Finite Group Databasebeta

← C73×#25159 #32934563

Subgroups — C73×#25159 #32934563

Order 18688.

1212 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C73C211yesmaximal, characteristic, complemented
2C2×#449×C73C211yesmaximal, characteristic, complemented
3C2×#449×C73C211yesmaximal, characteristic, complemented
4C2×C4×SD16×C73C211yesmaximal, characteristic, complemented
5C73×#2428C211yesmaximal, characteristic, complemented
6C73×#2341C211yesmaximal, characteristic, complemented
7C73×#2065C211yesmaximal, characteristic, complemented
8C73×#2034C211yesmaximal, characteristic, complemented
9C73×#2033C211yesmaximal, characteristic, complemented
10C73×#2011C211yesmaximal, characteristic, complemented
11C73×#1970C211yesmaximal, characteristic, complemented
12C73×#1923C211yesmaximal, characteristic, complemented
13C73×#1880C211yesmaximal, characteristic, complemented
14C73×#1879C211yesmaximal, characteristic, complemented
15C73×#1863C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C22×D8×C73C2211yescharacteristic
20C22×D8×C73C2211yescharacteristic
21C2×#127×C73C2211yescharacteristic
22C2×#121×C73—21no—
23C2×#121×C73C2211yescharacteristic
24C2×#121×C73C2211yescharacteristic
25C2×C4×Q8×C73C2211yescharacteristic
26C2×C4×Q8×C73C2211yescharacteristic
27C2×C4×D4×C73C2211yescharacteristic
28#460×C73—24no—
29#449×C73—24no—
30#449×C73—24no—
31C4×SD16×C73—24no—
32C2×#107×C73C2211yescharacteristic
33C2×#106×C73C2211yescharacteristic
34C2×C4⋊C8×C73C2211yescharacteristic
35C2×#103×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×C22⋊C8×C73C2211yescharacteristic
44C2×C22⋊C8×C73C2211yescharacteristic
45C2×C4×C8×C73C2211yescharacteristic
46#394×C73—21no—
47#392×C73—21no—
48#390×C73—21no—
49#390×C73—21no—
50#390×C73C2211yescharacteristic
51#390×C73C2211yescharacteristic
52#390×C73C2211yescharacteristic
53#389×C73C2211yescharacteristic
54#386×C73—21no—
55#380×C73—21no—
56#380×C73C2211yescharacteristic
57C4×C22⋊C4×C73—21no—
58C4×C22⋊C4×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×C73C2211yescharacteristic
63C2×#41×C73—22no—
64C2×#41×C73—22no—
65C2×#41×C73—22no—
66C2×#41×C73—22no—
67C2×#41×C73—41no—
68C2×#41×C73—41no—
69C22×Q8×C73C2311yescharacteristic
70C22×D4×C73—21no—
71C22×D4×C73—21no—
72C22×D4×C73—21no—
73C22×D4×C73—21no—
74C22×D4×C73—21no—
75C22×D4×C73C2311yescharacteristic
76C22×D4×C73C2311yescharacteristic
77C22×D4×C73C2311yescharacteristic
78C23×C4×C73—21no—
79C23×C4×C73—21no—
80C23×C4×C73C2311yescharacteristic
81C2×SD16×C73—22no—
82C2×SD16×C73—22no—
83C2×SD16×C73—22no—
84C2×SD16×C73—22no—
85C2×SD16×C73—22no—
86C2×SD16×C73D414yescomplemented
87C2×D8×C73—22no—
88C2×D8×C73—22no—
89C2×D8×C73—22no—
90C2×D8×C73—22no—
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—41no—
99#121×C73—22no—
100#121×C73—22no—
101#121×C73—44no—
102#121×C73—41no—
103#121×C73—41no—
104C4×Q8×C73—22no—
105C4×Q8×C73—22no—
106C4×Q8×C73—41no—
107C4×Q8×C73—41no—
108C4×D4×C73—22no—
109C4×D4×C73—41no—
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73—21no—
113C2×C4⋊C4×C73C2311yescharacteristic
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×C73D411yescharacteristic
