Finite Group Databasebeta

← C73×#25128 #32934532

Subgroups — C73×#25128 #32934532

Order 18688.

1292 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C73C211yesmaximal, characteristic, complemented
2C2×#450×C73C211yesmaximal, characteristic, complemented
3C2×#435×C73C211yesmaximal, characteristic, complemented
4C22×#102×C73C211yesmaximal, characteristic, complemented
5C73×#2417C211yesmaximal, characteristic, complemented
6C73×#2408C211yesmaximal, characteristic
7C73×#2067C211yesmaximal, characteristic, complemented
8C73×#2055C211yesmaximal, characteristic, complemented
9C73×#2033C211yesmaximal, characteristic, complemented
10C73×#2000C211yesmaximal, characteristic, complemented
11C73×#1973C211yesmaximal, characteristic, complemented
12C73×#1936C211yesmaximal, characteristic, complemented
13C73×#1895C211yesmaximal, characteristic, complemented
14C73×#1892C211yesmaximal, characteristic, complemented
15C73×#1852C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C22×M16×C73C2211yescharacteristic, complemented
20C23×C8×C73C2211yescharacteristic
21C2×C22⋊Q8×C73C2211yescharacteristic
22C2×C22⋊Q8×C73C2211yescharacteristic, complemented
23C2×#121×C73C2211yescharacteristic
24C2×#121×C73C2211yescharacteristic
25C2×#120×C73—21no—
26C2×C4×D4×C73C2211yescharacteristic
27C22×C4⋊C4×C73C2211yescharacteristic
28#468×C73—24no—
29#450×C73—24no—
30#435×C73—24no—
31C2×#107×C73C2211yescharacteristic, complemented
32C2×#107×C73C2211yescharacteristic, complemented
33C2×C4⋊C8×C73C2211yescharacteristic, complemented
34C2×#103×C73C2211yescharacteristic, complemented
35C2×#103×C73C2211yescharacteristic, complemented
36C2×#102×C73—24no—
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×C22⋊C8×C73C2211yescharacteristic
44C2×C22⋊C8×C73C2211yescharacteristic, complemented
45C2×#97×C73C2211yescharacteristic, complemented
46#398×C73—21no—
47#396×C73—21no—
48#394×C73—21no—
49#392×C73—21no—
50#391×C73C2211yescharacteristic, complemented
51#390×C73C2211yescharacteristic
52#390×C73C2211yescharacteristic
53#389×C73C2211yescharacteristic, complemented
54#386×C73—21no—
55#380×C73—21no—
56#380×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic, complemented
58#379×C73—21no—
59#340×C73C2211yescharacteristic, complemented
60#340×C73C2211yescharacteristic, complemented
61#340×C73C2211yescharacteristic, complemented
62#340×C73C2211yescharacteristic, complemented
63C25×C73—21no—
64C22×Q8×C73C2311yescharacteristic
65C22×D4×C73—22no—
66C22×D4×C73—22no—
67C22×D4×C73—21no—
68C22×D4×C73—21no—
69C22×D4×C73—22no—
70C22×D4×C73—21no—
71C22×D4×C73—22no—
72C22×D4×C73—41no—
73C22×D4×C73—41no—
74C22×D4×C73D411yescharacteristic
75C22×D4×C73C2311yescharacteristic
76C22×D4×C73C2311yescharacteristic
77C23×C4×C73—21no—
78C23×C4×C73C2311yescharacteristic
79C23×C4×C73C2311yescharacteristic
80C2×SD16×C73—22no—
81C2×SD16×C73—22no—
82C2×SD16×C73—22no—
83C2×SD16×C73—22no—
84C2×SD16×C73—41no—
85C2×SD16×C73—41no—
86C2×M16×C73—22no—
87C2×M16×C73—22no—
88C2×M16×C73—41no—
89C22×C8×C73—22no—
90C22×C8×C73—22no—
91C22×C8×C73—41no—
92C22×C8×C73C2311yescharacteristic
93C22×C8×C73C2311yescharacteristic
94C22×C8×C73C2311yescharacteristic
95C22×C8×C73C2311yescharacteristic
96C22⋊Q8×C73—22no—
97C22⋊Q8×C73—22no—
98C22⋊Q8×C73—22no—
99C22⋊Q8×C73—41no—
100#121×C73—22no—
101#121×C73—22no—
102#121×C73—41no—
103#121×C73—41no—
104#120×C73—44no—
105C4×D4×C73—22no—
106C4×D4×C73—22no—
107C2×C4⋊C4×C73—22no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73—41no—
113C2×C4⋊C4×C73D411yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
