Finite Group Databasebeta

← C73×#23972 #32933376

Subgroups — C73×#23972 #32933376

Order 18688.

1516 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C73C211yesmaximal, characteristic, complemented
2C2×#449×C73C211yesmaximal, characteristic, complemented
3C2×#417×C73C211yesmaximal, characteristic, complemented
4C73×#2407C211yesmaximal, characteristic, complemented
5C73×#2024C211yesmaximal, characteristic, complemented
6C73×#2023C211yesmaximal, characteristic, complemented
7C73×#2000C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic, complemented
9C73×#1895C211yesmaximal, characteristic, complemented
10C73×#1879C211yesmaximal, characteristic, complemented
11C73×#1877C211yesmaximal, characteristic, complemented
12C73×#1874C211yesmaximal, characteristic, complemented
13C73×#1872C211yesmaximal, characteristic, complemented
14C73×#1870C211yesmaximal, characteristic, complemented
15C73×#1824C211yesmaximal, characteristic, complemented
16C22×#41×C73—21no—
17C22×#41×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C22×D8×C73C2211yescharacteristic
20C22×M16×C73C2211yescharacteristic
21#547×C73—24no—
22#547×C73—24no—
23C2×C4⋊Q8×C73C2211yescharacteristic
24C2×#123×C73—21no—
25C2×#123×C73—21no—
26C2×C22⋊Q8×C73—21no—
27C2×C22⋊Q8×C73C2211yescharacteristic
28C2×#121×C73C2211yescharacteristic
29C2×#121×C73C2211yescharacteristic
30C2×#121×C73C2211yescharacteristic
31C2×C4×D4×C73C2211yescharacteristic
32C2×C4×D4×C73C2211yescharacteristic
33C22×C4⋊C4×C73C2211yescharacteristic
34C22×C4⋊C4×C73C2211yescharacteristic
35#449×C73—24no—
36#417×C73—24no—
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#103×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44C2×#102×C73C2211yescharacteristic
45C2×C22⋊C8×C73C2211yescharacteristic
46C2×C22⋊C8×C73C2211yescharacteristic
47C2×C22⋊C8×C73C2211yescharacteristic
48#394×C73—21no—
49#392×C73—21no—
50#391×C73C2211yescharacteristic
51#390×C73C2211yescharacteristic
52#386×C73—21no—
53#385×C73—21no—
54#380×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×C73C2211yescharacteristic
63C2×#41×C73—28no—
64C2×#41×C73—22no—
65C2×#41×C73—22no—
66C2×#41×C73—22no—
67C2×#41×C73—22no—
68C2×#41×C73—41no—
69C2×#41×C73—41no—
70C2×#41×C73—44no—
71C2×#41×C73—44no—
72C22×Q8×C73—21no—
73C22×Q8×C73C2311yescharacteristic
74C22×D4×C73—21no—
75C22×D4×C73—21no—
76C22×D4×C73—21no—
77C22×D4×C73—21no—
78C22×D4×C73D411yescharacteristic
79C22×D4×C73C2311yescharacteristic
80C22×D4×C73C2311yescharacteristic
81C23×C4×C73—21no—
82C23×C4×C73—21no—
83C23×C4×C73—21no—
84C23×C4×C73—21no—
85C23×C4×C73C2311yescharacteristic
86C23×C4×C73C2311yescharacteristic
87C2×SD16×C73—22no—
88C2×SD16×C73—22no—
89C2×SD16×C73—41no—
90C2×D8×C73—22no—
91C2×D8×C73—22no—
92C2×D8×C73—41no—
93C2×M16×C73—22no—
94C2×M16×C73—41no—
95C2×M16×C73—41no—
96C22×C8×C73C2311yescharacteristic
97C22×C8×C73C2311yescharacteristic
