Finite Group Databasebeta

← C73×#24050 #32933454

Subgroups — C73×#24050 #32933454

Order 18688.

1450 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C73C211yesmaximal, characteristic
2C2×#485×C73C211yesmaximal, characteristic, complemented
3C2×#418×C73C211yesmaximal, characteristic, complemented
4C73×#2485C211yesmaximal, characteristic, complemented
5C73×#2042C211yesmaximal, characteristic, complemented
6C73×#2042C211yesmaximal, characteristic, complemented
7C73×#2034C211yesmaximal, characteristic, complemented
8C73×#2033C211yesmaximal, characteristic, complemented
9C73×#1894C211yesmaximal, characteristic, complemented
10C73×#1870C211yesmaximal, characteristic, complemented
11C73×#1864C211yesmaximal, characteristic, complemented
12C73×#1862C211yesmaximal, characteristic, complemented
13C73×#1788C211yesmaximal, characteristic, complemented
14C73×#1788C211yesmaximal, characteristic, complemented
15C73×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C23×D4×C73C2211yescharacteristic
18C22×M16×C73C2211yescharacteristic
19#546×C73—24no—
20#546×C73—24no—
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
29C2×#117×C73C2211yescharacteristic
30C22×C22⋊C4×C73—21no—
31#485×C73—24no—
32C2×#107×C73C2211yescharacteristic, complemented
33C2×#106×C73C2211yescharacteristic, complemented
34#418×C73—24no—
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, complemented
49C2×C22⋊C8×C73C2211yescharacteristic, complemented
50#397×C73—21no—
51#394×C73—21no—
52#389×C73C2211yescharacteristic, complemented
53#389×C73C2211yescharacteristic, complemented
54#388×C73—21no—
55#387×C73—21no—
56#380×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic, complemented
58#380×C73C2211yescharacteristic, complemented
59#340×C73C2211yescharacteristic, complemented
60#340×C73C2211yescharacteristic, complemented
61#336×C73C2211yescharacteristic, complemented
62#336×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—22no—
72C22×D4×C73—22no—
73C22×D4×C73—21no—
74C22×D4×C73—21no—
75C22×D4×C73—21no—
76C22×D4×C73—22no—
77C22×D4×C73—41no—
78C22×D4×C73—41no—
79C22×D4×C73D414yes—
80C22×D4×C73D411yescharacteristic
81C22×D4×C73C2311yescharacteristic
82C22×D4×C73C2311yescharacteristic
83C23×C4×C73—21no—
84C23×C4×C73—21no—
85C23×C4×C73C2311yescharacteristic
86C23×C4×C73C2311yescharacteristic
87C2×M16×C73—22no—
88C2×M16×C73—41no—
89C2×M16×C73—41no—
90C22×C8×C73C2311yescharacteristic
91C22×C8×C73C2311yescharacteristic
92C22×C8×C73C2311yescharacteristic
93C22×C8×C73C2311yescharacteristic
94#124×C73—22no—
95#124×C73—22no—
96#123×C73—28no—
97C22⋊Q8×C73—22no—
98C22⋊Q8×C73D414yes—
99#121×C73—28no—
100#121×C73—22no—
101#121×C73—22no—
102#120×C73—28no—
103C4×D4×C73—22no—
104C4×D4×C73—22no—
105C4×D4×C73—22no—
106C4×D4×C73—22no—
107#117×C73—22no—
108#117×C73—22no—
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73D411yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C22⋊C4×C73—28no—
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×C73—21no—
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73D411yescharacteristic
129C2×C22⋊C4×C73D411yescharacteristic
130C2×C42×C73—21no—
131C2×C42×C73C2311yescharacteristic
132#107×C73—22no—
133#106×C73—22no—
134#103×C73—22no—
135#103×C73—22no—
136#103×C73—41no—
137#103×C73—41no—
138#102×C73—22no—
139#102×C73—22no—
140#102×C73—22no—
141#102×C73—22no—
142#102×C73—22no—
143#102×C73—22no—
144#102×C73—41no—
