Finite Group Databasebeta

← C73×#25653 #32935057

Subgroups — C73×#25653 #32935057

Order 18688.

1082 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#559×C73C211yesmaximal, characteristic
2C2×#488×C73C211yesmaximal, characteristic, complemented
3C2×#478×C73C211yesmaximal, characteristic, complemented
4C73×#2584C211yesmaximal, characteristic, complemented
5C73×#2042C211yesmaximal, characteristic, complemented
6C73×#2042C211yesmaximal, characteristic, complemented
7C73×#2041C211yesmaximal, characteristic
8C73×#2041C211yesmaximal, characteristic
9C73×#1984C211yesmaximal, characteristic, complemented
10C73×#1983C211yesmaximal, characteristic, complemented
11C73×#1865C211yesmaximal, characteristic, complemented
12C73×#1864C211yesmaximal, characteristic, complemented
13C73×#1863C211yesmaximal, characteristic, complemented
14C73×#1862C211yesmaximal, characteristic, complemented
15C4×#102×C73C211yesmaximal, characteristic, complemented
16#559×C73—24no—
17#559×C73—24no—
18C2×#127×C73C2211yescharacteristic
19C2×#125×C73C2211yescharacteristic
20C2×#124×C73—21no—
21C2×#124×C73C2211yescharacteristic
22C2×#124×C73C2211yescharacteristic
23C2×#123×C73—21no—
24C2×#123×C73—21no—
25C2×C4×Q8×C73C2211yescharacteristic
26C2×C4×Q8×C73C2211yescharacteristic
27C2×C4×D4×C73—21no—
28C2×C4×D4×C73C2211yescharacteristic
29C2×C4×D4×C73C2211yescharacteristic
30#488×C73—24no—
31#478×C73—24no—
32C2×#107×C73C2211yescharacteristic
33C2×#106×C73C2211yescharacteristic
34C2×C4⋊C8×C73C2211yescharacteristic
35C2×#103×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44C2×#102×C73C2211yescharacteristic
45C2×#102×C73C2211yescharacteristic
46C2×#102×C73C2211yescharacteristic
47C2×C4×C8×C73C2211yescharacteristic
48#398×C73—21no—
49#395×C73—21no—
50#389×C73—21no—
51#389×C73—21no—
52#389×C73C2211yescharacteristic
53#389×C73C2211yescharacteristic
54#389×C73C2211yescharacteristic
55#389×C73C2211yescharacteristic
56C4×C4⋊C4×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×C73C2211yescharacteristic
63C22×Q8×C73D411yescharacteristic
64C22×Q8×C73C2311yescharacteristic
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73C2311yescharacteristic
68C22×D4×C73C2311yescharacteristic
69C23×C4×C73—21no—
70C23×C4×C73—21no—
71C22×C8×C73C2311yescharacteristic
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75#127×C73—22no—
76#127×C73—22no—
77#125×C73—22no—
78#125×C73—22no—
79#124×C73—28no—
80#124×C73—22no—
81#124×C73—22no—
82#124×C73—22no—
83#124×C73D414yes—
84#123×C73—28no—
85#123×C73—28no—
86C4×Q8×C73—22no—
87C4×Q8×C73—22no—
88C4×Q8×C73—22no—
89C4×Q8×C73—22no—
90C4×D4×C73—28no—
91C4×D4×C73—22no—
92C4×D4×C73—22no—
93C4×D4×C73—22no—
94C4×D4×C73D414yes—
95C2×C4⋊C4×C73—21no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73D411yescharacteristic
103C2×C4⋊C4×C73D411yescharacteristic
104C2×C4⋊C4×C73D411yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C4⋊C4×C73C2311yescharacteristic
108C2×C4⋊C4×C73C2311yescharacteristic
109C2×C4⋊C4×C73C2311yescharacteristic
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73—21no—
112C2×C22⋊C4×C73—21no—
113C2×C22⋊C4×C73—21no—
114C2×C22⋊C4×C73—21no—
115C2×C22⋊C4×C73—21no—
116C2×C42×C73—21no—
117C2×C42×C73—21no—
118C2×C42×C73C2311yescharacteristic
119C2×C42×C73C2311yescharacteristic
120C2×C42×C73C2311yescharacteristic
121#107×C73—22no—
122#106×C73—22no—
123C4⋊C8×C73—22no—
124#103×C73—22no—
125#103×C73—22no—
126#103×C73—22no—
127#103×C73—22no—
128#102×C73—22no—
129#102×C73—22no—
130#102×C73—22no—
131#102×C73—22no—
132#102×C73—22no—
133#102×C73—22no—
134#102×C73—22no—
135#102×C73—22no—
136C4×C8×C73—22no—
137#95×C73—21no—
138#95×C73—21no—
139#95×C73—21no—
140#95×C73—21no—
141#95×C73—21no—
142C24×C73—21no—
143C24×C73—21no—
