Finite Group Databasebeta

← C73×#24769 #32934173

Subgroups — C73×#24769 #32934173

Order 18688.

946 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#470×C73C211yesmaximal, characteristic, complemented
2C2×#465×C73C211yesmaximal, characteristic
3C2×#464×C73C211yesmaximal, characteristic, complemented
4C2×#424×C73C211yesmaximal, characteristic, complemented
5C73×#2620C211yesmaximal, characteristic
6C73×#2323C211yesmaximal, characteristic, complemented
7C73×#2066C211yesmaximal, characteristic, complemented
8C73×#2065C211yesmaximal, characteristic, complemented
9C73×#2056C211yesmaximal, characteristic, complemented
10C73×#2055C211yesmaximal, characteristic, complemented
11C73×#1983C211yesmaximal, characteristic, complemented
12C73×#1948C211yesmaximal, characteristic, complemented
13C73×#1895C211yesmaximal, characteristic
14C73×#1892C211yesmaximal, characteristic, complemented
15C73×#1803C211yesmaximal, characteristic, complemented
16C22×Q16×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×M16×C73C2211yescharacteristic
19C23×C8×C73C2211yescharacteristic
20C2×#124×C73C2211yescharacteristic
21C2×C22⋊Q8×C73C2211yescharacteristic
22C2×C22⋊Q8×C73C2211yescharacteristic
23C2×#121×C73C2211yescharacteristic
24C2×C4×Q8×C73C2211yescharacteristic
25C2×#117×C73C2211yescharacteristic
26#470×C73—24no—
27#465×C73—24no—
28#464×C73—24no—
29C2×#106×C73C2211yescharacteristic
30C2×#106×C73C2211yescharacteristic
31#424×C73—24no—
32C2×C4⋊C8×C73C2211yescharacteristic
33C2×C4⋊C8×C73C2211yescharacteristic
34C2×C4⋊C8×C73C2211yescharacteristic
35C2×C4⋊C8×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#103×C73C2211yescharacteristic
40C2×#103×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44#396×C73—21no—
45#396×C73—21no—
46#394×C73—21no—
47#394×C73—21no—
48#391×C73C2211yescharacteristic
49#391×C73C2211yescharacteristic
50#390×C73C2211yescharacteristic
51#389×C73—21no—
52#389×C73C2211yescharacteristic
53#388×C73—21no—
54#388×C73—21no—
55#387×C73—21no—
56#384×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63C22×Q8×C73C2311yescharacteristic
64C22×Q8×C73C2311yescharacteristic
65C22×D4×C73—21no—
66C22×D4×C73C2311yescharacteristic
67C23×C4×C73C2311yescharacteristic
68C2×Q16×C73—22no—
69C2×Q16×C73—22no—
70C2×Q16×C73—41no—
71C2×SD16×C73—22no—
72C2×SD16×C73—22no—
73C2×SD16×C73—41no—
74C2×M16×C73—22no—
75C2×M16×C73—22no—
76C2×M16×C73—41no—
77C22×C8×C73—22no—
78C22×C8×C73—22no—
79C22×C8×C73—41no—
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82C22×C8×C73C2311yescharacteristic
83C22×C8×C73C2311yescharacteristic
84#124×C73—22no—
85#124×C73—22no—
86C22⋊Q8×C73—22no—
87C22⋊Q8×C73—22no—
88C22⋊Q8×C73—22no—
89C22⋊Q8×C73D414yes—
90#121×C73—22no—
91#121×C73—22no—
92C4×Q8×C73—22no—
93C4×Q8×C73—22no—
94#117×C73—22no—
95#117×C73—22no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73D411yescharacteristic
103C2×C4⋊C4×C73D411yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C4⋊C4×C73C2311yescharacteristic
108C2×C4⋊C4×C73C2311yescharacteristic
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
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×C73D411yescharacteristic
118C2×C22⋊C4×C73D411yescharacteristic
119C2×C42×C73—21no—
120C2×C42×C73—21no—
121C2×C42×C73C2311yescharacteristic
122C2×C42×C73C2311yescharacteristic
123#106×C73—22no—
124#106×C73—22no—
125C4⋊C8×C73—22no—
126C4⋊C8×C73—22no—
127C4⋊C8×C73—22no—
128C4⋊C8×C73D414yescomplemented
129#103×C73—22no—
130#103×C73—22no—
131#103×C73—22no—
132#103×C73—22no—
133#103×C73—41no—
134#102×C73—22no—