128C2×C22⋊C4×C73D411yescharacteristic
129C2×C42×C73—21no—
130C2×C42×C73—21no—
131C2×C42×C73C2311yescharacteristic
132C2×C42×C73C2311yescharacteristic
133#107×C73—41no—
134#106×C73—22no—
135C4⋊C8×C73—22no—
136#103×C73—22no—
137#103×C73D414yescomplemented
138#102×C73—22no—
139#102×C73—22no—
140#102×C73—22no—
141#102×C73—22no—
142#102×C73—22no—
143#102×C73—41no—
144C22⋊C8×C73—22no—
145C22⋊C8×C73—22no—
146C4×C8×C73—22no—
147#95×C73—21no—
148#95×C73—21no—
149#95×C73D411yescharacteristic
150#95×C73D411yescharacteristic
151C24×C73—21no—
152C24×C73—21no—
153C24×C73—21no—
154C24×C73C2×D411yescharacteristic
155#41×C73—44no—
156#41×C73—44no—
157#41×C73—44no—
158#41×C73—44no—
159C2×Q8×C73—21no—
160C2×Q8×C73—21no—
161C2×Q8×C73—21no—
162C2×Q8×C73C2×D412yes—
163C2×Q8×C73C2×D412yes—
164C2×Q8×C73#4112yes—
165C2×D4×C73—24no—
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—42no—
183C2×D4×C73—42no—
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—42no—
191C2×D4×C73—42no—
192C2×D4×C73—81no—
193C2×D4×C73—81no—
194C2×D4×C73—81no—
195C2×D4×C73—81no—
196C2×D4×C73C2×D412yes—
197C2×D4×C73#4112yes—
198C22×C4×C73—21no—
199C22×C4×C73—24no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—42no—
211C22×C4×C73—42no—
212C22×C4×C73—42no—
213C22×C4×C73—42no—
214C22×C4×C73—81no—
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2×D411yescharacteristic
219C22×C4×C73C2×D411yescharacteristic
220C22×C4×C73C2411yescharacteristic
221SD16×C73—28no—
222SD16×C73—44no—
223D8×C73—44no—
224D8×C73—44no—
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×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73C2×D412yes—
236C2×C8×C73C2×D412yes—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—42no—
245C4⋊C4×C73—42no—
246C4⋊C4×C73—42no—
247C4⋊C4×C73C2×D412yes—
248C22⋊C4×C73—22no—
249C22⋊C4×C73—22no—
250C22⋊C4×C73—42no—
251C22⋊C4×C73—42no—
252C22⋊C4×C73—42no—
253C22⋊C4×C73—42no—
254C22⋊C4×C73—42no—
255C22⋊C4×C73—42no—
256C22⋊C4×C73—81no—
257C22⋊C4×C73—81no—
258C22⋊C4×C73—81no—
259C22⋊C4×C73—81no—
260C42×C73—21no—
261C42×C73—21no—
262C42×C73—21no—
263C42×C73—21no—
264C42×C73—42no—
265C42×C73—42no—
266C23×C73—21no—
267C23×C73—22no—
268C23×C73—22no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—21no—
274C23×C73—21no—
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×C73—41no—
292C23×C73—41no—
293C23×C73—41no—
294C23×C73C22×D411yescharacteristic
295Q8×C73—22no—
296Q8×C73—22no—
297Q8×C73—22no—
298Q8×C73#12114yescomplemented
299D4×C73—22no—
300D4×C73—22no—
301D4×C73—22no—
302D4×C73—22no—
303D4×C73—48no—
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—84no—
313D4×C73—84no—
314D4×C73—84no—
315D4×C73—84no—
316C2×C4×C73—22no—
317C2×C4×C73—21no—
318C2×C4×C73—21no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
321C2×C4×C73—21no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—21no—
326C2×C4×C73—22no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—21no—
330C2×C4×C73—21no—
331C2×C4×C73—21no—
332C2×C4×C73—21no—
333C2×C4×C73—48no—
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—41no—
344C2×C4×C73—41no—
345C2×C4×C73—41no—
346C2×C4×C73—41no—
347C2×C4×C73—41no—
348C2×C4×C73—41no—
349C2×C4×C73—84no—
