Finite Group Databasebeta

← C73×#25561 #32934965

Subgroups — C73×#25561 #32934965

Order 18688.

1124 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C73C211yesmaximal, characteristic
2C2×#483×C73C211yesmaximal, characteristic, complemented
3C2×#470×C73C211yesmaximal, characteristic, complemented
4C73×#2415C211yesmaximal, characteristic
5C73×#2058C211yesmaximal, characteristic, complemented
6C73×#2035C211yesmaximal, characteristic, complemented
7C73×#2024C211yesmaximal, characteristic, complemented
8C73×#2001C211yesmaximal, characteristic, complemented
9C73×#1878C211yesmaximal, characteristic, complemented
10C73×#1873C211yesmaximal, characteristic, complemented
11C73×#1872C211yesmaximal, characteristic, complemented
12C73×#1870C211yesmaximal, characteristic
13C73×#1865C211yesmaximal, characteristic, complemented
14C73×#1853C211yesmaximal, characteristic, complemented
15C73×#1736C211yesmaximal, characteristic, complemented
16C22×Q16×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18#554×C73—24no—
19#554×C73—24no—
20C2×C4⋊Q8×C73C2211yescharacteristic
21C2×#125×C73—21no—
22C2×C22⋊Q8×C73—21no—
23C2×C22⋊Q8×C73—21no—
24C2×C22⋊Q8×C73C2211yescharacteristic
25C2×C22⋊Q8×C73C2211yescharacteristic
26C2×C22⋊Q8×C73C2211yescharacteristic
27C2×C22⋊Q8×C73C2211yescharacteristic
28C2×C4×Q8×C73C2211yescharacteristic
29C2×C4×D4×C73—21no—
30C2×C4×D4×C73C2211yescharacteristic
31C2×#117×C73C2211yescharacteristic
32C22×C4⋊C4×C73C2211yescharacteristic
33C22×C4⋊C4×C73C2211yescharacteristic
34#483×C73—24no—
35#470×C73—24no—
36C2×#106×C73C2211yescharacteristic
37C2×#106×C73C2211yescharacteristic
38C2×#106×C73C2211yescharacteristic
39C2×#103×C73C2211yescharacteristic
40C2×#103×C73C2211yescharacteristic
41C2×#103×C73C2211yescharacteristic
42C2×#103×C73C2211yescharacteristic
43C2×#103×C73C2211yescharacteristic
44C2×#103×C73C2211yescharacteristic
45C2×C22⋊C8×C73C2211yescharacteristic
46C2×C22⋊C8×C73C2211yescharacteristic
47C2×C22⋊C8×C73C2211yescharacteristic
48#397×C73—21no—
49#394×C73—21no—
50#391×C73C2211yescharacteristic
51#389×C73—21no—
52#389×C73C2211yescharacteristic
53#388×C73—21no—
54#380×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×C73C2211yescharacteristic
63C22×Q8×C73—21no—
64C22×Q8×C73C2311yescharacteristic
65C22×Q8×C73C2311yescharacteristic
66C22×D4×C73D411yescharacteristic
67C23×C4×C73—21no—
68C23×C4×C73—21no—
69C23×C4×C73C2311yescharacteristic
70C23×C4×C73C2311yescharacteristic
71C2×Q16×C73—22no—
72C2×Q16×C73—22no—
73C2×Q16×C73—41no—
74C2×M16×C73—22no—
75C2×M16×C73—22no—
76C2×M16×C73—41no—
77C22×C8×C73C2311yescharacteristic
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C4⋊Q8×C73—22no—
82C4⋊Q8×C73—22no—
83#125×C73—28no—
84C22⋊Q8×C73—28no—
85C22⋊Q8×C73—28no—
86C22⋊Q8×C73—22no—
87C22⋊Q8×C73—22no—
88C22⋊Q8×C73—22no—
89C22⋊Q8×C73—22no—
90C22⋊Q8×C73—22no—
91C22⋊Q8×C73—22no—
92C22⋊Q8×C73—41no—
93C22⋊Q8×C73D414yes—
94C4×Q8×C73—22no—
