Finite Group Databasebeta

← C73×#25221 #32934625

Subgroups — C73×#25221 #32934625

Order 18688.

962 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C73C211yesmaximal, characteristic, complemented
2C2×#469×C73C211yesmaximal, characteristic
3C73×#2501C211yesmaximal, characteristic, complemented
4C73×#2363C211yesmaximal, characteristic, complemented
5C73×#2084C211yesmaximal, characteristic, complemented
6C73×#2071C211yesmaximal, characteristic, complemented
7C73×#2065C211yesmaximal, characteristic, complemented
8C73×#2054C211yesmaximal, characteristic, complemented
9C73×#1948C211yesmaximal, characteristic, complemented
10C73×#1926C211yesmaximal, characteristic, complemented
11C73×#1879C211yesmaximal, characteristic, complemented
12C73×#1875C211yesmaximal, characteristic, complemented
13C73×#1851C211yesmaximal, characteristic, complemented
14C73×#1802C211yesmaximal, characteristic, complemented
15C73×#1736C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18C2×#123×C73—21no—
19C2×#123×C73—21no—
20C2×#121×C73C2211yescharacteristic
21C2×#121×C73C2211yescharacteristic
22C2×C4×D4×C73C2211yescharacteristic
23C2×#117×C73C2211yescharacteristic
24C22×C4⋊C4×C73C2211yescharacteristic
25#481×C73—24no—
26#469×C73—24no—
27C2×#106×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29C2×#106×C73C2211yescharacteristic
30C2×C4⋊C8×C73C2211yescharacteristic
31C2×C4⋊C8×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39#399×C73—21no—
40#399×C73—21no—
41#390×C73—21no—
42#390×C73C2211yescharacteristic
43#390×C73C2211yescharacteristic
44#390×C73C2211yescharacteristic
45#389×C73C2211yescharacteristic
46#388×C73—21no—
47#386×C73—21no—
48#384×C73C2211yescharacteristic
49#384×C73C2211yescharacteristic
50C4×C4⋊C4×C73C2211yescharacteristic
51C4×C22⋊C4×C73—21no—
52C4×C22⋊C4×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×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×C73C2311yescharacteristic
68C2×D8×C73—22no—
69C2×D8×C73—22no—
70C2×D8×C73—41no—
71C2×M16×C73—22no—
72C2×M16×C73—22no—
73C2×M16×C73—41no—
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77C22×C8×C73C2311yescharacteristic
78#123×C73—44no—
79#123×C73—44no—
80#121×C73—22no—
81#121×C73—22no—
82#121×C73—22no—
83#121×C73D414yes—
84C4×D4×C73—22no—
85C4×D4×C73—41no—
86#117×C73—22no—
87#117×C73—41no—
88C2×C4⋊C4×C73—22no—
89C2×C4⋊C4×C73—22no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
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×C22⋊C4×C73D411yescharacteristic
113C2×C22⋊C4×C73D411yescharacteristic
114C2×C42×C73—21no—
115C2×C42×C73—21no—
116C2×C42×C73C2311yescharacteristic
117C2×C42×C73C2311yescharacteristic
118#106×C73—22no—
119#106×C73—22no—
120#106×C73—22no—
121C4⋊C8×C73—22no—
122C4⋊C8×C73—41no—
123#102×C73—22no—
124#102×C73—22no—
125#102×C73—22no—
126#102×C73—22no—
127#102×C73—22no—
128#102×C73—41no—
129C22⋊C8×C73—22no—
130#95×C73—21no—
131#95×C73—21no—
132#95×C73D411yescharacteristic
133#95×C73D411yescharacteristic
134C24×C73—21no—
135C24×C73—21no—
136C24×C73C2×D411yescharacteristic
137C2×D4×C73—24no—
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—21no—
148C2×D4×C73—21no—
149C2×D4×C73—42no—
150C2×D4×C73—42no—
151C2×D4×C73—42no—
152C2×D4×C73—81no—
153C2×D4×C73—81no—
154C2×D4×C73C2×D412yes—
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—42no—
166C22×C4×C73—42no—
167C22×C4×C73—42no—
168C22×C4×C73—42no—
