Finite Group Databasebeta

← C73×#26832 #32936236

Subgroups — C73×#26832 #32936236

Order 18688.

892 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#486×C73C211yesmaximal, characteristic
2C2×#440×C73C211yesmaximal, characteristic, complemented
3C73×#2451C211yesmaximal, characteristic, complemented
4C73×#2445C211yesmaximal, characteristic
5C73×#2067C211yesmaximal, characteristic, complemented
6C73×#2057C211yesmaximal, characteristic, complemented
7C73×#2055C211yesmaximal, characteristic, complemented
8C73×#2014C211yesmaximal, characteristic
9C73×#1973C211yesmaximal, characteristic, complemented
10C73×#1936C211yesmaximal, characteristic, complemented
11C73×#1936C211yesmaximal, characteristic, complemented
12C73×#1933C211yesmaximal, characteristic, complemented
13C73×#1880C211yesmaximal, characteristic, complemented
14C73×#1862C211yesmaximal, characteristic, complemented
15C73×#1771C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C2×C4⋊Q8×C73C2211yescharacteristic
19C2×#127×C73C2211yescharacteristic
20C2×#123×C73—21no—
21C2×C4×Q8×C73C2211yescharacteristic
22C2×C4×D4×C73C2211yescharacteristic
23#486×C73—24no—
24#440×C73—24no—
25C2×#107×C73C2211yescharacteristic
26C2×#107×C73C2211yescharacteristic
27C2×C4⋊C8×C73C2211yescharacteristic
28C2×#103×C73C2211yescharacteristic
29C2×#103×C73C2211yescharacteristic
30C2×#102×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#97×C73C2211yescharacteristic
37C2×#97×C73C2211yescharacteristic
38C2×C4×C8×C73C2211yescharacteristic
39#398×C73—21no—
40#395×C73—21no—
41#394×C73—21no—
42#394×C73—21no—
43#391×C73—21no—
44#391×C73C2211yescharacteristic
45#391×C73C2211yescharacteristic
46#390×C73C2211yescharacteristic
47#390×C73C2211yescharacteristic
48#390×C73C2211yescharacteristic
49#389×C73C2211yescharacteristic
50#389×C73C2211yescharacteristic
51#389×C73C2211yescharacteristic
52#387×C73—21no—
53#386×C73—21no—
54C4×C4⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73—21no—
62C22×Q8×C73C2311yescharacteristic
63C22×D4×C73—21no—
64C22×D4×C73—21no—
65C22×D4×C73C2311yescharacteristic
66C22×D4×C73C2311yescharacteristic
67C23×C4×C73—21no—
68C2×SD16×C73—22no—
69C2×SD16×C73—22no—
70C2×SD16×C73—22no—
71C2×SD16×C73—22no—
72C2×SD16×C73—22no—
73C2×SD16×C73—41no—
74C22×C8×C73C2311yescharacteristic
75C22×C8×C73C2311yescharacteristic
76C22×C8×C73C2311yescharacteristic
77C22×C8×C73C2311yescharacteristic
78C4⋊Q8×C73—22no—
79C4⋊Q8×C73—41no—
80#127×C73—22no—
81#127×C73—41no—
82#123×C73—44no—
83C4×Q8×C73—22no—
84C4×Q8×C73—41no—
85C4×D4×C73—22no—
86C4×D4×C73—41no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73D411yescharacteristic
93C2×C4⋊C4×C73D411yescharacteristic
94C2×C4⋊C4×C73C2311yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C22⋊C4×C73—21no—
100C2×C22⋊C4×C73—21no—
101C2×C22⋊C4×C73—21no—
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73—21no—
106C2×C42×C73—21no—
107C2×C42×C73C2311yescharacteristic
108C2×C42×C73C2311yescharacteristic
109C2×C42×C73C2311yescharacteristic
110#107×C73—22no—
111#107×C73—41no—
112C4⋊C8×C73—22no—
113#103×C73—22no—
114#103×C73—22no—
115#102×C73—22no—
116#102×C73—22no—
117#102×C73—22no—
118#102×C73—22no—
119#102×C73—22no—
120#102×C73D414yes—
121#97×C73—22no—
122#97×C73—22no—
123C4×C8×C73—22no—
124#95×C73—21no—
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73D411yescharacteristic
132#95×C73D411yescharacteristic
133C24×C73—21no—
134C24×C73—21no—
135C2×Q8×C73—21no—
136C2×Q8×C73—21no—
137C2×Q8×C73—21no—
138C2×Q8×C73—21no—
139C2×Q8×C73—21no—
