Finite Group Databasebeta

← C73×#25558 #32934962

Subgroups — C73×#25558 #32934962

Order 18688.

1102 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#556×C73C211yesmaximal, characteristic
2C2×#485×C73C211yesmaximal, characteristic, complemented
3C2×#470×C73C211yesmaximal, characteristic, complemented
4C73×#2417C211yesmaximal, 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×#1863C211yesmaximal, characteristic, complemented
14C73×#1854C211yesmaximal, characteristic, complemented
15C73×#1736C211yesmaximal, characteristic, complemented
16C22×Q16×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18#556×C73—24no—
19#556×C73—24no—
20C2×C4⋊Q8×C73C2211yescharacteristic
21C2×#126×C73—21no—
22C2×#126×C73—21no—
23C2×#124×C73—21no—
24C2×C22⋊Q8×C73C2211yescharacteristic
25C2×C22⋊Q8×C73C2211yescharacteristic
26C2×C22⋊Q8×C73C2211yescharacteristic
27C2×C22⋊Q8×C73C2211yescharacteristic
28C2×C4×Q8×C73—21no—
29C2×C4×Q8×C73C2211yescharacteristic
30C2×C4×D4×C73C2211yescharacteristic
31C2×#117×C73C2211yescharacteristic
32C2×#117×C73C2211yescharacteristic
33C22×C4⋊C4×C73C2211yescharacteristic
34#485×C73—24no—
35#470×C73—24no—
36C2×#107×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#398×C73—21no—
49#396×C73—21no—
50#391×C73C2211yescharacteristic
51#389×C73C2211yescharacteristic
52#386×C73—21no—
53#380×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×C73C2311yescharacteristic
69C23×C4×C73C2311yescharacteristic
70C2×Q16×C73—22no—
71C2×Q16×C73—22no—
72C2×Q16×C73—41no—
73C2×M16×C73—22no—
74C2×M16×C73—22no—
75C2×M16×C73—41no—
76C22×C8×C73C2311yescharacteristic
77C22×C8×C73C2311yescharacteristic
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C4⋊Q8×C73—22no—
81C4⋊Q8×C73—22no—
82#126×C73—28no—
83#126×C73—28no—
84#124×C73—28no—
85C22⋊Q8×C73—22no—
86C22⋊Q8×C73—22no—
87C22⋊Q8×C73—22no—
88C22⋊Q8×C73—22no—
89C22⋊Q8×C73—22no—
90C22⋊Q8×C73—22no—
91C22⋊Q8×C73—41no—
92C22⋊Q8×C73D414yes—
93C4×Q8×C73—28no—
94C4×Q8×C73—22no—
95C4×Q8×C73—22no—
96C4×D4×C73—22no—
97C4×D4×C73—22no—
98#117×C73—22no—
99#117×C73—22no—
100#117×C73—22no—
101#117×C73D414yes—
102C2×C4⋊C4×C73—21no—
103C2×C4⋊C4×C73—21no—
104C2×C4⋊C4×C73—21no—
105C2×C4⋊C4×C73—21no—
106C2×C4⋊C4×C73—22no—
107C2×C4⋊C4×C73—21no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73—41no—
112C2×C4⋊C4×C73D411yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C4⋊C4×C73C2311yescharacteristic
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×C73D411yescharacteristic
127C2×C22⋊C4×C73D411yescharacteristic
128C2×C42×C73—21no—
129C2×C42×C73—21no—
130C2×C42×C73—21no—
131C2×C42×C73C2311yescharacteristic
132#107×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—42no—
163C2×Q8×C73—42no—
164C2×Q8×C73C2×D412yes—
165C2×D4×C73—22no—
166C2×D4×C73—22no—
167C2×D4×C73—41no—
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—21no—
178C22×C4×C73—21no—
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—42no—
187C22×C4×C73—42no—
188C22×C4×C73—81no—
189C22×C4×C73C2×D411yescharacteristic
190C22×C4×C73C2×D411yescharacteristic
191C22×C4×C73C2×D411yescharacteristic
192C22×C4×C73C2×D412yes—
193C22×C4×C73C2×D412yes—
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73C2411yescharacteristic
196Q16×C73—44no—
197M16×C73—44no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
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#4112yes—
