Finite Group Databasebeta

← C73×#25132 #32934536

Subgroups — C73×#25132 #32934536

Order 18688.

1314 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C73C211yesmaximal, characteristic, complemented
2C2×#447×C73C211yesmaximal, characteristic, complemented
3C2×#436×C73C211yesmaximal, characteristic, complemented
4C2×#418×C73C211yesmaximal, characteristic, complemented
5C73×#2414C211yesmaximal, characteristic, complemented
6C73×#2408C211yesmaximal, characteristic, complemented
7C73×#2065C211yesmaximal, characteristic, complemented
8C73×#2054C211yesmaximal, characteristic, complemented
9C73×#2033C211yesmaximal, characteristic, complemented
10C73×#1999C211yesmaximal, characteristic, complemented
11C73×#1970C211yesmaximal, characteristic, complemented
12C73×#1934C211yesmaximal, characteristic, complemented
13C73×#1895C211yesmaximal, characteristic, complemented
14C73×#1895C211yesmaximal, characteristic, complemented
15C73×#1854C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C22×D8×C73C2211yescharacteristic
18C22×D8×C73C2211yescharacteristic
19C22×M16×C73C2211yescharacteristic
20C22×M16×C73C2211yescharacteristic, complemented
21C2×#121×C73C2211yescharacteristic
22C2×#121×C73C2211yescharacteristic
23C2×#121×C73C2211yescharacteristic
24C2×#121×C73C2211yescharacteristic, complemented
25C2×#120×C73—21no—
26C2×C4×D4×C73C2211yescharacteristic
27C2×#117×C73C2211yescharacteristic
28#469×C73—24no—
29#447×C73—24no—
30#436×C73—24no—
31C2×#107×C73C2211yescharacteristic, complemented
32C2×#106×C73C2211yescharacteristic, complemented
33C2×C4⋊C8×C73C2211yescharacteristic, complemented
34#418×C73—24no—
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic, complemented
42C2×#102×C73C2211yescharacteristic, complemented
43C2×C22⋊C8×C73C2211yescharacteristic
44C2×C22⋊C8×C73C2211yescharacteristic, complemented
45C2×C4×C8×C73C2211yescharacteristic, complemented
46#394×C73—21no—
47#394×C73—21no—
48#392×C73—21no—
49#392×C73—21no—
50#390×C73—21no—
51#390×C73C2211yescharacteristic
52#390×C73C2211yescharacteristic
53#390×C73C2211yescharacteristic, complemented
54#389×C73C2211yescharacteristic, complemented
55#388×C73—21no—
56#380×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic, complemented
58#379×C73—21no—
59#340×C73C2211yescharacteristic, complemented
60#340×C73C2211yescharacteristic, complemented
61#340×C73C2211yescharacteristic, complemented
62#340×C73C2211yescharacteristic, complemented
63C25×C73—21no—
64C22×D4×C73—22no—
65C22×D4×C73—22no—
66C22×D4×C73—21no—
67C22×D4×C73—21no—
68C22×D4×C73—21no—
69C22×D4×C73—21no—
70C22×D4×C73—22no—
71C22×D4×C73—21no—
72C22×D4×C73—22no—
73C22×D4×C73—41no—
74C22×D4×C73—41no—
75C22×D4×C73D411yescharacteristic
76C22×D4×C73C2311yescharacteristic
77C22×D4×C73C2311yescharacteristic
78C22×D4×C73C2311yescharacteristic
79C23×C4×C73C2311yescharacteristic
80C23×C4×C73C2311yescharacteristic
81C2×D8×C73—22no—
82C2×D8×C73—22no—
83C2×D8×C73—22no—
84C2×D8×C73—22no—
85C2×D8×C73—41no—
86C2×D8×C73—41no—
87C2×M16×C73—22no—
88C2×M16×C73—22no—
89C2×M16×C73—22no—
90C2×M16×C73—22no—
91C2×M16×C73—41no—
92C2×M16×C73—41no—
93C22×C8×C73C2311yescharacteristic
