Finite Group Databasebeta

← C73×#25376 #32934780

Subgroups — C73×#25376 #32934780

Order 18688.

1162 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#496×C73C211yesmaximal, characteristic, complemented
2C2×#463×C73C211yesmaximal, characteristic, complemented
3C2×#459×C73C211yesmaximal, characteristic, complemented
4C2×#459×C73C211yesmaximal, characteristic, complemented
5C73×#2544C211yesmaximal, characteristic, complemented
6C73×#2366C211yesmaximal, characteristic, complemented
7C73×#2055C211yesmaximal, characteristic, complemented
8C73×#2054C211yesmaximal, characteristic, complemented
9C73×#2012C211yesmaximal, characteristic, complemented
10C73×#2011C211yesmaximal, characteristic, complemented
11C73×#1983C211yesmaximal, characteristic, complemented
12C73×#1940C211yesmaximal, characteristic, complemented
13C73×#1879C211yesmaximal, characteristic, complemented
14C73×#1877C211yesmaximal, characteristic, complemented
15C73×#1762C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×D8×C73C2211yescharacteristic
19C22×D8×C73C2211yescharacteristic
20C22×D8×C73C2211yescharacteristic
21C22×D8×C73C2211yescharacteristic
22C2×#127×C73C2211yescharacteristic
23C2×#127×C73C2211yescharacteristic
24C2×#124×C73C2211yescharacteristic
25C2×#124×C73C2211yescharacteristic
26C2×C4×D4×C73—21no—
27C2×C4×D4×C73C2211yescharacteristic
28C2×C4×D4×C73C2211yescharacteristic
29C2×C4×D4×C73C2211yescharacteristic
30#496×C73—24no—
31#463×C73—24no—
32#459×C73—24no—
33#459×C73—24no—
34C2×C4⋊C8×C73C2211yescharacteristic
35C2×C4⋊C8×C73C2211yescharacteristic
36C2×C4⋊C8×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44C2×#102×C73C2211yescharacteristic
45C2×#97×C73C2211yescharacteristic
46#394×C73—21no—
47#394×C73—21no—
48#391×C73C2211yescharacteristic
49#390×C73—21no—
50#390×C73C2211yescharacteristic
51#390×C73C2211yescharacteristic
52#390×C73C2211yescharacteristic
53#386×C73—21no—
54#386×C73—21no—
55#386×C73—21no—
56#386×C73—21no—
57C4×C4⋊C4×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×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
70C22×D4×C73C2311yescharacteristic
71C22×D4×C73C2311yescharacteristic
72C23×C4×C73—21no—
73C23×C4×C73—21no—
74C23×C4×C73—21no—
75C2×SD16×C73—22no—
76C2×SD16×C73—22no—
77C2×SD16×C73—22no—
78C2×SD16×C73—22no—
79C2×SD16×C73—41no—
80C2×SD16×C73—41no—
81C2×D8×C73—22no—
82C2×D8×C73—22no—
83C2×D8×C73—22no—
84C2×D8×C73—22no—
85C2×D8×C73—22no—
86C2×D8×C73—22no—
87C2×D8×C73—22no—
88C2×D8×C73—22no—
89C2×D8×C73—41no—
90C2×D8×C73—41no—
91C2×D8×C73—41no—
92C2×D8×C73—41no—
93C22×C8×C73C2311yescharacteristic
94C22×C8×C73C2311yescharacteristic
95C22×C8×C73C2311yescharacteristic
96C22×C8×C73C2311yescharacteristic
97#127×C73—22no—
98#127×C73—22no—
99#127×C73—41no—
100#127×C73D414yescomplemented
101#124×C73—22no—
102#124×C73—22no—
103#124×C73—22no—
104#124×C73—41no—
105C4×D4×C73—22no—
106C4×D4×C73—22no—
107C4×D4×C73—22no—
108C4×D4×C73—22no—
109C4×D4×C73—41no—
110C4×D4×C73—41no—
111C4×D4×C73—44no—
112C2×C4⋊C4×C73D411yescharacteristic
113C2×C4⋊C4×C73D411yescharacteristic
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×C73—21no—
129C2×C22⋊C4×C73—21no—
130C2×C42×C73—21no—
131C2×C42×C73C2311yescharacteristic
