Finite Group Databasebeta

← C73×#24017 #32933421

Subgroups — C73×#24017 #32933421

Order 18688.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C73C211yesmaximal, characteristic
2C2×#485×C73C211yesmaximal, characteristic, complemented
3C2×#482×C73C211yesmaximal, characteristic, complemented
4C73×#2311C211yesmaximal, characteristic, complemented
5C73×#2036C211yesmaximal, characteristic, complemented
6C73×#2035C211yesmaximal, characteristic, complemented
7C73×#2034C211yesmaximal, characteristic, complemented
8C73×#2033C211yesmaximal, characteristic, complemented
9C73×#1874C211yesmaximal, characteristic, complemented
10C73×#1872C211yesmaximal, characteristic, complemented
11C73×#1853C211yesmaximal, characteristic, complemented
12C73×#1852C211yesmaximal, characteristic, complemented
13C73×#1788C211yesmaximal, characteristic, complemented
14C73×#1788C211yesmaximal, characteristic, complemented
15C73×#1780C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C22×#41×C73C2211yescharacteristic
18#537×C73—24no—
19#537×C73—24no—
20C2×C22⋊Q8×C73—21no—
21C2×C22⋊Q8×C73C2211yescharacteristic
22C2×C22⋊Q8×C73C2211yescharacteristic
23C2×#121×C73—21no—
24C2×#121×C73—21no—
25C2×#121×C73—21no—
26C2×#121×C73C2211yescharacteristic
27C2×#121×C73C2211yescharacteristic
28C2×#117×C73C2211yescharacteristic
29C22×C4⋊C4×C73C2211yescharacteristic
30C22×C4⋊C4×C73C2211yescharacteristic
31#485×C73—24no—
32#482×C73—24no—
33C2×#107×C73C2211yescharacteristic
34C2×#107×C73C2211yescharacteristic
35C2×#106×C73C2211yescharacteristic
36C2×#106×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#103×C73C2211yescharacteristic
40C2×#103×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
48C2×C22⋊C8×C73C2211yescharacteristic
49C2×C22⋊C8×C73C2211yescharacteristic
50C2×C22⋊C8×C73C2211yescharacteristic
51#391×C73—21no—
52#390×C73—21no—
53#386×C73—21no—
54#386×C73—21no—
55#380×C73C2211yescharacteristic
56#380×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58#380×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63C2×#41×C73—22no—
64C2×#41×C73—22no—
65C2×#41×C73—22no—
66C2×#41×C73—22no—
67C2×#41×C73—22no—
68C2×#41×C73—22no—
69C2×#41×C73—22no—
70C2×#41×C73—22no—
71C2×#41×C73—41no—
72C2×#41×C73—41no—
73C2×#41×C73—41no—
74C2×#41×C73—41no—
75C22×Q8×C73D411yescharacteristic
76C22×Q8×C73C2311yescharacteristic
77C22×D4×C73—21no—
78C22×D4×C73—21no—
79C22×D4×C73—21no—
80C22×D4×C73D411yescharacteristic
81C22×D4×C73D411yescharacteristic
82C22×D4×C73D411yescharacteristic
83C22×D4×C73C2311yescharacteristic
84C23×C4×C73—21no—
85C23×C4×C73—21no—
86C23×C4×C73—21no—
87C23×C4×C73C2311yescharacteristic
88C23×C4×C73C2311yescharacteristic
89C23×C4×C73C2311yescharacteristic
90C22×C8×C73C2311yescharacteristic
91C22×C8×C73C2311yescharacteristic
92C22×C8×C73C2311yescharacteristic
93C22×C8×C73C2311yescharacteristic
94C22⋊Q8×C73—28no—
95C22⋊Q8×C73—22no—
96C22⋊Q8×C73—22no—
97C22⋊Q8×C73—22no—
98C22⋊Q8×C73D414yes—
99#121×C73—28no—
100#121×C73—28no—
101#121×C73—28no—
102#121×C73—22no—
103#121×C73—22no—
104#121×C73—22no—
105#121×C73D414yes—
106#117×C73—22no—
107#117×C73—22no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73—22no—
112C2×C4⋊C4×C73—22no—
113C2×C4⋊C4×C73—21no—