94C22×C8×C73C2311yescharacteristic
95C22×C8×C73C2311yescharacteristic
96C22×C8×C73C2311yescharacteristic
97#121×C73—22no—
98#121×C73—22no—
99#121×C73—22no—
100#121×C73—22no—
101#121×C73—22no—
102#121×C73—41no—
103#121×C73—41no—
104#121×C73—41no—
105#120×C73—44no—
106C4×D4×C73—22no—
107C4×D4×C73—22no—
108#117×C73—22no—
109#117×C73—41no—
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73D411yescharacteristic
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C22⋊C4×C73—21no—
118C2×C22⋊C4×C73—21no—
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×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—21no—
130C2×C22⋊C4×C73D411yescharacteristic
131C2×C22⋊C4×C73D411yescharacteristic
132C2×C42×C73—21no—
133C2×C42×C73C2311yescharacteristic
134#107×C73—41no—
135#106×C73—22no—
136C4⋊C8×C73—22no—
137#102×C73—22no—
138#102×C73—22no—
139#102×C73—22no—
140#102×C73—22no—
141#102×C73—22no—
142#102×C73—22no—
143#102×C73—41no—
144#102×C73D414yescomplemented
145C22⋊C8×C73—22no—
146C22⋊C8×C73D414yescomplemented
147C4×C8×C73—22no—
148#95×C73—21no—
149#95×C73—21no—
150#95×C73—21no—
151C24×C73—21no—
152C24×C73—21no—
153C24×C73—21no—
154C24×C73—42no—
155C24×C73—42no—
156C24×C73—42no—
157C24×C73—42no—
158C24×C73—42no—
159C24×C73—81no—
160C24×C73—81no—
161C24×C73C2×D411yescharacteristic
162C24×C73C2×D411yescharacteristic
163C2×D4×C73—28no—
164C2×D4×C73—22no—
165C2×D4×C73—22no—
166C2×D4×C73—21no—
167C2×D4×C73—21no—
168C2×D4×C73—21no—
169C2×D4×C73—21no—
170C2×D4×C73—21no—
171C2×D4×C73—21no—
172C2×D4×C73—21no—
173C2×D4×C73—21no—
174C2×D4×C73—21no—
175C2×D4×C73—21no—
176C2×D4×C73—21no—
177C2×D4×C73—21no—
178C2×D4×C73—21no—
179C2×D4×C73—21no—
180C2×D4×C73—21no—
181C2×D4×C73—21no—
182C2×D4×C73—44no—
183C2×D4×C73—44no—
184C2×D4×C73—41no—
185C2×D4×C73—42no—
186C2×D4×C73—42no—
187C2×D4×C73—44no—
188C2×D4×C73—42no—
189C2×D4×C73—42no—
190C2×D4×C73—42no—
191C2×D4×C73—42no—
192C2×D4×C73—42no—
193C2×D4×C73—42no—
194C2×D4×C73—42no—
195C2×D4×C73—42no—
196C2×D4×C73—81no—
197C2×D4×C73—81no—
198C2×D4×C73—81no—
199C2×D4×C73—81no—
200C2×D4×C73—81no—
201C2×D4×C73C2×D412yes—
202C2×D4×C73#4112yes—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73C2×D411yescharacteristic
219C22×C4×C73C2×D411yescharacteristic
220C22×C4×C73C2×D411yescharacteristic
221C22×C4×C73C2×D412yes—
222C22×C4×C73C2×D411yescharacteristic
223C22×C4×C73#4112yes—
224C22×C4×C73C2411yescharacteristic
225D8×C73—44no—
226D8×C73—44no—
227M16×C73—44no—
228M16×C73—44no—
229C2×C8×C73—21no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
237C2×C8×C73—21no—
238C2×C8×C73C2×D412yes—
239C2×C8×C73C2×D412yes—
240C2×C8×C73C2×D412yes—
241C4⋊C4×C73—22no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73—21no—
248C4⋊C4×C73—21no—
249C4⋊C4×C73—21no—
250C4⋊C4×C73—21no—
251C4⋊C4×C73—81no—
252C4⋊C4×C73C2×D412yes—
253C22⋊C4×C73—22no—
254C22⋊C4×C73—22no—
255C22⋊C4×C73—42no—
256C22⋊C4×C73—42no—
257C22⋊C4×C73—42no—
258C22⋊C4×C73—42no—
259C22⋊C4×C73—42no—
260C22⋊C4×C73—42no—
261C22⋊C4×C73—42no—
262C22⋊C4×C73—42no—
263C22⋊C4×C73—42no—
264C22⋊C4×C73—81no—
265C22⋊C4×C73—81no—
266C22⋊C4×C73—81no—
267C22⋊C4×C73—81no—
