Finite Group Databasebeta

← C73×#25684 #32935088

Subgroups — C73×#25684 #32935088

Order 18688.

1024 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#542×C73C211yesmaximal, characteristic
2C2×#501×C73C211yesmaximal, characteristic, complemented
3C2×#488×C73C211yesmaximal, characteristic, complemented
4C73×#2629C211yesmaximal, characteristic, complemented
5C73×#2036C211yesmaximal, characteristic, complemented
6C73×#2035C211yesmaximal, characteristic, complemented
7C73×#2034C211yesmaximal, characteristic
8C73×#2033C211yesmaximal, characteristic
9C73×#1990C211yesmaximal, characteristic, complemented
10C73×#1959C211yesmaximal, characteristic, complemented
11C73×#1865C211yesmaximal, characteristic, complemented
12C73×#1864C211yesmaximal, characteristic, complemented
13C73×#1863C211yesmaximal, characteristic, complemented
14C73×#1862C211yesmaximal, characteristic, complemented
15C73×#1750C211yesmaximal, characteristic, complemented
16#542×C73—24no—
17#542×C73—24no—
18C2×C4⋊Q8×C73C2211yescharacteristic
19C2×#126×C73—21no—
20C2×#125×C73C2211yescharacteristic
21C2×#124×C73—21no—
22C2×#124×C73C2211yescharacteristic
23C2×#123×C73—21no—
24C2×C22⋊Q8×C73—21no—
25C2×C22⋊Q8×C73C2211yescharacteristic
26C2×#121×C73C2211yescharacteristic
27C2×C4×Q8×C73C2211yescharacteristic
28C2×C4×D4×C73C2211yescharacteristic
29C2×#117×C73C2211yescharacteristic
30#501×C73—24no—
31#488×C73—24no—
32C2×#107×C73C2211yescharacteristic
33C2×#107×C73C2211yescharacteristic
34C2×#106×C73C2211yescharacteristic
35C2×#106×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#103×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44C2×C22⋊C8×C73C2211yescharacteristic
45C2×C22⋊C8×C73C2211yescharacteristic
46C2×#97×C73C2211yescharacteristic
47C2×C4×C8×C73C2211yescharacteristic
48#398×C73—21no—
49#398×C73—21no—
50#396×C73—21no—
51#396×C73—21no—
52#389×C73C2211yescharacteristic
53#389×C73C2211yescharacteristic
54#384×C73C2211yescharacteristic
55#380×C73C2211yescharacteristic
56#380×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×C73C2211yescharacteristic
63C22×Q8×C73—21no—
64C22×Q8×C73C2311yescharacteristic
65C22×D4×C73—21no—
66C22×D4×C73C2311yescharacteristic
67C23×C4×C73—21no—
68C23×C4×C73C2311yescharacteristic
69C22×C8×C73C2311yescharacteristic
70C22×C8×C73C2311yescharacteristic
71C22×C8×C73C2311yescharacteristic
72C22×C8×C73C2311yescharacteristic
73C4⋊Q8×C73—22no—
74C4⋊Q8×C73D414yes—
75#126×C73—28no—
76#125×C73—22no—
77#125×C73—22no—
78#124×C73—28no—
79#124×C73—22no—
80#124×C73D414yes—
81#123×C73—28no—
82C22⋊Q8×C73—28no—
83C22⋊Q8×C73—22no—
84C22⋊Q8×C73—22no—
85#121×C73—22no—
86#121×C73—22no—
87C4×Q8×C73—22no—
88C4×Q8×C73—22no—
89C4×D4×C73—22no—
90C4×D4×C73—22no—
91#117×C73—22no—
92#117×C73—22no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—21no—
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×C73C2311yescharacteristic
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×C22⋊C4×C73—21no—
117C2×C22⋊C4×C73D411yescharacteristic
118C2×C22⋊C4×C73D411yescharacteristic
119C2×C42×C73—21no—
120C2×C42×C73C2311yescharacteristic
121C2×C42×C73C2311yescharacteristic
122#107×C73—22no—
123#107×C73—22no—
124#106×C73—22no—
125#106×C73—22no—
126#103×C73—22no—
127#103×C73—22no—
128#103×C73—22no—
129#103×C73—22no—
130#102×C73—22no—
131#102×C73—22no—
132#102×C73—22no—
133#102×C73—22no—
134C22⋊C8×C73—22no—
135C22⋊C8×C73—22no—
136#97×C73—22no—
137C4×C8×C73—22no—
138#95×C73—21no—
139#95×C73—21no—
140#95×C73—21no—
141#95×C73—21no—
142C24×C73—21no—
143C24×C73C2×D411yescharacteristic
144C2×Q8×C73—24no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×Q8×C73—81no—
151C2×Q8×C73—81no—
