Finite Group Databasebeta

← C73×#28930 #32938334

Subgroups — C73×#28930 #32938334

Order 18688.

1002 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
1C2×#490×C73C211yesmaximal, characteristic, complemented
2C2×#466×C73C211yesmaximal, characteristic, complemented
3C73×#2490C211yesmaximal, characteristic, complemented
4C73×#2428C211yesmaximal, characteristic, complemented
5C73×#2059C211yesmaximal, characteristic, complemented
6C73×#2034C211yesmaximal, characteristic, complemented
7C73×#2011C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic, complemented
9C73×#1972C211yesmaximal, characteristic, complemented
10C73×#1936C211yesmaximal, characteristic, complemented
11C73×#1925C211yesmaximal, characteristic, complemented
12C73×#1893C211yesmaximal, characteristic, complemented
13C73×#1879C211yesmaximal, characteristic, complemented
14C73×#1762C211yesmaximal, characteristic, complemented
15C73×#1752C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C23×C8×C73C2211yescharacteristic
19C2×#127×C73C2211yescharacteristic
20C2×#125×C73C2211yescharacteristic
21C2×#121×C73—21no—
22C2×#121×C73C2211yescharacteristic
23C2×#121×C73C2211yescharacteristic
24C2×#121×C73C2211yescharacteristic
25C2×C4×D4×C73C2211yescharacteristic
26#490×C73—24no—
27#466×C73—24no—
28C2×#107×C73C2211yescharacteristic
29C2×#106×C73C2211yescharacteristic
30C2×#102×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×#97×C73C2211yescharacteristic
40C2×#97×C73C2211yescharacteristic
41#397×C73—21no—
42#394×C73—21no—
43#394×C73—21no—
44#392×C73—21no—
45#390×C73—21no—
46#390×C73C2211yescharacteristic
47#390×C73C2211yescharacteristic
48#390×C73C2211yescharacteristic
49#389×C73C2211yescharacteristic
50#388×C73—21no—
51#386×C73—21no—
52#380×C73C2211yescharacteristic
53C4×C4⋊C4×C73C2211yescharacteristic
54C4×C22⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×D4×C73—21no—
62C22×D4×C73—21no—
63C22×D4×C73—21no—
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73C2311yescharacteristic
67C22×D4×C73C2311yescharacteristic
68C22×D4×C73C2311yescharacteristic
69C23×C4×C73—21no—
70C23×C4×C73C2311yescharacteristic
71C2×D8×C73—22no—
72C2×D8×C73—22no—
73C2×D8×C73—22no—
74C2×D8×C73—41no—
75C2×D8×C73—41no—
76C2×D8×C73—41no—
77C22×C8×C73—22no—
78C22×C8×C73—22no—
79C22×C8×C73—41no—
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82C22×C8×C73C2311yescharacteristic
83C22×C8×C73C2311yescharacteristic
84#127×C73—22no—
85#127×C73—41no—
86#125×C73—22no—
87#125×C73—41no—
88#121×C73—22no—
89#121×C73—22no—
90#121×C73—22no—
91#121×C73—44no—
92#121×C73—41no—
93#121×C73—41no—
94#121×C73—41no—
95C4×D4×C73—22no—
96C4×D4×C73—41no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73—21no—
112C2×C22⋊C4×C73—21no—
113C2×C22⋊C4×C73—21no—
114C2×C22⋊C4×C73—21no—
115C2×C22⋊C4×C73—21no—
116C2×C22⋊C4×C73D411yescharacteristic
117C2×C22⋊C4×C73D411yescharacteristic
118C2×C42×C73—21no—
119C2×C42×C73C2311yescharacteristic
120C2×C42×C73C2311yescharacteristic
121#107×C73—22no—
122#106×C73—41no—
123#102×C73—22no—
124#102×C73—22no—
125#102×C73—22no—
126#102×C73—22no—
127#102×C73—22no—
128#102×C73—22no—
129#102×C73—22no—
130#102×C73D414yescomplemented
131C22⋊C8×C73—22no—
132#97×C73—22no—
133#97×C73—41no—
134#95×C73—21no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73D411yescharacteristic
138#95×C73D411yescharacteristic
139C24×C73—21no—
140C24×C73—21no—
141C24×C73—21no—
142C24×C73C2×D411yescharacteristic
143C2×D4×C73—21no—
144C2×D4×C73—21no—
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—21no—