268C42×C73—21no—
269C42×C73—21no—
270C42×C73—42no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—21no—
274C23×C73—21no—
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—22no—
279C23×C73—21no—
280C23×C73—22no—
281C23×C73—21no—
282C23×C73—21no—
283C23×C73—21no—
284C23×C73—21no—
285C23×C73—21no—
286C23×C73—48no—
287C23×C73—41no—
288C23×C73—41no—
289C23×C73—41no—
290C23×C73—41no—
291C23×C73—41no—
292C23×C73—41no—
293C23×C73—41no—
294C23×C73—41no—
295C23×C73—41no—
296C23×C73—41no—
297C23×C73—41no—
298C23×C73—41no—
299C23×C73—41no—
300C23×C73—41no—
301C23×C73—41no—
302C23×C73—41no—
303C23×C73—41no—
304C23×C73—41no—
305C23×C73—41no—
306C23×C73—84no—
307C23×C73—84no—
308C23×C73—84no—
309C23×C73—84no—
310C23×C73—84no—
311C23×C73—84no—
312C23×C73#12112yes—
313C23×C73C22×D411yescharacteristic
314D4×C73—22no—
315D4×C73—22no—
316D4×C73—22no—
317D4×C73—22no—
318D4×C73—44no—
319D4×C73—48no—
320D4×C73—41no—
321D4×C73—41no—
322D4×C73—41no—
323D4×C73—41no—
324D4×C73—41no—
325D4×C73—41no—
326D4×C73—41no—
327D4×C73—41no—
328D4×C73—84no—
329D4×C73—84no—
330D4×C73—84no—
331D4×C73—84no—
332C2×C4×C73—21no—
333C2×C4×C73—21no—
334C2×C4×C73—21no—
335C2×C4×C73—21no—
336C2×C4×C73—22no—
337C2×C4×C73—22no—
338C2×C4×C73—22no—
339C2×C4×C73—22no—
340C2×C4×C73—21no—
341C2×C4×C73—21no—
342C2×C4×C73—22no—
343C2×C4×C73—21no—
344C2×C4×C73—21no—
345C2×C4×C73—21no—
346C2×C4×C73—21no—
347C2×C4×C73—41no—
348C2×C4×C73—41no—
349C2×C4×C73—41no—
350C2×C4×C73—41no—
351C2×C4×C73—41no—
352C2×C4×C73—41no—
353C2×C4×C73—41no—
354C2×C4×C73—41no—
355C2×C4×C73—41no—
356C2×C4×C73—41no—
357C2×C4×C73—41no—
358C2×C4×C73—41no—
359C2×C4×C73—41no—
360C2×C4×C73—41no—
361C2×C4×C73—41no—
362C2×C4×C73—41no—
363C2×C4×C73—41no—
364C2×C4×C73—41no—
365C2×C4×C73#12112yes—
366C2×C4×C73AGL(1,ℤ/8)12yes—
367C2×C4×C73C22×D411yescharacteristic
368C2×C4×C73C22×D411yescharacteristic
369C2×C4×C73C2×#4111yescharacteristic
370C2×C4×C73C2×#4111yescharacteristic
371C2×C4×C73H(5,𝔽2)11yescharacteristic
372C2×C4×C73H(5,𝔽2)11yescharacteristic
373C8×C73—22no—
374C8×C73—22no—
375C8×C73—22no—
376C8×C73—41no—
377C22×C73—22no—
378C22×C73—22no—
379C22×C73—22no—
380C22×C73—41no—
381C22×C73—41no—
382C22×C73—41no—
383C22×C73—41no—
384C22×C73—41no—
385C22×C73—42no—
386C22×C73—42no—
387C22×C73—41no—
388C22×C73—42no—
389C22×C73—41no—
390C22×C73—42no—
391C22×C73—41no—
392C22×C73—41no—
393C22×C73—41no—
394C22×C73—42no—
395C22×C73—41no—
396C22×C73—42no—
397C22×C73—816no—
398C22×C73—81no—
399C22×C73—81no—
400C22×C73—81no—
401C22×C73—81no—
402C22×C73—81no—
403C22×C73—81no—
404C22×C73—81no—
405C22×C73—81no—
406C22×C73—81no—
407C22×C73—81no—
408C22×C73—81no—
409C22×C73—81no—
410C22×C73—81no—
411C22×C73—81no—
412C22×C73—81no—
413C22×C73C2×#12111yescharacteristic
414C22×C73D4211yescharacteristic
415C22×C73#54611yescharacteristic
416C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
417C22×C73#57511yescharacteristic
418C22×C73#57611yescharacteristic
419C22×C73#57611yescharacteristic
420C4×C73—22no—
421C4×C73—22no—
422C4×C73—41no—
423C4×C73—42no—
424C4×C73—41no—
425C4×C73—81no—
426C4×C73—81no—
427C4×C73—81no—
428C4×C73—81no—
429C4×C73#52511yescharacteristic