210C4⋊C4×C73—24no—
211C4⋊C4×C73—24no—
212C4⋊C4×C73—24no—
213C4⋊C4×C73—24no—
214C4⋊C4×C73—22no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73—21no—
217C4⋊C4×C73—21no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—42no—
224C4⋊C4×C73—42no—
225C4⋊C4×C73—42no—
226C4⋊C4×C73—81no—
227C4⋊C4×C73C2×D412yes—
228C4⋊C4×C73C2×D412yes—
229C4⋊C4×C73C2×D412yes—
230C4⋊C4×C73#4112yes—
231C22⋊C4×C73—24no—
232C22⋊C4×C73—24no—
233C22⋊C4×C73—24no—
234C22⋊C4×C73—24no—
235C22⋊C4×C73—22no—
236C22⋊C4×C73—22no—
237C22⋊C4×C73—42no—
238C22⋊C4×C73—42no—
239C22⋊C4×C73—81no—
240C42×C73—24no—
241C42×C73—24no—
242C42×C73—24no—
243C42×C73—21no—
244C42×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
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#12012yes—
259C23×C73C22×D411yescharacteristic
260Q8×C73—22no—
261Q8×C73—22no—
262Q8×C73—48no—
263Q8×C73—41no—
264Q8×C73—41no—
265Q8×C73—41no—
266Q8×C73—41no—
267Q8×C73—41no—
268Q8×C73—41no—
269D4×C73—44no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—22no—
284C2×C4×C73—22no—
285C2×C4×C73—21no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
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—84no—
313C2×C4×C73#12012yes—
314C2×C4×C73#13712yes—
315C2×C4×C73C22×D411yescharacteristic
316C2×C4×C73C22×D411yescharacteristic
317C2×C4×C73C2×#4111yescharacteristic
318C2×C4×C73C2×#4111yescharacteristic
319C2×C4×C73H(5,𝔽2)11yescharacteristic
320C2×C4×C732−1+411yescharacteristic
321C8×C73—22no—
322C8×C73—41no—
323C8×C73—41no—
324C8×C73—41no—
325C22×C73—22no—
326C22×C73—22no—
327C22×C73—22no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—41no—
331C22×C73—41no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73—41no—
335C22×C73—41no—
336C22×C73—41no—
337C22×C73—41no—
338C22×C73—41no—
339C22×C73C2×#12011yescharacteristic
340C22×C73#54611yescharacteristic
341C22×C73#54711yescharacteristic
342C22×C73C2×#13711yescharacteristic
343C22×C73#57511yescharacteristic
344C22×C73#57711yescharacteristic
345C22×C73#57811yescharacteristic
346C4×C73—22no—
347C4×C73—22no—
348C4×C73—41no—
349C4×C73—42no—
350C4×C73—42no—
351C4×C73—42no—
352C4×C73—41no—
353C4×C73—42no—
354C4×C73—42no—
355C4×C73—81no—
356C4×C73—81no—
357C4×C73—81no—
358C4×C73#53211yescharacteristic
359C4×C73#53711yescharacteristic
360C4×C73#54611yescharacteristic
361C4×C73#54711yescharacteristic
362#25558C7311yesmaximal, characteristic, direct product factor, Sylow
363C2×C73—42no—
364C2×C73—81no—
365C2×C73#243011yescharacteristic
366C2×C73#300711yescharacteristic
367C2×C73#301311yescharacteristic
368C2×C73#331111yescharacteristic
369C2×C73#332811yescharacteristic
370C2×C73#334911yescharacteristic
371C2×C73#335611yescharacteristic
372C2×#556C2×C7311yescharacteristic
373C2×#485C2×C7311yescharacteristic, complemented
374C2×#470C2×C7311yescharacteristic, complemented
375#2417C2×C7311yescharacteristic
376#2058C2×C7311yescharacteristic, complemented
377#2035C2×C7311yescharacteristic, complemented
378#2024C2×C7311yescharacteristic, complemented
379#2001C2×C7311yescharacteristic, complemented
380#1878C2×C7311yescharacteristic, complemented
381#1873C2×C7311yescharacteristic, complemented
382#1872C2×C7311yescharacteristic, complemented
383#1870C2×C7311yescharacteristic
384#1863C2×C7311yescharacteristic, complemented
385#1854C2×C7311yescharacteristic, complemented
