Finite Group Databasebeta

← C73×#26354 #32935758

Subgroups — C73×#26354 #32935758

Order 18688.

904 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#476×C73C211yesmaximal, characteristic, complemented
2C2×#428×C73C211yesmaximal, characteristic, complemented
3C73×#2439C211yesmaximal, characteristic, complemented
4C73×#2361C211yesmaximal, characteristic
5C73×#2092C211yesmaximal, characteristic, complemented
6C73×#2086C211yesmaximal, characteristic, complemented
7C73×#2065C211yesmaximal, characteristic, complemented
8C73×#2058C211yesmaximal, characteristic, complemented
9C73×#1949C211yesmaximal, characteristic, complemented
10C73×#1919C211yesmaximal, characteristic, complemented
11C73×#1895C211yesmaximal, characteristic
12C73×#1875C211yesmaximal, characteristic
13C73×#1862C211yesmaximal, characteristic, complemented
14C73×#1853C211yesmaximal, characteristic, complemented
15C73×#1851C211yesmaximal, characteristic, complemented
16C22×M16×C73C2211yescharacteristic
17C2×C4⋊Q8×C73C2211yescharacteristic
18C2×#121×C73C2211yescharacteristic
19C2×C4×D4×C73—21no—
20C2×C4×D4×C73C2211yescharacteristic
21C2×#117×C73C2211yescharacteristic
22C22×C4⋊C4×C73C2211yescharacteristic
23#476×C73—24no—
24#428×C73—24no—
25C2×#107×C73C2211yescharacteristic
26C2×#107×C73C2211yescharacteristic
27C2×#106×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29C2×#106×C73C2211yescharacteristic
30C2×#106×C73C2211yescharacteristic
31C2×C4⋊C8×C73C2211yescharacteristic
32C2×C4⋊C8×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38#396×C73—21no—
39#393×C73—21no—
40#391×C73—21no—
41#390×C73C2211yescharacteristic
42#389×C73C2211yescharacteristic
43#389×C73C2211yescharacteristic
44#389×C73C2211yescharacteristic
45#388×C73—21no—
46#387×C73—21no—
47#386×C73—21no—
48#385×C73—21no—
49#382×C73C2211yescharacteristic
50#380×C73C2211yescharacteristic
51C4×C4⋊C4×C73C2211yescharacteristic
52C4×C22⋊C4×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73—21no—
62C22×D4×C73—21no—
63C22×D4×C73C2311yescharacteristic
64C23×C4×C73—21no—
65C23×C4×C73—21no—
66C23×C4×C73C2311yescharacteristic
67C2×M16×C73—22no—
68C2×M16×C73—22no—
69C2×M16×C73—22no—
70C22×C8×C73C2311yescharacteristic
71C22×C8×C73C2311yescharacteristic
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C4⋊Q8×C73—22no—
75C4⋊Q8×C73—41no—
76#121×C73—22no—
77#121×C73Q814yescomplemented
78C4×D4×C73—22no—
79C4×D4×C73—41no—
80C4×D4×C73—44no—
81#117×C73—22no—
82#117×C73—41no—
83C2×C4⋊C4×C73—22no—
84C2×C4⋊C4×C73—21no—
85C2×C4⋊C4×C73—21no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73—41no—
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73C2311yescharacteristic
92C2×C4⋊C4×C73C2311yescharacteristic
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73C2311yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C22⋊C4×C73—21no—
98C2×C22⋊C4×C73—21no—
99C2×C22⋊C4×C73—21no—
100C2×C22⋊C4×C73—21no—
101C2×C22⋊C4×C73—21no—
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73D411yescharacteristic
104C2×C22⋊C4×C73D411yescharacteristic
105C2×C42×C73—21no—
106C2×C42×C73—21no—
107C2×C42×C73C2311yescharacteristic
108C2×C42×C73C2311yescharacteristic
109#107×C73—22no—
110#107×C73—22no—
111#106×C73—22no—
112#106×C73—22no—
113#106×C73—41no—
114#106×C73D414yescomplemented
115C4⋊C8×C73—22no—
116C4⋊C8×C73—22no—
117#102×C73—22no—
118#102×C73—22no—
119#102×C73—22no—
120#102×C73—41no—
121C22⋊C8×C73—22no—
122#95×C73—21no—
123#95×C73—21no—
124#95×C73—21no—
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73D411yescharacteristic
130#95×C73D411yescharacteristic
131C24×C73—21no—
132C24×C73C2×D411yescharacteristic
