Finite Group Databasebeta

← C73×#23148 #32932552

Subgroups — C73×#23148 #32932552

Order 18688.

802 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3054C211yesmaximal, characteristic
2C73×#2933C211yesmaximal, characteristic, complemented
3C73×#2933C211yesmaximal, characteristic, complemented
4C73×#1938C211yesmaximal, characteristic, complemented
5C73×#1937C211yesmaximal, characteristic, complemented
6C73×#1922C211yesmaximal, characteristic, complemented
7C73×#1922C211yesmaximal, characteristic, complemented
8C73×#1876C211yesmaximal, characteristic, complemented
9C73×#1876C211yesmaximal, characteristic, complemented
10C73×#1871C211yesmaximal, characteristic, complemented
11C73×#1871C211yesmaximal, characteristic, complemented
12C73×#1765C211yesmaximal, characteristic, complemented
13C73×#1764C211yesmaximal, characteristic, complemented
14C73×#1753C211yesmaximal, characteristic, complemented
15C73×#1738C211yesmaximal, characteristic, complemented
16C2×#135×C73C2211yescharacteristic
17C2×#131×C73C2211yescharacteristic
18C2×#131×C73C2211yescharacteristic
19C22×M16×C73C2211yescharacteristic
20C22×M16×C73C2211yescharacteristic
21C22×M16×C73C2211yescharacteristic
22#525×C73C2211yescharacteristic
23#525×C73C2211yescharacteristic
24#470×C73C411yescharacteristic, complemented
25#470×C73C411yescharacteristic, complemented
26#469×C73C411yescharacteristic, complemented
27#469×C73C411yescharacteristic, complemented
28#468×C73C411yescharacteristic, complemented
29#468×C73C411yescharacteristic, complemented
30#468×C73C411yescharacteristic, complemented
31#468×C73C411yescharacteristic, complemented
32#436×C73—21no—
33#436×C73—21no—
34#435×C73—21no—
35#435×C73—21no—
36#435×C73—21no—
37#435×C73—21no—
38C8×D4×C73—21no—
39C8×D4×C73—21no—
40#427×C73C2211yescharacteristic
41#424×C73C2211yescharacteristic
42#424×C73C2211yescharacteristic
43C2×#104×C73C2211yescharacteristic
44C2×#104×C73C2211yescharacteristic
45C2×#104×C73C2211yescharacteristic
46C2×#104×C73C2211yescharacteristic
47#416×C73C2211yescharacteristic
48#416×C73C2211yescharacteristic
49#408×C73C2211yescharacteristic
50#408×C73C2211yescharacteristic
51C2×C22⋊C8×C73C2211yescharacteristic
52#405×C73C2211yescharacteristic
53#405×C73C2211yescharacteristic
54C2×#97×C73C2211yescharacteristic
55C2×C4×C8×C73C2211yescharacteristic
56C4×C22⋊C4×C73C2211yescharacteristic
57#341×C73C2211yescharacteristic
58#341×C73C2211yescharacteristic
59#341×C73C2211yescharacteristic
60#341×C73C2211yescharacteristic
61#339×C73C2211yescharacteristic
62#339×C73C2211yescharacteristic
63#339×C73C2211yescharacteristic
64#339×C73C2211yescharacteristic
65#336×C73C2211yescharacteristic
66#336×C73C2211yescharacteristic
67C2×#41×C73C2311yescharacteristic
68C2×#41×C73C2311yescharacteristic
69C23×C4×C73C2311yescharacteristic
70#135×C73—41no—
71#135×C73—41no—
72C2×Q16×C73C2×C411yescharacteristic
73C2×SD16×C73C2×C411yescharacteristic
74C2×SD16×C73C2×C411yescharacteristic
75C2×D8×C73C2×C411yescharacteristic
76#131×C73—22no—
77#131×C73—22no—
78#131×C73—41no—
79#131×C73—41no—
80C2×M16×C73—21no—
81C2×M16×C73—21no—
82C2×M16×C73—21no—
83C2×M16×C73—21no—
84C2×M16×C73—22no—
