Finite Group Databasebeta

← C73×#24395 #32933799

Subgroups — C73×#24395 #32933799

Order 18688.

1450 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C73C211yesmaximal, characteristic
2C2×#470×C73C211yesmaximal, characteristic, complemented
3C2×#465×C73C211yesmaximal, characteristic, complemented
4C2×#452×C73C211yesmaximal, characteristic, complemented
5C2×#408×C73C211yesmaximal, characteristic, complemented
6C73×#2616C211yesmaximal, characteristic, complemented
7C73×#2035C211yesmaximal, characteristic, complemented
8C73×#2034C211yesmaximal, characteristic, complemented
9C73×#2001C211yesmaximal, characteristic, complemented
10C73×#2000C211yesmaximal, characteristic, complemented
11C73×#1895C211yesmaximal, characteristic, complemented
12C73×#1892C211yesmaximal, characteristic, complemented
13C73×#1872C211yesmaximal, characteristic, complemented
14C73×#1853C211yesmaximal, characteristic, complemented
15C73×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C22×#41×C73C2211yescharacteristic
18C22×Q16×C73C2211yescharacteristic
19C22×SD16×C73C2211yescharacteristic
20C22×M16×C73C2211yescharacteristic
21C23×C8×C73C2211yescharacteristic
22#537×C73—24no—
23#537×C73—24no—
24C2×C22⋊Q8×C73—21no—
25C2×C22⋊Q8×C73C2211yescharacteristic
26C2×C22⋊Q8×C73C2211yescharacteristic
27C2×C22⋊Q8×C73C2211yescharacteristic
28C2×C22⋊Q8×C73C2211yescharacteristic
29C2×C22⋊Q8×C73C2211yescharacteristic
30C2×#121×C73—21no—
31C2×#121×C73—21no—
32C2×#121×C73—21no—
33C2×#121×C73C2211yescharacteristic
34C2×#121×C73C2211yescharacteristic
35C22×C4⋊C4×C73C2211yescharacteristic
36#470×C73—24no—
37#465×C73—24no—
38#452×C73—24no—
39C2×#106×C73C2211yescharacteristic
40C2×#106×C73C2211yescharacteristic
41C2×#103×C73C2211yescharacteristic
42C2×#103×C73C2211yescharacteristic
43C2×#103×C73C2211yescharacteristic
44C2×#103×C73C2211yescharacteristic
45C2×#103×C73C2211yescharacteristic
46C2×#102×C73C2211yescharacteristic
47C2×#102×C73C2211yescharacteristic
48C2×#102×C73C2211yescharacteristic
49#408×C73—24no—
50C2×C22⋊C8×C73C2211yescharacteristic
51C2×C22⋊C8×C73C2211yescharacteristic
52C2×C22⋊C8×C73C2211yescharacteristic
53C2×C22⋊C8×C73C2211yescharacteristic
54#395×C73—21no—
55#394×C73—21no—
56#394×C73—21no—
57#394×C73—21no—
58#380×C73C2211yescharacteristic
59#380×C73C2211yescharacteristic
60#380×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63#340×C73C2211yescharacteristic
64#340×C73C2211yescharacteristic
65C2×#41×C73—22no—
66C2×#41×C73—22no—
67C2×#41×C73—22no—
68C2×#41×C73—22no—
69C2×#41×C73—22no—
70C2×#41×C73—22no—
71C2×#41×C73—22no—
72C2×#41×C73—22no—
73C2×#41×C73—41no—
74C2×#41×C73—41no—
75C2×#41×C73—41no—
76C2×#41×C73—41no—
77C22×Q8×C73D411yescharacteristic
78C22×Q8×C73C2311yescharacteristic
79C22×Q8×C73C2311yescharacteristic
80C22×D4×C73—21no—
81C22×D4×C73—21no—
82C22×D4×C73—21no—
83C22×D4×C73D411yescharacteristic
84C22×D4×C73D411yescharacteristic
85C22×D4×C73D411yescharacteristic
86C22×D4×C73C2311yescharacteristic
87C23×C4×C73—21no—
88C23×C4×C73—21no—
89C23×C4×C73C2311yescharacteristic
90C23×C4×C73C2311yescharacteristic
