Finite Group Databasebeta

← C73×#25204 #32934608

Subgroups — C73×#25204 #32934608

Order 18688.

940 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#483×C73C211yesmaximal, characteristic, complemented
2C2×#465×C73C211yesmaximal, characteristic
3C73×#2501C211yesmaximal, characteristic
4C73×#2360C211yesmaximal, characteristic, complemented
5C73×#2084C211yesmaximal, characteristic, complemented
6C73×#2072C211yesmaximal, characteristic, complemented
7C73×#2065C211yesmaximal, characteristic, complemented
8C73×#2055C211yesmaximal, characteristic, complemented
9C73×#1948C211yesmaximal, characteristic, complemented
10C73×#1926C211yesmaximal, characteristic, complemented
11C73×#1880C211yesmaximal, characteristic, complemented
12C73×#1874C211yesmaximal, characteristic
13C73×#1850C211yesmaximal, characteristic, complemented
14C73×#1803C211yesmaximal, characteristic, complemented
15C2×#340×C73C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C23×C8×C73C2211yescharacteristic
18C2×#123×C73—21no—
19C2×#123×C73—21no—
20C2×C22⋊Q8×C73C2211yescharacteristic
21C2×#121×C73C2211yescharacteristic
22C2×C4×Q8×C73C2211yescharacteristic
23C22×C4⋊C4×C73C2211yescharacteristic
24C22×C4⋊C4×C73C2211yescharacteristic
25#483×C73—24no—
26#465×C73—24no—
27C2×#106×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29C2×#106×C73C2211yescharacteristic
30C2×C4⋊C8×C73C2211yescharacteristic
31C2×C4⋊C8×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#103×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39#399×C73—21no—
40#399×C73—21no—
41#391×C73C2211yescharacteristic
42#390×C73C2211yescharacteristic
43#390×C73C2211yescharacteristic
44#389×C73—21no—
45#389×C73C2211yescharacteristic
46#387×C73—21no—
47#385×C73—21no—
48#384×C73C2211yescharacteristic
49#384×C73C2211yescharacteristic
50C4×C4⋊C4×C73C2211yescharacteristic
51C4×C22⋊C4×C73—21no—
52C4×C22⋊C4×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73C2311yescharacteristic
62C22×D4×C73—21no—
63C22×D4×C73C2311yescharacteristic
64C23×C4×C73—21no—
65C23×C4×C73—21no—
66C23×C4×C73C2311yescharacteristic
67C2×SD16×C73—22no—
68C2×SD16×C73—22no—
69C2×SD16×C73—41no—
70C22×C8×C73—22no—
71C22×C8×C73—22no—
72C22×C8×C73—41no—
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77#123×C73—44no—
78#123×C73—44no—
79C22⋊Q8×C73—22no—
80C22⋊Q8×C73D414yes—
81#121×C73—22no—
82#121×C73—22no—
83C4×Q8×C73—22no—
84C4×Q8×C73—41no—
85C2×C4⋊C4×C73—21no—
86C2×C4⋊C4×C73—22no—
87C2×C4⋊C4×C73—22no—
88C2×C4⋊C4×C73—22no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—41no—
98C2×C4⋊C4×C73C2311yescharacteristic
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×C73D411yescharacteristic
111C2×C22⋊C4×C73D411yescharacteristic
112C2×C42×C73—21no—
113C2×C42×C73—21no—
114C2×C42×C73C2311yescharacteristic
115C2×C42×C73C2311yescharacteristic
116#106×C73—22no—
117#106×C73—22no—
118#106×C73—22no—
119C4⋊C8×C73—22no—
120C4⋊C8×C73—41no—
121#103×C73—22no—
122#103×C73—22no—
123#103×C73—22no—
124#102×C73—22no—
125#102×C73—22no—
126#102×C73—41no—
127C22⋊C8×C73—22no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132#95×C73D411yescharacteristic
133#95×C73D411yescharacteristic
134C24×C73—21no—
135C24×C73C2×D411yescharacteristic
136C2×Q8×C73—21no—
137C2×Q8×C73—21no—
138C2×Q8×C73—21no—
139C2×Q8×C73—21no—
140C2×Q8×C73—21no—
141C2×Q8×C73C2×D412yes—
142C2×D4×C73—21no—
143C2×D4×C73—21no—
144C2×D4×C73—21no—
145C2×D4×C73—21no—