132C2×C42×C73C2311yescharacteristic
133C2×C42×C73C2311yescharacteristic
134C4⋊C8×C73—22no—
135C4⋊C8×C73—22no—
136C4⋊C8×C73—22no—
137#103×C73—22no—
138#103×C73—41no—
139#102×C73—22no—
140#102×C73—22no—
141#102×C73—22no—
142#102×C73—22no—
143#102×C73—41no—
144#102×C73D414yescomplemented
145#97×C73—22no—
146#95×C73—21no—
147#95×C73—21no—
148#95×C73—21no—
149#95×C73D411yescharacteristic
150#95×C73D411yescharacteristic
151C24×C73—21no—
152C24×C73—21no—
153C24×C73—21no—
154C24×C73—21no—
155C2×Q8×C73—21no—
156C2×Q8×C73—21no—
157C2×Q8×C73—21no—
158C2×Q8×C73—21no—
159C2×Q8×C73—21no—
160C2×Q8×C73—21no—
161C2×D4×C73—24no—
162C2×D4×C73—24no—
163C2×D4×C73—21no—
164C2×D4×C73—21no—
165C2×D4×C73—21no—
166C2×D4×C73—21no—
167C2×D4×C73—21no—
168C2×D4×C73—21no—
169C2×D4×C73—21no—
170C2×D4×C73—21no—
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—21no—
182C2×D4×C73—21no—
183C2×D4×C73—21no—
184C2×D4×C73—42no—
185C2×D4×C73—42no—
186C2×D4×C73—42no—
187C2×D4×C73—42no—
188C2×D4×C73—42no—
189C2×D4×C73—42no—
190C2×D4×C73—81no—
191C2×D4×C73—81no—
192C2×D4×C73—81no—
193C2×D4×C73—81no—
194C2×D4×C73C2×D412yes—
195C2×D4×C73C2×D412yes—
196C2×D4×C73C2×D412yes—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—42no—
202C22×C4×C73—42no—
203C22×C4×C73—42no—
204C22×C4×C73—42no—
205C22×C4×C73—42no—
206C22×C4×C73—81no—
207C22×C4×C73—81no—
208C22×C4×C73—81no—
209C22×C4×C73—81no—
210C22×C4×C73C2×D411yescharacteristic
211C22×C4×C73C2×D411yescharacteristic
212C22×C4×C73C2×D411yescharacteristic
213C22×C4×C73C2×D411yescharacteristic
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2411yescharacteristic
217SD16×C73—44no—
218SD16×C73—44no—
219D8×C73—44no—
220D8×C73—44no—
221D8×C73—44no—
222D8×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×C73—21no—
233C2×C8×C73C2×D412yes—
234C2×C8×C73#4112yes—
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—41no—
242C4⋊C4×C73C2×D412yes—
243C22⋊C4×C73—42no—
244C22⋊C4×C73—42no—
245C22⋊C4×C73—42no—
246C22⋊C4×C73—42no—
247C22⋊C4×C73—42no—
248C22⋊C4×C73—42no—
249C22⋊C4×C73—42no—
250C22⋊C4×C73—42no—
251C22⋊C4×C73—42no—
252C22⋊C4×C73—81no—
253C22⋊C4×C73—81no—
254C22⋊C4×C73—81no—
255C22⋊C4×C73—81no—
256C42×C73—21no—
257C42×C73—21no—
258C42×C73—21no—
259C42×C73—21no—
260C42×C73—42no—
261C42×C73C2×D412yes—
262C42×C73#4112yes—
263C23×C73—22no—
264C23×C73—22no—
265C23×C73—22no—
266C23×C73—41no—
267C23×C73—41no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—41no—
272C23×C73—41no—
273C23×C73—41no—
274C23×C73—41no—
275C23×C73—41no—
276C23×C73—41no—
277C23×C73—41no—
278C23×C73—41no—
279C23×C73—41no—
280C23×C73—41no—
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×C73C22×D411yescharacteristic
292Q8×C73—41no—
293Q8×C73—41no—
294Q8×C73—41no—
295Q8×C73—41no—
296D4×C73—22no—
297D4×C73—22no—
298D4×C73—22no—
299D4×C73—22no—
300D4×C73—22no—
301D4×C73—22no—
302D4×C73—48no—
303D4×C73—41no—
304D4×C73—41no—
305D4×C73—41no—
306D4×C73—41no—
307D4×C73—41no—
308D4×C73—41no—
309D4×C73—41no—
310D4×C73—41no—
311D4×C73—41no—
312D4×C73—41no—
313D4×C73—84no—
314D4×C73—84no—
315D4×C73—84no—
316C2×C4×C73—21no—
317C2×C4×C73—21no—
318C2×C4×C73—21no—
319C2×C4×C73—21no—
320C2×C4×C73—21no—
321C2×C4×C73—21no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—22no—
