Finite Group Databasebeta

← C73×#22918 #32932322

Subgroups — C73×#22918 #32932322

Order 18688.

942 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C73C211yesmaximal, characteristic
2C73×#2361C211yesmaximal, characteristic
3C73×#2345C211yesmaximal, characteristic, complemented
4C73×#1941C211yesmaximal, characteristic, complemented
5C73×#1934C211yesmaximal, characteristic, complemented
6C73×#1926C211yesmaximal, characteristic, complemented
7C73×#1920C211yesmaximal, characteristic, complemented
8C73×#1919C211yesmaximal, characteristic, complemented
9C73×#1893C211yesmaximal, characteristic
10C73×#1864C211yesmaximal, characteristic, complemented
11C73×#1853C211yesmaximal, characteristic, complemented
12C4×#106×C73C211yesmaximal, characteristic, complemented
13C4×#102×C73C211yesmaximal, characteristic, complemented
14C8×C22⋊C4×C73C211yesmaximal, characteristic, complemented
15C2×#340×C73C211yesmaximal, characteristic, complemented
16C23×C8×C73C2211yescharacteristic
17C2×#121×C73C2211yescharacteristic
18C2×C4×D4×C73—21no—
19C2×C4×D4×C73C2211yescharacteristic
20C22×C4⋊C4×C73C2211yescharacteristic
21C22×C4⋊C4×C73C2211yescharacteristic
22#481×C73C418yescomplemented
23C2×#106×C73C2211yescharacteristic
24C2×#106×C73C2211yescharacteristic
25C2×#106×C73C2211yescharacteristic
26C2×#106×C73C2211yescharacteristic
27C2×#102×C73C2211yescharacteristic
28C2×#102×C73C2211yescharacteristic
29C2×#102×C73C2211yescharacteristic
30C2×#102×C73C2211yescharacteristic
31C2×C22⋊C8×C73C2211yescharacteristic
32C2×C4×C8×C73C2211yescharacteristic
33C2×C4×C8×C73C2211yescharacteristic
34#390×C73C2211yescharacteristic
35#389×C73C2211yescharacteristic
36#389×C73C2211yescharacteristic
37#389×C73C2211yescharacteristic
38#388×C73—21no—
39#387×C73—21no—
40#387×C73—21no—
41#386×C73—21no—
42#385×C73—21no—
43#380×C73—21no—
44#380×C73C2211yescharacteristic
45C4×C4⋊C4×C73C2211yescharacteristic
46C4×C4⋊C4×C73C2211yescharacteristic
47C4×C4⋊C4×C73C2211yescharacteristic
48C4×C22⋊C4×C73—21no—
49C4×C22⋊C4×C73C2211yescharacteristic
50#340×C73C2211yescharacteristic
51#340×C73C2211yescharacteristic
52#340×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60C22×D4×C73—21no—
61C22×D4×C73C2311yescharacteristic
62C23×C4×C73—21no—
63C23×C4×C73—21no—
64C23×C4×C73—21no—
65C23×C4×C73C2311yescharacteristic
66C22×C8×C73—22no—
67C22×C8×C73—22no—
68C22×C8×C73—41no—
69C22×C8×C73C2311yescharacteristic
70C22×C8×C73C2311yescharacteristic
71C22×C8×C73C2311yescharacteristic
72C22×C8×C73C2311yescharacteristic
73#121×C73—22no—
74#121×C73C2×C414yes—
75C4×D4×C73—22no—
76C4×D4×C73—41no—
77C4×D4×C73—44no—
78C2×C4⋊C4×C73—21no—
79C2×C4⋊C4×C73—22no—
80C2×C4⋊C4×C73—22no—
81C2×C4⋊C4×C73—21no—
82C2×C4⋊C4×C73—21no—
83C2×C4⋊C4×C73—21no—
84C2×C4⋊C4×C73—21no—
85C2×C4⋊C4×C73—41no—
86C2×C4⋊C4×C73C2×C414yescomplemented
87C2×C4⋊C4×C73C2311yescharacteristic
88C2×C4⋊C4×C73C2311yescharacteristic
89C2×C4⋊C4×C73C2311yescharacteristic
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73C2311yescharacteristic
92C2×C4⋊C4×C73C2311yescharacteristic
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C22⋊C4×C73—21no—
95C2×C22⋊C4×C73—21no—
96C2×C22⋊C4×C73—21no—
