Finite Group Databasebeta

← C73×#25890 #32935294

Subgroups — C73×#25890 #32935294

Order 18688.

1432 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C73C211yesmaximal, characteristic
2C2×#488×C73C211yesmaximal, characteristic, complemented
3C2×#478×C73C211yesmaximal, characteristic, complemented
4C73×#2562C211yesmaximal, characteristic, complemented
5C73×#2036C211yesmaximal, characteristic, complemented
6C73×#2035C211yesmaximal, characteristic, complemented
7C73×#2034C211yesmaximal, characteristic, complemented
8C73×#2033C211yesmaximal, characteristic, complemented
9C73×#1983C211yesmaximal, characteristic, complemented
10C73×#1954C211yesmaximal, characteristic, complemented
11C73×#1788C211yesmaximal, characteristic, complemented
12C73×#1788C211yesmaximal, characteristic, complemented
13C73×#1786C211yesmaximal, characteristic, complemented
14C73×#1786C211yesmaximal, characteristic, complemented
15C4×#102×C73C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C23×D4×C73C2211yescharacteristic
18#546×C73—24no—
19#546×C73—24no—
20C2×#125×C73C2211yescharacteristic, complemented
21C2×#124×C73C2211yescharacteristic
22C2×#123×C73—21no—
23C2×C22⋊Q8×C73C2211yescharacteristic
24C2×#121×C73—21no—
25C2×#121×C73C2211yescharacteristic
26C2×#120×C73—21no—
27C2×C4×D4×C73C2211yescharacteristic
28C2×C4×D4×C73C2211yescharacteristic
29C22×C22⋊C4×C73—21no—
30#488×C73—24no—
31#478×C73—24no—
32C2×#107×C73C2211yescharacteristic, complemented
33C2×#106×C73C2211yescharacteristic, complemented
34C2×C4⋊C8×C73C2211yescharacteristic, complemented
35C2×#103×C73C2211yescharacteristic, complemented
36C2×#103×C73C2211yescharacteristic, complemented
37C2×#103×C73C2211yescharacteristic, complemented
38C2×#103×C73C2211yescharacteristic, complemented
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44C2×#102×C73C2211yescharacteristic
45C2×#102×C73C2211yescharacteristic
46C2×#102×C73C2211yescharacteristic
47C2×C22⋊C8×C73C2211yescharacteristic
48C2×C22⋊C8×C73C2211yescharacteristic
49C2×C22⋊C8×C73C2211yescharacteristic, complemented
50C2×C22⋊C8×C73C2211yescharacteristic, complemented
51C2×C4×C8×C73C2211yescharacteristic, complemented
52#400×C73—21no—
53#394×C73—21no—
54#388×C73—21no—
55#388×C73—21no—
56#380×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58#380×C73C2211yescharacteristic, complemented
59#380×C73C2211yescharacteristic, complemented
60C4×C4⋊C4×C73C2211yescharacteristic, complemented
61#340×C73C2211yescharacteristic, complemented
62#340×C73C2211yescharacteristic, complemented
63C25×C73—21no—
64C2×#41×C73—22no—
65C2×#41×C73—22no—
66C2×#41×C73—22no—
67C2×#41×C73—22no—
68C2×#41×C73—41no—
69C2×#41×C73—41no—
70C22×Q8×C73C2311yescharacteristic
71C22×D4×C73—21no—
72C22×D4×C73—21no—
73C22×D4×C73—22no—
74C22×D4×C73—22no—
75C22×D4×C73—22no—
76C22×D4×C73—22no—
77C22×D4×C73—21no—
78C22×D4×C73—41no—
79C22×D4×C73—41no—
80C22×D4×C73D411yescharacteristic
81C22×D4×C73C2311yescharacteristic
82C22×D4×C73C2311yescharacteristic
83C23×C4×C73—21no—
84C23×C4×C73—21no—
85C23×C4×C73C2311yescharacteristic
86C23×C4×C73C2311yescharacteristic
87C22×C8×C73C2311yescharacteristic
88C22×C8×C73C2311yescharacteristic
89C22×C8×C73C2311yescharacteristic
90C22×C8×C73C2311yescharacteristic
91#125×C73—22no—
92#125×C73—22no—
93#124×C73—22no—
94#124×C73D414yes—
95#123×C73—28no—
96C22⋊Q8×C73—22no—
97C22⋊Q8×C73—22no—
98#121×C73—28no—
99#121×C73—22no—
100#121×C73—22no—
101#120×C73—28no—
102C4×D4×C73—22no—
103C4×D4×C73—22no—
104C4×D4×C73—22no—
105C4×D4×C73D414yes—
106C2×C4⋊C4×C73—21no—
107C2×C4⋊C4×C73—21no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73D411yescharacteristic