145#102×C73—41no—
146C22⋊C8×C73—22no—
147C22⋊C8×C73—41no—
148C22⋊C8×C73—41no—
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—21no—
156C24×C73—24no—
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—28no—
176C2×D4×C73—24no—
177C2×D4×C73—22no—
178C2×D4×C73—24no—
179C2×D4×C73—24no—
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—44no—
189C2×D4×C73—44no—
190C2×D4×C73—44no—
191C2×D4×C73—41no—
192C2×D4×C73—41no—
193C2×D4×C73—42no—
194C2×D4×C73—42no—
195C2×D4×C73—42no—
196C2×D4×C73—42no—
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—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—24no—
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—21no—
221C22×C4×C73—42no—
222C22×C4×C73—42no—
223C22×C4×C73—81no—
224C22×C4×C73—81no—
225C22×C4×C73C2×D411yescharacteristic
226C22×C4×C73C2×D411yescharacteristic
227C22×C4×C73C2×D411yescharacteristic
228C22×C4×C73C2×D411yescharacteristic
229C22×C4×C73C2×D412yes—
230C22×C4×C73C2×D412yes—
231C22×C4×C73C2411yescharacteristic
232M16×C73—44no—
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—
244C2×C8×C73—21no—
245C4⋊C4×C73—24no—
246C4⋊C4×C73—22no—
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—21no—
256C4⋊C4×C73—42no—
257C4⋊C4×C73—81no—
258C4⋊C4×C73C2×D412yes—
259C22⋊C4×C73—24no—
260C22⋊C4×C73—24no—
261C22⋊C4×C73—24no—
262C22⋊C4×C73—24no—
263C22⋊C4×C73—22no—
264C22⋊C4×C73—24no—
265C22⋊C4×C73—22no—
266C22⋊C4×C73—42no—
267C22⋊C4×C73—42no—
268C22⋊C4×C73—81no—
269C22⋊C4×C73—81no—
270C42×C73—21no—
271C42×C73—21no—
272C42×C73—42no—
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—21no—
282C23×C73—22no—
283C23×C73—21no—
284C23×C73—21no—
285C23×C73—21no—
286C23×C73—21no—
287C23×C73—21no—
288C23×C73—21no—
289C23×C73—21no—
290C23×C73—48no—
291C23×C73—48no—
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—84no—
303C23×C73—84no—
304C23×C73—84no—
305C23×C73—84no—
306C23×C73—84no—
307C23×C73#12012yes—
308C23×C73C22×D411yescharacteristic
309Q8×C73—22no—
310Q8×C73—22no—
311Q8×C73—41no—
312Q8×C73—41no—
313D4×C73—22no—
314D4×C73—22no—
315D4×C73—22no—
316D4×C73—22no—
317D4×C73—22no—
318D4×C73—48no—
319D4×C73—44no—
320D4×C73—48no—
321D4×C73—41no—
322D4×C73—41no—
323D4×C73—84no—
324D4×C73#12314yes—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—21no—
332C2×C4×C73—21no—
333C2×C4×C73—22no—
334C2×C4×C73—21no—
335C2×C4×C73—22no—
336C2×C4×C73—21no—
337C2×C4×C73—21no—
338C2×C4×C73—21no—
339C2×C4×C73—21no—
340C2×C4×C73—21no—
341C2×C4×C73—21no—
342C2×C4×C73—48no—
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—41no—
362C2×C4×C73—41no—
363C2×C4×C73—84no—
364C2×C4×C73#12012yes—
365C2×C4×C73C22×D411yescharacteristic
366C2×C4×C73C22×D411yescharacteristic
367C2×C4×C73C2×#4111yescharacteristic
368C2×C4×C73C2×#4111yescharacteristic
369C2×C4×C73H(5,𝔽2)11yescharacteristic
370C2×C4×C73H(5,𝔽2)11yescharacteristic
371C8×C73—41no—
372C8×C73—41no—
373C8×C73—41no—
374C8×C73—41no—
375C22×C73—22no—
376C22×C73—24no—
377C22×C73—22no—
378C22×C73—22no—
379C22×C73—42no—
380C22×C73—42no—
381C22×C73—41no—
382C22×C73—42no—
383C22×C73—41no—
384C22×C73—42no—
385C22×C73—41no—
386C22×C73—42no—
387C22×C73—41no—
388C22×C73—42no—
389C22×C73—41no—
390C22×C73—42no—
391C22×C73—41no—
392C22×C73—42no—
393C22×C73—41no—
394C22×C73—42no—
395C22×C73—41no—
396C22×C73—41no—
397C22×C73—41no—
398C22×C73—41no—
399C22×C73—816no—
400C22×C73—81no—
401C22×C73—81no—
402C22×C73—81no—
403C22×C73—81no—