85C2×M16×C73—22no—
86C2×M16×C73—41no—
87C2×M16×C73—41no—
88C2×M16×C73—41no—
89C2×M16×C73—41no—
90C2×M16×C73C2×C411yescharacteristic
91C2×M16×C73C2×C411yescharacteristic
92C2×M16×C73C2×C411yescharacteristic
93C2×M16×C73C2×C411yescharacteristic
94C2×M16×C73C2311yescharacteristic
95C2×M16×C73C2311yescharacteristic
96C2×M16×C73C2311yescharacteristic
97C2×M16×C73C2311yescharacteristic
98C22×C8×C73—21no—
99C22×C8×C73—21no—
100C22×C8×C73—21no—
101C22×C8×C73—21no—
102C22×C8×C73C2311yescharacteristic
103C22×C8×C73C2311yescharacteristic
104C22×C8×C73C2311yescharacteristic
105C22×C8×C73C2311yescharacteristic
106#123×C73—21no—
107#123×C73—21no—
108C22⋊Q8×C73C2×C411yescharacteristic
109C22⋊Q8×C73C2×C411yescharacteristic
110C22⋊Q8×C73C2×C411yescharacteristic
111C22⋊Q8×C73C2×C411yescharacteristic
112#121×C73C2×C411yescharacteristic
113#121×C73C2×C411yescharacteristic
114#121×C73C2×C411yescharacteristic
115#121×C73C2×C411yescharacteristic
116#120×C73—21no—
117#120×C73—21no—
118C4×D4×C73—21no—
119C4×D4×C73—21no—
120C4×D4×C73—21no—
121C4×D4×C73—21no—
122#117×C73C2311yescharacteristic
123#117×C73C2311yescharacteristic
124C2×C22⋊C4×C73—21no—
125C2×C42×C73C2311yescharacteristic
126C2×C42×C73C2311yescharacteristic
127#107×C73C2×C411yescharacteristic
128#107×C73C2×C411yescharacteristic
129#106×C73C2×C411yescharacteristic
130#106×C73C2×C411yescharacteristic
131C4⋊C8×C73—21no—
132C4⋊C8×C73—21no—
133C4⋊C8×C73—21no—
134C4⋊C8×C73—21no—
135#104×C73—22no—
136#104×C73—22no—
137#104×C73—41no—
138#104×C73—41no—
139#103×C73C2×C411yescharacteristic
140#103×C73C2×C411yescharacteristic
141#103×C73C2×C411yescharacteristic
142#103×C73C2×C411yescharacteristic
143#102×C73C2×C411yescharacteristic
144#102×C73C2×C411yescharacteristic
145#102×C73C2×C411yescharacteristic
146#102×C73C2×C411yescharacteristic
147C22⋊C8×C73—21no—
148C22⋊C8×C73—21no—
149C22⋊C8×C73—21no—
150C22⋊C8×C73—21no—
151C22⋊C8×C73D411yescharacteristic
152C22⋊C8×C73D411yescharacteristic
153C22⋊C8×C73D411yescharacteristic
154C22⋊C8×C73D411yescharacteristic
155#97×C73—21no—
156#97×C73—21no—
157#97×C73—41no—
158C4×C8×C73—21no—
159C4×C8×C73—21no—
160C4×C8×C73—41no—
161#95×C73—21no—
162C24×C73#4111yescharacteristic
163#41×C73—21no—
164#41×C73—21no—
165#41×C73—21no—
166#41×C73—21no—
167#41×C73—21no—
168#41×C73—21no—
169#41×C73—21no—
170#41×C73—21no—
171C2×Q8×C73C22×C411yescharacteristic
172C2×Q8×C73C22×C411yescharacteristic
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×C73C22×C411yescharacteristic
180C2×D4×C73C22×C411yescharacteristic
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73C22×C411yescharacteristic
190C22×C4×C73C22×C411yescharacteristic
191C22×C4×C73C2×D411yescharacteristic
192C22×C4×C73C2×D411yescharacteristic
193C22×C4×C73#4111yescharacteristic
194C22×C4×C73C2411yescharacteristic
195Q16×C73—41no—
196SD16×C73—41no—
197SD16×C73—41no—
198D8×C73—41no—
199M16×C73—21no—
200M16×C73—21no—
201M16×C73—21no—
202M16×C73—21no—
203M16×C73—21no—
204M16×C73—21no—
205M16×C73—41no—
206M16×C73—41no—
207M16×C73—41no—
208M16×C73—41no—
209M16×C73—42no—
210M16×C73—42no—
211M16×C73—42no—
212M16×C73—42no—
213M16×C73#4112yes—