146C2×D4×C73—21no—
147C2×D4×C73—21no—
148C2×D4×C73—42no—
149C2×D4×C73—42no—
150C2×D4×C73—42no—
151C22×C4×C73—21no—
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—42no—
163C22×C4×C73—42no—
164C22×C4×C73—42no—
165C22×C4×C73—42no—
166C22×C4×C73—42no—
167C22×C4×C73—81no—
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D412yes—
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73#4112yes—
175C22×C4×C73C2411yescharacteristic
176SD16×C73—44no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—44no—
189C2×C8×C73#4112yes—
190C4⋊C4×C73—24no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—42no—
202C4⋊C4×C73—42no—
203C4⋊C4×C73—42no—
204C4⋊C4×C73—42no—
205C4⋊C4×C73—42no—
206C4⋊C4×C73—42no—
207C4⋊C4×C73—42no—
208C4⋊C4×C73—81no—
209C4⋊C4×C73C2×D412yes—
210C4⋊C4×C73#4112yes—
211C22⋊C4×C73—24no—
212C22⋊C4×C73—22no—
213C22⋊C4×C73—42no—
214C22⋊C4×C73—42no—
215C22⋊C4×C73—42no—
216C22⋊C4×C73—42no—
217C22⋊C4×C73—42no—
218C22⋊C4×C73SD1614yescomplemented
219C42×C73—21no—
220C42×C73—21no—
221C42×C73—21no—
222C42×C73—21no—
223C42×C73—42no—
224C42×C73—81no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—41no—
230C23×C73—41no—
231C23×C73—41no—
232C23×C73—41no—
233C23×C73—41no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73#12112yes—
237C23×C73C2×SD1612yes—
238C23×C73AGL(1,ℤ/8)12yes—
239C23×C73C22×D411yescharacteristic
240Q8×C73—22no—
241Q8×C73—22no—
242Q8×C73—41no—
243Q8×C73—41no—
244D4×C73—41no—
245D4×C73—41no—
246D4×C73—41no—
247D4×C73—41no—
248D4×C73—84no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
260C2×C4×C73—22no—
261C2×C4×C73—21no—
262C2×C4×C73—22no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—84no—
287C2×C4×C73—84no—
288C2×C4×C73#12112yes—
289C2×C4×C73C2×SD1612yes—
290C2×C4×C73C2×SD1612yes—
291C2×C4×C73C22×D411yescharacteristic
292C2×C4×C73C2×#4111yescharacteristic
293C2×C4×C73C2×#4111yescharacteristic
294C2×C4×C73C2×#4111yescharacteristic
295C2×C4×C73H(5,𝔽2)11yescharacteristic
296C2×C4×C732−1+411yescharacteristic
297C8×C73—22no—
298C8×C73—41no—
299C8×C73—41no—
300C8×C73—41no—
301C22×C73—22no—
302C22×C73—22no—
303C22×C73—22no—
304C22×C73—22no—
305C22×C73—22no—
306C22×C73—22no—
307C22×C73—81no—
308C22×C73—81no—
309C22×C73—81no—
310C22×C73—81no—
311C22×C73—81no—
312C22×C73—81no—
313C22×C73—81no—
314C22×C73#46014yes—
315C22×C73C2×#12111yescharacteristic
316C22×C73#54611yescharacteristic
317C22×C73#54711yescharacteristic
318C22×C73C22×SD1611yescharacteristic
319C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
320C22×C73#57711yescharacteristic
321C22×C73#57811yescharacteristic
322C4×C73—22no—
323C4×C73—22no—
324C4×C73—22no—
325C4×C73—41no—
326C4×C73—42no—
327C4×C73—42no—
328C4×C73—41no—
329C4×C73—42no—
330C4×C73—81no—
331C4×C73—81no—
332C4×C73—81no—
333C4×C73—81no—
334C4×C73#52911yescharacteristic
335C4×C73#53911yescharacteristic
336C4×C73#54611yescharacteristic
337C4×C73#54711yescharacteristic
338#25204C7311yesmaximal, characteristic, direct product factor, Sylow
339C2×C73—24no—
340C2×C73—161no—
341C2×C73#242511yescharacteristic
342C2×C73C2×#46011yescharacteristic
343C2×C73#304611yescharacteristic
344C2×C73#329811yescharacteristic
345C2×C73#330611yescharacteristic
346C2×C73#333511yescharacteristic
347C2×C73#334311yescharacteristic
348C2×#483C2×C7311yescharacteristic, complemented
349C2×#465C2×C7311yescharacteristic
350#2501C2×C7311yescharacteristic
351#2360C2×C7311yescharacteristic, complemented
