Finite Group Databasebeta

← C73×#26601 #32936005

Subgroups — C73×#26601 #32936005

Order 18688.

1084 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C73C211yesmaximal, characteristic, complemented
2C2×#442×C73C211yesmaximal, characteristic, complemented
3C73×#2445C211yesmaximal, characteristic, complemented
4C73×#2366C211yesmaximal, characteristic, complemented
5C73×#2065C211yesmaximal, characteristic, complemented
6C73×#2011C211yesmaximal, characteristic, complemented
7C73×#2011C211yesmaximal, characteristic, complemented
8C73×#2011C211yesmaximal, characteristic, complemented
9C73×#1972C211yesmaximal, characteristic, complemented
10C73×#1926C211yesmaximal, characteristic, complemented
11C73×#1926C211yesmaximal, characteristic, complemented
12C73×#1917C211yesmaximal, characteristic, complemented
13C73×#1879C211yesmaximal, characteristic, complemented
14C73×#1879C211yesmaximal, characteristic, complemented
15C73×#1864C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C22×D8×C73C2211yescharacteristic
19C22×D8×C73C2211yescharacteristic
20C2×#127×C73C2211yescharacteristic
21C2×#127×C73C2211yescharacteristic
22C2×#123×C73—21no—
23C2×C4×D4×C73—21no—
24C2×C4×D4×C73C2211yescharacteristic
25C2×C4×D4×C73C2211yescharacteristic
26C2×C4×D4×C73C2211yescharacteristic
27#459×C73—24no—
28#442×C73—24no—
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×#97×C73C2211yescharacteristic
41#394×C73—21no—
42#394×C73—21no—
43#390×C73—21no—
44#390×C73C2211yescharacteristic
45#390×C73C2211yescharacteristic
46#390×C73C2211yescharacteristic
47#390×C73C2211yescharacteristic
48#390×C73C2211yescharacteristic
49#389×C73C2211yescharacteristic
50#386×C73—21no—
51#386×C73—21no—
52#386×C73—21no—
53C4×C4⋊C4×C73C2211yescharacteristic
54C4×C4⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×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×C73C2311yescharacteristic
66C22×D4×C73C2311yescharacteristic
67C22×D4×C73C2311yescharacteristic
68C22×D4×C73C2311yescharacteristic
69C23×C4×C73—21no—
70C23×C4×C73—21no—
71C23×C4×C73—21no—
72C2×D8×C73—22no—
73C2×D8×C73—22no—
74C2×D8×C73—22no—
75C2×D8×C73—22no—
76C2×D8×C73—22no—
77C2×D8×C73—22no—
78C2×D8×C73—22no—
79C2×D8×C73—22no—
80C2×D8×C73—41no—
81C2×D8×C73—41no—
82C2×D8×C73—41no—
83C2×D8×C73—41no—
84C22×C8×C73C2311yescharacteristic
85C22×C8×C73C2311yescharacteristic
86C22×C8×C73C2311yescharacteristic
87C22×C8×C73C2311yescharacteristic
88#127×C73—22no—
89#127×C73—22no—
90#127×C73—22no—
91#127×C73—41no—
92#123×C73—44no—
93C4×D4×C73—22no—
94C4×D4×C73—22no—
95C4×D4×C73—22no—
96C4×D4×C73—41no—
97C4×D4×C73—41no—
98C4×D4×C73—41no—
99C4×D4×C73—44no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73D411yescharacteristic
102C2×C4⋊C4×C73D411yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
117C2×C22⋊C4×C73—21no—
118C2×C22⋊C4×C73—21no—
119C2×C22⋊C4×C73—21no—
120C2×C42×C73—21no—
121C2×C42×C73C2311yescharacteristic
122C2×C42×C73C2311yescharacteristic
123C2×C42×C73C2311yescharacteristic
124#106×C73—22no—
125#106×C73—41no—
126C4⋊C8×C73—22no—
127#102×C73—22no—
128#102×C73—22no—
129#102×C73—22no—
130#102×C73—22no—
131#102×C73—41no—
132#102×C73—41no—
133#102×C73—41no—
134#102×C73D414yescomplemented
135#97×C73—22no—
136#95×C73—21no—
137#95×C73—21no—
138#95×C73D411yescharacteristic
139#95×C73D411yescharacteristic
140C24×C73—21no—
141C24×C73—21no—
142C24×C73—21no—
143C24×C73—21no—
144C2×D4×C73—24no—
145C2×D4×C73—24no—
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—21no—
161C2×D4×C73—21no—
162C2×D4×C73—21no—
163C2×D4×C73—21no—
164C2×D4×C73—21no—
165C2×D4×C73—21no—
166C2×D4×C73—21no—
167C2×D4×C73—42no—
168C2×D4×C73—42no—
169C2×D4×C73—42no—
170C2×D4×C73—42no—
