Finite Group Databasebeta

← C73×#25124 #32934528

Subgroups — C73×#25124 #32934528

Order 18688.

1362 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C73C211yesmaximal, characteristic, complemented
2C2×#447×C73C211yesmaximal, characteristic, complemented
3C2×#435×C73C211yesmaximal, characteristic, complemented
4C22×#102×C73C211yesmaximal, characteristic, complemented
5C73×#2416C211yesmaximal, characteristic, complemented
6C73×#2408C211yesmaximal, characteristic, complemented
7C73×#2065C211yesmaximal, characteristic, complemented
8C73×#2054C211yesmaximal, characteristic, complemented
9C73×#2034C211yesmaximal, characteristic, complemented
10C73×#1999C211yesmaximal, characteristic, complemented
11C73×#1972C211yesmaximal, characteristic, complemented
12C73×#1936C211yesmaximal, characteristic, complemented
13C73×#1895C211yesmaximal, characteristic, complemented
14C73×#1893C211yesmaximal, characteristic, complemented
15C73×#1853C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C22×D8×C73C2211yescharacteristic
19C22×M16×C73C2211yescharacteristic, complemented
20C23×C8×C73C2211yescharacteristic
21C2×#121×C73—21no—
22C2×#121×C73C2211yescharacteristic
23C2×#121×C73C2211yescharacteristic
24C2×#121×C73C2211yescharacteristic
25C2×#121×C73C2211yescharacteristic, complemented
26C2×#120×C73—21no—
27C2×C4×D4×C73C2211yescharacteristic
28C22×C4⋊C4×C73C2211yescharacteristic
29#469×C73—24no—
30#447×C73—24no—
31#435×C73—24no—
32C2×#106×C73C2211yescharacteristic, complemented
33C2×#106×C73C2211yescharacteristic, complemented
34C2×C4⋊C8×C73C2211yescharacteristic, complemented
35C2×#102×C73—24no—
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic, complemented
43C2×#102×C73C2211yescharacteristic, complemented
44C2×C22⋊C8×C73C2211yescharacteristic
45C2×C22⋊C8×C73C2211yescharacteristic, complemented
46C2×#97×C73C2211yescharacteristic, complemented
47#396×C73—21no—
48#394×C73—21no—
49#394×C73—21no—
50#392×C73—21no—
51#390×C73C2211yescharacteristic
52#390×C73C2211yescharacteristic
53#390×C73C2211yescharacteristic, complemented
54#389×C73C2211yescharacteristic, complemented
55#386×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×D4×C73—22no—
65C22×D4×C73—22no—
66C22×D4×C73—21no—
67C22×D4×C73—21no—
68C22×D4×C73—21no—
69C22×D4×C73—21no—
70C22×D4×C73—22no—
71C22×D4×C73—21no—
72C22×D4×C73—22no—
73C22×D4×C73—41no—
74C22×D4×C73—41no—
75C22×D4×C73D411yescharacteristic
76C22×D4×C73C2311yescharacteristic
77C22×D4×C73C2311yescharacteristic
78C22×D4×C73C2311yescharacteristic
79C23×C4×C73—21no—
80C23×C4×C73C2311yescharacteristic
81C23×C4×C73C2311yescharacteristic
82C2×D8×C73—22no—
83C2×D8×C73—22no—
84C2×D8×C73—22no—
85C2×D8×C73—22no—
86C2×D8×C73—41no—
87C2×D8×C73—41no—
88C2×M16×C73—22no—
89C2×M16×C73—22no—
90C2×M16×C73—41no—
91C22×C8×C73—22no—
92C22×C8×C73—22no—
93C22×C8×C73—41no—
94C22×C8×C73C2311yescharacteristic
95C22×C8×C73C2311yescharacteristic
96C22×C8×C73C2311yescharacteristic
97C22×C8×C73C2311yescharacteristic
98#121×C73—22no—
99#121×C73—22no—
100#121×C73—22no—
101#121×C73—22no—
102#121×C73—22no—
103#121×C73—41no—
104#121×C73—41no—
105#121×C73—41no—
106#121×C73—44no—
107#120×C73—44no—
108C4×D4×C73—22no—
109C4×D4×C73—22no—
110C2×C4⋊C4×C73—22no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73—21no—
113C2×C4⋊C4×C73—41no—
114C2×C4⋊C4×C73D411yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
130C2×C22⋊C4×C73—21no—
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73D411yescharacteristic
133C2×C22⋊C4×C73D411yescharacteristic
134C2×C42×C73C2311yescharacteristic
135#106×C73—22no—
136#106×C73—41no—
137C4⋊C8×C73—22no—