140C2×Q8×C73—42no—
141C2×Q8×C73—42no—
142C2×Q8×C73—81no—
143C2×Q8×C73#4112yes—
144C2×D4×C73—21no—
145C2×D4×C73—21no—
146C2×D4×C73—21no—
147C2×D4×C73—21no—
148C2×D4×C73—21no—
149C2×D4×C73—21no—
150C2×D4×C73—21no—
151C2×D4×C73—21no—
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—42no—
156C2×D4×C73—42no—
157C2×D4×C73—42no—
158C2×D4×C73—42no—
159C2×D4×C73—81no—
160C2×D4×C73—81no—
161C2×D4×C73C2×D412yes—
162C22×C4×C73—21no—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—42no—
169C22×C4×C73—42no—
170C22×C4×C73—81no—
171C22×C4×C73C2×D411yescharacteristic
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D411yescharacteristic
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2411yescharacteristic
178SD16×C73—28no—
179SD16×C73—44no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73C2×D412yes—
190C2×C8×C73#4112yes—
191C2×C8×C73#4112yes—
192C4⋊C4×C73—22no—
193C4⋊C4×C73—22no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—21no—
198C4⋊C4×C73—21no—
199C4⋊C4×C73—21no—
200C4⋊C4×C73—21no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—42no—
204C4⋊C4×C73—42no—
205C4⋊C4×C73—42no—
206C4⋊C4×C73—81no—
207C4⋊C4×C73—81no—
208C4⋊C4×C73C2×D412yes—
209C22⋊C4×C73—42no—
210C22⋊C4×C73—42no—
211C22⋊C4×C73—42no—
212C22⋊C4×C73—42no—
213C22⋊C4×C73—81no—
214C22⋊C4×C73—81no—
215C22⋊C4×C73—81no—
216C42×C73—21no—
217C42×C73—21no—
218C42×C73—21no—
219C42×C73—21no—
220C42×C73—21no—
221C42×C73—21no—
222C42×C73—42no—
223C23×C73—22no—
224C23×C73—41no—
225C23×C73—41no—
226C23×C73—41no—
227C23×C73—41no—
228C23×C73—41no—
229C23×C73—41no—
230C23×C73—41no—
231C23×C73—41no—
232C23×C73—41no—
233C23×C73—41no—
234C23×C73—41no—
235C23×C73—41no—
236C23×C73—41no—
237C23×C73C22×D411yescharacteristic
238Q8×C73—22no—
239Q8×C73—22no—
240Q8×C73—41no—
241Q8×C73—41no—
242Q8×C73—84no—
243D4×C73—22no—
244D4×C73—22no—
245D4×C73—41no—
246D4×C73—41no—
247D4×C73—41no—
248D4×C73—41no—
249D4×C73—41no—
250D4×C73—41no—
251D4×C73—84no—
252D4×C73—84no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—22no—
262C2×C4×C73—22no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—41no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—84no—
288C2×C4×C73AGL(1,ℤ/8)12yes—
289C2×C4×C73#13712yes—
290C2×C4×C73C22×D411yescharacteristic
291C2×C4×C73C2×#4111yescharacteristic
292C2×C4×C73C2×#4111yescharacteristic
293C2×C4×C73C2×#4111yescharacteristic
294C2×C4×C73H(5,𝔽2)11yescharacteristic
295C2×C4×C732−1+411yescharacteristic
296C8×C73—22no—
297C8×C73—22no—
298C8×C73—22no—
299C8×C73—41no—
300C22×C73—42no—
301C22×C73—42no—
302C22×C73—42no—
303C22×C73—81no—
304C22×C73—81no—
305C22×C73—81no—
306C22×C73—81no—
307C22×C73—81no—
308C22×C73—81no—
309C22×C73—81no—
310C22×C73—81no—
311C22×C73—81no—
312C22×C73—81no—
313C22×C73—81no—
314C22×C73#53211yescharacteristic
315C22×C73D4211yescharacteristic
316C22×C73#54811yescharacteristic
317C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
318C22×C73C2×#13711yescharacteristic
319C22×C73#57611yescharacteristic
320C22×C73#57711yescharacteristic
321C4×C73—22no—
322C4×C73—22no—
323C4×C73—41no—
324C4×C73—41no—
325C4×C73—42no—
326C4×C73—41no—
327C4×C73—42no—
328C4×C73—41no—
329C4×C73—81no—
330C4×C73—81no—
331C4×C73—81no—
332C4×C73—81no—
333C4×C73#52511yescharacteristic
334C4×C73#54211yescharacteristic
335C4×C73#54711yescharacteristic
336C4×C73#55111yescharacteristic
337#26832C7311yesmaximal, characteristic, direct product factor, Sylow
338C2×C73—82no—
339C2×C73—161no—
340C2×C73#246111yescharacteristic
341C2×C73#317911yescharacteristic
