Finite Group Databasebeta

← C73×#24913 #32934317

Subgroups — C73×#24913 #32934317

Order 18688.

1226 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C73C211yesmaximal, characteristic
2C2×#442×C73C211yesmaximal, characteristic, complemented
3C73×#2422C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C73C211yesmaximal, characteristic, complemented
5C73×#2094C211yesmaximal, characteristic, complemented
6C73×#2077C211yesmaximal, characteristic, complemented
7C73×#2054C211yesmaximal, characteristic, complemented
8C73×#2034C211yesmaximal, characteristic, complemented
9C73×#1936C211yesmaximal, characteristic, complemented
10C73×#1924C211yesmaximal, characteristic, complemented
11C73×#1879C211yesmaximal, characteristic, complemented
12C73×#1879C211yesmaximal, characteristic, complemented
13C73×#1864C211yesmaximal, characteristic, complemented
14C73×#1802C211yesmaximal, characteristic, complemented
15C73×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C22×D8×C73C2211yescharacteristic
19C2×#123×C73—21no—
20C2×#121×C73C2211yescharacteristic
21C2×C4×D4×C73C2211yescharacteristic
22C2×C4×D4×C73C2211yescharacteristic
23C2×C4×D4×C73C2211yescharacteristic, complemented
24C22×C22⋊C4×C73—21no—
25#447×C73—24no—
26#442×C73—24no—
27C2×#106×C73C2211yescharacteristic, complemented
28C2×#106×C73C2211yescharacteristic, complemented
29C2×C4⋊C8×C73C2211yescharacteristic, complemented
30C2×#102×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic, complemented
37C2×#102×C73C2211yescharacteristic, complemented
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×C22⋊C8×C73C2211yescharacteristic
40C2×#97×C73C2211yescharacteristic, complemented
41#397×C73—21no—
42#394×C73—21no—
43#390×C73C2211yescharacteristic
44#390×C73C2211yescharacteristic
45#390×C73C2211yescharacteristic, complemented
46#389×C73C2211yescharacteristic, complemented
47#386×C73—21no—
48#386×C73—21no—
49#385×C73—21no—
50#384×C73C2211yescharacteristic, complemented
51#380×C73C2211yescharacteristic
52#380×C73C2211yescharacteristic
53#379×C73—21no—
54C4×C22⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic, complemented
56#340×C73C2211yescharacteristic, complemented
57#340×C73C2211yescharacteristic, complemented
58#340×C73C2211yescharacteristic, complemented
59#336×C73C2211yescharacteristic, complemented
60#336×C73C2211yescharacteristic, complemented
61C25×C73—21no—
62C22×D4×C73—22no—
63C22×D4×C73—22no—
64C22×D4×C73—22no—
65C22×D4×C73—22no—
66C22×D4×C73—21no—
67C22×D4×C73—21no—
68C22×D4×C73—41no—
69C22×D4×C73—41no—
70C22×D4×C73C2311yescharacteristic
71C22×D4×C73C2311yescharacteristic
72C22×D4×C73C2311yescharacteristic
73C23×C4×C73—21no—
74C23×C4×C73—21no—
75C23×C4×C73—21no—
76C23×C4×C73C2311yescharacteristic
77C2×D8×C73—22no—
78C2×D8×C73—22no—
79C2×D8×C73—22no—
80C2×D8×C73—22no—
81C2×D8×C73—41no—
82C2×D8×C73D414yes—
83C22×C8×C73C2311yescharacteristic
84C22×C8×C73C2311yescharacteristic
85C22×C8×C73C2311yescharacteristic
86C22×C8×C73C2311yescharacteristic
87#123×C73—44no—
88#121×C73—22no—
89#121×C73—41no—
90C4×D4×C73—22no—
91C4×D4×C73—22no—
92C4×D4×C73—22no—
93C4×D4×C73—41no—
94C4×D4×C73—41no—
95C4×D4×C73—41no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73—21no—
112C2×C22⋊C4×C73—21no—
113C2×C22⋊C4×C73—21no—
114C2×C22⋊C4×C73—21no—
115C2×C22⋊C4×C73—21no—
116C2×C22⋊C4×C73—44no—
117C2×C22⋊C4×C73D411yescharacteristic
118C2×C22⋊C4×C73D411yescharacteristic
119C2×C42×C73C2311yescharacteristic