352#2084C2×C7311yescharacteristic, complemented
353#2072C2×C7311yescharacteristic, complemented
354#2065C2×C7311yescharacteristic, complemented
355#2055C2×C7311yescharacteristic, complemented
356#1948C2×C7311yescharacteristic, complemented
357#1926C2×C7311yescharacteristic, complemented
358#1880C2×C7311yescharacteristic, complemented
359#1874C2×C7311yescharacteristic
360#1850C2×C7311yescharacteristic, complemented
361#1803C2×C7311yescharacteristic, complemented
362C2×#340C2×C7311yescharacteristic, complemented
363C73#2520411yescharacteristic, direct product factor, Sylow
364C22×SD16C22×C7311yescharacteristic
365C23×C8C22×C7311yescharacteristic
366C2×#123—21no—
367C2×#123—21no—
368C2×C22⋊Q8C22×C7311yescharacteristic
369C2×#121C22×C7311yescharacteristic
370C2×C4×Q8C22×C7311yescharacteristic
371C22×C4⋊C4C22×C7311yescharacteristic
372C22×C4⋊C4C22×C7311yescharacteristic
373#483—24no—
374#465—24no—
375C2×#106C22×C7311yescharacteristic
376C2×#106C22×C7311yescharacteristic
377C2×#106C22×C7311yescharacteristic
378C2×C4⋊C8C22×C7311yescharacteristic
379C2×C4⋊C8C22×C7311yescharacteristic
380C2×#103C22×C7311yescharacteristic
381C2×#103C22×C7311yescharacteristic
382C2×#103C22×C7311yescharacteristic
383C2×#102C22×C7311yescharacteristic
384C2×#102C22×C7311yescharacteristic
385C2×#102C22×C7311yescharacteristic
386C2×C22⋊C8C22×C7311yescharacteristic
387#399—21no—
388#399—21no—
389#391C22×C7311yescharacteristic
390#390C22×C7311yescharacteristic
391#390C22×C7311yescharacteristic
392#389—21no—
393#389C22×C7311yescharacteristic
394#387—21no—
395#385—21no—
396#384C22×C7311yescharacteristic
397#384C22×C7311yescharacteristic
398C4×C4⋊C4C22×C7311yescharacteristic
399C4×C22⋊C4—21no—
400C4×C22⋊C4C22×C7311yescharacteristic
401#340C22×C7311yescharacteristic
402#340C22×C7311yescharacteristic
403#340C22×C7311yescharacteristic
404#340C22×C7311yescharacteristic
405#340C22×C7311yescharacteristic
406#340C22×C7311yescharacteristic
407#336C22×C7311yescharacteristic
408#336C22×C7311yescharacteristic
409C22×Q8C23×C7311yescharacteristic
410C22×D4—21no—
411C22×D4C23×C7311yescharacteristic
412C23×C4—21no—
413C23×C4—21no—
414C23×C4C23×C7311yescharacteristic
415C2×SD16—22no—
416C2×SD16—22no—
417C2×SD16—41no—
418C22×C8—22no—
419C22×C8—22no—
420C22×C8—41no—
421C22×C8C23×C7311yescharacteristic
422C22×C8C23×C7311yescharacteristic
423C22×C8C23×C7311yescharacteristic
424C22×C8C23×C7311yescharacteristic
425#123—44no—
426#123—44no—
427C22⋊Q8—22no—
428C22⋊Q8D4×C7314yes—
429#121—22no—
430#121—22no—
431C4×Q8—22no—
432C4×Q8—41no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—41no—
446C2×C4⋊C4C23×C7311yescharacteristic
447C2×C4⋊C4C23×C7311yescharacteristic
448C2×C4⋊C4C23×C7311yescharacteristic
449C2×C4⋊C4C23×C7311yescharacteristic
450C2×C4⋊C4C23×C7311yescharacteristic
451C2×C4⋊C4C23×C7311yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4D4×C7311yescharacteristic
459C2×C22⋊C4D4×C7311yescharacteristic
460C2×C42—21no—
461C2×C42—21no—
462C2×C42C23×C7311yescharacteristic
463C2×C42C23×C7311yescharacteristic
464#106—22no—
465#106—22no—
466#106—22no—
467C4⋊C8—22no—
468C4⋊C8—41no—
469#103—22no—
470#103—22no—
471#103—22no—
472#102—22no—
473#102—22no—
474#102—41no—
475C22⋊C8—22no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95D4×C7311yescharacteristic
481#95D4×C7311yescharacteristic
482C24—21no—
483C24C2×D4×C7311yescharacteristic
