Finite Group Databasebeta

← C73×#25168 #32934572

Subgroups — C73×#25168 #32934572

Order 18688.

1396 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C73C211yesmaximal, characteristic, complemented
2C2×#447×C73C211yesmaximal, characteristic, complemented
3C2×#447×C73C211yesmaximal, characteristic, complemented
4C2×#442×C73C211yesmaximal, characteristic, complemented
5C73×#2428C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C73C211yesmaximal, characteristic, complemented
7C73×#2065C211yesmaximal, characteristic, complemented
8C73×#2034C211yesmaximal, characteristic, complemented
9C73×#2034C211yesmaximal, characteristic, complemented
10C73×#2011C211yesmaximal, characteristic, complemented
11C73×#1972C211yesmaximal, characteristic, complemented
12C73×#1924C211yesmaximal, characteristic, complemented
13C73×#1879C211yesmaximal, characteristic, complemented
14C73×#1879C211yesmaximal, characteristic, complemented
15C73×#1864C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C22×D8×C73C2211yescharacteristic
19C22×D8×C73C2211yescharacteristic
20C22×D8×C73C2211yescharacteristic
21C2×#127×C73C2211yescharacteristic, complemented
22C2×#121×C73—21no—
23C2×#121×C73C2211yescharacteristic
24C2×#121×C73C2211yescharacteristic
25C2×C4×D4×C73C2211yescharacteristic
26C2×C4×D4×C73C2211yescharacteristic
27C2×C4×D4×C73C2211yescharacteristic, complemented
28C22×C22⋊C4×C73—21no—
29#459×C73—24no—
30#447×C73—24no—
31#447×C73—24no—
32#442×C73—24no—
33C2×#106×C73C2211yescharacteristic, complemented
34C2×#106×C73C2211yescharacteristic, complemented
35C2×C4⋊C8×C73C2211yescharacteristic, complemented
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic, complemented
41C2×#102×C73C2211yescharacteristic, complemented
42C2×#102×C73C2211yescharacteristic, complemented
43C2×#102×C73C2211yescharacteristic, complemented
44C2×C22⋊C8×C73C2211yescharacteristic
45C2×C22⋊C8×C73C2211yescharacteristic
46C2×#97×C73C2211yescharacteristic, complemented
47#394×C73—21no—
48#392×C73—21no—
49#390×C73C2211yescharacteristic
50#390×C73C2211yescharacteristic
51#390×C73C2211yescharacteristic, complemented
52#389×C73C2211yescharacteristic, complemented
53#386×C73—21no—
54#386×C73—21no—
55#386×C73—21no—
56#380×C73C2211yescharacteristic
57#379×C73—21no—
58C4×C22⋊C4×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic, complemented
60#340×C73C2211yescharacteristic, complemented
61#336×C73C2211yescharacteristic, complemented
62#336×C73C2211yescharacteristic, complemented
63C25×C73—21no—
64C22×D4×C73—22no—
65C22×D4×C73—22no—
66C22×D4×C73—22no—
67C22×D4×C73—22no—
68C22×D4×C73—21no—
69C22×D4×C73—21no—
70C22×D4×C73—21no—
71C22×D4×C73—21no—
72C22×D4×C73—21no—
73C22×D4×C73—41no—
74C22×D4×C73—41no—
75C22×D4×C73C2311yescharacteristic
76C22×D4×C73C2311yescharacteristic
77C22×D4×C73C2311yescharacteristic
78C22×D4×C73C2311yescharacteristic
79C23×C4×C73—21no—
80C23×C4×C73—21no—
81C23×C4×C73—21no—
82C23×C4×C73C2311yescharacteristic
83C2×D8×C73—22no—
84C2×D8×C73—22no—
85C2×D8×C73—22no—
86C2×D8×C73—22no—
87C2×D8×C73—22no—
88C2×D8×C73—22no—
89C2×D8×C73—22no—
90C2×D8×C73—22no—
91C2×D8×C73—22no—
92C2×D8×C73—41no—
93C2×D8×C73—41no—
94C2×D8×C73D414yescomplemented
95C22×C8×C73C2311yescharacteristic
96C22×C8×C73C2311yescharacteristic
97C22×C8×C73C2311yescharacteristic
98C22×C8×C73C2311yescharacteristic
99#127×C73—22no—
100#127×C73—41no—
101#121×C73—22no—
102#121×C73—22no—
103#121×C73—44no—
104#121×C73—41no—
105#121×C73—41no—
106C4×D4×C73—22no—
107C4×D4×C73—22no—
108C4×D4×C73—22no—
109C4×D4×C73—41no—
110C4×D4×C73—41no—
111C4×D4×C73—41no—
