Finite Group Databasebeta

← C73×#25304 #32934708

Subgroups — C73×#25304 #32934708

Order 18688.

906 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C73C211yesmaximal, characteristic
2C2×#446×C73C211yesmaximal, characteristic, complemented
3C73×#2580C211yesmaximal, characteristic, complemented
4C73×#2548C211yesmaximal, characteristic, complemented
5C73×#2067C211yesmaximal, characteristic, complemented
6C73×#2065C211yesmaximal, characteristic, complemented
7C73×#2054C211yesmaximal, characteristic, complemented
8C73×#2054C211yesmaximal, characteristic, complemented
9C73×#1972C211yesmaximal, characteristic, complemented
10C73×#1970C211yesmaximal, characteristic, complemented
11C73×#1961C211yesmaximal, characteristic, complemented
12C73×#1949C211yesmaximal, characteristic, complemented
13C73×#1936C211yesmaximal, characteristic, complemented
14C73×#1934C211yesmaximal, characteristic, complemented
15C73×#1762C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C2×#127×C73C2211yescharacteristic
19C2×#124×C73—21no—
20C2×C4×Q8×C73C2211yescharacteristic
21C2×C4×D4×C73C2211yescharacteristic
22#459×C73—24no—
23#446×C73—24no—
24C2×#107×C73C2211yescharacteristic
25C2×#106×C73C2211yescharacteristic
26C2×C4⋊C8×C73C2211yescharacteristic
27C2×C4⋊C8×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#399×C73—21no—
41#394×C73—21no—
42#394×C73—21no—
43#393×C73—21no—
44#390×C73—21no—
45#390×C73C2211yescharacteristic
46#390×C73C2211yescharacteristic
47#390×C73C2211yescharacteristic
48#390×C73C2211yescharacteristic
49#390×C73C2211yescharacteristic
50#390×C73C2211yescharacteristic
51#389×C73C2211yescharacteristic
52#389×C73C2211yescharacteristic
53#385×C73—21no—
54#385×C73—21no—
55#382×C73C2211yescharacteristic
56C4×C4⋊C4×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61C22×Q8×C73D411yescharacteristic
62C22×D4×C73—21no—
63C22×D4×C73—21no—
64C22×D4×C73C2311yescharacteristic
65C22×D4×C73C2311yescharacteristic
66C22×D4×C73C2311yescharacteristic
67C23×C4×C73—21no—
68C2×D8×C73—22no—
69C2×D8×C73—22no—
70C2×D8×C73—22no—
71C2×D8×C73—22no—
72C2×D8×C73—41no—
73C2×D8×C73—41no—
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77C22×C8×C73C2311yescharacteristic
78#127×C73—22no—
79#127×C73—22no—
80#124×C73—44no—
81C4×Q8×C73—22no—
82C4×Q8×C73—22no—
83C4×D4×C73—22no—
84C4×D4×C73—22no—
85C2×C4⋊C4×C73—21no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73D411yescharacteristic
88C2×C4⋊C4×C73D411yescharacteristic
89C2×C4⋊C4×C73D411yescharacteristic
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73C2311yescharacteristic
92C2×C4⋊C4×C73C2311yescharacteristic
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73C2311yescharacteristic
95C2×C22⋊C4×C73—21no—
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×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C42×C73—21no—
109C2×C42×C73C2311yescharacteristic
110C2×C42×C73C2311yescharacteristic
111C2×C42×C73C2311yescharacteristic
112#107×C73—41no—
113#106×C73—41no—
114C4⋊C8×C73—22no—
115C4⋊C8×C73—22no—
116C4⋊C8×C73D414yes—
117#102×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—41no—
124#102×C73—41no—
125#97×C73—22no—
126#97×C73—22no—
127C4×C8×C73—22no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132#95×C73—21no—
133C24×C73—21no—
134C24×C73—21no—
135C24×C73—21no—
136C2×Q8×C73—22no—
137C2×Q8×C73—22no—
138C2×Q8×C73—41no—