98C22×C8×C73C2311yescharacteristic
99C22×C8×C73C2311yescharacteristic
100C4⋊Q8×C73—22no—
101C4⋊Q8×C73—22no—
102#123×C73—28no—
103#123×C73—28no—
104C22⋊Q8×C73—28no—
105C22⋊Q8×C73—22no—
106C22⋊Q8×C73—41no—
107#121×C73—22no—
108#121×C73—22no—
109#121×C73—22no—
110#121×C73—22no—
111#121×C73—41no—
112#121×C73D414yescomplemented
113C4×D4×C73—22no—
114C4×D4×C73—22no—
115C4×D4×C73—22no—
116C4×D4×C73—22no—
117C2×C4⋊C4×C73—21no—
118C2×C4⋊C4×C73—21no—
119C2×C4⋊C4×C73—22no—
120C2×C4⋊C4×C73—21no—
121C2×C4⋊C4×C73—22no—
122C2×C4⋊C4×C73—22no—
123C2×C4⋊C4×C73—21no—
124C2×C4⋊C4×C73D411yescharacteristic
125C2×C4⋊C4×C73D414yescomplemented
126C2×C4⋊C4×C73C2311yescharacteristic
127C2×C4⋊C4×C73C2311yescharacteristic
128C2×C4⋊C4×C73C2311yescharacteristic
129C2×C4⋊C4×C73C2311yescharacteristic
130C2×C4⋊C4×C73C2311yescharacteristic
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—21no—
133C2×C22⋊C4×C73—21no—
134C2×C22⋊C4×C73—21no—
135C2×C22⋊C4×C73—21no—
136C2×C22⋊C4×C73—21no—
137C2×C22⋊C4×C73—21no—
138C2×C22⋊C4×C73—21no—
139C2×C22⋊C4×C73D411yescharacteristic
140C2×C22⋊C4×C73D411yescharacteristic
141C2×C42×C73C2311yescharacteristic
142#103×C73—22no—
143#103×C73—22no—
144#103×C73—22no—
145#102×C73—22no—
146#102×C73—22no—
147#102×C73—22no—
148#102×C73—41no—
149#102×C73—41no—
150C22⋊C8×C73—22no—
151C22⋊C8×C73—41no—
152C22⋊C8×C73—41no—
153#95×C73—21no—
154#95×C73—21no—
155#95×C73—21no—
156C24×C73—21no—
157C24×C73—21no—
158C24×C73C2×D411yescharacteristic
159C24×C73C2×D411yescharacteristic
160#41×C73—28no—
161#41×C73—44no—
162#41×C73—44no—
163#41×C73—44no—
164#41×C73—432no—
165C2×Q8×C73—24no—
166C2×Q8×C73—21no—
167C2×Q8×C73—21no—
168C2×Q8×C73—21no—
169C2×Q8×C73—21no—
170C2×Q8×C73—21no—
171C2×Q8×C73—42no—
172C2×Q8×C73—42no—
173C2×Q8×C73#4112yescomplemented
174C2×D4×C73—22no—
175C2×D4×C73—22no—
176C2×D4×C73—24no—
177C2×D4×C73—24no—
178C2×D4×C73—22no—
179C2×D4×C73—21no—
180C2×D4×C73—21no—
181C2×D4×C73—21no—
182C2×D4×C73—21no—
183C2×D4×C73—21no—
184C2×D4×C73—21no—
185C2×D4×C73—21no—
186C2×D4×C73—21no—
187C2×D4×C73—21no—
188C2×D4×C73—21no—
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—42no—
197C2×D4×C73—42no—
198C2×D4×C73—81no—
199C2×D4×C73C2×D412yes—
200C2×D4×C73#4112yescomplemented
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—24no—
206C22×C4×C73—24no—
207C22×C4×C73—24no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—42no—
221C22×C4×C73—42no—
222C22×C4×C73—42no—
223C22×C4×C73—42no—
224C22×C4×C73—42no—
225C22×C4×C73—42no—
226C22×C4×C73—42no—
227C22×C4×C73—42no—
228C22×C4×C73—42no—
229C22×C4×C73C2×D411yescharacteristic
230C22×C4×C73C2×D411yescharacteristic
231C22×C4×C73C2×D411yescharacteristic
232C22×C4×C73C2×D412yes—
233C22×C4×C73C2×D412yes—
234C22×C4×C73C2×D411yescharacteristic
235C22×C4×C73C2411yescharacteristic
236SD16×C73—44no—
237D8×C73—44no—
238M16×C73—44no—
239C2×C8×C73—21no—
240C2×C8×C73—21no—