404C22×C73C2×#12011yescharacteristic
405C22×C73#54611yescharacteristic
406C22×C73#54611yescharacteristic
407C22×C73#57511yescharacteristic
408C22×C73#57511yescharacteristic
409C22×C73#57611yescharacteristic
410C22×C73#57711yescharacteristic
411C4×C73—22no—
412C4×C73—41no—
413C4×C73—42no—
414C4×C73—41no—
415C4×C73—41no—
416C4×C73—42no—
417C4×C73—81no—
418C4×C73—81no—
419C4×C73—81no—
420C4×C73—81no—
421C4×C73C2×#12311yescharacteristic
422C4×C73#53411yescharacteristic
423C4×C73#54611yescharacteristic
424C4×C73#54611yescharacteristic
425#24050C7311yesmaximal, characteristic, direct product factor, Sylow
426C2×C73—42no—
427C2×C73—44no—
428C2×C73—81no—
429C2×C73—82no—
430C2×C73#240511yescharacteristic
431C2×C73#300511yescharacteristic
432C2×C73#301211yescharacteristic
433C2×C73#331111yescharacteristic
434C2×C73#331911yescharacteristic
435C2×C73#332211yescharacteristic
436C2×C73#332311yescharacteristic
437C2×#546C2×C7311yescharacteristic
438C2×#485C2×C7311yescharacteristic, complemented
439C2×#418C2×C7311yescharacteristic, complemented
440#2485C2×C7311yescharacteristic, complemented
441#2042C2×C7311yescharacteristic, complemented
442#2042C2×C7311yescharacteristic, complemented
443#2034C2×C7311yescharacteristic, complemented
444#2033C2×C7311yescharacteristic, complemented
445#1894C2×C7311yescharacteristic, complemented
446#1870C2×C7311yescharacteristic, complemented
447#1864C2×C7311yescharacteristic, complemented
448#1862C2×C7311yescharacteristic, complemented
449#1788C2×C7311yescharacteristic, complemented
450#1788C2×C7311yescharacteristic, complemented
451#1786C2×C7311yescharacteristic, complemented
452C73#2405011yescharacteristic, direct product factor, Sylow
453C22×#41C22×C7311yescharacteristic
454C23×D4C22×C7311yescharacteristic
455C22×M16C22×C7311yescharacteristic
456#546—24no—
457#546—24no—
458C2×#124C22×C7311yescharacteristic
459C2×#123—21no—
460C2×C22⋊Q8C22×C7311yescharacteristic
461C2×#121—21no—
462C2×#121C22×C7311yescharacteristic
463C2×#120—21no—
464C2×C4×D4C22×C7311yescharacteristic
465C2×C4×D4C22×C7311yescharacteristic
466C2×#117C22×C7311yescharacteristic
467C22×C22⋊C4—21no—
468#485—24no—
469C2×#107C22×C7311yescharacteristic, complemented
470C2×#106C22×C7311yescharacteristic, complemented
471#418—24no—
472C2×#103C22×C7311yescharacteristic, complemented
473C2×#103C22×C7311yescharacteristic, complemented
474C2×#103C22×C7311yescharacteristic, complemented
475C2×#103C22×C7311yescharacteristic, complemented
476C2×#102C22×C7311yescharacteristic
477C2×#102C22×C7311yescharacteristic
478C2×#102C22×C7311yescharacteristic
479C2×#102C22×C7311yescharacteristic
480C2×#102C22×C7311yescharacteristic
481C2×#102C22×C7311yescharacteristic
482C2×#102C22×C7311yescharacteristic
483C2×#102C22×C7311yescharacteristic
484C2×C22⋊C8C22×C7311yescharacteristic
485C2×C22⋊C8C22×C7311yescharacteristic, complemented
486C2×C22⋊C8C22×C7311yescharacteristic, complemented
487#397—21no—
488#394—21no—
489#389C22×C7311yescharacteristic, complemented
490#389C22×C7311yescharacteristic, complemented
491#388—21no—
492#387—21no—
493#380C22×C7311yescharacteristic
494#380C22×C7311yescharacteristic, complemented
495#380C22×C7311yescharacteristic, complemented
496#340C22×C7311yescharacteristic, complemented
497#340C22×C7311yescharacteristic, complemented
498#336C22×C7311yescharacteristic, complemented
499#336C22×C7311yescharacteristic, complemented