91C23×C4×C73C2311yescharacteristic
92C2×Q16×C73—22no—
93C2×Q16×C73—22no—
94C2×Q16×C73—41no—
95C2×SD16×C73—22no—
96C2×SD16×C73—22no—
97C2×SD16×C73—41no—
98C2×M16×C73—22no—
99C2×M16×C73—22no—
100C2×M16×C73—41no—
101C22×C8×C73—22no—
102C22×C8×C73—22no—
103C22×C8×C73—41no—
104C22×C8×C73C2311yescharacteristic
105C22×C8×C73C2311yescharacteristic
106C22×C8×C73C2311yescharacteristic
107C22×C8×C73C2311yescharacteristic
108C22⋊Q8×C73—28no—
109C22⋊Q8×C73—22no—
110C22⋊Q8×C73—22no—
111C22⋊Q8×C73—22no—
112C22⋊Q8×C73—22no—
113C22⋊Q8×C73—22no—
114C22⋊Q8×C73—22no—
115C22⋊Q8×C73—22no—
116C22⋊Q8×C73—41no—
117C22⋊Q8×C73—41no—
118C22⋊Q8×C73D414yes—
119#121×C73—28no—
120#121×C73—28no—
121#121×C73—28no—
122#121×C73—22no—
123#121×C73—22no—
124#121×C73—22no—
125#121×C73D414yes—
126C2×C4⋊C4×C73—21no—
127C2×C4⋊C4×C73—21no—
128C2×C4⋊C4×C73—21no—
129C2×C4⋊C4×C73—22no—
130C2×C4⋊C4×C73—22no—
131C2×C4⋊C4×C73—21no—
132C2×C4⋊C4×C73—21no—
133C2×C4⋊C4×C73—21no—
134C2×C4⋊C4×C73C2311yescharacteristic
135C2×C4⋊C4×C73C2311yescharacteristic
136C2×C4⋊C4×C73C2311yescharacteristic
137C2×C4⋊C4×C73C2311yescharacteristic
138C2×C4⋊C4×C73C2311yescharacteristic
139C2×C22⋊C4×C73—21no—
140C2×C22⋊C4×C73—21no—
141C2×C22⋊C4×C73—21no—
142C2×C22⋊C4×C73—21no—
143C2×C22⋊C4×C73—21no—
144C2×C22⋊C4×C73—21no—
145C2×C22⋊C4×C73—21no—
146C2×C22⋊C4×C73—21no—
147C2×C22⋊C4×C73—21no—
148C2×C22⋊C4×C73—21no—
149#106×C73—22no—
150#106×C73—22no—
151#103×C73—22no—
152#103×C73—22no—
153#103×C73—22no—
154#103×C73—22no—
155#103×C73—41no—
156#102×C73—22no—
157#102×C73—22no—
158#102×C73—41no—
159C22⋊C8×C73—22no—
160C22⋊C8×C73—22no—
161C22⋊C8×C73—22no—
162C22⋊C8×C73D414yescomplemented
163#95×C73—21no—
164#95×C73—21no—
165#95×C73—21no—
166C24×C73—21no—
167C24×C73C2×D411yescharacteristic
168C24×C73C2×D411yescharacteristic
169C24×C73C2×D411yescharacteristic
170#41×C73—44no—
171#41×C73—44no—
172#41×C73—44no—
173#41×C73—44no—
174#41×C73—44no—
175#41×C73—44no—
176#41×C73—44no—
177#41×C73—44no—
178C2×Q8×C73—22no—
179C2×Q8×C73—22no—
180C2×Q8×C73—21no—
181C2×Q8×C73—21no—
182C2×Q8×C73—21no—
183C2×Q8×C73—21no—
184C2×Q8×C73—21no—
185C2×Q8×C73—21no—
186C2×Q8×C73—21no—
187C2×Q8×C73—21no—
188C2×Q8×C73—21no—
189C2×Q8×C73—21no—
190C2×Q8×C73—21no—
191C2×Q8×C73—41no—
192C2×Q8×C73C2×D412yes—
193C2×D4×C73—24no—
194C2×D4×C73—22no—
195C2×D4×C73—22no—
196C2×D4×C73—22no—
197C2×D4×C73—22no—
198C2×D4×C73—24no—
199C2×D4×C73—24no—
200C2×D4×C73—22no—
201C2×D4×C73—22no—
202C2×D4×C73—21no—
203C2×D4×C73—21no—
204C2×D4×C73—21no—
205C2×D4×C73—21no—
206C2×D4×C73—21no—
207C2×D4×C73—41no—
208C2×D4×C73—41no—
209C2×D4×C73—41no—
210C2×D4×C73—42no—
211C2×D4×C73—42no—
212C2×D4×C73—81no—
213C2×D4×C73—81no—
214C2×D4×C73—81no—
215C2×D4×C73—81no—
216C2×D4×C73C2×D412yes—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—24no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—24no—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—42no—
241C22×C4×C73—42no—
242C22×C4×C73—81no—
243C22×C4×C73—81no—
244C22×C4×C73C2×D411yescharacteristic
245C22×C4×C73C2×D411yescharacteristic
246C22×C4×C73C2×D412yes—
247C22×C4×C73C2×D412yes—