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—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×C73#4112yes—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—42no—
169C22×C4×C73—81no—
170C22×C4×C73—81no—
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2411yescharacteristic
178D8×C73—44no—
179D8×C73—44no—
180C2×C8×C73—21no—
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×C73C2×D412yes—
190C2×C8×C73C2×D412yes—
191C2×C8×C73#4112yes—
192C4⋊C4×C73—22no—
193C4⋊C4×C73—22no—
194C4⋊C4×C73—22no—
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—21no—
205C4⋊C4×C73—81no—
206C4⋊C4×C73—81no—
207C22⋊C4×C73—42no—
208C22⋊C4×C73—42no—
209C22⋊C4×C73—42no—
210C22⋊C4×C73—42no—
211C22⋊C4×C73—42no—
212C22⋊C4×C73—42no—
213C22⋊C4×C73—42no—
214C22⋊C4×C73—81no—
215C22⋊C4×C73—81no—
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—
225C42×C73C2×D412yes—
226C42×C73#4112yes—
227C23×C73—22no—
228C23×C73—41no—
229C23×C73—41no—
230C23×C73—41no—
231C23×C73—41no—
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×C73C22×D411yescharacteristic
249Q8×C73—44no—
250D4×C73—22no—
251D4×C73—22no—
252D4×C73—41no—
253D4×C73—41no—
254D4×C73—41no—
255D4×C73—41no—
256D4×C73—41no—
257D4×C73—41no—
258D4×C73—41no—
259D4×C73—41no—
260D4×C73—41no—
261D4×C73—41no—
262D4×C73—84no—
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—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
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—84no—
295C2×C4×C73#12112yes—
296C2×C4×C73#12112yes—
297C2×C4×C73AGL(1,ℤ/8)12yes—
298C2×C4×C73C22×D411yescharacteristic
299C2×C4×C73C2×#4111yescharacteristic
300C2×C4×C73C2×#4111yescharacteristic
301C2×C4×C73C2×#4111yescharacteristic
302C2×C4×C73H(5,𝔽2)11yescharacteristic
303C2×C4×C732−1+411yescharacteristic
304C8×C73—22no—
305C8×C73—22no—
306C8×C73—22no—
307C8×C73—41no—
308C22×C73—42no—
309C22×C73—42no—
310C22×C73—42no—
311C22×C73—81no—
312C22×C73—81no—
313C22×C73—81no—
314C22×C73—81no—
315C22×C73—81no—
316C22×C73—81no—
317C22×C73—81no—
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×C73C2×#12111yescharacteristic
330C22×C73#54811yescharacteristic
331C22×C73#55011yescharacteristic
332C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C73#57511yescharacteristic
334C22×C73#57611yescharacteristic
335C22×C73#57611yescharacteristic
336C4×C73—22no—
337C4×C73—22no—
338C4×C73—22no—
339C4×C73—41no—
340C4×C73—41no—
341C4×C73—41no—
342C4×C73—81no—
343C4×C73—81no—
344C4×C73—81no—
345C4×C73—81no—
346C4×C73—81no—
347C4×C73#52911yescharacteristic
348C4×C73#54211yescharacteristic
349C4×C73#54611yescharacteristic
350C4×C73#54811yescharacteristic
351#25304C7311yesmaximal, characteristic, direct product factor, Sylow
352C2×C73—82no—
353C2×C73—161no—
354C2×C73—161no—
355C2×C73#242611yescharacteristic
356C2×C73#305511yescharacteristic
357C2×C73#305811yescharacteristic
358C2×C73#336611yescharacteristic
359C2×C73#337011yescharacteristic
360C2×C73#339911yescharacteristic
361C2×C73#340311yescharacteristic
362C2×#459C2×C7311yescharacteristic
363C2×#446C2×C7311yescharacteristic, complemented
364#2580C2×C7311yescharacteristic, complemented
365#2548C2×C7311yescharacteristic, complemented
366#2067C2×C7311yescharacteristic, complemented
367#2065C2×C7311yescharacteristic, complemented
368#2054C2×C7311yescharacteristic, complemented
369#2054C2×C7311yescharacteristic, complemented
370#1972C2×C7311yescharacteristic, complemented
371#1970C2×C7311yescharacteristic, complemented