500C25—21no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C22×Q8C23×C7311yescharacteristic
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—22no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4D4×C7314yes—
517C22×D4D4×C7311yescharacteristic
518C22×D4C23×C7311yescharacteristic
519C22×D4C23×C7311yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C7311yescharacteristic
523C23×C4C23×C7311yescharacteristic
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—41no—
527C22×C8C23×C7311yescharacteristic
528C22×C8C23×C7311yescharacteristic
529C22×C8C23×C7311yescharacteristic
530C22×C8C23×C7311yescharacteristic
531#124—22no—
532#124—22no—
533#123—28no—
534C22⋊Q8—22no—
535C22⋊Q8D4×C7314yes—
536#121—28no—
537#121—22no—
538#121—22no—
539#120—28no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544#117—22no—
545#117—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4D4×C7311yescharacteristic
550C2×C4⋊C4C23×C7311yescharacteristic
551C2×C4⋊C4C23×C7311yescharacteristic
552C2×C4⋊C4C23×C7311yescharacteristic
553C2×C4⋊C4C23×C7311yescharacteristic
554C2×C4⋊C4C23×C7311yescharacteristic
555C2×C22⋊C4—28no—
556C2×C22⋊C4—21no—
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⋊C4D4×C7311yescharacteristic
566C2×C22⋊C4D4×C7311yescharacteristic
567C2×C42—21no—
568C2×C42C23×C7311yescharacteristic
569#107—22no—
570#106—22no—
571#103—22no—
572#103—22no—
573#103—41no—
574#103—41no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—22no—
579#102—22no—
580#102—22no—
581#102—41no—
582#102—41no—
583C22⋊C8—22no—
584C22⋊C8—41no—
585C22⋊C8—41no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590#95—21no—
591C24—21no—
592C24—21no—
593C24—24no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—42no—
598C24—81no—
599C24—81no—
600C24C2×D4×C7311yescharacteristic
601C24C2×D4×C7311yescharacteristic
602#41—44no—
603#41—44no—
604#41—44no—
605#41—44no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8C2×D4×C7312yes—
612C2×D4—28no—
613C2×D4—24no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
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—44no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4C2×D4×C7312yes—
637C2×D4C2×D4×C7312yes—
638C2×D4#41×C7312yes—
639C2×D4#41×C7312yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—24no—
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—81no—
661C22×C4—81no—
662C22×C4C2×D4×C7311yescharacteristic
663C22×C4C2×D4×C7311yescharacteristic
664C22×C4C2×D4×C7311yescharacteristic
665C22×C4C2×D4×C7311yescharacteristic
666C22×C4C2×D4×C7312yes—
667C22×C4C2×D4×C7312yes—
668C22×C4C24×C7311yescharacteristic
669M16—44no—
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—
680C2×C8—21no—
681C2×C8—21no—
682C4⋊C4—24no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—42no—
694C4⋊C4—81no—
695C4⋊C4C2×D4×C7312yes—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—24no—
702C22⋊C4—22no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C42—21no—
708C42—21no—
709C42—42no—
710C23—22no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—22no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—48no—
728C23—48no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23—84no—
744C23#120×C7312yes—
745C23C22×D4×C7311yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—41no—
749Q8—41no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—44no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4#123×C7314yes—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—48no—
