Finite Group Databasebeta

← C73×#23975 #32933379

Subgroups — C73×#23975 #32933379

Order 18688.

1326 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C73C211yesmaximal, characteristic, complemented
2C2×#449×C73C211yesmaximal, characteristic, complemented
3C2×#417×C73C211yesmaximal, characteristic, complemented
4C73×#2407C211yesmaximal, characteristic, complemented
5C73×#2026C211yesmaximal, characteristic, complemented
6C73×#2025C211yesmaximal, characteristic, complemented
7C73×#2000C211yesmaximal, characteristic, complemented
8C73×#1999C211yesmaximal, characteristic, complemented
9C73×#1895C211yesmaximal, characteristic, complemented
10C73×#1879C211yesmaximal, characteristic, complemented
11C73×#1877C211yesmaximal, characteristic, complemented
12C73×#1875C211yesmaximal, characteristic, complemented
13C73×#1873C211yesmaximal, characteristic, complemented
14C73×#1870C211yesmaximal, characteristic, complemented
15C73×#1823C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×D8×C73C2211yescharacteristic
19C22×M16×C73C2211yescharacteristic
20#553×C73—24no—
21#553×C73—24no—
22C2×#126×C73—21no—
23C2×#125×C73C2211yescharacteristic
24C2×#123×C73—21no—
25C2×C22⋊Q8×C73C2211yescharacteristic
26C2×#121×C73—21no—
27C2×#121×C73C2211yescharacteristic
28C2×#121×C73C2211yescharacteristic
29C2×#121×C73C2211yescharacteristic
30C2×C4×D4×C73—21no—
31C2×C4×D4×C73C2211yescharacteristic
32C2×C4×D4×C73C2211yescharacteristic
33C2×#117×C73C2211yescharacteristic
34C22×C4⋊C4×C73C2211yescharacteristic
35#449×C73—24no—
36#417×C73—24no—
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#103×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44C2×#102×C73C2211yescharacteristic
45C2×C22⋊C8×C73C2211yescharacteristic
46C2×C22⋊C8×C73C2211yescharacteristic
47C2×C22⋊C8×C73C2211yescharacteristic
48#394×C73—21no—
49#392×C73—21no—
50#391×C73C2211yescharacteristic
51#390×C73C2211yescharacteristic
52#386×C73—21no—
53#385×C73—21no—
54#380×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×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×C73D411yescharacteristic
75C22×D4×C73C2311yescharacteristic
76C22×D4×C73C2311yescharacteristic
77C23×C4×C73—21no—
78C23×C4×C73—21no—
79C23×C4×C73—21no—
80C23×C4×C73C2311yescharacteristic
81C23×C4×C73C2311yescharacteristic
82C2×SD16×C73—22no—
83C2×SD16×C73—22no—
84C2×SD16×C73—41no—
85C2×D8×C73—22no—
86C2×D8×C73—22no—
87C2×D8×C73—41no—
88C2×M16×C73—22no—
89C2×M16×C73—41no—
90C2×M16×C73—41no—
91C22×C8×C73C2311yescharacteristic
92C22×C8×C73C2311yescharacteristic
93C22×C8×C73C2311yescharacteristic
94C22×C8×C73C2311yescharacteristic
95#126×C73—28no—
96#125×C73—22no—
97#125×C73—22no—
98#123×C73—28no—
99C22⋊Q8×C73—22no—
100C22⋊Q8×C73—41no—
101#121×C73—28no—
102#121×C73—22no—
103#121×C73—22no—
104#121×C73—22no—
105#121×C73—22no—
106#121×C73—41no—
107#121×C73D414yescomplemented
108C4×D4×C73—28no—
109C4×D4×C73—22no—
110C4×D4×C73—22no—
111C4×D4×C73—22no—
112C4×D4×C73—22no—
113#117×C73—22no—
114#117×C73—22no—
115C2×C4⋊C4×C73—21no—
116C2×C4⋊C4×C73—22no—
117C2×C4⋊C4×C73—21no—
118C2×C4⋊C4×C73—21no—
119C2×C4⋊C4×C73—21no—
120C2×C4⋊C4×C73D411yescharacteristic
121C2×C4⋊C4×C73D414yescomplemented
122C2×C4⋊C4×C73C2311yescharacteristic
123C2×C4⋊C4×C73C2311yescharacteristic
124C2×C4⋊C4×C73C2311yescharacteristic
125C2×C4⋊C4×C73C2311yescharacteristic