326C2×C4×C73—21no—
327C2×C4×C73—21no—
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—84no—
344C2×C4×C73—84no—
345C2×C4×C73—84no—
346C2×C4×C73#12112yes—
347C2×C4×C73#12112yes—
348C2×C4×C73AGL(1,ℤ/8)12yes—
349C2×C4×C73C22×D411yescharacteristic
350C2×C4×C73C22×D411yescharacteristic
351C2×C4×C73C2×#4111yescharacteristic
352C2×C4×C73C2×#4111yescharacteristic
353C2×C4×C73H(5,𝔽2)11yescharacteristic
354C2×C4×C73H(5,𝔽2)11yescharacteristic
355C8×C73—22no—
356C8×C73—22no—
357C8×C73—41no—
358C8×C73—41no—
359C22×C73—42no—
360C22×C73—42no—
361C22×C73—42no—
362C22×C73—42no—
363C22×C73—42no—
364C22×C73—42no—
365C22×C73—42no—
366C22×C73—42no—
367C22×C73—42no—
368C22×C73—81no—
369C22×C73—81no—
370C22×C73—81no—
371C22×C73—81no—
372C22×C73—81no—
373C22×C73—81no—
374C22×C73—81no—
375C22×C73—81no—
376C22×C73—81no—
377C22×C73—81no—
378C22×C73—81no—
379C22×C73—81no—
380C22×C73—81no—
381C22×C73—81no—
382C22×C73—81no—
383C22×C73—81no—
384C22×C73—81no—
385C22×C73—81no—
386C22×C73—81no—
387C22×C73C2×#12111yescharacteristic
388C22×C73D4211yescharacteristic
389C22×C73#55011yescharacteristic
390C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
391C22×C73#57511yescharacteristic
392C22×C73#57611yescharacteristic
393C22×C73#57611yescharacteristic
394C4×C73—22no—
395C4×C73—22no—
396C4×C73—22no—
397C4×C73—41no—
398C4×C73—42no—
399C4×C73—41no—
400C4×C73—41no—
401C4×C73—81no—
402C4×C73—81no—
403C4×C73—81no—
404C4×C73#53211yescharacteristic
405C4×C73#54011yescharacteristic
406C4×C73D4211yescharacteristic
407C4×C73#54611yescharacteristic
408#25376C7311yesmaximal, characteristic, direct product factor, Sylow
409C2×C73—82no—
410C2×C73—82no—
411C2×C73—82no—
412C2×C73—161no—
413C2×C73#242811yescharacteristic
414C2×C73#303611yescharacteristic
415C2×C73#304111yescharacteristic
416C2×C73#326411yescharacteristic
417C2×C73#326811yescharacteristic
418C2×C73#339911yescharacteristic
419C2×C73#340311yescharacteristic
420C2×#496C2×C7311yescharacteristic, complemented
421C2×#463C2×C7311yescharacteristic, complemented
422C2×#459C2×C7311yescharacteristic, complemented
423C2×#459C2×C7311yescharacteristic, complemented
424#2544C2×C7311yescharacteristic, complemented
425#2366C2×C7311yescharacteristic, complemented
426#2055C2×C7311yescharacteristic, complemented
427#2054C2×C7311yescharacteristic, complemented
428#2012C2×C7311yescharacteristic, complemented
429#2011C2×C7311yescharacteristic, complemented
430#1983C2×C7311yescharacteristic, complemented
431#1940C2×C7311yescharacteristic, complemented
432#1879C2×C7311yescharacteristic, complemented
433#1877C2×C7311yescharacteristic, complemented
434#1762C2×C7311yescharacteristic, complemented
435C73#2537611yescharacteristic, direct product factor, Sylow
436C22×SD16C22×C7311yescharacteristic
437C22×SD16C22×C7311yescharacteristic
438C22×D8C22×C7311yescharacteristic
439C22×D8C22×C7311yescharacteristic
440C22×D8C22×C7311yescharacteristic
441C22×D8C22×C7311yescharacteristic
442C2×#127C22×C7311yescharacteristic
443C2×#127C22×C7311yescharacteristic
444C2×#124C22×C7311yescharacteristic
445C2×#124C22×C7311yescharacteristic
446C2×C4×D4—21no—
447C2×C4×D4C22×C7311yescharacteristic
448C2×C4×D4C22×C7311yescharacteristic