110C2×C4⋊C4×C73C2311yescharacteristic
111C2×C4⋊C4×C73C2311yescharacteristic
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C22⋊C4×C73—28no—
116C2×C22⋊C4×C73—21no—
117C2×C22⋊C4×C73—21no—
118C2×C22⋊C4×C73—21no—
119C2×C22⋊C4×C73—21no—
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×C73D411yescharacteristic
126C2×C22⋊C4×C73D411yescharacteristic
127C2×C42×C73—21no—
128C2×C42×C73C2311yescharacteristic
129#107×C73—22no—
130#106×C73—22no—
131C4⋊C8×C73—22no—
132#103×C73—22no—
133#103×C73—22no—
134#103×C73—41no—
135#103×C73—41no—
136#102×C73—22no—
137#102×C73—22no—
138#102×C73—22no—
139#102×C73—22no—
140#102×C73—22no—
141#102×C73—22no—
142#102×C73—41no—
143#102×C73—41no—
144C22⋊C8×C73—41no—
145C22⋊C8×C73—41no—
146C22⋊C8×C73—41no—
147C22⋊C8×C73—41no—
148C4×C8×C73—22no—
149#95×C73—21no—
150#95×C73—21no—
151#95×C73—21no—
152#95×C73—21no—
153#95×C73—21no—
154C24×C73—21no—
155C24×C73—24no—
156C24×C73—21no—
157C24×C73—42no—
158C24×C73—42no—
159C24×C73—42no—
160C24×C73—42no—
161C24×C73—81no—
162C24×C73—81no—
163C24×C73C2×D411yescharacteristic
164C24×C73C2×D411yescharacteristic
165#41×C73—44no—
166#41×C73—44no—
167#41×C73—44no—
168#41×C73—44no—
169C2×Q8×C73—21no—
170C2×Q8×C73—21no—
171C2×Q8×C73—21no—
172C2×Q8×C73—21no—
173C2×Q8×C73—21no—
174C2×Q8×C73C2×D412yes—
175C2×D4×C73—24no—
176C2×D4×C73—24no—
177C2×D4×C73—22no—
178C2×D4×C73—24no—
179C2×D4×C73—22no—
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—41no—
189C2×D4×C73—42no—
190C2×D4×C73—42no—
191C2×D4×C73—44no—
192C2×D4×C73—44no—
193C2×D4×C73—44no—
194C2×D4×C73—42no—
195C2×D4×C73—42no—
196C2×D4×C73—44no—
197C2×D4×C73—81no—
198C2×D4×C73—81no—
199C2×D4×C73C2×D412yes—
200C2×D4×C73C2×D412yes—
201C2×D4×C73#4112yes—
202C2×D4×C73#4112yes—
203C22×C4×C73—24no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
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—24no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—42no—
224C22×C4×C73—42no—
225C22×C4×C73—81no—
226C22×C4×C73—81no—
227C22×C4×C73C2×D411yescharacteristic
228C22×C4×C73C2×D411yescharacteristic
229C22×C4×C73C2×D411yescharacteristic
230C22×C4×C73C2×D411yescharacteristic
231C22×C4×C73C2411yescharacteristic
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
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—
244C4⋊C4×C73—24no—
245C4⋊C4×C73—22no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73—21no—
248C4⋊C4×C73—21no—
249C4⋊C4×C73—21no—
250C4⋊C4×C73—21no—
251C4⋊C4×C73—21no—
252C4⋊C4×C73—21no—
253C4⋊C4×C73—21no—
254C4⋊C4×C73—21no—
255C4⋊C4×C73—42no—
256C4⋊C4×C73—42no—
257C4⋊C4×C73C2×D412yes—
258C22⋊C4×C73—24no—
259C22⋊C4×C73—24no—
260C22⋊C4×C73—22no—
261C22⋊C4×C73—24no—
262C22⋊C4×C73—24no—
263C22⋊C4×C73—24no—
264C22⋊C4×C73—22no—
265C22⋊C4×C73—42no—
266C22⋊C4×C73—42no—
267C22⋊C4×C73—81no—
268C22⋊C4×C73—81no—
269C42×C73—81no—
270C42×C73C2×D412yes—
271C42×C73C2×D412yes—
272C23×C73—21no—
273C23×C73—22no—
274C23×C73—21no—
275C23×C73—21no—
276C23×C73—22no—
277C23×C73—22no—
278C23×C73—21no—
279C23×C73—21no—
280C23×C73—21no—
281C23×C73—22no—
282C23×C73—21no—
283C23×C73—21no—
284C23×C73—21no—
285C23×C73—21no—
286C23×C73—21no—
287C23×C73—21no—
288C23×C73—21no—
289C23×C73—48no—
290C23×C73—48no—
291C23×C73—41no—
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—84no—
302C23×C73—84no—
303C23×C73—84no—
304C23×C73—84no—
305C23×C73—84no—
306C23×C73#13512yes—
307C23×C73C22×D411yescharacteristic
308Q8×C73—22no—
309Q8×C73—22no—
310Q8×C73—41no—
311Q8×C73—41no—
312D4×C73—22no—
313D4×C73—22no—
314D4×C73—22no—
315D4×C73—22no—
316D4×C73—22no—