144C2×Q8×C73—22no—
145C2×Q8×C73—22no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×Q8×C73—21no—
151C2×Q8×C73—41no—
152C2×Q8×C73C2×D412yes—
153C2×D4×C73—24no—
154C2×D4×C73—24no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—21no—
159C2×D4×C73—21no—
160C2×D4×C73—21no—
161C2×D4×C73—21no—
162C2×D4×C73—21no—
163C2×D4×C73—21no—
164C2×D4×C73—21no—
165C2×D4×C73—42no—
166C2×D4×C73—42no—
167C2×D4×C73—81no—
168C2×D4×C73—81no—
169C2×D4×C73C2×D412yes—
170C2×D4×C73C2×D412yes—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—24no—
176C22×C4×C73—24no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—81no—
180C22×C4×C73—81no—
181C22×C4×C73—81no—
182C22×C4×C73—81no—
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73C2×D411yescharacteristic
185C22×C4×C73C2×D411yescharacteristic
186C22×C4×C73C2×D411yescharacteristic
187C22×C4×C73C2×D411yescharacteristic
188C22×C4×C73C2×D411yescharacteristic
189C22×C4×C73C2411yescharacteristic
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73—21no—
195C2×C8×C73—21no—
196C2×C8×C73—21no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C4⋊C4×C73—24no—
203C4⋊C4×C73—22no—
204C4⋊C4×C73—22no—
205C4⋊C4×C73—22no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—42no—
214C4⋊C4×C73—42no—
215C4⋊C4×C73—42no—
216C4⋊C4×C73—42no—
217C4⋊C4×C73—81no—
218C4⋊C4×C73—81no—
219C4⋊C4×C73C2×D412yes—
220C4⋊C4×C73#4112yes—
221C4⋊C4×C73#4112yes—
222C22⋊C4×C73—24no—
223C22⋊C4×C73—24no—
224C22⋊C4×C73—24no—
225C22⋊C4×C73—24no—
226C22⋊C4×C73—24no—
227C22⋊C4×C73—24no—
228C42×C73—24no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—21no—
232C42×C73—21no—
233C42×C73—81no—
234C42×C73C2×D412yes—
235C42×C73C2×D412yes—
236C23×C73—22no—
237C23×C73—22no—
238C23×C73—41no—
239C23×C73—41no—
240C23×C73—41no—
241C23×C73—41no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73—41no—
245C23×C73—41no—
246C23×C73—41no—
247C23×C73—41no—
248C23×C73—41no—
249C23×C73—41no—
250C23×C73C22×D411yescharacteristic
251Q8×C73—22no—
252Q8×C73—22no—
253Q8×C73—44no—
254Q8×C73—41no—
255Q8×C73—41no—
256D4×C73—22no—
257D4×C73—22no—
258D4×C73—22no—
259D4×C73—22no—
260D4×C73—48no—
261D4×C73—41no—
262D4×C73—41no—
263D4×C73—41no—
264D4×C73—41no—
265D4×C73—84no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—22no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—22no—
276C2×C4×C73—21no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—84no—
300C2×C4×C73—84no—
301C2×C4×C73#12012yes—
302C2×C4×C73#12012yes—
303C2×C4×C73#13512yes—
304C2×C4×C73C22×D411yescharacteristic
305C2×C4×C73C22×D411yescharacteristic
306C2×C4×C73C2×#4111yescharacteristic
307C2×C4×C73C2×#4111yescharacteristic
308C2×C4×C732−1+411yescharacteristic
309C2×C4×C732−1+411yescharacteristic
310C8×C73—41no—
311C8×C73—41no—
312C8×C73—41no—
313C8×C73—41no—
314C22×C73—42no—
315C22×C73—42no—
316C22×C73—42no—
317C22×C73—42no—
318C22×C73—42no—
319C22×C73—42no—
320C22×C73—81no—
321C22×C73—81no—
322C22×C73—81no—
323C22×C73—81no—
324C22×C73—81no—
325C22×C73—81no—
326C22×C73—81no—
327C22×C73—81no—
328C22×C73C2×#12011yescharacteristic
329C22×C73#54811yescharacteristic
330C22×C73#54811yescharacteristic
331C22×C73C2×#13511yescharacteristic
332C22×C73#57511yescharacteristic
333C22×C73#57611yescharacteristic
334C22×C73#57711yescharacteristic
335C4×C73—22no—
336C4×C73—22no—
337C4×C73—22no—
338C4×C73—42no—
339C4×C73—42no—
340C4×C73—42no—
341C4×C73—41no—
342C4×C73—41no—
343C4×C73—41no—
344C4×C73—42no—
345C4×C73—81no—
346C4×C73—81no—
347C4×C73#53211yescharacteristic
348C4×C73#53611yescharacteristic
349C4×C73#54711yescharacteristic
350C4×C73#54711yescharacteristic
351#25653C7311yesmaximal, characteristic, direct product factor, Sylow
352C2×C73—82no—
353C2×C73—82no—
354C2×C73#243211yescharacteristic