449C2×C4×D4C22×C7311yescharacteristic
450#496—24no—
451#463—24no—
452#459—24no—
453#459—24no—
454C2×C4⋊C8C22×C7311yescharacteristic
455C2×C4⋊C8C22×C7311yescharacteristic
456C2×C4⋊C8C22×C7311yescharacteristic
457C2×#103C22×C7311yescharacteristic
458C2×#103C22×C7311yescharacteristic
459C2×#102C22×C7311yescharacteristic
460C2×#102C22×C7311yescharacteristic
461C2×#102C22×C7311yescharacteristic
462C2×#102C22×C7311yescharacteristic
463C2×#102C22×C7311yescharacteristic
464C2×#102C22×C7311yescharacteristic
465C2×#97C22×C7311yescharacteristic
466#394—21no—
467#394—21no—
468#391C22×C7311yescharacteristic
469#390—21no—
470#390C22×C7311yescharacteristic
471#390C22×C7311yescharacteristic
472#390C22×C7311yescharacteristic
473#386—21no—
474#386—21no—
475#386—21no—
476#386—21no—
477C4×C4⋊C4C22×C7311yescharacteristic
478C4×C4⋊C4C22×C7311yescharacteristic
479#340C22×C7311yescharacteristic
480#340C22×C7311yescharacteristic
481#336C22×C7311yescharacteristic
482#336C22×C7311yescharacteristic
483C22×Q8C23×C7311yescharacteristic
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4C23×C7311yescharacteristic
489C22×D4C23×C7311yescharacteristic
490C22×D4C23×C7311yescharacteristic
491C22×D4C23×C7311yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—22no—
504C2×D8—22no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—22no—
509C2×D8—41no—
510C2×D8—41no—
511C2×D8—41no—
512C2×D8—41no—
513C22×C8C23×C7311yescharacteristic
514C22×C8C23×C7311yescharacteristic
515C22×C8C23×C7311yescharacteristic
516C22×C8C23×C7311yescharacteristic
517#127—22no—
518#127—22no—
519#127—41no—
520#127D4×C7314yescomplemented
521#124—22no—
522#124—22no—
523#124—22no—
524#124—41no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—41no—
530C4×D4—41no—
531C4×D4—44no—
532C2×C4⋊C4D4×C7311yescharacteristic
533C2×C4⋊C4D4×C7311yescharacteristic
534C2×C4⋊C4C23×C7311yescharacteristic
535C2×C4⋊C4C23×C7311yescharacteristic
536C2×C4⋊C4C23×C7311yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
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×C42—21no—
551C2×C42C23×C7311yescharacteristic
552C2×C42C23×C7311yescharacteristic
553C2×C42C23×C7311yescharacteristic
554C4⋊C8—22no—
555C4⋊C8—22no—
556C4⋊C8—22no—
557#103—22no—
558#103—41no—
559#102—22no—
560#102—22no—
561#102—22no—
562#102—22no—
563#102—41no—
564#102D4×C7314yescomplemented
565#97—22no—
566#95—21no—
567#95—21no—
568#95—21no—
569#95D4×C7311yescharacteristic
570#95D4×C7311yescharacteristic
571C24—21no—
572C24—21no—
573C24—21no—
574C24—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×D4—24no—
582C2×D4—24no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—81no—
611C2×D4—81no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4C2×D4×C7312yes—
615C2×D4C2×D4×C7312yes—
616C2×D4C2×D4×C7312yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—81no—
627C22×C4—81no—
628C22×C4—81no—
629C22×C4—81no—
630C22×C4C2×D4×C7311yescharacteristic
631C22×C4C2×D4×C7311yescharacteristic
632C22×C4C2×D4×C7311yescharacteristic
633C22×C4C2×D4×C7311yescharacteristic
634C22×C4C2×D4×C7311yescharacteristic
635C22×C4C2×D4×C7311yescharacteristic
636C22×C4C24×C7311yescharacteristic
637SD16—44no—
638SD16—44no—
639D8—44no—
640D8—44no—
641D8—44no—
