescharacteristic
25#482×C73—24no—
26#481×C73—24no—
27C2×#107×C73C2211yescharacteristic
28C2×#107×C73C2211yescharacteristic
29C2×#106×C73C2211yescharacteristic
30C2×#106×C73C2211yescharacteristic
31C2×C4⋊C8×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×C22⋊C8×C73C2211yescharacteristic
41C2×C22⋊C8×C73C2211yescharacteristic
42C2×C22⋊C8×C73C2211yescharacteristic
43C2×C22⋊C8×C73C2211yescharacteristic
44C2×#97×C73C2211yescharacteristic
45#392×C73—21no—
46#392×C73—21no—
47#390×C73—21no—
48#388×C73—21no—
49#387×C73—21no—
50#386×C73—21no—
51#382×C73C2211yescharacteristic
52#380×C73C2211yescharacteristic
53#380×C73C2211yescharacteristic
54C4×C4⋊C4×C73C2211yescharacteristic
55C4×C4⋊C4×C73C2211yescharacteristic
56C4×C22⋊C4×C73—21no—
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61C22×D4×C73—21no—
62C22×D4×C73—21no—
63C22×D4×C73—21no—
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73D411yescharacteristic
68C22×D4×C73C2311yescharacteristic
69C22×D4×C73C2311yescharacteristic
70C23×C4×C73—21no—
71C23×C4×C73C2311yescharacteristic
72C23×C4×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77#127×C73—22no—
78#127×C73—22no—
79#127×C73—44no—
80#121×C73—22no—
81#121×C73—22no—
82#121×C73—22no—
83#121×C73—22no—
84#121×C73—41no—
85#121×C73—41no—
86#121×C73—41no—
87#121×C73—41no—
88C4×D4×C73—22no—
89C4×D4×C73—22no—
90#117×C73—22no—
91#117×C73—41no—
92C2×C4⋊C4×C73—22no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—41no—
95C2×C4⋊C4×C73D411yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73D411yescharacteristic
110C2×C22⋊C4×C73D411yescharacteristic
111C2×C42×C73—21no—
112C2×C42×C73—21no—
113C2×C42×C73—21no—
114C2×C42×C73C2311yescharacteristic
115#107×C73—22no—
116#107×C73—22no—
117#106×C73—22no—
118#106×C73D414yescomplemented
119C4⋊C8×C73—22no—
120#102×C73—22no—
121#102×C73—22no—
122#102×C73—22no—
123#102×C73—22no—
124#102×C73—41no—
125#102×C73—41no—
126#102×C73—41no—
127#102×C73—41no—
128C22⋊C8×C73—22no—
129C22⋊C8×C73—22no—
130C22⋊C8×C73—41no—
131C22⋊C8×C73—41no—
132#97×C73—22no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73—21no—
138#95×C73—21no—
139C24×C73—21no—
140C24×C73—21no—
141C24×C73C2×D411yescharacteristic
142C24×C73C2×D411yescharacteristic
143C2×D4×C73—22no—
144C2×D4×C73—22no—
145C2×D4×C73—21no—
146C2×D4×C73—21no—
147C2×D4×C73—21no—
148C2×D4×C73—21no—
149C2×D4×C73—21no—
150C2×D4×C73—21no—
151C2×D4×C73—21no—
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—41no—
158C2×D4×C73—42no—
159C2×D4×C73—42no—
160C2×D4×C73—42no—
161C2×D4×C73—42no—
162C2×D4×C73—42no—
163C2×D4×C73—42no—
164C2×D4×C73—42no—
165C2×D4×C73—42no—
166C2×D4×C73—42no—
167C2×D4×C73—42no—
168C2×D4×C73—42no—
169C2×D4×C73—42no—
170C2×D4×C73—81no—
171C2×D4×C73—81no—
172C2×D4×C73—81no—
173C2×D4×C73—81no—
174C2×D4×C73—81no—
175C2×D4×C73—81no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—42no—
195C22×C4×C73—42no—
196C22×C4×C73—81no—
197C22×C4×C73C2×D411yescharacteristic
198C22×C4×C73C2×D411yescharacteristic
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2411yescharacteristic
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73C2×D412yes—
214C4⋊C4×C73—22no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73—21no—
217C4⋊C4×C73—21no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—42no—
225C4⋊C4×C73C2×D412yes—
226C4⋊C4×C73C2×D412yes—
227C4⋊C4×C73#4112yes—
228C22⋊C4×C73—22no—