126C2×C4⋊C4×C73C2311yescharacteristic
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—21no—
130C2×C22⋊C4×C73—21no—
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—21no—
133C2×C22⋊C4×C73—21no—
134C2×C22⋊C4×C73—21no—
135C2×C22⋊C4×C73—21no—
136C2×C22⋊C4×C73D411yescharacteristic
137C2×C22⋊C4×C73D411yescharacteristic
138C2×C42×C73—21no—
139C2×C42×C73C2311yescharacteristic
140#103×C73—22no—
141#103×C73—22no—
142#103×C73—22no—
143#102×C73—22no—
144#102×C73—22no—
145#102×C73—22no—
146#102×C73—41no—
147#102×C73—41no—
148C22⋊C8×C73—22no—
149C22⋊C8×C73—41no—
150C22⋊C8×C73—41no—
151#95×C73—21no—
152#95×C73—21no—
153#95×C73—21no—
154C24×C73—21no—
155C24×C73—21no—
156C24×C73C2×D411yescharacteristic
157C24×C73C2×D411yescharacteristic
158#41×C73—28no—
159#41×C73—44no—
160#41×C73—44no—
161#41×C73—44no—
162C2×Q8×C73—21no—
163C2×Q8×C73—21no—
164C2×Q8×C73—21no—
165C2×Q8×C73—21no—
166C2×Q8×C73—21no—
167C2×Q8×C73#4112yes—
168C2×D4×C73—22no—
169C2×D4×C73—24no—
170C2×D4×C73—24no—
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—41no—
182C2×D4×C73—41no—
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—81no—
191C2×D4×C73—81no—
192C2×D4×C73—81no—
193C2×D4×C73C2×D412yes—
194C2×D4×C73#4112yes—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—24no—
204C22×C4×C73—24no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—42no—
214C22×C4×C73—42no—
215C22×C4×C73—42no—
216C22×C4×C73—81no—
217C22×C4×C73—81no—
218C22×C4×C73—81no—
219C22×C4×C73—81no—
220C22×C4×C73C2×D411yescharacteristic
221C22×C4×C73C2×D411yescharacteristic
222C22×C4×C73C2×D411yescharacteristic
223C22×C4×C73C2×D411yescharacteristic
224C22×C4×C73C2×D412yes—
225C22×C4×C73C2×D412yes—
226C22×C4×C73C2411yescharacteristic
227SD16×C73—44no—
228D8×C73—44no—
229M16×C73—44no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
237C2×C8×C73—21no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
240C2×C8×C73—21no—
241C2×C8×C73—21no—
242C4⋊C4×C73—24no—
243C4⋊C4×C73—24no—
244C4⋊C4×C73—24no—
245C4⋊C4×C73—22no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73—21no—
248C4⋊C4×C73—21no—
249C4⋊C4×C73—21no—
250C4⋊C4×C73—21no—
251C4⋊C4×C73—21no—
252C4⋊C4×C73—21no—
253C4⋊C4×C73—42no—
254C4⋊C4×C73C2×D412yes—
255C4⋊C4×C73C2×D412yes—
256C4⋊C4×C73C2×D412yes—
257C22⋊C4×C73—24no—
258C22⋊C4×C73—24no—
259C22⋊C4×C73—24no—
260C22⋊C4×C73—22no—
261C22⋊C4×C73—24no—
262C22⋊C4×C73—22no—
263C22⋊C4×C73—42no—
264C22⋊C4×C73—42no—
265C22⋊C4×C73—42no—
266C22⋊C4×C73—81no—
267C22⋊C4×C73—81no—
268C42×C73—24no—
269C42×C73—21no—
270C42×C73—21no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—21no—
274C23×C73—21no—
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—22no—
279C23×C73—21no—
280C23×C73—22no—
281C23×C73—21no—
282C23×C73—21no—
283C23×C73—21no—
284C23×C73—21no—
285C23×C73—21no—
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×C73—41no—
295C23×C73—41no—
296C23×C73—41no—
297C23×C73—41no—
298C23×C73#12012yes—
299C23×C73C22×D411yescharacteristic
300Q8×C73—22no—
301Q8×C73—22no—
302Q8×C73—41no—
303Q8×C73—41no—
304D4×C73—22no—
305D4×C73—22no—
306D4×C73—22no—
307D4×C73—22no—
308D4×C73—44no—
309D4×C73—48no—
310D4×C73—48no—
311D4×C73—41no—
312D4×C73—41no—
313D4×C73—41no—
314D4×C73—41no—
315D4×C73—84no—
316D4×C73—84no—
317C2×C4×C73—21no—
318C2×C4×C73—21no—
319C2×C4×C73—22no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—22no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—22no—