342C2×C73#318211yescharacteristic
343C2×C73#326411yescharacteristic
344C2×C73#326611yescharacteristic
345C2×C73#336811yescharacteristic
346C2×C73#337511yescharacteristic
347C2×#486C2×C7311yescharacteristic
348C2×#440C2×C7311yescharacteristic, complemented
349#2451C2×C7311yescharacteristic, complemented
350#2445C2×C7311yescharacteristic
351#2067C2×C7311yescharacteristic, complemented
352#2057C2×C7311yescharacteristic, complemented
353#2055C2×C7311yescharacteristic, complemented
354#2014C2×C7311yescharacteristic
355#1973C2×C7311yescharacteristic, complemented
356#1936C2×C7311yescharacteristic, complemented
357#1936C2×C7311yescharacteristic, complemented
358#1933C2×C7311yescharacteristic, complemented
359#1880C2×C7311yescharacteristic, complemented
360#1862C2×C7311yescharacteristic, complemented
361#1771C2×C7311yescharacteristic, complemented
362C73#2683211yescharacteristic, direct product factor, Sylow
363C22×SD16C22×C7311yescharacteristic
364C22×SD16C22×C7311yescharacteristic
365C2×C4⋊Q8C22×C7311yescharacteristic
366C2×#127C22×C7311yescharacteristic
367C2×#123—21no—
368C2×C4×Q8C22×C7311yescharacteristic
369C2×C4×D4C22×C7311yescharacteristic
370#486—24no—
371#440—24no—
372C2×#107C22×C7311yescharacteristic
373C2×#107C22×C7311yescharacteristic
374C2×C4⋊C8C22×C7311yescharacteristic
375C2×#103C22×C7311yescharacteristic
376C2×#103C22×C7311yescharacteristic
377C2×#102C22×C7311yescharacteristic
378C2×#102C22×C7311yescharacteristic
379C2×#102C22×C7311yescharacteristic
380C2×#102C22×C7311yescharacteristic
381C2×#102C22×C7311yescharacteristic
382C2×#102C22×C7311yescharacteristic
383C2×#97C22×C7311yescharacteristic
384C2×#97C22×C7311yescharacteristic
385C2×C4×C8C22×C7311yescharacteristic
386#398—21no—
387#395—21no—
388#394—21no—
389#394—21no—
390#391—21no—
391#391C22×C7311yescharacteristic
392#391C22×C7311yescharacteristic
393#390C22×C7311yescharacteristic
394#390C22×C7311yescharacteristic
395#390C22×C7311yescharacteristic
396#389C22×C7311yescharacteristic
397#389C22×C7311yescharacteristic
398#389C22×C7311yescharacteristic
399#387—21no—
400#386—21no—
401C4×C4⋊C4C22×C7311yescharacteristic
402#340C22×C7311yescharacteristic
403#340C22×C7311yescharacteristic
404#340C22×C7311yescharacteristic
405#340C22×C7311yescharacteristic
406#336C22×C7311yescharacteristic
407#336C22×C7311yescharacteristic
408C22×Q8—21no—
409C22×Q8C23×C7311yescharacteristic
410C22×D4—21no—
411C22×D4—21no—
412C22×D4C23×C7311yescharacteristic
413C22×D4C23×C7311yescharacteristic
414C23×C4—21no—
415C2×SD16—22no—
416C2×SD16—22no—
417C2×SD16—22no—
418C2×SD16—22no—
419C2×SD16—22no—
420C2×SD16—41no—
421C22×C8C23×C7311yescharacteristic
422C22×C8C23×C7311yescharacteristic
423C22×C8C23×C7311yescharacteristic
424C22×C8C23×C7311yescharacteristic
425C4⋊Q8—22no—
426C4⋊Q8—41no—
427#127—22no—
428#127—41no—
429#123—44no—
430C4×Q8—22no—
431C4×Q8—41no—
432C4×D4—22no—
433C4×D4—41no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4D4×C7311yescharacteristic
440C2×C4⋊C4D4×C7311yescharacteristic
441C2×C4⋊C4C23×C7311yescharacteristic
442C2×C4⋊C4C23×C7311yescharacteristic
443C2×C4⋊C4C23×C7311yescharacteristic
444C2×C4⋊C4C23×C7311yescharacteristic
445C2×C4⋊C4C23×C7311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C42—21no—
454C2×C42C23×C7311yescharacteristic
455C2×C42C23×C7311yescharacteristic
456C2×C42C23×C7311yescharacteristic
457#107—22no—
458#107—41no—
459C4⋊C8—22no—
460#103—22no—
461#103—22no—
462#102—22no—
463#102—22no—
464#102—22no—
465#102—22no—
466#102—22no—
467#102D4×C7314yes—