317D4×C73—44no—
318D4×C73—48no—
319D4×C73—48no—
320D4×C73—41no—
321D4×C73—41no—
322D4×C73—84no—
323D4×C73#12414yes—
324C2×C4×C73—21no—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
327C2×C4×C73—21no—
328C2×C4×C73—22no—
329C2×C4×C73—21no—
330C2×C4×C73—22no—
331C2×C4×C73—21no—
332C2×C4×C73—21no—
333C2×C4×C73—21no—
334C2×C4×C73—21no—
335C2×C4×C73—21no—
336C2×C4×C73—48no—
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—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—84no—
362C2×C4×C73#12012yes—
363C2×C4×C73#12012yes—
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—24no—
375C22×C73—22no—
376C22×C73—22no—
377C22×C73—22no—
378C22×C73—41no—
379C22×C73—42no—
380C22×C73—42no—
381C22×C73—41no—
382C22×C73—42no—
383C22×C73—42no—
384C22×C73—41no—
385C22×C73—42no—
386C22×C73—41no—
387C22×C73—42no—
388C22×C73—41no—
389C22×C73—42no—
390C22×C73—41no—
391C22×C73—42no—
392C22×C73—41no—
393C22×C73—42no—
394C22×C73—41no—
395C22×C73—41no—
396C22×C73—41no—
397C22×C73—41no—
398C22×C73—816no—
399C22×C73—81no—
400C22×C73—81no—
401C22×C73—81no—
402C22×C73—81no—
403C22×C73C2×#12011yescharacteristic
404C22×C73#54611yescharacteristic
405C22×C73#54611yescharacteristic
406C22×C73C2×#13511yescharacteristic
407C22×C73#57511yescharacteristic
408C22×C73#57611yescharacteristic
409C22×C73#57711yescharacteristic
410C4×C73—22no—
411C4×C73—22no—
412C4×C73—41no—
413C4×C73—41no—
414C4×C73—42no—
415C4×C73—42no—
416C4×C73—81no—
417C4×C73—81no—
418C4×C73—81no—
419C4×C73—81no—
420C4×C73C2×#12411yescharacteristic
421C4×C73#53511yescharacteristic
422C4×C73#54611yescharacteristic
423C4×C73#54611yescharacteristic
424#25890C7311yesmaximal, characteristic, direct product factor, Sylow
425C2×C73—42no—
426C2×C73—44no—
427C2×C73—81no—
428C2×C73—82no—
429C2×C73#243511yescharacteristic
430C2×C73#300211yescharacteristic
431C2×C73#301211yescharacteristic
432C2×C73#329611yescharacteristic
433C2×C73#329711yescharacteristic
434C2×C73#332211yescharacteristic
435C2×C73#332311yescharacteristic
436C2×#546C2×C7311yescharacteristic
437C2×#488C2×C7311yescharacteristic, complemented
438C2×#478C2×C7311yescharacteristic, complemented
439#2562C2×C7311yescharacteristic, complemented
440#2036C2×C7311yescharacteristic, complemented
441#2035C2×C7311yescharacteristic, complemented
442#2034C2×C7311yescharacteristic, complemented
443#2033C2×C7311yescharacteristic, complemented
444#1983C2×C7311yescharacteristic, complemented
445#1954C2×C7311yescharacteristic, complemented
446#1788C2×C7311yescharacteristic, complemented
447#1788C2×C7311yescharacteristic, complemented
448#1786C2×C7311yescharacteristic, complemented
449#1786C2×C7311yescharacteristic, complemented
450C4×#102C2×C7311yescharacteristic, complemented
451C73#2589011yescharacteristic, direct product factor, Sylow
452C22×#41C22×C7311yescharacteristic
453C23×D4C22×C7311yescharacteristic
454#546—24no—
455#546—24no—
456C2×#125C22×C7311yescharacteristic, complemented
457C2×#124C22×C7311yescharacteristic
458C2×#123—21no—
459C2×C22⋊Q8C22×C7311yescharacteristic
460C2×#121—21no—
461C2×#121C22×C7311yescharacteristic
462C2×#120—21no—
463C2×C4×D4C22×C7311yescharacteristic
464C2×C4×D4C22×C7311yescharacteristic
465C22×C22⋊C4—21no—
466#488—24no—
467#478—24no—
468C2×#107C22×C7311yescharacteristic, complemented
469C2×#106C22×C7311yescharacteristic, complemented
470C2×C4⋊C8C22×C7311yescharacteristic, complemented
471C2×#103C22×C7311yescharacteristic, complemented
472C2×#103C22×C7311yescharacteristic, complemented
473C2×#103C22×C7311yescharacteristic, complemented
474C2×#103C22×C7311yescharacteristic, complemented