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×C73D414yescomplemented
146C22⋊C8×C73—22no—
147C22⋊C8×C73D414yescomplemented
148#97×C73—22no—
149#95×C73—21no—
150#95×C73—21no—
151#95×C73—21no—
152C24×C73—21no—
153C24×C73—21no—
154C24×C73—21no—
155C24×C73—42no—
156C24×C73—42no—
157C24×C73—42no—
158C24×C73—42no—
159C24×C73—42no—
160C24×C73—81no—
161C24×C73—81no—
162C24×C73C2×D411yescharacteristic
163C24×C73C2×D411yescharacteristic
164C2×D4×C73—28no—
165C2×D4×C73—22no—
166C2×D4×C73—22no—
167C2×D4×C73—22no—
168C2×D4×C73—21no—
169C2×D4×C73—21no—
170C2×D4×C73—21no—
171C2×D4×C73—21no—
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—21no—
183C2×D4×C73—21no—
184C2×D4×C73—44no—
185C2×D4×C73—44no—
186C2×D4×C73—42no—
187C2×D4×C73—42no—
188C2×D4×C73—44no—
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—42no—
199C2×D4×C73—81no—
200C2×D4×C73—81no—
201C2×D4×C73—81no—
202C2×D4×C73C2×D412yes—
203C2×D4×C73#4112yes—
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—21no—
219C22×C4×C73—42no—
220C22×C4×C73—42no—
221C22×C4×C73—81no—
222C22×C4×C73C2×D411yescharacteristic
223C22×C4×C73C2×D411yescharacteristic
224C22×C4×C73C2×D411yescharacteristic
225C22×C4×C73C2×D411yescharacteristic
226C22×C4×C73C2×D412yes—
227C22×C4×C73#4112yes—
228C22×C4×C73C2411yescharacteristic
229D8×C73—44no—
230D8×C73—44no—
231M16×C73—44no—
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—44no—
242C2×C8×C73C2×D412yes—
243C2×C8×C73C2×D412yes—
244C2×C8×C73C2×D412yes—
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—22no—
259C22⋊C4×C73—22no—
260C22⋊C4×C73—42no—
261C22⋊C4×C73—42no—
262C22⋊C4×C73—42no—
263C22⋊C4×C73—42no—
264C22⋊C4×C73—42no—
265C22⋊C4×C73—42no—
266C22⋊C4×C73—42no—
267C22⋊C4×C73—42no—
268C22⋊C4×C73—42no—
269C22⋊C4×C73—81no—
270C22⋊C4×C73—81no—
271C22⋊C4×C73—81no—
272C42×C73—21no—
273C42×C73—21no—
274C23×C73—21no—
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—21no—
279C23×C73—22no—
280C23×C73—21no—
281C23×C73—22no—
282C23×C73—21no—
283C23×C73—21no—
284C23×C73—21no—
285C23×C73—21no—
286C23×C73—21no—
287C23×C73—48no—
288C23×C73—41no—
289C23×C73—41no—
290C23×C73—41no—
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—41no—
302C23×C73—41no—
303C23×C73—41no—
304C23×C73—41no—
305C23×C73—41no—
306C23×C73—41no—
307C23×C73—84no—
308C23×C73—84no—
309C23×C73—84no—
310C23×C73—84no—
311C23×C73—84no—
312C23×C73—84no—
313C23×C73#12112yes—
314C23×C73AGL(1,ℤ/8)12yes—
315C23×C73AGL(1,ℤ/8)12yes—
316C23×C73C22×D411yescharacteristic
317D4×C73—22no—
318D4×C73—22no—
319D4×C73—22no—
320D4×C73—22no—
321D4×C73—48no—
322D4×C73—44no—
323D4×C73—41no—
324D4×C73—41no—
325D4×C73—41no—
326D4×C73—41no—
327D4×C73—41no—
328D4×C73—41no—
329D4×C73—41no—
330D4×C73—41no—
331D4×C73—84no—
332D4×C73—84no—
333D4×C73—84no—
334D4×C73—84no—
335C2×C4×C73—21no—
336C2×C4×C73—21no—
337C2×C4×C73—22no—
338C2×C4×C73—22no—
339C2×C4×C73—22no—
340C2×C4×C73—22no—
341C2×C4×C73—21no—
342C2×C4×C73—21no—
343C2×C4×C73—21no—
344C2×C4×C73—21no—
345C2×C4×C73—22no—
346C2×C4×C73—21no—
347C2×C4×C73—21no—
348C2×C4×C73—21no—
349C2×C4×C73—21no—
350C2×C4×C73—21no—
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—41no—
366C2×C4×C73—41no—
367C2×C4×C73—41no—
368C2×C4×C73—41no—
369C2×C4×C73—84no—
370C2×C4×C73#12112yes—
371C2×C4×C73C22×D411yescharacteristic
372C2×C4×C73C22×D411yescharacteristic
373C2×C4×C73C2×#4111yescharacteristic
374C2×C4×C73C2×#4111yescharacteristic
375C2×C4×C73H(5,𝔽2)11yescharacteristic
376C2×C4×C73H(5,𝔽2)11yescharacteristic
377C8×C73—22no—
378C8×C73—22no—
379C8×C73—22no—
380C8×C73—41no—
381C22×C73—22no—
382C22×C73—22no—
383C22×C73—22no—
384C22×C73—22no—
