Finite Group Databasebeta

← C73×#25136 #32934540

Subgroups — C73×#25136 #32934540

Order 18688.

1264 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C73C211yesmaximal, characteristic, complemented
2C2×#450×C73C211yesmaximal, characteristic, complemented
3C2×#436×C73C211yesmaximal, characteristic, complemented
4C2×#418×C73C211yesmaximal, characteristic, complemented
5C73×#2415C211yesmaximal, characteristic, complemented
6C73×#2408C211yesmaximal, characteristic
7C73×#2067C211yesmaximal, characteristic, complemented
8C73×#2055C211yesmaximal, characteristic, complemented
9C73×#2034C211yesmaximal, characteristic, complemented
10C73×#2000C211yesmaximal, characteristic, complemented
11C73×#1968C211yesmaximal, characteristic, complemented
12C73×#1934C211yesmaximal, characteristic, complemented
13C73×#1895C211yesmaximal, characteristic, complemented
14C73×#1894C211yesmaximal, characteristic, complemented
15C73×#1854C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C22×M16×C73C2211yescharacteristic
20C22×M16×C73C2211yescharacteristic, complemented
21C2×C22⋊Q8×C73C2211yescharacteristic
22C2×C22⋊Q8×C73C2211yescharacteristic, complemented
23C2×#121×C73C2211yescharacteristic
24C2×#121×C73C2211yescharacteristic
25C2×#120×C73—21no—
26C2×C4×D4×C73C2211yescharacteristic
27C2×#117×C73C2211yescharacteristic
28#468×C73—24no—
29#450×C73—24no—
30#436×C73—24no—
31C2×#107×C73C2211yescharacteristic, complemented
32C2×#106×C73C2211yescharacteristic, complemented
33C2×C4⋊C8×C73C2211yescharacteristic, complemented
34#418×C73—24no—
35C2×#103×C73C2211yescharacteristic, complemented
36C2×#103×C73C2211yescharacteristic, complemented
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×C22⋊C8×C73C2211yescharacteristic
44C2×C22⋊C8×C73C2211yescharacteristic, complemented
45C2×C4×C8×C73C2211yescharacteristic, complemented
46#397×C73—21no—
47#394×C73—21no—
48#394×C73—21no—
49#392×C73—21no—
50#391×C73C2211yescharacteristic, complemented
51#390×C73C2211yescharacteristic
52#390×C73C2211yescharacteristic
53#389×C73—21no—
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×Q8×C73C2311yescharacteristic
65C22×D4×C73—22no—
66C22×D4×C73—22no—
67C22×D4×C73—21no—
68C22×D4×C73—21no—
69C22×D4×C73—22no—
70C22×D4×C73—21no—
71C22×D4×C73—22no—
72C22×D4×C73—41no—
73C22×D4×C73—41no—
74C22×D4×C73D411yescharacteristic
75C22×D4×C73C2311yescharacteristic
76C22×D4×C73C2311yescharacteristic
77C23×C4×C73C2311yescharacteristic
78C23×C4×C73C2311yescharacteristic
79C2×SD16×C73—22no—
80C2×SD16×C73—22no—
81C2×SD16×C73—22no—
82C2×SD16×C73—22no—
83C2×SD16×C73—41no—
84C2×SD16×C73—41no—
85C2×M16×C73—22no—
86C2×M16×C73—22no—
87C2×M16×C73—22no—
88C2×M16×C73—22no—
89C2×M16×C73—41no—
90C2×M16×C73—41no—
91C22×C8×C73C2311yescharacteristic
92C22×C8×C73C2311yescharacteristic
93C22×C8×C73C2311yescharacteristic
94C22×C8×C73C2311yescharacteristic
95C22⋊Q8×C73—22no—
96C22⋊Q8×C73—22no—
97C22⋊Q8×C73—22no—
98C22⋊Q8×C73—41no—
99#121×C73—22no—
100#121×C73—22no—
101#121×C73—41no—
102#121×C73—41no—
103#120×C73—44no—
104C4×D4×C73—22no—
105C4×D4×C73—22no—
106#117×C73—22no—
107#117×C73—41no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—21no—
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×C73D411yescharacteristic
129C2×C22⋊C4×C73D411yescharacteristic
130C2×C42×C73—21no—
131C2×C42×C73C2311yescharacteristic
132#107×C73—22no—
133#106×C73—41no—
134C4⋊C8×C73—22no—
135#103×C73—22no—
136#103×C73—41no—