95C4×Q8×C73—22no—
96C4×D4×C73—28no—
97C4×D4×C73—22no—
98C4×D4×C73—22no—
99#117×C73—22no—
100#117×C73—41no—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73—21no—
103C2×C4⋊C4×C73—22no—
104C2×C4⋊C4×C73—21no—
105C2×C4⋊C4×C73—21no—
106C2×C4⋊C4×C73—21no—
107C2×C4⋊C4×C73—21no—
108C2×C4⋊C4×C73—22no—
109C2×C4⋊C4×C73—22no—
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73—21no—
113C2×C4⋊C4×C73D411yescharacteristic
114C2×C4⋊C4×C73D414yes—
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C4⋊C4×C73C2311yescharacteristic
119C2×C4⋊C4×C73C2311yescharacteristic
120C2×C4⋊C4×C73C2311yescharacteristic
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×C73D411yescharacteristic
128C2×C22⋊C4×C73D411yescharacteristic
129C2×C42×C73—21no—
130C2×C42×C73—21no—
131C2×C42×C73C2311yescharacteristic
132#106×C73—22no—
133#106×C73—22no—
134#106×C73—22no—
135#103×C73—22no—
136#103×C73—22no—
137#103×C73—22no—
138#103×C73—22no—
139#103×C73—22no—
140#103×C73—41no—
141C22⋊C8×C73—22no—
142C22⋊C8×C73—22no—
143C22⋊C8×C73—41no—
144#95×C73—21no—
145#95×C73—21no—
146#95×C73—21no—
147#95×C73—21no—
148C24×C73C2×D411yescharacteristic
149C24×C73C2×D411yescharacteristic
150C2×Q8×C73—24no—
151C2×Q8×C73—21no—
152C2×Q8×C73—21no—
153C2×Q8×C73—21no—
154C2×Q8×C73—21no—
155C2×Q8×C73—21no—
156C2×Q8×C73—21no—
157C2×Q8×C73—21no—
158C2×Q8×C73—21no—
159C2×Q8×C73—21no—
160C2×Q8×C73—21no—
161C2×Q8×C73—21no—
162C2×Q8×C73—81no—
163C2×Q8×C73—81no—
164C2×Q8×C73C2×D412yes—
165C2×D4×C73—22no—
166C2×D4×C73—22no—
167C2×D4×C73—22no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—24no—
178C22×C4×C73—24no—
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—81no—
189C22×C4×C73—81no—
190C22×C4×C73—81no—
191C22×C4×C73—81no—
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73C2×D412yes—
196C22×C4×C73C2×D412yes—
197C22×C4×C73C2×D411yescharacteristic
198C22×C4×C73C2411yescharacteristic
199Q16×C73—44no—
200M16×C73—44no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73#4112yes—
213C4⋊C4×C73—24no—
214C4⋊C4×C73—24no—
215C4⋊C4×C73—24no—
216C4⋊C4×C73—24no—
217C4⋊C4×C73—24no—
218C4⋊C4×C73—24no—
219C4⋊C4×C73—22no—
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—42no—
229C4⋊C4×C73—42no—
230C4⋊C4×C73—42no—
231C4⋊C4×C73C2×D412yes—
232C4⋊C4×C73C2×D412yes—
233C4⋊C4×C73C2×D412yes—
234C4⋊C4×C73#4112yes—
235C22⋊C4×C73—24no—
236C22⋊C4×C73—24no—
237C22⋊C4×C73—22no—
238C22⋊C4×C73—22no—
239C22⋊C4×C73—42no—
240C22⋊C4×C73—42no—
241C22⋊C4×C73—42no—
242C22⋊C4×C73—42no—
243C42×C73—24no—
244C42×C73—21no—
245C42×C73—21no—
246C42×C73—42no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73#12012yes—
260C23×C73#13712yes—
261C23×C73C22×D411yescharacteristic
262Q8×C73—22no—
263Q8×C73—22no—
264Q8×C73—41no—
265Q8×C73—41no—
266Q8×C73—41no—
267Q8×C73—41no—
268Q8×C73—41no—
269Q8×C73—41no—
270Q8×C73—84no—
271D4×C73—28no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—21no—
282C2×C4×C73—22no—
283C2×C4×C73—21no—