326C2×C4×C73—21no—
327C2×C4×C73—22no—
328C2×C4×C73—22no—
329C2×C4×C73—21no—
330C2×C4×C73—22no—
331C2×C4×C73—21no—
332C2×C4×C73—21no—
333C2×C4×C73—21no—
334C2×C4×C73—21no—
335C2×C4×C73—21no—
336C2×C4×C73—48no—
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—41no—
350C2×C4×C73—41no—
351C2×C4×C73—41no—
352C2×C4×C73—41no—
353C2×C4×C73—41no—
354C2×C4×C73—41no—
355C2×C4×C73—84no—
356C2×C4×C73—84no—
357C2×C4×C73#12012yes—
358C2×C4×C73C22×D411yescharacteristic
359C2×C4×C73C22×D411yescharacteristic
360C2×C4×C73C2×#4111yescharacteristic
361C2×C4×C73C2×#4111yescharacteristic
362C2×C4×C73H(5,𝔽2)11yescharacteristic
363C2×C4×C73H(5,𝔽2)11yescharacteristic
364C8×C73—41no—
365C8×C73—41no—
366C8×C73—41no—
367C8×C73—41no—
368C22×C73—22no—
369C22×C73—22no—
370C22×C73—22no—
371C22×C73—41no—
372C22×C73—41no—
373C22×C73—41no—
374C22×C73—41no—
375C22×C73—42no—
376C22×C73—41no—
377C22×C73—42no—
378C22×C73—41no—
379C22×C73—42no—
380C22×C73—42no—
381C22×C73—41no—
382C22×C73—41no—
383C22×C73—42no—
384C22×C73—41no—
385C22×C73—41no—
386C22×C73—42no—
387C22×C73—41no—
388C22×C73—81no—
389C22×C73—81no—
390C22×C73—81no—
391C22×C73—81no—
392C22×C73—81no—
393C22×C73—81no—
394C22×C73—81no—
395C22×C73—81no—
396C22×C73C2×#12011yescharacteristic
397C22×C73#54611yescharacteristic
398C22×C73#54611yescharacteristic
399C22×C73#57511yescharacteristic
400C22×C73#57511yescharacteristic
401C22×C73#57611yescharacteristic
402C22×C73#57711yescharacteristic
403C4×C73—22no—
404C4×C73—41no—
405C4×C73—42no—
406C4×C73—41no—
407C4×C73—42no—
408C4×C73—41no—
409C4×C73—42no—
410C4×C73—42no—
411C4×C73—81no—
412C4×C73—81no—
413C4×C73#52511yescharacteristic
414C4×C73#53511yescharacteristic
415C4×C73#54611yescharacteristic
416C4×C73#54611yescharacteristic
417#23975C7311yesmaximal, characteristic, direct product factor, Sylow
418C2×C73—42no—
419C2×C73—81no—
420C2×C73—82no—
421C2×C73—82no—
422C2×C73#240411yescharacteristic
423C2×C73#300511yescharacteristic
424C2×C73#301211yescharacteristic
425C2×C73#330711yescharacteristic
426C2×C73#330911yescharacteristic
427C2×C73#332211yescharacteristic
428C2×C73#332611yescharacteristic
429C2×#553C2×C7311yescharacteristic, complemented
430C2×#449C2×C7311yescharacteristic, complemented
431C2×#417C2×C7311yescharacteristic, complemented
432#2407C2×C7311yescharacteristic, complemented
433#2026C2×C7311yescharacteristic, complemented
434#2025C2×C7311yescharacteristic, complemented
435#2000C2×C7311yescharacteristic, complemented
436#1999C2×C7311yescharacteristic, complemented
437#1895C2×C7311yescharacteristic, complemented
438#1879C2×C7311yescharacteristic, complemented
439#1877C2×C7311yescharacteristic, complemented
440#1875C2×C7311yescharacteristic, complemented
441#1873C2×C7311yescharacteristic, complemented
442#1870C2×C7311yescharacteristic, complemented
443#1823C2×C7311yescharacteristic, complemented
444C73#2397511yescharacteristic, direct product factor, Sylow
445C22×#41C22×C7311yescharacteristic
446C22×SD16C22×C7311yescharacteristic
447C22×D8C22×C7311yescharacteristic
448C22×M16C22×C7311yescharacteristic
449#553—24no—
450#553—24no—
451C2×#126—21no—
452C2×#125C22×C7311yescharacteristic
453C2×#123—21no—
454C2×C22⋊Q8C22×C7311yescharacteristic
455C2×#121—21no—
456C2×#121C22×C7311yescharacteristic
457C2×#121C22×C7311yescharacteristic