112C2×C4⋊C4×C73—21no—
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
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×C73—21no—
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—44no—
130C2×C22⋊C4×C73D411yescharacteristic
131C2×C22⋊C4×C73D411yescharacteristic
132C2×C42×C73C2311yescharacteristic
133C2×C42×C73C2311yescharacteristic
134#106×C73—22no—
135#106×C73—41no—
136C4⋊C8×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—22no—
143#102×C73—41no—
144#102×C73D414yescomplemented
145C22⋊C8×C73—22no—
146C22⋊C8×C73—22no—
147#97×C73—22no—
148#95×C73—21no—
149#95×C73—21no—
150#95×C73D411yescharacteristic
151#95×C73D411yescharacteristic
152C24×C73—21no—
153C24×C73—24no—
154C24×C73—21no—
155C24×C73—21no—
156C24×C73—21no—
157C24×C73—42no—
158C24×C73—42no—
159C24×C73—42no—
160C24×C73—42no—
161C24×C73—81no—
162C24×C73—81no—
163C24×C73C2×D411yescharacteristic
164C2×D4×C73—24no—
165C2×D4×C73—21no—
166C2×D4×C73—21no—
167C2×D4×C73—21no—
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—42no—
185C2×D4×C73—42no—
186C2×D4×C73—42no—
187C2×D4×C73—42no—
188C2×D4×C73—42no—
189C2×D4×C73—42no—
190C2×D4×C73—44no—
191C2×D4×C73—44no—
192C2×D4×C73—44no—
193C2×D4×C73—44no—
194C2×D4×C73—42no—
195C2×D4×C73—42no—
196C2×D4×C73—42no—
197C2×D4×C73—42no—
198C2×D4×C73—81no—
199C2×D4×C73—81no—
200C2×D4×C73—81no—
201C2×D4×C73—81no—
202C2×D4×C73C2×D412yes—
203C2×D4×C73C2×D412yes—
204C2×D4×C73C2×D412yes—
205C2×D4×C73#4112yes—
206C2×D4×C73#4112yes—
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—42no—
218C22×C4×C73—42no—
219C22×C4×C73—42no—
220C22×C4×C73—42no—
221C22×C4×C73—42no—
222C22×C4×C73—42no—
223C22×C4×C73—81no—
224C22×C4×C73—81no—
225C22×C4×C73—81no—
226C22×C4×C73C2×D411yescharacteristic
227C22×C4×C73C2×D411yescharacteristic
228C22×C4×C73C2×D411yescharacteristic
229C22×C4×C73C2×D411yescharacteristic
230C22×C4×C73C2×D411yescharacteristic
231C22×C4×C73C2411yescharacteristic
232D8×C73—28no—
233D8×C73—44no—
234D8×C73—44no—
235D8×C73—44no—
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—
245C2×C8×C73—21no—
246C2×C8×C73C2×D412yes—
247C2×C8×C73C2×D412yes—
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×C73C2×D412yes—
257C22⋊C4×C73—22no—
258C22⋊C4×C73—22no—
259C22⋊C4×C73—42no—
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—81no—
269C22⋊C4×C73—81no—
270C22⋊C4×C73—81no—
271C42×C73—21no—
272C42×C73—21no—
273C42×C73—21no—
274C42×C73—21no—
275C23×C73—21no—
276C23×C73—22no—
277C23×C73—22no—
278C23×C73—22no—
279C23×C73—21no—
280C23×C73—21no—
281C23×C73—21no—
282C23×C73—21no—
283C23×C73—21no—
284C23×C73—22no—
285C23×C73—22no—
286C23×C73—48no—
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—41no—
308C23×C73—41no—
309C23×C73—41no—
310C23×C73—41no—
311C23×C73—84no—
312C23×C73—84no—
313C23×C73—84no—
314C23×C73—84no—
315C23×C73—84no—
316C23×C73AGL(1,ℤ/8)12yes—
317C23×C73C22×D411yescharacteristic
318D4×C73—22no—
319D4×C73—22no—
320D4×C73—22no—
321D4×C73—22no—
322D4×C73—22no—
323D4×C73—22no—
324D4×C73—22no—
325D4×C73—48no—
326D4×C73—41no—
327D4×C73—41no—
328D4×C73—41no—
329D4×C73—41no—
330D4×C73—41no—
331D4×C73—41no—
332D4×C73—41no—
333D4×C73—41no—
334D4×C73—84no—
335D4×C73—84no—
336D4×C73—84no—
337D4×C73—84no—
338D4×C73#12114yescomplemented
339C2×C4×C73—21no—
340C2×C4×C73—21no—
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—21no—
352C2×C4×C73—21no—
353C2×C4×C73—21no—
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—84no—
371C2×C4×C73—84no—
372C2×C4×C73AGL(1,ℤ/8)12yes—
373C2×C4×C73C22×D411yescharacteristic
374C2×C4×C73C22×D411yescharacteristic
375C2×C4×C73C2×#4111yescharacteristic
