Finite Group Databasebeta

← C73×#24901 #32934305

Subgroups — C73×#24901 #32934305

Order 18688.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#450×C73C211yesmaximal, characteristic
2C2×C4×SD16×C73C211yesmaximal, characteristic, complemented
3C73×#2423C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C73C211yesmaximal, characteristic
5C73×#2094C211yesmaximal, characteristic, complemented
6C73×#2077C211yesmaximal, characteristic, complemented
7C73×#2055C211yesmaximal, characteristic, complemented
8C73×#2035C211yesmaximal, characteristic, complemented
9C73×#1934C211yesmaximal, characteristic, complemented
10C73×#1923C211yesmaximal, characteristic, complemented
11C73×#1880C211yesmaximal, characteristic, complemented
12C73×#1877C211yesmaximal, characteristic, complemented
13C73×#1864C211yesmaximal, characteristic, complemented
14C73×#1802C211yesmaximal, characteristic, complemented
15C73×#1786C211yesmaximal, characteristic
16C23×D4×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C2×C22⋊Q8×C73C2211yescharacteristic
20C2×C4×Q8×C73C2211yescharacteristic, complemented
21C2×C4×D4×C73C2211yescharacteristic
22C2×C4×D4×C73C2211yescharacteristic
23C22×C22⋊C4×C73—21no—
24#450×C73—24no—
25C4×SD16×C73—24no—
26C2×#106×C73C2211yescharacteristic, complemented
27C2×#106×C73C2211yescharacteristic, complemented
28C2×C4⋊C8×C73C2211yescharacteristic, complemented
29C2×#103×C73C2211yescharacteristic, complemented
30C2×#103×C73C2211yescharacteristic, complemented
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×C4×C8×C73C2211yescharacteristic, complemented
40#399×C73—21no—
41#398×C73—21no—
42#391×C73C2211yescharacteristic, complemented
43#390×C73C2211yescharacteristic
44#390×C73C2211yescharacteristic
45#389×C73C2211yescharacteristic, complemented
46#388×C73—21no—
47#387×C73—21no—
48#386×C73—21no—
49#386×C73—21no—
50#384×C73C2211yescharacteristic, complemented
51#380×C73C2211yescharacteristic
52#380×C73C2211yescharacteristic
53#379×C73—21no—
54C4×C22⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic, complemented
56#340×C73C2211yescharacteristic, complemented
57#340×C73C2211yescharacteristic, complemented
58#340×C73C2211yescharacteristic, complemented
59#336×C73C2211yescharacteristic, complemented
60#336×C73C2211yescharacteristic, complemented
61C25×C73—21no—
62C22×Q8×C73C2311yescharacteristic
63C22×D4×C73—22no—
64C22×D4×C73—22no—
65C22×D4×C73—22no—
66C22×D4×C73—22no—
67C22×D4×C73—21no—
68C22×D4×C73—41no—
69C22×D4×C73—41no—
70C22×D4×C73C2311yescharacteristic
71C22×D4×C73C2311yescharacteristic
72C23×C4×C73—21no—
73C23×C4×C73—21no—
74C23×C4×C73C2311yescharacteristic
75C2×SD16×C73—22no—
76C2×SD16×C73—22no—
77C2×SD16×C73—22no—
78C2×SD16×C73—22no—
79C2×SD16×C73—41no—
80C2×SD16×C73D414yes—
81C22×C8×C73C2311yescharacteristic
82C22×C8×C73C2311yescharacteristic
83C22×C8×C73C2311yescharacteristic
84C22×C8×C73C2311yescharacteristic
85C22⋊Q8×C73—22no—
86C22⋊Q8×C73—41no—
87C4×Q8×C73—22no—
88C4×Q8×C73—41no—
89C4×D4×C73—22no—
90C4×D4×C73—22no—
91C4×D4×C73—41no—
92C4×D4×C73—41no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73—21no—
112C2×C22⋊C4×C73—44no—
113C2×C22⋊C4×C73D411yescharacteristic
114C2×C22⋊C4×C73D411yescharacteristic
115C2×C42×C73—21no—
116C2×C42×C73C2311yescharacteristic