129C2×C22⋊C4×C73D411yescharacteristic
130C2×C22⋊C4×C73D411yescharacteristic
131C2×C42×C73C2311yescharacteristic
132#107×C73—22no—
133#107×C73—41no—
134C4⋊C8×C73—22no—
135#103×C73—22no—
136#103×C73—41no—
137#102×C73—22no—
138#102×C73—22no—
139#102×C73—22no—
140#102×C73—22no—
141#102×C73—22no—
142#102×C73D414yescomplemented
143C22⋊C8×C73—22no—
144C22⋊C8×C73D414yescomplemented
145#97×C73—22no—
146#95×C73—21no—
147#95×C73—21no—
148#95×C73—21no—
149#95×C73—21no—
150#95×C73—21no—
151C24×C73—21no—
152C24×C73—21no—
153C24×C73—42no—
154C24×C73—42no—
155C24×C73—42no—
156C24×C73—42no—
157C24×C73—42no—
158C24×C73—81no—
159C24×C73—81no—
160C24×C73C2×D411yescharacteristic
161C24×C73C2×D411yescharacteristic
162C2×Q8×C73—21no—
163C2×Q8×C73—21no—
164C2×Q8×C73—21no—
165C2×Q8×C73—21no—
166C2×Q8×C73—21no—
167C2×Q8×C73—21no—
168C2×D4×C73—28no—
169C2×D4×C73—22no—
170C2×D4×C73—22no—
171C2×D4×C73—22no—
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—44no—
183C2×D4×C73—44no—
184C2×D4×C73—42no—
185C2×D4×C73—42no—
186C2×D4×C73—44no—
187C2×D4×C73—42no—
188C2×D4×C73—42no—
189C2×D4×C73—42no—
190C2×D4×C73—42no—
191C2×D4×C73—42no—
192C2×D4×C73—81no—
193C2×D4×C73—81no—
194C2×D4×C73C2×D412yes—
195C2×D4×C73#4112yes—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
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—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—42no—
213C22×C4×C73—42no—
214C22×C4×C73—81no—
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2×D411yescharacteristic
219C22×C4×C73C2×D412yes—
220C22×C4×C73#4112yes—
221C22×C4×C73C2411yescharacteristic
222SD16×C73—44no—
223SD16×C73—44no—
224M16×C73—44no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
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—44no—
235C2×C8×C73C2×D412yes—
236C2×C8×C73C2×D412yes—
237C2×C8×C73C2×D412yes—
238C4⋊C4×C73—22no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73—21no—
248C4⋊C4×C73—42no—
249C4⋊C4×C73—42no—
250C4⋊C4×C73—42no—
251C4⋊C4×C73—81no—
252C4⋊C4×C73C2×D412yes—
253C22⋊C4×C73—22no—
254C22⋊C4×C73—22no—
255C22⋊C4×C73—42no—
256C22⋊C4×C73—42no—
257C22⋊C4×C73—42no—
258C22⋊C4×C73—42no—
259C22⋊C4×C73—42no—
260C22⋊C4×C73—42no—
261C22⋊C4×C73—42no—
262C22⋊C4×C73—81no—
263C22⋊C4×C73—81no—
264C22⋊C4×C73—81no—
265C42×C73—21no—
266C42×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—21no—
279C23×C73—21no—
280C23×C73—48no—
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—84no—
294C23×C73—84no—
295C23×C73—84no—
296C23×C73—84no—
297C23×C73—84no—
298C23×C73—84no—
299C23×C73#12112yes—
300C23×C73AGL(1,ℤ/8)12yes—
301C23×C73#13712yes—
302C23×C73C22×D411yescharacteristic
303Q8×C73—41no—
304Q8×C73—41no—
305Q8×C73—41no—
306Q8×C73—41no—
307D4×C73—22no—
308D4×C73—22no—
309D4×C73—22no—
310D4×C73—22no—
311D4×C73—48no—
312D4×C73—44no—
313D4×C73—41no—
314D4×C73—41no—
315D4×C73—41no—
316D4×C73—41no—
317D4×C73—84no—
318D4×C73—84no—
319C2×C4×C73—21no—
320C2×C4×C73—21no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
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—21no—
333C2×C4×C73—21no—
334C2×C4×C73—21no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
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—84no—
357C2×C4×C73#12112yes—
358C2×C4×C73C22×D411yescharacteristic
359C2×C4×C73C22×D411yescharacteristic
360C2×C4×C73C2×#4111yescharacteristic
361C2×C4×C73C2×#4111yescharacteristic
362C2×C4×C73H(5,𝔽2)11yescharacteristic
363C2×C4×C73H(5,𝔽2)11yescharacteristic
364C8×C73—22no—
365C8×C73—22no—
366C8×C73—22no—
367C8×C73—41no—
368C22×C73—22no—
