Finite Group Databasebeta

← C73×#24768 #32934172

Subgroups — C73×#24768 #32934172

Order 18688.

1004 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C73C211yesmaximal, characteristic, complemented
2C2×#465×C73C211yesmaximal, characteristic, complemented
3C2×#460×C73C211yesmaximal, characteristic, complemented
4C2×#424×C73C211yesmaximal, characteristic, complemented
5C73×#2619C211yesmaximal, characteristic
6C73×#2323C211yesmaximal, characteristic, complemented
7C73×#2067C211yesmaximal, characteristic, complemented
8C73×#2065C211yesmaximal, characteristic, complemented
9C73×#2055C211yesmaximal, characteristic, complemented
10C73×#2055C211yesmaximal, characteristic, complemented
11C73×#1982C211yesmaximal, characteristic, complemented
12C73×#1949C211yesmaximal, characteristic, complemented
13C73×#1895C211yesmaximal, characteristic, complemented
14C73×#1893C211yesmaximal, characteristic, complemented
15C73×#1805C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×M16×C73C2211yescharacteristic
19C23×C8×C73C2211yescharacteristic
20C2×#127×C73C2211yescharacteristic
21C2×C22⋊Q8×C73C2211yescharacteristic
22C2×#121×C73C2211yescharacteristic
23C2×#121×C73C2211yescharacteristic
24C2×C4×Q8×C73C2211yescharacteristic
25C2×#117×C73C2211yescharacteristic
26#468×C73—24no—
27#465×C73—24no—
28#460×C73—24no—
29C2×#107×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×#102×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44#394×C73—21no—
45#394×C73—21no—
46#392×C73—21no—
47#392×C73—21no—
48#391×C73C2211yescharacteristic
49#390×C73C2211yescharacteristic
50#390×C73C2211yescharacteristic
51#389×C73—21no—
52#389×C73C2211yescharacteristic
53#388×C73—21no—
54#388×C73—21no—
55#387×C73—21no—
56#382×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63C22×Q8×C73C2311yescharacteristic
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73—21no—
68C22×D4×C73C2311yescharacteristic
69C22×D4×C73C2311yescharacteristic
70C23×C4×C73C2311yescharacteristic
71C2×SD16×C73—22no—
72C2×SD16×C73—22no—
73C2×SD16×C73—22no—
74C2×SD16×C73—22no—
75C2×SD16×C73—41no—
76C2×SD16×C73—41no—
77C2×M16×C73—22no—
78C2×M16×C73—22no—
79C2×M16×C73—41no—
80C22×C8×C73—22no—
81C22×C8×C73—22no—
82C22×C8×C73—41no—
83C22×C8×C73C2311yescharacteristic
84C22×C8×C73C2311yescharacteristic
85C22×C8×C73C2311yescharacteristic
86C22×C8×C73C2311yescharacteristic
87#127×C73—22no—
88#127×C73—22no—
89C22⋊Q8×C73—22no—
90C22⋊Q8×C73D414yescomplemented
91#121×C73—22no—
92#121×C73—22no—
93#121×C73—22no—
94#121×C73—22no—
95C4×Q8×C73—22no—
96C4×Q8×C73—22no—
97#117×C73—22no—
98#117×C73—22no—
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#107×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#102×C73—22no—
132#102×C73—22no—
133#102×C73—22no—
134#102×C73—22no—
135#102×C73—41no—
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×C73—21no—
146C24×C73C2×D411yescharacteristic
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×Q8×C73—21no—
151C2×Q8×C73—21no—
152C2×Q8×C73C2×D412yes—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
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—21no—
165C2×D4×C73—42no—
166C2×D4×C73—42no—
167C2×D4×C73—42no—
168C2×D4×C73—42no—
169C2×D4×C73—81no—
170C2×D4×C73—81no—
171C2×D4×C73—81no—
172C2×D4×C73—81no—
173C2×D4×C73—81no—
174C2×D4×C73—81no—
175C2×D4×C73—81no—
176C2×D4×C73—81no—
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—21no—
187C22×C4×C73C2×D411yescharacteristic
188C22×C4×C73C2×D411yescharacteristic
189C22×C4×C73C2×D411yescharacteristic
190C22×C4×C73C2×D411yescharacteristic
191C22×C4×C73C2×D411yescharacteristic
192C22×C4×C73C2×D412yes—