152C2×Q8×C73C2×D412yes—
153C2×D4×C73—24no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—21no—
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—24no—
166C22×C4×C73—21no—
167C22×C4×C73—21no—
168C22×C4×C73—21no—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—81no—
177C22×C4×C73—81no—
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D411yescharacteristic
181C22×C4×C73C2×D411yescharacteristic
182C22×C4×C73C2×D411yescharacteristic
183C22×C4×C73C2411yescharacteristic
184C2×C8×C73—21no—
185C2×C8×C73—21no—
186C2×C8×C73—21no—
187C2×C8×C73—21no—
188C2×C8×C73—21no—
189C2×C8×C73—21no—
190C2×C8×C73—21no—
191C2×C8×C73—21no—
192C2×C8×C73—21no—
193C2×C8×C73—21no—
194C2×C8×C73#4112yes—
195C2×C8×C73#4112yes—
196C4⋊C4×C73—24no—
197C4⋊C4×C73—24no—
198C4⋊C4×C73—24no—
199C4⋊C4×C73—22no—
200C4⋊C4×C73—22no—
201C4⋊C4×C73—21no—
202C4⋊C4×C73—21no—
203C4⋊C4×C73—21no—
204C4⋊C4×C73—21no—
205C4⋊C4×C73—21no—
206C4⋊C4×C73—21no—
207C4⋊C4×C73—21no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—42no—
212C4⋊C4×C73—42no—
213C4⋊C4×C73—81no—
214C4⋊C4×C73—81no—
215C4⋊C4×C73—81no—
216C4⋊C4×C73—81no—
217C4⋊C4×C73C2×D412yes—
218C4⋊C4×C73C2×D412yes—
219C22⋊C4×C73—24no—
220C22⋊C4×C73—24no—
221C22⋊C4×C73—24no—
222C22⋊C4×C73—24no—
223C22⋊C4×C73—24no—
224C22⋊C4×C73—22no—
225C22⋊C4×C73—22no—
226C22⋊C4×C73—81no—
227C22⋊C4×C73—81no—
228C42×C73—24no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73C2×D412yes—
232C42×C73C2×D412yes—
233C23×C73—21no—
234C23×C73—22no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—41no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73—41no—
245C23×C73—41no—
246C23×C73—41no—
247C23×C73C22×D411yescharacteristic
248Q8×C73—22no—
249Q8×C73—22no—
250Q8×C73—41no—
251Q8×C73—41no—
252Q8×C73—84no—
253D4×C73—22no—
254D4×C73—22no—
255D4×C73—41no—
256D4×C73—41no—
257D4×C73—84no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—22no—
264C2×C4×C73—21no—
265C2×C4×C73—22no—
266C2×C4×C73—21no—
267C2×C4×C73—22no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—21no—
272C2×C4×C73—21no—
273C2×C4×C73—21no—
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—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—84no—
297C2×C4×C73#12012yes—
298C2×C4×C73#12012yes—
299C2×C4×C73C22×D411yescharacteristic
300C2×C4×C73C22×D411yescharacteristic
301C2×C4×C73C2×#4111yescharacteristic
302C2×C4×C73C2×#4111yescharacteristic
303C2×C4×C732−1+411yescharacteristic
304C2×C4×C732−1+411yescharacteristic
305C8×C73—22no—
306C8×C73—22no—
307C8×C73—41no—
308C8×C73—41no—
309C22×C73—41no—
310C22×C73—41no—
311C22×C73—41no—
312C22×C73—42no—
313C22×C73—41no—
314C22×C73—41no—
315C22×C73—42no—
316C22×C73—41no—
317C22×C73—41no—
318C22×C73—42no—
319C22×C73—81no—
320C22×C73—81no—
321C22×C73—81no—
322C22×C73—81no—
323C22×C73C2×#12011yescharacteristic
324C22×C73#53211yescharacteristic
325C22×C73#53611yescharacteristic
326C22×C73#57611yescharacteristic
327C22×C73#57711yescharacteristic
328C22×C73#57711yescharacteristic
329C22×C73#57811yescharacteristic
330C4×C73—22no—
331C4×C73—22no—
332C4×C73—41no—
333C4×C73—42no—
334C4×C73—41no—
335C4×C73—42no—
336C4×C73—42no—
337C4×C73—41no—
338C4×C73—81no—
339C4×C73—81no—
340C4×C73—81no—
341C4×C73—81no—
342C4×C73#54711yescharacteristic
343C4×C73#54711yescharacteristic
344C4×C73#54811yescharacteristic
345C4×C73#54811yescharacteristic
346#25684C7311yesmaximal, characteristic, direct product factor, Sylow
347C2×C73—81no—
348C2×C73—82no—
349C2×C73#243211yescharacteristic
350C2×C73#301211yescharacteristic
351C2×C73#301311yescharacteristic
352C2×C73#317811yescharacteristic
353C2×C73#317911yescharacteristic
354C2×C73#324311yescharacteristic
355C2×C73#324411yescharacteristic