248C22×C4×C73C2×D411yescharacteristic
249C22×C4×C73C2×D412yes—
250C22×C4×C73#4112yes—
251C22×C4×C73C2411yescharacteristic
252Q16×C73—44no—
253SD16×C73—44no—
254M16×C73—44no—
255C2×C8×C73—21no—
256C2×C8×C73—21no—
257C2×C8×C73—21no—
258C2×C8×C73—21no—
259C2×C8×C73—21no—
260C2×C8×C73—21no—
261C2×C8×C73—21no—
262C2×C8×C73—21no—
263C2×C8×C73—21no—
264C2×C8×C73—21no—
265C2×C8×C73—44no—
266C2×C8×C73C2×D412yes—
267C2×C8×C73C2×D412yes—
268C4⋊C4×C73—24no—
269C4⋊C4×C73—24no—
270C4⋊C4×C73—24no—
271C4⋊C4×C73—21no—
272C4⋊C4×C73—21no—
273C4⋊C4×C73—21no—
274C4⋊C4×C73—21no—
275C4⋊C4×C73—21no—
276C4⋊C4×C73—21no—
277C4⋊C4×C73—21no—
278C4⋊C4×C73—21no—
279C4⋊C4×C73—42no—
280C4⋊C4×C73—42no—
281C4⋊C4×C73—42no—
282C4⋊C4×C73C2×D412yes—
283C4⋊C4×C73C2×D412yes—
284C22⋊C4×C73—24no—
285C22⋊C4×C73—24no—
286C22⋊C4×C73—24no—
287C22⋊C4×C73—24no—
288C22⋊C4×C73—42no—
289C22⋊C4×C73—42no—
290C22⋊C4×C73—42no—
291C22⋊C4×C73—81no—
292C22⋊C4×C73—81no—
293C22⋊C4×C73—81no—
294C23×C73—21no—
295C23×C73—21no—
296C23×C73—21no—
297C23×C73—21no—
298C23×C73—21no—
299C23×C73—21no—
300C23×C73—21no—
301C23×C73—21no—
302C23×C73—21no—
303C23×C73—21no—
304C23×C73—21no—
305C23×C73—21no—
306C23×C73—21no—
307C23×C73—22no—
308C23×C73—21no—
309C23×C73—21no—
310C23×C73—21no—
311C23×C73—21no—
312C23×C73—21no—
313C23×C73—21no—
314C23×C73—41no—
315C23×C73—41no—
316C23×C73—41no—
317C23×C73—41no—
318C23×C73—41no—
319C23×C73—41no—
320C23×C73#12012yes—
321C23×C73#12112yes—
322C23×C73C22×D411yescharacteristic
323Q8×C73—22no—
324Q8×C73—22no—
325Q8×C73—44no—
326Q8×C73—41no—
327Q8×C73—41no—
328Q8×C73—41no—
329Q8×C73—41no—
330Q8×C73—41no—
331Q8×C73—41no—
332D4×C73—22no—
333D4×C73—22no—
334D4×C73—44no—
335D4×C73—44no—
336D4×C73—44no—
337D4×C73—48no—
338D4×C73—41no—
339D4×C73—41no—
340D4×C73—84no—
341D4×C73—84no—
342C2×C4×C73—21no—
343C2×C4×C73—21no—
344C2×C4×C73—21no—
345C2×C4×C73—21no—
346C2×C4×C73—22no—
347C2×C4×C73—22no—
348C2×C4×C73—22no—
349C2×C4×C73—22no—
350C2×C4×C73—22no—
351C2×C4×C73—22no—
352C2×C4×C73—22no—
353C2×C4×C73—22no—
354C2×C4×C73—22no—
355C2×C4×C73—22no—
356C2×C4×C73—22no—
357C2×C4×C73—21no—
358C2×C4×C73—21no—
359C2×C4×C73—21no—
360C2×C4×C73—48no—
361C2×C4×C73—41no—
362C2×C4×C73—41no—
363C2×C4×C73—41no—
364C2×C4×C73—41no—
365C2×C4×C73—41no—
366C2×C4×C73—41no—
367C2×C4×C73—41no—
368C2×C4×C73—41no—
369C2×C4×C73—41no—
370C2×C4×C73—41no—
371C2×C4×C73—41no—
372C2×C4×C73—41no—
373C2×C4×C73—41no—
374C2×C4×C73—41no—
375C2×C4×C73—41no—
376C2×C4×C73—41no—
377C2×C4×C73—41no—
378C2×C4×C73—41no—
379C2×C4×C73—41no—
380C2×C4×C73—41no—
381C2×C4×C73—41no—
382C2×C4×C73—41no—
383C2×C4×C73—84no—
384C2×C4×C73#12012yes—
385C2×C4×C73#12112yes—
386C2×C4×C73C22×D411yescharacteristic
387C2×C4×C73C22×D411yescharacteristic
388C2×C4×C73C22×D411yescharacteristic
389C2×C4×C73C2×#4111yescharacteristic
390C2×C4×C73H(5,𝔽2)11yescharacteristic
391C2×C4×C73H(5,𝔽2)11yescharacteristic
392C8×C73—22no—
393C8×C73—22no—
394C8×C73—41no—
395C8×C73—41no—
396C22×C73—22no—
397C22×C73—22no—
398C22×C73—22no—
399C22×C73—22no—
400C22×C73—22no—
401C22×C73—22no—
402C22×C73—41no—
403C22×C73—41no—
404C22×C73—41no—