114C2×C4⋊C4×C73—41no—
115C2×C4⋊C4×C73—41no—
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C4⋊C4×C73C2311yescharacteristic
120C2×C4⋊C4×C73C2311yescharacteristic
121C2×C4⋊C4×C73C2311yescharacteristic
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×C22⋊C4×C73—21no—
131C2×C42×C73—21no—
132#107×C73—22no—
133#107×C73—22no—
134#106×C73—22no—
135#106×C73—22no—
136#103×C73—22no—
137#103×C73—22no—
138#103×C73—41no—
139#103×C73—41no—
140#102×C73—22no—
141#102×C73—22no—
142#102×C73—41no—
143#102×C73—41no—
144C22⋊C8×C73—22no—
145C22⋊C8×C73—22no—
146C22⋊C8×C73—22no—
147C22⋊C8×C73—22no—
148C22⋊C8×C73—41no—
149C22⋊C8×C73—41no—
150#95×C73—21no—
151#95×C73—21no—
152#95×C73—21no—
153#95×C73—21no—
154C24×C73—21no—
155C24×C73C2×D411yescharacteristic
156C24×C73C2×D411yescharacteristic
157C24×C73C2×D411yescharacteristic
158#41×C73—44no—
159#41×C73—44no—
160#41×C73—44no—
161#41×C73—44no—
162#41×C73—44no—
163#41×C73—44no—
164#41×C73—44no—
165#41×C73—44no—
166C2×Q8×C73—22no—
167C2×Q8×C73—22no—
168C2×Q8×C73—21no—
169C2×Q8×C73—21no—
170C2×Q8×C73—21no—
171C2×Q8×C73—21no—
172C2×Q8×C73—21no—
173C2×Q8×C73—41no—
174C2×Q8×C73C2×D412yes—
175C2×D4×C73—24no—
176C2×D4×C73—22no—
177C2×D4×C73—22no—
178C2×D4×C73—22no—
179C2×D4×C73—22no—
180C2×D4×C73—24no—
181C2×D4×C73—24no—
182C2×D4×C73—22no—
183C2×D4×C73—22no—
184C2×D4×C73—21no—
185C2×D4×C73—21no—
186C2×D4×C73—21no—
187C2×D4×C73—21no—
188C2×D4×C73—21no—
189C2×D4×C73—41no—
190C2×D4×C73—41no—
191C2×D4×C73—41no—
192C2×D4×C73—42no—
193C2×D4×C73—42no—
194C2×D4×C73—81no—
195C2×D4×C73—81no—
196C2×D4×C73—81no—
197C2×D4×C73—81no—
198C2×D4×C73C2×D412yes—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—24no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—24no—
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—21no—
221C22×C4×C73—21no—
222C22×C4×C73—42no—
223C22×C4×C73—42no—
224C22×C4×C73—42no—
225C22×C4×C73—81no—
226C22×C4×C73—81no—
227C22×C4×C73—81no—
228C22×C4×C73—81no—
229C22×C4×C73C2×D411yescharacteristic
230C22×C4×C73C2×D411yescharacteristic
231C22×C4×C73C2×D412yes—
232C22×C4×C73C2×D412yes—
233C22×C4×C73C2×D411yescharacteristic
234C22×C4×C73#4112yes—
235C22×C4×C73#4112yes—
236C22×C4×C73C2411yescharacteristic
237C2×C8×C73—21no—
238C2×C8×C73—21no—
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—
249C4⋊C4×C73—24no—
250C4⋊C4×C73—24no—
251C4⋊C4×C73—24no—
252C4⋊C4×C73—21no—
253C4⋊C4×C73—21no—
254C4⋊C4×C73—21no—
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—
265C22⋊C4×C73—24no—
266C22⋊C4×C73—24no—
267C22⋊C4×C73—24no—
268C22⋊C4×C73—24no—
269C22⋊C4×C73—42no—
270C22⋊C4×C73—81no—
271C22⋊C4×C73—81no—
272C22⋊C4×C73—81no—
273C22⋊C4×C73—81no—
274C42×C73—42no—
275C23×C73—21no—
276C23×C73—21no—
277C23×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—22no—
289C23×C73—21no—
290C23×C73—21no—
291C23×C73—21no—
292C23×C73—21no—
293C23×C73—21no—
294C23×C73—21no—
295C23×C73—41no—
296C23×C73—41no—
297C23×C73—41no—
298C23×C73—41no—
299C23×C73—41no—
300C23×C73—41no—
301C23×C73#12012yes—
302C23×C73#12312yes—
303C23×C73C22×D411yescharacteristic
304Q8×C73—22no—
305Q8×C73—22no—
306Q8×C73—44no—
307Q8×C73—41no—
308Q8×C73—41no—
309D4×C73—22no—
310D4×C73—22no—
311D4×C73—44no—
312D4×C73—44no—
313D4×C73—44no—