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8C2×D4×C7312yes—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—81no—
516C22×C4C2×D4×C7311yescharacteristic
517C22×C4C2×D4×C7311yescharacteristic
518C22×C4C2×D4×C7311yescharacteristic
519C22×C4C2×D4×C7312yes—
520C22×C4C2×D4×C7311yescharacteristic
521C22×C4C2×D4×C7311yescharacteristic
522C22×C4#41×C7312yes—
523C22×C4C24×C7311yescharacteristic
524SD16—44no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—44no—
537C2×C8#41×C7312yes—
538C4⋊C4—24no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—81no—
557C4⋊C4C2×D4×C7312yes—
558C4⋊C4#41×C7312yes—
559C22⋊C4—24no—
560C22⋊C4—22no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4SD16×C7314yescomplemented
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C42—81no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23#121×C7312yes—
585C23C2×SD16×C7312yes—
586C23AGL(1,ℤ/8)×C7312yes—
587C23C22×D4×C7311yescharacteristic
588Q8—22no—
589Q8—22no—
590Q8—41no—
591Q8—41no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—84no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—84no—
635C2×C4—84no—
636C2×C4#121×C7312yes—
637C2×C4C2×SD16×C7312yes—
638C2×C4C2×SD16×C7312yes—
639C2×C4C22×D4×C7311yescharacteristic
640C2×C4C2×#41×C7311yescharacteristic
641C2×C4C2×#41×C7311yescharacteristic
642C2×C4C2×#41×C7311yescharacteristic
643C2×C4H(5,𝔽2)×C7311yescharacteristic
644C2×C42−1+4×C7311yescharacteristic
645C8—22no—
646C8—41no—
647C8—41no—
648C8—41no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22#460×C7314yes—
663C22C2×#121×C7311yescharacteristic
664C22#546×C7311yescharacteristic
665C22#547×C7311yescharacteristic
666C22C22×SD16×C7311yescharacteristic
667C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
668C22#577×C7311yescharacteristic
669C22#578×C7311yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—42no—
674C4—41no—
675C4—42no—
676C4—41no—
677C4—42no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4#529×C7311yescharacteristic
683C4#539×C7311yescharacteristic
684C4#546×C7311yescharacteristic
685C4#547×C7311yescharacteristic
686C2—24no—
687C2—161no—
688C2C73×#242511yescharacteristic
689C2C2×#460×C7311yescharacteristic
690C2C73×#304611yescharacteristic
691C2C73×#329811yescharacteristic
692C2C73×#330611yescharacteristic
693C2C73×#333511yescharacteristic
694C2C73×#334311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#121×C73C22
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×#483×C73C2semidirect
4. C73×#2360C2semidirect
5. C73×#2084C2semidirect
6. C73×#2072C2semidirect
7. C73×#2065C2semidirect
8. C73×#2055C2semidirect
9. C73×#1948C2semidirect
10. C73×#1926C2semidirect
11. C73×#1880C2semidirect
13. C73×#1850C2semidirect
14. C73×#1803C2semidirect
15. C2×#340×C73C2semidirect
218. C22⋊C4×C73SD16semidirect
338. #25204C73direct (N × H)
348. C2×#483C2×C73semidirect
351. #2360C2×C73semidirect
352. #2084C2×C73semidirect
353. #2072C2×C73semidirect
354. #2065C2×C73semidirect
355. #2055C2×C73semidirect
356. #1948C2×C73semidirect
357. #1926C2×C73semidirect
358. #1880C2×C73semidirect
360. #1850C2×C73semidirect
361. #1803C2×C73semidirect
362. C2×#340C2×C73semidirect
363. C73#25204direct (N × H)
566. C22⋊C4SD16×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#483×C732
C2×#465×C732
C73×#25012
C73×#23602
C73×#20842
C73×#20722
C73×#20652
C73×#20552
C73×#19482
C73×#19262
C73×#18802
C73×#18742
C73×#18502
C73×#18032
C2×#340×C732
#2520473