458C2×#121C22×C7311yescharacteristic
459C2×C4×D4—21no—
460C2×C4×D4C22×C7311yescharacteristic
461C2×C4×D4C22×C7311yescharacteristic
462C2×#117C22×C7311yescharacteristic
463C22×C4⋊C4C22×C7311yescharacteristic
464#449—24no—
465#417—24no—
466C2×#103C22×C7311yescharacteristic
467C2×#103C22×C7311yescharacteristic
468C2×#103C22×C7311yescharacteristic
469C2×#102C22×C7311yescharacteristic
470C2×#102C22×C7311yescharacteristic
471C2×#102C22×C7311yescharacteristic
472C2×#102C22×C7311yescharacteristic
473C2×#102C22×C7311yescharacteristic
474C2×C22⋊C8C22×C7311yescharacteristic
475C2×C22⋊C8C22×C7311yescharacteristic
476C2×C22⋊C8C22×C7311yescharacteristic
477#394—21no—
478#392—21no—
479#391C22×C7311yescharacteristic
480#390C22×C7311yescharacteristic
481#386—21no—
482#385—21no—
483#380C22×C7311yescharacteristic
484#340C22×C7311yescharacteristic
485#340C22×C7311yescharacteristic
486#340C22×C7311yescharacteristic
487#340C22×C7311yescharacteristic
488#340C22×C7311yescharacteristic
489#340C22×C7311yescharacteristic
490#336C22×C7311yescharacteristic
491#336C22×C7311yescharacteristic
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C22×Q8C23×C7311yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4D4×C7311yescharacteristic
504C22×D4C23×C7311yescharacteristic
505C22×D4C23×C7311yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C23×C7311yescharacteristic
510C23×C4C23×C7311yescharacteristic
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—41no—
517C2×M16—22no—
518C2×M16—41no—
519C2×M16—41no—
520C22×C8C23×C7311yescharacteristic
521C22×C8C23×C7311yescharacteristic
522C22×C8C23×C7311yescharacteristic
523C22×C8C23×C7311yescharacteristic
524#126—28no—
525#125—22no—
526#125—22no—
527#123—28no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—28no—
531#121—22no—
532#121—22no—
533#121—22no—
534#121—22no—
535#121—41no—
536#121D4×C7314yescomplemented
537C4×D4—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4D4×C7311yescharacteristic
550C2×C4⋊C4D4×C7314yescomplemented
551C2×C4⋊C4C23×C7311yescharacteristic
552C2×C4⋊C4C23×C7311yescharacteristic
553C2×C4⋊C4C23×C7311yescharacteristic
554C2×C4⋊C4C23×C7311yescharacteristic
555C2×C4⋊C4C23×C7311yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4D4×C7311yescharacteristic
566C2×C22⋊C4D4×C7311yescharacteristic
567C2×C42—21no—
568C2×C42C23×C7311yescharacteristic
569#103—22no—
570#103—22no—
571#103—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—41no—
576#102—41no—
577C22⋊C8—22no—
578C22⋊C8—41no—
579C22⋊C8—41no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—21no—
584C24—21no—
585C24C2×D4×C7311yescharacteristic
586C24C2×D4×C7311yescharacteristic
587#41—28no—
588#41—44no—
589#41—44no—
590#41—44no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8#41×C7312yes—
597C2×D4—22no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4C2×D4×C7312yes—
623C2×D4#41×C7312yes—
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—24no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4—81no—
649C22×C4C2×D4×C7311yescharacteristic
650C22×C4C2×D4×C7311yescharacteristic
651C22×C4C2×D4×C7311yescharacteristic
652C22×C4C2×D4×C7311yescharacteristic
653C22×C4C2×D4×C7312yes—
654C22×C4C2×D4×C7312yes—
655C22×C4C24×C7311yescharacteristic
656SD16—44no—
657D8—44no—