385C22×C73—22no—
386C22×C73—22no—
387C22×C73—41no—
388C22×C73—42no—
389C22×C73—42no—
390C22×C73—41no—
391C22×C73—42no—
392C22×C73—41no—
393C22×C73—42no—
394C22×C73—41no—
395C22×C73—42no—
396C22×C73—41no—
397C22×C73—41no—
398C22×C73—41no—
399C22×C73—42no—
400C22×C73—816no—
401C22×C73—81no—
402C22×C73—81no—
403C22×C73—81no—
404C22×C73—81no—
405C22×C73—81no—
406C22×C73—81no—
407C22×C73—81no—
408C22×C73—81no—
409C22×C73—81no—
410C22×C73—81no—
411C22×C73—81no—
412C22×C73—81no—
413C22×C73—81no—
414C22×C73—81no—
415C22×C73—81no—
416C22×C73#46914yescomplemented
417C22×C73C2×#12111yescharacteristic
418C22×C73D4211yescharacteristic
419C22×C73#54611yescharacteristic
420C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
421C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
422C22×C73#57611yescharacteristic
423C22×C73#57711yescharacteristic
424C4×C73—22no—
425C4×C73—41no—
426C4×C73—42no—
427C4×C73—41no—
428C4×C73—41no—
429C4×C73—81no—
430C4×C73—81no—
431C4×C73—81no—
432C4×C73—81no—
433C4×C73#52511yescharacteristic
434C4×C73#53811yescharacteristic
435C4×C73D4211yescharacteristic
436C4×C73#54611yescharacteristic
437#25124C7311yesmaximal, characteristic, direct product factor, Sylow
438C2×C73—24no—
439C2×C73—81no—
440C2×C73—82no—
441C2×C73—82no—
442C2×C73—161no—
443C2×C73#242411yescharacteristic
444C2×C73C2×#46911yescharacteristic
445C2×C73#306211yescharacteristic
446C2×C73#326411yescharacteristic
447C2×C73#326511yescharacteristic
448C2×C73#330611yescharacteristic
449C2×C73#331811yescharacteristic
450C2×#469C2×C7311yescharacteristic, complemented
451C2×#447C2×C7311yescharacteristic, complemented
452C2×#435C2×C7311yescharacteristic, complemented
453C22×#102C2×C7311yescharacteristic, complemented
454#2416C2×C7311yescharacteristic, complemented
455#2408C2×C7311yescharacteristic, complemented
456#2065C2×C7311yescharacteristic, complemented
457#2054C2×C7311yescharacteristic, complemented
458#2034C2×C7311yescharacteristic, complemented
459#1999C2×C7311yescharacteristic, complemented
460#1972C2×C7311yescharacteristic, complemented
461#1936C2×C7311yescharacteristic, complemented
462#1895C2×C7311yescharacteristic, complemented
463#1893C2×C7311yescharacteristic, complemented
464#1853C2×C7311yescharacteristic, complemented
465C73#2512411yescharacteristic, direct product factor, Sylow
466C23×D4C22×C7311yescharacteristic
467C22×D8C22×C7311yescharacteristic
468C22×D8C22×C7311yescharacteristic
469C22×M16C22×C7311yescharacteristic, complemented
470C23×C8C22×C7311yescharacteristic
471C2×#121—21no—
472C2×#121C22×C7311yescharacteristic
473C2×#121C22×C7311yescharacteristic
474C2×#121C22×C7311yescharacteristic
475C2×#121C22×C7311yescharacteristic, complemented
476C2×#120—21no—
477C2×C4×D4C22×C7311yescharacteristic
478C22×C4⋊C4C22×C7311yescharacteristic
479#469—24no—
480#447—24no—
481#435—24no—
482C2×#106C22×C7311yescharacteristic, complemented
483C2×#106C22×C7311yescharacteristic, complemented
484C2×C4⋊C8C22×C7311yescharacteristic, complemented
485C2×#102—24no—
486C2×#102C22×C7311yescharacteristic
487C2×#102C22×C7311yescharacteristic
488C2×#102C22×C7311yescharacteristic
489C2×#102C22×C7311yescharacteristic
490C2×#102C22×C7311yescharacteristic
491C2×#102C22×C7311yescharacteristic
492C2×#102C22×C7311yescharacteristic, complemented
493C2×#102C22×C7311yescharacteristic, complemented
494C2×C22⋊C8C22×C7311yescharacteristic
495C2×C22⋊C8C22×C7311yescharacteristic, complemented
496C2×#97C22×C7311yescharacteristic, complemented
497#396—21no—
498#394—21no—
499#394—21no—
500#392—21no—
501#390C22×C7311yescharacteristic
502#390C22×C7311yescharacteristic