376C2×C4×C73C2×#4111yescharacteristic
377C2×C4×C73H(5,𝔽2)11yescharacteristic
378C2×C4×C73H(5,𝔽2)11yescharacteristic
379C8×C73—22no—
380C8×C73—22no—
381C8×C73—41no—
382C8×C73—41no—
383C22×C73—22no—
384C22×C73—24no—
385C22×C73—22no—
386C22×C73—22no—
387C22×C73—42no—
388C22×C73—41no—
389C22×C73—42no—
390C22×C73—41no—
391C22×C73—42no—
392C22×C73—41no—
393C22×C73—42no—
394C22×C73—42no—
395C22×C73—42no—
396C22×C73—41no—
397C22×C73—42no—
398C22×C73—42no—
399C22×C73—42no—
400C22×C73—42no—
401C22×C73—42no—
402C22×C73—42no—
403C22×C73—816no—
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—81no—
417C22×C73—81no—
418C22×C73—81no—
419C22×C73#52511yescharacteristic
420C22×C73D4211yescharacteristic
421C22×C73D4211yescharacteristic
422C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C73#57611yescharacteristic
425C22×C73#57611yescharacteristic
426C4×C73—22no—
427C4×C73—41no—
428C4×C73—41no—
429C4×C73—41no—
430C4×C73—42no—
431C4×C73—41no—
432C4×C73—81no—
433C4×C73—81no—
434C4×C73—81no—
435C4×C73C2×#12111yescharacteristic
436C4×C73#53811yescharacteristic
437C4×C73#54611yescharacteristic
438C4×C73#54611yescharacteristic
439#25168C7311yesmaximal, characteristic, direct product factor, Sylow
440C2×C73—42no—
441C2×C73—44no—
442C2×C73—82no—
443C2×C73—82no—
444C2×C73—161no—
445C2×C73#242411yescharacteristic
446C2×C73#310911yescharacteristic
447C2×C73#312211yescharacteristic
448C2×C73#326411yescharacteristic
449C2×C73#326411yescharacteristic
450C2×C73#326411yescharacteristic
451C2×C73#327411yescharacteristic
452C2×#459C2×C7311yescharacteristic, complemented
453C2×#447C2×C7311yescharacteristic, complemented
454C2×#447C2×C7311yescharacteristic, complemented
455C2×#442C2×C7311yescharacteristic, complemented
456#2428C2×C7311yescharacteristic, complemented
457D4×C22⋊C4C2×C7311yescharacteristic, complemented
458#2065C2×C7311yescharacteristic, complemented
459#2034C2×C7311yescharacteristic, complemented
460#2034C2×C7311yescharacteristic, complemented
461#2011C2×C7311yescharacteristic, complemented
462#1972C2×C7311yescharacteristic, complemented
463#1924C2×C7311yescharacteristic, complemented
464#1879C2×C7311yescharacteristic, complemented
465#1879C2×C7311yescharacteristic, complemented
466#1864C2×C7311yescharacteristic, complemented
467C73#2516811yescharacteristic, direct product factor, Sylow
468C23×D4C22×C7311yescharacteristic
469C22×D8C22×C7311yescharacteristic
470C22×D8C22×C7311yescharacteristic
471C22×D8C22×C7311yescharacteristic
472C22×D8C22×C7311yescharacteristic
473C2×#127C22×C7311yescharacteristic, complemented
474C2×#121—21no—
475C2×#121C22×C7311yescharacteristic
476C2×#121C22×C7311yescharacteristic
477C2×C4×D4C22×C7311yescharacteristic
478C2×C4×D4C22×C7311yescharacteristic
479C2×C4×D4C22×C7311yescharacteristic, complemented
480C22×C22⋊C4—21no—
481#459—24no—
482#447—24no—
483#447—24no—
484#442—24no—
485C2×#106C22×C7311yescharacteristic, complemented
486C2×#106C22×C7311yescharacteristic, complemented
487C2×C4⋊C8C22×C7311yescharacteristic, complemented
488C2×#102C22×C7311yescharacteristic
489C2×#102C22×C7311yescharacteristic
490C2×#102C22×C7311yescharacteristic
491C2×#102C22×C7311yescharacteristic
492C2×#102C22×C7311yescharacteristic, complemented
493C2×#102C22×C7311yescharacteristic, complemented
494C2×#102C22×C7311yescharacteristic, complemented
495C2×#102C22×C7311yescharacteristic, complemented
496C2×C22⋊C8C22×C7311yescharacteristic
497C2×C22⋊C8C22×C7311yescharacteristic
498C2×#97C22×C7311yescharacteristic, complemented
499#394—21no—
500#392—21no—
501#390C22×C7311yescharacteristic
