Finite Group Databasebeta

← C73×#26834 #32936238

Subgroups — C73×#26834 #32936238

Order 18688.

960 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#486×C73C211yesmaximal, characteristic, complemented
2C2×#442×C73C211yesmaximal, characteristic, complemented
3C73×#2452C211yesmaximal, characteristic, complemented
4C73×#2445C211yesmaximal, characteristic, complemented
5C73×#2065C211yesmaximal, characteristic, complemented
6C73×#2058C211yesmaximal, characteristic, complemented
7C73×#2054C211yesmaximal, characteristic, complemented
8C73×#2011C211yesmaximal, characteristic
9C73×#1972C211yesmaximal, characteristic, complemented
10C73×#1936C211yesmaximal, characteristic, complemented
11C73×#1936C211yesmaximal, characteristic, complemented
12C73×#1934C211yesmaximal, characteristic, complemented
13C73×#1879C211yesmaximal, characteristic, complemented
14C73×#1864C211yesmaximal, characteristic, complemented
15C73×#1771C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C2×C4⋊Q8×C73C2211yescharacteristic
19C2×#127×C73C2211yescharacteristic
20C2×#123×C73—21no—
21C2×C22⋊Q8×C73—21no—
22C2×C4×D4×C73C2211yescharacteristic
23C2×C4×D4×C73C2211yescharacteristic
24#486×C73—24no—
25#442×C73—24no—
26C2×#106×C73C2211yescharacteristic
27C2×#106×C73C2211yescharacteristic
28C2×C4⋊C8×C73C2211yescharacteristic
29C2×#102×C73C2211yescharacteristic
30C2×#102×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#97×C73C2211yescharacteristic
38C2×#97×C73C2211yescharacteristic
39C2×C4×C8×C73C2211yescharacteristic
40#396×C73—21no—
41#394×C73—21no—
42#394×C73—21no—
43#393×C73—21no—
44#390×C73C2211yescharacteristic
45#390×C73C2211yescharacteristic
46#390×C73C2211yescharacteristic
47#390×C73C2211yescharacteristic
48#390×C73C2211yescharacteristic
49#389×C73C2211yescharacteristic
50#389×C73C2211yescharacteristic
51#389×C73C2211yescharacteristic
52#386×C73—21no—
53#385×C73—21no—
54C4×C4⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73—21no—
62C22×D4×C73—21no—
63C22×D4×C73—21no—
64C22×D4×C73C2311yescharacteristic
65C22×D4×C73C2311yescharacteristic
66C22×D4×C73C2311yescharacteristic
67C23×C4×C73—21no—
68C23×C4×C73—21no—
69C2×D8×C73—22no—
70C2×D8×C73—22no—
71C2×D8×C73—22no—
72C2×D8×C73—22no—
73C2×D8×C73—22no—
74C2×D8×C73—41no—
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77C22×C8×C73C2311yescharacteristic
78C22×C8×C73C2311yescharacteristic
79C4⋊Q8×C73—22no—
80C4⋊Q8×C73—41no—
81#127×C73—22no—
82#127×C73—41no—
83#123×C73—44no—
84C22⋊Q8×C73—44no—
85C4×D4×C73—22no—
86C4×D4×C73—22no—
87C4×D4×C73—41no—
88C4×D4×C73—41no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73D411yescharacteristic
94C2×C4⋊C4×C73D411yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
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×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×C42×C73C2311yescharacteristic
113C2×C42×C73C2311yescharacteristic
114C2×C42×C73C2311yescharacteristic
115#106×C73—22no—
116#106×C73—41no—
117C4⋊C8×C73—22no—
118#102×C73—22no—
119#102×C73—22no—
120#102×C73—22no—
121#102×C73—22no—
122#102×C73—22no—
123#102×C73—22no—
124#102×C73—22no—
125#102×C73D414yes—
126#97×C73—22no—
127#97×C73—22no—
128C4×C8×C73—22no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132#95×C73D411yescharacteristic
133#95×C73D411yescharacteristic
134C24×C73—21no—
135C24×C73—21no—
136C24×C73—21no—
137C2×Q8×C73—42no—
138C2×Q8×C73—42no—
139C2×Q8×C73—81no—
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—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—42no—
157C2×D4×C73—42no—
