Finite Group Databasebeta

← C73×#24789 #32934193

Subgroups — C73×#24789 #32934193

Order 18688.

1032 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C73C211yesmaximal, characteristic, complemented
2C2×#465×C73C211yesmaximal, characteristic, complemented
3C2×#435×C73C211yesmaximal, characteristic, complemented
4C2×#428×C73C211yesmaximal, characteristic, complemented
5C73×#2416C211yesmaximal, characteristic
6C73×#2415C211yesmaximal, characteristic, complemented
7C73×#2068C211yesmaximal, characteristic, complemented
8C73×#2065C211yesmaximal, characteristic, complemented
9C73×#2035C211yesmaximal, characteristic, complemented
10C73×#2033C211yesmaximal, characteristic, complemented
11C73×#1973C211yesmaximal, characteristic, complemented
12C73×#1944C211yesmaximal, characteristic, complemented
13C73×#1875C211yesmaximal, characteristic, complemented
14C73×#1872C211yesmaximal, characteristic, complemented
15C73×#1808C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18C23×C8×C73C2211yescharacteristic
19C2×C22⋊Q8×C73C2211yescharacteristic
20C2×C22⋊Q8×C73C2211yescharacteristic
21C2×#121×C73—21no—
22C2×#121×C73C2211yescharacteristic
23C2×#121×C73C2211yescharacteristic
24C2×C4×D4×C73C2211yescharacteristic
25C2×#117×C73C2211yescharacteristic
26C22×C4⋊C4×C73C2211yescharacteristic
27#468×C73—24no—
28#465×C73—24no—
29#435×C73—24no—
30#428×C73—24no—
31C2×#107×C73C2211yescharacteristic
32C2×#107×C73C2211yescharacteristic
33C2×#107×C73C2211yescharacteristic
34C2×#106×C73C2211yescharacteristic
35C2×#106×C73C2211yescharacteristic
36C2×C4⋊C8×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#103×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×C22⋊C8×C73C2211yescharacteristic
44C2×C22⋊C8×C73C2211yescharacteristic
45C2×#97×C73C2211yescharacteristic
46#397×C73—21no—
47#396×C73—21no—
48#394×C73—21no—
49#394×C73—21no—
50#391×C73C2211yescharacteristic
51#390×C73C2211yescharacteristic
52#389×C73—21no—
53#389×C73C2211yescharacteristic
54#389×C73C2211yescharacteristic
55#388×C73—21no—
56#386×C73—21no—
57#380×C73C2211yescharacteristic
58#380×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63C22×Q8×C73C2311yescharacteristic
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73D411yescharacteristic
67C22×D4×C73C2311yescharacteristic
68C23×C4×C73—21no—
69C23×C4×C73C2311yescharacteristic
70C23×C4×C73C2311yescharacteristic
71C2×SD16×C73—22no—
72C2×SD16×C73—22no—
73C2×SD16×C73—22no—
74C2×M16×C73—22no—
75C2×M16×C73—22no—
76C2×M16×C73D414yescomplemented
77C22×C8×C73—22no—
78C22×C8×C73—22no—
79C22×C8×C73—22no—
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82C22×C8×C73C2311yescharacteristic
83C22×C8×C73C2311yescharacteristic
84C22⋊Q8×C73—22no—
85C22⋊Q8×C73—22no—
86C22⋊Q8×C73—22no—
87C22⋊Q8×C73—41no—
88#121×C73—22no—
89#121×C73—22no—
90#121×C73—22no—
91#121×C73—41no—
92#121×C73—44no—
93C4×D4×C73—22no—
94C4×D4×C73—22no—
95#117×C73—22no—
96#117×C73—41no—
97C2×C4⋊C4×C73—22no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73—21no—
103C2×C4⋊C4×C73—41no—
104C2×C4⋊C4×C73D411yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C4⋊C4×C73C2311yescharacteristic
108C2×C4⋊C4×C73C2311yescharacteristic
109C2×C4⋊C4×C73C2311yescharacteristic
110C2×C4⋊C4×C73C2311yescharacteristic
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—21no—
117C2×C22⋊C4×C73—21no—
118C2×C22⋊C4×C73—21no—
119C2×C22⋊C4×C73—21no—
120C2×C22⋊C4×C73D411yescharacteristic
121C2×C22⋊C4×C73D411yescharacteristic
122C2×C42×C73—21no—
123C2×C42×C73C2311yescharacteristic
124#107×C73—22no—
125#107×C73—22no—
126#107×C73—22no—
127#106×C73—22no—
128#106×C73D414yescomplemented
129C4⋊C8×C73—22no—
130#103×C73—22no—
131#103×C73—22no—
132#103×C73—41no—
133#102×C73—22no—
