Finite Group Databasebeta

← C73×#25380 #32934784

Subgroups — C73×#25380 #32934784

Order 18688.

1184 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#496×C73C211yesmaximal, characteristic, complemented
2C2×#460×C73C211yesmaximal, characteristic, complemented
3C2×#463×C73C211yesmaximal, characteristic, complemented
4C2×#459×C73C211yesmaximal, characteristic, complemented
5C73×#2541C211yesmaximal, characteristic, complemented
6C73×#2367C211yesmaximal, characteristic, complemented
7C73×#2055C211yesmaximal, characteristic, complemented
8C73×#2054C211yesmaximal, characteristic, complemented
9C73×#2014C211yesmaximal, characteristic, complemented
10C73×#2011C211yesmaximal, characteristic, complemented
11C73×#1982C211yesmaximal, characteristic, complemented
12C73×#1940C211yesmaximal, characteristic, complemented
13C73×#1880C211yesmaximal, characteristic, complemented
14C73×#1879C211yesmaximal, characteristic, complemented
15C73×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C22×D8×C73C2211yescharacteristic
20C22×D8×C73C2211yescharacteristic
21C22×D8×C73C2211yescharacteristic
22C2×#127×C73C2211yescharacteristic
23C2×#127×C73C2211yescharacteristic
24C2×#127×C73C2211yescharacteristic
25C2×#124×C73C2211yescharacteristic
26C2×#121×C73—21no—
27C2×#121×C73—21no—
28C2×C4×Q8×C73C2211yescharacteristic
29C2×C4×D4×C73C2211yescharacteristic
30C2×C4×D4×C73C2211yescharacteristic
31#496×C73—24no—
32#463×C73—24no—
33#460×C73—24no—
34#459×C73—24no—
35C2×C4⋊C8×C73C2211yescharacteristic
36C2×C4⋊C8×C73C2211yescharacteristic
37C2×C4⋊C8×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44C2×#102×C73C2211yescharacteristic
45C2×#102×C73C2211yescharacteristic
46C2×#97×C73C2211yescharacteristic
47#392×C73—21no—
48#392×C73—21no—
49#391×C73C2211yescharacteristic
50#390×C73C2211yescharacteristic
51#390×C73C2211yescharacteristic
52#390×C73C2211yescharacteristic
53#388×C73—21no—
54#388×C73—21no—
55#385×C73—21no—
56C4×C4⋊C4×C73C2211yescharacteristic
57C4×C4⋊C4×C73C2211yescharacteristic
58C4×C22⋊C4×C73—21no—
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×C73C2211yescharacteristic
63C22×Q8×C73C2311yescharacteristic
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73—21no—
68C22×D4×C73—21no—
69C22×D4×C73—21no—
70C22×D4×C73C2311yescharacteristic
71C22×D4×C73C2311yescharacteristic
72C22×D4×C73C2311yescharacteristic
73C22×D4×C73C2311yescharacteristic
74C23×C4×C73—21no—
75C23×C4×C73—21no—
76C2×SD16×C73—22no—
77C2×SD16×C73—22no—
78C2×SD16×C73—22no—
79C2×SD16×C73—22no—
80C2×SD16×C73—22no—
81C2×SD16×C73—22no—
82C2×SD16×C73—41no—
83C2×SD16×C73—41no—
84C2×SD16×C73—41no—
85C2×D8×C73—22no—
86C2×D8×C73—22no—
87C2×D8×C73—22no—
88C2×D8×C73—22no—
89C2×D8×C73—22no—
90C2×D8×C73—22no—
91C2×D8×C73—41no—
92C2×D8×C73—41no—
93C2×D8×C73—41no—
94C22×C8×C73C2311yescharacteristic
95C22×C8×C73C2311yescharacteristic
96C22×C8×C73C2311yescharacteristic
97C22×C8×C73C2311yescharacteristic
98#127×C73—22no—
99#127×C73—22no—
100#127×C73—22no—
101#127×C73—22no—
102#127×C73—41no—
103#127×C73—41no—
104#124×C73—22no—
105#124×C73D414yescomplemented
106#121×C73—44no—
107#121×C73—44no—
108C4×Q8×C73—22no—
109C4×Q8×C73—41no—
110C4×D4×C73—22no—
111C4×D4×C73—22no—
112C4×D4×C73—22no—
113C4×D4×C73—41no—
114C2×C4⋊C4×C73—21no—
115C2×C4⋊C4×C73D411yescharacteristic
116C2×C4⋊C4×C73D411yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C4⋊C4×C73C2311yescharacteristic
