Finite Group Databasebeta

← C73×#25200 #32934604

Subgroups — C73×#25200 #32934604

Order 18688.

1024 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480×C73C211yesmaximal, characteristic, complemented
2C2×#466×C73C211yesmaximal, characteristic
3C73×#2501C211yesmaximal, characteristic, complemented
4C73×#2361C211yesmaximal, characteristic, complemented
5C73×#2083C211yesmaximal, characteristic, complemented
6C73×#2071C211yesmaximal, characteristic, complemented
7C73×#2067C211yesmaximal, characteristic, complemented
8C73×#2054C211yesmaximal, characteristic, complemented
9C73×#1947C211yesmaximal, characteristic, complemented
10C73×#1925C211yesmaximal, characteristic, complemented
11C73×#1879C211yesmaximal, characteristic, complemented
12C73×#1874C211yesmaximal, characteristic, complemented
13C73×#1850C211yesmaximal, characteristic, complemented
14C73×#1802C211yesmaximal, characteristic, complemented
15C2×#340×C73C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C23×C8×C73C2211yescharacteristic
18C2×#123×C73—21no—
19C2×#123×C73—21no—
20C2×#121×C73C2211yescharacteristic
21C2×#121×C73C2211yescharacteristic
22C2×C4×D4×C73—21no—
23C2×C4×D4×C73C2211yescharacteristic
24C22×C4⋊C4×C73C2211yescharacteristic
25C22×C4⋊C4×C73C2211yescharacteristic
26#480×C73—24no—
27#466×C73—24no—
28C2×#107×C73C2211yescharacteristic
29C2×#107×C73C2211yescharacteristic
30C2×#107×C73C2211yescharacteristic
31C2×C4⋊C8×C73C2211yescharacteristic
32C2×C4⋊C8×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×C22⋊C8×C73C2211yescharacteristic
40#399×C73—21no—
41#399×C73—21no—
42#390×C73C2211yescharacteristic
43#390×C73C2211yescharacteristic
44#390×C73C2211yescharacteristic
45#389×C73C2211yescharacteristic
46#388×C73—21no—
47#386×C73—21no—
48#385×C73—21no—
49#384×C73C2211yescharacteristic
50#384×C73C2211yescharacteristic
51C4×C4⋊C4×C73C2211yescharacteristic
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×C73—21no—
68C23×C4×C73C2311yescharacteristic
69C2×D8×C73—22no—
70C2×D8×C73—22no—
71C2×D8×C73—41no—
72C22×C8×C73—22no—
73C22×C8×C73—22no—
74C22×C8×C73—41no—
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77C22×C8×C73C2311yescharacteristic
78C22×C8×C73C2311yescharacteristic
79#123×C73—44no—
80#123×C73—44no—
81#121×C73—22no—
82#121×C73—22no—
83#121×C73—22no—
84#121×C73D414yes—
85C4×D4×C73—22no—
86C4×D4×C73—41no—
87C4×D4×C73—44no—
88C2×C4⋊C4×C73—22no—
89C2×C4⋊C4×C73—22no—
90C2×C4⋊C4×C73—22no—
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×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—41no—
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
113C2×C22⋊C4×C73—21no—
114C2×C22⋊C4×C73D411yescharacteristic
115C2×C22⋊C4×C73D411yescharacteristic
116C2×C42×C73—21no—
117C2×C42×C73C2311yescharacteristic
118C2×C42×C73C2311yescharacteristic
119#107×C73—22no—
120#107×C73—22no—
121#107×C73—22no—
122C4⋊C8×C73—22no—
123C4⋊C8×C73—41no—
124#102×C73—22no—
125#102×C73—22no—
126#102×C73—22no—
127#102×C73—22no—
128#102×C73—22no—
129#102×C73—41no—
130C22⋊C8×C73—22no—
131#95×C73—21no—
132#95×C73—21no—
133#95×C73D411yescharacteristic
134#95×C73D411yescharacteristic
135C24×C73—21no—
136C24×C73—21no—
137C24×C73C2×D411yescharacteristic
138C2×D4×C73—24no—
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—21no—
150C2×D4×C73—42no—
151C2×D4×C73—42no—
152C2×D4×C73—42no—
153C2×D4×C73—42no—
154C2×D4×C73—42no—
155C2×D4×C73C2×D412yes—
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—42no—
173C22×C4×C73—81no—
174C22×C4×C73—81no—
