Finite Group Databasebeta

← C73×#26547 #32935951

Subgroups — C73×#26547 #32935951

Order 18688.

956 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C73C211yesmaximal, characteristic, complemented
2C2×C4×D8×C73C211yesmaximal, characteristic, complemented
3C73×#2420C211yesmaximal, characteristic, complemented
4C73×#2361C211yesmaximal, characteristic, complemented
5C73×#2092C211yesmaximal, characteristic, complemented
6C73×#2054C211yesmaximal, characteristic, complemented
7C73×#2034C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic
9C73×#1949C211yesmaximal, characteristic, complemented
10C73×#1941C211yesmaximal, characteristic, complemented
11C73×#1926C211yesmaximal, characteristic, complemented
12C73×#1923C211yesmaximal, characteristic, complemented
13C73×#1864C211yesmaximal, characteristic, complemented
14C73×#1862C211yesmaximal, characteristic, complemented
15C73×#1852C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C2×#121×C73C2211yescharacteristic
18C2×#121×C73C2211yescharacteristic
19C2×C4×D4×C73—21no—
20C2×C4×D4×C73C2211yescharacteristic
21C2×C4×D4×C73C2211yescharacteristic
22C22×C4⋊C4×C73C2211yescharacteristic
23#481×C73—24no—
24C4×D8×C73—24no—
25C2×#107×C73C2211yescharacteristic
26C2×#107×C73C2211yescharacteristic
27C2×#106×C73C2211yescharacteristic
28C2×#106×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×C22⋊C8×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×C4×C8×C73C2211yescharacteristic
40#397×C73—21no—
41#394×C73—21no—
42#390×C73C2211yescharacteristic
43#390×C73C2211yescharacteristic
44#389×C73C2211yescharacteristic
45#389×C73C2211yescharacteristic
46#388×C73—21no—
47#386×C73—21no—
48#386×C73—21no—
49#385×C73—21no—
50#382×C73C2211yescharacteristic
51#381×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×C73C2311yescharacteristic
64C22×D4×C73C2311yescharacteristic
65C23×C4×C73—21no—
66C23×C4×C73—21no—
67C23×C4×C73—21no—
68C23×C4×C73C2311yescharacteristic
69C2×D8×C73—22no—
70C2×D8×C73—22no—
71C2×D8×C73—22no—
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76#121×C73—22no—
77#121×C73—22no—
78#121×C73—22no—
79#121×C73—41no—
80C4×D4×C73—22no—
81C4×D4×C73—22no—
82C4×D4×C73—41no—
83C4×D4×C73—41no—
84C4×D4×C73—44no—
85C2×C4⋊C4×C73—22no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73—41no—
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73C2311yescharacteristic
92C2×C4⋊C4×C73C2311yescharacteristic
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73C2311yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C22⋊C4×C73—21no—
97C2×C22⋊C4×C73—21no—
98C2×C22⋊C4×C73—21no—
99C2×C22⋊C4×C73—21no—
100C2×C22⋊C4×C73—21no—
101C2×C22⋊C4×C73—21no—
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73D411yescharacteristic
106C2×C22⋊C4×C73D411yescharacteristic
107C2×C42×C73—21no—
108C2×C42×C73C2311yescharacteristic
109C2×C42×C73C2311yescharacteristic
110#107×C73—22no—
111#107×C73—41no—
112#106×C73—22no—
113#106×C73—22no—
114#106×C73—22no—
115C4⋊C8×C73—22no—
116#102×C73—22no—
117#102×C73—22no—
118#102×C73—22no—
119#102×C73—22no—
120#102×C73—41no—
121#102×C73D414yescomplemented
122C22⋊C8×C73—22no—
123C22⋊C8×C73—22no—
124C4×C8×C73—22no—
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73D411yescharacteristic
132#95×C73D411yescharacteristic
133C24×C73—21no—
134C24×C73—21no—
135C24×C73C2×D411yescharacteristic
136C2×D4×C73—24no—
137C2×D4×C73—21no—
138C2×D4×C73—21no—
139C2×D4×C73—21no—
140C2×D4×C73—21no—
141C2×D4×C73—21no—
142C2×D4×C73—21no—
143C2×D4×C73—21no—
144C2×D4×C73—21no—