642D8—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8C2×D4×C7312yes—
654C2×C8#41×C7312yes—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—41no—
662C4⋊C4C2×D4×C7312yes—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—81no—
673C22⋊C4—81no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—42no—
681C42C2×D4×C7312yes—
682C42#41×C7312yes—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23C22×D4×C7311yescharacteristic
712Q8—41no—
713Q8—41no—
714Q8—41no—
715Q8—41no—
716D4—22no—
717D4—22no—
718D4—22no—
719D4—22no—
720D4—22no—
721D4—22no—
722D4—48no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—84no—
734D4—84no—
735D4—84no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—84no—
764C2×C4—84no—
765C2×C4—84no—
766C2×C4#121×C7312yes—
767C2×C4#121×C7312yes—
768C2×C4AGL(1,ℤ/8)×C7312yes—
769C2×C4C22×D4×C7311yescharacteristic
770C2×C4C22×D4×C7311yescharacteristic
771C2×C4C2×#41×C7311yescharacteristic
772C2×C4C2×#41×C7311yescharacteristic
773C2×C4H(5,𝔽2)×C7311yescharacteristic
774C2×C4H(5,𝔽2)×C7311yescharacteristic
775C8—22no—
776C8—22no—
777C8—41no—
778C8—41no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22C2×#121×C7311yescharacteristic
808C22D42×C7311yescharacteristic
809C22#550×C7311yescharacteristic
810C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
811C22#575×C7311yescharacteristic
812C22#576×C7311yescharacteristic
813C22#576×C7311yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—41no—
818C4—42no—
819C4—41no—
820C4—41no—
821C4—81no—
822C4—81no—
823C4—81no—
824C4#532×C7311yescharacteristic
825C4#540×C7311yescharacteristic
826C4D42×C7311yescharacteristic
827C4#546×C7311yescharacteristic
828C2—82no—
829C2—82no—
830C2—82no—
831C2—161no—
832C2C73×#242811yescharacteristic
833C2C73×#303611yescharacteristic
834C2C73×#304111yescharacteristic
835C2C73×#326411yescharacteristic
836C2C73×#326811yescharacteristic
837C2C73×#339911yescharacteristic
838C2C73×#340311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C4⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#496×C73C2semidirect
2. C2×#463×C73C2semidirect
3. C2×#459×C73C2semidirect
4. C2×#459×C73C2semidirect
5. C73×#2544C2semidirect
6. C73×#2366C2semidirect
7. C73×#2055C2semidirect
8. C73×#2054C2semidirect
9. C73×#2012C2semidirect
10. C73×#2011C2semidirect
11. C73×#1983C2semidirect
12. C73×#1940C2semidirect
13. C73×#1879C2semidirect
14. C73×#1877C2semidirect
15. C73×#1762C2semidirect
100. #127×C73D4semidirect
144. #102×C73D4semidirect
408. #25376C73direct (N × H)
420. C2×#496C2×C73semidirect
421. C2×#463C2×C73semidirect
422. C2×#459C2×C73semidirect
423. C2×#459C2×C73semidirect
424. #2544C2×C73semidirect
425. #2366C2×C73semidirect
426. #2055C2×C73semidirect
427. #2054C2×C73semidirect
428. #2012C2×C73semidirect
429. #2011C2×C73semidirect
430. #1983C2×C73semidirect
431. #1940C2×C73semidirect
432. #1879C2×C73semidirect
433. #1877C2×C73semidirect
434. #1762C2×C73semidirect
435. C73#25376direct (N × H)
520. #127D4×C73semidirect
564. #102D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#496×C732
C2×#463×C732
C2×#459×C732
C73×#25442
C73×#23662
C73×#20552
C73×#20542
C73×#20122
C73×#20112
C73×#19832
C73×#19402
C73×#18792
C73×#18772
C73×#17622
#2537673