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C2×C8×C73—21no—
244C2×C8×C73—21no—
245C2×C8×C73—21no—
246C2×C8×C73—21no—
247C2×C8×C73—21no—
248C2×C8×C73—21no—
249C2×C8×C73—21no—
250C2×C8×C73—21no—
251C4⋊C4×C73—24no—
252C4⋊C4×C73—24no—
253C4⋊C4×C73—24no—
254C4⋊C4×C73—22no—
255C4⋊C4×C73—21no—
256C4⋊C4×C73—21no—
257C4⋊C4×C73—21no—
258C4⋊C4×C73—21no—
259C4⋊C4×C73—21no—
260C4⋊C4×C73—21no—
261C4⋊C4×C73—21no—
262C4⋊C4×C73—42no—
263C4⋊C4×C73C2×D412yes—
264C4⋊C4×C73C2×D412yes—
265C4⋊C4×C73C2×D412yes—
266C22⋊C4×C73—24no—
267C22⋊C4×C73—24no—
268C22⋊C4×C73—22no—
269C22⋊C4×C73—24no—
270C22⋊C4×C73—22no—
271C22⋊C4×C73—42no—
272C22⋊C4×C73—42no—
273C22⋊C4×C73—42no—
274C22⋊C4×C73—81no—
275C22⋊C4×C73—81no—
276C42×C73—21no—
277C42×C73—21no—
278C23×C73—21no—
279C23×C73—21no—
280C23×C73—21no—
281C23×C73—21no—
282C23×C73—21no—
283C23×C73—21no—
284C23×C73—21no—
285C23×C73—21no—
286C23×C73—21no—
287C23×C73—21no—
288C23×C73—21no—
289C23×C73—21no—
290C23×C73—22no—
291C23×C73—22no—
292C23×C73—41no—
293C23×C73—41no—
294C23×C73—41no—
295C23×C73—41no—
296C23×C73—41no—
297C23×C73—41no—
298C23×C73—41no—
299C23×C73—41no—
300C23×C73—41no—
301C23×C73—41no—
302C23×C73—41no—
303C23×C73—41no—
304C23×C73#12012yes—
305C23×C73AGL(1,ℤ/8)12yes—
306C23×C73C22×D411yescharacteristic
307Q8×C73—22no—
308Q8×C73—22no—
309Q8×C73—48no—
310Q8×C73—41no—
311Q8×C73—41no—
312D4×C73—28no—
313D4×C73—22no—
314D4×C73—22no—
315D4×C73—22no—
316D4×C73—22no—
317D4×C73—48no—
318D4×C73—48no—
319D4×C73—48no—
320D4×C73—41no—
321D4×C73—41no—
322D4×C73—41no—
323D4×C73—41no—
324D4×C73—84no—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—22no—
332C2×C4×C73—22no—
333C2×C4×C73—21no—
334C2×C4×C73—21no—
335C2×C4×C73—22no—
336C2×C4×C73—22no—
337C2×C4×C73—22no—
338C2×C4×C73—21no—
339C2×C4×C73—22no—
340C2×C4×C73—21no—
341C2×C4×C73—21no—
342C2×C4×C73—21no—
343C2×C4×C73—48no—
344C2×C4×C73—48no—
345C2×C4×C73—48no—
346C2×C4×C73—48no—
347C2×C4×C73—41no—
348C2×C4×C73—41no—
349C2×C4×C73—41no—
350C2×C4×C73—41no—
351C2×C4×C73—41no—
352C2×C4×C73—41no—
353C2×C4×C73—41no—
354C2×C4×C73—41no—
355C2×C4×C73—41no—
356C2×C4×C73—41no—
357C2×C4×C73—41no—
358C2×C4×C73—41no—
359C2×C4×C73—41no—
360C2×C4×C73—41no—
361C2×C4×C73—41no—
362C2×C4×C73—41no—
363C2×C4×C73—41no—
364C2×C4×C73—41no—
365C2×C4×C73#12012yes—
366C2×C4×C73AGL(1,ℤ/8)12yes—
367C2×C4×C73C22×D411yescharacteristic
368C2×C4×C73C22×D411yescharacteristic
369C2×C4×C73C2×#4111yescharacteristic
370C2×C4×C73C2×#4111yescharacteristic
371C2×C4×C73H(5,𝔽2)11yescharacteristic
372C2×C4×C73H(5,𝔽2)11yescharacteristic
373C8×C73—41no—
374C8×C73—41no—
375C8×C73—41no—
376C8×C73—41no—
377C22×C73—22no—
378C22×C73—22no—
379C22×C73—22no—
380C22×C73—22no—
381C22×C73—22no—
382C22×C73—22no—
383C22×C73—41no—
384C22×C73—41no—
385C22×C73—41no—
386C22×C73—41no—
387C22×C73—41no—
388C22×C73—41no—
389C22×C73—41no—
390C22×C73—41no—
391C22×C73—42no—
392C22×C73—42no—
393C22×C73—42no—