350C2×C4×C73#13512yes—
351C2×C4×C73AGL(1,ℤ/8)12yes—
352C2×C4×C73C22×D411yescharacteristic
353C2×C4×C73C22×D411yescharacteristic
354C2×C4×C73C2×#4111yescharacteristic
355C2×C4×C73C2×#4111yescharacteristic
356C2×C4×C73H(5,𝔽2)11yescharacteristic
357C2×C4×C73H(5,𝔽2)11yescharacteristic
358C8×C73—22no—
359C8×C73—22no—
360C8×C73—41no—
361C8×C73—41no—
362C22×C73—41no—
363C22×C73—42no—
364C22×C73—41no—
365C22×C73—42no—
366C22×C73—42no—
367C22×C73—41no—
368C22×C73—42no—
369C22×C73—41no—
370C22×C73—41no—
371C22×C73—42no—
372C22×C73—42no—
373C22×C73—41no—
374C22×C73—41no—
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×C73—81no—
388C22×C73—81no—
389C22×C73—81no—
390C22×C73#52511yescharacteristic
391C22×C73D4211yescharacteristic
392C22×C73D4211yescharacteristic
393C22×C73C2×#13511yescharacteristic
394C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C73#57611yescharacteristic
396C22×C73#57711yescharacteristic
397C4×C73—24no—
398C4×C73—22no—
399C4×C73—22no—
400C4×C73—41no—
401C4×C73—42no—
402C4×C73—41no—
403C4×C73—41no—
404C4×C73—81no—
405C4×C73—81no—
406C4×C73—81no—
407C4×C73C2×#12111yescharacteristic
408C4×C73#53811yescharacteristic
409C4×C73#54611yescharacteristic
410C4×C73#54611yescharacteristic
411#25159C7311yesmaximal, characteristic, direct product factor, Sylow
412C2×C73—81no—
413C2×C73—82no—
414C2×C73—82no—
415C2×C73—161no—
416C2×C73#242411yescharacteristic
417C2×C73#310611yescharacteristic
418C2×C73#311911yescharacteristic
419C2×C73#326511yescharacteristic
420C2×C73#327411yescharacteristic
421C2×C73#328211yescharacteristic
422C2×C73#328711yescharacteristic
423C2×#460C2×C7311yescharacteristic, complemented
424C2×#449C2×C7311yescharacteristic, complemented
425C2×#449C2×C7311yescharacteristic, complemented
426C2×C4×SD16C2×C7311yescharacteristic, complemented
427#2428C2×C7311yescharacteristic, complemented
428#2341C2×C7311yescharacteristic, complemented
429#2065C2×C7311yescharacteristic, complemented
430#2034C2×C7311yescharacteristic, complemented
431#2033C2×C7311yescharacteristic, complemented
432#2011C2×C7311yescharacteristic, complemented
433#1970C2×C7311yescharacteristic, complemented
434#1923C2×C7311yescharacteristic, complemented
435#1880C2×C7311yescharacteristic, complemented
436#1879C2×C7311yescharacteristic, complemented
437#1863C2×C7311yescharacteristic, complemented
438C73#2515911yescharacteristic, direct product factor, Sylow
439C22×#41C22×C7311yescharacteristic
440C22×SD16C22×C7311yescharacteristic
441C22×SD16C22×C7311yescharacteristic
442C22×D8C22×C7311yescharacteristic
443C22×D8C22×C7311yescharacteristic
444C2×#127C22×C7311yescharacteristic
445C2×#121—21no—
446C2×#121C22×C7311yescharacteristic
447C2×#121C22×C7311yescharacteristic
448C2×C4×Q8C22×C7311yescharacteristic
449C2×C4×Q8C22×C7311yescharacteristic
450C2×C4×D4C22×C7311yescharacteristic
451#460—24no—
452#449—24no—
453#449—24no—
454C4×SD16—24no—
455C2×#107C22×C7311yescharacteristic
456C2×#106C22×C7311yescharacteristic
457C2×C4⋊C8C22×C7311yescharacteristic
458C2×#103C22×C7311yescharacteristic
459C2×#103C22×C7311yescharacteristic
460C2×#102C22×C7311yescharacteristic
461C2×#102C22×C7311yescharacteristic