97C2×C22⋊C4×C73—21no—
98C2×C22⋊C4×C73—21no—
99C2×C22⋊C4×C73D411yescharacteristic
100C2×C22⋊C4×C73D411yescharacteristic
101C2×C42×C73—21no—
102C2×C42×C73—21no—
103C2×C42×C73—21no—
104C2×C42×C73C2311yescharacteristic
105C2×C42×C73C2311yescharacteristic
106#106×C73—22no—
107#106×C73—41no—
108#106×C73C2×C414yescomplemented
109#106×C73C2×C414yescomplemented
110#102×C73—22no—
111#102×C73—41no—
112#102×C73C2×C414yescomplemented
113#102×C73C2×C414yescomplemented
114C22⋊C8×C73C2×C414yescomplemented
115C4×C8×C73—22no—
116C4×C8×C73—41no—
117#95×C73—21no—
118#95×C73—21no—
119#95×C73—21no—
120#95×C73—21no—
121#95×C73—21no—
122#95×C73—21no—
123#95×C73—21no—
124#95×C73D411yescharacteristic
125#95×C73D411yescharacteristic
126C24×C73—21no—
127C24×C73C2×D411yescharacteristic
128C2×D4×C73—24no—
129C2×D4×C73—21no—
130C2×D4×C73—21no—
131C2×D4×C73—21no—
132C2×D4×C73—21no—
133C2×D4×C73—21no—
134C2×D4×C73—42no—
135C2×D4×C73—42no—
136C2×D4×C73C22×C412yes—
137C22×C4×C73—21no—
138C22×C4×C73—21no—
139C22×C4×C73—21no—
140C22×C4×C73—21no—
141C22×C4×C73—21no—
142C22×C4×C73—21no—
143C22×C4×C73—21no—
144C22×C4×C73—21no—
145C22×C4×C73—24no—
146C22×C4×C73—21no—
147C22×C4×C73—21no—
148C22×C4×C73—21no—
149C22×C4×C73—42no—
150C22×C4×C73—42no—
151C22×C4×C73—42no—
152C22×C4×C73—42no—
153C22×C4×C73—81no—
154C22×C4×C73—81no—
155C22×C4×C73—81no—
156C22×C4×C73—81no—
157C22×C4×C73C22×C412yes—
158C22×C4×C73C2×D411yescharacteristic
159C22×C4×C73C2×D411yescharacteristic
160C22×C4×C73C2×D411yescharacteristic
161C22×C4×C73C2×D411yescharacteristic
162C22×C4×C73C2×D411yescharacteristic
163C22×C4×C73#4112yes—
164C22×C4×C73C2411yescharacteristic
165C2×C8×C73—21no—
166C2×C8×C73—21no—
167C2×C8×C73—21no—
168C2×C8×C73—21no—
169C2×C8×C73—21no—
170C2×C8×C73—21no—
171C2×C8×C73—21no—
172C2×C8×C73—21no—
173C2×C8×C73—21no—
174C2×C8×C73—44no—
175C2×C8×C73C22×C412yes—
176C2×C8×C73C22×C412yes—
177C2×C8×C73#4112yes—
178C4⋊C4×C73—24no—
179C4⋊C4×C73—21no—
180C4⋊C4×C73—21no—
181C4⋊C4×C73—21no—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—42no—
190C4⋊C4×C73—42no—
191C4⋊C4×C73—81no—
192C4⋊C4×C73—81no—
193C4⋊C4×C73C22×C412yes—
194C4⋊C4×C73C22×C412yes—
195C4⋊C4×C73C22×C412yes—
196C4⋊C4×C73#4112yes—
197C22⋊C4×C73—22no—
198C22⋊C4×C73—24no—
199C22⋊C4×C73—42no—
200C22⋊C4×C73—42no—
201C22⋊C4×C73—42no—
202C22⋊C4×C73—81no—
203C22⋊C4×C73SD1614yes—
204C42×C73—21no—
205C42×C73—21no—
206C42×C73—21no—
207C42×C73—21no—
208C42×C73—42no—
209C42×C73—81no—
210C42×C73—81no—
211C23×C73—21no—
212C23×C73—21no—
213C23×C73—21no—
214C23×C73—21no—
215C23×C73—22no—
216C23×C73—41no—
217C23×C73—41no—
218C23×C73—41no—
219C23×C73—41no—
220C23×C73—41no—
221C23×C73—41no—
222C23×C73C4×D412yes—
223C23×C73C2×SD1612yes—
224C23×C73#13512yes—
225C23×C73C22×D411yescharacteristic
226D4×C73—22no—
227D4×C73—22no—
228D4×C73—48no—
229D4×C73—41no—
230D4×C73—41no—
231C2×C4×C73—21no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—22no—
238C2×C4×C73—22no—
239C2×C4×C73—22no—
240C2×C4×C73—22no—
241C2×C4×C73—22no—
242C2×C4×C73—22no—
243C2×C4×C73—22no—
244C2×C4×C73—21no—
245C2×C4×C73—22no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—41no—
252C2×C4×C73—41no—
253C2×C4×C73—41no—
254C2×C4×C73—41no—
