Finite Group Databasebeta

← C73×#26984 #32936388

Subgroups — C73×#26984 #32936388

Order 18688.

1050 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C73C211yesmaximal, characteristic, complemented
2C2×#442×C73C211yesmaximal, characteristic, complemented
3C73×#2428C211yesmaximal, characteristic, complemented
4C73×#2422C211yesmaximal, characteristic, complemented
5C73×#2084C211yesmaximal, characteristic, complemented
6C73×#2034C211yesmaximal, characteristic, complemented
7C73×#2011C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic, complemented
9C73×#1957C211yesmaximal, characteristic, complemented
10C73×#1936C211yesmaximal, characteristic, complemented
11C73×#1934C211yesmaximal, characteristic, complemented
12C73×#1895C211yesmaximal, characteristic, complemented
13C73×#1879C211yesmaximal, characteristic, complemented
14C73×#1864C211yesmaximal, characteristic, complemented
15C73×#1753C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C22×M16×C73C2211yescharacteristic
19C2×#127×C73C2211yescharacteristic
20C2×#123×C73—21no—
21C2×#121×C73—21no—
22C2×#121×C73C2211yescharacteristic
23C2×#121×C73C2211yescharacteristic
24C2×#121×C73C2211yescharacteristic
25C2×C4×D4×C73C2211yescharacteristic
26C2×C4×D4×C73C2211yescharacteristic
27#469×C73—24no—
28#442×C73—24no—
29C2×#106×C73C2211yescharacteristic
30C2×#106×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×#97×C73C2211yescharacteristic
41C2×C4×C8×C73C2211yescharacteristic
42#397×C73—21no—
43#394×C73—21no—
44#394×C73—21no—
45#392×C73—21no—
46#390×C73C2211yescharacteristic
47#390×C73C2211yescharacteristic
48#389×C73C2211yescharacteristic
49#389×C73C2211yescharacteristic
50#386×C73—21no—
51#385×C73—21no—
52#384×C73C2211yescharacteristic
53#380×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×C73—21no—
71C23×C4×C73C2311yescharacteristic
72C2×D8×C73—22no—
73C2×D8×C73—22no—
74C2×D8×C73—22no—
75C2×D8×C73—22no—
76C2×D8×C73—22no—
77C2×D8×C73—41no—
78C2×M16×C73—22no—
79C2×M16×C73—22no—
80C2×M16×C73—41no—
81C22×C8×C73C2311yescharacteristic
82C22×C8×C73C2311yescharacteristic
83C22×C8×C73C2311yescharacteristic
84C22×C8×C73C2311yescharacteristic
85#127×C73—22no—
86#127×C73—41no—
87#123×C73—44no—
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—22no—
97C4×D4×C73—41no—
98C4×D4×C73—41no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73—21no—
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
117C2×C22⋊C4×C73—21no—
118C2×C22⋊C4×C73D411yescharacteristic
119C2×C22⋊C4×C73D411yescharacteristic
120C2×C42×C73C2311yescharacteristic
121C2×C42×C73C2311yescharacteristic
122#106×C73—22no—
123#106×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×C73—41no—
131#102×C73D414yescomplemented
132C22⋊C8×C73—22no—
133#97×C73—22no—
134C4×C8×C73—41no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73—21no—
138#95×C73D411yescharacteristic
139#95×C73D411yescharacteristic
140C24×C73—21no—
141C24×C73—21no—
142C24×C73—21no—
143C24×C73C2×D411yescharacteristic
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—
176C2×D4×C73#4112yes—
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—42no—
189C22×C4×C73—42no—
190C22×C4×C73—42no—
191C22×C4×C73—42no—
192C22×C4×C73—81no—
193C22×C4×C73—81no—
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73C2×D411yescharacteristic
196C22×C4×C73C2×D411yescharacteristic
197C22×C4×C73C2×D411yescharacteristic
198C22×C4×C73C2×D411yescharacteristic
199C22×C4×C73C2411yescharacteristic
