Finite Group Databasebeta

← C73×#26954 #32936358

Subgroups — C73×#26954 #32936358

Order 18688.

1026 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×#482×C73C211yesmaximal, characteristic, complemented
2C2×#459×C73C211yesmaximal, characteristic, complemented
3C73×#2428C211yesmaximal, characteristic, complemented
4C73×#2363C211yesmaximal, characteristic, complemented
5C73×#2088C211yesmaximal, characteristic, complemented
6C73×#2041C211yesmaximal, characteristic, complemented
7C73×#1999C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic, complemented
9C73×#1972C211yesmaximal, characteristic, complemented
10C73×#1925C211yesmaximal, characteristic, complemented
11C73×#1924C211yesmaximal, characteristic, complemented
12C73×#1879C211yesmaximal, characteristic, complemented
13C73×#1875C211yesmaximal, characteristic, complemented
14C73×#1862C211yesmaximal, characteristic, complemented
15C73×#1762C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C2×#127×C73C2211yescharacteristic
19C2×#121×C73—21no—
20C2×#121×C73C2211yescharacteristic
21C2×#121×C73C2211yescharacteristic
22C2×#121×C73C2211yescharacteristic
23C2×C4×D4×C73C2211yescharacteristic
24C2×C4×D4×C73C2211yescharacteristic
25C2×#117×C73C2211yescharacteristic
26#482×C73—24no—
27#459×C73—24no—
28C2×#107×C73C2211yescharacteristic
29C2×#106×C73C2211yescharacteristic
30C2×C4⋊C8×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×C22⋊C8×C73C2211yescharacteristic
40C2×C22⋊C8×C73C2211yescharacteristic
41C2×#97×C73C2211yescharacteristic
42#394×C73—21no—
43#392×C73—21no—
44#390×C73—21no—
45#390×C73C2211yescharacteristic
46#390×C73C2211yescharacteristic
47#389×C73C2211yescharacteristic
48#389×C73C2211yescharacteristic
49#388×C73—21no—
50#386×C73—21no—
51#386×C73—21no—
52C4×C4⋊C4×C73C2211yescharacteristic
53C4×C22⋊C4×C73—21no—
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×C73—21no—
71C23×C4×C73C2311yescharacteristic
72C2×D8×C73—22no—
73C2×D8×C73—22no—
74C2×D8×C73—22no—
75C2×D8×C73—22no—
76C2×D8×C73—41no—
77C2×D8×C73—41no—
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82#127×C73—22no—
83#127×C73—41no—
84#121×C73—22no—
85#121×C73—22no—
86#121×C73—22no—
87#121×C73—22no—
88#121×C73—44no—
89#121×C73—41no—
90#121×C73—41no—
91C4×D4×C73—22no—
92C4×D4×C73—22no—
93C4×D4×C73—41no—
94C4×D4×C73—41no—
95#117×C73—22no—
96#117×C73—41no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
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×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×C73D411yescharacteristic
115C2×C22⋊C4×C73D411yescharacteristic
116C2×C42×C73—21no—
117C2×C42×C73—21no—
118C2×C42×C73C2311yescharacteristic
119C2×C42×C73C2311yescharacteristic
120#107×C73—22no—
121#106×C73—22no—
122C4⋊C8×C73—22no—
123#102×C73—22no—
124#102×C73—22no—
125#102×C73—22no—
126#102×C73—22no—
127#102×C73—22no—
128#102×C73—41no—
129#102×C73—41no—
130#102×C73D414yescomplemented
131C22⋊C8×C73—22no—
132C22⋊C8×C73—41no—
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—24no—
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—81no—
169C2×D4×C73—81no—
170C2×D4×C73—81no—
171C2×D4×C73—81no—
172C2×D4×C73—81no—
173C2×D4×C73—81no—
174C2×D4×C73C2×D412yes—
175C2×D4×C73#4112yes—
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—42no—
190C22×C4×C73—42no—
191C22×C4×C73—81no—
192C22×C4×C73—81no—
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73C2×D411yescharacteristic