171C2×D4×C73—42no—
172C2×D4×C73—42no—
173C2×D4×C73—81no—
174C2×D4×C73—81no—
175C2×D4×C73—81no—
176C2×D4×C73—81no—
177C2×D4×C73C2×D412yes—
178C2×D4×C73#4112yes—
179C2×D4×C73#4112yes—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—42no—
185C22×C4×C73—42no—
186C22×C4×C73—42no—
187C22×C4×C73—42no—
188C22×C4×C73—42no—
189C22×C4×C73—42no—
190C22×C4×C73—81no—
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×C73C2×D411yescharacteristic
199C22×C4×C73C2411yescharacteristic
200D8×C73—28no—
201D8×C73—44no—
202D8×C73—44no—
203D8×C73—44no—
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×C73—21no—
214C2×C8×C73C2×D412yes—
215C2×C8×C73#4112yes—
216C4⋊C4×C73—22no—
217C4⋊C4×C73—22no—
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—21no—
225C4⋊C4×C73—42no—
226C4⋊C4×C73C2×D412yes—
227C22⋊C4×C73—42no—
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—
237C22⋊C4×C73—81no—
238C22⋊C4×C73—81no—
239C22⋊C4×C73—81no—
240C42×C73—21no—
241C42×C73—21no—
242C42×C73—21no—
243C42×C73—21no—
244C42×C73—21no—
245C42×C73—21no—
246C42×C73—42no—
247C23×C73—22no—
248C23×C73—22no—
249C23×C73—22no—
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×C73—41no—
270C23×C73—41no—
271C23×C73—41no—
272C23×C73—41no—
273C23×C73—41no—
274C23×C73—41no—
275C23×C73C22×D411yescharacteristic
276D4×C73—22no—
277D4×C73—22no—
278D4×C73—22no—
279D4×C73—22no—
280D4×C73—22no—
281D4×C73—22no—
282D4×C73—48no—
283D4×C73—41no—
284D4×C73—41no—
285D4×C73—41no—
286D4×C73—41no—
287D4×C73—41no—
288D4×C73—41no—
289D4×C73—41no—
290D4×C73—41no—
291D4×C73—41no—
292D4×C73—41no—
293D4×C73—84no—
294D4×C73—84no—
295D4×C73—84no—
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—22no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—21no—
312C2×C4×C73—21no—
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—41no—
324C2×C4×C73—84no—
325C2×C4×C73—84no—
326C2×C4×C73—84no—
327C2×C4×C73AGL(1,ℤ/8)12yes—
328C2×C4×C73AGL(1,ℤ/8)12yes—
329C2×C4×C73C22×D411yescharacteristic
330C2×C4×C73C2×#4111yescharacteristic
331C2×C4×C73C2×#4111yescharacteristic
332C2×C4×C73C2×#4111yescharacteristic
333C2×C4×C73H(5,𝔽2)11yescharacteristic
334C2×C4×C73H(5,𝔽2)11yescharacteristic
335C8×C73—22no—
336C8×C73—22no—
337C8×C73—41no—
338C8×C73—41no—
339C22×C73—42no—
340C22×C73—42no—
341C22×C73—42no—
342C22×C73—42no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—42no—
346C22×C73—42no—
347C22×C73—42no—
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—81no—
364C22×C73—81no—
365C22×C73—81no—
366C22×C73—81no—
367C22×C73#52511yescharacteristic
368C22×C73D4211yescharacteristic
369C22×C73#55011yescharacteristic
370C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C73#57611yescharacteristic
373C22×C73#57611yescharacteristic
374C4×C73—22no—
375C4×C73—22no—
376C4×C73—41no—
377C4×C73—41no—
378C4×C73—42no—
379C4×C73—41no—
380C4×C73—41no—
381C4×C73—81no—
382C4×C73—81no—
383C4×C73—81no—
384C4×C73#52511yescharacteristic
385C4×C73#53811yescharacteristic
386C4×C73#54611yescharacteristic
387C4×C73#55311yescharacteristic
388#26601C7311yesmaximal, characteristic, direct product factor, Sylow
389C2×C73—82no—
390C2×C73—82no—
391C2×C73—82no—
392C2×C73—161no—
393C2×C73#245611yescharacteristic
394C2×C73#310911yescharacteristic
395C2×C73#312211yescharacteristic
396C2×C73#326411yescharacteristic
397C2×C73#327411yescharacteristic
398C2×C73#339911yescharacteristic
399C2×C73#339911yescharacteristic
400C2×#459C2×C7311yescharacteristic, complemented
401C2×#442C2×C7311yescharacteristic, complemented
402#2445C2×C7311yescharacteristic, complemented
403#2366C2×C7311yescharacteristic, complemented
404#2065C2×C7311yescharacteristic, complemented