169C22×C4×C73—42no—
170C22×C4×C73—81no—
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D412yes—
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73#4112yes—
178C22×C4×C73C2411yescharacteristic
179D8×C73—44no—
180M16×C73—44no—
181C2×C8×C73—21no—
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×C73#4112yes—
193C4⋊C4×C73—21no—
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—42no—
204C4⋊C4×C73—42no—
205C4⋊C4×C73—42no—
206C4⋊C4×C73—42no—
207C4⋊C4×C73—42no—
208C4⋊C4×C73—81no—
209C4⋊C4×C73C2×D412yes—
210C4⋊C4×C73#4112yes—
211C22⋊C4×C73—24no—
212C22⋊C4×C73—22no—
213C22⋊C4×C73—22no—
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—42no—
221C22⋊C4×C73—42no—
222C22⋊C4×C73—81no—
223C42×C73—21no—
224C42×C73—21no—
225C42×C73—21no—
226C42×C73—21no—
227C42×C73—42no—
228C42×C73—81no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—22no—
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#12112yes—
250C23×C73C22×D411yescharacteristic
251D4×C73—22no—
252D4×C73—22no—
253D4×C73—41no—
254D4×C73—41no—
255D4×C73—41no—
256D4×C73—41no—
257D4×C73—41no—
258D4×C73—41no—
259D4×C73—84no—
260D4×C73—84no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—21no—
273C2×C4×C73—22no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
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—41no—
294C2×C4×C73—41no—
295C2×C4×C73—84no—
296C2×C4×C73—84no—
297C2×C4×C73#12112yes—
298C2×C4×C73AGL(1,ℤ/8)12yes—
299C2×C4×C73AGL(1,ℤ/8)12yes—
300C2×C4×C73C22×D411yescharacteristic
301C2×C4×C73C2×#4111yescharacteristic
302C2×C4×C73C2×#4111yescharacteristic
303C2×C4×C73C2×#4111yescharacteristic
304C2×C4×C73H(5,𝔽2)11yescharacteristic
305C2×C4×C732−1+411yescharacteristic
306C8×C73—22no—
307C8×C73—41no—
308C8×C73—41no—
309C8×C73—41no—
310C22×C73—22no—
311C22×C73—22no—
312C22×C73—22no—
313C22×C73—41no—
314C22×C73—41no—
315C22×C73—41no—
316C22×C73—41no—
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—81no—
329C22×C73—81no—
330C22×C73—81no—
331C22×C73C2×#12111yescharacteristic
332C22×C73#54611yescharacteristic
333C22×C73#54711yescharacteristic
334C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
335C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C73#57711yescharacteristic
337C22×C73#57711yescharacteristic
338C4×C73—22no—
339C4×C73—22no—
340C4×C73—22no—
341C4×C73—41no—
342C4×C73—41no—
343C4×C73—42no—
344C4×C73—42no—
345C4×C73—81no—
346C4×C73—81no—
347C4×C73—81no—
348C4×C73—81no—
349C4×C73#52911yescharacteristic
350C4×C73#53911yescharacteristic
351C4×C73#54611yescharacteristic
352C4×C73#54711yescharacteristic
353#25221C7311yesmaximal, characteristic, direct product factor, Sylow
354C2×C73—42no—
355C2×C73—82no—
356C2×C73—161no—
357C2×C73#242511yescharacteristic
358C2×C73#303811yescharacteristic
359C2×C73#304211yescharacteristic
360C2×C73#330611yescharacteristic
361C2×C73#333211yescharacteristic
362C2×C73#334511yescharacteristic
363C2×C73#335411yescharacteristic
364C2×#481C2×C7311yescharacteristic, complemented
365C2×#469C2×C7311yescharacteristic
366#2501C2×C7311yescharacteristic, complemented
367#2363C2×C7311yescharacteristic, complemented
368#2084C2×C7311yescharacteristic, complemented
369#2071C2×C7311yescharacteristic, complemented
370#2065C2×C7311yescharacteristic, complemented
371#2054C2×C7311yescharacteristic, complemented
372#1948C2×C7311yescharacteristic, complemented
373#1926C2×C7311yescharacteristic, complemented