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D412yes—
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73#4112yes—
182C22×C4×C73C2411yescharacteristic
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×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—44no—
196C2×C8×C73#4112yes—
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—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×C73—42no—
212C4⋊C4×C73—42no—
213C4⋊C4×C73—42no—
214C4⋊C4×C73C2×D412yes—
215C4⋊C4×C73#4112yes—
216C22⋊C4×C73—22no—
217C22⋊C4×C73—24no—
218C22⋊C4×C73—42no—
219C22⋊C4×C73—42no—
220C22⋊C4×C73—42no—
221C22⋊C4×C73—42no—
222C22⋊C4×C73—42no—
223C22⋊C4×C73—42no—
224C22⋊C4×C73—42no—
225C22⋊C4×C73—81no—
226C22⋊C4×C73D814yescomplemented
227C42×C73—21no—
228C42×C73—21no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—42no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—22no—
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#12112yes—
251C23×C73C2×D812yes—
252C23×C73AGL(1,ℤ/8)12yes—
253C23×C73C22×D411yescharacteristic
254D4×C73—22no—
255D4×C73—22no—
256D4×C73—48no—
257D4×C73—41no—
258D4×C73—41no—
259D4×C73—41no—
260D4×C73—41no—
261D4×C73—41no—
262D4×C73—41no—
263D4×C73—84no—
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—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—21no—
276C2×C4×C73—22no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
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—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—84no—
299C2×C4×C73—84no—
300C2×C4×C73—84no—
301C2×C4×C73#12112yes—
302C2×C4×C73C2×D812yes—
303C2×C4×C73C2×D812yes—
304C2×C4×C73C22×D411yescharacteristic
305C2×C4×C73C2×#4111yescharacteristic
306C2×C4×C73C2×#4111yescharacteristic
307C2×C4×C73C2×#4111yescharacteristic
308C2×C4×C73H(5,𝔽2)11yescharacteristic
309C2×C4×C732−1+411yescharacteristic
310C8×C73—22no—
311C8×C73—41no—
312C8×C73—41no—
313C8×C73—41no—
314C22×C73—22no—
315C22×C73—22no—
316C22×C73—22no—
317C22×C73—22no—
318C22×C73—22no—
319C22×C73—22no—
320C22×C73—42no—
321C22×C73—42no—
322C22×C73—42no—
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—81no—
334C22×C73#45914yes—
335C22×C73C2×#12111yescharacteristic
336C22×C73#54611yescharacteristic
337C22×C73#54711yescharacteristic
338C22×C73C22×D811yescharacteristic
339C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
340C22×C73#57711yescharacteristic
341C22×C73#57811yescharacteristic
342C4×C73—22no—
343C4×C73—22no—
344C4×C73—22no—
345C4×C73—41no—
346C4×C73—42no—
347C4×C73—42no—
348C4×C73—41no—
349C4×C73—81no—
350C4×C73—81no—
351C4×C73—81no—
352C4×C73—81no—
353C4×C73#52911yescharacteristic
354C4×C73#53911yescharacteristic
355C4×C73#54611yescharacteristic
356C4×C73#54711yescharacteristic
357#25200C7311yesmaximal, characteristic, direct product factor, Sylow
358C2×C73—24no—
359C2×C73—82no—
360C2×C73—161no—
361C2×C73#242511yescharacteristic
362C2×C73C2×#45911yescharacteristic
363C2×C73#304611yescharacteristic
364C2×C73#329411yescharacteristic
365C2×C73#330811yescharacteristic
366C2×C73#333411yescharacteristic
367C2×C73#334511yescharacteristic
368C2×#480C2×C7311yescharacteristic, complemented
369C2×#466C2×C7311yescharacteristic
370#2501C2×C7311yescharacteristic, complemented
371#2361C2×C7311yescharacteristic, complemented
372#2083C2×C7311yescharacteristic, complemented
373#2071C2×C7311yescharacteristic, complemented
374#2067C2×C7311yescharacteristic, complemented
375#2054C2×C7311yescharacteristic, complemented
376#1947C2×C7311yescharacteristic, complemented