394C22×C73—42no—
395C22×C73—42no—
396C22×C73—42no—
397C22×C73—81no—
398C22×C73—81no—
399C22×C73—81no—
400C22×C73—81no—
401C22×C73—81no—
402C22×C73—81no—
403C22×C73—81no—
404C22×C73—81no—
405C22×C73C2×#12011yescharacteristic
406C22×C73#54611yescharacteristic
407C22×C73#54611yescharacteristic
408C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C73#57711yescharacteristic
411C22×C73#57811yescharacteristic
412C4×C73—22no—
413C4×C73—22no—
414C4×C73—41no—
415C4×C73—42no—
416C4×C73—42no—
417C4×C73—42no—
418C4×C73—42no—
419C4×C73—41no—
420C4×C73—81no—
421C4×C73—81no—
422C4×C73#52511yescharacteristic
423C4×C73#53511yescharacteristic
424C4×C73#54611yescharacteristic
425C4×C73#54611yescharacteristic
426#23972C7311yesmaximal, characteristic, direct product factor, Sylow
427C2×C73—42no—
428C2×C73—42no—
429C2×C73—82no—
430C2×C73—82no—
431C2×C73#240411yescharacteristic
432C2×C73#300311yescharacteristic
433C2×C73#301311yescharacteristic
434C2×C73#330611yescharacteristic
435C2×C73#330811yescharacteristic
436C2×C73#333011yescharacteristic
437C2×C73#333211yescharacteristic
438C2×#547C2×C7311yescharacteristic, complemented
439C2×#449C2×C7311yescharacteristic, complemented
440C2×#417C2×C7311yescharacteristic, complemented
441#2407C2×C7311yescharacteristic, complemented
442#2024C2×C7311yescharacteristic, complemented
443#2023C2×C7311yescharacteristic, complemented
444#2000C2×C7311yescharacteristic, complemented
445#1999C2×C7311yescharacteristic, complemented
446#1895C2×C7311yescharacteristic, complemented
447#1879C2×C7311yescharacteristic, complemented
448#1877C2×C7311yescharacteristic, complemented
449#1874C2×C7311yescharacteristic, complemented
450#1872C2×C7311yescharacteristic, complemented
451#1870C2×C7311yescharacteristic, complemented
452#1824C2×C7311yescharacteristic, complemented
453C73#2397211yescharacteristic, direct product factor, Sylow
454C22×#41—21no—
455C22×#41C22×C7311yescharacteristic
456C22×SD16C22×C7311yescharacteristic
457C22×D8C22×C7311yescharacteristic
458C22×M16C22×C7311yescharacteristic
459#547—24no—
460#547—24no—
461C2×C4⋊Q8C22×C7311yescharacteristic
462C2×#123—21no—
463C2×#123—21no—
464C2×C22⋊Q8—21no—
465C2×C22⋊Q8C22×C7311yescharacteristic
466C2×#121C22×C7311yescharacteristic
467C2×#121C22×C7311yescharacteristic
468C2×#121C22×C7311yescharacteristic
469C2×C4×D4C22×C7311yescharacteristic
470C2×C4×D4C22×C7311yescharacteristic
471C22×C4⋊C4C22×C7311yescharacteristic
472C22×C4⋊C4C22×C7311yescharacteristic
473#449—24no—
474#417—24no—
475C2×#103C22×C7311yescharacteristic
476C2×#103C22×C7311yescharacteristic
477C2×#103C22×C7311yescharacteristic
478C2×#102C22×C7311yescharacteristic
479C2×#102C22×C7311yescharacteristic
480C2×#102C22×C7311yescharacteristic
481C2×#102C22×C7311yescharacteristic
482C2×#102C22×C7311yescharacteristic
483C2×C22⋊C8C22×C7311yescharacteristic
484C2×C22⋊C8C22×C7311yescharacteristic