214M16×C73#4112yes—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—42no—
228C2×C8×C73—42no—
229C2×C8×C73—42no—
230C2×C8×C73—42no—
231C2×C8×C73C22×C411yescharacteristic
232C2×C8×C73C22×C411yescharacteristic
233C2×C8×C73C22×C411yescharacteristic
234C2×C8×C73C22×C411yescharacteristic
235C2×C8×C73C2×D411yescharacteristic
236C2×C8×C73C2×D411yescharacteristic
237C2×C8×C73C2×D411yescharacteristic
238C2×C8×C73C2×D411yescharacteristic
239C4⋊C4×C73—21no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73C22×C411yescharacteristic
244C4⋊C4×C73C22×C411yescharacteristic
245C4⋊C4×C73C22×C411yescharacteristic
246C4⋊C4×C73C22×C411yescharacteristic
247C22⋊C4×C73—21no—
248C22⋊C4×C73—21no—
249C22⋊C4×C73—21no—
250C22⋊C4×C73—21no—
251C22⋊C4×C73—21no—
252C22⋊C4×C73—21no—
253C22⋊C4×C73—21no—
254C22⋊C4×C73—21no—
255C22⋊C4×C73—21no—
256C22⋊C4×C73—21no—
257C22⋊C4×C73—42no—
258C42×C73—21no—
259C42×C73—21no—
260C42×C73—21no—
261C42×C73—21no—
262C42×C73—21no—
263C42×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73C4×D411yescharacteristic
271C23×C73C4×D411yescharacteristic
272C23×C73C2×#4111yescharacteristic
273Q8×C73—21no—
274Q8×C73—21no—
275Q8×C73—21no—
276Q8×C73—21no—
277D4×C73—21no—
278D4×C73—21no—
279D4×C73—21no—
280D4×C73—21no—
281D4×C73—42no—
282D4×C73—42no—
283D4×C73—41no—
284D4×C73—41no—
285D4×C73—41no—
286D4×C73—41no—
287D4×C73—81no—
288D4×C73—81no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—22no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
310C2×C4×C73—41no—
311C2×C4×C73—41no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
314C2×C4×C73—41no—
315C2×C4×C73C4×D411yescharacteristic
316C2×C4×C73C4×D411yescharacteristic
317C2×C4×C73C23×C411yescharacteristic
318C2×C4×C73C22×D411yescharacteristic
319C2×C4×C73C2×#4111yescharacteristic
320C2×C4×C73C2×#4111yescharacteristic
321C2×C4×C73H(5,𝔽2)11yescharacteristic
322C2×C4×C73H(5,𝔽2)11yescharacteristic
323C8×C73—21no—
324C8×C73—21no—
325C8×C73—21no—
326C8×C73—21no—
327C8×C73—21no—
328C8×C73—21no—
329C8×C73—21no—
330C8×C73—21no—
331C8×C73—22no—
332C8×C73—22no—
333C8×C73—41no—
334C8×C73—41no—
335C22×C73—21no—
336C22×C73—21no—
337C22×C73—21no—
338C22×C73—21no—
339C22×C73—21no—
340C22×C73—21no—
341C22×C73—21no—
342C22×C73—21no—
343C22×C73—41no—
344C22×C73—41no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—81no—
350C22×C73—81no—
351C22×C73C2×C4×D411yescharacteristic
352C22×C73#55311yescharacteristic
353C22×C73#55311yescharacteristic
354C4×C73—21no—
355C4×C73—21no—
356C4×C73—42no—
357C4×C73—41no—
358C4×C73—41no—
359C4×C73—41no—
360C4×C73—41no—
361C4×C73—41no—
362C4×C73—41no—
363C4×C73—81no—
364C4×C73C4×#4111yescharacteristic
365C4×C73#51811yescharacteristic
366C4×C73#54611yescharacteristic
367C4×C73#54611yescharacteristic
368#23148C7311yesmaximal, characteristic, direct product factor, Sylow
369C2×C73—21no—
370C2×C73—21no—
371C2×C73—41no—
372C2×C73—41no—
373C2×C73—81no—
374C2×C73—81no—
375C2×C73#236411yescharacteristic
376C2×C73#295511yescharacteristic
377C2×C73#295611yescharacteristic
378#3054C2×C7311yescharacteristic
379#2933C2×C7311yescharacteristic, complemented
380#2933C2×C7311yescharacteristic, complemented