193C22×C4×C73#4112yes—
194C22×C4×C73C2411yescharacteristic
195SD16×C73—44no—
196SD16×C73—44no—
197M16×C73—44no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
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—44no—
209C2×C8×C73C2×D412yes—
210C2×C8×C73C2×D412yes—
211C4⋊C4×C73—24no—
212C4⋊C4×C73—22no—
213C4⋊C4×C73—22no—
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—21no—
223C4⋊C4×C73—42no—
224C4⋊C4×C73—81no—
225C4⋊C4×C73C2×D412yes—
226C22⋊C4×C73—24no—
227C22⋊C4×C73—22no—
228C22⋊C4×C73—22no—
229C22⋊C4×C73—42no—
230C22⋊C4×C73—42no—
231C22⋊C4×C73—81no—
232C22⋊C4×C73—81no—
233C22⋊C4×C73—81no—
234C22⋊C4×C73—81no—
235C22⋊C4×C73—81no—
236C42×C73—21no—
237C42×C73—21no—
238C42×C73—42no—
239C42×C73—81no—
240C42×C73C2×D412yes—
241C42×C73#4112yes—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—41no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
255C23×C73—41no—
256C23×C73—41no—
257C23×C73—41no—
258C23×C73—41no—
259C23×C73—41no—
260C23×C73—41no—
261C23×C73—41no—
262C23×C73#12112yes—
263C23×C73C22×D411yescharacteristic
264Q8×C73—22no—
265Q8×C73—22no—
266Q8×C73—41no—
267Q8×C73—41no—
268D4×C73—41no—
269D4×C73—41no—
270D4×C73—41no—
271D4×C73—41no—
272D4×C73—41no—
273D4×C73—41no—
274D4×C73—41no—
275D4×C73—41no—
276D4×C73—84no—
277D4×C73—84no—
278D4×C73—84no—
279D4×C73—84no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—21no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—22no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—22no—
293C2×C4×C73—22no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—41no—
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#12112yes—
315C2×C4×C73#12112yes—
316C2×C4×C73#12112yes—
317C2×C4×C73C22×D411yescharacteristic
318C2×C4×C73C22×D411yescharacteristic
319C2×C4×C73C2×#4111yescharacteristic
320C2×C4×C73C2×#4111yescharacteristic
321C2×C4×C73H(5,𝔽2)11yescharacteristic
322C2×C4×C732−1+411yescharacteristic
323C8×C73—22no—
324C8×C73—22no—
325C8×C73—41no—
326C8×C73—41no—
327C22×C73—22no—
328C22×C73—22no—
329C22×C73—22no—
330C22×C73—41no—
331C22×C73—41no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73—81no—
335C22×C73—81no—
336C22×C73—81no—
337C22×C73—81no—
338C22×C73—81no—
339C22×C73—81no—
340C22×C73—81no—
341C22×C73—81no—
342C22×C73—81no—
343C22×C73—81no—
344C22×C73—81no—
345C22×C73—81no—
346C22×C73—81no—
347C22×C73—81no—
348C22×C73C2×#12111yescharacteristic
349C22×C73C2×#12111yescharacteristic
350C22×C73#53711yescharacteristic
351C22×C73#57611yescharacteristic
352C22×C73#57711yescharacteristic
353C22×C73#57711yescharacteristic
354C22×C73#57711yescharacteristic
355C4×C73—22no—
356C4×C73—22no—
357C4×C73—22no—
358C4×C73—42no—
359C4×C73—42no—
360C4×C73—41no—
361C4×C73—41no—
362C4×C73—81no—
363C4×C73—81no—
364C4×C73—81no—
365C4×C73—81no—
366C4×C73D4211yescharacteristic
367C4×C73#54711yescharacteristic
368C4×C73#54811yescharacteristic
369C4×C73#55311yescharacteristic
370#24768C7311yesmaximal, characteristic, direct product factor, Sylow
371C2×C73—42no—
372C2×C73—161no—
373C2×C73—161no—
374C2×C73#241611yescharacteristic
375C2×C73#304311yescharacteristic
376C2×C73#304511yescharacteristic
377C2×C73#305711yescharacteristic
378C2×C73#306211yescharacteristic
379C2×C73#325711yescharacteristic
380C2×C73#326011yescharacteristic
381C2×#468C2×C7311yescharacteristic, complemented
382C2×#465C2×C7311yescharacteristic, complemented
383C2×#460C2×C7311yescharacteristic, complemented
384C2×#424C2×C7311yescharacteristic, complemented
385#2619C2×C7311yescharacteristic
386#2323C2×C7311yescharacteristic, complemented
387#2067C2×C7311yescharacteristic, complemented
388#2065C2×C7311yescharacteristic, complemented