134#102×C73—22no—
135#102×C73—41no—
136C22⋊C8×C73—22no—
137C22⋊C8×C73—22no—
138#97×C73—22no—
139#95×C73—21no—
140#95×C73—21no—
141#95×C73—21no—
142#95×C73—21no—
143#95×C73—21no—
144#95×C73—21no—
145C24×C73—21no—
146C24×C73C2×D411yescharacteristic
147C24×C73C2×D411yescharacteristic
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×Q8×C73—21no—
151C2×Q8×C73—21no—
152C2×Q8×C73—21no—
153C2×Q8×C73—21no—
154C2×D4×C73—22no—
155C2×D4×C73—22no—
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—41no—
163C2×D4×C73—42no—
164C2×D4×C73—42no—
165C2×D4×C73—42no—
166C2×D4×C73—42no—
167C2×D4×C73—42no—
168C2×D4×C73—81no—
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×D411yescharacteristic
193C22×C4×C73C2×D412yes—
194C22×C4×C73#4112yes—
195C22×C4×C73C2411yescharacteristic
196SD16×C73—44no—
197M16×C73—28no—
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—44no—
207C2×C8×C73C2×D412yes—
208C2×C8×C73C2×D412yes—
209C2×C8×C73C2×D412yes—
210C2×C8×C73#4112yes—
211C4⋊C4×C73—22no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
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—42no—
223C4⋊C4×C73—42no—
224C4⋊C4×C73—42no—
225C4⋊C4×C73—42no—
226C4⋊C4×C73—42no—
227C4⋊C4×C73C2×D412yes—
228C4⋊C4×C73C2×D412yes—
229C22⋊C4×C73—22no—
230C22⋊C4×C73—22no—
231C22⋊C4×C73—42no—
232C22⋊C4×C73—42no—
233C22⋊C4×C73—42no—
234C22⋊C4×C73—42no—
235C22⋊C4×C73—42no—
236C22⋊C4×C73—42no—
237C22⋊C4×C73—42no—
238C22⋊C4×C73—42no—
239C22⋊C4×C73—81no—
240C42×C73—21no—
241C42×C73—21no—
242C42×C73—42no—
243C23×C73—21no—
244C23×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—41no—
256C23×C73—41no—
257C23×C73—41no—
258C23×C73—41no—
259C23×C73—41no—
260C23×C73—41no—
261C23×C73—41no—
262C23×C73#12112yes—
263C23×C73AGL(1,ℤ/8)12yes—
264C23×C73C22×D411yescharacteristic
265Q8×C73—41no—
266Q8×C73—41no—
267Q8×C73—41no—
268Q8×C73—41no—
269D4×C73—44no—
270D4×C73—41no—
271D4×C73—41no—
272D4×C73—41no—
273D4×C73—41no—
274D4×C73—84no—
275D4×C73—84no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—22no—
286C2×C4×C73—21no—
287C2×C4×C73—22no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
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—41no—
315C2×C4×C73—41no—
316C2×C4×C73—84no—
317C2×C4×C73#12112yes—
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#12114yescomplemented
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×C73—81no—
343C22×C73—81no—
344C22×C73—81no—
345C22×C73—81no—
346C22×C73—81no—
347C22×C73—81no—
348C22×C73—81no—
349C22×C73C2×#12111yescharacteristic
350C22×C73D4211yescharacteristic
351C22×C73#54711yescharacteristic
352C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C73#57511yescharacteristic
354C22×C73#57711yescharacteristic
355C22×C73#57811yescharacteristic
356C4×C73—22no—
357C4×C73—41no—
358C4×C73—42no—
359C4×C73—42no—
360C4×C73—41no—
361C4×C73—41no—
362C4×C73—81no—
363C4×C73—81no—
364C4×C73—81no—
365C4×C73—81no—
366C4×C73—81no—
367C4×C73C2×#12111yescharacteristic
368C4×C73#53711yescharacteristic
369C4×C73#54811yescharacteristic
370C4×C73#55311yescharacteristic
371#24789C7311yesmaximal, characteristic, direct product factor, Sylow
372C2×C73—42no—
373C2×C73—42no—
374C2×C73—161no—
375C2×C73#241611yescharacteristic
376C2×C73#305511yescharacteristic
377C2×C73#306311yescharacteristic
378C2×C73#326511yescharacteristic
379C2×C73#326911yescharacteristic
380C2×C73#334311yescharacteristic
381C2×C73#335011yescharacteristic
382C2×#468C2×C7311yescharacteristic, complemented
383C2×#465C2×C7311yescharacteristic, complemented
384C2×#435C2×C7311yescharacteristic, complemented
385C2×#428C2×C7311yescharacteristic, complemented
386#2416C2×C7311yescharacteristic
387#2415C2×C7311yescharacteristic, complemented