369C22×C73—22no—
370C22×C73—22no—
371C22×C73—22no—
372C22×C73—22no—
373C22×C73—22no—
374C22×C73—41no—
375C22×C73—42no—
376C22×C73—42no—
377C22×C73—41no—
378C22×C73—42no—
379C22×C73—41no—
380C22×C73—42no—
381C22×C73—41no—
382C22×C73—41no—
383C22×C73—42no—
384C22×C73—41no—
385C22×C73—42no—
386C22×C73—41no—
387C22×C73—816no—
388C22×C73—81no—
389C22×C73—81no—
390C22×C73—81no—
391C22×C73—81no—
392C22×C73—81no—
393C22×C73—81no—
394C22×C73—81no—
395C22×C73—81no—
396C22×C73#46814yescomplemented
397C22×C73C2×#12111yescharacteristic
398C22×C73D4211yescharacteristic
399C22×C73#54611yescharacteristic
400C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C73C2×#13711yescharacteristic
402C22×C73#57611yescharacteristic
403C22×C73#57711yescharacteristic
404C4×C73—22no—
405C4×C73—41no—
406C4×C73—42no—
407C4×C73—41no—
408C4×C73—41no—
409C4×C73—81no—
410C4×C73—81no—
411C4×C73—81no—
412C4×C73—81no—
413C4×C73—81no—
414C4×C73#52511yescharacteristic
415C4×C73#53811yescharacteristic
416C4×C73D4211yescharacteristic
417C4×C73#54611yescharacteristic
418#25128C7311yesmaximal, characteristic, direct product factor, Sylow
419C2×C73—24no—
420C2×C73—81no—
421C2×C73—82no—
422C2×C73—82no—
423C2×C73#242411yescharacteristic
424C2×C73C2×#46811yescharacteristic
425C2×C73#306211yescharacteristic
426C2×C73#326411yescharacteristic
427C2×C73#326611yescharacteristic
428C2×C73#331011yescharacteristic
429C2×C73#331411yescharacteristic
430C2×#468C2×C7311yescharacteristic, complemented
431C2×#450C2×C7311yescharacteristic, complemented
432C2×#435C2×C7311yescharacteristic, complemented
433C22×#102C2×C7311yescharacteristic, complemented
434#2417C2×C7311yescharacteristic, complemented
435#2408C2×C7311yescharacteristic
436#2067C2×C7311yescharacteristic, complemented
437#2055C2×C7311yescharacteristic, complemented
438#2033C2×C7311yescharacteristic, complemented
439#2000C2×C7311yescharacteristic, complemented
440#1973C2×C7311yescharacteristic, complemented
441#1936C2×C7311yescharacteristic, complemented
442#1895C2×C7311yescharacteristic, complemented
443#1892C2×C7311yescharacteristic, complemented
444#1852C2×C7311yescharacteristic, complemented
445C73#2512811yescharacteristic, direct product factor, Sylow
446C23×D4C22×C7311yescharacteristic
447C22×SD16C22×C7311yescharacteristic
448C22×SD16C22×C7311yescharacteristic
449C22×M16C22×C7311yescharacteristic, complemented
450C23×C8C22×C7311yescharacteristic
451C2×C22⋊Q8C22×C7311yescharacteristic
452C2×C22⋊Q8C22×C7311yescharacteristic, complemented
453C2×#121C22×C7311yescharacteristic
454C2×#121C22×C7311yescharacteristic
455C2×#120—21no—
456C2×C4×D4C22×C7311yescharacteristic
457C22×C4⋊C4C22×C7311yescharacteristic
458#468—24no—
459#450—24no—
460#435—24no—
461C2×#107C22×C7311yescharacteristic, complemented
462C2×#107C22×C7311yescharacteristic, complemented
463C2×C4⋊C8C22×C7311yescharacteristic, complemented
464C2×#103C22×C7311yescharacteristic, complemented
465C2×#103C22×C7311yescharacteristic, complemented
466C2×#102—24no—
467C2×#102C22×C7311yescharacteristic
468C2×#102C22×C7311yescharacteristic
469C2×#102C22×C7311yescharacteristic
470C2×#102C22×C7311yescharacteristic
471C2×#102C22×C7311yescharacteristic
472C2×#102C22×C7311yescharacteristic
473C2×C22⋊C8C22×C7311yescharacteristic
474C2×C22⋊C8C22×C7311yescharacteristic, complemented
475C2×#97C22×C7311yescharacteristic, complemented
476#398—21no—
477#396—21no—
478#394—21no—
479#392—21no—
480#391C22×C7311yescharacteristic, complemented
481#390C22×C7311yescharacteristic
482#390C22×C7311yescharacteristic