200D8×C73—28no—
201D8×C73—44no—
202M16×C73—44no—
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—
213C2×C8×C73#4112yes—
214C2×C8×C73#4112yes—
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×C73—42no—
226C4⋊C4×C73—42no—
227C4⋊C4×C73—81no—
228C4⋊C4×C73C2×D412yes—
229C22⋊C4×C73—22no—
230C22⋊C4×C73—22no—
231C22⋊C4×C73—42no—
232C22⋊C4×C73—42no—
233C22⋊C4×C73—42no—
234C22⋊C4×C73—42no—
235C22⋊C4×C73—42no—
236C22⋊C4×C73—42no—
237C22⋊C4×C73—42no—
238C22⋊C4×C73—42no—
239C22⋊C4×C73—42no—
240C22⋊C4×C73—81no—
241C42×C73—21no—
242C42×C73—21no—
243C42×C73—21no—
244C42×C73—21no—
245C23×C73—21no—
246C23×C73—22no—
247C23×C73—21no—
248C23×C73—22no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
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×C73—41no—
272C23×C73—41no—
273C23×C73C22×D411yescharacteristic
274D4×C73—22no—
275D4×C73—22no—
276D4×C73—22no—
277D4×C73—22no—
278D4×C73—41no—
279D4×C73—41no—
280D4×C73—41no—
281D4×C73—41no—
282D4×C73—41no—
283D4×C73—41no—
284D4×C73—41no—
285D4×C73—41no—
286D4×C73—84no—
287D4×C73—84no—
288D4×C73—84no—
289D4×C73—84no—
290D4×C73—84no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—22no—
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—41no—
323C2×C4×C73—84no—
324C2×C4×C73—84no—
325C2×C4×C73AGL(1,ℤ/8)12yes—
326C2×C4×C73AGL(1,ℤ/8)12yes—
327C2×C4×C73C22×D411yescharacteristic
328C2×C4×C73C2×#4111yescharacteristic
329C2×C4×C73C2×#4111yescharacteristic
330C2×C4×C73C2×#4111yescharacteristic
331C2×C4×C73H(5,𝔽2)11yescharacteristic
332C2×C4×C73H(5,𝔽2)11yescharacteristic
333C8×C73—22no—
334C8×C73—22no—
335C8×C73—22no—
336C8×C73—41no—
337C22×C73—41no—
338C22×C73—41no—
339C22×C73—41no—
340C22×C73—42no—
341C22×C73—42no—
342C22×C73—41no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—41no—
346C22×C73—42no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—42no—
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—81no—
364C22×C73—81no—
365C22×C73#53211yescharacteristic
366C22×C73D4211yescharacteristic
367C22×C73#54611yescharacteristic
368C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C73#57611yescharacteristic
371C22×C73#57711yescharacteristic
372C4×C73—22no—
373C4×C73—22no—
374C4×C73—41no—
375C4×C73—41no—
376C4×C73—42no—
377C4×C73—41no—
378C4×C73—81no—
379C4×C73—81no—
380C4×C73—81no—
381C4×C73—81no—
382C4×C73#52511yescharacteristic
383C4×C73#54011yescharacteristic
384C4×C73#54611yescharacteristic
385C4×C73#55311yescharacteristic
386#26984C7311yesmaximal, characteristic, direct product factor, Sylow
387C2×C73—81no—
388C2×C73—82no—
389C2×C73—82no—
390C2×C73—161no—
391C2×C73#246411yescharacteristic
392C2×C73#317911yescharacteristic
393C2×C73#318411yescharacteristic
394C2×C73#327211yescharacteristic
395C2×C73#327411yescharacteristic
396C2×C73#330611yescharacteristic
397C2×C73#331811yescharacteristic
398C2×#469C2×C7311yescharacteristic, complemented
399C2×#442C2×C7311yescharacteristic, complemented
400#2428C2×C7311yescharacteristic, complemented
401#2422C2×C7311yescharacteristic, complemented
402#2084C2×C7311yescharacteristic, complemented
403#2034C2×C7311yescharacteristic, complemented
404#2011C2×C7311yescharacteristic, complemented
405#1999C2×C7311yescharacteristic, complemented
406#1957C2×C7311yescharacteristic, complemented
407#1936C2×C7311yescharacteristic, complemented
408#1934C2×C7311yescharacteristic, complemented
409#1895C2×C7311yescharacteristic, complemented
410#1879C2×C7311yescharacteristic, complemented