356C2×#542C2×C7311yescharacteristic
357C2×#501C2×C7311yescharacteristic, complemented
358C2×#488C2×C7311yescharacteristic, complemented
359#2629C2×C7311yescharacteristic, complemented
360#2036C2×C7311yescharacteristic, complemented
361#2035C2×C7311yescharacteristic, complemented
362#2034C2×C7311yescharacteristic
363#2033C2×C7311yescharacteristic
364#1990C2×C7311yescharacteristic, complemented
365#1959C2×C7311yescharacteristic, complemented
366#1865C2×C7311yescharacteristic, complemented
367#1864C2×C7311yescharacteristic, complemented
368#1863C2×C7311yescharacteristic, complemented
369#1862C2×C7311yescharacteristic, complemented
370#1750C2×C7311yescharacteristic, complemented
371C73#2568411yescharacteristic, direct product factor, Sylow
372#542—24no—
373#542—24no—
374C2×C4⋊Q8C22×C7311yescharacteristic
375C2×#126—21no—
376C2×#125C22×C7311yescharacteristic
377C2×#124—21no—
378C2×#124C22×C7311yescharacteristic
379C2×#123—21no—
380C2×C22⋊Q8—21no—
381C2×C22⋊Q8C22×C7311yescharacteristic
382C2×#121C22×C7311yescharacteristic
383C2×C4×Q8C22×C7311yescharacteristic
384C2×C4×D4C22×C7311yescharacteristic
385C2×#117C22×C7311yescharacteristic
386#501—24no—
387#488—24no—
388C2×#107C22×C7311yescharacteristic
389C2×#107C22×C7311yescharacteristic
390C2×#106C22×C7311yescharacteristic
391C2×#106C22×C7311yescharacteristic
392C2×#103C22×C7311yescharacteristic
393C2×#103C22×C7311yescharacteristic
394C2×#103C22×C7311yescharacteristic
395C2×#103C22×C7311yescharacteristic
396C2×#102C22×C7311yescharacteristic
397C2×#102C22×C7311yescharacteristic
398C2×#102C22×C7311yescharacteristic
399C2×#102C22×C7311yescharacteristic
400C2×C22⋊C8C22×C7311yescharacteristic
401C2×C22⋊C8C22×C7311yescharacteristic
402C2×#97C22×C7311yescharacteristic
403C2×C4×C8C22×C7311yescharacteristic
404#398—21no—
405#398—21no—
406#396—21no—
407#396—21no—
408#389C22×C7311yescharacteristic
409#389C22×C7311yescharacteristic
410#384C22×C7311yescharacteristic
411#380C22×C7311yescharacteristic
412#380C22×C7311yescharacteristic
413#340C22×C7311yescharacteristic
414#340C22×C7311yescharacteristic
415#340C22×C7311yescharacteristic
416#340C22×C7311yescharacteristic
417#336C22×C7311yescharacteristic
418#336C22×C7311yescharacteristic
419C22×Q8—21no—
420C22×Q8C23×C7311yescharacteristic
421C22×D4—21no—
422C22×D4C23×C7311yescharacteristic
423C23×C4—21no—
424C23×C4C23×C7311yescharacteristic
425C22×C8C23×C7311yescharacteristic
426C22×C8C23×C7311yescharacteristic
427C22×C8C23×C7311yescharacteristic
428C22×C8C23×C7311yescharacteristic
429C4⋊Q8—22no—
430C4⋊Q8D4×C7314yes—
431#126—28no—
432#125—22no—
433#125—22no—
434#124—28no—
435#124—22no—
436#124D4×C7314yes—
437#123—28no—
438C22⋊Q8—28no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441#121—22no—
442#121—22no—
443C4×Q8—22no—
444C4×Q8—22no—
445C4×D4—22no—
446C4×D4—22no—
447#117—22no—
448#117—22no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4D4×C7311yescharacteristic
459C2×C4⋊C4D4×C7311yescharacteristic
460C2×C4⋊C4C23×C7311yescharacteristic
461C2×C4⋊C4C23×C7311yescharacteristic
462C2×C4⋊C4C23×C7311yescharacteristic
463C2×C4⋊C4C23×C7311yescharacteristic
464C2×C4⋊C4C23×C7311yescharacteristic
465C2×C4⋊C4C23×C7311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4D4×C7311yescharacteristic
474C2×C22⋊C4D4×C7311yescharacteristic
475C2×C42—21no—
476C2×C42C23×C7311yescharacteristic
477C2×C42C23×C7311yescharacteristic
478#107—22no—
479#107—22no—
480#106—22no—
481#106—22no—
482#103—22no—
483#103—22no—
484#103—22no—
485#103—22no—
486#102—22no—
487#102—22no—
488#102—22no—
489#102—22no—
490C22⋊C8—22no—
491C22⋊C8—22no—
492#97—22no—