158C2×D4×C73—42no—
159C2×D4×C73—42no—
160C2×D4×C73—81no—
161C2×D4×C73—81no—
162C2×D4×C73C2×D412yes—
163C2×D4×C73#4112yes—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—42no—
170C22×C4×C73—42no—
171C22×C4×C73—42no—
172C22×C4×C73—42no—
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×C73C2×D411yescharacteristic
181C22×C4×C73C2411yescharacteristic
182D8×C73—28no—
183D8×C73—44no—
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×C73—21no—
193C2×C8×C73C2×D412yes—
194C2×C8×C73#4112yes—
195C2×C8×C73#4112yes—
196C4⋊C4×C73—22no—
197C4⋊C4×C73—22no—
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—21no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73—42no—
208C4⋊C4×C73—42no—
209C4⋊C4×C73—42no—
210C4⋊C4×C73—42no—
211C4⋊C4×C73C2×D412yes—
212C22⋊C4×C73—42no—
213C22⋊C4×C73—42no—
214C22⋊C4×C73—42no—
215C22⋊C4×C73—42no—
216C22⋊C4×C73—42no—
217C22⋊C4×C73—42no—
218C22⋊C4×C73—42no—
219C22⋊C4×C73—42no—
220C22⋊C4×C73—81no—
221C22⋊C4×C73—81no—
222C22⋊C4×C73—81no—
223C22⋊C4×C73—81no—
224C42×C73—21no—
225C42×C73—21no—
226C42×C73—21no—
227C42×C73—21no—
228C42×C73—21no—
229C42×C73—21no—
230C23×C73—22no—
231C23×C73—22no—
232C23×C73—41no—
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—41no—
246C23×C73—41no—
247C23×C73—41no—
248C23×C73—41no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73C22×D411yescharacteristic
252Q8×C73—84no—
253D4×C73—22no—
254D4×C73—22no—
255D4×C73—22no—
256D4×C73—22no—
257D4×C73—41no—
258D4×C73—41no—
259D4×C73—41no—
260D4×C73—41no—
261D4×C73—41no—
262D4×C73—41no—
263D4×C73—41no—
264D4×C73—41no—
265D4×C73—84no—
266D4×C73—84no—
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—21no—
274C2×C4×C73—21no—
275C2×C4×C73—22no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
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—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—84no—
299C2×C4×C73—84no—
300C2×C4×C73AGL(1,ℤ/8)12yes—
301C2×C4×C73AGL(1,ℤ/8)12yes—
302C2×C4×C73C22×D411yescharacteristic
303C2×C4×C73C2×#4111yescharacteristic
304C2×C4×C73C2×#4111yescharacteristic
305C2×C4×C73C2×#4111yescharacteristic
306C2×C4×C73H(5,𝔽2)11yescharacteristic
307C2×C4×C732−1+411yescharacteristic
308C8×C73—22no—
309C8×C73—22no—
310C8×C73—22no—
311C8×C73—41no—
312C22×C73—42no—
313C22×C73—42no—
314C22×C73—42no—
315C22×C73—42no—
316C22×C73—42no—
317C22×C73—42no—
318C22×C73—81no—
319C22×C73—81no—
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—81no—
329C22×C73—81no—
330C22×C73—81no—
331C22×C73—81no—
332C22×C73—81no—
333C22×C73#53211yescharacteristic
334C22×C73D4211yescharacteristic
335C22×C73#54811yescharacteristic
336C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
337C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C73#57611yescharacteristic
339C22×C73#57711yescharacteristic
340C4×C73—22no—
341C4×C73—22no—
342C4×C73—41no—
343C4×C73—41no—
344C4×C73—41no—
345C4×C73—42no—
346C4×C73—41no—
347C4×C73—81no—
348C4×C73—81no—
349C4×C73—81no—
350C4×C73—81no—
351C4×C73#52511yescharacteristic
352C4×C73#54211yescharacteristic
353C4×C73#54711yescharacteristic
354C4×C73#55111yescharacteristic
355#26834C7311yesmaximal, characteristic, direct product factor, Sylow
356C2×C73—82no—
357C2×C73—82no—
358C2×C73—161no—
359C2×C73#246111yescharacteristic
360C2×C73#317911yescharacteristic
361C2×C73#318411yescharacteristic
362C2×C73#326411yescharacteristic
363C2×C73#326511yescharacteristic
364C2×C73#336611yescharacteristic
365C2×C73#337311yescharacteristic
366C2×#486C2×C7311yescharacteristic, complemented
367C2×#442C2×C7311yescharacteristic, complemented