388#2068C2×C7311yescharacteristic, complemented
389#2065C2×C7311yescharacteristic, complemented
390#2035C2×C7311yescharacteristic, complemented
391#2033C2×C7311yescharacteristic, complemented
392#1973C2×C7311yescharacteristic, complemented
393#1944C2×C7311yescharacteristic, complemented
394#1875C2×C7311yescharacteristic, complemented
395#1872C2×C7311yescharacteristic, complemented
396#1808C2×C7311yescharacteristic, complemented
397C73#2478911yescharacteristic, direct product factor, Sylow
398C22×SD16C22×C7311yescharacteristic
399C22×M16C22×C7311yescharacteristic
400C23×C8C22×C7311yescharacteristic
401C2×C22⋊Q8C22×C7311yescharacteristic
402C2×C22⋊Q8C22×C7311yescharacteristic
403C2×#121—21no—
404C2×#121C22×C7311yescharacteristic
405C2×#121C22×C7311yescharacteristic
406C2×C4×D4C22×C7311yescharacteristic
407C2×#117C22×C7311yescharacteristic
408C22×C4⋊C4C22×C7311yescharacteristic
409#468—24no—
410#465—24no—
411#435—24no—
412#428—24no—
413C2×#107C22×C7311yescharacteristic
414C2×#107C22×C7311yescharacteristic
415C2×#107C22×C7311yescharacteristic
416C2×#106C22×C7311yescharacteristic
417C2×#106C22×C7311yescharacteristic
418C2×C4⋊C8C22×C7311yescharacteristic
419C2×#103C22×C7311yescharacteristic
420C2×#103C22×C7311yescharacteristic
421C2×#103C22×C7311yescharacteristic
422C2×#102C22×C7311yescharacteristic
423C2×#102C22×C7311yescharacteristic
424C2×#102C22×C7311yescharacteristic
425C2×C22⋊C8C22×C7311yescharacteristic
426C2×C22⋊C8C22×C7311yescharacteristic
427C2×#97C22×C7311yescharacteristic
428#397—21no—
429#396—21no—
430#394—21no—
431#394—21no—
432#391C22×C7311yescharacteristic
433#390C22×C7311yescharacteristic
434#389—21no—
435#389C22×C7311yescharacteristic
436#389C22×C7311yescharacteristic
437#388—21no—
438#386—21no—
439#380C22×C7311yescharacteristic
440#380C22×C7311yescharacteristic
441#340C22×C7311yescharacteristic
442#340C22×C7311yescharacteristic
443#340C22×C7311yescharacteristic
444#340C22×C7311yescharacteristic
445C22×Q8C23×C7311yescharacteristic
446C22×D4—21no—
447C22×D4—21no—
448C22×D4D4×C7311yescharacteristic
449C22×D4C23×C7311yescharacteristic
450C23×C4—21no—
451C23×C4C23×C7311yescharacteristic
452C23×C4C23×C7311yescharacteristic
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×M16—22no—
457C2×M16—22no—
458C2×M16D4×C7314yescomplemented
459C22×C8—22no—
460C22×C8—22no—
461C22×C8—22no—
462C22×C8C23×C7311yescharacteristic
463C22×C8C23×C7311yescharacteristic
464C22×C8C23×C7311yescharacteristic
465C22×C8C23×C7311yescharacteristic
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8—22no—
469C22⋊Q8—41no—
470#121—22no—
471#121—22no—
472#121—22no—
473#121—41no—
474#121—44no—
475C4×D4—22no—
476C4×D4—22no—
477#117—22no—
478#117—41no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—41no—
486C2×C4⋊C4D4×C7311yescharacteristic
487C2×C4⋊C4C23×C7311yescharacteristic
488C2×C4⋊C4C23×C7311yescharacteristic
489C2×C4⋊C4C23×C7311yescharacteristic
490C2×C4⋊C4C23×C7311yescharacteristic
491C2×C4⋊C4C23×C7311yescharacteristic
492C2×C4⋊C4C23×C7311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
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×C42C23×C7311yescharacteristic
506#107—22no—
507#107—22no—
508#107—22no—
509#106—22no—
510#106D4×C7314yescomplemented
511C4⋊C8—22no—
512#103—22no—
513#103—22no—
514#103—41no—
515#102—22no—
516#102—22no—
517#102—41no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520#97—22no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527C24—21no—
528C24C2×D4×C7311yescharacteristic
529C24C2×D4×C7311yescharacteristic
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—41no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—81no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