502#390C22×C7311yescharacteristic
503#390C22×C7311yescharacteristic, complemented
504#389C22×C7311yescharacteristic, complemented
505#386—21no—
506#386—21no—
507#386—21no—
508#380C22×C7311yescharacteristic
509#379—21no—
510C4×C22⋊C4C22×C7311yescharacteristic
511#340C22×C7311yescharacteristic, complemented
512#340C22×C7311yescharacteristic, complemented
513#336C22×C7311yescharacteristic, complemented
514#336C22×C7311yescharacteristic, complemented
515C25—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4C23×C7311yescharacteristic
528C22×D4C23×C7311yescharacteristic
529C22×D4C23×C7311yescharacteristic
530C22×D4C23×C7311yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4C23×C7311yescharacteristic
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8D4×C7314yescomplemented
547C22×C8C23×C7311yescharacteristic
548C22×C8C23×C7311yescharacteristic
549C22×C8C23×C7311yescharacteristic
550C22×C8C23×C7311yescharacteristic
551#127—22no—
552#127—41no—
553#121—22no—
554#121—22no—
555#121—44no—
556#121—41no—
557#121—41no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4C23×C7311yescharacteristic
566C2×C4⋊C4C23×C7311yescharacteristic
567C2×C4⋊C4C23×C7311yescharacteristic
568C2×C4⋊C4C23×C7311yescharacteristic
569C2×C22⋊C4—21no—
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—44no—
582C2×C22⋊C4D4×C7311yescharacteristic
583C2×C22⋊C4D4×C7311yescharacteristic
584C2×C42C23×C7311yescharacteristic
585C2×C42C23×C7311yescharacteristic
586#106—22no—
587#106—41no—
588C4⋊C8—22no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—41no—
596#102D4×C7314yescomplemented
597C22⋊C8—22no—
598C22⋊C8—22no—
599#97—22no—
600#95—21no—
601#95—21no—
602#95D4×C7311yescharacteristic
603#95D4×C7311yescharacteristic
604C24—21no—
605C24—24no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—42no—
613C24—81no—
614C24—81no—
615C24C2×D4×C7311yescharacteristic
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—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—21no—
635C2×D4—21no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—81no—
651C2×D4—81no—
652C2×D4—81no—
653C2×D4—81no—
654C2×D4C2×D4×C7312yes—
655C2×D4C2×D4×C7312yes—
656C2×D4C2×D4×C7312yes—
657C2×D4#41×C7312yes—
658C2×D4#41×C7312yes—
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—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4—81no—
678C22×C4C2×D4×C7311yescharacteristic
679C22×C4C2×D4×C7311yescharacteristic
680C22×C4C2×D4×C7311yescharacteristic
681C22×C4C2×D4×C7311yescharacteristic
682C22×C4C2×D4×C7311yescharacteristic
683C22×C4C24×C7311yescharacteristic
684D8—28no—
685D8—44no—
686D8—44no—
687D8—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8C2×D4×C7312yes—
699C2×C8C2×D4×C7312yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—42no—
708C4⋊C4C2×D4×C7312yes—
709C22⋊C4—22no—
710C22⋊C4—22no—
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—42no—
720C22⋊C4—81no—
721C22⋊C4—81no—
722C22⋊C4—81no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—22no—
738C23—48no—
739C23—48no—
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—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—84no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23AGL(1,ℤ/8)×C7312yes—
769C23C22×D4×C7311yescharacteristic
770D4—22no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—22no—
775D4—22no—
776D4—22no—
777D4—48no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—84no—
787D4—84no—
788D4—84no—
789D4—84no—
790D4#121×C7314yescomplemented
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