468#97—22no—
469#97—22no—
470C4×C8—22no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95D4×C7311yescharacteristic
479#95D4×C7311yescharacteristic
480C24—21no—
481C24—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×Q8—81no—
490C2×Q8#41×C7312yes—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—81no—
507C2×D4—81no—
508C2×D4C2×D4×C7312yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—81no—
518C22×C4C2×D4×C7311yescharacteristic
519C22×C4C2×D4×C7311yescharacteristic
520C22×C4C2×D4×C7311yescharacteristic
521C22×C4C2×D4×C7311yescharacteristic
522C22×C4C2×D4×C7311yescharacteristic
523C22×C4C2×D4×C7311yescharacteristic
524C22×C4C24×C7311yescharacteristic
525SD16—28no—
526SD16—44no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8C2×D4×C7312yes—
537C2×C8#41×C7312yes—
538C2×C8#41×C7312yes—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—81no—
554C4⋊C4—81no—
555C4⋊C4C2×D4×C7312yes—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—42no—
570C23—22no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23C22×D4×C7311yescharacteristic
585Q8—22no—
586Q8—22no—
587Q8—41no—
588Q8—41no—
589Q8—84no—
590D4—22no—
591D4—22no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—41no—
598D4—84no—
599D4—84no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—84no—
635C2×C4AGL(1,ℤ/8)×C7312yes—
636C2×C4#137×C7312yes—
637C2×C4C22×D4×C7311yescharacteristic
638C2×C4C2×#41×C7311yescharacteristic
639C2×C4C2×#41×C7311yescharacteristic
640C2×C4C2×#41×C7311yescharacteristic
641C2×C4H(5,𝔽2)×C7311yescharacteristic
642C2×C42−1+4×C7311yescharacteristic
643C8—22no—
644C8—22no—
645C8—22no—
646C8—41no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22#532×C7311yescharacteristic
662C22D42×C7311yescharacteristic
663C22#548×C7311yescharacteristic
664C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
665C22C2×#137×C7311yescharacteristic
666C22#576×C7311yescharacteristic
667C22#577×C7311yescharacteristic
668C4—22no—
669C4—22no—
670C4—42no—
671C4—41no—
672C4—42no—
673C4—41no—
674C4—41no—
675C4—41no—
676C4—81no—
677C4—81no—
678C4—81no—
679C4—81no—
680C4#525×C7311yescharacteristic
681C4#542×C7311yescharacteristic
682C4#547×C7311yescharacteristic
683C4#551×C7311yescharacteristic
684C2—82no—
685C2—161no—
686C2C73×#246111yescharacteristic
687C2C73×#317911yescharacteristic
688C2C73×#318211yescharacteristic
689C2C73×#326411yescharacteristic
690C2C73×#326611yescharacteristic
691C2C73×#336811yescharacteristic
692C2C73×#337511yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#127×C73C22
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
2. C2×#440×C73C2semidirect
3. C73×#2451C2semidirect
5. C73×#2067C2semidirect
6. C73×#2057C2semidirect
7. C73×#2055C2semidirect
9. C73×#1973C2semidirect
10. C73×#1936C2semidirect
11. C73×#1936C2semidirect
12. C73×#1933C2semidirect
13. C73×#1880C2semidirect
14. C73×#1862C2semidirect
15. C73×#1771C2semidirect
337. #26832C73direct (N × H)
348. C2×#440C2×C73semidirect
349. #2451C2×C73semidirect
351. #2067C2×C73semidirect
352. #2057C2×C73semidirect
353. #2055C2×C73semidirect
355. #1973C2×C73semidirect
356. #1936C2×C73semidirect
357. #1936C2×C73semidirect
358. #1933C2×C73semidirect
359. #1880C2×C73semidirect
360. #1862C2×C73semidirect
361. #1771C2×C73semidirect
362. C73#26832direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#486×C732
C2×#440×C732
C73×#24512
C73×#24452
C73×#20672
C73×#20572
C73×#20552
C73×#20142
C73×#19732
C73×#19362
C73×#19332
C73×#18802
C73×#18622
C73×#17712
#2683273