405C22×C73—41no—
406C22×C73—41no—
407C22×C73—41no—
408C22×C73—41no—
409C22×C73—41no—
410C22×C73—42no—
411C22×C73—41no—
412C22×C73—41no—
413C22×C73—41no—
414C22×C73—41no—
415C22×C73—42no—
416C22×C73—41no—
417C22×C73—42no—
418C22×C73—41no—
419C22×C73—41no—
420C22×C73—81no—
421C22×C73—81no—
422C22×C73—81no—
423C22×C73—81no—
424C22×C73C2×#12011yescharacteristic
425C22×C73C2×#12111yescharacteristic
426C22×C73#53411yescharacteristic
427C22×C73#57711yescharacteristic
428C22×C73#57711yescharacteristic
429C22×C73#57711yescharacteristic
430C22×C73#57811yescharacteristic
431C4×C73—22no—
432C4×C73—22no—
433C4×C73—41no—
434C4×C73—42no—
435C4×C73—42no—
436C4×C73—42no—
437C4×C73—81no—
438C4×C73—81no—
439C4×C73—81no—
440C4×C73—81no—
441C4×C73D4211yescharacteristic
442C4×C73D4211yescharacteristic
443C4×C73#54611yescharacteristic
444C4×C73#54611yescharacteristic
445#24395C7311yesmaximal, characteristic, direct product factor, Sylow
446C2×C73—42no—
447C2×C73—42no—
448C2×C73—81no—
449C2×C73—82no—
450C2×C73#241011yescharacteristic
451C2×C73#300911yescharacteristic
452C2×C73#301311yescharacteristic
453C2×C73#306011yescharacteristic
454C2×C73#306311yescharacteristic
455C2×C73#320111yescharacteristic
456C2×C73#320411yescharacteristic
457C2×#537C2×C7311yescharacteristic
458C2×#470C2×C7311yescharacteristic, complemented
459C2×#465C2×C7311yescharacteristic, complemented
460C2×#452C2×C7311yescharacteristic, complemented
461C2×#408C2×C7311yescharacteristic, complemented
462#2616C2×C7311yescharacteristic, complemented
463#2035C2×C7311yescharacteristic, complemented
464#2034C2×C7311yescharacteristic, complemented
465#2001C2×C7311yescharacteristic, complemented
466#2000C2×C7311yescharacteristic, complemented
467#1895C2×C7311yescharacteristic, complemented
468#1892C2×C7311yescharacteristic, complemented
469#1872C2×C7311yescharacteristic, complemented
470#1853C2×C7311yescharacteristic, complemented
471#1788C2×C7311yescharacteristic, complemented
472C73#2439511yescharacteristic, direct product factor, Sylow
473C22×#41C22×C7311yescharacteristic
474C22×#41C22×C7311yescharacteristic
475C22×Q16C22×C7311yescharacteristic
476C22×SD16C22×C7311yescharacteristic
477C22×M16C22×C7311yescharacteristic
478C23×C8C22×C7311yescharacteristic
479#537—24no—
480#537—24no—
481C2×C22⋊Q8—21no—
482C2×C22⋊Q8C22×C7311yescharacteristic
483C2×C22⋊Q8C22×C7311yescharacteristic
484C2×C22⋊Q8C22×C7311yescharacteristic
485C2×C22⋊Q8C22×C7311yescharacteristic
486C2×C22⋊Q8C22×C7311yescharacteristic
487C2×#121—21no—
488C2×#121—21no—
489C2×#121—21no—
490C2×#121C22×C7311yescharacteristic
491C2×#121C22×C7311yescharacteristic
492C22×C4⋊C4C22×C7311yescharacteristic
493#470—24no—
494#465—24no—
495#452—24no—
496C2×#106C22×C7311yescharacteristic
497C2×#106C22×C7311yescharacteristic
498C2×#103C22×C7311yescharacteristic
499C2×#103C22×C7311yescharacteristic
500C2×#103C22×C7311yescharacteristic
501C2×#103C22×C7311yescharacteristic
502C2×#103C22×C7311yescharacteristic
503C2×#102C22×C7311yescharacteristic
504C2×#102C22×C7311yescharacteristic
505C2×#102C22×C7311yescharacteristic
506#408—24no—