475C2×#102C22×C7311yescharacteristic
476C2×#102C22×C7311yescharacteristic
477C2×#102C22×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, complemented
486C2×C22⋊C8C22×C7311yescharacteristic, complemented
487C2×C4×C8C22×C7311yescharacteristic, complemented
488#400—21no—
489#394—21no—
490#388—21no—
491#388—21no—
492#380C22×C7311yescharacteristic
493#380C22×C7311yescharacteristic
494#380C22×C7311yescharacteristic, complemented
495#380C22×C7311yescharacteristic, complemented
496C4×C4⋊C4C22×C7311yescharacteristic, complemented
497#340C22×C7311yescharacteristic, complemented
498#340C22×C7311yescharacteristic, complemented
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C23×C7311yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4D4×C7311yescharacteristic
517C22×D4C23×C7311yescharacteristic
518C22×D4C23×C7311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C23×C7311yescharacteristic
522C23×C4C23×C7311yescharacteristic
523C22×C8C23×C7311yescharacteristic
524C22×C8C23×C7311yescharacteristic
525C22×C8C23×C7311yescharacteristic
526C22×C8C23×C7311yescharacteristic
527#125—22no—
528#125—22no—
529#124—22no—
530#124D4×C7314yes—
531#123—28no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534#121—28no—
535#121—22no—
536#121—22no—
537#120—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4D4×C7314yes—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4D4×C7311yescharacteristic
546C2×C4⋊C4C23×C7311yescharacteristic
547C2×C4⋊C4C23×C7311yescharacteristic
548C2×C4⋊C4C23×C7311yescharacteristic
549C2×C4⋊C4C23×C7311yescharacteristic
550C2×C4⋊C4C23×C7311yescharacteristic
551C2×C22⋊C4—28no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4D4×C7311yescharacteristic
562C2×C22⋊C4D4×C7311yescharacteristic
563C2×C42—21no—
564C2×C42C23×C7311yescharacteristic
565#107—22no—
566#106—22no—
567C4⋊C8—22no—
568#103—22no—
569#103—22no—
570#103—41no—
571#103—41no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—41no—
579#102—41no—
580C22⋊C8—41no—
581C22⋊C8—41no—
582C22⋊C8—41no—
583C22⋊C8—41no—
584C4×C8—22no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590C24—21no—
591C24—24no—
592C24—21no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—81no—
598C24—81no—
599C24C2×D4×C7311yescharacteristic
600C24C2×D4×C7311yescharacteristic
601#41—44no—
602#41—44no—
603#41—44no—
604#41—44no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8C2×D4×C7312yes—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C7312yes—
636C2×D4C2×D4×C7312yes—
637C2×D4#41×C7312yes—
638C2×D4#41×C7312yes—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
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—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4C2×D4×C7311yescharacteristic
664C22×C4C2×D4×C7311yescharacteristic
665C22×C4C2×D4×C7311yescharacteristic
666C22×C4C2×D4×C7311yescharacteristic
667C22×C4C24×C7311yescharacteristic
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C4⋊C4—24no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4C2×D4×C7312yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C42—81no—
706C42C2×D4×C7312yes—
707C42C2×D4×C7312yes—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—48no—
726C23—48no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—84no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23#135×C7312yes—
743C23C22×D4×C7311yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—41no—
747Q8—41no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—44no—
754D4—48no—
755D4—48no—
756D4—41no—
757D4—41no—
758D4—84no—