117C2×C42×C73C2311yescharacteristic
118#106×C73—22no—
119#106×C73—41no—
120C4⋊C8×C73—41no—
121#103×C73—22no—
122#103×C73—41no—
123#102×C73—22no—
124#102×C73—22no—
125#102×C73—22no—
126#102×C73—22no—
127#102×C73—22no—
128#102×C73—41no—
129C22⋊C8×C73—22no—
130C22⋊C8×C73—41no—
131C4×C8×C73—22no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73D411yescharacteristic
138#95×C73D411yescharacteristic
139C24×C73—21no—
140C24×C73—24no—
141C24×C73—21no—
142C24×C73—42no—
143C24×C73—42no—
144C24×C73—42no—
145C24×C73—42no—
146C24×C73—81no—
147C24×C73—81no—
148C24×C73C2×D411yescharacteristic
149C2×Q8×C73—21no—
150C2×Q8×C73—21no—
151C2×Q8×C73—21no—
152C2×Q8×C73—21no—
153C2×Q8×C73—21no—
154C2×Q8×C73C2×D412yes—
155C2×D4×C73—24no—
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—21no—
163C2×D4×C73—21no—
164C2×D4×C73—42no—
165C2×D4×C73—42no—
166C2×D4×C73—44no—
167C2×D4×C73—44no—
168C2×D4×C73—44no—
169C2×D4×C73—44no—
170C2×D4×C73C2×D412yes—
171C2×D4×C73#4112yes—
172C2×D4×C73#4112yes—
173C2×D4×C73#4112yes—
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—42no—
189C22×C4×C73—42no—
190C22×C4×C73—81no—
191C22×C4×C73—81no—
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73C2×D411yescharacteristic
194C22×C4×C73C2×D411yescharacteristic
195C22×C4×C73C2×D411yescharacteristic
196C22×C4×C73C2×D411yescharacteristic
197C22×C4×C73C2411yescharacteristic
198SD16×C73—28no—
199SD16×C73—44no—
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—21no—
210C2×C8×C73—21no—
211C2×C8×C73C2×D412yes—
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—81no—
226C4⋊C4×C73—81no—
227C22⋊C4×C73—41no—
228C22⋊C4×C73—42no—
229C22⋊C4×C73—42no—
230C22⋊C4×C73—42no—
231C22⋊C4×C73—42no—
232C22⋊C4×C73—42no—
233C22⋊C4×C73—42no—
234C22⋊C4×C73—81no—
235C22⋊C4×C73—81no—
236C22⋊C4×C73—81no—
237C22⋊C4×C73SD1614yescomplemented
238C42×C73—21no—
239C42×C73—21no—
240C42×C73—21no—
241C42×C73—21no—
242C42×C73—42no—
243C23×C73—21no—
244C23×C73—22no—
245C23×C73—21no—
246C23×C73—22no—
247C23×C73—22no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—22no—
253C23×C73—48no—
254C23×C73—48no—
255C23×C73—41no—
256C23×C73—41no—
257C23×C73—41no—
258C23×C73—41no—
259C23×C73—41no—
260C23×C73—41no—
261C23×C73—41no—
262C23×C73—41no—
263C23×C73—41no—
264C23×C73—41no—
265C23×C73—84no—
266C23×C73—84no—
267C23×C73—84no—
268C23×C73—84no—
269C23×C73—84no—
270C23×C73C2×SD1612yes—
271C23×C73C22×D411yescharacteristic
272Q8×C73—22no—
273Q8×C73—22no—
274Q8×C73—41no—
275Q8×C73—41no—
276D4×C73—22no—
277D4×C73—22no—
278D4×C73—22no—
279D4×C73—22no—
280D4×C73—22no—
281D4×C73—48no—
282D4×C73—41no—
283D4×C73—41no—
284D4×C73#12314yes—
285C2×C4×C73—21no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—22no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
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—41no—
317C2×C4×C73—41no—
318C2×C4×C73—41no—
319C2×C4×C73—41no—
320C2×C4×C73—84no—
321C2×C4×C73—84no—
322C2×C4×C73C2×SD1612yes—
323C2×C4×C73C2×SD1612yes—
324C2×C4×C73C22×D411yescharacteristic
325C2×C4×C73C2×#4111yescharacteristic
326C2×C4×C73C2×#4111yescharacteristic
327C2×C4×C73C2×#4111yescharacteristic
328C2×C4×C73H(5,𝔽2)11yescharacteristic
329C2×C4×C73H(5,𝔽2)11yescharacteristic
330C8×C73—22no—
331C8×C73—41no—
332C8×C73—41no—
333C8×C73—41no—