381#1938C2×C7311yescharacteristic, complemented
382#1937C2×C7311yescharacteristic, complemented
383#1922C2×C7311yescharacteristic, complemented
384#1922C2×C7311yescharacteristic, complemented
385#1876C2×C7311yescharacteristic, complemented
386#1876C2×C7311yescharacteristic, complemented
387#1871C2×C7311yescharacteristic, complemented
388#1871C2×C7311yescharacteristic, complemented
389#1765C2×C7311yescharacteristic, complemented
390#1764C2×C7311yescharacteristic, complemented
391#1753C2×C7311yescharacteristic, complemented
392#1738C2×C7311yescharacteristic, complemented
393C73#2314811yescharacteristic, direct product factor, Sylow
394C2×#135C22×C7311yescharacteristic
395C2×#131C22×C7311yescharacteristic
396C2×#131C22×C7311yescharacteristic
397C22×M16C22×C7311yescharacteristic
398C22×M16C22×C7311yescharacteristic
399C22×M16C22×C7311yescharacteristic
400#525C22×C7311yescharacteristic
401#525C22×C7311yescharacteristic
402#470C4×C7311yescharacteristic, complemented
403#470C4×C7311yescharacteristic, complemented
404#469C4×C7311yescharacteristic, complemented
405#469C4×C7311yescharacteristic, complemented
406#468C4×C7311yescharacteristic, complemented
407#468C4×C7311yescharacteristic, complemented
408#468C4×C7311yescharacteristic, complemented
409#468C4×C7311yescharacteristic, complemented
410#436—21no—
411#436—21no—
412#435—21no—
413#435—21no—
414#435—21no—
415#435—21no—
416C8×D4—21no—
417C8×D4—21no—
418#427C22×C7311yescharacteristic
419#424C22×C7311yescharacteristic
420#424C22×C7311yescharacteristic
421C2×#104C22×C7311yescharacteristic
422C2×#104C22×C7311yescharacteristic
423C2×#104C22×C7311yescharacteristic
424C2×#104C22×C7311yescharacteristic
425#416C22×C7311yescharacteristic
426#416C22×C7311yescharacteristic
427#408C22×C7311yescharacteristic
428#408C22×C7311yescharacteristic
429C2×C22⋊C8C22×C7311yescharacteristic
430#405C22×C7311yescharacteristic
431#405C22×C7311yescharacteristic
432C2×#97C22×C7311yescharacteristic
433C2×C4×C8C22×C7311yescharacteristic
434C4×C22⋊C4C22×C7311yescharacteristic
435#341C22×C7311yescharacteristic
436#341C22×C7311yescharacteristic
437#341C22×C7311yescharacteristic
438#341C22×C7311yescharacteristic
439#339C22×C7311yescharacteristic
440#339C22×C7311yescharacteristic
441#339C22×C7311yescharacteristic
442#339C22×C7311yescharacteristic
443#336C22×C7311yescharacteristic
444#336C22×C7311yescharacteristic
445C2×#41C23×C7311yescharacteristic
446C2×#41C23×C7311yescharacteristic
447C23×C4C23×C7311yescharacteristic
448#135—41no—
449#135—41no—
450C2×Q16C2×C4×C7311yescharacteristic
451C2×SD16C2×C4×C7311yescharacteristic
452C2×SD16C2×C4×C7311yescharacteristic
453C2×D8C2×C4×C7311yescharacteristic
454#131—22no—
455#131—22no—
456#131—41no—
457#131—41no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—22no—
463C2×M16—22no—
464C2×M16—41no—
465C2×M16—41no—
466C2×M16—41no—
467C2×M16—41no—
468C2×M16C2×C4×C7311yescharacteristic
469C2×M16C2×C4×C7311yescharacteristic
470C2×M16C2×C4×C7311yescharacteristic
471C2×M16C2×C4×C7311yescharacteristic
472C2×M16C23×C7311yescharacteristic
473C2×M16C23×C7311yescharacteristic
474C2×M16C23×C7311yescharacteristic
475C2×M16C23×C7311yescharacteristic