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—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—81no—
571C22×C4C2×D4×C7311yescharacteristic
572C22×C4C2×D4×C7311yescharacteristic
573C22×C4C2×D4×C7311yescharacteristic
574C22×C4C2×D4×C7311yescharacteristic
575C22×C4C2×D4×C7312yes—
576C22×C4#41×C7312yes—
577C22×C4C24×C7311yescharacteristic
578SD16—44no—
579M16—28no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—44no—
589C2×C8C2×D4×C7312yes—
590C2×C8C2×D4×C7312yes—
591C2×C8C2×D4×C7312yes—
592C2×C8#41×C7312yes—
593C4⋊C4—22no—
594C4⋊C4—21no—
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—21no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4C2×D4×C7312yes—
610C4⋊C4C2×D4×C7312yes—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—81no—
622C42—21no—
623C42—21no—
624C42—42no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23#121×C7312yes—
645C23AGL(1,ℤ/8)×C7312yes—
646C23C22×D4×C7311yescharacteristic
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651D4—44no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—84no—
657D4—84no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
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—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—84no—
699C2×C4#121×C7312yes—
700C2×C4C22×D4×C7311yescharacteristic
701C2×C4C22×D4×C7311yescharacteristic
702C2×C4C2×#41×C7311yescharacteristic
703C2×C4C2×#41×C7311yescharacteristic
704C2×C4H(5,𝔽2)×C7311yescharacteristic
705C2×C42−1+4×C7311yescharacteristic
706C8—22no—
707C8—41no—
708C8—41no—
709C8#121×C7314yescomplemented
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22C2×#121×C7311yescharacteristic
732C22D42×C7311yescharacteristic
733C22#547×C7311yescharacteristic
734C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
735C22#575×C7311yescharacteristic
736C22#577×C7311yescharacteristic
737C22#578×C7311yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—81no—
745C4—81no—
746C4—81no—
747C4—81no—
748C4—81no—
749C4C2×#121×C7311yescharacteristic
750C4#537×C7311yescharacteristic
751C4#548×C7311yescharacteristic
752C4#553×C7311yescharacteristic
753C2—42no—
754C2—42no—
755C2—161no—
756C2C73×#241611yescharacteristic
757C2C73×#305511yescharacteristic
758C2C73×#306311yescharacteristic
759C2C73×#326511yescharacteristic
760C2C73×#326911yescharacteristic
761C2C73×#334311yescharacteristic
762C2C73×#335011yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2416C2
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
1. C2×#468×C73C2semidirect
2. C2×#465×C73C2semidirect
3. C2×#435×C73C2semidirect
4. C2×#428×C73C2semidirect
6. C73×#2415C2semidirect
7. C73×#2068C2semidirect
8. C73×#2065C2semidirect
9. C73×#2035C2semidirect
10. C73×#2033C2semidirect
11. C73×#1973C2semidirect
12. C73×#1944C2semidirect
13. C73×#1875C2semidirect
14. C73×#1872C2semidirect
15. C73×#1808C2semidirect
76. C2×M16×C73D4semidirect
128. #106×C73D4semidirect
327. C8×C73#121semidirect
371. #24789C73direct (N × H)
382. C2×#468C2×C73semidirect
383. C2×#465C2×C73semidirect
384. C2×#435C2×C73semidirect
385. C2×#428C2×C73semidirect
387. #2415C2×C73semidirect
388. #2068C2×C73semidirect
389. #2065C2×C73semidirect
390. #2035C2×C73semidirect
391. #2033C2×C73semidirect
392. #1973C2×C73semidirect
393. #1944C2×C73semidirect
394. #1875C2×C73semidirect
395. #1872C2×C73semidirect
396. #1808C2×C73semidirect
397. C73#24789direct (N × H)
458. C2×M16D4×C73semidirect
510. #106D4×C73semidirect
709. C8#121×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C732
C2×#465×C732
C2×#435×C732
C2×#428×C732
C73×#24162
C73×#24152
C73×#20682
C73×#20652
C73×#20352
C73×#20332
C73×#19732
C73×#19442
C73×#18752
C73×#18722
C73×#18082
#2478973