229C22⋊C4×C73—22no—
230C22⋊C4×C73—42no—
231C22⋊C4×C73—42no—
232C22⋊C4×C73—42no—
233C22⋊C4×C73—42no—
234C22⋊C4×C73—42no—
235C22⋊C4×C73—42no—
236C22⋊C4×C73—81no—
237C42×C73—42no—
238C42×C73—42no—
239C42×C73—81no—
240C42×C73#4112yes—
241C42×C73#4112yes—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—41no—
256C23×C73—41no—
257C23×C73—41no—
258C23×C73—41no—
259C23×C73—41no—
260C23×C73—41no—
261C23×C73—41no—
262C23×C73—41no—
263C23×C73—41no—
264C23×C73—41no—
265C23×C73—41no—
266C23×C73—41no—
267C23×C73—41no—
268C23×C73—41no—
269C23×C73AGL(1,ℤ/8)12yes—
270C23×C73C22×D411yescharacteristic
271D4×C73—44no—
272D4×C73—41no—
273D4×C73—41no—
274D4×C73—41no—
275D4×C73—41no—
276D4×C73—41no—
277D4×C73—41no—
278D4×C73—41no—
279D4×C73—41no—
280D4×C73—84no—
281D4×C73—84no—
282D4×C73—84no—
283D4×C73—84no—
284D4×C73—84no—
285D4×C73—84no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—21no—
296C2×C4×C73—22no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—41no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
310C2×C4×C73—41no—
311C2×C4×C73—41no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
314C2×C4×C73—41no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73—41no—
318C2×C4×C73—41no—
319C2×C4×C73—41no—
320C2×C4×C73—41no—
321C2×C4×C73—41no—
322C2×C4×C73—84no—
323C2×C4×C73#12312yes—
324C2×C4×C73#12312yes—
325C2×C4×C73C22×D411yescharacteristic
326C2×C4×C73C2×#4111yescharacteristic
327C2×C4×C73C2×#4111yescharacteristic
328C2×C4×C73C2×#4111yescharacteristic
329C2×C4×C73H(5,𝔽2)11yescharacteristic
330C2×C4×C73H(5,𝔽2)11yescharacteristic
331C8×C73—22no—
332C8×C73—41no—
333C8×C73—41no—
334C8×C73—41no—
335C22×C73—22no—
336C22×C73—22no—
337C22×C73—22no—
338C22×C73—41no—
339C22×C73—41no—
340C22×C73—41no—
341C22×C73—41no—
342C22×C73—41no—
343C22×C73—41no—
344C22×C73—41no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—81no—
350C22×C73—81no—
351C22×C73—81no—
352C22×C73—81no—
353C22×C73—81no—
354C22×C73—81no—
355C22×C73—81no—
356C22×C73—81no—
357C22×C73—81no—
358C22×C73—81no—
359C22×C73—81no—
360C22×C73—81no—
361C22×C73—81no—
362C22×C73—81no—
363C22×C73C2×#12311yescharacteristic
364C22×C73D4211yescharacteristic
365C22×C73#54611yescharacteristic
366C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C73#57511yescharacteristic
368C22×C73#57611yescharacteristic
369C22×C73#57711yescharacteristic
370C4×C73—22no—
371C4×C73—22no—
372C4×C73—41no—
373C4×C73—41no—
374C4×C73—42no—
375C4×C73—42no—
376C4×C73—42no—
377C4×C73—81no—
378C4×C73—81no—
379C4×C73—81no—
380C4×C73#53211yescharacteristic
381C4×C73#54011yescharacteristic
382C4×C73#55011yescharacteristic
383C4×C73#55911yescharacteristic
384#26246C7311yesmaximal, characteristic, direct product factor, Sylow
385C2×C73—42no—
386C2×C73—81no—
387C2×C73—161no—
388C2×C73—161no—
389C2×C73#244511yescharacteristic
390C2×C73#309411yescharacteristic
391C2×C73#309611yescharacteristic
392C2×C73#326511yescharacteristic
393C2×C73#326811yescharacteristic
394C2×C73#331711yescharacteristic
395C2×C73#331811yescharacteristic
396C2×#481C2×C7311yescharacteristic, complemented
397C2×#482C2×C7311yescharacteristic, complemented
398#2541C2×C7311yescharacteristic
399#2352C2×C7311yescharacteristic, complemented
400#2034C2×C7311yescharacteristic, complemented
401#2033C2×C7311yescharacteristic, complemented
402#2033C2×C7311yescharacteristic, complemented