135#102×C73—22no—
136#102×C73—41no—
137#95×C73—21no—
138#95×C73—21no—
139#95×C73—21no—
140#95×C73—21no—
141#95×C73—21no—
142#95×C73—21no—
143#95×C73—21no—
144C24×C73—21no—
145C24×C73C2×D411yescharacteristic
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
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×Q8×C73—21no—
155C2×Q8×C73—21no—
156C2×Q8×C73—21no—
157C2×Q8×C73C2×D412yes—
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—81no—
166C2×D4×C73—81no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
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×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2×D412yes—
184C22×C4×C73#4112yes—
185C22×C4×C73C2411yescharacteristic
186Q16×C73—44no—
187SD16×C73—44no—
188M16×C73—44no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—44no—
200C2×C8×C73C2×D412yes—
201C2×C8×C73C2×D412yes—
202C4⋊C4×C73—24no—
203C4⋊C4×C73—22no—
204C4⋊C4×C73—22no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—42no—
215C4⋊C4×C73—42no—
216C4⋊C4×C73—81no—
217C4⋊C4×C73—81no—
218C4⋊C4×C73—81no—
219C4⋊C4×C73C2×D412yes—
220C22⋊C4×C73—24no—
221C22⋊C4×C73—22no—
222C22⋊C4×C73—22no—
223C22⋊C4×C73—42no—
224C22⋊C4×C73—42no—
225C22⋊C4×C73—42no—
226C22⋊C4×C73—42no—
227C22⋊C4×C73—81no—
228C22⋊C4×C73—81no—
229C22⋊C4×C73—81no—
230C42×C73—21no—
231C42×C73—21no—
232C42×C73—42no—
233C42×C73—81no—
234C42×C73C2×D412yes—
235C42×C73#4112yes—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73—41no—
245C23×C73—41no—
246C23×C73—41no—
247C23×C73—41no—
248C23×C73—41no—
249C23×C73#12112yes—
250C23×C73C22×D411yescharacteristic
251Q8×C73—22no—
252Q8×C73—22no—
253Q8×C73—41no—
254Q8×C73—41no—
255Q8×C73—41no—
256Q8×C73—41no—
257Q8×C73—41no—
258Q8×C73—41no—
259D4×C73—41no—
260D4×C73—41no—
261D4×C73—41no—
262D4×C73—41no—
263D4×C73—84no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
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#12112yes—
302C2×C4×C73#12112yes—
303C2×C4×C73#12112yes—
304C2×C4×C73C22×D411yescharacteristic
305C2×C4×C73C22×D411yescharacteristic
306C2×C4×C73C2×#4111yescharacteristic
307C2×C4×C73C2×#4111yescharacteristic
308C2×C4×C73H(5,𝔽2)11yescharacteristic
309C2×C4×C732−1+411yescharacteristic
310C8×C73—22no—
311C8×C73—22no—
312C8×C73—41no—
313C8×C73—41no—
314C22×C73—22no—
315C22×C73—22no—
316C22×C73—22no—
317C22×C73—41no—
318C22×C73—41no—
319C22×C73—41no—
320C22×C73—41no—
321C22×C73—81no—
322C22×C73—81no—
323C22×C73—81no—
324C22×C73—81no—
325C22×C73—81no—
326C22×C73—81no—
327C22×C73—81no—
328C22×C73C2×#12111yescharacteristic
329C22×C73C2×#12111yescharacteristic
330C22×C73#53711yescharacteristic
331C22×C73#57711yescharacteristic
332C22×C73#57711yescharacteristic
333C22×C73#57711yescharacteristic
334C22×C73#57811yescharacteristic
335C4×C73—22no—
336C4×C73—22no—
337C4×C73—22no—
338C4×C73—42no—
339C4×C73—42no—
340C4×C73—41no—
341C4×C73—41no—
342C4×C73—81no—
343C4×C73—81no—
344C4×C73—81no—
345C4×C73—81no—
346C4×C73—81no—
347C4×C73D4211yescharacteristic
348C4×C73#54711yescharacteristic
349C4×C73#54811yescharacteristic
350C4×C73#55311yescharacteristic
351#24769C7311yesmaximal, characteristic, direct product factor, Sylow
352C2×C73—42no—
353C2×C73—161no—
354C2×C73#241611yescharacteristic
355C2×C73#304311yescharacteristic
356C2×C73#304611yescharacteristic
357C2×C73#306011yescharacteristic
358C2×C73#306311yescharacteristic
359C2×C73#325811yescharacteristic
360C2×C73#326311yescharacteristic
361C2×#470C2×C7311yescharacteristic, complemented
362C2×#465C2×C7311yescharacteristic
363C2×#464C2×C7311yescharacteristic, complemented