145C2×D4×C73—21no—
146C2×D4×C73—21no—
147C2×D4×C73—42no—
148C2×D4×C73—42no—
149C2×D4×C73—42no—
150C2×D4×C73—42no—
151C2×D4×C73—81no—
152C2×D4×C73C2×D412yes—
153C2×D4×C73#4112yes—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—42no—
167C22×C4×C73—42no—
168C22×C4×C73—42no—
169C22×C4×C73—42no—
170C22×C4×C73—42no—
171C22×C4×C73—42no—
172C22×C4×C73—81no—
173C22×C4×C73—81no—
174C22×C4×C73—81no—
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2411yescharacteristic
181D8×C73—28no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73C2×D412yes—
193C2×C8×C73#4112yes—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—42no—
205C4⋊C4×C73—42no—
206C4⋊C4×C73—81no—
207C4⋊C4×C73C2×D412yes—
208C4⋊C4×C73#4112yes—
209C22⋊C4×C73—24no—
210C22⋊C4×C73—22no—
211C22⋊C4×C73—22no—
212C22⋊C4×C73—42no—
213C22⋊C4×C73—42no—
214C22⋊C4×C73—42no—
215C22⋊C4×C73—42no—
216C22⋊C4×C73—81no—
217C22⋊C4×C73—81no—
218C22⋊C4×C73—81no—
219C22⋊C4×C73—81no—
220C42×C73—21no—
221C42×C73—21no—
222C42×C73—21no—
223C42×C73—21no—
224C42×C73—42no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—22no—
232C23×C73—22no—
233C23×C73—41no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73—41no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73—41no—
241C23×C73—41no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73—41no—
245C23×C73#13512yes—
246C23×C73C22×D411yescharacteristic
247D4×C73—22no—
248D4×C73—22no—
249D4×C73—22no—
250D4×C73—22no—
251D4×C73—48no—
252D4×C73—41no—
253D4×C73—41no—
254D4×C73—41no—
255D4×C73—41no—
256D4×C73—84no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—22no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—22no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—84no—
294C2×C4×C73—84no—
295C2×C4×C73—84no—
296C2×C4×C73AGL(1,ℤ/8)12yes—
297C2×C4×C73C22×D411yescharacteristic
298C2×C4×C73C2×#4111yescharacteristic
299C2×C4×C73C2×#4111yescharacteristic
300C2×C4×C73C2×#4111yescharacteristic
301C2×C4×C73H(5,𝔽2)11yescharacteristic
302C2×C4×C732−1+411yescharacteristic
303C8×C73—22no—
304C8×C73—22no—
305C8×C73—41no—
306C8×C73—41no—
307C22×C73—22no—
308C22×C73—22no—
309C22×C73—22no—
310C22×C73—41no—
311C22×C73—41no—
312C22×C73—41no—
313C22×C73—41no—
314C22×C73—42no—
315C22×C73—42no—
316C22×C73—42no—
317C22×C73—42no—
318C22×C73—42no—
319C22×C73—42no—
320C22×C73—81no—
321C22×C73—81no—
322C22×C73—81no—
323C22×C73—81no—
324C22×C73—81no—
325C22×C73—81no—
326C22×C73—81no—
327C22×C73—81no—
328C22×C73#52511yescharacteristic
329C22×C73D4211yescharacteristic
330C22×C73#54711yescharacteristic
331C22×C73C2×#13511yescharacteristic
332C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C73#57611yescharacteristic
334C22×C73#57711yescharacteristic
335C4×C73—22no—
336C4×C73—41no—
337C4×C73—41no—
338C4×C73—42no—
339C4×C73—41no—
340C4×C73—42no—
341C4×C73—41no—
342C4×C73—81no—
343C4×C73—81no—
344C4×C73—81no—
345C4×C73—81no—
346C4×C73#52511yescharacteristic
347C4×C73#53911yescharacteristic
348C4×C73#54711yescharacteristic
349C4×C73#55911yescharacteristic
350#26547C7311yesmaximal, characteristic, direct product factor, Sylow
351C2×C73—42no—
352C2×C73—82no—
353C2×C73—82no—
354C2×C73#245511yescharacteristic
355C2×C73#310511yescharacteristic
356C2×C73#311911yescharacteristic
357C2×C73#326411yescharacteristic
358C2×C73#328211yescharacteristic
359C2×C73#333911yescharacteristic
360C2×C73#335411yescharacteristic
361C2×#481C2×C7311yescharacteristic, complemented
362C2×C4×D8C2×C7311yescharacteristic, complemented
363#2420C2×C7311yescharacteristic, complemented