314D4×C73—48no—
315D4×C73—41no—
316D4×C73—41no—
317D4×C73—84no—
318D4×C73—84no—
319C2×C4×C73—21no—
320C2×C4×C73—21no—
321C2×C4×C73—21no—
322C2×C4×C73—21no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—22no—
326C2×C4×C73—22no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—22no—
332C2×C4×C73—22no—
333C2×C4×C73—22no—
334C2×C4×C73—21no—
335C2×C4×C73—21no—
336C2×C4×C73—21no—
337C2×C4×C73—48no—
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—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—84no—
361C2×C4×C73—84no—
362C2×C4×C73#12012yes—
363C2×C4×C73#12312yes—
364C2×C4×C73C22×D411yescharacteristic
365C2×C4×C73C22×D411yescharacteristic
366C2×C4×C73C2×#4111yescharacteristic
367C2×C4×C73C2×#4111yescharacteristic
368C2×C4×C73H(5,𝔽2)11yescharacteristic
369C2×C4×C73H(5,𝔽2)11yescharacteristic
370C8×C73—41no—
371C8×C73—41no—
372C8×C73—41no—
373C8×C73—41no—
374C22×C73—22no—
375C22×C73—22no—
376C22×C73—22no—
377C22×C73—22no—
378C22×C73—22no—
379C22×C73—22no—
380C22×C73—41no—
381C22×C73—41no—
382C22×C73—41no—
383C22×C73—41no—
384C22×C73—41no—
385C22×C73—41no—
386C22×C73—41no—
387C22×C73—41no—
388C22×C73—41no—
389C22×C73—41no—
390C22×C73—42no—
391C22×C73—41no—
392C22×C73—41no—
393C22×C73—41no—
394C22×C73—41no—
395C22×C73—42no—
396C22×C73—41no—
397C22×C73—42no—
398C22×C73—81no—
399C22×C73—81no—
400C22×C73—81no—
401C22×C73—81no—
402C22×C73C2×#12011yescharacteristic
403C22×C73C2×#12311yescharacteristic
404C22×C73#53411yescharacteristic
405C22×C73#57611yescharacteristic
406C22×C73#57711yescharacteristic
407C22×C73#57711yescharacteristic
408C22×C73#57811yescharacteristic
409C4×C73—22no—
410C4×C73—22no—
411C4×C73—41no—
412C4×C73—42no—
413C4×C73—42no—
414C4×C73—42no—
415C4×C73—81no—
416C4×C73—81no—
417C4×C73—81no—
418C4×C73—81no—
419C4×C73#54611yescharacteristic
420C4×C73#54611yescharacteristic
421C4×C73#54611yescharacteristic
422C4×C73#54611yescharacteristic
423#24017C7311yesmaximal, characteristic, direct product factor, Sylow
424C2×C73—42no—
425C2×C73—42no—
426C2×C73—81no—
427C2×C73—82no—
428C2×C73#240511yescharacteristic
429C2×C73#301211yescharacteristic
430C2×C73#301311yescharacteristic
431C2×C73#309811yescharacteristic
432C2×C73#309911yescharacteristic
433C2×C73#319811yescharacteristic
434C2×C73#320111yescharacteristic
435C2×#537C2×C7311yescharacteristic
436C2×#485C2×C7311yescharacteristic, complemented
437C2×#482C2×C7311yescharacteristic, complemented
438#2311C2×C7311yescharacteristic, complemented
439#2036C2×C7311yescharacteristic, complemented
440#2035C2×C7311yescharacteristic, complemented
441#2034C2×C7311yescharacteristic, complemented
442#2033C2×C7311yescharacteristic, complemented
443#1874C2×C7311yescharacteristic, complemented
444#1872C2×C7311yescharacteristic, complemented
445#1853C2×C7311yescharacteristic, complemented
446#1852C2×C7311yescharacteristic, complemented
447#1788C2×C7311yescharacteristic, complemented
448#1788C2×C7311yescharacteristic, complemented
449#1780C2×C7311yescharacteristic, complemented
450C73#2401711yescharacteristic, direct product factor, Sylow
451C22×#41C22×C7311yescharacteristic
452C22×#41C22×C7311yescharacteristic
453#537—24no—
454#537—24no—
455C2×C22⋊Q8—21no—