430C4×C73#53811yescharacteristic
431C4×C73D4211yescharacteristic
432C4×C73#54611yescharacteristic
433#25132C7311yesmaximal, characteristic, direct product factor, Sylow
434C2×C73—42no—
435C2×C73—81no—
436C2×C73—82no—
437C2×C73—82no—
438C2×C73—161no—
439C2×C73#242411yescharacteristic
440C2×C73#305511yescharacteristic
441C2×C73#305811yescharacteristic
442C2×C73#327311yescharacteristic
443C2×C73#327411yescharacteristic
444C2×C73#332211yescharacteristic
445C2×C73#332511yescharacteristic
446C2×#469C2×C7311yescharacteristic, complemented
447C2×#447C2×C7311yescharacteristic, complemented
448C2×#436C2×C7311yescharacteristic, complemented
449C2×#418C2×C7311yescharacteristic, complemented
450#2414C2×C7311yescharacteristic, complemented
451#2408C2×C7311yescharacteristic, complemented
452#2065C2×C7311yescharacteristic, complemented
453#2054C2×C7311yescharacteristic, complemented
454#2033C2×C7311yescharacteristic, complemented
455#1999C2×C7311yescharacteristic, complemented
456#1970C2×C7311yescharacteristic, complemented
457#1934C2×C7311yescharacteristic, complemented
458#1895C2×C7311yescharacteristic, complemented
459#1895C2×C7311yescharacteristic, complemented
460#1854C2×C7311yescharacteristic, complemented
461C73#2513211yescharacteristic, direct product factor, Sylow
462C23×D4C22×C7311yescharacteristic
463C22×D8C22×C7311yescharacteristic
464C22×D8C22×C7311yescharacteristic
465C22×M16C22×C7311yescharacteristic
466C22×M16C22×C7311yescharacteristic, complemented
467C2×#121C22×C7311yescharacteristic
468C2×#121C22×C7311yescharacteristic
469C2×#121C22×C7311yescharacteristic
470C2×#121C22×C7311yescharacteristic, complemented
471C2×#120—21no—
472C2×C4×D4C22×C7311yescharacteristic
473C2×#117C22×C7311yescharacteristic
474#469—24no—
475#447—24no—
476#436—24no—
477C2×#107C22×C7311yescharacteristic, complemented
478C2×#106C22×C7311yescharacteristic, complemented
479C2×C4⋊C8C22×C7311yescharacteristic, complemented
480#418—24no—
481C2×#102C22×C7311yescharacteristic
482C2×#102C22×C7311yescharacteristic
483C2×#102C22×C7311yescharacteristic
484C2×#102C22×C7311yescharacteristic
485C2×#102C22×C7311yescharacteristic
486C2×#102C22×C7311yescharacteristic
487C2×#102C22×C7311yescharacteristic, complemented
488C2×#102C22×C7311yescharacteristic, complemented
489C2×C22⋊C8C22×C7311yescharacteristic
490C2×C22⋊C8C22×C7311yescharacteristic, complemented
491C2×C4×C8C22×C7311yescharacteristic, complemented
492#394—21no—
493#394—21no—
494#392—21no—
495#392—21no—
496#390—21no—
497#390C22×C7311yescharacteristic
498#390C22×C7311yescharacteristic
499#390C22×C7311yescharacteristic, complemented
500#389C22×C7311yescharacteristic, complemented
501#388—21no—
502#380C22×C7311yescharacteristic
503#380C22×C7311yescharacteristic, complemented
504#379—21no—
505#340C22×C7311yescharacteristic, complemented
506#340C22×C7311yescharacteristic, complemented
507#340C22×C7311yescharacteristic, complemented
508#340C22×C7311yescharacteristic, complemented
509C25—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4D4×C7311yescharacteristic
522C22×D4C23×C7311yescharacteristic
523C22×D4C23×C7311yescharacteristic