355C2×C73#300211yescharacteristic
356C2×C73#301211yescharacteristic
357C2×C73#336111yescharacteristic
358C2×C73#336511yescharacteristic
359C2×C73#337011yescharacteristic
360C2×C73#337111yescharacteristic
361C2×#559C2×C7311yescharacteristic
362C2×#488C2×C7311yescharacteristic, complemented
363C2×#478C2×C7311yescharacteristic, complemented
364#2584C2×C7311yescharacteristic, complemented
365#2042C2×C7311yescharacteristic, complemented
366#2042C2×C7311yescharacteristic, complemented
367#2041C2×C7311yescharacteristic
368#2041C2×C7311yescharacteristic
369#1984C2×C7311yescharacteristic, complemented
370#1983C2×C7311yescharacteristic, complemented
371#1865C2×C7311yescharacteristic, complemented
372#1864C2×C7311yescharacteristic, complemented
373#1863C2×C7311yescharacteristic, complemented
374#1862C2×C7311yescharacteristic, complemented
375C4×#102C2×C7311yescharacteristic, complemented
376C73#2565311yescharacteristic, direct product factor, Sylow
377#559—24no—
378#559—24no—
379C2×#127C22×C7311yescharacteristic
380C2×#125C22×C7311yescharacteristic
381C2×#124—21no—
382C2×#124C22×C7311yescharacteristic
383C2×#124C22×C7311yescharacteristic
384C2×#123—21no—
385C2×#123—21no—
386C2×C4×Q8C22×C7311yescharacteristic
387C2×C4×Q8C22×C7311yescharacteristic
388C2×C4×D4—21no—
389C2×C4×D4C22×C7311yescharacteristic
390C2×C4×D4C22×C7311yescharacteristic
391#488—24no—
392#478—24no—
393C2×#107C22×C7311yescharacteristic
394C2×#106C22×C7311yescharacteristic
395C2×C4⋊C8C22×C7311yescharacteristic
396C2×#103C22×C7311yescharacteristic
397C2×#103C22×C7311yescharacteristic
398C2×#103C22×C7311yescharacteristic
399C2×#103C22×C7311yescharacteristic
400C2×#102C22×C7311yescharacteristic
401C2×#102C22×C7311yescharacteristic
402C2×#102C22×C7311yescharacteristic
403C2×#102C22×C7311yescharacteristic
404C2×#102C22×C7311yescharacteristic
405C2×#102C22×C7311yescharacteristic
406C2×#102C22×C7311yescharacteristic
407C2×#102C22×C7311yescharacteristic
408C2×C4×C8C22×C7311yescharacteristic
409#398—21no—
410#395—21no—
411#389—21no—
412#389—21no—
413#389C22×C7311yescharacteristic
414#389C22×C7311yescharacteristic
415#389C22×C7311yescharacteristic
416#389C22×C7311yescharacteristic
417C4×C4⋊C4C22×C7311yescharacteristic
418#340C22×C7311yescharacteristic
419#340C22×C7311yescharacteristic
420#336C22×C7311yescharacteristic
421#336C22×C7311yescharacteristic
422#336C22×C7311yescharacteristic
423#336C22×C7311yescharacteristic
424C22×Q8D4×C7311yescharacteristic
425C22×Q8C23×C7311yescharacteristic
426C22×D4—21no—
427C22×D4—21no—
428C22×D4C23×C7311yescharacteristic
429C22×D4C23×C7311yescharacteristic
430C23×C4—21no—
431C23×C4—21no—
432C22×C8C23×C7311yescharacteristic
433C22×C8C23×C7311yescharacteristic
434C22×C8C23×C7311yescharacteristic
435C22×C8C23×C7311yescharacteristic
436#127—22no—
437#127—22no—
438#125—22no—
439#125—22no—
440#124—28no—
441#124—22no—
442#124—22no—
443#124—22no—
444#124D4×C7314yes—
445#123—28no—
446#123—28no—
447C4×Q8—22no—
448C4×Q8—22no—
449C4×Q8—22no—
450C4×Q8—22no—
451C4×D4—28no—
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—22no—
455C4×D4D4×C7314yes—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4D4×C7311yescharacteristic
464C2×C4⋊C4D4×C7311yescharacteristic
465C2×C4⋊C4D4×C7311yescharacteristic
466C2×C4⋊C4C23×C7311yescharacteristic
467C2×C4⋊C4C23×C7311yescharacteristic
468C2×C4⋊C4C23×C7311yescharacteristic
469C2×C4⋊C4C23×C7311yescharacteristic
470C2×C4⋊C4C23×C7311yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42C23×C7311yescharacteristic
480C2×C42C23×C7311yescharacteristic
481C2×C42C23×C7311yescharacteristic
482#107—22no—
483#106—22no—
484C4⋊C8—22no—
485#103—22no—
486#103—22no—
487#103—22no—
488#103—22no—
489#102—22no—
490#102—22no—
491#102—22no—