196C22×C4×C73C2×D411yescharacteristic
197C22×C4×C73C2×D411yescharacteristic
198C22×C4×C73C2411yescharacteristic
199D8×C73—44no—
200D8×C73—44no—
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—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73C2×D412yes—
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—21no—
220C4⋊C4×C73—42no—
221C4⋊C4×C73—81no—
222C4⋊C4×C73C2×D412yes—
223C4⋊C4×C73#4112yes—
224C4⋊C4×C73#4112yes—
225C22⋊C4×C73—24no—
226C22⋊C4×C73—22no—
227C22⋊C4×C73—41no—
228C22⋊C4×C73—42no—
229C22⋊C4×C73—42no—
230C22⋊C4×C73—42no—
231C22⋊C4×C73—42no—
232C22⋊C4×C73—42no—
233C22⋊C4×C73—42no—
234C22⋊C4×C73—42no—
235C22⋊C4×C73—81no—
236C22⋊C4×C73—81no—
237C42×C73—21no—
238C42×C73—21no—
239C42×C73—21no—
240C42×C73—21no—
241C42×C73—42no—
242C42×C73—81no—
243C23×C73—22no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—22no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
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×C73—41no—
270C23×C73—41no—
271C23×C73C22×D411yescharacteristic
272D4×C73—22no—
273D4×C73—22no—
274D4×C73—22no—
275D4×C73—22no—
276D4×C73—41no—
277D4×C73—41no—
278D4×C73—41no—
279D4×C73—41no—
280D4×C73—41no—
281D4×C73—41no—
282D4×C73—41no—
283D4×C73—41no—
284D4×C73—84no—
285D4×C73—84no—
286D4×C73—84no—
287D4×C73—84no—
288D4×C73—84no—
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—22no—
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—21no—
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—84no—
324C2×C4×C73AGL(1,ℤ/8)12yes—
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—41no—
336C22×C73—42no—
337C22×C73—41no—
338C22×C73—42no—
339C22×C73—41no—
340C22×C73—42no—
341C22×C73—42no—
342C22×C73—41no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
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—81no—
362C22×C73—81no—
363C22×C73#52511yescharacteristic
364C22×C73D4211yescharacteristic
365C22×C73#54611yescharacteristic
366C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C73#57511yescharacteristic
368C22×C73#57611yescharacteristic
369C22×C73#57611yescharacteristic
370C4×C73—22no—
371C4×C73—42no—
372C4×C73—41no—
373C4×C73—42no—
374C4×C73—41no—
375C4×C73—41no—
376C4×C73—41no—
377C4×C73—42no—
378C4×C73—81no—
379C4×C73—81no—
380C4×C73#53211yescharacteristic
381C4×C73#54011yescharacteristic
382C4×C73#54611yescharacteristic
383C4×C73#55311yescharacteristic
384#26954C7311yesmaximal, characteristic, direct product factor, Sylow
385C2×C73—81no—
386C2×C73—82no—
387C2×C73—82no—
388C2×C73—161no—
389C2×C73#246411yescharacteristic
390C2×C73#311511yescharacteristic
391C2×C73#312211yescharacteristic
392C2×C73#326411yescharacteristic
393C2×C73#326811yescharacteristic
394C2×C73#330911yescharacteristic
395C2×C73#332511yescharacteristic
396C2×#482C2×C7311yescharacteristic, complemented
397C2×#459C2×C7311yescharacteristic, complemented
398#2428C2×C7311yescharacteristic, complemented
399#2363C2×C7311yescharacteristic, complemented
400#2088C2×C7311yescharacteristic, complemented
401#2041C2×C7311yescharacteristic, complemented
402#1999C2×C7311yescharacteristic, complemented
403#1999C2×C7311yescharacteristic, complemented
404#1972C2×C7311yescharacteristic, complemented
405#1925C2×C7311yescharacteristic, complemented
406#1924C2×C7311yescharacteristic, complemented
407#1879C2×C7311yescharacteristic, complemented