485C2×C22⋊C8C22×C7311yescharacteristic
486#394—21no—
487#392—21no—
488#391C22×C7311yescharacteristic
489#390C22×C7311yescharacteristic
490#386—21no—
491#385—21no—
492#380C22×C7311yescharacteristic
493#340C22×C7311yescharacteristic
494#340C22×C7311yescharacteristic
495#340C22×C7311yescharacteristic
496#340C22×C7311yescharacteristic
497#340C22×C7311yescharacteristic
498#340C22×C7311yescharacteristic
499#336C22×C7311yescharacteristic
500#336C22×C7311yescharacteristic
501C2×#41—28no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—44no—
509C2×#41—44no—
510C22×Q8—21no—
511C22×Q8C23×C7311yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4D4×C7311yescharacteristic
517C22×D4C23×C7311yescharacteristic
518C22×D4C23×C7311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C23×C7311yescharacteristic
524C23×C4C23×C7311yescharacteristic
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—41no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C22×C8C23×C7311yescharacteristic
535C22×C8C23×C7311yescharacteristic
536C22×C8C23×C7311yescharacteristic
537C22×C8C23×C7311yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540#123—28no—
541#123—28no—
542C22⋊Q8—28no—
543C22⋊Q8—22no—
544C22⋊Q8—41no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—41no—
550#121D4×C7314yescomplemented
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4D4×C7311yescharacteristic
563C2×C4⋊C4D4×C7314yescomplemented
564C2×C4⋊C4C23×C7311yescharacteristic
565C2×C4⋊C4C23×C7311yescharacteristic
566C2×C4⋊C4C23×C7311yescharacteristic
567C2×C4⋊C4C23×C7311yescharacteristic
568C2×C4⋊C4C23×C7311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4D4×C7311yescharacteristic
578C2×C22⋊C4D4×C7311yescharacteristic
579C2×C42C23×C7311yescharacteristic
580#103—22no—
581#103—22no—
582#103—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—41no—
587#102—41no—
588C22⋊C8—22no—
589C22⋊C8—41no—
590C22⋊C8—41no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—21no—
595C24—21no—
596C24C2×D4×C7311yescharacteristic
597C24C2×D4×C7311yescharacteristic
598#41—28no—
599#41—44no—
600#41—44no—
601#41—44no—
602#41—432no—
603C2×Q8—24no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8#41×C7312yescomplemented
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—81no—
637C2×D4C2×D4×C7312yes—
638C2×D4#41×C7312yescomplemented
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C7311yescharacteristic
668C22×C4C2×D4×C7311yescharacteristic
669C22×C4C2×D4×C7311yescharacteristic
670C22×C4C2×D4×C7312yes—
671C22×C4C2×D4×C7312yes—
672C22×C4C2×D4×C7311yescharacteristic
673C22×C4C24×C7311yescharacteristic
674SD16—44no—
675D8—44no—
676M16—44no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—42no—
701C4⋊C4C2×D4×C7312yes—
702C4⋊C4C2×D4×C7312yes—
703C4⋊C4C2×D4×C7312yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—22no—
707C22⋊C4—24no—