372#1961C2×C7311yescharacteristic, complemented
373#1949C2×C7311yescharacteristic, complemented
374#1936C2×C7311yescharacteristic, complemented
375#1934C2×C7311yescharacteristic, complemented
376#1762C2×C7311yescharacteristic, complemented
377C73#2530411yescharacteristic, direct product factor, Sylow
378C22×D8C22×C7311yescharacteristic
379C22×D8C22×C7311yescharacteristic
380C2×#127C22×C7311yescharacteristic
381C2×#124—21no—
382C2×C4×Q8C22×C7311yescharacteristic
383C2×C4×D4C22×C7311yescharacteristic
384#459—24no—
385#446—24no—
386C2×#107C22×C7311yescharacteristic
387C2×#106C22×C7311yescharacteristic
388C2×C4⋊C8C22×C7311yescharacteristic
389C2×C4⋊C8C22×C7311yescharacteristic
390C2×C4⋊C8C22×C7311yescharacteristic
391C2×#102C22×C7311yescharacteristic
392C2×#102C22×C7311yescharacteristic
393C2×#102C22×C7311yescharacteristic
394C2×#102C22×C7311yescharacteristic
395C2×#102C22×C7311yescharacteristic
396C2×#102C22×C7311yescharacteristic
397C2×#102C22×C7311yescharacteristic
398C2×#102C22×C7311yescharacteristic
399C2×#97C22×C7311yescharacteristic
400C2×#97C22×C7311yescharacteristic
401C2×C4×C8C22×C7311yescharacteristic
402#399—21no—
403#394—21no—
404#394—21no—
405#393—21no—
406#390—21no—
407#390C22×C7311yescharacteristic
408#390C22×C7311yescharacteristic
409#390C22×C7311yescharacteristic
410#390C22×C7311yescharacteristic
411#390C22×C7311yescharacteristic
412#390C22×C7311yescharacteristic
413#389C22×C7311yescharacteristic
414#389C22×C7311yescharacteristic
415#385—21no—
416#385—21no—
417#382C22×C7311yescharacteristic
418C4×C4⋊C4C22×C7311yescharacteristic
419#340C22×C7311yescharacteristic
420#340C22×C7311yescharacteristic
421#340C22×C7311yescharacteristic
422#340C22×C7311yescharacteristic
423C22×Q8D4×C7311yescharacteristic
424C22×D4—21no—
425C22×D4—21no—
426C22×D4C23×C7311yescharacteristic
427C22×D4C23×C7311yescharacteristic
428C22×D4C23×C7311yescharacteristic
429C23×C4—21no—
430C2×D8—22no—
431C2×D8—22no—
432C2×D8—22no—
433C2×D8—22no—
434C2×D8—41no—
435C2×D8—41no—
436C22×C8C23×C7311yescharacteristic
437C22×C8C23×C7311yescharacteristic
438C22×C8C23×C7311yescharacteristic
439C22×C8C23×C7311yescharacteristic
440#127—22no—
441#127—22no—
442#124—44no—
443C4×Q8—22no—
444C4×Q8—22no—
445C4×D4—22no—
446C4×D4—22no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4D4×C7311yescharacteristic
450C2×C4⋊C4D4×C7311yescharacteristic
451C2×C4⋊C4D4×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⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C42—21no—
471C2×C42C23×C7311yescharacteristic
472C2×C42C23×C7311yescharacteristic
473C2×C42C23×C7311yescharacteristic
474#107—41no—
475#106—41no—
476C4⋊C8—22no—
477C4⋊C8—22no—
478C4⋊C8D4×C7314yes—
479#102—22no—
480#102—22no—
481#102—22no—
482#102—22no—
483#102—22no—
484#102—22no—
485#102—41no—
486#102—41no—
487#97—22no—
488#97—22no—
489C4×C8—22no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495C24—21no—
496C24—21no—
497C24—21no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—41no—
501C2×D4—21no—
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—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—81no—
523C2×D4—81no—
524C2×D4#41×C7312yes—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4C2×D4×C7311yescharacteristic
534C22×C4C2×D4×C7311yescharacteristic
535C22×C4C2×D4×C7311yescharacteristic
536C22×C4C2×D4×C7311yescharacteristic
537C22×C4C2×D4×C7311yescharacteristic