120C2×C42×C73C2311yescharacteristic
121#106×C73—22no—
122#106×C73—41no—
123C4⋊C8×C73—41no—
124#102×C73—22no—
125#102×C73—22no—
126#102×C73—22no—
127#102×C73—22no—
128#102×C73—22no—
129#102×C73—22no—
130#102×C73—41no—
131#102×C73—41no—
132C22⋊C8×C73—22no—
133C22⋊C8×C73—41no—
134#97×C73—22no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73—21no—
138#95×C73D411yescharacteristic
139#95×C73D411yescharacteristic
140C24×C73—21no—
141C24×C73—24no—
142C24×C73—21no—
143C24×C73—21no—
144C24×C73—42no—
145C24×C73—42no—
146C24×C73—42no—
147C24×C73—42no—
148C24×C73—81no—
149C24×C73—81no—
150C24×C73C2×D411yescharacteristic
151C2×D4×C73—24no—
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—21no—
159C2×D4×C73—21no—
160C2×D4×C73—21no—
161C2×D4×C73—21no—
162C2×D4×C73—21no—
163C2×D4×C73—21no—
164C2×D4×C73—21no—
165C2×D4×C73—42no—
166C2×D4×C73—42no—
167C2×D4×C73—44no—
168C2×D4×C73—44no—
169C2×D4×C73—44no—
170C2×D4×C73—44no—
171C2×D4×C73—42no—
172C2×D4×C73—42no—
173C2×D4×C73—81no—
174C2×D4×C73C2×D412yes—
175C2×D4×C73C2×D412yes—
176C2×D4×C73#4112yes—
177C2×D4×C73#4112yes—
178C2×D4×C73#4112yes—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—42no—
191C22×C4×C73—42no—
192C22×C4×C73—42no—
193C22×C4×C73—42no—
194C22×C4×C73—42no—
195C22×C4×C73—42no—
196C22×C4×C73—81no—
197C22×C4×C73—81no—
198C22×C4×C73—81no—
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201C22×C4×C73C2×D411yescharacteristic
202C22×C4×C73C2×D411yescharacteristic
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2411yescharacteristic
205D8×C73—28no—
206D8×C73—44no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73C2×D412yes—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—21no—
226C4⋊C4×C73—21no—
227C4⋊C4×C73—21no—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—42no—
230C4⋊C4×C73—42no—
231C4⋊C4×C73—81no—
232C22⋊C4×C73—22no—
233C22⋊C4×C73—22no—
234C22⋊C4×C73—42no—
235C22⋊C4×C73—42no—
236C22⋊C4×C73—42no—
237C22⋊C4×C73—42no—
238C22⋊C4×C73—42no—
239C22⋊C4×C73—42no—
240C22⋊C4×C73—42no—
241C22⋊C4×C73—42no—
242C22⋊C4×C73—42no—
243C22⋊C4×C73—42no—
244C22⋊C4×C73—81no—
245C22⋊C4×C73—81no—
246C42×C73—21no—
247C42×C73—21no—
248C42×C73—21no—
249C42×C73—21no—
250C23×C73—21no—
251C23×C73—22no—
252C23×C73—22no—
253C23×C73—21no—
254C23×C73—22no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73—22no—
260C23×C73—22no—
261C23×C73—48no—
262C23×C73—48no—
263C23×C73—41no—
264C23×C73—41no—
265C23×C73—41no—
266C23×C73—41no—
267C23×C73—41no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—41no—
272C23×C73—41no—
273C23×C73—41no—
274C23×C73—41no—
275C23×C73—41no—
276C23×C73—41no—
277C23×C73—41no—
278C23×C73—41no—
279C23×C73—84no—
280C23×C73—84no—
281C23×C73—84no—
282C23×C73—84no—
283C23×C73—84no—
284C23×C73AGL(1,ℤ/8)12yes—
285C23×C73C22×D411yescharacteristic
286D4×C73—22no—
287D4×C73—22no—
288D4×C73—22no—
289D4×C73—22no—
290D4×C73—22no—
291D4×C73—22no—
292D4×C73—22no—
293D4×C73—48no—
294D4×C73—41no—
295D4×C73—41no—
296D4×C73—41no—
297D4×C73—41no—
298D4×C73—84no—
299D4×C73#12314yescomplemented
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—21no—
312C2×C4×C73—21no—
313C2×C4×C73—21no—
314C2×C4×C73—41no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73—41no—
318C2×C4×C73—41no—
319C2×C4×C73—41no—
320C2×C4×C73—41no—
321C2×C4×C73—41no—
322C2×C4×C73—41no—
323C2×C4×C73—41no—
324C2×C4×C73—41no—
325C2×C4×C73—41no—
326C2×C4×C73—41no—
327C2×C4×C73—41no—
328C2×C4×C73—41no—
329C2×C4×C73—41no—