137#102×C73—22no—
138#102×C73—22no—
139#102×C73—22no—
140#102×C73—22no—
141#102×C73—22no—
142#102×C73D414yescomplemented
143C22⋊C8×C73—22no—
144C22⋊C8×C73D414yescomplemented
145C4×C8×C73—22no—
146#95×C73—21no—
147#95×C73—21no—
148#95×C73—21no—
149#95×C73—21no—
150#95×C73—21no—
151C24×C73—21no—
152C24×C73—21no—
153C24×C73—42no—
154C24×C73—42no—
155C24×C73—42no—
156C24×C73—42no—
157C24×C73—42no—
158C24×C73—81no—
159C24×C73—81no—
160C24×C73C2×D411yescharacteristic
161C24×C73C2×D411yescharacteristic
162C2×Q8×C73—21no—
163C2×Q8×C73—21no—
164C2×Q8×C73—21no—
165C2×Q8×C73—21no—
166C2×Q8×C73—21no—
167C2×Q8×C73—21no—
168C2×D4×C73—28no—
169C2×D4×C73—22no—
170C2×D4×C73—22no—
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—44no—
182C2×D4×C73—44no—
183C2×D4×C73—41no—
184C2×D4×C73—42no—
185C2×D4×C73—42no—
186C2×D4×C73—44no—
187C2×D4×C73—42no—
188C2×D4×C73—42no—
189C2×D4×C73—42no—
190C2×D4×C73—42no—
191C2×D4×C73—42no—
192C2×D4×C73—81no—
193C2×D4×C73—81no—
194C2×D4×C73C2×D412yes—
195C2×D4×C73#4112yes—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
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×C73C2×D411yescharacteristic
213C22×C4×C73C2×D411yescharacteristic
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73C2×D412yes—
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73#4112yes—
218C22×C4×C73C2411yescharacteristic
219SD16×C73—44no—
220SD16×C73—44no—
221M16×C73—44no—
222M16×C73—44no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73C2×D412yes—
233C2×C8×C73C2×D412yes—
234C2×C8×C73C2×D412yes—
235C4⋊C4×C73—22no—
236C4⋊C4×C73—21no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—42no—
246C4⋊C4×C73—42no—
247C4⋊C4×C73—42no—
248C4⋊C4×C73C2×D412yes—
249C22⋊C4×C73—22no—
250C22⋊C4×C73—22no—
251C22⋊C4×C73—42no—
252C22⋊C4×C73—42no—
253C22⋊C4×C73—42no—
254C22⋊C4×C73—42no—
255C22⋊C4×C73—42no—
256C22⋊C4×C73—42no—
257C22⋊C4×C73—42no—
258C22⋊C4×C73—42no—
259C22⋊C4×C73—42no—
260C22⋊C4×C73—81no—
261C22⋊C4×C73—81no—
262C42×C73—21no—
263C42×C73—21no—
264C42×C73—42no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—21no—
279C23×C73—21no—
280C23×C73—48no—
281C23×C73—41no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73—41no—
285C23×C73—41no—
286C23×C73—41no—
287C23×C73—41no—
288C23×C73—41no—
289C23×C73—41no—
290C23×C73—41no—
291C23×C73—41no—
292C23×C73—41no—
293C23×C73—84no—
294C23×C73—84no—
295C23×C73—84no—
296C23×C73—84no—
297C23×C73—84no—
298C23×C73—84no—
299C23×C73#12112yes—
300C23×C73C22×D411yescharacteristic
301Q8×C73—41no—
302Q8×C73—41no—
303Q8×C73—41no—
304Q8×C73—41no—
305D4×C73—22no—
306D4×C73—22no—
307D4×C73—22no—
308D4×C73—22no—
309D4×C73—44no—
310D4×C73—48no—
311D4×C73—41no—
312D4×C73—41no—
313D4×C73—41no—
314D4×C73—41no—
315D4×C73—84no—
316D4×C73—84no—
317C2×C4×C73—21no—
318C2×C4×C73—21no—
319C2×C4×C73—21no—
320C2×C4×C73—21no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—22no—
324C2×C4×C73—22no—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
327C2×C4×C73—22no—
328C2×C4×C73—21no—
329C2×C4×C73—21no—
330C2×C4×C73—21no—
331C2×C4×C73—21no—
332C2×C4×C73—41no—
333C2×C4×C73—41no—
334C2×C4×C73—41no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
337C2×C4×C73—41no—
338C2×C4×C73—41no—
339C2×C4×C73—41no—
340C2×C4×C73—41no—
341C2×C4×C73—41no—
342C2×C4×C73—41no—
343C2×C4×C73—41no—
344C2×C4×C73—41no—
345C2×C4×C73—41no—
346C2×C4×C73—41no—
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#12112yes—
354C2×C4×C73AGL(1,ℤ/8)12yes—