334C22×C73—22no—
335C22×C73—24no—
336C22×C73—22no—
337C22×C73—22no—
338C22×C73—42no—
339C22×C73—41no—
340C22×C73—42no—
341C22×C73—41no—
342C22×C73—41no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—42no—
346C22×C73—41no—
347C22×C73—42no—
348C22×C73—42no—
349C22×C73—42no—
350C22×C73—42no—
351C22×C73—816no—
352C22×C73—81no—
353C22×C73—81no—
354C22×C73—81no—
355C22×C73—81no—
356C22×C73#52511yescharacteristic
357C22×C73D4211yescharacteristic
358C22×C73#54611yescharacteristic
359C22×C73C22×SD1611yescharacteristic
360C22×C73#57511yescharacteristic
361C22×C73#57611yescharacteristic
362C22×C73#57711yescharacteristic
363C4×C73—22no—
364C4×C73—22no—
365C4×C73—41no—
366C4×C73—42no—
367C4×C73—41no—
368C4×C73—41no—
369C4×C73—81no—
370C4×C73—81no—
371C4×C73—81no—
372C4×C73—81no—
373C4×C73—81no—
374C4×C73C2×#12311yescharacteristic
375C4×C73#53811yescharacteristic
376C4×C73#54611yescharacteristic
377C4×C73#55111yescharacteristic
378#24901C7311yesmaximal, characteristic, direct product factor, Sylow
379C2×C73—42no—
380C2×C73—44no—
381C2×C73—82no—
382C2×C73#241811yescharacteristic
383C2×C73#310111yescharacteristic
384C2×C73#311811yescharacteristic
385C2×C73#326811yescharacteristic
386C2×C73D4×SD1611yescharacteristic
387C2×C73#329511yescharacteristic
388C2×C73#332311yescharacteristic
389C2×#450C2×C7311yescharacteristic
390C2×C4×SD16C2×C7311yescharacteristic, complemented
391#2423C2×C7311yescharacteristic, complemented
392D4×C22⋊C4C2×C7311yescharacteristic
393#2094C2×C7311yescharacteristic, complemented
394#2077C2×C7311yescharacteristic, complemented
395#2055C2×C7311yescharacteristic, complemented
396#2035C2×C7311yescharacteristic, complemented
397#1934C2×C7311yescharacteristic, complemented
398#1923C2×C7311yescharacteristic, complemented
399#1880C2×C7311yescharacteristic, complemented
400#1877C2×C7311yescharacteristic, complemented
401#1864C2×C7311yescharacteristic, complemented
402#1802C2×C7311yescharacteristic, complemented
403#1786C2×C7311yescharacteristic
404C73#2490111yescharacteristic, direct product factor, Sylow
405C23×D4C22×C7311yescharacteristic
406C22×SD16C22×C7311yescharacteristic
407C22×SD16C22×C7311yescharacteristic
408C2×C22⋊Q8C22×C7311yescharacteristic
409C2×C4×Q8C22×C7311yescharacteristic, complemented
410C2×C4×D4C22×C7311yescharacteristic
411C2×C4×D4C22×C7311yescharacteristic
412C22×C22⋊C4—21no—
413#450—24no—
414C4×SD16—24no—
415C2×#106C22×C7311yescharacteristic, complemented
416C2×#106C22×C7311yescharacteristic, complemented
417C2×C4⋊C8C22×C7311yescharacteristic, complemented
418C2×#103C22×C7311yescharacteristic, complemented
419C2×#103C22×C7311yescharacteristic, complemented
420C2×#102C22×C7311yescharacteristic
421C2×#102C22×C7311yescharacteristic
422C2×#102C22×C7311yescharacteristic
423C2×#102C22×C7311yescharacteristic
424C2×#102C22×C7311yescharacteristic
425C2×#102C22×C7311yescharacteristic
426C2×C22⋊C8C22×C7311yescharacteristic
427C2×C22⋊C8C22×C7311yescharacteristic
428C2×C4×C8C22×C7311yescharacteristic, complemented
429#399—21no—
430#398—21no—
431#391C22×C7311yescharacteristic, complemented
432#390C22×C7311yescharacteristic
433#390C22×C7311yescharacteristic
434#389C22×C7311yescharacteristic, complemented
435#388—21no—
436#387—21no—
437#386—21no—
438#386—21no—