364#2361C2×C7311yescharacteristic, complemented
365#2092C2×C7311yescharacteristic, complemented
366#2054C2×C7311yescharacteristic, complemented
367#2034C2×C7311yescharacteristic, complemented
368#1999C2×C7311yescharacteristic
369#1949C2×C7311yescharacteristic, complemented
370#1941C2×C7311yescharacteristic, complemented
371#1926C2×C7311yescharacteristic, complemented
372#1923C2×C7311yescharacteristic, complemented
373#1864C2×C7311yescharacteristic, complemented
374#1862C2×C7311yescharacteristic, complemented
375#1852C2×C7311yescharacteristic, complemented
376C73#2654711yescharacteristic, direct product factor, Sylow
377C22×D8C22×C7311yescharacteristic
378C2×#121C22×C7311yescharacteristic
379C2×#121C22×C7311yescharacteristic
380C2×C4×D4—21no—
381C2×C4×D4C22×C7311yescharacteristic
382C2×C4×D4C22×C7311yescharacteristic
383C22×C4⋊C4C22×C7311yescharacteristic
384#481—24no—
385C4×D8—24no—
386C2×#107C22×C7311yescharacteristic
387C2×#107C22×C7311yescharacteristic
388C2×#106C22×C7311yescharacteristic
389C2×#106C22×C7311yescharacteristic
390C2×#106C22×C7311yescharacteristic
391C2×C4⋊C8C22×C7311yescharacteristic
392C2×#102C22×C7311yescharacteristic
393C2×#102C22×C7311yescharacteristic
394C2×#102C22×C7311yescharacteristic
395C2×#102C22×C7311yescharacteristic
396C2×#102C22×C7311yescharacteristic
397C2×#102C22×C7311yescharacteristic
398C2×C22⋊C8C22×C7311yescharacteristic
399C2×C22⋊C8C22×C7311yescharacteristic
400C2×C4×C8C22×C7311yescharacteristic
401#397—21no—
402#394—21no—
403#390C22×C7311yescharacteristic
404#390C22×C7311yescharacteristic
405#389C22×C7311yescharacteristic
406#389C22×C7311yescharacteristic
407#388—21no—
408#386—21no—
409#386—21no—
410#385—21no—
411#382C22×C7311yescharacteristic
412#381—21no—
413#380C22×C7311yescharacteristic
414C4×C4⋊C4C22×C7311yescharacteristic
415C4×C22⋊C4C22×C7311yescharacteristic
416#340C22×C7311yescharacteristic
417#340C22×C7311yescharacteristic
418#340C22×C7311yescharacteristic
419#340C22×C7311yescharacteristic
420#336C22×C7311yescharacteristic
421#336C22×C7311yescharacteristic
422C22×D4—21no—
423C22×D4—21no—
424C22×D4C23×C7311yescharacteristic
425C22×D4C23×C7311yescharacteristic
426C23×C4—21no—
427C23×C4—21no—
428C23×C4—21no—
429C23×C4C23×C7311yescharacteristic
430C2×D8—22no—
431C2×D8—22no—
432C2×D8—22no—
433C22×C8C23×C7311yescharacteristic
434C22×C8C23×C7311yescharacteristic
435C22×C8C23×C7311yescharacteristic
436C22×C8C23×C7311yescharacteristic
437#121—22no—
438#121—22no—
439#121—22no—
440#121—41no—
441C4×D4—22no—
442C4×D4—22no—
443C4×D4—41no—
444C4×D4—41no—
445C4×D4—44no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—41no—
451C2×C4⋊C4C23×C7311yescharacteristic
452C2×C4⋊C4C23×C7311yescharacteristic
453C2×C4⋊C4C23×C7311yescharacteristic
454C2×C4⋊C4C23×C7311yescharacteristic
455C2×C4⋊C4C23×C7311yescharacteristic
456C2×C4⋊C4C23×C7311yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4D4×C7311yescharacteristic
467C2×C22⋊C4D4×C7311yescharacteristic
468C2×C42—21no—
469C2×C42C23×C7311yescharacteristic
470C2×C42C23×C7311yescharacteristic
471#107—22no—
472#107—41no—
473#106—22no—
474#106—22no—
475#106—22no—
476C4⋊C8—22no—
477#102—22no—
478#102—22no—
479#102—22no—
480#102—22no—
481#102—41no—
482#102D4×C7314yescomplemented
483C22⋊C8—22no—
484C22⋊C8—22no—
485C4×C8—22no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95D4×C7311yescharacteristic
493#95D4×C7311yescharacteristic
494C24—21no—
495C24—21no—
496C24C2×D4×C7311yescharacteristic