158C2×D4×C73—21no—
159C2×D4×C73—21no—
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×C73C2×D412yes—
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—42no—
188C22×C4×C73—42no—
189C22×C4×C73—81no—
190C22×C4×C73C2×D411yescharacteristic
191C22×C4×C73C2×D411yescharacteristic
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73C2411yescharacteristic
196D8×C73—44no—
197D8×C73—44no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73—44no—
208C2×C8×C73C2×D412yes—
209C2×C8×C73#4112yes—
210C2×C8×C73#4112yes—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73—21no—
217C4⋊C4×C73—21no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—42no—
220C4⋊C4×C73—42no—
221C4⋊C4×C73—42no—
222C4⋊C4×C73C2×D412yes—
223C4⋊C4×C73#4112yes—
224C22⋊C4×C73—22no—
225C22⋊C4×C73—41no—
226C22⋊C4×C73—42no—
227C22⋊C4×C73—42no—
228C22⋊C4×C73—42no—
229C22⋊C4×C73—42no—
230C22⋊C4×C73—42no—
231C22⋊C4×C73—42no—
232C22⋊C4×C73—81no—
233C22⋊C4×C73—81no—
234C22⋊C4×C73—81no—
235C22⋊C4×C73—81no—
236C22⋊C4×C73—81no—
237C42×C73—21no—
238C42×C73—21no—
239C42×C73—21no—
240C42×C73—21no—
241C42×C73—81no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—22no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
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—22no—
272D4×C73—22no—
273D4×C73—41no—
274D4×C73—41no—
275D4×C73—41no—
276D4×C73—41no—
277D4×C73—41no—
278D4×C73—41no—
279D4×C73—41no—
280D4×C73—41no—
281D4×C73—41no—
282D4×C73—41no—
283D4×C73—84no—
284D4×C73—84no—
285D4×C73—84no—
286D4×C73—84no—
287D4×C73—84no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—22no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—22no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
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×C73C22×D411yescharacteristic
324C2×C4×C73C2×#4111yescharacteristic
325C2×C4×C73C2×#4111yescharacteristic
326C2×C4×C73C2×#4111yescharacteristic
327C2×C4×C73H(5,𝔽2)11yescharacteristic
328C2×C4×C73H(5,𝔽2)11yescharacteristic
329C8×C73—22no—
330C8×C73—22no—
331C8×C73—22no—
332C8×C73—41no—
333C22×C73—22no—
334C22×C73—22no—
335C22×C73—22no—
336C22×C73—41no—
337C22×C73—41no—
338C22×C73—41no—
339C22×C73—41no—
340C22×C73—42no—
341C22×C73—42no—
342C22×C73—42no—
343C22×C73—81no—
344C22×C73—81no—
345C22×C73—81no—
346C22×C73—81no—
347C22×C73—81no—
348C22×C73—81no—
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#53211yescharacteristic
362C22×C73D4211yescharacteristic
363C22×C73#54611yescharacteristic
364C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C73#57511yescharacteristic
366C22×C73#57611yescharacteristic
367C22×C73#57611yescharacteristic
368C4×C73—41no—
369C4×C73—42no—
370C4×C73—41no—
371C4×C73—41no—
372C4×C73—41no—
373C4×C73—42no—
374C4×C73—41no—
375C4×C73—81no—
376C4×C73—81no—
377C4×C73—81no—
378C4×C73#53211yescharacteristic
379C4×C73#53811yescharacteristic
380C4×C73#54611yescharacteristic
381C4×C73#55511yescharacteristic
382#28930C7311yesmaximal, characteristic, direct product factor, Sylow
383C2×C73—42no—
384C2×C73—82no—
385C2×C73—161no—
386C2×C73—161no—
387C2×C73#255511yescharacteristic
388C2×C73#317611yescharacteristic
389C2×C73#318011yescharacteristic
390C2×C73#326411yescharacteristic
391C2×C73#326811yescharacteristic
392C2×C73#330911yescharacteristic
393C2×C73#331811yescharacteristic
394C2×#490C2×C7311yescharacteristic, complemented
395C2×#466C2×C7311yescharacteristic, complemented
396#2490C2×C7311yescharacteristic, complemented
397#2428C2×C7311yescharacteristic, complemented
398#2059C2×C7311yescharacteristic, complemented