403#2033C2×C7311yescharacteristic, complemented
404#1982C2×C7311yescharacteristic, complemented
405#1961C2×C7311yescharacteristic, complemented
406#1955C2×C7311yescharacteristic, complemented
407#1949C2×C7311yescharacteristic, complemented
408#1875C2×C7311yescharacteristic, complemented
409#1874C2×C7311yescharacteristic, complemented
410#1776C2×C7311yescharacteristic, complemented
411C73#2624611yescharacteristic, direct product factor, Sylow
412C2×#127—21no—
413C2×#127C22×C7311yescharacteristic
414C2×#121C22×C7311yescharacteristic
415C2×#121C22×C7311yescharacteristic
416C2×#121C22×C7311yescharacteristic
417C2×#121C22×C7311yescharacteristic
418C2×C4×D4C22×C7311yescharacteristic
419C2×#117C22×C7311yescharacteristic
420C22×C4⋊C4C22×C7311yescharacteristic
421#482—24no—
422#481—24no—
423C2×#107C22×C7311yescharacteristic
424C2×#107C22×C7311yescharacteristic
425C2×#106C22×C7311yescharacteristic
426C2×#106C22×C7311yescharacteristic
427C2×C4⋊C8C22×C7311yescharacteristic
428C2×#102C22×C7311yescharacteristic
429C2×#102C22×C7311yescharacteristic
430C2×#102C22×C7311yescharacteristic
431C2×#102C22×C7311yescharacteristic
432C2×#102C22×C7311yescharacteristic
433C2×#102C22×C7311yescharacteristic
434C2×#102C22×C7311yescharacteristic
435C2×#102C22×C7311yescharacteristic
436C2×C22⋊C8C22×C7311yescharacteristic
437C2×C22⋊C8C22×C7311yescharacteristic
438C2×C22⋊C8C22×C7311yescharacteristic
439C2×C22⋊C8C22×C7311yescharacteristic
440C2×#97C22×C7311yescharacteristic
441#392—21no—
442#392—21no—
443#390—21no—
444#388—21no—
445#387—21no—
446#386—21no—
447#382C22×C7311yescharacteristic
448#380C22×C7311yescharacteristic
449#380C22×C7311yescharacteristic
450C4×C4⋊C4C22×C7311yescharacteristic
451C4×C4⋊C4C22×C7311yescharacteristic
452C4×C22⋊C4—21no—
453#340C22×C7311yescharacteristic
454#340C22×C7311yescharacteristic
455#340C22×C7311yescharacteristic
456#340C22×C7311yescharacteristic
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4D4×C7311yescharacteristic
464C22×D4C23×C7311yescharacteristic
465C22×D4C23×C7311yescharacteristic
466C23×C4—21no—
467C23×C4C23×C7311yescharacteristic
468C23×C4C23×C7311yescharacteristic
469C22×C8C23×C7311yescharacteristic
470C22×C8C23×C7311yescharacteristic
471C22×C8C23×C7311yescharacteristic
472C22×C8C23×C7311yescharacteristic
473#127—22no—
474#127—22no—
475#127—44no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—41no—
481#121—41no—
482#121—41no—
483#121—41no—
484C4×D4—22no—
485C4×D4—22no—
486#117—22no—
487#117—41no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—41no—
491C2×C4⋊C4D4×C7311yescharacteristic
492C2×C4⋊C4C23×C7311yescharacteristic
493C2×C4⋊C4C23×C7311yescharacteristic
494C2×C4⋊C4C23×C7311yescharacteristic
495C2×C4⋊C4C23×C7311yescharacteristic
496C2×C4⋊C4C23×C7311yescharacteristic
497C2×C4⋊C4C23×C7311yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4D4×C7311yescharacteristic
506C2×C22⋊C4D4×C7311yescharacteristic
507C2×C42—21no—
508C2×C42—21no—
509C2×C42—21no—
510C2×C42C23×C7311yescharacteristic
511#107—22no—
512#107—22no—
513#106—22no—
514#106D4×C7314yescomplemented
515C4⋊C8—22no—
516#102—22no—
517#102—22no—
518#102—22no—
519#102—22no—
520#102—41no—
521#102—41no—
522#102—41no—
523#102—41no—
524C22⋊C8—22no—
525C22⋊C8—22no—
526C22⋊C8—41no—
527C22⋊C8—41no—
528#97—22no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535C24—21no—
536C24—21no—
537C24C2×D4×C7311yescharacteristic