503#390C22×C7311yescharacteristic, complemented
504#389C22×C7311yescharacteristic, complemented
505#386—21no—
506#380C22×C7311yescharacteristic
507#380C22×C7311yescharacteristic, complemented
508#379—21no—
509#340C22×C7311yescharacteristic, complemented
510#340C22×C7311yescharacteristic, complemented
511#340C22×C7311yescharacteristic, complemented
512#340C22×C7311yescharacteristic, complemented
513C25—21no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4D4×C7311yescharacteristic
526C22×D4C23×C7311yescharacteristic
527C22×D4C23×C7311yescharacteristic
528C22×D4C23×C7311yescharacteristic
529C23×C4—21no—
530C23×C4C23×C7311yescharacteristic
531C23×C4C23×C7311yescharacteristic
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—41no—
537C2×D8—41no—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16—41no—
541C22×C8—22no—
542C22×C8—22no—
543C22×C8—41no—
544C22×C8C23×C7311yescharacteristic
545C22×C8C23×C7311yescharacteristic
546C22×C8C23×C7311yescharacteristic
547C22×C8C23×C7311yescharacteristic
548#121—22no—
549#121—22no—
550#121—22no—
551#121—22no—
552#121—22no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—44no—
557#120—44no—
558C4×D4—22no—
559C4×D4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4D4×C7311yescharacteristic
565C2×C4⋊C4C23×C7311yescharacteristic
566C2×C4⋊C4C23×C7311yescharacteristic
567C2×C4⋊C4C23×C7311yescharacteristic
568C2×C4⋊C4C23×C7311yescharacteristic
569C2×C4⋊C4C23×C7311yescharacteristic
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⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4D4×C7311yescharacteristic
583C2×C22⋊C4D4×C7311yescharacteristic
584C2×C42C23×C7311yescharacteristic
585#106—22no—
586#106—41no—
587C4⋊C8—22no—
588#102—22no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—41no—
595#102D4×C7314yescomplemented
596C22⋊C8—22no—
597C22⋊C8D4×C7314yescomplemented
598#97—22no—
599#95—21no—
600#95—21no—
601#95—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—81no—
611C24—81no—
612C24C2×D4×C7311yescharacteristic
613C24C2×D4×C7311yescharacteristic
614C2×D4—28no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
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—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—44no—
635C2×D4—44no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—44no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—81no—
650C2×D4—81no—
651C2×D4—81no—
652C2×D4C2×D4×C7312yes—
653C2×D4#41×C7312yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—81no—
672C22×C4C2×D4×C7311yescharacteristic
673C22×C4C2×D4×C7311yescharacteristic
674C22×C4C2×D4×C7311yescharacteristic
675C22×C4C2×D4×C7311yescharacteristic
676C22×C4C2×D4×C7312yes—
677C22×C4#41×C7312yes—
678C22×C4C24×C7311yescharacteristic
679D8—44no—
680D8—44no—
681M16—44no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—44no—
692C2×C8C2×D4×C7312yes—
693C2×C8C2×D4×C7312yes—
694C2×C8C2×D4×C7312yes—
695C4⋊C4—22no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—42no—
707C4⋊C4C2×D4×C7312yes—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—81no—
720C22⋊C4—81no—
721C22⋊C4—81no—
722C42—21no—
723C42—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—48no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23—84no—
761C23—84no—
762C23—84no—
763C23#121×C7312yes—
764C23AGL(1,ℤ/8)×C7312yes—
765C23AGL(1,ℤ/8)×C7312yes—
766C23C22×D4×C7311yescharacteristic
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—44no—
773D4—41no—
774D4—41no—
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—84no—
782D4—84no—
783D4—84no—
784D4—84no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—84no—