330C2×C4×C73—41no—
331C2×C4×C73—41no—
332C2×C4×C73—41no—
333C2×C4×C73—84no—
334C2×C4×C73—84no—
335C2×C4×C73—84no—
336C2×C4×C73AGL(1,ℤ/8)12yes—
337C2×C4×C73C22×D411yescharacteristic
338C2×C4×C73C2×#4111yescharacteristic
339C2×C4×C73C2×#4111yescharacteristic
340C2×C4×C73C2×#4111yescharacteristic
341C2×C4×C73H(5,𝔽2)11yescharacteristic
342C2×C4×C73H(5,𝔽2)11yescharacteristic
343C8×C73—22no—
344C8×C73—41no—
345C8×C73—41no—
346C8×C73—41no—
347C22×C73—22no—
348C22×C73—24no—
349C22×C73—22no—
350C22×C73—22no—
351C22×C73—42no—
352C22×C73—41no—
353C22×C73—42no—
354C22×C73—41no—
355C22×C73—42no—
356C22×C73—42no—
357C22×C73—41no—
358C22×C73—42no—
359C22×C73—42no—
360C22×C73—41no—
361C22×C73—42no—
362C22×C73—42no—
363C22×C73—42no—
364C22×C73—42no—
365C22×C73—42no—
366C22×C73—42no—
367C22×C73—816no—
368C22×C73—81no—
369C22×C73—81no—
370C22×C73—81no—
371C22×C73—81no—
372C22×C73—81no—
373C22×C73—81no—
374C22×C73—81no—
375C22×C73—81no—
376C22×C73#52511yescharacteristic
377C22×C73D4211yescharacteristic
378C22×C73#54611yescharacteristic
379C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
380C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
381C22×C73#57611yescharacteristic
382C22×C73#57711yescharacteristic
383C4×C73—22no—
384C4×C73—41no—
385C4×C73—41no—
386C4×C73—41no—
387C4×C73—41no—
388C4×C73—81no—
389C4×C73—81no—
390C4×C73—81no—
391C4×C73—81no—
392C4×C73—81no—
393C4×C73C2×#12311yescharacteristic
394C4×C73#53811yescharacteristic
395C4×C73#54611yescharacteristic
396C4×C73#55111yescharacteristic
397#24913C7311yesmaximal, characteristic, direct product factor, Sylow
398C2×C73—42no—
399C2×C73—44no—
400C2×C73—82no—
401C2×C73—82no—
402C2×C73#241811yescharacteristic
403C2×C73#310911yescharacteristic
404C2×C73#311811yescharacteristic
405C2×C73#326411yescharacteristic
406C2×C73#327211yescharacteristic
407C2×C73#330611yescharacteristic
408C2×C73#331811yescharacteristic
409C2×#447C2×C7311yescharacteristic
410C2×#442C2×C7311yescharacteristic, complemented
411#2422C2×C7311yescharacteristic, complemented
412D4×C22⋊C4C2×C7311yescharacteristic, complemented
413#2094C2×C7311yescharacteristic, complemented
414#2077C2×C7311yescharacteristic, complemented
415#2054C2×C7311yescharacteristic, complemented
416#2034C2×C7311yescharacteristic, complemented
417#1936C2×C7311yescharacteristic, complemented
418#1924C2×C7311yescharacteristic, complemented
419#1879C2×C7311yescharacteristic, complemented
420#1879C2×C7311yescharacteristic, complemented
421#1864C2×C7311yescharacteristic, complemented
422#1802C2×C7311yescharacteristic, complemented
423#1786C2×C7311yescharacteristic, complemented
424C73#2491311yescharacteristic, direct product factor, Sylow
425C23×D4C22×C7311yescharacteristic
426C22×D8C22×C7311yescharacteristic
427C22×D8C22×C7311yescharacteristic
428C2×#123—21no—
429C2×#121C22×C7311yescharacteristic
430C2×C4×D4C22×C7311yescharacteristic
431C2×C4×D4C22×C7311yescharacteristic
432C2×C4×D4C22×C7311yescharacteristic, complemented
433C22×C22⋊C4—21no—
434#447—24no—
435#442—24no—
436C2×#106C22×C7311yescharacteristic, complemented
437C2×#106C22×C7311yescharacteristic, complemented
438C2×C4⋊C8C22×C7311yescharacteristic, complemented
439C2×#102C22×C7311yescharacteristic
440C2×#102C22×C7311yescharacteristic
441C2×#102C22×C7311yescharacteristic
442C2×#102C22×C7311yescharacteristic
443C2×#102C22×C7311yescharacteristic
444C2×#102C22×C7311yescharacteristic
445C2×#102C22×C7311yescharacteristic, complemented