708C22⋊C4—22no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23#120×C7312yes—
743C23AGL(1,ℤ/8)×C7312yes—
744C23C22×D4×C7311yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—48no—
748Q8—41no—
749Q8—41no—
750D4—28no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—84no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4#120×C7312yes—
804C2×C4AGL(1,ℤ/8)×C7312yes—
805C2×C4C22×D4×C7311yescharacteristic
806C2×C4C22×D4×C7311yescharacteristic
807C2×C4C2×#41×C7311yescharacteristic
808C2×C4C2×#41×C7311yescharacteristic
809C2×C4H(5,𝔽2)×C7311yescharacteristic
810C2×C4H(5,𝔽2)×C7311yescharacteristic
811C8—41no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#120×C7311yescharacteristic
844C22#546×C7311yescharacteristic
845C22#546×C7311yescharacteristic
846C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
847C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
848C22#577×C7311yescharacteristic
849C22#578×C7311yescharacteristic
850C4—22no—
851C4—22no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—41no—
856C4—41no—
857C4—42no—
858C4—81no—
859C4—81no—
860C4#525×C7311yescharacteristic
861C4#535×C7311yescharacteristic
862C4#546×C7311yescharacteristic
863C4#546×C7311yescharacteristic
864C2—42no—
865C2—42no—
866C2—82no—
867C2—82no—
868C2C73×#240411yescharacteristic
869C2C73×#300311yescharacteristic
870C2C73×#301311yescharacteristic
871C2C73×#330611yescharacteristic
872C2C73×#330811yescharacteristic
873C2C73×#333011yescharacteristic
874C2C73×#333211yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C4×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#547×C73C2semidirect
2. C2×#449×C73C2semidirect
3. C2×#417×C73C2semidirect
4. C73×#2407C2semidirect
5. C73×#2024C2semidirect
6. C73×#2023C2semidirect
7. C73×#2000C2semidirect
8. C73×#1999C2semidirect
9. C73×#1895C2semidirect
10. C73×#1879C2semidirect
11. C73×#1877C2semidirect
12. C73×#1874C2semidirect
13. C73×#1872C2semidirect
14. C73×#1870C2semidirect
15. C73×#1824C2semidirect
112. #121×C73D4semidirect
125. C2×C4⋊C4×C73D4semidirect
173. C2×Q8×C73#41semidirect
200. C2×D4×C73#41semidirect
426. #23972C73direct (N × H)
438. C2×#547C2×C73semidirect
439. C2×#449C2×C73semidirect
440. C2×#417C2×C73semidirect
441. #2407C2×C73semidirect
442. #2024C2×C73semidirect
443. #2023C2×C73semidirect
444. #2000C2×C73semidirect
445. #1999C2×C73semidirect
446. #1895C2×C73semidirect
447. #1879C2×C73semidirect
448. #1877C2×C73semidirect
449. #1874C2×C73semidirect
450. #1872C2×C73semidirect
451. #1870C2×C73semidirect
452. #1824C2×C73semidirect
453. C73#23972direct (N × H)
550. #121D4×C73semidirect
563. C2×C4⋊C4D4×C73semidirect
611. C2×Q8#41×C73semidirect
638. C2×D4#41×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C732
C2×#449×C732
C2×#417×C732
C73×#24072
C73×#20242
C73×#20232
C73×#20002
C73×#19992
C73×#18952
C73×#18792
C73×#18772
C73×#18742
C73×#18722
C73×#18702
C73×#18242
#2397273