399#2034C2×C7311yescharacteristic, complemented
400#2011C2×C7311yescharacteristic, complemented
401#1999C2×C7311yescharacteristic, complemented
402#1972C2×C7311yescharacteristic, complemented
403#1936C2×C7311yescharacteristic, complemented
404#1925C2×C7311yescharacteristic, complemented
405#1893C2×C7311yescharacteristic, complemented
406#1879C2×C7311yescharacteristic, complemented
407#1762C2×C7311yescharacteristic, complemented
408#1752C2×C7311yescharacteristic, complemented
409C73#2893011yescharacteristic, direct product factor, Sylow
410C22×D8C22×C7311yescharacteristic
411C22×D8C22×C7311yescharacteristic
412C23×C8C22×C7311yescharacteristic
413C2×#127C22×C7311yescharacteristic
414C2×#125C22×C7311yescharacteristic
415C2×#121—21no—
416C2×#121C22×C7311yescharacteristic
417C2×#121C22×C7311yescharacteristic
418C2×#121C22×C7311yescharacteristic
419C2×C4×D4C22×C7311yescharacteristic
420#490—24no—
421#466—24no—
422C2×#107C22×C7311yescharacteristic
423C2×#106C22×C7311yescharacteristic
424C2×#102C22×C7311yescharacteristic
425C2×#102C22×C7311yescharacteristic
426C2×#102C22×C7311yescharacteristic
427C2×#102C22×C7311yescharacteristic
428C2×#102C22×C7311yescharacteristic
429C2×#102C22×C7311yescharacteristic
430C2×#102C22×C7311yescharacteristic
431C2×#102C22×C7311yescharacteristic
432C2×C22⋊C8C22×C7311yescharacteristic
433C2×#97C22×C7311yescharacteristic
434C2×#97C22×C7311yescharacteristic
435#397—21no—
436#394—21no—
437#394—21no—
438#392—21no—
439#390—21no—
440#390C22×C7311yescharacteristic
441#390C22×C7311yescharacteristic
442#390C22×C7311yescharacteristic
443#389C22×C7311yescharacteristic
444#388—21no—
445#386—21no—
446#380C22×C7311yescharacteristic
447C4×C4⋊C4C22×C7311yescharacteristic
448C4×C22⋊C4C22×C7311yescharacteristic
449#340C22×C7311yescharacteristic
450#340C22×C7311yescharacteristic
451#340C22×C7311yescharacteristic
452#340C22×C7311yescharacteristic
453#336C22×C7311yescharacteristic
454#336C22×C7311yescharacteristic
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4C23×C7311yescharacteristic
461C22×D4C23×C7311yescharacteristic
462C22×D4C23×C7311yescharacteristic
463C23×C4—21no—
464C23×C4C23×C7311yescharacteristic
465C2×D8—22no—
466C2×D8—22no—
467C2×D8—22no—
468C2×D8—41no—
469C2×D8—41no—
470C2×D8—41no—
471C22×C8—22no—
472C22×C8—22no—
473C22×C8—41no—
474C22×C8C23×C7311yescharacteristic
475C22×C8C23×C7311yescharacteristic
476C22×C8C23×C7311yescharacteristic
477C22×C8C23×C7311yescharacteristic
478#127—22no—
479#127—41no—
480#125—22no—
481#125—41no—
482#121—22no—
483#121—22no—
484#121—22no—
485#121—44no—
486#121—41no—
487#121—41no—
488#121—41no—
489C4×D4—22no—
490C4×D4—41no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4C23×C7311yescharacteristic
495C2×C4⋊C4C23×C7311yescharacteristic
496C2×C4⋊C4C23×C7311yescharacteristic
497C2×C4⋊C4C23×C7311yescharacteristic
498C2×C4⋊C4C23×C7311yescharacteristic
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⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4D4×C7311yescharacteristic
511C2×C22⋊C4D4×C7311yescharacteristic
512C2×C42—21no—
513C2×C42C23×C7311yescharacteristic
514C2×C42C23×C7311yescharacteristic
515#107—22no—
516#106—41no—
517#102—22no—
518#102—22no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102D4×C7314yescomplemented
525C22⋊C8—22no—
526#97—22no—
527#97—41no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95D4×C7311yescharacteristic
532#95D4×C7311yescharacteristic
533C24—21no—
534C24—21no—
535C24—21no—
536C24C2×D4×C7311yescharacteristic
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