364C2×#424C2×C7311yescharacteristic, complemented
365#2620C2×C7311yescharacteristic
366#2323C2×C7311yescharacteristic, complemented
367#2066C2×C7311yescharacteristic, complemented
368#2065C2×C7311yescharacteristic, complemented
369#2056C2×C7311yescharacteristic, complemented
370#2055C2×C7311yescharacteristic, complemented
371#1983C2×C7311yescharacteristic, complemented
372#1948C2×C7311yescharacteristic, complemented
373#1895C2×C7311yescharacteristic
374#1892C2×C7311yescharacteristic, complemented
375#1803C2×C7311yescharacteristic, complemented
376C73#2476911yescharacteristic, direct product factor, Sylow
377C22×Q16C22×C7311yescharacteristic
378C22×SD16C22×C7311yescharacteristic
379C22×M16C22×C7311yescharacteristic
380C23×C8C22×C7311yescharacteristic
381C2×#124C22×C7311yescharacteristic
382C2×C22⋊Q8C22×C7311yescharacteristic
383C2×C22⋊Q8C22×C7311yescharacteristic
384C2×#121C22×C7311yescharacteristic
385C2×C4×Q8C22×C7311yescharacteristic
386C2×#117C22×C7311yescharacteristic
387#470—24no—
388#465—24no—
389#464—24no—
390C2×#106C22×C7311yescharacteristic
391C2×#106C22×C7311yescharacteristic
392#424—24no—
393C2×C4⋊C8C22×C7311yescharacteristic
394C2×C4⋊C8C22×C7311yescharacteristic
395C2×C4⋊C8C22×C7311yescharacteristic
396C2×C4⋊C8C22×C7311yescharacteristic
397C2×#103C22×C7311yescharacteristic
398C2×#103C22×C7311yescharacteristic
399C2×#103C22×C7311yescharacteristic
400C2×#103C22×C7311yescharacteristic
401C2×#103C22×C7311yescharacteristic
402C2×#102C22×C7311yescharacteristic
403C2×#102C22×C7311yescharacteristic
404C2×#102C22×C7311yescharacteristic
405#396—21no—
406#396—21no—
407#394—21no—
408#394—21no—
409#391C22×C7311yescharacteristic
410#391C22×C7311yescharacteristic
411#390C22×C7311yescharacteristic
412#389—21no—
413#389C22×C7311yescharacteristic
414#388—21no—
415#388—21no—
416#387—21no—
417#384C22×C7311yescharacteristic
418#380C22×C7311yescharacteristic
419C4×C4⋊C4C22×C7311yescharacteristic
420#340C22×C7311yescharacteristic
421#340C22×C7311yescharacteristic
422#340C22×C7311yescharacteristic
423#340C22×C7311yescharacteristic
424C22×Q8C23×C7311yescharacteristic
425C22×Q8C23×C7311yescharacteristic
426C22×D4—21no—
427C22×D4C23×C7311yescharacteristic
428C23×C4C23×C7311yescharacteristic
429C2×Q16—22no—
430C2×Q16—22no—
431C2×Q16—41no—
432C2×SD16—22no—
433C2×SD16—22no—
434C2×SD16—41no—
435C2×M16—22no—
436C2×M16—22no—
437C2×M16—41no—
438C22×C8—22no—
439C22×C8—22no—
440C22×C8—41no—
441C22×C8C23×C7311yescharacteristic
442C22×C8C23×C7311yescharacteristic
443C22×C8C23×C7311yescharacteristic
444C22×C8C23×C7311yescharacteristic
445#124—22no—
446#124—22no—
447C22⋊Q8—22no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8D4×C7314yes—
451#121—22no—
452#121—22no—
453C4×Q8—22no—
454C4×Q8—22no—
455#117—22no—
456#117—22no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4D4×C7311yescharacteristic
464C2×C4⋊C4D4×C7311yescharacteristic
465C2×C4⋊C4C23×C7311yescharacteristic
466C2×C4⋊C4C23×C7311yescharacteristic
467C2×C4⋊C4C23×C7311yescharacteristic
468C2×C4⋊C4C23×C7311yescharacteristic
469C2×C4⋊C4C23×C7311yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4D4×C7311yescharacteristic
479C2×C22⋊C4D4×C7311yescharacteristic
480C2×C42—21no—
481C2×C42—21no—
482C2×C42C23×C7311yescharacteristic
483C2×C42C23×C7311yescharacteristic
484#106—22no—
485#106—22no—
486C4⋊C8—22no—
487C4⋊C8—22no—
488C4⋊C8—22no—
489C4⋊C8D4×C7314yescomplemented
490#103—22no—
491#103—22no—
492#103—22no—
493#103—22no—
494#103—41no—
495#102—22no—
496#102—22no—
497#102—41no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505C24—21no—