476C22×C8—21no—
477C22×C8—21no—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8C23×C7311yescharacteristic
481C22×C8C23×C7311yescharacteristic
482C22×C8C23×C7311yescharacteristic
483C22×C8C23×C7311yescharacteristic
484#123—21no—
485#123—21no—
486C22⋊Q8C2×C4×C7311yescharacteristic
487C22⋊Q8C2×C4×C7311yescharacteristic
488C22⋊Q8C2×C4×C7311yescharacteristic
489C22⋊Q8C2×C4×C7311yescharacteristic
490#121C2×C4×C7311yescharacteristic
491#121C2×C4×C7311yescharacteristic
492#121C2×C4×C7311yescharacteristic
493#121C2×C4×C7311yescharacteristic
494#120—21no—
495#120—21no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—21no—
500#117C23×C7311yescharacteristic
501#117C23×C7311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C42C23×C7311yescharacteristic
504C2×C42C23×C7311yescharacteristic
505#107C2×C4×C7311yescharacteristic
506#107C2×C4×C7311yescharacteristic
507#106C2×C4×C7311yescharacteristic
508#106C2×C4×C7311yescharacteristic
509C4⋊C8—21no—
510C4⋊C8—21no—
511C4⋊C8—21no—
512C4⋊C8—21no—
513#104—22no—
514#104—22no—
515#104—41no—
516#104—41no—
517#103C2×C4×C7311yescharacteristic
518#103C2×C4×C7311yescharacteristic
519#103C2×C4×C7311yescharacteristic
520#103C2×C4×C7311yescharacteristic
521#102C2×C4×C7311yescharacteristic
522#102C2×C4×C7311yescharacteristic
523#102C2×C4×C7311yescharacteristic
524#102C2×C4×C7311yescharacteristic
525C22⋊C8—21no—
526C22⋊C8—21no—
527C22⋊C8—21no—
528C22⋊C8—21no—
529C22⋊C8D4×C7311yescharacteristic
530C22⋊C8D4×C7311yescharacteristic
531C22⋊C8D4×C7311yescharacteristic
532C22⋊C8D4×C7311yescharacteristic
533#97—21no—
534#97—21no—
535#97—41no—
536C4×C8—21no—
537C4×C8—21no—
538C4×C8—41no—
539#95—21no—
540C24#41×C7311yescharacteristic
541#41—21no—
542#41—21no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549C2×Q8C22×C4×C7311yescharacteristic
550C2×Q8C22×C4×C7311yescharacteristic
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4C22×C4×C7311yescharacteristic
558C2×D4C22×C4×C7311yescharacteristic
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4C22×C4×C7311yescharacteristic
568C22×C4C22×C4×C7311yescharacteristic
569C22×C4C2×D4×C7311yescharacteristic
570C22×C4C2×D4×C7311yescharacteristic
571C22×C4#41×C7311yescharacteristic
572C22×C4C24×C7311yescharacteristic
573Q16—41no—
574SD16—41no—
575SD16—41no—
576D8—41no—
577M16—21no—
578M16—21no—
579M16—21no—
580M16—21no—
581M16—21no—
582M16—21no—
583M16—41no—
584M16—41no—
585M16—41no—
586M16—41no—
587M16—42no—
588M16—42no—
589M16—42no—
590M16—42no—
591M16#41×C7312yes—
592M16#41×C7312yes—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—42no—
606C2×C8—42no—
607C2×C8—42no—
608C2×C8—42no—
609C2×C8C22×C4×C7311yescharacteristic
610C2×C8C22×C4×C7311yescharacteristic
611C2×C8C22×C4×C7311yescharacteristic
612C2×C8C22×C4×C7311yescharacteristic
613C2×C8C2×D4×C7311yescharacteristic
614C2×C8C2×D4×C7311yescharacteristic
615C2×C8C2×D4×C7311yescharacteristic
616C2×C8C2×D4×C7311yescharacteristic
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4C22×C4×C7311yescharacteristic
622C4⋊C4C22×C4×C7311yescharacteristic
623C4⋊C4C22×C4×C7311yescharacteristic
624C4⋊C4C22×C4×C7311yescharacteristic