524C22×D4C23×C7311yescharacteristic
525C23×C4C23×C7311yescharacteristic
526C23×C4C23×C7311yescharacteristic
527C2×D8—22no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—22no—
531C2×D8—41no—
532C2×D8—41no—
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—41no—
539C22×C8C23×C7311yescharacteristic
540C22×C8C23×C7311yescharacteristic
541C22×C8C23×C7311yescharacteristic
542C22×C8C23×C7311yescharacteristic
543#121—22no—
544#121—22no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—41no—
549#121—41no—
550#121—41no—
551#120—44no—
552C4×D4—22no—
553C4×D4—22no—
554#117—22no—
555#117—41no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4D4×C7311yescharacteristic
558C2×C4⋊C4C23×C7311yescharacteristic
559C2×C4⋊C4C23×C7311yescharacteristic
560C2×C4⋊C4C23×C7311yescharacteristic
561C2×C4⋊C4C23×C7311yescharacteristic
562C2×C4⋊C4C23×C7311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4D4×C7311yescharacteristic
577C2×C22⋊C4D4×C7311yescharacteristic
578C2×C42—21no—
579C2×C42C23×C7311yescharacteristic
580#107—41no—
581#106—22no—
582C4⋊C8—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—22no—
587#102—22no—
588#102—22no—
589#102—41no—
590#102D4×C7314yescomplemented
591C22⋊C8—22no—
592C22⋊C8D4×C7314yescomplemented
593C4×C8—22no—
594#95—21no—
595#95—21no—
596#95—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—42no—
601C24—42no—
602C24—42no—
603C24—42no—
604C24—42no—
605C24—81no—
606C24—81no—
607C24C2×D4×C7311yescharacteristic
608C24C2×D4×C7311yescharacteristic
609C2×D4—28no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—41no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4C2×D4×C7312yes—
648C2×D4#41×C7312yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4C2×D4×C7311yescharacteristic
665C22×C4C2×D4×C7311yescharacteristic
666C22×C4C2×D4×C7311yescharacteristic
667C22×C4C2×D4×C7312yes—
668C22×C4C2×D4×C7311yescharacteristic
669C22×C4#41×C7312yes—
670C22×C4C24×C7311yescharacteristic
671D8—44no—
672D8—44no—
673M16—44no—
674M16—44no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8C2×D4×C7312yes—
685C2×C8C2×D4×C7312yes—
686C2×C8C2×D4×C7312yes—
687C4⋊C4—22no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—81no—
698C4⋊C4C2×D4×C7312yes—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C42—42no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—22no—
725C23—21no—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—48no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23#121×C7312yes—
759C23C22×D4×C7311yescharacteristic
760D4—22no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—44no—
765D4—48no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—41no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4—84no—
775D4—84no—
776D4—84no—
777D4—84no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4#121×C7312yes—
812C2×C4AGL(1,ℤ/8)×C7312yes—
813C2×C4C22×D4×C7311yescharacteristic
814C2×C4C22×D4×C7311yescharacteristic
815C2×C4C2×#41×C7311yescharacteristic
816C2×C4C2×#41×C7311yescharacteristic
817C2×C4H(5,𝔽2)×C7311yescharacteristic
818C2×C4H(5,𝔽2)×C7311yescharacteristic
819C8—22no—
820C8—22no—
821C8—22no—