120C2×C22⋊C4×C73—21no—
121C2×C22⋊C4×C73—21no—
122C2×C22⋊C4×C73—21no—
123C2×C22⋊C4×C73—21no—
124C2×C22⋊C4×C73—21no—
125C2×C22⋊C4×C73—21no—
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—21no—
130C2×C42×C73—21no—
131C2×C42×C73—21no—
132C2×C42×C73C2311yescharacteristic
133C2×C42×C73C2311yescharacteristic
134C2×C42×C73C2311yescharacteristic
135C4⋊C8×C73—22no—
136C4⋊C8×C73—22no—
137C4⋊C8×C73—22no—
138#103×C73—22no—
139#102×C73—22no—
140#102×C73—22no—
141#102×C73—22no—
142#102×C73—22no—
143#102×C73—41no—
144#102×C73—41no—
145#102×C73D414yescomplemented
146#97×C73—22no—
147#95×C73—21no—
148#95×C73—21no—
149#95×C73—21no—
150#95×C73D411yescharacteristic
151#95×C73D411yescharacteristic
152C24×C73—21no—
153C24×C73—21no—
154C24×C73—21no—
155C24×C73—21no—
156C2×Q8×C73—21no—
157C2×Q8×C73—21no—
158C2×Q8×C73—21no—
159C2×Q8×C73—21no—
160C2×Q8×C73—21no—
161C2×Q8×C73C2×D412yes—
162C2×D4×C73—21no—
163C2×D4×C73—21no—
164C2×D4×C73—21no—
165C2×D4×C73—21no—
166C2×D4×C73—21no—
167C2×D4×C73—21no—
168C2×D4×C73—21no—
169C2×D4×C73—21no—
170C2×D4×C73—21no—
171C2×D4×C73—21no—
172C2×D4×C73—21no—
173C2×D4×C73—21no—
174C2×D4×C73—21no—
175C2×D4×C73—21no—
176C2×D4×C73—21no—
177C2×D4×C73—21no—
178C2×D4×C73—21no—
179C2×D4×C73—21no—
180C2×D4×C73—21no—
181C2×D4×C73—21no—
182C2×D4×C73—21no—
183C2×D4×C73—21no—
184C2×D4×C73—42no—
185C2×D4×C73—42no—
186C2×D4×C73—42no—
187C2×D4×C73—42no—
188C2×D4×C73—42no—
189C2×D4×C73—42no—
190C2×D4×C73—42no—
191C2×D4×C73—42no—
192C2×D4×C73—42no—
193C2×D4×C73—42no—
194C2×D4×C73—42no—
195C2×D4×C73—42no—
196C2×D4×C73—81no—
197C2×D4×C73—81no—
198C2×D4×C73—81no—
199C2×D4×C73—81no—
200C2×D4×C73—81no—
201C2×D4×C73—81no—
202C2×D4×C73C2×D412yes—
203C2×D4×C73C2×D412yes—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—42no—
209C22×C4×C73—42no—
210C22×C4×C73—42no—
211C22×C4×C73—42no—
212C22×C4×C73—42no—
213C22×C4×C73—81no—
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2×D411yescharacteristic
219C22×C4×C73C2×D411yescharacteristic
220C22×C4×C73C2411yescharacteristic
221SD16×C73—44no—
222SD16×C73—44no—
223SD16×C73—44no—
224D8×C73—44no—
225D8×C73—44no—
226D8×C73—44no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
237C2×C8×C73C2×D412yes—
238C2×C8×C73#4112yes—
239C4⋊C4×C73—22no—
240C4⋊C4×C73—22no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—42no—
247C4⋊C4×C73C2×D412yes—
248C22⋊C4×C73—24no—
249C22⋊C4×C73—24no—
250C22⋊C4×C73—42no—
251C22⋊C4×C73—42no—
252C22⋊C4×C73—42no—
253C22⋊C4×C73—42no—
254C22⋊C4×C73—42no—
255C22⋊C4×C73—42no—
256C22⋊C4×C73—42no—
257C22⋊C4×C73—81no—
258C42×C73—21no—
259C42×C73—21no—
260C42×C73—21no—
261C42×C73—21no—
262C42×C73—42no—
263C42×C73—81no—
264C42×C73C2×D412yes—
265C42×C73#4112yes—
266C23×C73—22no—
267C23×C73—22no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—41no—
272C23×C73—41no—
273C23×C73—41no—
274C23×C73—41no—
275C23×C73—41no—
276C23×C73—41no—
277C23×C73—41no—
278C23×C73—41no—
279C23×C73—41no—
280C23×C73—41no—
281C23×C73—41no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73—41no—
285C23×C73—41no—
286C23×C73—41no—
287C23×C73—41no—
288C23×C73—41no—
289C23×C73—41no—
290C23×C73—41no—
291C23×C73—41no—
292C23×C73—41no—
293C23×C73—41no—
294C23×C73C22×D411yescharacteristic
295Q8×C73—22no—
296Q8×C73—22no—
297Q8×C73—41no—
298Q8×C73—41no—
299D4×C73—22no—
300D4×C73—22no—
301D4×C73—22no—
302D4×C73—22no—
303D4×C73—41no—
304D4×C73—41no—