483#389C22×C7311yescharacteristic, complemented
484#386—21no—
485#380—21no—
486#380C22×C7311yescharacteristic
487#380C22×C7311yescharacteristic, complemented
488#379—21no—
489#340C22×C7311yescharacteristic, complemented
490#340C22×C7311yescharacteristic, complemented
491#340C22×C7311yescharacteristic, complemented
492#340C22×C7311yescharacteristic, complemented
493C25—21no—
494C22×Q8C23×C7311yescharacteristic
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4D4×C7311yescharacteristic
505C22×D4C23×C7311yescharacteristic
506C22×D4C23×C7311yescharacteristic
507C23×C4—21no—
508C23×C4C23×C7311yescharacteristic
509C23×C4C23×C7311yescharacteristic
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—41no—
519C22×C8—22no—
520C22×C8—22no—
521C22×C8—41no—
522C22×C8C23×C7311yescharacteristic
523C22×C8C23×C7311yescharacteristic
524C22×C8C23×C7311yescharacteristic
525C22×C8C23×C7311yescharacteristic
526C22⋊Q8—22no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—22no—
531#121—22no—
532#121—41no—
533#121—41no—
534#120—44no—
535C4×D4—22no—
536C4×D4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4D4×C7311yescharacteristic
544C2×C4⋊C4C23×C7311yescharacteristic
545C2×C4⋊C4C23×C7311yescharacteristic
546C2×C4⋊C4C23×C7311yescharacteristic
547C2×C4⋊C4C23×C7311yescharacteristic
548C2×C4⋊C4C23×C7311yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
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⋊C4D4×C7311yescharacteristic
560C2×C22⋊C4D4×C7311yescharacteristic
561C2×C42C23×C7311yescharacteristic
562#107—22no—
563#107—41no—
564C4⋊C8—22no—
565#103—22no—
566#103—41no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102D4×C7314yescomplemented
573C22⋊C8—22no—
574C22⋊C8D4×C7314yescomplemented
575#97—22no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—21no—
580#95—21no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—81no—
589C24—81no—
590C24C2×D4×C7311yescharacteristic
591C24C2×D4×C7311yescharacteristic
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×D4—28no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—44no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—44no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—81no—
623C2×D4—81no—
624C2×D4C2×D4×C7312yes—
625C2×D4#41×C7312yes—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
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—42no—
643C22×C4—42no—
644C22×C4—81no—
645C22×C4C2×D4×C7311yescharacteristic
646C22×C4C2×D4×C7311yescharacteristic
647C22×C4C2×D4×C7311yescharacteristic
648C22×C4C2×D4×C7311yescharacteristic
649C22×C4C2×D4×C7312yes—
650C22×C4#41×C7312yes—
651C22×C4C24×C7311yescharacteristic
652SD16—44no—
653SD16—44no—
654M16—44no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—44no—
665C2×C8C2×D4×C7312yes—
666C2×C8C2×D4×C7312yes—
667C2×C8C2×D4×C7312yes—
668C4⋊C4—22no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—81no—
682C4⋊C4C2×D4×C7312yes—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—81no—
693C22⋊C4—81no—
694C22⋊C4—81no—
695C42—21no—
696C42—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—48no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23#121×C7312yes—
730C23AGL(1,ℤ/8)×C7312yes—
731C23#137×C7312yes—
732C23C22×D4×C7311yescharacteristic
733Q8—41no—
734Q8—41no—
735Q8—41no—
736Q8—41no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—44no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4—84no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
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—84no—