456C2×C22⋊Q8C22×C7311yescharacteristic
457C2×C22⋊Q8C22×C7311yescharacteristic
458C2×#121—21no—
459C2×#121—21no—
460C2×#121—21no—
461C2×#121C22×C7311yescharacteristic
462C2×#121C22×C7311yescharacteristic
463C2×#117C22×C7311yescharacteristic
464C22×C4⋊C4C22×C7311yescharacteristic
465C22×C4⋊C4C22×C7311yescharacteristic
466#485—24no—
467#482—24no—
468C2×#107C22×C7311yescharacteristic
469C2×#107C22×C7311yescharacteristic
470C2×#106C22×C7311yescharacteristic
471C2×#106C22×C7311yescharacteristic
472C2×#103C22×C7311yescharacteristic
473C2×#103C22×C7311yescharacteristic
474C2×#103C22×C7311yescharacteristic
475C2×#103C22×C7311yescharacteristic
476C2×#102C22×C7311yescharacteristic
477C2×#102C22×C7311yescharacteristic
478C2×#102C22×C7311yescharacteristic
479C2×#102C22×C7311yescharacteristic
480C2×C22⋊C8C22×C7311yescharacteristic
481C2×C22⋊C8C22×C7311yescharacteristic
482C2×C22⋊C8C22×C7311yescharacteristic
483C2×C22⋊C8C22×C7311yescharacteristic
484C2×C22⋊C8C22×C7311yescharacteristic
485C2×C22⋊C8C22×C7311yescharacteristic
486#391—21no—
487#390—21no—
488#386—21no—
489#386—21no—
490#380C22×C7311yescharacteristic
491#380C22×C7311yescharacteristic
492#380C22×C7311yescharacteristic
493#380C22×C7311yescharacteristic
494#340C22×C7311yescharacteristic
495#340C22×C7311yescharacteristic
496#340C22×C7311yescharacteristic
497#340C22×C7311yescharacteristic
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8D4×C7311yescharacteristic
511C22×Q8C23×C7311yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C7311yescharacteristic
516C22×D4D4×C7311yescharacteristic
517C22×D4D4×C7311yescharacteristic
518C22×D4C23×C7311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C7311yescharacteristic
523C23×C4C23×C7311yescharacteristic
524C23×C4C23×C7311yescharacteristic
525C22×C8C23×C7311yescharacteristic
526C22×C8C23×C7311yescharacteristic
527C22×C8C23×C7311yescharacteristic
528C22×C8C23×C7311yescharacteristic
529C22⋊Q8—28no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8D4×C7314yes—
534#121—28no—
535#121—28no—
536#121—28no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121D4×C7314yes—
541#117—22no—
542#117—22no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4C23×C7311yescharacteristic
552C2×C4⋊C4C23×C7311yescharacteristic
553C2×C4⋊C4C23×C7311yescharacteristic
554C2×C4⋊C4C23×C7311yescharacteristic
555C2×C4⋊C4C23×C7311yescharacteristic
556C2×C4⋊C4C23×C7311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C42—21no—
567#107—22no—
568#107—22no—
569#106—22no—
570#106—22no—
571#103—22no—
572#103—22no—
573#103—41no—
574#103—41no—
575#102—22no—
576#102—22no—
577#102—41no—
578#102—41no—
579C22⋊C8—22no—
580C22⋊C8—22no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—41no—
584C22⋊C8—41no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24C2×D4×C7311yescharacteristic
591C24C2×D4×C7311yescharacteristic
592C24C2×D4×C7311yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—41no—
609C2×Q8C2×D4×C7312yes—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4C2×D4×C7312yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
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—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4—81no—
664C22×C4C2×D4×C7311yescharacteristic