305D4×C73—41no—
306D4×C73—41no—
307D4×C73—41no—
308D4×C73—41no—
309D4×C73—41no—
310D4×C73—41no—
311D4×C73—41no—
312D4×C73—41no—
313D4×C73—41no—
314D4×C73—41no—
315D4×C73—84no—
316D4×C73—84no—
317D4×C73—84no—
318D4×C73—84no—
319D4×C73—84no—
320D4×C73—84no—
321C2×C4×C73—21no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—22no—
330C2×C4×C73—21no—
331C2×C4×C73—21no—
332C2×C4×C73—22no—
333C2×C4×C73—21no—
334C2×C4×C73—21no—
335C2×C4×C73—21no—
336C2×C4×C73—21no—
337C2×C4×C73—41no—
338C2×C4×C73—41no—
339C2×C4×C73—41no—
340C2×C4×C73—41no—
341C2×C4×C73—41no—
342C2×C4×C73—41no—
343C2×C4×C73—41no—
344C2×C4×C73—41no—
345C2×C4×C73—41no—
346C2×C4×C73—41no—
347C2×C4×C73—84no—
348C2×C4×C73—84no—
349C2×C4×C73#12112yes—
350C2×C4×C73#12112yes—
351C2×C4×C73AGL(1,ℤ/8)12yes—
352C2×C4×C73AGL(1,ℤ/8)12yes—
353C2×C4×C73C22×D411yescharacteristic
354C2×C4×C73C22×D411yescharacteristic
355C2×C4×C73C2×#4111yescharacteristic
356C2×C4×C73C2×#4111yescharacteristic
357C2×C4×C73H(5,𝔽2)11yescharacteristic
358C2×C4×C73H(5,𝔽2)11yescharacteristic
359C8×C73—22no—
360C8×C73—22no—
361C8×C73—41no—
362C8×C73—41no—
363C22×C73—42no—
364C22×C73—42no—
365C22×C73—42no—
366C22×C73—42no—
367C22×C73—42no—
368C22×C73—42no—
369C22×C73—81no—
370C22×C73—81no—
371C22×C73—81no—
372C22×C73—81no—
373C22×C73—81no—
374C22×C73—81no—
375C22×C73—81no—
376C22×C73—81no—
377C22×C73—81no—
378C22×C73—81no—
379C22×C73—81no—
380C22×C73—81no—
381C22×C73—81no—
382C22×C73—81no—
383C22×C73—81no—
384C22×C73—81no—
385C22×C73—81no—
386C22×C73—81no—
387C22×C73—81no—
388C22×C73—81no—
389C22×C73—81no—
390C22×C73—81no—
391C22×C73C2×#12111yescharacteristic
392C22×C73D4211yescharacteristic
393C22×C73#55011yescharacteristic
394C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
396C22×C73#57611yescharacteristic
397C22×C73#57711yescharacteristic
398C4×C73—22no—
399C4×C73—22no—
400C4×C73—22no—
401C4×C73—22no—
402C4×C73—42no—
403C4×C73—41no—
404C4×C73—42no—
405C4×C73—41no—
406C4×C73—81no—
407C4×C73—81no—
408C4×C73#53211yescharacteristic
409C4×C73#54011yescharacteristic
410C4×C73D4211yescharacteristic
411C4×C73#54611yescharacteristic
412#25380C7311yesmaximal, characteristic, direct product factor, Sylow
413C2×C73—82no—
414C2×C73—82no—
415C2×C73—161no—
416C2×C73—161no—
417C2×C73#242811yescharacteristic
418C2×C73#303811yescharacteristic
419C2×C73#304511yescharacteristic
420C2×C73#326411yescharacteristic
421C2×C73#326511yescharacteristic
422C2×C73#339711yescharacteristic
423C2×C73#339911yescharacteristic
424C2×#496C2×C7311yescharacteristic, complemented
425C2×#460C2×C7311yescharacteristic, complemented
426C2×#463C2×C7311yescharacteristic, complemented
427C2×#459C2×C7311yescharacteristic, complemented
428#2541C2×C7311yescharacteristic, complemented
429#2367C2×C7311yescharacteristic, complemented
430#2055C2×C7311yescharacteristic, complemented
431#2054C2×C7311yescharacteristic, complemented
432#2014C2×C7311yescharacteristic, complemented
433#2011C2×C7311yescharacteristic, complemented
434#1982C2×C7311yescharacteristic, complemented
435#1940C2×C7311yescharacteristic, complemented
436#1880C2×C7311yescharacteristic, complemented
437#1879C2×C7311yescharacteristic, complemented
438#1762C2×C7311yescharacteristic, complemented
439C73#2538011yescharacteristic, direct product factor, Sylow
440C22×SD16C22×C7311yescharacteristic
441C22×SD16C22×C7311yescharacteristic