507C2×C22⋊C8C22×C7311yescharacteristic
508C2×C22⋊C8C22×C7311yescharacteristic
509C2×C22⋊C8C22×C7311yescharacteristic
510C2×C22⋊C8C22×C7311yescharacteristic
511#395—21no—
512#394—21no—
513#394—21no—
514#394—21no—
515#380C22×C7311yescharacteristic
516#380C22×C7311yescharacteristic
517#380C22×C7311yescharacteristic
518#340C22×C7311yescharacteristic
519#340C22×C7311yescharacteristic
520#340C22×C7311yescharacteristic
521#340C22×C7311yescharacteristic
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41—41no—
534C22×Q8D4×C7311yescharacteristic
535C22×Q8C23×C7311yescharacteristic
536C22×Q8C23×C7311yescharacteristic
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4D4×C7311yescharacteristic
541C22×D4D4×C7311yescharacteristic
542C22×D4D4×C7311yescharacteristic
543C22×D4C23×C7311yescharacteristic
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C23×C7311yescharacteristic
547C23×C4C23×C7311yescharacteristic
548C23×C4C23×C7311yescharacteristic
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—41no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×M16—22no—
556C2×M16—22no—
557C2×M16—41no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—41no—
561C22×C8C23×C7311yescharacteristic
562C22×C8C23×C7311yescharacteristic
563C22×C8C23×C7311yescharacteristic
564C22×C8C23×C7311yescharacteristic
565C22⋊Q8—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8D4×C7314yes—
576#121—28no—
577#121—28no—
578#121—28no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121D4×C7314yes—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4C23×C7311yescharacteristic
592C2×C4⋊C4C23×C7311yescharacteristic
593C2×C4⋊C4C23×C7311yescharacteristic
594C2×C4⋊C4C23×C7311yescharacteristic
595C2×C4⋊C4C23×C7311yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606#106—22no—
607#106—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—22no—
612#103—41no—
613#102—22no—
614#102—22no—
615#102—41no—
616C22⋊C8—22no—
617C22⋊C8—22no—
618C22⋊C8—22no—
619C22⋊C8D4×C7314yescomplemented
620#95—21no—
621#95—21no—
622#95—21no—
623C24—21no—
624C24C2×D4×C7311yescharacteristic
625C24C2×D4×C7311yescharacteristic
626C24C2×D4×C7311yescharacteristic
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—41no—
649C2×Q8C2×D4×C7312yes—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—41no—
665C2×D4—41no—
666C2×D4—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—81no—
670C2×D4—81no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4C2×D4×C7312yes—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—24no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—24no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—81no—
700C22×C4—81no—
701C22×C4C2×D4×C7311yescharacteristic
702C22×C4C2×D4×C7311yescharacteristic
703C22×C4C2×D4×C7312yes—
704C22×C4C2×D4×C7312yes—
705C22×C4C2×D4×C7311yescharacteristic
706C22×C4C2×D4×C7312yes—
707C22×C4#41×C7312yes—
708C22×C4C24×C7311yescharacteristic
709Q16—44no—
710SD16—44no—
711M16—44no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—44no—
723C2×C8C2×D4×C7312yes—