665C22×C4C2×D4×C7311yescharacteristic
666C22×C4C2×D4×C7312yes—
667C22×C4C2×D4×C7312yes—
668C22×C4C2×D4×C7311yescharacteristic
669C22×C4#41×C7312yes—
670C22×C4#41×C7312yes—
671C22×C4C24×C7311yescharacteristic
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—42no—
698C4⋊C4C2×D4×C7312yes—
699C4⋊C4C2×D4×C7312yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C42—42no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23#120×C7312yes—
737C23#123×C7312yes—
738C23C22×D4×C7311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—44no—
742Q8—41no—
743Q8—41no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—48no—
750D4—41no—
751D4—41no—
752D4—84no—
753D4—84no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
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—84no—
796C2×C4—84no—
797C2×C4#120×C7312yes—
798C2×C4#123×C7312yes—
799C2×C4C22×D4×C7311yescharacteristic
800C2×C4C22×D4×C7311yescharacteristic
801C2×C4C2×#41×C7311yescharacteristic
802C2×C4C2×#41×C7311yescharacteristic
803C2×C4H(5,𝔽2)×C7311yescharacteristic
804C2×C4H(5,𝔽2)×C7311yescharacteristic
805C8—41no—
806C8—41no—
807C8—41no—
808C8—41no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—41no—
826C22—42no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22C2×#120×C7311yescharacteristic
838C22C2×#123×C7311yescharacteristic
839C22#534×C7311yescharacteristic
840C22#576×C7311yescharacteristic
841C22#577×C7311yescharacteristic
842C22#577×C7311yescharacteristic
843C22#578×C7311yescharacteristic
844C4—22no—
845C4—22no—
846C4—42no—
847C4—42no—
848C4—41no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4#546×C7311yescharacteristic
855C4#546×C7311yescharacteristic
856C4#546×C7311yescharacteristic
857C4#546×C7311yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—82no—
862C2C73×#240511yescharacteristic
863C2C73×#301211yescharacteristic
864C2C73×#301311yescharacteristic
865C2C73×#309811yescharacteristic
866C2C73×#309911yescharacteristic
867C2C73×#319811yescharacteristic
868C2C73×#320111yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#537×C73C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C22×#41×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#485×C73C2semidirect
3. C2×#482×C73C2semidirect
4. C73×#2311C2semidirect
5. C73×#2036C2semidirect
6. C73×#2035C2semidirect
7. C73×#2034C2semidirect
8. C73×#2033C2semidirect
9. C73×#1874C2semidirect
10. C73×#1872C2semidirect
11. C73×#1853C2semidirect
12. C73×#1852C2semidirect
13. C73×#1788C2semidirect
14. C73×#1788C2semidirect
15. C73×#1780C2semidirect
423. #24017C73direct (N × H)
436. C2×#485C2×C73semidirect
437. C2×#482C2×C73semidirect
438. #2311C2×C73semidirect
439. #2036C2×C73semidirect
440. #2035C2×C73semidirect
441. #2034C2×C73semidirect
442. #2033C2×C73semidirect
443. #1874C2×C73semidirect
444. #1872C2×C73semidirect
445. #1853C2×C73semidirect
446. #1852C2×C73semidirect
447. #1788C2×C73semidirect
448. #1788C2×C73semidirect
449. #1780C2×C73semidirect
450. C73#24017direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#537×C732
C2×#485×C732
C2×#482×C732
C73×#23112
C73×#20362
C73×#20352
C73×#20342
C73×#20332
C73×#18742
C73×#18722
C73×#18532
C73×#18522
C73×#17882
C73×#17802
#2401773