386#1736C2×C7311yescharacteristic, complemented
387C73#2555811yescharacteristic, direct product factor, Sylow
388C22×Q16C22×C7311yescharacteristic
389C22×M16C22×C7311yescharacteristic
390#556—24no—
391#556—24no—
392C2×C4⋊Q8C22×C7311yescharacteristic
393C2×#126—21no—
394C2×#126—21no—
395C2×#124—21no—
396C2×C22⋊Q8C22×C7311yescharacteristic
397C2×C22⋊Q8C22×C7311yescharacteristic
398C2×C22⋊Q8C22×C7311yescharacteristic
399C2×C22⋊Q8C22×C7311yescharacteristic
400C2×C4×Q8—21no—
401C2×C4×Q8C22×C7311yescharacteristic
402C2×C4×D4C22×C7311yescharacteristic
403C2×#117C22×C7311yescharacteristic
404C2×#117C22×C7311yescharacteristic
405C22×C4⋊C4C22×C7311yescharacteristic
406#485—24no—
407#470—24no—
408C2×#107C22×C7311yescharacteristic
409C2×#106C22×C7311yescharacteristic
410C2×#106C22×C7311yescharacteristic
411C2×#103C22×C7311yescharacteristic
412C2×#103C22×C7311yescharacteristic
413C2×#103C22×C7311yescharacteristic
414C2×#103C22×C7311yescharacteristic
415C2×#103C22×C7311yescharacteristic
416C2×#103C22×C7311yescharacteristic
417C2×C22⋊C8C22×C7311yescharacteristic
418C2×C22⋊C8C22×C7311yescharacteristic
419C2×C22⋊C8C22×C7311yescharacteristic
420#398—21no—
421#396—21no—
422#391C22×C7311yescharacteristic
423#389C22×C7311yescharacteristic
424#386—21no—
425#380—21no—
426#380C22×C7311yescharacteristic
427#340C22×C7311yescharacteristic
428#340C22×C7311yescharacteristic
429#340C22×C7311yescharacteristic
430#340C22×C7311yescharacteristic
431#340C22×C7311yescharacteristic
432#340C22×C7311yescharacteristic
433#336C22×C7311yescharacteristic
434#336C22×C7311yescharacteristic
435C22×Q8—21no—
436C22×Q8C23×C7311yescharacteristic
437C22×Q8C23×C7311yescharacteristic
438C22×D4D4×C7311yescharacteristic
439C23×C4—21no—
440C23×C4C23×C7311yescharacteristic
441C23×C4C23×C7311yescharacteristic
442C2×Q16—22no—
443C2×Q16—22no—
444C2×Q16—41no—
445C2×M16—22no—
446C2×M16—22no—
447C2×M16—41no—
448C22×C8C23×C7311yescharacteristic
449C22×C8C23×C7311yescharacteristic
450C22×C8C23×C7311yescharacteristic
451C22×C8C23×C7311yescharacteristic
452C4⋊Q8—22no—
453C4⋊Q8—22no—
454#126—28no—
455#126—28no—
456#124—28no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—22no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—22no—
463C22⋊Q8—41no—
464C22⋊Q8D4×C7314yes—
465C4×Q8—28no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×D4—22no—
469C4×D4—22no—
470#117—22no—
471#117—22no—
472#117—22no—
473#117D4×C7314yes—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
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—41no—
484C2×C4⋊C4D4×C7311yescharacteristic
485C2×C4⋊C4C23×C7311yescharacteristic
486C2×C4⋊C4C23×C7311yescharacteristic
487C2×C4⋊C4C23×C7311yescharacteristic
488C2×C4⋊C4C23×C7311yescharacteristic
489C2×C4⋊C4C23×C7311yescharacteristic
490C2×C4⋊C4C23×C7311yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4D4×C7311yescharacteristic
499C2×C22⋊C4D4×C7311yescharacteristic
500C2×C42—21no—
501C2×C42—21no—
502C2×C42—21no—
503C2×C42C23×C7311yescharacteristic
504#107—22no—
505#106—22no—
506#106—22no—
507#103—22no—
508#103—22no—
509#103—22no—
510#103—22no—
511#103—22no—
512#103—41no—
513C22⋊C8—22no—
514C22⋊C8—22no—
515C22⋊C8—41no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520C24C2×D4×C7311yescharacteristic
521C24C2×D4×C7311yescharacteristic