658M16—44no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—22no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—42no—
683C4⋊C4C2×D4×C7312yes—
684C4⋊C4C2×D4×C7312yes—
685C4⋊C4C2×D4×C7312yes—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—22no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—81no—
696C22⋊C4—81no—
697C42—24no—
698C42—21no—
699C42—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23#120×C7312yes—
728C23C22×D4×C7311yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—41no—
732Q8—41no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—44no—
738D4—48no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—84no—
745D4—84no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—48no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4#120×C7312yes—
787C2×C4C22×D4×C7311yescharacteristic
788C2×C4C22×D4×C7311yescharacteristic
789C2×C4C2×#41×C7311yescharacteristic
790C2×C4C2×#41×C7311yescharacteristic
791C2×C4H(5,𝔽2)×C7311yescharacteristic
792C2×C4H(5,𝔽2)×C7311yescharacteristic
793C8—41no—
794C8—41no—
795C8—41no—
796C8—41no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—42no—
806C22—42no—
807C22—41no—
808C22—41no—
809C22—42no—
810C22—41no—
811C22—41no—
812C22—42no—
813C22—41no—
814C22—42no—
815C22—41no—
816C22—42no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22C2×#120×C7311yescharacteristic
826C22#546×C7311yescharacteristic
827C22#546×C7311yescharacteristic
828C22#575×C7311yescharacteristic
829C22#575×C7311yescharacteristic
830C22#576×C7311yescharacteristic
831C22#577×C7311yescharacteristic
832C4—22no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—42no—
837C4—42no—
838C4—41no—
839C4—42no—
840C4—81no—
841C4—81no—
842C4#525×C7311yescharacteristic
843C4#535×C7311yescharacteristic
844C4#546×C7311yescharacteristic
845C4#546×C7311yescharacteristic
846C2—42no—
847C2—81no—
848C2—82no—
849C2—82no—
850C2C73×#240411yescharacteristic
851C2C73×#300511yescharacteristic
852C2C73×#301211yescharacteristic
853C2C73×#330711yescharacteristic
854C2C73×#330911yescharacteristic
855C2C73×#332211yescharacteristic
856C2C73×#332611yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C4×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#553×C73C2semidirect
2. C2×#449×C73C2semidirect
3. C2×#417×C73C2semidirect
4. C73×#2407C2semidirect
5. C73×#2026C2semidirect
6. C73×#2025C2semidirect
7. C73×#2000C2semidirect
8. C73×#1999C2semidirect
9. C73×#1895C2semidirect
10. C73×#1879C2semidirect
11. C73×#1877C2semidirect
12. C73×#1875C2semidirect
13. C73×#1873C2semidirect
14. C73×#1870C2semidirect
15. C73×#1823C2semidirect
107. #121×C73D4semidirect
121. C2×C4⋊C4×C73D4semidirect
417. #23975C73direct (N × H)
429. C2×#553C2×C73semidirect
430. C2×#449C2×C73semidirect
431. C2×#417C2×C73semidirect
432. #2407C2×C73semidirect
433. #2026C2×C73semidirect
434. #2025C2×C73semidirect
435. #2000C2×C73semidirect
436. #1999C2×C73semidirect
437. #1895C2×C73semidirect
438. #1879C2×C73semidirect
439. #1877C2×C73semidirect
440. #1875C2×C73semidirect
441. #1873C2×C73semidirect
442. #1870C2×C73semidirect
443. #1823C2×C73semidirect
444. C73#23975direct (N × H)
536. #121D4×C73semidirect
550. C2×C4⋊C4D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C732
C2×#449×C732
C2×#417×C732
C73×#24072
C73×#20262
C73×#20252
C73×#20002
C73×#19992
C73×#18952
C73×#18792
C73×#18772
C73×#18752
C73×#18732
C73×#18702
C73×#18232
#2397573