355C2×C4×C73C22×D411yescharacteristic
356C2×C4×C73C22×D411yescharacteristic
357C2×C4×C73C2×#4111yescharacteristic
358C2×C4×C73C2×#4111yescharacteristic
359C2×C4×C73H(5,𝔽2)11yescharacteristic
360C2×C4×C73H(5,𝔽2)11yescharacteristic
361C8×C73—22no—
362C8×C73—22no—
363C8×C73—22no—
364C8×C73—41no—
365C22×C73—22no—
366C22×C73—22no—
367C22×C73—22no—
368C22×C73—41no—
369C22×C73—41no—
370C22×C73—41no—
371C22×C73—41no—
372C22×C73—41no—
373C22×C73—42no—
374C22×C73—42no—
375C22×C73—41no—
376C22×C73—42no—
377C22×C73—41no—
378C22×C73—42no—
379C22×C73—41no—
380C22×C73—41no—
381C22×C73—41no—
382C22×C73—42no—
383C22×C73—41no—
384C22×C73—42no—
385C22×C73—816no—
386C22×C73—81no—
387C22×C73—81no—
388C22×C73—81no—
389C22×C73—81no—
390C22×C73—81no—
391C22×C73—81no—
392C22×C73—81no—
393C22×C73—81no—
394C22×C73C2×#12111yescharacteristic
395C22×C73D4211yescharacteristic
396C22×C73#54611yescharacteristic
397C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
398C22×C73#57511yescharacteristic
399C22×C73#57711yescharacteristic
400C22×C73#57711yescharacteristic
401C4×C73—22no—
402C4×C73—22no—
403C4×C73—41no—
404C4×C73—42no—
405C4×C73—41no—
406C4×C73—81no—
407C4×C73—81no—
408C4×C73—81no—
409C4×C73—81no—
410C4×C73—81no—
411C4×C73#52511yescharacteristic
412C4×C73#53811yescharacteristic
413C4×C73D4211yescharacteristic
414C4×C73#54611yescharacteristic
415#25136C7311yesmaximal, characteristic, direct product factor, Sylow
416C2×C73—42no—
417C2×C73—81no—
418C2×C73—82no—
419C2×C73—82no—
420C2×C73#242411yescharacteristic
421C2×C73#305511yescharacteristic
422C2×C73#305711yescharacteristic
423C2×C73#327211yescharacteristic
424C2×C73#327511yescharacteristic
425C2×C73#332311yescharacteristic
426C2×C73#332411yescharacteristic
427C2×#468C2×C7311yescharacteristic, complemented
428C2×#450C2×C7311yescharacteristic, complemented
429C2×#436C2×C7311yescharacteristic, complemented
430C2×#418C2×C7311yescharacteristic, complemented
431#2415C2×C7311yescharacteristic, complemented
432#2408C2×C7311yescharacteristic
433#2067C2×C7311yescharacteristic, complemented
434#2055C2×C7311yescharacteristic, complemented
435#2034C2×C7311yescharacteristic, complemented
436#2000C2×C7311yescharacteristic, complemented
437#1968C2×C7311yescharacteristic, complemented
438#1934C2×C7311yescharacteristic, complemented
439#1895C2×C7311yescharacteristic, complemented
440#1894C2×C7311yescharacteristic, complemented
441#1854C2×C7311yescharacteristic, complemented
442C73#2513611yescharacteristic, direct product factor, Sylow
443C23×D4C22×C7311yescharacteristic
444C22×SD16C22×C7311yescharacteristic
445C22×SD16C22×C7311yescharacteristic
446C22×M16C22×C7311yescharacteristic
447C22×M16C22×C7311yescharacteristic, complemented
448C2×C22⋊Q8C22×C7311yescharacteristic
449C2×C22⋊Q8C22×C7311yescharacteristic, complemented
450C2×#121C22×C7311yescharacteristic
451C2×#121C22×C7311yescharacteristic
452C2×#120—21no—
453C2×C4×D4C22×C7311yescharacteristic
454C2×#117C22×C7311yescharacteristic
455#468—24no—
456#450—24no—
457#436—24no—
458C2×#107C22×C7311yescharacteristic, complemented
459C2×#106C22×C7311yescharacteristic, complemented
460C2×C4⋊C8C22×C7311yescharacteristic, complemented
461#418—24no—
462C2×#103C22×C7311yescharacteristic, complemented
463C2×#103C22×C7311yescharacteristic, complemented
464C2×#102C22×C7311yescharacteristic
465C2×#102C22×C7311yescharacteristic
466C2×#102C22×C7311yescharacteristic