411#1864C2×C7311yescharacteristic, complemented
412#1753C2×C7311yescharacteristic, complemented
413C73#2698411yescharacteristic, direct product factor, Sylow
414C22×D8C22×C7311yescharacteristic
415C22×D8C22×C7311yescharacteristic
416C22×M16C22×C7311yescharacteristic
417C2×#127C22×C7311yescharacteristic
418C2×#123—21no—
419C2×#121—21no—
420C2×#121C22×C7311yescharacteristic
421C2×#121C22×C7311yescharacteristic
422C2×#121C22×C7311yescharacteristic
423C2×C4×D4C22×C7311yescharacteristic
424C2×C4×D4C22×C7311yescharacteristic
425#469—24no—
426#442—24no—
427C2×#106C22×C7311yescharacteristic
428C2×#106C22×C7311yescharacteristic
429C2×#102C22×C7311yescharacteristic
430C2×#102C22×C7311yescharacteristic
431C2×#102C22×C7311yescharacteristic
432C2×#102C22×C7311yescharacteristic
433C2×#102C22×C7311yescharacteristic
434C2×#102C22×C7311yescharacteristic
435C2×#102C22×C7311yescharacteristic
436C2×#102C22×C7311yescharacteristic
437C2×C22⋊C8C22×C7311yescharacteristic
438C2×#97C22×C7311yescharacteristic
439C2×C4×C8C22×C7311yescharacteristic
440#397—21no—
441#394—21no—
442#394—21no—
443#392—21no—
444#390C22×C7311yescharacteristic
445#390C22×C7311yescharacteristic
446#389C22×C7311yescharacteristic
447#389C22×C7311yescharacteristic
448#386—21no—
449#385—21no—
450#384C22×C7311yescharacteristic
451#380C22×C7311yescharacteristic
452C4×C22⋊C4C22×C7311yescharacteristic
453#340C22×C7311yescharacteristic
454#340C22×C7311yescharacteristic
455#340C22×C7311yescharacteristic
456#340C22×C7311yescharacteristic
457#336C22×C7311yescharacteristic
458#336C22×C7311yescharacteristic
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4C23×C7311yescharacteristic
465C22×D4C23×C7311yescharacteristic
466C22×D4C23×C7311yescharacteristic
467C23×C4—21no—
468C23×C4—21no—
469C23×C4C23×C7311yescharacteristic
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—41no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—41no—
479C22×C8C23×C7311yescharacteristic
480C22×C8C23×C7311yescharacteristic
481C22×C8C23×C7311yescharacteristic
482C22×C8C23×C7311yescharacteristic
483#127—22no—
484#127—41no—
485#123—44no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—44no—
490#121—41no—
491#121—41no—
492#121—41no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—41no—
496C4×D4—41no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4C23×C7311yescharacteristic
502C2×C4⋊C4C23×C7311yescharacteristic
503C2×C4⋊C4C23×C7311yescharacteristic
504C2×C4⋊C4C23×C7311yescharacteristic
505C2×C4⋊C4C23×C7311yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4D4×C7311yescharacteristic
517C2×C22⋊C4D4×C7311yescharacteristic
518C2×C42C23×C7311yescharacteristic
519C2×C42C23×C7311yescharacteristic
520#106—22no—
521#106—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—41no—
527#102—41no—
528#102—41no—
529#102D4×C7314yescomplemented
530C22⋊C8—22no—
531#97—22no—
532C4×C8—41no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95D4×C7311yescharacteristic
537#95D4×C7311yescharacteristic
538C24—21no—
539C24—21no—
540C24—21no—
541C24C2×D4×C7311yescharacteristic
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—21no—
557C2×D4—21no—
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—42no—
567C2×D4—42no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4C2×D4×C7312yes—
574C2×D4#41×C7312yes—
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—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4C2×D4×C7311yescharacteristic