538C22×C4C2×D4×C7311yescharacteristic
539C22×C4C24×C7311yescharacteristic
540D8—44no—
541D8—44no—
542C2×C8—21no—
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×C8C2×D4×C7312yes—
552C2×C8C2×D4×C7312yes—
553C2×C8#41×C7312yes—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
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—81no—
568C4⋊C4—81no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C22⋊C4—81no—
579C22⋊C4—81no—
580C22⋊C4—81no—
581C22⋊C4—81no—
582C42—21no—
583C42—21no—
584C42—21no—
585C42—21no—
586C42—42no—
587C42C2×D4×C7312yes—
588C42#41×C7312yes—
589C23—22no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
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—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23C22×D4×C7311yescharacteristic
611Q8—44no—
612D4—22no—
613D4—22no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—41no—
624D4—84no—
625D4—84no—
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—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
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—41no—
655C2×C4—41no—
656C2×C4—84no—
657C2×C4#121×C7312yes—
658C2×C4#121×C7312yes—
659C2×C4AGL(1,ℤ/8)×C7312yes—
660C2×C4C22×D4×C7311yescharacteristic
661C2×C4C2×#41×C7311yescharacteristic
662C2×C4C2×#41×C7311yescharacteristic
663C2×C4C2×#41×C7311yescharacteristic
664C2×C4H(5,𝔽2)×C7311yescharacteristic
665C2×C42−1+4×C7311yescharacteristic
666C8—22no—
667C8—22no—
668C8—22no—
669C8—41no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22C2×#121×C7311yescharacteristic
692C22#548×C7311yescharacteristic
693C22#550×C7311yescharacteristic
694C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
695C22#575×C7311yescharacteristic
696C22#576×C7311yescharacteristic
697C22#576×C7311yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4#529×C7311yescharacteristic
710C4#542×C7311yescharacteristic
711C4#546×C7311yescharacteristic
712C4#548×C7311yescharacteristic
713C2—82no—
714C2—161no—
715C2—161no—
716C2C73×#242611yescharacteristic
717C2C73×#305511yescharacteristic
718C2C73×#305811yescharacteristic
719C2C73×#336611yescharacteristic
720C2C73×#337011yescharacteristic
721C2C73×#339911yescharacteristic
722C2C73×#340311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#459×C73C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C4×Q8×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#446×C73C2semidirect
3. C73×#2580C2semidirect
4. C73×#2548C2semidirect
5. C73×#2067C2semidirect
6. C73×#2065C2semidirect
7. C73×#2054C2semidirect
8. C73×#2054C2semidirect
9. C73×#1972C2semidirect
10. C73×#1970C2semidirect
11. C73×#1961C2semidirect
12. C73×#1949C2semidirect
13. C73×#1936C2semidirect
14. C73×#1934C2semidirect
15. C73×#1762C2semidirect
351. #25304C73direct (N × H)
363. C2×#446C2×C73semidirect
364. #2580C2×C73semidirect
365. #2548C2×C73semidirect
366. #2067C2×C73semidirect
367. #2065C2×C73semidirect
368. #2054C2×C73semidirect
369. #2054C2×C73semidirect
370. #1972C2×C73semidirect
371. #1970C2×C73semidirect
372. #1961C2×C73semidirect
373. #1949C2×C73semidirect
374. #1936C2×C73semidirect
375. #1934C2×C73semidirect
376. #1762C2×C73semidirect
377. C73#25304direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#459×C732
C2×#446×C732
C73×#25802
C73×#25482
C73×#20672
C73×#20652
C73×#20542
C73×#19722
C73×#19702
C73×#19612
C73×#19492
C73×#19362
C73×#19342
C73×#17622
#2530473