255C2×C4×C73—41no—
256C2×C4×C73—41no—
257C2×C4×C73—41no—
258C2×C4×C73—41no—
259C2×C4×C73—41no—
260C2×C4×C73—41no—
261C2×C4×C73—41no—
262C2×C4×C73—41no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—84no—
269C2×C4×C73—84no—
270C2×C4×C73—84no—
271C2×C4×C73C4×D412yes—
272C2×C4×C73C2×SD1612yes—
273C2×C4×C73C2×SD1612yes—
274C2×C4×C73C23×C411yescharacteristic
275C2×C4×C73C2×#4111yescharacteristic
276C2×C4×C73C2×#4111yescharacteristic
277C2×C4×C73C2×#4111yescharacteristic
278C2×C4×C73H(5,𝔽2)11yescharacteristic
279C2×C4×C732−1+411yescharacteristic
280C8×C73—22no—
281C8×C73—22no—
282C8×C73—22no—
283C8×C73—41no—
284C22×C73—22no—
285C22×C73—22no—
286C22×C73—22no—
287C22×C73—22no—
288C22×C73—22no—
289C22×C73—22no—
290C22×C73—42no—
291C22×C73—42no—
292C22×C73—42no—
293C22×C73—81no—
294C22×C73—81no—
295C22×C73—81no—
296C22×C73—81no—
297C22×C73C4×SD1614yes—
298C22×C73C2×C4×D411yescharacteristic
299C22×C73#54611yescharacteristic
300C22×C73#54711yescharacteristic
301C22×C73C22×SD1611yescharacteristic
302C22×C73C2×#13511yescharacteristic
303C22×C73#57611yescharacteristic
304C22×C73#57711yescharacteristic
305C4×C73—22no—
306C4×C73—22no—
307C4×C73—22no—
308C4×C73—41no—
309C4×C73—42no—
310C4×C73—42no—
311C4×C73—42no—
312C4×C73—42no—
313C4×C73—41no—
314C4×C73—81no—
315C4×C73—81no—
316C4×C73—81no—
317C4×C73C4×#4111yescharacteristic
318C4×C73#52011yescharacteristic
319C4×C73#55111yescharacteristic
320C4×C73#55211yescharacteristic
321#22918C7311yesmaximal, characteristic, direct product factor, Sylow
322C2×C73—24no—
323C2×C73—82no—
324C2×C73#235911yescharacteristic
325C2×C73C2×C4×SD1611yescharacteristic
326C2×C73#294611yescharacteristic
327C2×C73#329511yescharacteristic
328C2×C73#330111yescharacteristic
329C2×C73#333511yescharacteristic
330C2×C73#333911yescharacteristic
331C2×#481C2×C7311yescharacteristic
332#2361C2×C7311yescharacteristic
333#2345C2×C7311yescharacteristic, complemented
334#1941C2×C7311yescharacteristic, complemented
335#1934C2×C7311yescharacteristic, complemented
336#1926C2×C7311yescharacteristic, complemented
337#1920C2×C7311yescharacteristic, complemented
338#1919C2×C7311yescharacteristic, complemented
339#1893C2×C7311yescharacteristic
340#1864C2×C7311yescharacteristic, complemented
341#1853C2×C7311yescharacteristic, complemented
342C4×#106C2×C7311yescharacteristic, complemented
343C4×#102C2×C7311yescharacteristic, complemented
344C8×C22⋊C4C2×C7311yescharacteristic, complemented
345C2×#340C2×C7311yescharacteristic, complemented
346C73#2291811yescharacteristic, direct product factor, Sylow
347C23×C8C22×C7311yescharacteristic
348C2×#121C22×C7311yescharacteristic
349C2×C4×D4—21no—
350C2×C4×D4C22×C7311yescharacteristic
351C22×C4⋊C4C22×C7311yescharacteristic
352C22×C4⋊C4C22×C7311yescharacteristic
353#481C4×C7318yescomplemented
354C2×#106C22×C7311yescharacteristic
355C2×#106C22×C7311yescharacteristic
356C2×#106C22×C7311yescharacteristic
357C2×#106C22×C7311yescharacteristic
358C2×#102C22×C7311yescharacteristic
359C2×#102C22×C7311yescharacteristic
360C2×#102C22×C7311yescharacteristic
361C2×#102C22×C7311yescharacteristic
362C2×C22⋊C8C22×C7311yescharacteristic
363C2×C4×C8C22×C7311yescharacteristic