368#2452C2×C7311yescharacteristic, complemented
369#2445C2×C7311yescharacteristic, complemented
370#2065C2×C7311yescharacteristic, complemented
371#2058C2×C7311yescharacteristic, complemented
372#2054C2×C7311yescharacteristic, complemented
373#2011C2×C7311yescharacteristic
374#1972C2×C7311yescharacteristic, complemented
375#1936C2×C7311yescharacteristic, complemented
376#1936C2×C7311yescharacteristic, complemented
377#1934C2×C7311yescharacteristic, complemented
378#1879C2×C7311yescharacteristic, complemented
379#1864C2×C7311yescharacteristic, complemented
380#1771C2×C7311yescharacteristic, complemented
381C73#2683411yescharacteristic, direct product factor, Sylow
382C22×D8C22×C7311yescharacteristic
383C22×D8C22×C7311yescharacteristic
384C2×C4⋊Q8C22×C7311yescharacteristic
385C2×#127C22×C7311yescharacteristic
386C2×#123—21no—
387C2×C22⋊Q8—21no—
388C2×C4×D4C22×C7311yescharacteristic
389C2×C4×D4C22×C7311yescharacteristic
390#486—24no—
391#442—24no—
392C2×#106C22×C7311yescharacteristic
393C2×#106C22×C7311yescharacteristic
394C2×C4⋊C8C22×C7311yescharacteristic
395C2×#102C22×C7311yescharacteristic
396C2×#102C22×C7311yescharacteristic
397C2×#102C22×C7311yescharacteristic
398C2×#102C22×C7311yescharacteristic
399C2×#102C22×C7311yescharacteristic
400C2×#102C22×C7311yescharacteristic
401C2×#102C22×C7311yescharacteristic
402C2×#102C22×C7311yescharacteristic
403C2×#97C22×C7311yescharacteristic
404C2×#97C22×C7311yescharacteristic
405C2×C4×C8C22×C7311yescharacteristic
406#396—21no—
407#394—21no—
408#394—21no—
409#393—21no—
410#390C22×C7311yescharacteristic
411#390C22×C7311yescharacteristic
412#390C22×C7311yescharacteristic
413#390C22×C7311yescharacteristic
414#390C22×C7311yescharacteristic
415#389C22×C7311yescharacteristic
416#389C22×C7311yescharacteristic
417#389C22×C7311yescharacteristic
418#386—21no—
419#385—21no—
420C4×C4⋊C4C22×C7311yescharacteristic
421#340C22×C7311yescharacteristic
422#340C22×C7311yescharacteristic
423#340C22×C7311yescharacteristic
424#340C22×C7311yescharacteristic
425#336C22×C7311yescharacteristic
426#336C22×C7311yescharacteristic
427C22×Q8—21no—
428C22×D4—21no—
429C22×D4—21no—
430C22×D4C23×C7311yescharacteristic
431C22×D4C23×C7311yescharacteristic
432C22×D4C23×C7311yescharacteristic
433C23×C4—21no—
434C23×C4—21no—
435C2×D8—22no—
436C2×D8—22no—
437C2×D8—22no—
438C2×D8—22no—
439C2×D8—22no—
440C2×D8—41no—
441C22×C8C23×C7311yescharacteristic
442C22×C8C23×C7311yescharacteristic
443C22×C8C23×C7311yescharacteristic
444C22×C8C23×C7311yescharacteristic
445C4⋊Q8—22no—
446C4⋊Q8—41no—
447#127—22no—
448#127—41no—
449#123—44no—
450C22⋊Q8—44no—
451C4×D4—22no—
452C4×D4—22no—
453C4×D4—41no—
454C4×D4—41no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4D4×C7311yescharacteristic
460C2×C4⋊C4D4×C7311yescharacteristic
461C2×C4⋊C4C23×C7311yescharacteristic
462C2×C4⋊C4C23×C7311yescharacteristic
463C2×C4⋊C4C23×C7311yescharacteristic
464C2×C4⋊C4C23×C7311yescharacteristic
465C2×C4⋊C4C23×C7311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C42C23×C7311yescharacteristic
479C2×C42C23×C7311yescharacteristic
480C2×C42C23×C7311yescharacteristic
481#106—22no—
482#106—41no—
483C4⋊C8—22no—
484#102—22no—
485#102—22no—
486#102—22no—
487#102—22no—
488#102—22no—
489#102—22no—
490#102—22no—
491#102D4×C7314yes—
492#97—22no—
493#97—22no—
494C4×C8—22no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95D4×C7311yescharacteristic
499#95D4×C7311yescharacteristic
500C24—21no—
501C24—21no—
502C24—21no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—81no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4—81no—