284C2×C4×C73—22no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
310C2×C4×C73—41no—
311C2×C4×C73—41no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
314C2×C4×C73—84no—
315C2×C4×C73—84no—
316C2×C4×C73#12012yes—
317C2×C4×C73#13712yes—
318C2×C4×C73C22×D411yescharacteristic
319C2×C4×C73C22×D411yescharacteristic
320C2×C4×C73C2×#4111yescharacteristic
321C2×C4×C73C2×#4111yescharacteristic
322C2×C4×C73H(5,𝔽2)11yescharacteristic
323C2×C4×C732−1+411yescharacteristic
324C8×C73—22no—
325C8×C73—41no—
326C8×C73—41no—
327C8×C73—41no—
328C22×C73—22no—
329C22×C73—22no—
330C22×C73—22no—
331C22×C73—22no—
332C22×C73—22no—
333C22×C73—22no—
334C22×C73—41no—
335C22×C73—41no—
336C22×C73—41no—
337C22×C73—41no—
338C22×C73—41no—
339C22×C73—41no—
340C22×C73—41no—
341C22×C73—41no—
342C22×C73C2×#12011yescharacteristic
343C22×C73#54611yescharacteristic
344C22×C73#54711yescharacteristic
345C22×C73C2×#13711yescharacteristic
346C22×C73C2×#13711yescharacteristic
347C22×C73#57711yescharacteristic
348C22×C73#57711yescharacteristic
349C4×C73—22no—
350C4×C73—22no—
351C4×C73—42no—
352C4×C73—41no—
353C4×C73—42no—
354C4×C73—41no—
355C4×C73—42no—
356C4×C73—42no—
357C4×C73—42no—
358C4×C73—81no—
359C4×C73—81no—
360C4×C73—81no—
361C4×C73#53211yescharacteristic
362C4×C73#53711yescharacteristic
363C4×C73#54611yescharacteristic
364C4×C73#54711yescharacteristic
365#25561C7311yesmaximal, characteristic, direct product factor, Sylow
366C2×C73—42no—
367C2×C73—42no—
368C2×C73#243011yescharacteristic
369C2×C73#300411yescharacteristic
370C2×C73#300911yescharacteristic
371C2×C73#331611yescharacteristic
372C2×C73#333111yescharacteristic
373C2×C73#334411yescharacteristic
374C2×C73#335611yescharacteristic
375C2×#554C2×C7311yescharacteristic
376C2×#483C2×C7311yescharacteristic, complemented
377C2×#470C2×C7311yescharacteristic, complemented
378#2415C2×C7311yescharacteristic
379#2058C2×C7311yescharacteristic, complemented
380#2035C2×C7311yescharacteristic, complemented
381#2024C2×C7311yescharacteristic, complemented
382#2001C2×C7311yescharacteristic, complemented
383#1878C2×C7311yescharacteristic, complemented
384#1873C2×C7311yescharacteristic, complemented
385#1872C2×C7311yescharacteristic, complemented
386#1870C2×C7311yescharacteristic
387#1865C2×C7311yescharacteristic, complemented
388#1853C2×C7311yescharacteristic, complemented
389#1736C2×C7311yescharacteristic, complemented
390C73#2556111yescharacteristic, direct product factor, Sylow
391C22×Q16C22×C7311yescharacteristic
392C22×M16C22×C7311yescharacteristic
393#554—24no—
394#554—24no—
395C2×C4⋊Q8C22×C7311yescharacteristic
396C2×#125—21no—
397C2×C22⋊Q8—21no—
398C2×C22⋊Q8—21no—
399C2×C22⋊Q8C22×C7311yescharacteristic
400C2×C22⋊Q8C22×C7311yescharacteristic
401C2×C22⋊Q8C22×C7311yescharacteristic
402C2×C22⋊Q8C22×C7311yescharacteristic
403C2×C4×Q8C22×C7311yescharacteristic
404C2×C4×D4—21no—
405C2×C4×D4C22×C7311yescharacteristic