593C22×C4C2×D4×C7311yescharacteristic
594C22×C4C2×D4×C7311yescharacteristic
595C22×C4C2×D4×C7311yescharacteristic
596C22×C4C2×D4×C7311yescharacteristic
597C22×C4C24×C7311yescharacteristic
598D8—28no—
599D8—44no—
600M16—44no—
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×C8—21no—
610C2×C8C2×D4×C7312yes—
611C2×C8#41×C7312yes—
612C2×C8#41×C7312yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—81no—
626C4⋊C4C2×D4×C7312yes—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C23—21no—
644C23—22no—
645C23—21no—
646C23—22no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
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—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23C22×D4×C7311yescharacteristic
672D4—22no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—84no—
685D4—84no—
686D4—84no—
687D4—84no—
688D4—84no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
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—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4AGL(1,ℤ/8)×C7312yes—
724C2×C4AGL(1,ℤ/8)×C7312yes—
725C2×C4C22×D4×C7311yescharacteristic
726C2×C4C2×#41×C7311yescharacteristic
727C2×C4C2×#41×C7311yescharacteristic
728C2×C4C2×#41×C7311yescharacteristic
729C2×C4H(5,𝔽2)×C7311yescharacteristic
730C2×C4H(5,𝔽2)×C7311yescharacteristic
731C8—22no—
732C8—22no—
733C8—22no—
734C8—41no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—41no—
739C22—42no—
740C22—42no—
741C22—41no—
742C22—42no—
743C22—41no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22#532×C7311yescharacteristic
764C22D42×C7311yescharacteristic
765C22#546×C7311yescharacteristic
766C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
767C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
768C22#576×C7311yescharacteristic
769C22#577×C7311yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—42no—
775C4—41no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4#525×C7311yescharacteristic
781C4#540×C7311yescharacteristic
782C4#546×C7311yescharacteristic
783C4#553×C7311yescharacteristic
784C2—81no—
785C2—82no—
786C2—82no—
787C2—161no—
788C2C73×#246411yescharacteristic
789C2C73×#317911yescharacteristic
790C2C73×#318411yescharacteristic
791C2C73×#327211yescharacteristic
792C2C73×#327411yescharacteristic
793C2C73×#330611yescharacteristic
794C2C73×#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×#469×C73C2semidirect
2. C2×#442×C73C2semidirect
3. C73×#2428C2semidirect
4. C73×#2422C2semidirect
5. C73×#2084C2semidirect
6. C73×#2034C2semidirect
7. C73×#2011C2semidirect
8. C73×#1999C2semidirect
9. C73×#1957C2semidirect
10. C73×#1936C2semidirect
11. C73×#1934C2semidirect
12. C73×#1895C2semidirect
13. C73×#1879C2semidirect
14. C73×#1864C2semidirect
15. C73×#1753C2semidirect
131. #102×C73D4semidirect
386. #26984C73direct (N × H)
398. C2×#469C2×C73semidirect
399. C2×#442C2×C73semidirect
400. #2428C2×C73semidirect
401. #2422C2×C73semidirect
402. #2084C2×C73semidirect
403. #2034C2×C73semidirect
404. #2011C2×C73semidirect
405. #1999C2×C73semidirect
406. #1957C2×C73semidirect
407. #1936C2×C73semidirect
408. #1934C2×C73semidirect
409. #1895C2×C73semidirect
410. #1879C2×C73semidirect
411. #1864C2×C73semidirect
412. #1753C2×C73semidirect
413. C73#26984direct (N × H)
529. #102D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C732
C2×#442×C732
C73×#24282
C73×#24222
C73×#20842
C73×#20342
C73×#20112
C73×#19992
C73×#19572
C73×#19362
C73×#19342
C73×#18952
C73×#18792
C73×#18642
C73×#17532
#2698473