133C2×Q8×C73—42no—
134C2×Q8×C73—42no—
135C2×Q8×C73—81no—
136C2×D4×C73—24no—
137C2×D4×C73—21no—
138C2×D4×C73—21no—
139C2×D4×C73—21no—
140C2×D4×C73—21no—
141C2×D4×C73—21no—
142C2×D4×C73—42no—
143C2×D4×C73—42no—
144C2×D4×C73C2×Q812yes—
145C22×C4×C73—21no—
146C22×C4×C73—21no—
147C22×C4×C73—21no—
148C22×C4×C73—21no—
149C22×C4×C73—21no—
150C22×C4×C73—21no—
151C22×C4×C73—21no—
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—42no—
157C22×C4×C73—42no—
158C22×C4×C73—42no—
159C22×C4×C73—42no—
160C22×C4×C73—81no—
161C22×C4×C73—81no—
162C22×C4×C73C2×D411yescharacteristic
163C22×C4×C73C2×D411yescharacteristic
164C22×C4×C73C2×D411yescharacteristic
165C22×C4×C73C2×D411yescharacteristic
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73C2×Q812yes—
168C22×C4×C73#4112yes—
169C22×C4×C73C2411yescharacteristic
170M16×C73—28no—
171C2×C8×C73—21no—
172C2×C8×C73—21no—
173C2×C8×C73—21no—
174C2×C8×C73—21no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73C2×D412yes—
182C2×C8×C73#4112yes—
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—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—42no—
195C4⋊C4×C73—42no—
196C4⋊C4×C73—42no—
197C4⋊C4×C73—42no—
198C4⋊C4×C73—81no—
199C4⋊C4×C73C2×D412yes—
200C4⋊C4×C73C2×D412yes—
201C4⋊C4×C73C2×Q812yes—
202C22⋊C4×C73—24no—
203C22⋊C4×C73—22no—
204C22⋊C4×C73—41no—
205C22⋊C4×C73—42no—
206C22⋊C4×C73—42no—
207C22⋊C4×C73—42no—
208C22⋊C4×C73—81no—
209C22⋊C4×C73—81no—
210C42×C73—21no—
211C42×C73—21no—
212C42×C73—21no—
213C42×C73—21no—
214C42×C73—42no—
215C42×C73—42no—
216C23×C73—21no—
217C23×C73—21no—
218C23×C73—21no—
219C23×C73—21no—
220C23×C73—21no—
221C23×C73—21no—
222C23×C73—22no—
223C23×C73—41no—
224C23×C73—41no—
225C23×C73—41no—
226C23×C73—41no—
227C23×C73—41no—
228C23×C73—41no—
229C23×C73C22⋊Q812yes—
230C23×C73C22×D411yescharacteristic
231Q8×C73—84no—
232D4×C73—22no—
233D4×C73—22no—
234D4×C73—48no—
235D4×C73—41no—
236D4×C73—41no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—22no—
242C2×C4×C73—22no—
243C2×C4×C73—22no—
244C2×C4×C73—22no—
245C2×C4×C73—22no—
246C2×C4×C73—21no—
247C2×C4×C73—22no—
248C2×C4×C73—22no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
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—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—84no—
276C2×C4×C73—84no—
277C2×C4×C73C22⋊Q812yes—
278C2×C4×C73AGL(1,ℤ/8)12yes—
279C2×C4×C73C22×D411yescharacteristic
280C2×C4×C73C22×Q811yescharacteristic
281C2×C4×C73C2×#4111yescharacteristic
282C2×C4×C73C2×#4111yescharacteristic
283C2×C4×C73H(5,𝔽2)11yescharacteristic
284C2×C4×C732−1+411yescharacteristic
285C8×C73—22no—
286C8×C73—22no—
287C8×C73—41no—
288C8×C73—41no—
289C22×C73—22no—
290C22×C73—22no—
291C22×C73—22no—
292C22×C73—41no—
293C22×C73—41no—
294C22×C73—41no—
295C22×C73—41no—
296C22×C73—42no—
297C22×C73—42no—
298C22×C73—42no—
299C22×C73—81no—
300C22×C73—81no—
301C22×C73—81no—
302C22×C73—81no—
303C22×C73C2×C22⋊Q811yescharacteristic
304C22×C73D4211yescharacteristic
305C22×C73#54711yescharacteristic
306C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C73#57511yescharacteristic
308C22×C73#57711yescharacteristic
309C22×C73#57711yescharacteristic
310C4×C73—22no—
311C4×C73—22no—
312C4×C73—42no—
313C4×C73—41no—
314C4×C73—41no—
315C4×C73—42no—
316C4×C73—41no—
317C4×C73—42no—
318C4×C73—81no—
319C4×C73—81no—
320C4×C73—81no—
321C4×C73—81no—
322C4×C73#52511yescharacteristic
323C4×C73#53911yescharacteristic
324C4×C73D4×Q811yescharacteristic
325C4×C73#55411yescharacteristic
326#26354C7311yesmaximal, characteristic, direct product factor, Sylow
327C2×C73—42no—
328C2×C73—82no—
329C2×C73#244911yescharacteristic
330C2×C73#307711yescharacteristic