467C2×#102C22×C7311yescharacteristic
468C2×#102C22×C7311yescharacteristic
469C2×#102C22×C7311yescharacteristic
470C2×C22⋊C8C22×C7311yescharacteristic
471C2×C22⋊C8C22×C7311yescharacteristic, complemented
472C2×C4×C8C22×C7311yescharacteristic, complemented
473#397—21no—
474#394—21no—
475#394—21no—
476#392—21no—
477#391C22×C7311yescharacteristic, complemented
478#390C22×C7311yescharacteristic
479#390C22×C7311yescharacteristic
480#389—21no—
481#389C22×C7311yescharacteristic, complemented
482#388—21no—
483#380C22×C7311yescharacteristic
484#380C22×C7311yescharacteristic, complemented
485#379—21no—
486#340C22×C7311yescharacteristic, complemented
487#340C22×C7311yescharacteristic, complemented
488#340C22×C7311yescharacteristic, complemented
489#340C22×C7311yescharacteristic, complemented
490C25—21no—
491C22×Q8C23×C7311yescharacteristic
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4D4×C7311yescharacteristic
502C22×D4C23×C7311yescharacteristic
503C22×D4C23×C7311yescharacteristic
504C23×C4C23×C7311yescharacteristic
505C23×C4C23×C7311yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—41no—
511C2×SD16—41no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—41no—
517C2×M16—41no—
518C22×C8C23×C7311yescharacteristic
519C22×C8C23×C7311yescharacteristic
520C22×C8C23×C7311yescharacteristic
521C22×C8C23×C7311yescharacteristic
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8—41no—
526#121—22no—
527#121—22no—
528#121—41no—
529#121—41no—
530#120—44no—
531C4×D4—22no—
532C4×D4—22no—
533#117—22no—
534#117—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4D4×C7311yescharacteristic
539C2×C4⋊C4C23×C7311yescharacteristic
540C2×C4⋊C4C23×C7311yescharacteristic
541C2×C4⋊C4C23×C7311yescharacteristic
542C2×C4⋊C4C23×C7311yescharacteristic
543C2×C4⋊C4C23×C7311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4D4×C7311yescharacteristic
556C2×C22⋊C4D4×C7311yescharacteristic
557C2×C42—21no—
558C2×C42C23×C7311yescharacteristic
559#107—22no—
560#106—41no—
561C4⋊C8—22no—
562#103—22no—
563#103—41no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102D4×C7314yescomplemented
570C22⋊C8—22no—
571C22⋊C8D4×C7314yescomplemented
572C4×C8—22no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578C24—21no—
579C24—21no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—81no—
586C24—81no—
587C24C2×D4×C7311yescharacteristic
588C24C2×D4×C7311yescharacteristic
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×D4—28no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—41no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4C2×D4×C7312yes—
622C2×D4#41×C7312yes—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4C2×D4×C7311yescharacteristic
640C22×C4C2×D4×C7311yescharacteristic
641C22×C4C2×D4×C7311yescharacteristic
642C22×C4C2×D4×C7312yes—
643C22×C4C2×D4×C7311yescharacteristic
644C22×C4#41×C7312yes—
645C22×C4C24×C7311yescharacteristic
646SD16—44no—
647SD16—44no—
648M16—44no—
649M16—44no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8C2×D4×C7312yes—
660C2×C8C2×D4×C7312yes—
661C2×C8C2×D4×C7312yes—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4C2×D4×C7312yes—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—42no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23#121×C7312yes—
727C23C22×D4×C7311yescharacteristic
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—44no—
737D4—48no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—84no—