377#1925C2×C7311yescharacteristic, complemented
378#1879C2×C7311yescharacteristic, complemented
379#1874C2×C7311yescharacteristic, complemented
380#1850C2×C7311yescharacteristic, complemented
381#1802C2×C7311yescharacteristic, complemented
382C2×#340C2×C7311yescharacteristic, complemented
383C73#2520011yescharacteristic, direct product factor, Sylow
384C22×D8C22×C7311yescharacteristic
385C23×C8C22×C7311yescharacteristic
386C2×#123—21no—
387C2×#123—21no—
388C2×#121C22×C7311yescharacteristic
389C2×#121C22×C7311yescharacteristic
390C2×C4×D4—21no—
391C2×C4×D4C22×C7311yescharacteristic
392C22×C4⋊C4C22×C7311yescharacteristic
393C22×C4⋊C4C22×C7311yescharacteristic
394#480—24no—
395#466—24no—
396C2×#107C22×C7311yescharacteristic
397C2×#107C22×C7311yescharacteristic
398C2×#107C22×C7311yescharacteristic
399C2×C4⋊C8C22×C7311yescharacteristic
400C2×C4⋊C8C22×C7311yescharacteristic
401C2×#102C22×C7311yescharacteristic
402C2×#102C22×C7311yescharacteristic
403C2×#102C22×C7311yescharacteristic
404C2×#102C22×C7311yescharacteristic
405C2×#102C22×C7311yescharacteristic
406C2×#102C22×C7311yescharacteristic
407C2×C22⋊C8C22×C7311yescharacteristic
408#399—21no—
409#399—21no—
410#390C22×C7311yescharacteristic
411#390C22×C7311yescharacteristic
412#390C22×C7311yescharacteristic
413#389C22×C7311yescharacteristic
414#388—21no—
415#386—21no—
416#385—21no—
417#384C22×C7311yescharacteristic
418#384C22×C7311yescharacteristic
419C4×C4⋊C4C22×C7311yescharacteristic
420C4×C22⋊C4C22×C7311yescharacteristic
421#340C22×C7311yescharacteristic
422#340C22×C7311yescharacteristic
423#340C22×C7311yescharacteristic
424#340C22×C7311yescharacteristic
425#340C22×C7311yescharacteristic
426#340C22×C7311yescharacteristic
427#336C22×C7311yescharacteristic
428#336C22×C7311yescharacteristic
429C22×D4—21no—
430C22×D4—21no—
431C22×D4C23×C7311yescharacteristic
432C22×D4C23×C7311yescharacteristic
433C23×C4—21no—
434C23×C4—21no—
435C23×C4—21no—
436C23×C4C23×C7311yescharacteristic
437C2×D8—22no—
438C2×D8—22no—
439C2×D8—41no—
440C22×C8—22no—
441C22×C8—22no—
442C22×C8—41no—
443C22×C8C23×C7311yescharacteristic
444C22×C8C23×C7311yescharacteristic
445C22×C8C23×C7311yescharacteristic
446C22×C8C23×C7311yescharacteristic
447#123—44no—
448#123—44no—
449#121—22no—
450#121—22no—
451#121—22no—
452#121D4×C7314yes—
453C4×D4—22no—
454C4×D4—41no—
455C4×D4—44no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4C23×C7311yescharacteristic
468C2×C4⋊C4C23×C7311yescharacteristic
469C2×C4⋊C4C23×C7311yescharacteristic
470C2×C4⋊C4C23×C7311yescharacteristic
471C2×C4⋊C4C23×C7311yescharacteristic
472C2×C4⋊C4C23×C7311yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4D4×C7311yescharacteristic
483C2×C22⋊C4D4×C7311yescharacteristic
484C2×C42—21no—
485C2×C42C23×C7311yescharacteristic
486C2×C42C23×C7311yescharacteristic
487#107—22no—
488#107—22no—
489#107—22no—
490C4⋊C8—22no—
491C4⋊C8—41no—
492#102—22no—
493#102—22no—
494#102—22no—
495#102—22no—
496#102—22no—
497#102—41no—
498C22⋊C8—22no—
499#95—21no—
500#95—21no—
501#95D4×C7311yescharacteristic
502#95D4×C7311yescharacteristic
503C24—21no—
504C24—21no—
505C24C2×D4×C7311yescharacteristic
506C2×D4—24no—
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—42no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4C2×D4×C7312yes—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4C2×D4×C7311yescharacteristic
544C22×C4C2×D4×C7311yescharacteristic
545C22×C4C2×D4×C7311yescharacteristic
546C22×C4C2×D4×C7312yes—
547C22×C4C2×D4×C7311yescharacteristic
548C22×C4C2×D4×C7311yescharacteristic