442C22×SD16C22×C7311yescharacteristic
443C22×D8C22×C7311yescharacteristic
444C22×D8C22×C7311yescharacteristic
445C22×D8C22×C7311yescharacteristic
446C2×#127C22×C7311yescharacteristic
447C2×#127C22×C7311yescharacteristic
448C2×#127C22×C7311yescharacteristic
449C2×#124C22×C7311yescharacteristic
450C2×#121—21no—
451C2×#121—21no—
452C2×C4×Q8C22×C7311yescharacteristic
453C2×C4×D4C22×C7311yescharacteristic
454C2×C4×D4C22×C7311yescharacteristic
455#496—24no—
456#463—24no—
457#460—24no—
458#459—24no—
459C2×C4⋊C8C22×C7311yescharacteristic
460C2×C4⋊C8C22×C7311yescharacteristic
461C2×C4⋊C8C22×C7311yescharacteristic
462C2×#103C22×C7311yescharacteristic
463C2×#102C22×C7311yescharacteristic
464C2×#102C22×C7311yescharacteristic
465C2×#102C22×C7311yescharacteristic
466C2×#102C22×C7311yescharacteristic
467C2×#102C22×C7311yescharacteristic
468C2×#102C22×C7311yescharacteristic
469C2×#102C22×C7311yescharacteristic
470C2×#97C22×C7311yescharacteristic
471#392—21no—
472#392—21no—
473#391C22×C7311yescharacteristic
474#390C22×C7311yescharacteristic
475#390C22×C7311yescharacteristic
476#390C22×C7311yescharacteristic
477#388—21no—
478#388—21no—
479#385—21no—
480C4×C4⋊C4C22×C7311yescharacteristic
481C4×C4⋊C4C22×C7311yescharacteristic
482C4×C22⋊C4—21no—
483#340C22×C7311yescharacteristic
484#340C22×C7311yescharacteristic
485#336C22×C7311yescharacteristic
486#336C22×C7311yescharacteristic
487C22×Q8C23×C7311yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4C23×C7311yescharacteristic
495C22×D4C23×C7311yescharacteristic
496C22×D4C23×C7311yescharacteristic
497C22×D4C23×C7311yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C2×SD16—22no—
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×SD16—41no—
509C2×D8—22no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—41no—
516C2×D8—41no—
517C2×D8—41no—
518C22×C8C23×C7311yescharacteristic
519C22×C8C23×C7311yescharacteristic
520C22×C8C23×C7311yescharacteristic
521C22×C8C23×C7311yescharacteristic
522#127—22no—
523#127—22no—
524#127—22no—
525#127—22no—
526#127—41no—
527#127—41no—
528#124—22no—
529#124D4×C7314yescomplemented
530#121—44no—
531#121—44no—
532C4×Q8—22no—
533C4×Q8—41no—
534C4×D4—22no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—41no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4D4×C7311yescharacteristic
540C2×C4⋊C4D4×C7311yescharacteristic
541C2×C4⋊C4C23×C7311yescharacteristic
542C2×C4⋊C4C23×C7311yescharacteristic
543C2×C4⋊C4C23×C7311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C42—21no—
555C2×C42—21no—
556C2×C42C23×C7311yescharacteristic
557C2×C42C23×C7311yescharacteristic
558C2×C42C23×C7311yescharacteristic
559C4⋊C8—22no—
560C4⋊C8—22no—
561C4⋊C8—22no—
562#103—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—41no—
568#102—41no—
569#102D4×C7314yescomplemented
570#97—22no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95D4×C7311yescharacteristic
575#95D4×C7311yescharacteristic
576C24—21no—
577C24—21no—
578C24—21no—
579C24—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C7312yes—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4—81no—
623C2×D4—81no—
624C2×D4—81no—
625C2×D4—81no—
626C2×D4C2×D4×C7312yes—
627C2×D4C2×D4×C7312yes—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4C2×D4×C7311yescharacteristic
639C22×C4C2×D4×C7311yescharacteristic
640C22×C4C2×D4×C7311yescharacteristic
641C22×C4C2×D4×C7311yescharacteristic