408#1875C2×C7311yescharacteristic, complemented
409#1862C2×C7311yescharacteristic, complemented
410#1762C2×C7311yescharacteristic, complemented
411C73#2695411yescharacteristic, direct product factor, Sylow
412C22×D8C22×C7311yescharacteristic
413C22×D8C22×C7311yescharacteristic
414C2×#127C22×C7311yescharacteristic
415C2×#121—21no—
416C2×#121C22×C7311yescharacteristic
417C2×#121C22×C7311yescharacteristic
418C2×#121C22×C7311yescharacteristic
419C2×C4×D4C22×C7311yescharacteristic
420C2×C4×D4C22×C7311yescharacteristic
421C2×#117C22×C7311yescharacteristic
422#482—24no—
423#459—24no—
424C2×#107C22×C7311yescharacteristic
425C2×#106C22×C7311yescharacteristic
426C2×C4⋊C8C22×C7311yescharacteristic
427C2×#102C22×C7311yescharacteristic
428C2×#102C22×C7311yescharacteristic
429C2×#102C22×C7311yescharacteristic
430C2×#102C22×C7311yescharacteristic
431C2×#102C22×C7311yescharacteristic
432C2×#102C22×C7311yescharacteristic
433C2×#102C22×C7311yescharacteristic
434C2×#102C22×C7311yescharacteristic
435C2×C22⋊C8C22×C7311yescharacteristic
436C2×C22⋊C8C22×C7311yescharacteristic
437C2×#97C22×C7311yescharacteristic
438#394—21no—
439#392—21no—
440#390—21no—
441#390C22×C7311yescharacteristic
442#390C22×C7311yescharacteristic
443#389C22×C7311yescharacteristic
444#389C22×C7311yescharacteristic
445#388—21no—
446#386—21no—
447#386—21no—
448C4×C4⋊C4C22×C7311yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4C22×C7311yescharacteristic
451#340C22×C7311yescharacteristic
452#340C22×C7311yescharacteristic
453#340C22×C7311yescharacteristic
454#340C22×C7311yescharacteristic
455#336C22×C7311yescharacteristic
456#336C22×C7311yescharacteristic
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4C23×C7311yescharacteristic
463C22×D4C23×C7311yescharacteristic
464C22×D4C23×C7311yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4C23×C7311yescharacteristic
468C2×D8—22no—
469C2×D8—22no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—41no—
473C2×D8—41no—
474C22×C8C23×C7311yescharacteristic
475C22×C8C23×C7311yescharacteristic
476C22×C8C23×C7311yescharacteristic
477C22×C8C23×C7311yescharacteristic
478#127—22no—
479#127—41no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#121—44no—
485#121—41no—
486#121—41no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—41no—
490C4×D4—41no—
491#117—22no—
492#117—41no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4C23×C7311yescharacteristic
496C2×C4⋊C4C23×C7311yescharacteristic
497C2×C4⋊C4C23×C7311yescharacteristic
498C2×C4⋊C4C23×C7311yescharacteristic
499C2×C4⋊C4C23×C7311yescharacteristic
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×C42—21no—
514C2×C42C23×C7311yescharacteristic
515C2×C42C23×C7311yescharacteristic
516#107—22no—
517#106—22no—
518C4⋊C8—22no—
519#102—22no—
520#102—22no—
521#102—22no—
522#102—22no—
523#102—22no—
524#102—41no—
525#102—41no—
526#102D4×C7314yescomplemented
527C22⋊C8—22no—
528C22⋊C8—41no—
529#97—41no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95D4×C7311yescharacteristic
534#95D4×C7311yescharacteristic
535C24—21no—
536C24—21no—
537C24—21no—
538C24C2×D4×C7311yescharacteristic
539C2×D4—24no—
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—21no—
555C2×D4—21no—
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×D4—81no—
570C2×D4C2×D4×C7312yes—
571C2×D4#41×C7312yes—
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—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4C2×D4×C7311yescharacteristic