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—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—84no—
801C2×C4#120×C7312yes—
802C2×C4C22×D4×C7311yescharacteristic
803C2×C4C22×D4×C7311yescharacteristic
804C2×C4C2×#41×C7311yescharacteristic
805C2×C4C2×#41×C7311yescharacteristic
806C2×C4H(5,𝔽2)×C7311yescharacteristic
807C2×C4H(5,𝔽2)×C7311yescharacteristic
808C8—41no—
809C8—41no—
810C8—41no—
811C8—41no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—24no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—42no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—816no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22C2×#120×C7311yescharacteristic
842C22#546×C7311yescharacteristic
843C22#546×C7311yescharacteristic
844C22#575×C7311yescharacteristic
845C22#575×C7311yescharacteristic
846C22#576×C7311yescharacteristic
847C22#577×C7311yescharacteristic
848C4—22no—
849C4—41no—
850C4—41no—
851C4—42no—
852C4—41no—
853C4—42no—
854C4—81no—
855C4—81no—
856C4—81no—
857C4—81no—
858C4C2×#123×C7311yescharacteristic
859C4#534×C7311yescharacteristic
860C4#546×C7311yescharacteristic
861C4#546×C7311yescharacteristic
862C2—42no—
863C2—44no—
864C2—81no—
865C2—82no—
866C2C73×#240511yescharacteristic
867C2C73×#300511yescharacteristic
868C2C73×#301211yescharacteristic
869C2C73×#331111yescharacteristic
870C2C73×#331911yescharacteristic
871C2C73×#332211yescharacteristic
872C2C73×#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×#485×C73C2semidirect
3. C2×#418×C73C2semidirect
4. C73×#2485C2semidirect
5. C73×#2042C2semidirect
6. C73×#2042C2semidirect
7. C73×#2034C2semidirect
8. C73×#2033C2semidirect
9. C73×#1894C2semidirect
10. C73×#1870C2semidirect
11. C73×#1864C2semidirect
12. C73×#1862C2semidirect
13. C73×#1788C2semidirect
14. C73×#1788C2semidirect
15. C73×#1786C2semidirect
32. C2×#107×C73C22semidirect
33. C2×#106×C73C22semidirect
35. C2×#103×C73C22semidirect
36. C2×#103×C73C22semidirect
37. C2×#103×C73C22semidirect
38. C2×#103×C73C22semidirect
48. C2×C22⋊C8×C73C22semidirect
49. C2×C22⋊C8×C73C22semidirect
52. #389×C73C22semidirect
53. #389×C73C22semidirect
57. #380×C73C22semidirect
58. #380×C73C22semidirect
59. #340×C73C22semidirect
60. #340×C73C22semidirect
61. #336×C73C22semidirect
62. #336×C73C22semidirect
425. #24050C73direct (N × H)
438. C2×#485C2×C73semidirect
439. C2×#418C2×C73semidirect
440. #2485C2×C73semidirect
441. #2042C2×C73semidirect
442. #2042C2×C73semidirect
443. #2034C2×C73semidirect
444. #2033C2×C73semidirect
445. #1894C2×C73semidirect
446. #1870C2×C73semidirect
447. #1864C2×C73semidirect
448. #1862C2×C73semidirect
449. #1788C2×C73semidirect
450. #1788C2×C73semidirect
451. #1786C2×C73semidirect
452. C73#24050direct (N × H)
469. C2×#107C22×C73semidirect
470. C2×#106C22×C73semidirect
472. C2×#103C22×C73semidirect
473. C2×#103C22×C73semidirect
474. C2×#103C22×C73semidirect
475. C2×#103C22×C73semidirect
485. C2×C22⋊C8C22×C73semidirect
486. C2×C22⋊C8C22×C73semidirect
489. #389C22×C73semidirect
490. #389C22×C73semidirect
494. #380C22×C73semidirect
495. #380C22×C73semidirect
496. #340C22×C73semidirect
497. #340C22×C73semidirect
498. #336C22×C73semidirect
499. #336C22×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×#485×C732
C2×#418×C732
C73×#24852
C73×#20422
C73×#20342
C73×#20332
C73×#18942
C73×#18702
C73×#18642
C73×#18622
C73×#17882
C73×#17862
#2405073