405#2011C2×C7311yescharacteristic, complemented
406#2011C2×C7311yescharacteristic, complemented
407#2011C2×C7311yescharacteristic, complemented
408#1972C2×C7311yescharacteristic, complemented
409#1926C2×C7311yescharacteristic, complemented
410#1926C2×C7311yescharacteristic, complemented
411#1917C2×C7311yescharacteristic, complemented
412#1879C2×C7311yescharacteristic, complemented
413#1879C2×C7311yescharacteristic, complemented
414#1864C2×C7311yescharacteristic, complemented
415C73#2660111yescharacteristic, direct product factor, Sylow
416C22×D8C22×C7311yescharacteristic
417C22×D8C22×C7311yescharacteristic
418C22×D8C22×C7311yescharacteristic
419C22×D8C22×C7311yescharacteristic
420C2×#127C22×C7311yescharacteristic
421C2×#127C22×C7311yescharacteristic
422C2×#123—21no—
423C2×C4×D4—21no—
424C2×C4×D4C22×C7311yescharacteristic
425C2×C4×D4C22×C7311yescharacteristic
426C2×C4×D4C22×C7311yescharacteristic
427#459—24no—
428#442—24no—
429C2×#106C22×C7311yescharacteristic
430C2×#106C22×C7311yescharacteristic
431C2×C4⋊C8C22×C7311yescharacteristic
432C2×#102C22×C7311yescharacteristic
433C2×#102C22×C7311yescharacteristic
434C2×#102C22×C7311yescharacteristic
435C2×#102C22×C7311yescharacteristic
436C2×#102C22×C7311yescharacteristic
437C2×#102C22×C7311yescharacteristic
438C2×#102C22×C7311yescharacteristic
439C2×#102C22×C7311yescharacteristic
440C2×#97C22×C7311yescharacteristic
441#394—21no—
442#394—21no—
443#390—21no—
444#390C22×C7311yescharacteristic
445#390C22×C7311yescharacteristic
446#390C22×C7311yescharacteristic
447#390C22×C7311yescharacteristic
448#390C22×C7311yescharacteristic
449#389C22×C7311yescharacteristic
450#386—21no—
451#386—21no—
452#386—21no—
453C4×C4⋊C4C22×C7311yescharacteristic
454C4×C4⋊C4C22×C7311yescharacteristic
455#340C22×C7311yescharacteristic
456#340C22×C7311yescharacteristic
457#336C22×C7311yescharacteristic
458#336C22×C7311yescharacteristic
459#336C22×C7311yescharacteristic
460#336C22×C7311yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4C23×C7311yescharacteristic
466C22×D4C23×C7311yescharacteristic
467C22×D4C23×C7311yescharacteristic
468C22×D4C23×C7311yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—21no—
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—22no—
477C2×D8—22no—
478C2×D8—22no—
479C2×D8—22no—
480C2×D8—41no—
481C2×D8—41no—
482C2×D8—41no—
483C2×D8—41no—
484C22×C8C23×C7311yescharacteristic
485C22×C8C23×C7311yescharacteristic
486C22×C8C23×C7311yescharacteristic
487C22×C8C23×C7311yescharacteristic
488#127—22no—
489#127—22no—
490#127—22no—
491#127—41no—
492#123—44no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—41no—
497C4×D4—41no—
498C4×D4—41no—
499C4×D4—44no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4D4×C7311yescharacteristic
502C2×C4⋊C4D4×C7311yescharacteristic
503C2×C4⋊C4C23×C7311yescharacteristic
504C2×C4⋊C4C23×C7311yescharacteristic
505C2×C4⋊C4C23×C7311yescharacteristic
506C2×C4⋊C4C23×C7311yescharacteristic
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⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C42—21no—
521C2×C42C23×C7311yescharacteristic
522C2×C42C23×C7311yescharacteristic
523C2×C42C23×C7311yescharacteristic
524#106—22no—
525#106—41no—
526C4⋊C8—22no—
527#102—22no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—41no—
532#102—41no—
533#102—41no—
534#102D4×C7314yescomplemented
535#97—22no—
536#95—21no—
537#95—21no—
538#95D4×C7311yescharacteristic
539#95D4×C7311yescharacteristic
540C24—21no—
541C24—21no—
542C24—21no—
543C24—21no—
544C2×D4—24no—
545C2×D4—24no—
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—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4—81no—
577C2×D4C2×D4×C7312yes—
578C2×D4#41×C7312yes—