590C22×C4C2×D4×C7311yescharacteristic
591C22×C4C2×D4×C7311yescharacteristic
592C22×C4C2×D4×C7311yescharacteristic
593C22×C4C2×D4×C7311yescharacteristic
594C22×C4C24×C7311yescharacteristic
595D8—44no—
596D8—44no—
597C2×C8—21no—
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×C8C2×D4×C7312yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—42no—
617C4⋊C4—81no—
618C4⋊C4C2×D4×C7312yes—
619C4⋊C4#41×C7312yes—
620C4⋊C4#41×C7312yes—
621C22⋊C4—24no—
622C22⋊C4—22no—
623C22⋊C4—41no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—42no—
638C42—81no—
639C23—22no—
640C23—21no—
641C23—21no—
642C23—22no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
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—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23C22×D4×C7311yescharacteristic
668D4—22no—
669D4—22no—
670D4—22no—
671D4—22no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—84no—
681D4—84no—
682D4—84no—
683D4—84no—
684D4—84no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
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—84no—
720C2×C4AGL(1,ℤ/8)×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—41no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—42no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—41no—
743C22—42no—
744C22—81no—
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—
759C22#525×C7311yescharacteristic
760C22D42×C7311yescharacteristic
761C22#546×C7311yescharacteristic
762C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
763C22#575×C7311yescharacteristic
764C22#576×C7311yescharacteristic
765C22#576×C7311yescharacteristic
766C4—22no—
767C4—41no—
768C4—42no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—42no—
773C4—42no—
774C4—81no—
775C4—81no—
776C4#532×C7311yescharacteristic
777C4#540×C7311yescharacteristic
778C4#546×C7311yescharacteristic
779C4#553×C7311yescharacteristic
780C2—81no—
781C2—82no—
782C2—82no—
783C2—161no—
784C2C73×#246411yescharacteristic
785C2C73×#311511yescharacteristic
786C2C73×#312211yescharacteristic
787C2C73×#326411yescharacteristic
788C2C73×#326811yescharacteristic
789C2C73×#330911yescharacteristic
790C2C73×#332511yescharacteristic
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×#482×C73C2semidirect
2. C2×#459×C73C2semidirect
3. C73×#2428C2semidirect
4. C73×#2363C2semidirect
5. C73×#2088C2semidirect
6. C73×#2041C2semidirect
7. C73×#1999C2semidirect
8. C73×#1999C2semidirect
9. C73×#1972C2semidirect
10. C73×#1925C2semidirect
11. C73×#1924C2semidirect
12. C73×#1879C2semidirect
13. C73×#1875C2semidirect
14. C73×#1862C2semidirect
15. C73×#1762C2semidirect
130. #102×C73D4semidirect
384. #26954C73direct (N × H)
396. C2×#482C2×C73semidirect
397. C2×#459C2×C73semidirect
398. #2428C2×C73semidirect
399. #2363C2×C73semidirect
400. #2088C2×C73semidirect
401. #2041C2×C73semidirect
402. #1999C2×C73semidirect
403. #1999C2×C73semidirect
404. #1972C2×C73semidirect
405. #1925C2×C73semidirect
406. #1924C2×C73semidirect
407. #1879C2×C73semidirect
408. #1875C2×C73semidirect
409. #1862C2×C73semidirect
410. #1762C2×C73semidirect
411. C73#26954direct (N × H)
526. #102D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C732
C2×#459×C732
C73×#24282
C73×#23632
C73×#20882
C73×#20412
C73×#19992
C73×#19722
C73×#19252
C73×#19242
C73×#18792
C73×#18752
C73×#18622
C73×#17622
#2695473