331C2×C73#308411yescharacteristic
332C2×C73#326511yescharacteristic
333C2×C73#327511yescharacteristic
334C2×C73#335011yescharacteristic
335C2×C73#335411yescharacteristic
336C2×#476C2×C7311yescharacteristic, complemented
337C2×#428C2×C7311yescharacteristic, complemented
338#2439C2×C7311yescharacteristic, complemented
339#2361C2×C7311yescharacteristic
340#2092C2×C7311yescharacteristic, complemented
341#2086C2×C7311yescharacteristic, complemented
342#2065C2×C7311yescharacteristic, complemented
343#2058C2×C7311yescharacteristic, complemented
344#1949C2×C7311yescharacteristic, complemented
345#1919C2×C7311yescharacteristic, complemented
346#1895C2×C7311yescharacteristic
347#1875C2×C7311yescharacteristic
348#1862C2×C7311yescharacteristic, complemented
349#1853C2×C7311yescharacteristic, complemented
350#1851C2×C7311yescharacteristic, complemented
351C73#2635411yescharacteristic, direct product factor, Sylow
352C22×M16C22×C7311yescharacteristic
353C2×C4⋊Q8C22×C7311yescharacteristic
354C2×#121C22×C7311yescharacteristic
355C2×C4×D4—21no—
356C2×C4×D4C22×C7311yescharacteristic
357C2×#117C22×C7311yescharacteristic
358C22×C4⋊C4C22×C7311yescharacteristic
359#476—24no—
360#428—24no—
361C2×#107C22×C7311yescharacteristic
362C2×#107C22×C7311yescharacteristic
363C2×#106C22×C7311yescharacteristic
364C2×#106C22×C7311yescharacteristic
365C2×#106C22×C7311yescharacteristic
366C2×#106C22×C7311yescharacteristic
367C2×C4⋊C8C22×C7311yescharacteristic
368C2×C4⋊C8C22×C7311yescharacteristic
369C2×#102C22×C7311yescharacteristic
370C2×#102C22×C7311yescharacteristic
371C2×#102C22×C7311yescharacteristic
372C2×#102C22×C7311yescharacteristic
373C2×C22⋊C8C22×C7311yescharacteristic
374#396—21no—
375#393—21no—
376#391—21no—
377#390C22×C7311yescharacteristic
378#389C22×C7311yescharacteristic
379#389C22×C7311yescharacteristic
380#389C22×C7311yescharacteristic
381#388—21no—
382#387—21no—
383#386—21no—
384#385—21no—
385#382C22×C7311yescharacteristic
386#380C22×C7311yescharacteristic
387C4×C4⋊C4C22×C7311yescharacteristic
388C4×C22⋊C4C22×C7311yescharacteristic
389#340C22×C7311yescharacteristic
390#340C22×C7311yescharacteristic
391#340C22×C7311yescharacteristic
392#340C22×C7311yescharacteristic
393#340C22×C7311yescharacteristic
394#340C22×C7311yescharacteristic
395#336C22×C7311yescharacteristic
396#336C22×C7311yescharacteristic
397C22×Q8—21no—
398C22×D4—21no—
399C22×D4C23×C7311yescharacteristic
400C23×C4—21no—
401C23×C4—21no—
402C23×C4C23×C7311yescharacteristic
403C2×M16—22no—
404C2×M16—22no—
405C2×M16—22no—
406C22×C8C23×C7311yescharacteristic
407C22×C8C23×C7311yescharacteristic
408C22×C8C23×C7311yescharacteristic
409C22×C8C23×C7311yescharacteristic
410C4⋊Q8—22no—
411C4⋊Q8—41no—
412#121—22no—
413#121Q8×C7314yescomplemented
414C4×D4—22no—
415C4×D4—41no—
416C4×D4—44no—
417#117—22no—
418#117—41no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—41no—
426C2×C4⋊C4C23×C7311yescharacteristic
427C2×C4⋊C4C23×C7311yescharacteristic
428C2×C4⋊C4C23×C7311yescharacteristic
429C2×C4⋊C4C23×C7311yescharacteristic
430C2×C4⋊C4C23×C7311yescharacteristic
431C2×C4⋊C4C23×C7311yescharacteristic
432C2×C4⋊C4C23×C7311yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4D4×C7311yescharacteristic
440C2×C22⋊C4D4×C7311yescharacteristic
441C2×C42—21no—
442C2×C42—21no—
443C2×C42C23×C7311yescharacteristic
444C2×C42C23×C7311yescharacteristic
445#107—22no—
446#107—22no—
447#106—22no—
448#106—22no—
449#106—41no—
450#106D4×C7314yescomplemented
451C4⋊C8—22no—
452C4⋊C8—22no—
453#102—22no—
454#102—22no—
455#102—22no—
456#102—41no—
457C22⋊C8—22no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95D4×C7311yescharacteristic