492#102—22no—
493#102—22no—
494#102—22no—
495#102—22no—
496#102—22no—
497C4×C8—22no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503C24—21no—
504C24—21no—
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—41no—
513C2×Q8C2×D4×C7312yes—
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—81no—
529C2×D4—81no—
530C2×D4C2×D4×C7312yes—
531C2×D4C2×D4×C7312yes—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—81no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4—81no—
544C22×C4C2×D4×C7311yescharacteristic
545C22×C4C2×D4×C7311yescharacteristic
546C22×C4C2×D4×C7311yescharacteristic
547C22×C4C2×D4×C7311yescharacteristic
548C22×C4C2×D4×C7311yescharacteristic
549C22×C4C2×D4×C7311yescharacteristic
550C22×C4C24×C7311yescharacteristic
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C4⋊C4—24no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—81no—
579C4⋊C4—81no—
580C4⋊C4C2×D4×C7312yes—
581C4⋊C4#41×C7312yes—
582C4⋊C4#41×C7312yes—
583C22⋊C4—24no—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—24no—
589C42—24no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—81no—
595C42C2×D4×C7312yes—
596C42C2×D4×C7312yes—
597C23—22no—
598C23—22no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23C22×D4×C7311yescharacteristic
612Q8—22no—
613Q8—22no—
614Q8—44no—
615Q8—41no—
616Q8—41no—
617D4—22no—
618D4—22no—
619D4—22no—
620D4—22no—
621D4—48no—
622D4—41no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—84no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—84no—
661C2×C4—84no—
662C2×C4#120×C7312yes—
663C2×C4#120×C7312yes—
664C2×C4#135×C7312yes—
665C2×C4C22×D4×C7311yescharacteristic
666C2×C4C22×D4×C7311yescharacteristic
667C2×C4C2×#41×C7311yescharacteristic
668C2×C4C2×#41×C7311yescharacteristic
669C2×C42−1+4×C7311yescharacteristic
670C2×C42−1+4×C7311yescharacteristic
671C8—41no—
672C8—41no—
673C8—41no—
674C8—41no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×#120×C7311yescharacteristic
690C22#548×C7311yescharacteristic
691C22#548×C7311yescharacteristic
692C22C2×#135×C7311yescharacteristic
693C22#575×C7311yescharacteristic
694C22#576×C7311yescharacteristic
695C22#577×C7311yescharacteristic
696C4—22no—
697C4—22no—
698C4—22no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—81no—
707C4—81no—
708C4#532×C7311yescharacteristic
709C4#536×C7311yescharacteristic
710C4#547×C7311yescharacteristic
711C4#547×C7311yescharacteristic
712C2—82no—
713C2—82no—
714C2C73×#243211yescharacteristic
715C2C73×#300211yescharacteristic
716C2C73×#301211yescharacteristic
717C2C73×#336111yescharacteristic
718C2C73×#336511yescharacteristic
719C2C73×#337011yescharacteristic
720C2C73×#337111yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#127×C73C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C4×Q8×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#488×C73C2semidirect
3. C2×#478×C73C2semidirect
4. C73×#2584C2semidirect
5. C73×#2042C2semidirect
6. C73×#2042C2semidirect
9. C73×#1984C2semidirect
10. C73×#1983C2semidirect
11. C73×#1865C2semidirect
12. C73×#1864C2semidirect
13. C73×#1863C2semidirect
14. C73×#1862C2semidirect
15. C4×#102×C73C2semidirect
351. #25653C73direct (N × H)
362. C2×#488C2×C73semidirect
363. C2×#478C2×C73semidirect
364. #2584C2×C73semidirect
365. #2042C2×C73semidirect
366. #2042C2×C73semidirect
369. #1984C2×C73semidirect
370. #1983C2×C73semidirect
371. #1865C2×C73semidirect
372. #1864C2×C73semidirect
373. #1863C2×C73semidirect
374. #1862C2×C73semidirect
375. C4×#102C2×C73semidirect
376. C73#25653direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#559×C732
C2×#488×C732
C2×#478×C732
C73×#25842
C73×#20422
C73×#20412
C73×#19842
C73×#19832
C73×#18652
C73×#18642
C73×#18632
C73×#18622
C4×#102×C732
#2565373