389#2055C2×C7311yescharacteristic, complemented
390#2055C2×C7311yescharacteristic, complemented
391#1982C2×C7311yescharacteristic, complemented
392#1949C2×C7311yescharacteristic, complemented
393#1895C2×C7311yescharacteristic, complemented
394#1893C2×C7311yescharacteristic, complemented
395#1805C2×C7311yescharacteristic, complemented
396C73#2476811yescharacteristic, direct product factor, Sylow
397C22×SD16C22×C7311yescharacteristic
398C22×SD16C22×C7311yescharacteristic
399C22×M16C22×C7311yescharacteristic
400C23×C8C22×C7311yescharacteristic
401C2×#127C22×C7311yescharacteristic
402C2×C22⋊Q8C22×C7311yescharacteristic
403C2×#121C22×C7311yescharacteristic
404C2×#121C22×C7311yescharacteristic
405C2×C4×Q8C22×C7311yescharacteristic
406C2×#117C22×C7311yescharacteristic
407#468—24no—
408#465—24no—
409#460—24no—
410C2×#107C22×C7311yescharacteristic
411C2×#106C22×C7311yescharacteristic
412#424—24no—
413C2×C4⋊C8C22×C7311yescharacteristic
414C2×C4⋊C8C22×C7311yescharacteristic
415C2×C4⋊C8C22×C7311yescharacteristic
416C2×C4⋊C8C22×C7311yescharacteristic
417C2×#103C22×C7311yescharacteristic
418C2×#103C22×C7311yescharacteristic
419C2×#102C22×C7311yescharacteristic
420C2×#102C22×C7311yescharacteristic
421C2×#102C22×C7311yescharacteristic
422C2×#102C22×C7311yescharacteristic
423C2×#102C22×C7311yescharacteristic
424C2×#102C22×C7311yescharacteristic
425#394—21no—
426#394—21no—
427#392—21no—
428#392—21no—
429#391C22×C7311yescharacteristic
430#390C22×C7311yescharacteristic
431#390C22×C7311yescharacteristic
432#389—21no—
433#389C22×C7311yescharacteristic
434#388—21no—
435#388—21no—
436#387—21no—
437#382C22×C7311yescharacteristic
438#380C22×C7311yescharacteristic
439C4×C4⋊C4C22×C7311yescharacteristic
440#340C22×C7311yescharacteristic
441#340C22×C7311yescharacteristic
442#340C22×C7311yescharacteristic
443#340C22×C7311yescharacteristic
444C22×Q8C23×C7311yescharacteristic
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4C23×C7311yescharacteristic
450C22×D4C23×C7311yescharacteristic
451C23×C4C23×C7311yescharacteristic
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×SD16—41no—
457C2×SD16—41no—
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—41no—
461C22×C8—22no—
462C22×C8—22no—
463C22×C8—41no—
464C22×C8C23×C7311yescharacteristic
465C22×C8C23×C7311yescharacteristic
466C22×C8C23×C7311yescharacteristic
467C22×C8C23×C7311yescharacteristic
468#127—22no—
469#127—22no—
470C22⋊Q8—22no—
471C22⋊Q8D4×C7314yescomplemented
472#121—22no—
473#121—22no—
474#121—22no—
475#121—22no—
476C4×Q8—22no—
477C4×Q8—22no—
478#117—22no—
479#117—22no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4D4×C7311yescharacteristic
484C2×C4⋊C4D4×C7311yescharacteristic
485C2×C4⋊C4C23×C7311yescharacteristic
486C2×C4⋊C4C23×C7311yescharacteristic
487C2×C4⋊C4C23×C7311yescharacteristic
488C2×C4⋊C4C23×C7311yescharacteristic
489C2×C4⋊C4C23×C7311yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
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⋊C4D4×C7311yescharacteristic
499C2×C22⋊C4D4×C7311yescharacteristic
500C2×C42—21no—
501C2×C42—21no—
502C2×C42C23×C7311yescharacteristic
503C2×C42C23×C7311yescharacteristic
504#107—22no—
505#106—22no—
506C4⋊C8—22no—
507C4⋊C8—22no—
508C4⋊C8—22no—
509C4⋊C8D4×C7314yescomplemented
510#103—22no—
511#103—22no—
512#102—22no—
513#102—22no—
514#102—22no—
515#102—22no—
516#102—41no—
517#102—41no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525C24—21no—
526C24—21no—
527C24C2×D4×C7311yescharacteristic
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8C2×D4×C7312yes—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4—81no—