406C2×#117C22×C7311yescharacteristic
407C22×C4⋊C4C22×C7311yescharacteristic
408C22×C4⋊C4C22×C7311yescharacteristic
409#483—24no—
410#470—24no—
411C2×#106C22×C7311yescharacteristic
412C2×#106C22×C7311yescharacteristic
413C2×#106C22×C7311yescharacteristic
414C2×#103C22×C7311yescharacteristic
415C2×#103C22×C7311yescharacteristic
416C2×#103C22×C7311yescharacteristic
417C2×#103C22×C7311yescharacteristic
418C2×#103C22×C7311yescharacteristic
419C2×#103C22×C7311yescharacteristic
420C2×C22⋊C8C22×C7311yescharacteristic
421C2×C22⋊C8C22×C7311yescharacteristic
422C2×C22⋊C8C22×C7311yescharacteristic
423#397—21no—
424#394—21no—
425#391C22×C7311yescharacteristic
426#389—21no—
427#389C22×C7311yescharacteristic
428#388—21no—
429#380C22×C7311yescharacteristic
430#340C22×C7311yescharacteristic
431#340C22×C7311yescharacteristic
432#340C22×C7311yescharacteristic
433#340C22×C7311yescharacteristic
434#340C22×C7311yescharacteristic
435#340C22×C7311yescharacteristic
436#336C22×C7311yescharacteristic
437#336C22×C7311yescharacteristic
438C22×Q8—21no—
439C22×Q8C23×C7311yescharacteristic
440C22×Q8C23×C7311yescharacteristic
441C22×D4D4×C7311yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4C23×C7311yescharacteristic
445C23×C4C23×C7311yescharacteristic
446C2×Q16—22no—
447C2×Q16—22no—
448C2×Q16—41no—
449C2×M16—22no—
450C2×M16—22no—
451C2×M16—41no—
452C22×C8C23×C7311yescharacteristic
453C22×C8C23×C7311yescharacteristic
454C22×C8C23×C7311yescharacteristic
455C22×C8C23×C7311yescharacteristic
456C4⋊Q8—22no—
457C4⋊Q8—22no—
458#125—28no—
459C22⋊Q8—28no—
460C22⋊Q8—28no—
461C22⋊Q8—22no—
462C22⋊Q8—22no—
463C22⋊Q8—22no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—22no—
467C22⋊Q8—41no—
468C22⋊Q8D4×C7314yes—
469C4×Q8—22no—
470C4×Q8—22no—
471C4×D4—28no—
472C4×D4—22no—
473C4×D4—22no—
474#117—22no—
475#117—41no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4D4×C7311yescharacteristic
489C2×C4⋊C4D4×C7314yes—
490C2×C4⋊C4C23×C7311yescharacteristic
491C2×C4⋊C4C23×C7311yescharacteristic
492C2×C4⋊C4C23×C7311yescharacteristic
493C2×C4⋊C4C23×C7311yescharacteristic
494C2×C4⋊C4C23×C7311yescharacteristic
495C2×C4⋊C4C23×C7311yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4D4×C7311yescharacteristic
503C2×C22⋊C4D4×C7311yescharacteristic
504C2×C42—21no—
505C2×C42—21no—
506C2×C42C23×C7311yescharacteristic
507#106—22no—
508#106—22no—
509#106—22no—
510#103—22no—
511#103—22no—
512#103—22no—
513#103—22no—
514#103—22no—
515#103—41no—
516C22⋊C8—22no—
517C22⋊C8—22no—
518C22⋊C8—41no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523C24C2×D4×C7311yescharacteristic
524C24C2×D4×C7311yescharacteristic
525C2×Q8—24no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—81no—
538C2×Q8—81no—
539C2×Q8C2×D4×C7312yes—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—81no—
564C22×C4—81no—
565C22×C4—81no—
566C22×C4—81no—
567C22×C4C2×D4×C7311yescharacteristic
568C22×C4C2×D4×C7311yescharacteristic