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—41no—
820C2×C4—41no—
821C2×C4—84no—
822C2×C4—84no—
823C2×C4—84no—
824C2×C4AGL(1,ℤ/8)×C7312yes—
825C2×C4C22×D4×C7311yescharacteristic
826C2×C4C22×D4×C7311yescharacteristic
827C2×C4C2×#41×C7311yescharacteristic
828C2×C4C2×#41×C7311yescharacteristic
829C2×C4H(5,𝔽2)×C7311yescharacteristic
830C2×C4H(5,𝔽2)×C7311yescharacteristic
831C8—22no—
832C8—22no—
833C8—41no—
834C8—41no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—24no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—816no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22#525×C7311yescharacteristic
872C22D42×C7311yescharacteristic
873C22D42×C7311yescharacteristic
874C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
875C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
876C22#576×C7311yescharacteristic
877C22#576×C7311yescharacteristic
878C4—22no—
879C4—41no—
880C4—41no—
881C4—42no—
882C4—41no—
883C4—41no—
884C4—81no—
885C4—81no—
886C4—81no—
887C4C2×#121×C7311yescharacteristic
888C4#538×C7311yescharacteristic
889C4#546×C7311yescharacteristic
890C4#546×C7311yescharacteristic
891C2—42no—
892C2—44no—
893C2—82no—
894C2—82no—
895C2—161no—
896C2C73×#242411yescharacteristic
897C2C73×#310911yescharacteristic
898C2C73×#312211yescharacteristic
899C2C73×#326411yescharacteristic
900C2C73×#326411yescharacteristic
901C2C73×#326411yescharacteristic
902C2C73×#327411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#459×C73C2semidirect
2. C2×#447×C73C2semidirect
3. C2×#447×C73C2semidirect
4. C2×#442×C73C2semidirect
5. C73×#2428C2semidirect
6. D4×C22⋊C4×C73C2semidirect
7. C73×#2065C2semidirect
8. C73×#2034C2semidirect
9. C73×#2034C2semidirect
10. C73×#2011C2semidirect
11. C73×#1972C2semidirect
12. C73×#1924C2semidirect
13. C73×#1879C2semidirect
14. C73×#1879C2semidirect
15. C73×#1864C2semidirect
21. C2×#127×C73C22semidirect
27. C2×C4×D4×C73C22semidirect
33. C2×#106×C73C22semidirect
34. C2×#106×C73C22semidirect
35. C2×C4⋊C8×C73C22semidirect
40. C2×#102×C73C22semidirect
41. C2×#102×C73C22semidirect
42. C2×#102×C73C22semidirect
43. C2×#102×C73C22semidirect
46. C2×#97×C73C22semidirect
51. #390×C73C22semidirect
52. #389×C73C22semidirect
59. #340×C73C22semidirect
60. #340×C73C22semidirect
61. #336×C73C22semidirect
62. #336×C73C22semidirect
94. C2×D8×C73D4semidirect
144. #102×C73D4semidirect
338. D4×C73#121semidirect
439. #25168C73direct (N × H)
452. C2×#459C2×C73semidirect
453. C2×#447C2×C73semidirect
454. C2×#447C2×C73semidirect
455. C2×#442C2×C73semidirect
456. #2428C2×C73semidirect
457. D4×C22⋊C4C2×C73semidirect
458. #2065C2×C73semidirect
459. #2034C2×C73semidirect
460. #2034C2×C73semidirect
461. #2011C2×C73semidirect
462. #1972C2×C73semidirect
463. #1924C2×C73semidirect
464. #1879C2×C73semidirect
465. #1879C2×C73semidirect
466. #1864C2×C73semidirect
467. C73#25168direct (N × H)
473. C2×#127C22×C73semidirect
479. C2×C4×D4C22×C73semidirect
485. C2×#106C22×C73semidirect
486. C2×#106C22×C73semidirect
487. C2×C4⋊C8C22×C73semidirect
492. C2×#102C22×C73semidirect
493. C2×#102C22×C73semidirect
494. C2×#102C22×C73semidirect
495. C2×#102C22×C73semidirect
498. C2×#97C22×C73semidirect
503. #390C22×C73semidirect
504. #389C22×C73semidirect
511. #340C22×C73semidirect
512. #340C22×C73semidirect
513. #336C22×C73semidirect
514. #336C22×C73semidirect
546. C2×D8D4×C73semidirect
596. #102D4×C73semidirect
790. D4#121×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C732
C2×#447×C732
C2×#442×C732
C73×#24282
D4×C22⋊C4×C732
C73×#20652
C73×#20342
C73×#20112
C73×#19722
C73×#19242
C73×#18792
C73×#18642
#2516873