724C2×C8C2×D4×C7312yes—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4C2×D4×C7312yes—
740C4⋊C4C2×D4×C7312yes—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—81no—
749C22⋊C4—81no—
750C22⋊C4—81no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23#120×C7312yes—
778C23#121×C7312yes—
779C23C22×D4×C7311yescharacteristic
780Q8—22no—
781Q8—22no—
782Q8—44no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789D4—22no—
790D4—22no—
791D4—44no—
792D4—44no—
793D4—44no—
794D4—48no—
795D4—41no—
796D4—41no—
797D4—84no—
798D4—84no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—48no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—84no—
841C2×C4#120×C7312yes—
842C2×C4#121×C7312yes—
843C2×C4C22×D4×C7311yescharacteristic
844C2×C4C22×D4×C7311yescharacteristic
845C2×C4C22×D4×C7311yescharacteristic
846C2×C4C2×#41×C7311yescharacteristic
847C2×C4H(5,𝔽2)×C7311yescharacteristic
848C2×C4H(5,𝔽2)×C7311yescharacteristic
849C8—22no—
850C8—22no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—41no—
872C22—41no—
873C22—42no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22C2×#120×C7311yescharacteristic
882C22C2×#121×C7311yescharacteristic
883C22#534×C7311yescharacteristic
884C22#577×C7311yescharacteristic
885C22#577×C7311yescharacteristic
886C22#577×C7311yescharacteristic
887C22#578×C7311yescharacteristic
888C4—22no—
889C4—22no—
890C4—42no—
891C4—42no—
892C4—41no—
893C4—42no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4D42×C7311yescharacteristic
899C4D42×C7311yescharacteristic
900C4#546×C7311yescharacteristic
901C4#546×C7311yescharacteristic
902C2—42no—
903C2—42no—
904C2—81no—
905C2—82no—
906C2C73×#241011yescharacteristic
907C2C73×#300911yescharacteristic
908C2C73×#301311yescharacteristic
909C2C73×#306011yescharacteristic
910C2C73×#306311yescharacteristic
911C2C73×#320111yescharacteristic
912C2C73×#320411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#537×C73C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C22×#41×C73 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#470×C73C2semidirect
3. C2×#465×C73C2semidirect
4. C2×#452×C73C2semidirect
5. C2×#408×C73C2semidirect
6. C73×#2616C2semidirect
7. C73×#2035C2semidirect
8. C73×#2034C2semidirect
9. C73×#2001C2semidirect
10. C73×#2000C2semidirect
11. C73×#1895C2semidirect
12. C73×#1892C2semidirect
13. C73×#1872C2semidirect
14. C73×#1853C2semidirect
15. C73×#1788C2semidirect
162. C22⋊C8×C73D4semidirect
445. #24395C73direct (N × H)
458. C2×#470C2×C73semidirect
459. C2×#465C2×C73semidirect
460. C2×#452C2×C73semidirect
461. C2×#408C2×C73semidirect
462. #2616C2×C73semidirect
463. #2035C2×C73semidirect
464. #2034C2×C73semidirect
465. #2001C2×C73semidirect
466. #2000C2×C73semidirect
467. #1895C2×C73semidirect
468. #1892C2×C73semidirect
469. #1872C2×C73semidirect
470. #1853C2×C73semidirect
471. #1788C2×C73semidirect
472. C73#24395direct (N × H)
619. C22⋊C8D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C732
C2×#470×C732
C2×#465×C732
C2×#452×C732
C2×#408×C732
C73×#26162
C73×#20352
C73×#20342
C73×#20012
C73×#20002
C73×#18952
C73×#18922
C73×#18722
C73×#18532
C73×#17882
#2439573