787C2×C4#121×C7312yes—
788C2×C4C22×D4×C7311yescharacteristic
789C2×C4C22×D4×C7311yescharacteristic
790C2×C4C2×#41×C7311yescharacteristic
791C2×C4C2×#41×C7311yescharacteristic
792C2×C4H(5,𝔽2)×C7311yescharacteristic
793C2×C4H(5,𝔽2)×C7311yescharacteristic
794C8—22no—
795C8—22no—
796C8—22no—
797C8—41no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—41no—
810C22—42no—
811C22—41no—
812C22—42no—
813C22—41no—
814C22—41no—
815C22—42no—
816C22—42no—
817C22—816no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22#468×C7314yescomplemented
827C22C2×#121×C7311yescharacteristic
828C22D42×C7311yescharacteristic
829C22#546×C7311yescharacteristic
830C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
831C22C2×#137×C7311yescharacteristic
832C22#576×C7311yescharacteristic
833C22#577×C7311yescharacteristic
834C4—22no—
835C4—42no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4—81no—
843C4—81no—
844C4#525×C7311yescharacteristic
845C4#538×C7311yescharacteristic
846C4D42×C7311yescharacteristic
847C4#546×C7311yescharacteristic
848C2—24no—
849C2—81no—
850C2—82no—
851C2—82no—
852C2C73×#242411yescharacteristic
853C2C2×#468×C7311yescharacteristic
854C2C73×#306211yescharacteristic
855C2C73×#326411yescharacteristic
856C2C73×#326611yescharacteristic
857C2C73×#331011yescharacteristic
858C2C73×#331411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2408C2
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×#468×C73C2semidirect
2. C2×#450×C73C2semidirect
3. C2×#435×C73C2semidirect
4. C22×#102×C73C2semidirect
5. C73×#2417C2semidirect
7. C73×#2067C2semidirect
8. C73×#2055C2semidirect
9. C73×#2033C2semidirect
10. C73×#2000C2semidirect
11. C73×#1973C2semidirect
12. C73×#1936C2semidirect
13. C73×#1895C2semidirect
14. C73×#1892C2semidirect
15. C73×#1852C2semidirect
19. C22×M16×C73C22semidirect
22. C2×C22⋊Q8×C73C22semidirect
31. C2×#107×C73C22semidirect
32. C2×#107×C73C22semidirect
33. C2×C4⋊C8×C73C22semidirect
34. C2×#103×C73C22semidirect
35. C2×#103×C73C22semidirect
44. C2×C22⋊C8×C73C22semidirect
45. C2×#97×C73C22semidirect
50. #391×C73C22semidirect
53. #389×C73C22semidirect
57. #380×C73C22semidirect
59. #340×C73C22semidirect
60. #340×C73C22semidirect
61. #340×C73C22semidirect
62. #340×C73C22semidirect
142. #102×C73D4semidirect
144. C22⋊C8×C73D4semidirect
396. C22×C73#468semidirect
418. #25128C73direct (N × H)
430. C2×#468C2×C73semidirect
431. C2×#450C2×C73semidirect
432. C2×#435C2×C73semidirect
433. C22×#102C2×C73semidirect
434. #2417C2×C73semidirect
436. #2067C2×C73semidirect
437. #2055C2×C73semidirect
438. #2033C2×C73semidirect
439. #2000C2×C73semidirect
440. #1973C2×C73semidirect
441. #1936C2×C73semidirect
442. #1895C2×C73semidirect
443. #1892C2×C73semidirect
444. #1852C2×C73semidirect
445. C73#25128direct (N × H)
449. C22×M16C22×C73semidirect
452. C2×C22⋊Q8C22×C73semidirect
461. C2×#107C22×C73semidirect
462. C2×#107C22×C73semidirect
463. C2×C4⋊C8C22×C73semidirect
464. C2×#103C22×C73semidirect
465. C2×#103C22×C73semidirect
474. C2×C22⋊C8C22×C73semidirect
475. C2×#97C22×C73semidirect
480. #391C22×C73semidirect
483. #389C22×C73semidirect
487. #380C22×C73semidirect
489. #340C22×C73semidirect
490. #340C22×C73semidirect
491. #340C22×C73semidirect
492. #340C22×C73semidirect
572. #102D4×C73semidirect
574. C22⋊C8D4×C73semidirect
826. C22#468×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C732
C2×#450×C732
C2×#435×C732
C22×#102×C732
C73×#24172
C73×#24082
C73×#20672
C73×#20552
C73×#20332
C73×#20002
C73×#19732
C73×#19362
C73×#18952
C73×#18922
C73×#18522
#2512873