374#1879C2×C7311yescharacteristic, complemented
375#1875C2×C7311yescharacteristic, complemented
376#1851C2×C7311yescharacteristic, complemented
377#1802C2×C7311yescharacteristic, complemented
378#1736C2×C7311yescharacteristic, complemented
379C73#2522111yescharacteristic, direct product factor, Sylow
380C22×D8C22×C7311yescharacteristic
381C22×M16C22×C7311yescharacteristic
382C2×#123—21no—
383C2×#123—21no—
384C2×#121C22×C7311yescharacteristic
385C2×#121C22×C7311yescharacteristic
386C2×C4×D4C22×C7311yescharacteristic
387C2×#117C22×C7311yescharacteristic
388C22×C4⋊C4C22×C7311yescharacteristic
389#481—24no—
390#469—24no—
391C2×#106C22×C7311yescharacteristic
392C2×#106C22×C7311yescharacteristic
393C2×#106C22×C7311yescharacteristic
394C2×C4⋊C8C22×C7311yescharacteristic
395C2×C4⋊C8C22×C7311yescharacteristic
396C2×#102C22×C7311yescharacteristic
397C2×#102C22×C7311yescharacteristic
398C2×#102C22×C7311yescharacteristic
399C2×#102C22×C7311yescharacteristic
400C2×#102C22×C7311yescharacteristic
401C2×#102C22×C7311yescharacteristic
402C2×C22⋊C8C22×C7311yescharacteristic
403#399—21no—
404#399—21no—
405#390—21no—
406#390C22×C7311yescharacteristic
407#390C22×C7311yescharacteristic
408#390C22×C7311yescharacteristic
409#389C22×C7311yescharacteristic
410#388—21no—
411#386—21no—
412#384C22×C7311yescharacteristic
413#384C22×C7311yescharacteristic
414C4×C4⋊C4C22×C7311yescharacteristic
415C4×C22⋊C4—21no—
416C4×C22⋊C4C22×C7311yescharacteristic
417#340C22×C7311yescharacteristic
418#340C22×C7311yescharacteristic
419#340C22×C7311yescharacteristic
420#340C22×C7311yescharacteristic
421#340C22×C7311yescharacteristic
422#340C22×C7311yescharacteristic
423#336C22×C7311yescharacteristic
424#336C22×C7311yescharacteristic
425C22×D4—21no—
426C22×D4—21no—
427C22×D4C23×C7311yescharacteristic
428C22×D4C23×C7311yescharacteristic
429C23×C4—21no—
430C23×C4—21no—
431C23×C4C23×C7311yescharacteristic
432C2×D8—22no—
433C2×D8—22no—
434C2×D8—41no—
435C2×M16—22no—
436C2×M16—22no—
437C2×M16—41no—
438C22×C8C23×C7311yescharacteristic
439C22×C8C23×C7311yescharacteristic
440C22×C8C23×C7311yescharacteristic
441C22×C8C23×C7311yescharacteristic
442#123—44no—
443#123—44no—
444#121—22no—
445#121—22no—
446#121—22no—
447#121D4×C7314yes—
448C4×D4—22no—
449C4×D4—41no—
450#117—22no—
451#117—41no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4C23×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⋊C4D4×C7311yescharacteristic
477C2×C22⋊C4D4×C7311yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42C23×C7311yescharacteristic
481C2×C42C23×C7311yescharacteristic
482#106—22no—
483#106—22no—
484#106—22no—
485C4⋊C8—22no—
486C4⋊C8—41no—
487#102—22no—
488#102—22no—
489#102—22no—
490#102—22no—
491#102—22no—
492#102—41no—
493C22⋊C8—22no—
494#95—21no—
495#95—21no—
496#95D4×C7311yescharacteristic
497#95D4×C7311yescharacteristic
498C24—21no—
499C24—21no—
500C24C2×D4×C7311yescharacteristic
501C2×D4—24no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—81no—
517C2×D4—81no—
518C2×D4C2×D4×C7312yes—
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—21no—
528C22×C4—21no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—81no—
535C22×C4C2×D4×C7311yescharacteristic
536C22×C4C2×D4×C7311yescharacteristic
537C22×C4C2×D4×C7311yescharacteristic
538C22×C4C2×D4×C7312yes—
539C22×C4C2×D4×C7311yescharacteristic
540C22×C4C2×D4×C7311yescharacteristic
541C22×C4#41×C7312yes—