579C2×D4#41×C7312yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4—81no—
593C22×C4C2×D4×C7311yescharacteristic
594C22×C4C2×D4×C7311yescharacteristic
595C22×C4C2×D4×C7311yescharacteristic
596C22×C4C2×D4×C7311yescharacteristic
597C22×C4C2×D4×C7311yescharacteristic
598C22×C4C2×D4×C7311yescharacteristic
599C22×C4C24×C7311yescharacteristic
600D8—28no—
601D8—44no—
602D8—44no—
603D8—44no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8C2×D4×C7312yes—
615C2×C8#41×C7312yes—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—42no—
626C4⋊C4C2×D4×C7312yes—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—81no—
636C22⋊C4—81no—
637C22⋊C4—81no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—42no—
647C23—22no—
648C23—22no—
649C23—22no—
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—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23C22×D4×C7311yescharacteristic
676D4—22no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—84no—
694D4—84no—
695D4—84no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
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—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—84no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4AGL(1,ℤ/8)×C7312yes—
728C2×C4AGL(1,ℤ/8)×C7312yes—
729C2×C4C22×D4×C7311yescharacteristic
730C2×C4C2×#41×C7311yescharacteristic
731C2×C4C2×#41×C7311yescharacteristic
732C2×C4C2×#41×C7311yescharacteristic
733C2×C4H(5,𝔽2)×C7311yescharacteristic
734C2×C4H(5,𝔽2)×C7311yescharacteristic
735C8—22no—
736C8—22no—
737C8—41no—
738C8—41no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
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—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22#525×C7311yescharacteristic
768C22D42×C7311yescharacteristic
769C22#550×C7311yescharacteristic
770C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
771C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
772C22#576×C7311yescharacteristic
773C22#576×C7311yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—42no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4#525×C7311yescharacteristic
785C4#538×C7311yescharacteristic
786C4#546×C7311yescharacteristic
787C4#553×C7311yescharacteristic
788C2—82no—
789C2—82no—
790C2—82no—
791C2—161no—
792C2C73×#245611yescharacteristic
793C2C73×#310911yescharacteristic
794C2C73×#312211yescharacteristic
795C2C73×#326411yescharacteristic
796C2C73×#327411yescharacteristic
797C2C73×#339911yescharacteristic
798C2C73×#339911yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C4⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#459×C73C2semidirect
2. C2×#442×C73C2semidirect
3. C73×#2445C2semidirect
4. C73×#2366C2semidirect
5. C73×#2065C2semidirect
6. C73×#2011C2semidirect
7. C73×#2011C2semidirect
8. C73×#2011C2semidirect
9. C73×#1972C2semidirect
10. C73×#1926C2semidirect
11. C73×#1926C2semidirect
12. C73×#1917C2semidirect
13. C73×#1879C2semidirect
14. C73×#1879C2semidirect
15. C73×#1864C2semidirect
134. #102×C73D4semidirect
388. #26601C73direct (N × H)
400. C2×#459C2×C73semidirect
401. C2×#442C2×C73semidirect
402. #2445C2×C73semidirect
403. #2366C2×C73semidirect
404. #2065C2×C73semidirect
405. #2011C2×C73semidirect
406. #2011C2×C73semidirect
407. #2011C2×C73semidirect
408. #1972C2×C73semidirect
409. #1926C2×C73semidirect
410. #1926C2×C73semidirect
411. #1917C2×C73semidirect
412. #1879C2×C73semidirect
413. #1879C2×C73semidirect
414. #1864C2×C73semidirect
415. C73#26601direct (N × H)
534. #102D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C732
C2×#442×C732
C73×#24452
C73×#23662
C73×#20652
C73×#20112
C73×#19722
C73×#19262
C73×#19172
C73×#18792
C73×#18642
#2660173