820C2×C4#121×C7312yes—
821C2×C4C22×D4×C7311yescharacteristic
822C2×C4C22×D4×C7311yescharacteristic
823C2×C4C2×#41×C7311yescharacteristic
824C2×C4C2×#41×C7311yescharacteristic
825C2×C4H(5,𝔽2)×C7311yescharacteristic
826C2×C4H(5,𝔽2)×C7311yescharacteristic
827C8—22no—
828C8—22no—
829C8—22no—
830C8—41no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—42no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—42no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—816no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22#469×C7314yescomplemented
867C22C2×#121×C7311yescharacteristic
868C22D42×C7311yescharacteristic
869C22#546×C7311yescharacteristic
870C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
871C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
872C22#576×C7311yescharacteristic
873C22#577×C7311yescharacteristic
874C4—22no—
875C4—42no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4—81no—
883C4#525×C7311yescharacteristic
884C4#538×C7311yescharacteristic
885C4D42×C7311yescharacteristic
886C4#546×C7311yescharacteristic
887C2—24no—
888C2—81no—
889C2—82no—
890C2—82no—
891C2—161no—
892C2C73×#242411yescharacteristic
893C2C2×#469×C7311yescharacteristic
894C2C73×#306211yescharacteristic
895C2C73×#326411yescharacteristic
896C2C73×#326511yescharacteristic
897C2C73×#330611yescharacteristic
898C2C73×#331811yescharacteristic
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×#469×C73C2semidirect
2. C2×#447×C73C2semidirect
3. C2×#435×C73C2semidirect
4. C22×#102×C73C2semidirect
5. C73×#2416C2semidirect
6. C73×#2408C2semidirect
7. C73×#2065C2semidirect
8. C73×#2054C2semidirect
9. C73×#2034C2semidirect
10. C73×#1999C2semidirect
11. C73×#1972C2semidirect
12. C73×#1936C2semidirect
13. C73×#1895C2semidirect
14. C73×#1893C2semidirect
15. C73×#1853C2semidirect
19. C22×M16×C73C22semidirect
25. C2×#121×C73C22semidirect
32. C2×#106×C73C22semidirect
33. C2×#106×C73C22semidirect
34. C2×C4⋊C8×C73C22semidirect
42. C2×#102×C73C22semidirect
43. C2×#102×C73C22semidirect
45. C2×C22⋊C8×C73C22semidirect
46. C2×#97×C73C22semidirect
53. #390×C73C22semidirect
54. #389×C73C22semidirect
57. #380×C73C22semidirect
59. #340×C73C22semidirect
60. #340×C73C22semidirect
61. #340×C73C22semidirect
62. #340×C73C22semidirect
145. #102×C73D4semidirect
147. C22⋊C8×C73D4semidirect
416. C22×C73#469semidirect
437. #25124C73direct (N × H)
450. C2×#469C2×C73semidirect
451. C2×#447C2×C73semidirect
452. C2×#435C2×C73semidirect
453. C22×#102C2×C73semidirect
454. #2416C2×C73semidirect
455. #2408C2×C73semidirect
456. #2065C2×C73semidirect
457. #2054C2×C73semidirect
458. #2034C2×C73semidirect
459. #1999C2×C73semidirect
460. #1972C2×C73semidirect
461. #1936C2×C73semidirect
462. #1895C2×C73semidirect
463. #1893C2×C73semidirect
464. #1853C2×C73semidirect
465. C73#25124direct (N × H)
469. C22×M16C22×C73semidirect
475. C2×#121C22×C73semidirect
482. C2×#106C22×C73semidirect
483. C2×#106C22×C73semidirect
484. C2×C4⋊C8C22×C73semidirect
492. C2×#102C22×C73semidirect
493. C2×#102C22×C73semidirect
495. C2×C22⋊C8C22×C73semidirect
496. C2×#97C22×C73semidirect
503. #390C22×C73semidirect
504. #389C22×C73semidirect
507. #380C22×C73semidirect
509. #340C22×C73semidirect
510. #340C22×C73semidirect
511. #340C22×C73semidirect
512. #340C22×C73semidirect
595. #102D4×C73semidirect
597. C22⋊C8D4×C73semidirect
866. C22#469×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C732
C2×#447×C732
C2×#435×C732
C22×#102×C732
C73×#24162
C73×#24082
C73×#20652
C73×#20542
C73×#20342
C73×#19992
C73×#19722
C73×#19362
C73×#18952
C73×#18932
C73×#18532
#2512473