542C22×C4C24×C7311yescharacteristic
543D8—44no—
544M16—44no—
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×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8#41×C7312yes—
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—21no—
566C4⋊C4—21no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—81no—
573C4⋊C4C2×D4×C7312yes—
574C4⋊C4#41×C7312yes—
575C22⋊C4—24no—
576C22⋊C4—22no—
577C22⋊C4—22no—
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—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—42no—
592C42—81no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—22no—
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#121×C7312yes—
614C23C22×D4×C7311yescharacteristic
615D4—22no—
616D4—22no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—84no—
624D4—84no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
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—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—84no—
660C2×C4—84no—
661C2×C4#121×C7312yes—
662C2×C4AGL(1,ℤ/8)×C7312yes—
663C2×C4AGL(1,ℤ/8)×C7312yes—
664C2×C4C22×D4×C7311yescharacteristic
665C2×C4C2×#41×C7311yescharacteristic
666C2×C4C2×#41×C7311yescharacteristic
667C2×C4C2×#41×C7311yescharacteristic
668C2×C4H(5,𝔽2)×C7311yescharacteristic
669C2×C42−1+4×C7311yescharacteristic
670C8—22no—
671C8—41no—
672C8—41no—
673C8—41no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
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—
695C22C2×#121×C7311yescharacteristic
696C22#546×C7311yescharacteristic
697C22#547×C7311yescharacteristic
698C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
699C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
700C22#577×C7311yescharacteristic
701C22#577×C7311yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—42no—
706C4—42no—
707C4—41no—
708C4—41no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4—81no—
713C4#529×C7311yescharacteristic
714C4#539×C7311yescharacteristic
715C4#546×C7311yescharacteristic
716C4#547×C7311yescharacteristic
717C2—42no—
718C2—82no—
719C2—161no—
720C2C73×#242511yescharacteristic
721C2C73×#303811yescharacteristic
722C2C73×#304211yescharacteristic
723C2C73×#330611yescharacteristic
724C2C73×#333211yescharacteristic
725C2C73×#334511yescharacteristic
726C2C73×#335411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#469×C73C2
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
3. C73×#2501C2semidirect
4. C73×#2363C2semidirect
5. C73×#2084C2semidirect
6. C73×#2071C2semidirect
7. C73×#2065C2semidirect
8. C73×#2054C2semidirect
9. C73×#1948C2semidirect
10. C73×#1926C2semidirect
11. C73×#1879C2semidirect
12. C73×#1875C2semidirect
13. C73×#1851C2semidirect
14. C73×#1802C2semidirect
15. C73×#1736C2semidirect
353. #25221C73direct (N × H)
364. C2×#481C2×C73semidirect
366. #2501C2×C73semidirect
367. #2363C2×C73semidirect
368. #2084C2×C73semidirect
369. #2071C2×C73semidirect
370. #2065C2×C73semidirect
371. #2054C2×C73semidirect
372. #1948C2×C73semidirect
373. #1926C2×C73semidirect
374. #1879C2×C73semidirect
375. #1875C2×C73semidirect
376. #1851C2×C73semidirect
377. #1802C2×C73semidirect
378. #1736C2×C73semidirect
379. C73#25221direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#481×C732
C2×#469×C732
C73×#25012
C73×#23632
C73×#20842
C73×#20712
C73×#20652
C73×#20542
C73×#19482
C73×#19262
C73×#18792
C73×#18752
C73×#18512
C73×#18022
C73×#17362
#2522173