364C2×C4×C8C22×C7311yescharacteristic
365#390C22×C7311yescharacteristic
366#389C22×C7311yescharacteristic
367#389C22×C7311yescharacteristic
368#389C22×C7311yescharacteristic
369#388—21no—
370#387—21no—
371#387—21no—
372#386—21no—
373#385—21no—
374#380—21no—
375#380C22×C7311yescharacteristic
376C4×C4⋊C4C22×C7311yescharacteristic
377C4×C4⋊C4C22×C7311yescharacteristic
378C4×C4⋊C4C22×C7311yescharacteristic
379C4×C22⋊C4—21no—
380C4×C22⋊C4C22×C7311yescharacteristic
381#340C22×C7311yescharacteristic
382#340C22×C7311yescharacteristic
383#340C22×C7311yescharacteristic
384#340C22×C7311yescharacteristic
385#340C22×C7311yescharacteristic
386#340C22×C7311yescharacteristic
387#340C22×C7311yescharacteristic
388#340C22×C7311yescharacteristic
389#336C22×C7311yescharacteristic
390#336C22×C7311yescharacteristic
391C22×D4—21no—
392C22×D4C23×C7311yescharacteristic
393C23×C4—21no—
394C23×C4—21no—
395C23×C4—21no—
396C23×C4C23×C7311yescharacteristic
397C22×C8—22no—
398C22×C8—22no—
399C22×C8—41no—
400C22×C8C23×C7311yescharacteristic
401C22×C8C23×C7311yescharacteristic
402C22×C8C23×C7311yescharacteristic
403C22×C8C23×C7311yescharacteristic
404#121—22no—
405#121C2×C4×C7314yes—
406C4×D4—22no—
407C4×D4—41no—
408C4×D4—44no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—41no—
417C2×C4⋊C4C2×C4×C7314yescomplemented
418C2×C4⋊C4C23×C7311yescharacteristic
419C2×C4⋊C4C23×C7311yescharacteristic
420C2×C4⋊C4C23×C7311yescharacteristic
421C2×C4⋊C4C23×C7311yescharacteristic
422C2×C4⋊C4C23×C7311yescharacteristic
423C2×C4⋊C4C23×C7311yescharacteristic
424C2×C4⋊C4C23×C7311yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4D4×C7311yescharacteristic
431C2×C22⋊C4D4×C7311yescharacteristic
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42C23×C7311yescharacteristic
436C2×C42C23×C7311yescharacteristic
437#106—22no—
438#106—41no—
439#106C2×C4×C7314yescomplemented
440#106C2×C4×C7314yescomplemented
441#102—22no—
442#102—41no—
443#102C2×C4×C7314yescomplemented
444#102C2×C4×C7314yescomplemented
445C22⋊C8C2×C4×C7314yescomplemented
446C4×C8—22no—
447C4×C8—41no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95D4×C7311yescharacteristic
456#95D4×C7311yescharacteristic
457C24—21no—
458C24C2×D4×C7311yescharacteristic
459C2×D4—24no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4C22×C4×C7312yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—81no—
485C22×C4—81no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4C22×C4×C7312yes—
489C22×C4C2×D4×C7311yescharacteristic
490C22×C4C2×D4×C7311yescharacteristic
491C22×C4C2×D4×C7311yescharacteristic
492C22×C4C2×D4×C7311yescharacteristic
493C22×C4C2×D4×C7311yescharacteristic
494C22×C4#41×C7312yes—
495C22×C4C24×C7311yescharacteristic
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—44no—
506C2×C8C22×C4×C7312yes—
507C2×C8C22×C4×C7312yes—
508C2×C8#41×C7312yes—
509C4⋊C4—24no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—81no—
523C4⋊C4—81no—
524C4⋊C4C22×C4×C7312yes—
525C4⋊C4C22×C4×C7312yes—
526C4⋊C4C22×C4×C7312yes—
527C4⋊C4#41×C7312yes—
528C22⋊C4—22no—
529C22⋊C4—24no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—42no—
533C22⋊C4—81no—