497C2×D4—24no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C2×D4C2×D4×C7312yes—
514C2×D4#41×C7312yes—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—81no—
534C22×C4—81no—
535C22×C4—81no—
536C22×C4C2×D4×C7311yescharacteristic
537C22×C4C2×D4×C7311yescharacteristic
538C22×C4C2×D4×C7311yescharacteristic
539C22×C4C2×D4×C7311yescharacteristic
540C22×C4C2×D4×C7311yescharacteristic
541C22×C4C24×C7311yescharacteristic
542D8—28no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8C2×D4×C7312yes—
554C2×C8#41×C7312yes—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—81no—
568C4⋊C4C2×D4×C7312yes—
569C4⋊C4#41×C7312yes—
570C22⋊C4—24no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—81no—
578C22⋊C4—81no—
579C22⋊C4—81no—
580C22⋊C4—81no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—42no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—22no—
593C23—22no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23#135×C7312yes—
607C23C22×D4×C7311yescharacteristic
608D4—22no—
609D4—22no—
610D4—22no—
611D4—22no—
612D4—48no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—84no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—84no—
655C2×C4—84no—
656C2×C4—84no—
657C2×C4AGL(1,ℤ/8)×C7312yes—
658C2×C4C22×D4×C7311yescharacteristic
659C2×C4C2×#41×C7311yescharacteristic
660C2×C4C2×#41×C7311yescharacteristic
661C2×C4C2×#41×C7311yescharacteristic
662C2×C4H(5,𝔽2)×C7311yescharacteristic
663C2×C42−1+4×C7311yescharacteristic
664C8—22no—
665C8—22no—
666C8—41no—
667C8—41no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22#525×C7311yescharacteristic
690C22D42×C7311yescharacteristic
691C22#547×C7311yescharacteristic
692C22C2×#135×C7311yescharacteristic
693C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
694C22#576×C7311yescharacteristic
695C22#577×C7311yescharacteristic
696C4—22no—
697C4—41no—
698C4—42no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—42no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4#525×C7311yescharacteristic
708C4#539×C7311yescharacteristic
709C4#547×C7311yescharacteristic
710C4#559×C7311yescharacteristic
711C2—42no—
712C2—82no—
713C2—82no—
714C2C73×#245511yescharacteristic
715C2C73×#310511yescharacteristic
716C2C73×#311911yescharacteristic
717C2C73×#326411yescharacteristic
718C2C73×#328211yescharacteristic
719C2C73×#333911yescharacteristic
720C2C73×#335411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#1999C2
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×#481×C73C2semidirect
2. C2×C4×D8×C73C2semidirect
3. C73×#2420C2semidirect
4. C73×#2361C2semidirect
5. C73×#2092C2semidirect
6. C73×#2054C2semidirect
7. C73×#2034C2semidirect
9. C73×#1949C2semidirect
10. C73×#1941C2semidirect
11. C73×#1926C2semidirect
12. C73×#1923C2semidirect
13. C73×#1864C2semidirect
14. C73×#1862C2semidirect
15. C73×#1852C2semidirect
121. #102×C73D4semidirect
350. #26547C73direct (N × H)
361. C2×#481C2×C73semidirect
362. C2×C4×D8C2×C73semidirect
363. #2420C2×C73semidirect
364. #2361C2×C73semidirect
365. #2092C2×C73semidirect
366. #2054C2×C73semidirect
367. #2034C2×C73semidirect
369. #1949C2×C73semidirect
370. #1941C2×C73semidirect
371. #1926C2×C73semidirect
372. #1923C2×C73semidirect
373. #1864C2×C73semidirect
374. #1862C2×C73semidirect
375. #1852C2×C73semidirect
376. C73#26547direct (N × H)
482. #102D4×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×C4×D8×C732
C73×#24202
C73×#23612
C73×#20922
C73×#20542
C73×#20342
C73×#19992
C73×#19492
C73×#19412
C73×#19262
C73×#19232
C73×#18642
C73×#18622
C73×#18522
#2654773