569C22×C4C2×D4×C7311yescharacteristic
570C22×C4C2×D4×C7312yes—
571C22×C4C2×D4×C7312yes—
572C22×C4C2×D4×C7311yescharacteristic
573C22×C4C24×C7311yescharacteristic
574Q16—44no—
575M16—44no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8#41×C7312yes—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4C2×D4×C7312yes—
607C4⋊C4C2×D4×C7312yes—
608C4⋊C4C2×D4×C7312yes—
609C4⋊C4#41×C7312yes—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C42—24no—
619C42—21no—
620C42—21no—
621C42—42no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23#120×C7312yes—
635C23#137×C7312yes—
636C23C22×D4×C7311yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645Q8—84no—
646D4—28no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—84no—
690C2×C4—84no—
691C2×C4#120×C7312yes—
692C2×C4#137×C7312yes—
693C2×C4C22×D4×C7311yescharacteristic
694C2×C4C22×D4×C7311yescharacteristic
695C2×C4C2×#41×C7311yescharacteristic
696C2×C4C2×#41×C7311yescharacteristic
697C2×C4H(5,𝔽2)×C7311yescharacteristic
698C2×C42−1+4×C7311yescharacteristic
699C8—22no—
700C8—41no—
701C8—41no—
702C8—41no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22C2×#120×C7311yescharacteristic
718C22#546×C7311yescharacteristic
719C22#547×C7311yescharacteristic
720C22C2×#137×C7311yescharacteristic
721C22C2×#137×C7311yescharacteristic
722C22#577×C7311yescharacteristic
723C22#577×C7311yescharacteristic
724C4—22no—
725C4—22no—
726C4—41no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—42no—
733C4—81no—
734C4—81no—
735C4—81no—
736C4#532×C7311yescharacteristic
737C4#537×C7311yescharacteristic
738C4#546×C7311yescharacteristic
739C4#547×C7311yescharacteristic
740C2—42no—
741C2—42no—
742C2C73×#243011yescharacteristic
743C2C73×#300411yescharacteristic
744C2C73×#300911yescharacteristic
745C2C73×#331611yescharacteristic
746C2C73×#333111yescharacteristic
747C2C73×#334411yescharacteristic
748C2C73×#335611yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D4×C73D4
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
2. C2×#483×C73C2semidirect
3. C2×#470×C73C2semidirect
5. C73×#2058C2semidirect
6. C73×#2035C2semidirect
7. C73×#2024C2semidirect
8. C73×#2001C2semidirect
9. C73×#1878C2semidirect
10. C73×#1873C2semidirect
11. C73×#1872C2semidirect
13. C73×#1865C2semidirect
14. C73×#1853C2semidirect
15. C73×#1736C2semidirect
365. #25561C73direct (N × H)
376. C2×#483C2×C73semidirect
377. C2×#470C2×C73semidirect
379. #2058C2×C73semidirect
380. #2035C2×C73semidirect
381. #2024C2×C73semidirect
382. #2001C2×C73semidirect
383. #1878C2×C73semidirect
384. #1873C2×C73semidirect
385. #1872C2×C73semidirect
387. #1865C2×C73semidirect
388. #1853C2×C73semidirect
389. #1736C2×C73semidirect
390. C73#25561direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#554×C732
C2×#483×C732
C2×#470×C732
C73×#24152
C73×#20582
C73×#20352
C73×#20242
C73×#20012
C73×#18782
C73×#18732
C73×#18722
C73×#18702
C73×#18652
C73×#18532
C73×#17362
#2556173