534C22⋊C4SD16×C7314yes—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—42no—
540C42—81no—
541C42—81no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—22no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23C4×D4×C7312yes—
554C23C2×SD16×C7312yes—
555C23#135×C7312yes—
556C23C22×D4×C7311yescharacteristic
557D4—22no—
558D4—22no—
559D4—48no—
560D4—41no—
561D4—41no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—84no—
600C2×C4—84no—
601C2×C4—84no—
602C2×C4C4×D4×C7312yes—
603C2×C4C2×SD16×C7312yes—
604C2×C4C2×SD16×C7312yes—
605C2×C4C23×C4×C7311yescharacteristic
606C2×C4C2×#41×C7311yescharacteristic
607C2×C4C2×#41×C7311yescharacteristic
608C2×C4C2×#41×C7311yescharacteristic
609C2×C4H(5,𝔽2)×C7311yescharacteristic
610C2×C42−1+4×C7311yescharacteristic
611C8—22no—
612C8—22no—
613C8—22no—
614C8—41no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22C4×SD16×C7314yes—
629C22C2×C4×D4×C7311yescharacteristic
630C22#546×C7311yescharacteristic
631C22#547×C7311yescharacteristic
632C22C22×SD16×C7311yescharacteristic
633C22C2×#135×C7311yescharacteristic
634C22#576×C7311yescharacteristic
635C22#577×C7311yescharacteristic
636C4—22no—
637C4—22no—
638C4—22no—
639C4—42no—
640C4—41no—
641C4—41no—
642C4—42no—
643C4—42no—
644C4—42no—
645C4—81no—
646C4—81no—
647C4—81no—
648C4C4×#41×C7311yescharacteristic
649C4#520×C7311yescharacteristic
650C4#551×C7311yescharacteristic
651C4#552×C7311yescharacteristic
652C2—24no—
653C2—82no—
654C2C73×#235911yescharacteristic
655C2C2×C4×SD16×C7311yescharacteristic
656C2C73×#294611yescharacteristic
657C2C73×#329511yescharacteristic
658C2C73×#330111yescharacteristic
659C2C73×#333511yescharacteristic
660C2C73×#333911yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
prime radicalC2×#121×C73C22
LCSG ▷ C2×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
3. C73×#2345C2semidirect
4. C73×#1941C2semidirect
5. C73×#1934C2semidirect
6. C73×#1926C2semidirect
7. C73×#1920C2semidirect
8. C73×#1919C2semidirect
10. C73×#1864C2semidirect
11. C73×#1853C2semidirect
12. C4×#106×C73C2semidirect
13. C4×#102×C73C2semidirect
14. C8×C22⋊C4×C73C2semidirect
15. C2×#340×C73C2semidirect
22. #481×C73C4semidirect
86. C2×C4⋊C4×C73C2×C4semidirect
108. #106×C73C2×C4semidirect
109. #106×C73C2×C4semidirect
112. #102×C73C2×C4semidirect
113. #102×C73C2×C4semidirect
114. C22⋊C8×C73C2×C4semidirect
321. #22918C73direct (N × H)
333. #2345C2×C73semidirect
334. #1941C2×C73semidirect
335. #1934C2×C73semidirect
336. #1926C2×C73semidirect
337. #1920C2×C73semidirect
338. #1919C2×C73semidirect
340. #1864C2×C73semidirect
341. #1853C2×C73semidirect
342. C4×#106C2×C73semidirect
343. C4×#102C2×C73semidirect
344. C8×C22⋊C4C2×C73semidirect
345. C2×#340C2×C73semidirect
346. C73#22918direct (N × H)
353. #481C4×C73semidirect
417. C2×C4⋊C4C2×C4×C73semidirect
439. #106C2×C4×C73semidirect
440. #106C2×C4×C73semidirect
443. #102C2×C4×C73semidirect
444. #102C2×C4×C73semidirect
445. C22⋊C8C2×C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#481×C732
C73×#23612
C73×#23452
C73×#19412
C73×#19342
C73×#19262
C73×#19202
C73×#19192
C73×#18932
C73×#18642
C73×#18532
C4×#106×C732
C4×#102×C732
C8×C22⋊C4×C732
C2×#340×C732
#2291873