527C2×D4—81no—
528C2×D4C2×D4×C7312yes—
529C2×D4#41×C7312yes—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—81no—
540C22×C4—81no—
541C22×C4C2×D4×C7311yescharacteristic
542C22×C4C2×D4×C7311yescharacteristic
543C22×C4C2×D4×C7311yescharacteristic
544C22×C4C2×D4×C7311yescharacteristic
545C22×C4C2×D4×C7311yescharacteristic
546C22×C4C2×D4×C7311yescharacteristic
547C22×C4C24×C7311yescharacteristic
548D8—28no—
549D8—44no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8C2×D4×C7312yes—
560C2×C8#41×C7312yes—
561C2×C8#41×C7312yes—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4C2×D4×C7312yes—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—81no—
587C22⋊C4—81no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—21no—
595C42—21no—
596C23—22no—
597C23—22no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23C22×D4×C7311yescharacteristic
618Q8—84no—
619D4—22no—
620D4—22no—
621D4—22no—
622D4—22no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4—41no—
629D4—41no—
630D4—41no—
631D4—84no—
632D4—84no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—84no—
665C2×C4—84no—
666C2×C4AGL(1,ℤ/8)×C7312yes—
667C2×C4AGL(1,ℤ/8)×C7312yes—
668C2×C4C22×D4×C7311yescharacteristic
669C2×C4C2×#41×C7311yescharacteristic
670C2×C4C2×#41×C7311yescharacteristic
671C2×C4C2×#41×C7311yescharacteristic
672C2×C4H(5,𝔽2)×C7311yescharacteristic
673C2×C42−1+4×C7311yescharacteristic
674C8—22no—
675C8—22no—
676C8—22no—
677C8—41no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—42no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22#532×C7311yescharacteristic
700C22D42×C7311yescharacteristic
701C22#548×C7311yescharacteristic
702C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
703C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
704C22#576×C7311yescharacteristic
705C22#577×C7311yescharacteristic
706C4—22no—
707C4—22no—
708C4—41no—
709C4—42no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—81no—
714C4—81no—
715C4—81no—
716C4—81no—
717C4#525×C7311yescharacteristic
718C4#542×C7311yescharacteristic
719C4#547×C7311yescharacteristic
720C4#551×C7311yescharacteristic
721C2—82no—
722C2—82no—
723C2—161no—
724C2C73×#246111yescharacteristic
725C2C73×#317911yescharacteristic
726C2C73×#318411yescharacteristic
727C2C73×#326411yescharacteristic
728C2C73×#326511yescharacteristic
729C2C73×#336611yescharacteristic
730C2C73×#337311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2011C2
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×#486×C73C2semidirect
2. C2×#442×C73C2semidirect
3. C73×#2452C2semidirect
4. C73×#2445C2semidirect
5. C73×#2065C2semidirect
6. C73×#2058C2semidirect
7. C73×#2054C2semidirect
9. C73×#1972C2semidirect
10. C73×#1936C2semidirect
11. C73×#1936C2semidirect
12. C73×#1934C2semidirect
13. C73×#1879C2semidirect
14. C73×#1864C2semidirect
15. C73×#1771C2semidirect
355. #26834C73direct (N × H)
366. C2×#486C2×C73semidirect
367. C2×#442C2×C73semidirect
368. #2452C2×C73semidirect
369. #2445C2×C73semidirect
370. #2065C2×C73semidirect
371. #2058C2×C73semidirect
372. #2054C2×C73semidirect
374. #1972C2×C73semidirect
375. #1936C2×C73semidirect
376. #1936C2×C73semidirect
377. #1934C2×C73semidirect
378. #1879C2×C73semidirect
379. #1864C2×C73semidirect
380. #1771C2×C73semidirect
381. C73#26834direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#486×C732
C2×#442×C732
C73×#24522
C73×#24452
C73×#20652
C73×#20582
C73×#20542
C73×#20112
C73×#19722
C73×#19362
C73×#19342
C73×#18792
C73×#18642
C73×#17712
#2683473