446C2×#102C22×C7311yescharacteristic, complemented
447C2×C22⋊C8C22×C7311yescharacteristic
448C2×C22⋊C8C22×C7311yescharacteristic
449C2×#97C22×C7311yescharacteristic, complemented
450#397—21no—
451#394—21no—
452#390C22×C7311yescharacteristic
453#390C22×C7311yescharacteristic
454#390C22×C7311yescharacteristic, complemented
455#389C22×C7311yescharacteristic, complemented
456#386—21no—
457#386—21no—
458#385—21no—
459#384C22×C7311yescharacteristic, complemented
460#380C22×C7311yescharacteristic
461#380C22×C7311yescharacteristic
462#379—21no—
463C4×C22⋊C4C22×C7311yescharacteristic
464#340C22×C7311yescharacteristic, complemented
465#340C22×C7311yescharacteristic, complemented
466#340C22×C7311yescharacteristic, complemented
467#340C22×C7311yescharacteristic, complemented
468#336C22×C7311yescharacteristic, complemented
469#336C22×C7311yescharacteristic, complemented
470C25—21no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—41no—
478C22×D4—41no—
479C22×D4C23×C7311yescharacteristic
480C22×D4C23×C7311yescharacteristic
481C22×D4C23×C7311yescharacteristic
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C7311yescharacteristic
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—41no—
491C2×D8D4×C7314yes—
492C22×C8C23×C7311yescharacteristic
493C22×C8C23×C7311yescharacteristic
494C22×C8C23×C7311yescharacteristic
495C22×C8C23×C7311yescharacteristic
496#123—44no—
497#121—22no—
498#121—41no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—41no—
503C4×D4—41no—
504C4×D4—41no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4C23×C7311yescharacteristic
509C2×C4⋊C4C23×C7311yescharacteristic
510C2×C4⋊C4C23×C7311yescharacteristic
511C2×C4⋊C4C23×C7311yescharacteristic
512C2×C4⋊C4C23×C7311yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—44no—
526C2×C22⋊C4D4×C7311yescharacteristic
527C2×C22⋊C4D4×C7311yescharacteristic
528C2×C42C23×C7311yescharacteristic
529C2×C42C23×C7311yescharacteristic
530#106—22no—
531#106—41no—
532C4⋊C8—41no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—22no—
538#102—22no—
539#102—41no—
540#102—41no—
541C22⋊C8—22no—
542C22⋊C8—41no—
543#97—22no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95D4×C7311yescharacteristic
548#95D4×C7311yescharacteristic
549C24—21no—
550C24—24no—
551C24—21no—
552C24—21no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—81no—
558C24—81no—
559C24C2×D4×C7311yescharacteristic
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—44no—
579C2×D4—44no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—81no—
583C2×D4C2×D4×C7312yes—
584C2×D4C2×D4×C7312yes—
585C2×D4#41×C7312yes—
586C2×D4#41×C7312yes—
587C2×D4#41×C7312yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4C2×D4×C7311yescharacteristic
609C22×C4C2×D4×C7311yescharacteristic
610C22×C4C2×D4×C7311yescharacteristic
611C22×C4C2×D4×C7311yescharacteristic
612C22×C4C2×D4×C7311yescharacteristic
613C22×C4C24×C7311yescharacteristic
614D8—28no—
615D8—44no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8C2×D4×C7312yes—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—81no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—81no—
654C22⋊C4—81no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—22no—
670C23—48no—
671C23—48no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—84no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23AGL(1,ℤ/8)×C7312yes—
694C23C22×D4×C7311yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4#123×C7314yescomplemented