506C24C2×D4×C7311yescharacteristic
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8C2×D4×C7312yes—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—42no—
526C2×D4—81no—
527C2×D4—81no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4C2×D4×C7311yescharacteristic
540C22×C4C2×D4×C7311yescharacteristic
541C22×C4C2×D4×C7311yescharacteristic
542C22×C4C2×D4×C7311yescharacteristic
543C22×C4C2×D4×C7311yescharacteristic
544C22×C4C2×D4×C7312yes—
545C22×C4#41×C7312yes—
546C22×C4C24×C7311yescharacteristic
547Q16—44no—
548SD16—44no—
549M16—44no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—44no—
561C2×C8C2×D4×C7312yes—
562C2×C8C2×D4×C7312yes—
563C4⋊C4—24no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—81no—
578C4⋊C4—81no—
579C4⋊C4—81no—
580C4⋊C4C2×D4×C7312yes—
581C22⋊C4—24no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C22⋊C4—81no—
591C42—21no—
592C42—21no—
593C42—42no—
594C42—81no—
595C42C2×D4×C7312yes—
596C42#41×C7312yes—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23#121×C7312yes—
611C23C22×D4×C7311yescharacteristic
612Q8—22no—
613Q8—22no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—41no—
624D4—84no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4#121×C7312yes—
663C2×C4#121×C7312yes—
664C2×C4#121×C7312yes—
665C2×C4C22×D4×C7311yescharacteristic
666C2×C4C22×D4×C7311yescharacteristic
667C2×C4C2×#41×C7311yescharacteristic
668C2×C4C2×#41×C7311yescharacteristic
669C2×C4H(5,𝔽2)×C7311yescharacteristic
670C2×C42−1+4×C7311yescharacteristic
671C8—22no—
672C8—22no—
673C8—41no—
674C8—41no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×#121×C7311yescharacteristic
690C22C2×#121×C7311yescharacteristic
691C22#537×C7311yescharacteristic
692C22#577×C7311yescharacteristic
693C22#577×C7311yescharacteristic
694C22#577×C7311yescharacteristic
695C22#578×C7311yescharacteristic
696C4—22no—
697C4—22no—
698C4—22no—
699C4—42no—
700C4—41no—
701C4—41no—
702C4—42no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4D42×C7311yescharacteristic
709C4#547×C7311yescharacteristic
710C4#548×C7311yescharacteristic
711C4#553×C7311yescharacteristic
712C2—42no—
713C2—161no—
714C2C73×#241611yescharacteristic
715C2C73×#304311yescharacteristic
716C2C73×#304611yescharacteristic
717C2C73×#306011yescharacteristic
718C2C73×#306311yescharacteristic
719C2C73×#325811yescharacteristic
720C2C73×#326311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#121×C73C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×#117×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#470×C73C2semidirect
3. C2×#464×C73C2semidirect
4. C2×#424×C73C2semidirect
6. C73×#2323C2semidirect
7. C73×#2066C2semidirect
8. C73×#2065C2semidirect
9. C73×#2056C2semidirect
10. C73×#2055C2semidirect
11. C73×#1983C2semidirect
12. C73×#1948C2semidirect
14. C73×#1892C2semidirect
15. C73×#1803C2semidirect
128. C4⋊C8×C73D4semidirect
351. #24769C73direct (N × H)
361. C2×#470C2×C73semidirect
363. C2×#464C2×C73semidirect
364. C2×#424C2×C73semidirect
366. #2323C2×C73semidirect
367. #2066C2×C73semidirect
368. #2065C2×C73semidirect
369. #2056C2×C73semidirect
370. #2055C2×C73semidirect
371. #1983C2×C73semidirect
372. #1948C2×C73semidirect
374. #1892C2×C73semidirect
375. #1803C2×C73semidirect
376. C73#24769direct (N × H)
489. C4⋊C8D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#470×C732
C2×#465×C732
C2×#464×C732
C2×#424×C732
C73×#26202
C73×#23232
C73×#20662
C73×#20652
C73×#20562
C73×#20552
C73×#19832
C73×#19482
C73×#18952
C73×#18922
C73×#18032
#2476973