466#95D4×C7311yescharacteristic
467C24—21no—
468C24C2×D4×C7311yescharacteristic
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—81no—
472C2×D4—24no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4C2×Q8×C7312yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4C2×D4×C7311yescharacteristic
499C22×C4C2×D4×C7311yescharacteristic
500C22×C4C2×D4×C7311yescharacteristic
501C22×C4C2×D4×C7311yescharacteristic
502C22×C4C2×D4×C7311yescharacteristic
503C22×C4C2×Q8×C7312yes—
504C22×C4#41×C7312yes—
505C22×C4C24×C7311yescharacteristic
506M16—28no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8C2×D4×C7312yes—
518C2×C8#41×C7312yes—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—81no—
535C4⋊C4C2×D4×C7312yes—
536C4⋊C4C2×D4×C7312yes—
537C4⋊C4C2×Q8×C7312yes—
538C22⋊C4—24no—
539C22⋊C4—22no—
540C22⋊C4—41no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—81no—
545C22⋊C4—81no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—42no—
551C42—42no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—22no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23C22⋊Q8×C7312yes—
566C23C22×D4×C7311yescharacteristic
567Q8—84no—
568D4—22no—
569D4—22no—
570D4—48no—
571D4—41no—
572D4—41no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—84no—
612C2×C4—84no—
613C2×C4C22⋊Q8×C7312yes—
614C2×C4AGL(1,ℤ/8)×C7312yes—
615C2×C4C22×D4×C7311yescharacteristic
616C2×C4C22×Q8×C7311yescharacteristic
617C2×C4C2×#41×C7311yescharacteristic
618C2×C4C2×#41×C7311yescharacteristic
619C2×C4H(5,𝔽2)×C7311yescharacteristic
620C2×C42−1+4×C7311yescharacteristic
621C8—22no—
622C8—22no—
623C8—41no—
624C8—41no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22C2×C22⋊Q8×C7311yescharacteristic
640C22D42×C7311yescharacteristic
641C22#547×C7311yescharacteristic
642C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
643C22#575×C7311yescharacteristic
644C22#577×C7311yescharacteristic
645C22#577×C7311yescharacteristic
646C4—22no—
647C4—22no—
648C4—42no—
649C4—41no—
650C4—42no—
651C4—42no—
652C4—41no—
653C4—41no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4#525×C7311yescharacteristic
659C4#539×C7311yescharacteristic
660C4D4×Q8×C7311yescharacteristic
661C4#554×C7311yescharacteristic
662C2—42no—
663C2—82no—
664C2C73×#244911yescharacteristic
665C2C73×#307711yescharacteristic
666C2C73×#308411yescharacteristic
667C2C73×#326511yescharacteristic
668C2C73×#327511yescharacteristic
669C2C73×#335011yescharacteristic
670C2C73×#335411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#121×C73C22
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×#476×C73C2semidirect
2. C2×#428×C73C2semidirect
3. C73×#2439C2semidirect
5. C73×#2092C2semidirect
6. C73×#2086C2semidirect
7. C73×#2065C2semidirect
8. C73×#2058C2semidirect
9. C73×#1949C2semidirect
10. C73×#1919C2semidirect
13. C73×#1862C2semidirect
14. C73×#1853C2semidirect
15. C73×#1851C2semidirect
77. #121×C73Q8semidirect
114. #106×C73D4semidirect
326. #26354C73direct (N × H)
336. C2×#476C2×C73semidirect
337. C2×#428C2×C73semidirect
338. #2439C2×C73semidirect
340. #2092C2×C73semidirect
341. #2086C2×C73semidirect
342. #2065C2×C73semidirect
343. #2058C2×C73semidirect
344. #1949C2×C73semidirect
345. #1919C2×C73semidirect
348. #1862C2×C73semidirect
349. #1853C2×C73semidirect
350. #1851C2×C73semidirect
351. C73#26354direct (N × H)
413. #121Q8×C73semidirect
450. #106D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#476×C732
C2×#428×C732
C73×#24392
C73×#23612
C73×#20922
C73×#20862
C73×#20652
C73×#20582
C73×#19492
C73×#19192
C73×#18952
C73×#18752
C73×#18622
C73×#18532
C73×#18512
#2635473