551C2×D4—81no—
552C2×D4—81no—
553C2×D4—81no—
554C2×D4—81no—
555C2×D4—81no—
556C2×D4—81no—
557C2×D4—81no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4C2×D4×C7311yescharacteristic
569C22×C4C2×D4×C7311yescharacteristic
570C22×C4C2×D4×C7311yescharacteristic
571C22×C4C2×D4×C7311yescharacteristic
572C22×C4C2×D4×C7311yescharacteristic
573C22×C4C2×D4×C7312yes—
574C22×C4#41×C7312yes—
575C22×C4C24×C7311yescharacteristic
576SD16—44no—
577SD16—44no—
578M16—44no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—44no—
590C2×C8C2×D4×C7312yes—
591C2×C8C2×D4×C7312yes—
592C4⋊C4—24no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—42no—
605C4⋊C4—81no—
606C4⋊C4C2×D4×C7312yes—
607C22⋊C4—24no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—81no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C22⋊C4—81no—
616C22⋊C4—81no—
617C42—21no—
618C42—21no—
619C42—42no—
620C42—81no—
621C42C2×D4×C7312yes—
622C42#41×C7312yes—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23#121×C7312yes—
644C23C22×D4×C7311yescharacteristic
645Q8—22no—
646Q8—22no—
647Q8—41no—
648Q8—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—84no—
658D4—84no—
659D4—84no—
660D4—84no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4#121×C7312yes—
696C2×C4#121×C7312yes—
697C2×C4#121×C7312yes—
698C2×C4C22×D4×C7311yescharacteristic
699C2×C4C22×D4×C7311yescharacteristic
700C2×C4C2×#41×C7311yescharacteristic
701C2×C4C2×#41×C7311yescharacteristic
702C2×C4H(5,𝔽2)×C7311yescharacteristic
703C2×C42−1+4×C7311yescharacteristic
704C8—22no—
705C8—22no—
706C8—41no—
707C8—41no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22C2×#121×C7311yescharacteristic
730C22C2×#121×C7311yescharacteristic
731C22#537×C7311yescharacteristic
732C22#576×C7311yescharacteristic
733C22#577×C7311yescharacteristic
734C22#577×C7311yescharacteristic
735C22#577×C7311yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—42no—
740C4—41no—
741C4—41no—
742C4—42no—
743C4—81no—
744C4—81no—
745C4—81no—
746C4—81no—
747C4D42×C7311yescharacteristic
748C4#547×C7311yescharacteristic
749C4#548×C7311yescharacteristic
750C4#553×C7311yescharacteristic
751C2—42no—
752C2—161no—
753C2—161no—
754C2C73×#241611yescharacteristic
755C2C73×#304311yescharacteristic
756C2C73×#304511yescharacteristic
757C2C73×#305711yescharacteristic
758C2C73×#306211yescharacteristic
759C2C73×#325711yescharacteristic
760C2C73×#326011yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2619C2
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×#468×C73C2semidirect
2. C2×#465×C73C2semidirect
3. C2×#460×C73C2semidirect
4. C2×#424×C73C2semidirect
6. C73×#2323C2semidirect
7. C73×#2067C2semidirect
8. C73×#2065C2semidirect
9. C73×#2055C2semidirect
10. C73×#2055C2semidirect
11. C73×#1982C2semidirect
12. C73×#1949C2semidirect
13. C73×#1895C2semidirect
14. C73×#1893C2semidirect
15. C73×#1805C2semidirect
90. C22⋊Q8×C73D4semidirect
128. C4⋊C8×C73D4semidirect
370. #24768C73direct (N × H)
381. C2×#468C2×C73semidirect
382. C2×#465C2×C73semidirect
383. C2×#460C2×C73semidirect
384. C2×#424C2×C73semidirect
386. #2323C2×C73semidirect
387. #2067C2×C73semidirect
388. #2065C2×C73semidirect
389. #2055C2×C73semidirect
390. #2055C2×C73semidirect
391. #1982C2×C73semidirect
392. #1949C2×C73semidirect
393. #1895C2×C73semidirect
394. #1893C2×C73semidirect
395. #1805C2×C73semidirect
396. C73#24768direct (N × H)
471. C22⋊Q8D4×C73semidirect
509. C4⋊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×#465×C732
C2×#460×C732
C2×#424×C732
C73×#26192
C73×#23232
C73×#20672
C73×#20652
C73×#20552
C73×#19822
C73×#19492
C73×#18952
C73×#18932
C73×#18052
#2476873