493C4×C8—22no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498C24—21no—
499C24C2×D4×C7311yescharacteristic
500C2×Q8—24no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—81no—
507C2×Q8—81no—
508C2×Q8C2×D4×C7312yes—
509C2×D4—24no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—81no—
516C2×D4—81no—
517C2×D4C2×D4×C7312yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—24no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—81no—
533C22×C4—81no—
534C22×C4C2×D4×C7311yescharacteristic
535C22×C4C2×D4×C7311yescharacteristic
536C22×C4C2×D4×C7311yescharacteristic
537C22×C4C2×D4×C7311yescharacteristic
538C22×C4C2×D4×C7311yescharacteristic
539C22×C4C24×C7311yescharacteristic
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8#41×C7312yes—
551C2×C8#41×C7312yes—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—81no—
570C4⋊C4—81no—
571C4⋊C4—81no—
572C4⋊C4—81no—
573C4⋊C4C2×D4×C7312yes—
574C4⋊C4C2×D4×C7312yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C42—24no—
585C42—21no—
586C42—21no—
587C42C2×D4×C7312yes—
588C42C2×D4×C7312yes—
589C23—21no—
590C23—22no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23C22×D4×C7311yescharacteristic
604Q8—22no—
605Q8—22no—
606Q8—41no—
607Q8—41no—
608Q8—84no—
609D4—22no—
610D4—22no—
611D4—41no—
612D4—41no—
613D4—84no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—84no—
653C2×C4#120×C7312yes—
654C2×C4#120×C7312yes—
655C2×C4C22×D4×C7311yescharacteristic
656C2×C4C22×D4×C7311yescharacteristic
657C2×C4C2×#41×C7311yescharacteristic
658C2×C4C2×#41×C7311yescharacteristic
659C2×C42−1+4×C7311yescharacteristic
660C2×C42−1+4×C7311yescharacteristic
661C8—22no—
662C8—22no—
663C8—41no—
664C8—41no—
665C22—41no—
666C22—41no—
667C22—42no—
668C22—41no—
669C22—41no—
670C22—42no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C2×#120×C7311yescharacteristic
680C22#532×C7311yescharacteristic
681C22#536×C7311yescharacteristic
682C22#576×C7311yescharacteristic
683C22#577×C7311yescharacteristic
684C22#577×C7311yescharacteristic
685C22#578×C7311yescharacteristic
686C4—22no—
687C4—22no—
688C4—41no—
689C4—42no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—42no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4#547×C7311yescharacteristic
699C4#547×C7311yescharacteristic
700C4#548×C7311yescharacteristic
701C4#548×C7311yescharacteristic
702C2—81no—
703C2—82no—
704C2C73×#243211yescharacteristic
705C2C73×#301211yescharacteristic
706C2C73×#301311yescharacteristic
707C2C73×#317811yescharacteristic
708C2C73×#317911yescharacteristic
709C2C73×#324311yescharacteristic
710C2C73×#324411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#121×C73C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×#117×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#501×C73C2semidirect
3. C2×#488×C73C2semidirect
4. C73×#2629C2semidirect
5. C73×#2036C2semidirect
6. C73×#2035C2semidirect
9. C73×#1990C2semidirect
10. C73×#1959C2semidirect
11. C73×#1865C2semidirect
12. C73×#1864C2semidirect
13. C73×#1863C2semidirect
14. C73×#1862C2semidirect
15. C73×#1750C2semidirect
346. #25684C73direct (N × H)
357. C2×#501C2×C73semidirect
358. C2×#488C2×C73semidirect
359. #2629C2×C73semidirect
360. #2036C2×C73semidirect
361. #2035C2×C73semidirect
364. #1990C2×C73semidirect
365. #1959C2×C73semidirect
366. #1865C2×C73semidirect
367. #1864C2×C73semidirect
368. #1863C2×C73semidirect
369. #1862C2×C73semidirect
370. #1750C2×C73semidirect
371. C73#25684direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#542×C732
C2×#501×C732
C2×#488×C732
C73×#26292
C73×#20362
C73×#20352
C73×#20342
C73×#20332
C73×#19902
C73×#19592
C73×#18652
C73×#18642
C73×#18632
C73×#18622
C73×#17502
#2568473