743D4—84no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4#121×C7312yes—
781C2×C4AGL(1,ℤ/8)×C7312yes—
782C2×C4C22×D4×C7311yescharacteristic
783C2×C4C22×D4×C7311yescharacteristic
784C2×C4C2×#41×C7311yescharacteristic
785C2×C4C2×#41×C7311yescharacteristic
786C2×C4H(5,𝔽2)×C7311yescharacteristic
787C2×C4H(5,𝔽2)×C7311yescharacteristic
788C8—22no—
789C8—22no—
790C8—22no—
791C8—41no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—816no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22C2×#121×C7311yescharacteristic
822C22D42×C7311yescharacteristic
823C22#546×C7311yescharacteristic
824C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
825C22#575×C7311yescharacteristic
826C22#577×C7311yescharacteristic
827C22#577×C7311yescharacteristic
828C4—22no—
829C4—22no—
830C4—42no—
831C4—41no—
832C4—41no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—81no—
837C4—81no—
838C4#525×C7311yescharacteristic
839C4#538×C7311yescharacteristic
840C4D42×C7311yescharacteristic
841C4#546×C7311yescharacteristic
842C2—42no—
843C2—81no—
844C2—82no—
845C2—82no—
846C2C73×#242411yescharacteristic
847C2C73×#305511yescharacteristic
848C2C73×#305711yescharacteristic
849C2C73×#327211yescharacteristic
850C2C73×#327511yescharacteristic
851C2C73×#332311yescharacteristic
852C2C73×#332411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2408C2
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×#450×C73C2semidirect
3. C2×#436×C73C2semidirect
4. C2×#418×C73C2semidirect
5. C73×#2415C2semidirect
7. C73×#2067C2semidirect
8. C73×#2055C2semidirect
9. C73×#2034C2semidirect
10. C73×#2000C2semidirect
11. C73×#1968C2semidirect
12. C73×#1934C2semidirect
13. C73×#1895C2semidirect
14. C73×#1894C2semidirect
15. C73×#1854C2semidirect
20. C22×M16×C73C22semidirect
22. C2×C22⋊Q8×C73C22semidirect
31. C2×#107×C73C22semidirect
32. C2×#106×C73C22semidirect
33. C2×C4⋊C8×C73C22semidirect
35. C2×#103×C73C22semidirect
36. C2×#103×C73C22semidirect
44. C2×C22⋊C8×C73C22semidirect
45. C2×C4×C8×C73C22semidirect
50. #391×C73C22semidirect
54. #389×C73C22semidirect
57. #380×C73C22semidirect
59. #340×C73C22semidirect
60. #340×C73C22semidirect
61. #340×C73C22semidirect
62. #340×C73C22semidirect
142. #102×C73D4semidirect
144. C22⋊C8×C73D4semidirect
415. #25136C73direct (N × H)
427. C2×#468C2×C73semidirect
428. C2×#450C2×C73semidirect
429. C2×#436C2×C73semidirect
430. C2×#418C2×C73semidirect
431. #2415C2×C73semidirect
433. #2067C2×C73semidirect
434. #2055C2×C73semidirect
435. #2034C2×C73semidirect
436. #2000C2×C73semidirect
437. #1968C2×C73semidirect
438. #1934C2×C73semidirect
439. #1895C2×C73semidirect
440. #1894C2×C73semidirect
441. #1854C2×C73semidirect
442. C73#25136direct (N × H)
447. C22×M16C22×C73semidirect
449. C2×C22⋊Q8C22×C73semidirect
458. C2×#107C22×C73semidirect
459. C2×#106C22×C73semidirect
460. C2×C4⋊C8C22×C73semidirect
462. C2×#103C22×C73semidirect
463. C2×#103C22×C73semidirect
471. C2×C22⋊C8C22×C73semidirect
472. C2×C4×C8C22×C73semidirect
477. #391C22×C73semidirect
481. #389C22×C73semidirect
484. #380C22×C73semidirect
486. #340C22×C73semidirect
487. #340C22×C73semidirect
488. #340C22×C73semidirect
489. #340C22×C73semidirect
569. #102D4×C73semidirect
571. C22⋊C8D4×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×#450×C732
C2×#436×C732
C2×#418×C732
C73×#24152
C73×#24082
C73×#20672
C73×#20552
C73×#20342
C73×#20002
C73×#19682
C73×#19342
C73×#18952
C73×#18942
C73×#18542
#2513673