522C2×Q8—24no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
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—42no—
535C2×Q8—42no—
536C2×Q8C2×D4×C7312yes—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—41no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
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—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—81no—
561C22×C4C2×D4×C7311yescharacteristic
562C22×C4C2×D4×C7311yescharacteristic
563C22×C4C2×D4×C7311yescharacteristic
564C22×C4C2×D4×C7312yes—
565C22×C4C2×D4×C7312yes—
566C22×C4C2×D4×C7311yescharacteristic
567C22×C4C24×C7311yescharacteristic
568Q16—44no—
569M16—44no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8#41×C7312yes—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—81no—
599C4⋊C4C2×D4×C7312yes—
600C4⋊C4C2×D4×C7312yes—
601C4⋊C4C2×D4×C7312yes—
602C4⋊C4#41×C7312yes—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—24no—
606C22⋊C4—24no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—81no—
612C42—24no—
613C42—24no—
614C42—24no—
615C42—21no—
616C42—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23#120×C7312yes—
631C23C22×D4×C7311yescharacteristic
632Q8—22no—
633Q8—22no—
634Q8—48no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640Q8—41no—
641D4—44no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
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—84no—
685C2×C4#120×C7312yes—
686C2×C4#137×C7312yes—
687C2×C4C22×D4×C7311yescharacteristic
688C2×C4C22×D4×C7311yescharacteristic
689C2×C4C2×#41×C7311yescharacteristic
690C2×C4C2×#41×C7311yescharacteristic
691C2×C4H(5,𝔽2)×C7311yescharacteristic
692C2×C42−1+4×C7311yescharacteristic
693C8—22no—
694C8—41no—
695C8—41no—
696C8—41no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22C2×#120×C7311yescharacteristic
712C22#546×C7311yescharacteristic
713C22#547×C7311yescharacteristic
714C22C2×#137×C7311yescharacteristic
715C22#575×C7311yescharacteristic
716C22#577×C7311yescharacteristic
717C22#578×C7311yescharacteristic
718C4—22no—
719C4—22no—
720C4—42no—
721C4—42no—
722C4—41no—
723C4—42no—
724C4—42no—
725C4—41no—
726C4—42no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4#532×C7311yescharacteristic
731C4#537×C7311yescharacteristic
732C4#546×C7311yescharacteristic
733C4#547×C7311yescharacteristic
734C2—42no—
735C2—81no—
736C2C73×#243011yescharacteristic
737C2C73×#300711yescharacteristic
738C2C73×#301311yescharacteristic
739C2C73×#331111yescharacteristic
740C2C73×#332811yescharacteristic
741C2C73×#334911yescharacteristic
742C2C73×#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×#485×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×#1863C2semidirect
14. C73×#1854C2semidirect
15. C73×#1736C2semidirect
362. #25558C73direct (N × H)
373. C2×#485C2×C73semidirect
374. C2×#470C2×C73semidirect
376. #2058C2×C73semidirect
377. #2035C2×C73semidirect
378. #2024C2×C73semidirect
379. #2001C2×C73semidirect
380. #1878C2×C73semidirect
381. #1873C2×C73semidirect
382. #1872C2×C73semidirect
384. #1863C2×C73semidirect
385. #1854C2×C73semidirect
386. #1736C2×C73semidirect
387. C73#25558direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#556×C732
C2×#485×C732
C2×#470×C732
C73×#24172
C73×#20582
C73×#20352
C73×#20242
C73×#20012
C73×#18782
C73×#18732
C73×#18722
C73×#18702
C73×#18632
C73×#18542
C73×#17362
#2555873