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—21no—
634C22⋊C4—21no—
635C22⋊C4—42no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—41no—
647C23—41no—
648C23C4×D4×C7311yescharacteristic
649C23C4×D4×C7311yescharacteristic
650C23C2×#41×C7311yescharacteristic
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—21no—
655D4—21no—
656D4—21no—
657D4—21no—
658D4—21no—
659D4—42no—
660D4—42no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—81no—
666D4—81no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4C4×D4×C7311yescharacteristic
694C2×C4C4×D4×C7311yescharacteristic
695C2×C4C23×C4×C7311yescharacteristic
696C2×C4C22×D4×C7311yescharacteristic
697C2×C4C2×#41×C7311yescharacteristic
698C2×C4C2×#41×C7311yescharacteristic
699C2×C4H(5,𝔽2)×C7311yescharacteristic
700C2×C4H(5,𝔽2)×C7311yescharacteristic
701C8—21no—
702C8—21no—
703C8—21no—
704C8—21no—
705C8—21no—
706C8—21no—
707C8—21no—
708C8—21no—
709C8—22no—
710C8—22no—
711C8—41no—
712C8—41no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22C2×C4×D4×C7311yescharacteristic
730C22#553×C7311yescharacteristic
731C22#553×C7311yescharacteristic
732C4—21no—
733C4—21no—
734C4—42no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—81no—
742C4C4×#41×C7311yescharacteristic
743C4#518×C7311yescharacteristic
744C4#546×C7311yescharacteristic
745C4#546×C7311yescharacteristic
746C2—21no—
747C2—21no—
748C2—41no—
749C2—41no—
750C2—81no—
751C2—81no—
752C2C73×#236411yescharacteristic
753C2C73×#295511yescharacteristic
754C2C73×#295611yescharacteristic
subgroupG/H
centerC2×C4×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
socleC22×C73C2×C4×D4
prime radicalC73×#3054C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C73 ◁ C2×C22⋊C8×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#2933C2semidirect
3. C73×#2933C2semidirect
4. C73×#1938C2semidirect
5. C73×#1937C2semidirect
6. C73×#1922C2semidirect
7. C73×#1922C2semidirect
8. C73×#1876C2semidirect
9. C73×#1876C2semidirect
10. C73×#1871C2semidirect
11. C73×#1871C2semidirect
12. C73×#1765C2semidirect
13. C73×#1764C2semidirect
14. C73×#1753C2semidirect
15. C73×#1738C2semidirect
24. #470×C73C4semidirect
25. #470×C73C4semidirect
26. #469×C73C4semidirect
27. #469×C73C4semidirect
28. #468×C73C4semidirect
29. #468×C73C4semidirect
30. #468×C73C4semidirect
31. #468×C73C4semidirect
368. #23148C73direct (N × H)
379. #2933C2×C73semidirect
380. #2933C2×C73semidirect
381. #1938C2×C73semidirect
382. #1937C2×C73semidirect
383. #1922C2×C73semidirect
384. #1922C2×C73semidirect
385. #1876C2×C73semidirect
386. #1876C2×C73semidirect
387. #1871C2×C73semidirect
388. #1871C2×C73semidirect
389. #1765C2×C73semidirect
390. #1764C2×C73semidirect
391. #1753C2×C73semidirect
392. #1738C2×C73semidirect
393. C73#23148direct (N × H)
402. #470C4×C73semidirect
403. #470C4×C73semidirect
404. #469C4×C73semidirect
405. #469C4×C73semidirect
406. #468C4×C73semidirect
407. #468C4×C73semidirect
408. #468C4×C73semidirect
409. #468C4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#30542
C73×#29332
C73×#19382
C73×#19372
C73×#19222
C73×#18762
C73×#18712
C73×#17652
C73×#17642
C73×#17532
C73×#17382
#2314873