439#384C22×C7311yescharacteristic, complemented
440#380C22×C7311yescharacteristic
441#380C22×C7311yescharacteristic
442#379—21no—
443C4×C22⋊C4C22×C7311yescharacteristic
444#340C22×C7311yescharacteristic, complemented
445#340C22×C7311yescharacteristic, complemented
446#340C22×C7311yescharacteristic, complemented
447#340C22×C7311yescharacteristic, complemented
448#336C22×C7311yescharacteristic, complemented
449#336C22×C7311yescharacteristic, complemented
450C25—21no—
451C22×Q8C23×C7311yescharacteristic
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—21no—
457C22×D4—41no—
458C22×D4—41no—
459C22×D4C23×C7311yescharacteristic
460C22×D4C23×C7311yescharacteristic
461C23×C4—21no—
462C23×C4—21no—
463C23×C4C23×C7311yescharacteristic
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—41no—
469C2×SD16D4×C7314yes—
470C22×C8C23×C7311yescharacteristic
471C22×C8C23×C7311yescharacteristic
472C22×C8C23×C7311yescharacteristic
473C22×C8C23×C7311yescharacteristic
474C22⋊Q8—22no—
475C22⋊Q8—41no—
476C4×Q8—22no—
477C4×Q8—41no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—41no—
481C4×D4—41no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4C23×C7311yescharacteristic
488C2×C4⋊C4C23×C7311yescharacteristic
489C2×C4⋊C4C23×C7311yescharacteristic
490C2×C4⋊C4C23×C7311yescharacteristic
491C2×C4⋊C4C23×C7311yescharacteristic
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⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—44no—
502C2×C22⋊C4D4×C7311yescharacteristic
503C2×C22⋊C4D4×C7311yescharacteristic
504C2×C42—21no—
505C2×C42C23×C7311yescharacteristic
506C2×C42C23×C7311yescharacteristic
507#106—22no—
508#106—41no—
509C4⋊C8—41no—
510#103—22no—
511#103—41no—
512#102—22no—
513#102—22no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—41no—
518C22⋊C8—22no—
519C22⋊C8—41no—
520C4×C8—22no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95D4×C7311yescharacteristic
527#95D4×C7311yescharacteristic
528C24—21no—
529C24—24no—
530C24—21no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—81no—
536C24—81no—
537C24C2×D4×C7311yescharacteristic
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×D4×C7312yes—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4C2×D4×C7312yes—
560C2×D4#41×C7312yes—
561C2×D4#41×C7312yes—
562C2×D4#41×C7312yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4C2×D4×C7311yescharacteristic
582C22×C4C2×D4×C7311yescharacteristic
583C22×C4C2×D4×C7311yescharacteristic
584C22×C4C2×D4×C7311yescharacteristic
585C22×C4C2×D4×C7311yescharacteristic
586C22×C4C24×C7311yescharacteristic
587SD16—28no—
588SD16—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8C2×D4×C7312yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—81no—
615C4⋊C4—81no—
616C22⋊C4—41no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4SD16×C7314yescomplemented
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—42no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—48no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23C2×SD16×C7312yes—
660C23C22×D4×C7311yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—41no—
672D4—41no—
673D4#123×C7314yes—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
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—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4C2×SD16×C7312yes—