822C8—41no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—42no—
843C22—816no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22C2×#121×C7311yescharacteristic
860C22D42×C7311yescharacteristic
861C22#546×C7311yescharacteristic
862C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
863C22#575×C7311yescharacteristic
864C22#576×C7311yescharacteristic
865C22#576×C7311yescharacteristic
866C4—22no—
867C4—22no—
868C4—42no—
869C4—41no—
870C4—41no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4—81no—
875C4#525×C7311yescharacteristic
876C4#538×C7311yescharacteristic
877C4D42×C7311yescharacteristic
878C4#546×C7311yescharacteristic
879C2—42no—
880C2—81no—
881C2—82no—
882C2—82no—
883C2—161no—
884C2C73×#242411yescharacteristic
885C2C73×#305511yescharacteristic
886C2C73×#305811yescharacteristic
887C2C73×#327311yescharacteristic
888C2C73×#327411yescharacteristic
889C2C73×#332211yescharacteristic
890C2C73×#332511yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
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×#469×C73C2semidirect
2. C2×#447×C73C2semidirect
3. C2×#436×C73C2semidirect
4. C2×#418×C73C2semidirect
5. C73×#2414C2semidirect
6. C73×#2408C2semidirect
7. C73×#2065C2semidirect
8. C73×#2054C2semidirect
9. C73×#2033C2semidirect
10. C73×#1999C2semidirect
11. C73×#1970C2semidirect
12. C73×#1934C2semidirect
13. C73×#1895C2semidirect
14. C73×#1895C2semidirect
15. C73×#1854C2semidirect
20. C22×M16×C73C22semidirect
24. C2×#121×C73C22semidirect
31. C2×#107×C73C22semidirect
32. C2×#106×C73C22semidirect
33. C2×C4⋊C8×C73C22semidirect
41. C2×#102×C73C22semidirect
42. C2×#102×C73C22semidirect
44. C2×C22⋊C8×C73C22semidirect
45. C2×C4×C8×C73C22semidirect
53. #390×C73C22semidirect
54. #389×C73C22semidirect
57. #380×C73C22semidirect
59. #340×C73C22semidirect
60. #340×C73C22semidirect
61. #340×C73C22semidirect
62. #340×C73C22semidirect
144. #102×C73D4semidirect
146. C22⋊C8×C73D4semidirect
433. #25132C73direct (N × H)
446. C2×#469C2×C73semidirect
447. C2×#447C2×C73semidirect
448. C2×#436C2×C73semidirect
449. C2×#418C2×C73semidirect
450. #2414C2×C73semidirect
451. #2408C2×C73semidirect
452. #2065C2×C73semidirect
453. #2054C2×C73semidirect
454. #2033C2×C73semidirect
455. #1999C2×C73semidirect
456. #1970C2×C73semidirect
457. #1934C2×C73semidirect
458. #1895C2×C73semidirect
459. #1895C2×C73semidirect
460. #1854C2×C73semidirect
461. C73#25132direct (N × H)
466. C22×M16C22×C73semidirect
470. C2×#121C22×C73semidirect
477. C2×#107C22×C73semidirect
478. C2×#106C22×C73semidirect
479. C2×C4⋊C8C22×C73semidirect
487. C2×#102C22×C73semidirect
488. C2×#102C22×C73semidirect
490. C2×C22⋊C8C22×C73semidirect
491. C2×C4×C8C22×C73semidirect
499. #390C22×C73semidirect
500. #389C22×C73semidirect
503. #380C22×C73semidirect
505. #340C22×C73semidirect
506. #340C22×C73semidirect
507. #340C22×C73semidirect
508. #340C22×C73semidirect
590. #102D4×C73semidirect
592. C22⋊C8D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C732
C2×#447×C732
C2×#436×C732
C2×#418×C732
C73×#24142
C73×#24082
C73×#20652
C73×#20542
C73×#20332
C73×#19992
C73×#19702
C73×#19342
C73×#18952
C73×#18542
#2513273