642C22×C4C2×D4×C7311yescharacteristic
643C22×C4C2×D4×C7311yescharacteristic
644C22×C4C24×C7311yescharacteristic
645SD16—44no—
646SD16—44no—
647SD16—44no—
648D8—44no—
649D8—44no—
650D8—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8C2×D4×C7312yes—
662C2×C8#41×C7312yes—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4C2×D4×C7312yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—81no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—42no—
687C42—81no—
688C42C2×D4×C7312yes—
689C42#41×C7312yes—
690C23—22no—
691C23—22no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23C22×D4×C7311yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—41no—
722Q8—41no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—84no—
740D4—84no—
741D4—84no—
742D4—84no—
743D4—84no—
744D4—84no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4#121×C7312yes—
774C2×C4#121×C7312yes—
775C2×C4AGL(1,ℤ/8)×C7312yes—
776C2×C4AGL(1,ℤ/8)×C7312yes—
777C2×C4C22×D4×C7311yescharacteristic
778C2×C4C22×D4×C7311yescharacteristic
779C2×C4C2×#41×C7311yescharacteristic
780C2×C4C2×#41×C7311yescharacteristic
781C2×C4H(5,𝔽2)×C7311yescharacteristic
782C2×C4H(5,𝔽2)×C7311yescharacteristic
783C8—22no—
784C8—22no—
785C8—41no—
786C8—41no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22C2×#121×C7311yescharacteristic
816C22D42×C7311yescharacteristic
817C22#550×C7311yescharacteristic
818C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
819C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
820C22#576×C7311yescharacteristic
821C22#577×C7311yescharacteristic
822C4—22no—
823C4—22no—
824C4—22no—
825C4—22no—
826C4—41no—
827C4—42no—
828C4—41no—
829C4—42no—
830C4—81no—
831C4—81no—
832C4#532×C7311yescharacteristic
833C4#540×C7311yescharacteristic
834C4D42×C7311yescharacteristic
835C4#546×C7311yescharacteristic
836C2—82no—
837C2—82no—
838C2—161no—
839C2—161no—
840C2C73×#242811yescharacteristic
841C2C73×#303811yescharacteristic
842C2C73×#304511yescharacteristic
843C2C73×#326411yescharacteristic
844C2C73×#326511yescharacteristic
845C2C73×#339711yescharacteristic
846C2C73×#339911yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
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×#496×C73C2semidirect
2. C2×#460×C73C2semidirect
3. C2×#463×C73C2semidirect
4. C2×#459×C73C2semidirect
5. C73×#2541C2semidirect
6. C73×#2367C2semidirect
7. C73×#2055C2semidirect
8. C73×#2054C2semidirect
9. C73×#2014C2semidirect
10. C73×#2011C2semidirect
11. C73×#1982C2semidirect
12. C73×#1940C2semidirect
13. C73×#1880C2semidirect
14. C73×#1879C2semidirect
15. C73×#1762C2semidirect
105. #124×C73D4semidirect
145. #102×C73D4semidirect
412. #25380C73direct (N × H)
424. C2×#496C2×C73semidirect
425. C2×#460C2×C73semidirect
426. C2×#463C2×C73semidirect
427. C2×#459C2×C73semidirect
428. #2541C2×C73semidirect
429. #2367C2×C73semidirect
430. #2055C2×C73semidirect
431. #2054C2×C73semidirect
432. #2014C2×C73semidirect
433. #2011C2×C73semidirect
434. #1982C2×C73semidirect
435. #1940C2×C73semidirect
436. #1880C2×C73semidirect
437. #1879C2×C73semidirect
438. #1762C2×C73semidirect
439. C73#25380direct (N × H)
529. #124D4×C73semidirect
569. #102D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#496×C732
C2×#460×C732
C2×#463×C732
C2×#459×C732
C73×#25412
C73×#23672
C73×#20552
C73×#20542
C73×#20142
C73×#20112
C73×#19822
C73×#19402
C73×#18802
C73×#18792
C73×#17622
#2538073