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4AGL(1,ℤ/8)×C7312yes—
746C2×C4C22×D4×C7311yescharacteristic
747C2×C4C2×#41×C7311yescharacteristic
748C2×C4C2×#41×C7311yescharacteristic
749C2×C4C2×#41×C7311yescharacteristic
750C2×C4H(5,𝔽2)×C7311yescharacteristic
751C2×C4H(5,𝔽2)×C7311yescharacteristic
752C8—22no—
753C8—41no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—24no—
760C22—42no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—42no—
769C22—41no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—816no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22#525×C7311yescharacteristic
786C22D42×C7311yescharacteristic
787C22#546×C7311yescharacteristic
788C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
789C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
790C22#576×C7311yescharacteristic
791C22#577×C7311yescharacteristic
792C4—22no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4C2×#123×C7311yescharacteristic
803C4#538×C7311yescharacteristic
804C4#546×C7311yescharacteristic
805C4#551×C7311yescharacteristic
806C2—42no—
807C2—44no—
808C2—82no—
809C2—82no—
810C2C73×#241811yescharacteristic
811C2C73×#310911yescharacteristic
812C2C73×#311811yescharacteristic
813C2C73×#326411yescharacteristic
814C2C73×#327211yescharacteristic
815C2C73×#330611yescharacteristic
816C2C73×#331811yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#447×C73C2
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
2. C2×#442×C73C2semidirect
3. C73×#2422C2semidirect
4. D4×C22⋊C4×C73C2semidirect
5. C73×#2094C2semidirect
6. C73×#2077C2semidirect
7. C73×#2054C2semidirect
8. C73×#2034C2semidirect
9. C73×#1936C2semidirect
10. C73×#1924C2semidirect
11. C73×#1879C2semidirect
12. C73×#1879C2semidirect
13. C73×#1864C2semidirect
14. C73×#1802C2semidirect
15. C73×#1786C2semidirect
23. C2×C4×D4×C73C22semidirect
27. C2×#106×C73C22semidirect
28. C2×#106×C73C22semidirect
29. C2×C4⋊C8×C73C22semidirect
36. C2×#102×C73C22semidirect
37. C2×#102×C73C22semidirect
40. C2×#97×C73C22semidirect
45. #390×C73C22semidirect
46. #389×C73C22semidirect
50. #384×C73C22semidirect
55. #340×C73C22semidirect
56. #340×C73C22semidirect
57. #340×C73C22semidirect
58. #340×C73C22semidirect
59. #336×C73C22semidirect
60. #336×C73C22semidirect
299. D4×C73#123semidirect
397. #24913C73direct (N × H)
410. C2×#442C2×C73semidirect
411. #2422C2×C73semidirect
412. D4×C22⋊C4C2×C73semidirect
413. #2094C2×C73semidirect
414. #2077C2×C73semidirect
415. #2054C2×C73semidirect
416. #2034C2×C73semidirect
417. #1936C2×C73semidirect
418. #1924C2×C73semidirect
419. #1879C2×C73semidirect
420. #1879C2×C73semidirect
421. #1864C2×C73semidirect
422. #1802C2×C73semidirect
423. #1786C2×C73semidirect
424. C73#24913direct (N × H)
432. C2×C4×D4C22×C73semidirect
436. C2×#106C22×C73semidirect
437. C2×#106C22×C73semidirect
438. C2×C4⋊C8C22×C73semidirect
445. C2×#102C22×C73semidirect
446. C2×#102C22×C73semidirect
449. C2×#97C22×C73semidirect
454. #390C22×C73semidirect
455. #389C22×C73semidirect
459. #384C22×C73semidirect
464. #340C22×C73semidirect
465. #340C22×C73semidirect
466. #340C22×C73semidirect
467. #340C22×C73semidirect
468. #336C22×C73semidirect
469. #336C22×C73semidirect
708. D4#123×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C732
C2×#442×C732
C73×#24222
D4×C22⋊C4×C732
C73×#20942
C73×#20772
C73×#20542
C73×#20342
C73×#19362
C73×#19242
C73×#18792
C73×#18642
C73×#18022
C73×#17862
#2491373