549C22×C4#41×C7312yes—
550C22×C4C24×C7311yescharacteristic
551D8—44no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—44no—
564C2×C8#41×C7312yes—
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—21no—
574C4⋊C4—21no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4C2×D4×C7312yes—
583C4⋊C4#41×C7312yes—
584C22⋊C4—22no—
585C22⋊C4—24no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—81no—
594C22⋊C4D8×C7314yescomplemented
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—42no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—22no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23#121×C7312yes—
619C23C2×D8×C7312yes—
620C23AGL(1,ℤ/8)×C7312yes—
621C23C22×D4×C7311yescharacteristic
622D4—22no—
623D4—22no—
624D4—48no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4—41no—
629D4—41no—
630D4—41no—
631D4—84no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
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—41no—
665C2×C4—41no—
666C2×C4—84no—
667C2×C4—84no—
668C2×C4—84no—
669C2×C4#121×C7312yes—
670C2×C4C2×D8×C7312yes—
671C2×C4C2×D8×C7312yes—
672C2×C4C22×D4×C7311yescharacteristic
673C2×C4C2×#41×C7311yescharacteristic
674C2×C4C2×#41×C7311yescharacteristic
675C2×C4C2×#41×C7311yescharacteristic
676C2×C4H(5,𝔽2)×C7311yescharacteristic
677C2×C42−1+4×C7311yescharacteristic
678C8—22no—
679C8—41no—
680C8—41no—
681C8—41no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—42no—
689C22—42no—
690C22—42no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22#459×C7314yes—
703C22C2×#121×C7311yescharacteristic
704C22#546×C7311yescharacteristic
705C22#547×C7311yescharacteristic
706C22C22×D8×C7311yescharacteristic
707C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
708C22#577×C7311yescharacteristic
709C22#578×C7311yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—42no—
714C4—42no—
715C4—41no—
716C4—41no—
717C4—81no—
718C4—81no—
719C4—81no—
720C4—81no—
721C4#529×C7311yescharacteristic
722C4#539×C7311yescharacteristic
723C4#546×C7311yescharacteristic
724C4#547×C7311yescharacteristic
725C2—24no—
726C2—82no—
727C2—161no—
728C2C73×#242511yescharacteristic
729C2C2×#459×C7311yescharacteristic
730C2C73×#304611yescharacteristic
731C2C73×#329411yescharacteristic
732C2C73×#330811yescharacteristic
733C2C73×#333411yescharacteristic
734C2C73×#334511yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#466×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×#480×C73C2semidirect
3. C73×#2501C2semidirect
4. C73×#2361C2semidirect
5. C73×#2083C2semidirect
6. C73×#2071C2semidirect
7. C73×#2067C2semidirect
8. C73×#2054C2semidirect
9. C73×#1947C2semidirect
10. C73×#1925C2semidirect
11. C73×#1879C2semidirect
12. C73×#1874C2semidirect
13. C73×#1850C2semidirect
14. C73×#1802C2semidirect
15. C2×#340×C73C2semidirect
226. C22⋊C4×C73D8semidirect
357. #25200C73direct (N × H)
368. C2×#480C2×C73semidirect
370. #2501C2×C73semidirect
371. #2361C2×C73semidirect
372. #2083C2×C73semidirect
373. #2071C2×C73semidirect
374. #2067C2×C73semidirect
375. #2054C2×C73semidirect
376. #1947C2×C73semidirect
377. #1925C2×C73semidirect
378. #1879C2×C73semidirect
379. #1874C2×C73semidirect
380. #1850C2×C73semidirect
381. #1802C2×C73semidirect
382. C2×#340C2×C73semidirect
383. C73#25200direct (N × H)
594. C22⋊C4D8×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#480×C732
C2×#466×C732
C73×#25012
C73×#23612
C73×#20832
C73×#20712
C73×#20672
C73×#20542
C73×#19472
C73×#19252
C73×#18792
C73×#18742
C73×#18502
C73×#18022
C2×#340×C732
#2520073