462C2×#102C22×C7311yescharacteristic
463C2×#102C22×C7311yescharacteristic
464C2×#102C22×C7311yescharacteristic
465C2×#102C22×C7311yescharacteristic
466C2×C22⋊C8C22×C7311yescharacteristic
467C2×C22⋊C8C22×C7311yescharacteristic
468C2×C4×C8C22×C7311yescharacteristic
469#394—21no—
470#392—21no—
471#390—21no—
472#390—21no—
473#390C22×C7311yescharacteristic
474#390C22×C7311yescharacteristic
475#390C22×C7311yescharacteristic
476#389C22×C7311yescharacteristic
477#386—21no—
478#380—21no—
479#380C22×C7311yescharacteristic
480C4×C22⋊C4—21no—
481C4×C22⋊C4C22×C7311yescharacteristic
482#340C22×C7311yescharacteristic
483#340C22×C7311yescharacteristic
484#336C22×C7311yescharacteristic
485#336C22×C7311yescharacteristic
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—41no—
491C2×#41—41no—
492C22×Q8C23×C7311yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C23×C7311yescharacteristic
499C22×D4C23×C7311yescharacteristic
500C22×D4C23×C7311yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C23×C7311yescharacteristic
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16D4×C7314yescomplemented
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—41no—
515C2×D8—41no—
516C22×C8C23×C7311yescharacteristic
517C22×C8C23×C7311yescharacteristic
518C22×C8C23×C7311yescharacteristic
519C22×C8C23×C7311yescharacteristic
520#127—22no—
521#127—41no—
522#121—22no—
523#121—22no—
524#121—44no—
525#121—41no—
526#121—41no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—41no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4C23×C7311yescharacteristic
537C2×C4⋊C4C23×C7311yescharacteristic
538C2×C4⋊C4C23×C7311yescharacteristic
539C2×C4⋊C4C23×C7311yescharacteristic
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×C22⋊C4D4×C7311yescharacteristic
551C2×C22⋊C4D4×C7311yescharacteristic
552C2×C42—21no—
553C2×C42—21no—
554C2×C42C23×C7311yescharacteristic
555C2×C42C23×C7311yescharacteristic
556#107—41no—
557#106—22no—
558C4⋊C8—22no—
559#103—22no—
560#103D4×C7314yescomplemented
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569C4×C8—22no—
570#95—21no—
571#95—21no—
572#95D4×C7311yescharacteristic
573#95D4×C7311yescharacteristic
574C24—21no—
575C24—21no—
576C24—21no—
577C24C2×D4×C7311yescharacteristic
578#41—44no—
579#41—44no—
580#41—44no—
581#41—44no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C7312yes—
586C2×Q8C2×D4×C7312yes—
587C2×Q8#41×C7312yes—
588C2×D4—24no—
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—21no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C7312yes—
620C2×D4#41×C7312yes—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4C2×D4×C7311yescharacteristic
639C22×C4C2×D4×C7311yescharacteristic
640C22×C4C2×D4×C7311yescharacteristic
641C22×C4C2×D4×C7311yescharacteristic
642C22×C4C2×D4×C7311yescharacteristic
643C22×C4C24×C7311yescharacteristic
644SD16—28no—
645SD16—44no—
646D8—44no—
647D8—44no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8C2×D4×C7312yes—
659C2×C8C2×D4×C7312yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C2×D4×C7312yes—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—42no—
688C42—42no—
689C23—21no—
690C23—22no—