712C2×C4C2×SD16×C7312yes—
713C2×C4C22×D4×C7311yescharacteristic
714C2×C4C2×#41×C7311yescharacteristic
715C2×C4C2×#41×C7311yescharacteristic
716C2×C4C2×#41×C7311yescharacteristic
717C2×C4H(5,𝔽2)×C7311yescharacteristic
718C2×C4H(5,𝔽2)×C7311yescharacteristic
719C8—22no—
720C8—41no—
721C8—41no—
722C8—41no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—24no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—816no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22#525×C7311yescharacteristic
746C22D42×C7311yescharacteristic
747C22#546×C7311yescharacteristic
748C22C22×SD16×C7311yescharacteristic
749C22#575×C7311yescharacteristic
750C22#576×C7311yescharacteristic
751C22#577×C7311yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—42no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4—81no—
762C4—81no—
763C4C2×#123×C7311yescharacteristic
764C4#538×C7311yescharacteristic
765C4#546×C7311yescharacteristic
766C4#551×C7311yescharacteristic
767C2—42no—
768C2—44no—
769C2—82no—
770C2C73×#241811yescharacteristic
771C2C73×#310111yescharacteristic
772C2C73×#311811yescharacteristic
773C2C73×#326811yescharacteristic
774C2D4×SD16×C7311yescharacteristic
775C2C73×#329511yescharacteristic
776C2C73×#332311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC23×D4×C73C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C73C2semidirect
3. C73×#2423C2semidirect
5. C73×#2094C2semidirect
6. C73×#2077C2semidirect
7. C73×#2055C2semidirect
8. C73×#2035C2semidirect
9. C73×#1934C2semidirect
10. C73×#1923C2semidirect
11. C73×#1880C2semidirect
12. C73×#1877C2semidirect
13. C73×#1864C2semidirect
14. C73×#1802C2semidirect
20. C2×C4×Q8×C73C22semidirect
26. C2×#106×C73C22semidirect
27. C2×#106×C73C22semidirect
28. C2×C4⋊C8×C73C22semidirect
29. C2×#103×C73C22semidirect
30. C2×#103×C73C22semidirect
39. C2×C4×C8×C73C22semidirect
42. #391×C73C22semidirect
45. #389×C73C22semidirect
50. #384×C73C22semidirect
55. #340×C73C22semidirect
56. #340×C73C22semidirect
57. #340×C73C22semidirect
58. #340×C73C22semidirect
59. #336×C73C22semidirect
60. #336×C73C22semidirect
237. C22⋊C4×C73SD16semidirect
378. #24901C73direct (N × H)
390. C2×C4×SD16C2×C73semidirect
391. #2423C2×C73semidirect
393. #2094C2×C73semidirect
394. #2077C2×C73semidirect
395. #2055C2×C73semidirect
396. #2035C2×C73semidirect
397. #1934C2×C73semidirect
398. #1923C2×C73semidirect
399. #1880C2×C73semidirect
400. #1877C2×C73semidirect
401. #1864C2×C73semidirect
402. #1802C2×C73semidirect
404. C73#24901direct (N × H)
409. C2×C4×Q8C22×C73semidirect
415. C2×#106C22×C73semidirect
416. C2×#106C22×C73semidirect
417. C2×C4⋊C8C22×C73semidirect
418. C2×#103C22×C73semidirect
419. C2×#103C22×C73semidirect
428. C2×C4×C8C22×C73semidirect
431. #391C22×C73semidirect
434. #389C22×C73semidirect
439. #384C22×C73semidirect
444. #340C22×C73semidirect
445. #340C22×C73semidirect
446. #340C22×C73semidirect
447. #340C22×C73semidirect
448. #336C22×C73semidirect
449. #336C22×C73semidirect
626. C22⋊C4SD16×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#450×C732
C2×C4×SD16×C732
C73×#24232
D4×C22⋊C4×C732
C73×#20942
C73×#20772
C73×#20552
C73×#20352
C73×#19342
C73×#19232
C73×#18802
C73×#18772
C73×#18642
C73×#18022
C73×#17862
#2490173