759D4#124×C7314yes—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
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—41no—
796C2×C4—41no—
797C2×C4—84no—
798C2×C4#120×C7312yes—
799C2×C4#120×C7312yes—
800C2×C4C22×D4×C7311yescharacteristic
801C2×C4C22×D4×C7311yescharacteristic
802C2×C4C2×#41×C7311yescharacteristic
803C2×C4C2×#41×C7311yescharacteristic
804C2×C4H(5,𝔽2)×C7311yescharacteristic
805C2×C4H(5,𝔽2)×C7311yescharacteristic
806C8—41no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—24no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—41no—
820C22—42no—
821C22—41no—
822C22—42no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—42no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—816no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C2×#120×C7311yescharacteristic
840C22#546×C7311yescharacteristic
841C22#546×C7311yescharacteristic
842C22C2×#135×C7311yescharacteristic
843C22#575×C7311yescharacteristic
844C22#576×C7311yescharacteristic
845C22#577×C7311yescharacteristic
846C4—22no—
847C4—22no—
848C4—42no—
849C4—41no—
850C4—41no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4C2×#124×C7311yescharacteristic
857C4#535×C7311yescharacteristic
858C4#546×C7311yescharacteristic
859C4#546×C7311yescharacteristic
860C2—42no—
861C2—44no—
862C2—81no—
863C2—82no—
864C2C73×#243511yescharacteristic
865C2C73×#300211yescharacteristic
866C2C73×#301211yescharacteristic
867C2C73×#329611yescharacteristic
868C2C73×#329711yescharacteristic
869C2C73×#332211yescharacteristic
870C2C73×#332311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#546×C73C2
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
2. C2×#488×C73C2semidirect
3. C2×#478×C73C2semidirect
4. C73×#2562C2semidirect
5. C73×#2036C2semidirect
6. C73×#2035C2semidirect
7. C73×#2034C2semidirect
8. C73×#2033C2semidirect
9. C73×#1983C2semidirect
10. C73×#1954C2semidirect
11. C73×#1788C2semidirect
12. C73×#1788C2semidirect
13. C73×#1786C2semidirect
14. C73×#1786C2semidirect
15. C4×#102×C73C2semidirect
20. C2×#125×C73C22semidirect
32. C2×#107×C73C22semidirect
33. C2×#106×C73C22semidirect
34. C2×C4⋊C8×C73C22semidirect
35. C2×#103×C73C22semidirect
36. C2×#103×C73C22semidirect
37. C2×#103×C73C22semidirect
38. C2×#103×C73C22semidirect
49. C2×C22⋊C8×C73C22semidirect
50. C2×C22⋊C8×C73C22semidirect
51. C2×C4×C8×C73C22semidirect
58. #380×C73C22semidirect
59. #380×C73C22semidirect
60. C4×C4⋊C4×C73C22semidirect
61. #340×C73C22semidirect
62. #340×C73C22semidirect
424. #25890C73direct (N × H)
437. C2×#488C2×C73semidirect
438. C2×#478C2×C73semidirect
439. #2562C2×C73semidirect
440. #2036C2×C73semidirect
441. #2035C2×C73semidirect
442. #2034C2×C73semidirect
443. #2033C2×C73semidirect
444. #1983C2×C73semidirect
445. #1954C2×C73semidirect
446. #1788C2×C73semidirect
447. #1788C2×C73semidirect
448. #1786C2×C73semidirect
449. #1786C2×C73semidirect
450. C4×#102C2×C73semidirect
451. C73#25890direct (N × H)
456. C2×#125C22×C73semidirect
468. C2×#107C22×C73semidirect
469. C2×#106C22×C73semidirect
470. C2×C4⋊C8C22×C73semidirect
471. C2×#103C22×C73semidirect
472. C2×#103C22×C73semidirect
473. C2×#103C22×C73semidirect
474. C2×#103C22×C73semidirect
485. C2×C22⋊C8C22×C73semidirect
486. C2×C22⋊C8C22×C73semidirect
487. C2×C4×C8C22×C73semidirect
494. #380C22×C73semidirect
495. #380C22×C73semidirect
496. C4×C4⋊C4C22×C73semidirect
497. #340C22×C73semidirect
498. #340C22×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C732
C2×#488×C732
C2×#478×C732
C73×#25622
C73×#20362
C73×#20352
C73×#20342
C73×#20332
C73×#19832
C73×#19542
C73×#17882
C73×#17862
C4×#102×C732
#2589073