691C23—22no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
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—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23C22×D4×C7311yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8#121×C7314yescomplemented
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—48no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—84no—
736D4—84no—
737D4—84no—
738D4—84no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—48no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—84no—
773C2×C4#135×C7312yes—
774C2×C4AGL(1,ℤ/8)×C7312yes—
775C2×C4C22×D4×C7311yescharacteristic
776C2×C4C22×D4×C7311yescharacteristic
777C2×C4C2×#41×C7311yescharacteristic
778C2×C4C2×#41×C7311yescharacteristic
779C2×C4H(5,𝔽2)×C7311yescharacteristic
780C2×C4H(5,𝔽2)×C7311yescharacteristic
781C8—22no—
782C8—22no—
783C8—41no—
784C8—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—42no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—41no—
797C22—42no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22#525×C7311yescharacteristic
814C22D42×C7311yescharacteristic
815C22D42×C7311yescharacteristic
816C22C2×#135×C7311yescharacteristic
817C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
818C22#576×C7311yescharacteristic
819C22#577×C7311yescharacteristic
820C4—22no—
821C4—22no—
822C4—24no—
823C4—42no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4C2×#121×C7311yescharacteristic
831C4#538×C7311yescharacteristic
832C4#546×C7311yescharacteristic
833C4#546×C7311yescharacteristic
834C2—81no—
835C2—82no—
836C2—82no—
837C2—161no—
838C2C73×#242411yescharacteristic
839C2C73×#310611yescharacteristic
840C2C73×#311911yescharacteristic
841C2C73×#326511yescharacteristic
842C2C73×#327411yescharacteristic
843C2C73×#328211yescharacteristic
844C2C73×#328711yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
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
1. C2×#460×C73C2semidirect
2. C2×#449×C73C2semidirect
3. C2×#449×C73C2semidirect
4. C2×C4×SD16×C73C2semidirect
5. C73×#2428C2semidirect
6. C73×#2341C2semidirect
7. C73×#2065C2semidirect
8. C73×#2034C2semidirect
9. C73×#2033C2semidirect
10. C73×#2011C2semidirect
11. C73×#1970C2semidirect
12. C73×#1923C2semidirect
13. C73×#1880C2semidirect
14. C73×#1879C2semidirect
15. C73×#1863C2semidirect
86. C2×SD16×C73D4semidirect
137. #103×C73D4semidirect
298. Q8×C73#121semidirect
411. #25159C73direct (N × H)
423. C2×#460C2×C73semidirect
424. C2×#449C2×C73semidirect
425. C2×#449C2×C73semidirect
426. C2×C4×SD16C2×C73semidirect
427. #2428C2×C73semidirect
428. #2341C2×C73semidirect
429. #2065C2×C73semidirect
430. #2034C2×C73semidirect
431. #2033C2×C73semidirect
432. #2011C2×C73semidirect
433. #1970C2×C73semidirect
434. #1923C2×C73semidirect
435. #1880C2×C73semidirect
436. #1879C2×C73semidirect
437. #1863C2×C73semidirect
438. C73#25159direct (N × H)
509. C2×SD16D4×C73semidirect
560. #103D4×C73semidirect
721. Q8#121×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#460×C732
C2×#449×C732
C2×C4×SD16×C732
C73×#24282
C73×#23412
C73×#20652
C73×#20342
C73×#20332
C73×#20112
C73×#19702
C73×#19232
C73×#18802
C73×#18792
C73×#18632
#2515973