538C24C2×D4×C7311yescharacteristic
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—41no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—81no—
593C22×C4C2×D4×C7311yescharacteristic
594C22×C4C2×D4×C7311yescharacteristic
595C22×C4C2×D4×C7311yescharacteristic
596C22×C4C2×D4×C7311yescharacteristic
597C22×C4C24×C7311yescharacteristic
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8C2×D4×C7312yes—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—42no—
621C4⋊C4C2×D4×C7312yes—
622C4⋊C4C2×D4×C7312yes—
623C4⋊C4#41×C7312yes—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—81no—
633C42—42no—
634C42—42no—
635C42—81no—
636C42#41×C7312yes—
637C42#41×C7312yes—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23AGL(1,ℤ/8)×C7312yes—
666C23C22×D4×C7311yescharacteristic
667D4—44no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—84no—
677D4—84no—
678D4—84no—
679D4—84no—
680D4—84no—
681D4—84no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—84no—
719C2×C4#123×C7312yes—
720C2×C4#123×C7312yes—
721C2×C4C22×D4×C7311yescharacteristic
722C2×C4C2×#41×C7311yescharacteristic
723C2×C4C2×#41×C7311yescharacteristic
724C2×C4C2×#41×C7311yescharacteristic
725C2×C4H(5,𝔽2)×C7311yescharacteristic
726C2×C4H(5,𝔽2)×C7311yescharacteristic
727C8—22no—
728C8—41no—
729C8—41no—
730C8—41no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22C2×#123×C7311yescharacteristic
760C22D42×C7311yescharacteristic
761C22#546×C7311yescharacteristic
762C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
763C22#575×C7311yescharacteristic
764C22#576×C7311yescharacteristic
765C22#577×C7311yescharacteristic
766C4—22no—
767C4—22no—
768C4—41no—
769C4—41no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—81no—
774C4—81no—
775C4—81no—
776C4#532×C7311yescharacteristic
777C4#540×C7311yescharacteristic
778C4#550×C7311yescharacteristic
779C4#559×C7311yescharacteristic
780C2—42no—
781C2—81no—
782C2—161no—
783C2—161no—
784C2C73×#244511yescharacteristic
785C2C73×#309411yescharacteristic
786C2C73×#309611yescharacteristic
787C2C73×#326511yescharacteristic
788C2C73×#326811yescharacteristic
789C2C73×#331711yescharacteristic
790C2C73×#331811yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2541C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C4×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#481×C73C2semidirect
2. C2×#482×C73C2semidirect
4. C73×#2352C2semidirect
5. C73×#2034C2semidirect
6. C73×#2033C2semidirect
7. C73×#2033C2semidirect
8. C73×#2033C2semidirect
9. C73×#1982C2semidirect
10. C73×#1961C2semidirect
11. C73×#1955C2semidirect
12. C73×#1949C2semidirect
13. C73×#1875C2semidirect
14. C73×#1874C2semidirect
15. C73×#1776C2semidirect
118. #106×C73D4semidirect
384. #26246C73direct (N × H)
396. C2×#481C2×C73semidirect
397. C2×#482C2×C73semidirect
399. #2352C2×C73semidirect
400. #2034C2×C73semidirect
401. #2033C2×C73semidirect
402. #2033C2×C73semidirect
403. #2033C2×C73semidirect
404. #1982C2×C73semidirect
405. #1961C2×C73semidirect
406. #1955C2×C73semidirect
407. #1949C2×C73semidirect
408. #1875C2×C73semidirect
409. #1874C2×C73semidirect
410. #1776C2×C73semidirect
411. C73#26246direct (N × H)
514. #106D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#481×C732
C2×#482×C732
C73×#25412
C73×#23522
C73×#20342
C73×#20332
C73×#19822
C73×#19612
C73×#19552
C73×#19492
C73×#18752
C73×#18742
C73×#17762
#2624673