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—21no—
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—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4C2×D4×C7312yes—
570C22×C4—21no—
571C22×C4—21no—
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—42no—
582C22×C4—42no—
583C22×C4—81no—
584C22×C4C2×D4×C7311yescharacteristic
585C22×C4C2×D4×C7311yescharacteristic
586C22×C4C2×D4×C7311yescharacteristic
587C22×C4C2×D4×C7311yescharacteristic
588C22×C4C2×D4×C7311yescharacteristic
589C22×C4C24×C7311yescharacteristic
590D8—44no—
591D8—44no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—44no—
602C2×C8C2×D4×C7312yes—
603C2×C8#41×C7312yes—
604C2×C8#41×C7312yes—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4C2×D4×C7312yes—
617C4⋊C4#41×C7312yes—
618C22⋊C4—22no—
619C22⋊C4—41no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—81no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23AGL(1,ℤ/8)×C7312yes—
664C23C22×D4×C7311yescharacteristic
665D4—22no—
666D4—22no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—84no—
678D4—84no—
679D4—84no—
680D4—84no—
681D4—84no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
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—84no—
717C2×C4C22×D4×C7311yescharacteristic
718C2×C4C2×#41×C7311yescharacteristic
719C2×C4C2×#41×C7311yescharacteristic
720C2×C4C2×#41×C7311yescharacteristic
721C2×C4H(5,𝔽2)×C7311yescharacteristic
722C2×C4H(5,𝔽2)×C7311yescharacteristic
723C8—22no—
724C8—22no—
725C8—22no—
726C8—41no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22#532×C7311yescharacteristic
756C22D42×C7311yescharacteristic
757C22#546×C7311yescharacteristic
758C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
759C22#575×C7311yescharacteristic
760C22#576×C7311yescharacteristic
761C22#576×C7311yescharacteristic
762C4—41no—
763C4—42no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—81no—
770C4—81no—
771C4—81no—
772C4#532×C7311yescharacteristic
773C4#538×C7311yescharacteristic
774C4#546×C7311yescharacteristic
775C4#555×C7311yescharacteristic
776C2—42no—
777C2—82no—
778C2—161no—
779C2—161no—
780C2C73×#255511yescharacteristic
781C2C73×#317611yescharacteristic
782C2C73×#318011yescharacteristic
783C2C73×#326411yescharacteristic
784C2C73×#326811yescharacteristic
785C2C73×#330911yescharacteristic
786C2C73×#331811yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#490×C73C2semidirect
2. C2×#466×C73C2semidirect
3. C73×#2490C2semidirect
4. C73×#2428C2semidirect
5. C73×#2059C2semidirect
6. C73×#2034C2semidirect
7. C73×#2011C2semidirect
8. C73×#1999C2semidirect
9. C73×#1972C2semidirect
10. C73×#1936C2semidirect
11. C73×#1925C2semidirect
12. C73×#1893C2semidirect
13. C73×#1879C2semidirect
14. C73×#1762C2semidirect
15. C73×#1752C2semidirect
130. #102×C73D4semidirect
382. #28930C73direct (N × H)
394. C2×#490C2×C73semidirect
395. C2×#466C2×C73semidirect
396. #2490C2×C73semidirect
397. #2428C2×C73semidirect
398. #2059C2×C73semidirect
399. #2034C2×C73semidirect
400. #2011C2×C73semidirect
401. #1999C2×C73semidirect
402. #1972C2×C73semidirect
403. #1936C2×C73semidirect
404. #1925C2×C73semidirect
405. #1893C2×C73semidirect
406. #1879C2×C73semidirect
407. #1762C2×C73semidirect
408. #1752C2×C73semidirect
409. C73#28930direct (N × H)
524. #102D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#490×C732
C2×#466×C732
C73×#24902
C73×#24282
C73×#20592
C73×#20342
C73×#20112
C73×#19992
C73×#19722
C73×#19362
C73×#19252
C73×#18932
C73×#18792
C73×#17622
C73×#17522
#2893073