Finite Group Databasebeta

← C73×#22881 #32932285

Subgroups — C73×#22881 #32932285

Order 18688.

1058 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#451×C73C211yesmaximal, characteristic
2C2×C4×Q16×C73C211yesmaximal, characteristic, complemented
3C2×#419×C73C211yesmaximal, characteristic
4C73×#2362C211yesmaximal, characteristic
5Q8×C22⋊C4×C73C211yesmaximal, characteristic
6C73×#1971C211yesmaximal, characteristic, complemented
7C73×#1933C211yesmaximal, characteristic, complemented
8C73×#1928C211yesmaximal, characteristic, complemented
9C73×#1894C211yesmaximal, characteristic
10C73×#1878C211yesmaximal, characteristic, complemented
11C73×#1878C211yesmaximal, characteristic, complemented
12C73×#1865C211yesmaximal, characteristic, complemented
13C73×#1854C211yesmaximal, characteristic
14C73×#1763C211yesmaximal, characteristic, complemented
15C73×#1753C211yesmaximal, characteristic
16C23×Q8×C73C2211yescharacteristic
17C22×Q16×C73C2211yescharacteristic
18C22×Q16×C73C2211yescharacteristic
19C22×M16×C73C2211yescharacteristic
20C2×C22⋊Q8×C73C2211yescharacteristic
21C2×C4×Q8×C73C2211yescharacteristic
22C2×C4×Q8×C73C2211yescharacteristic
23C2×C4×Q8×C73C2211yescharacteristic
24C2×#117×C73C2211yescharacteristic
25#451×C73C418yescomplemented
26C4×Q16×C73—24no—
27C2×#107×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29#419×C73—24no—
30C2×#103×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#103×C73C2211yescharacteristic
35C2×#103×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×#97×C73C2211yescharacteristic
40C2×C4×C8×C73C2211yescharacteristic
41#391×C73—21no—
42#391×C73—21no—
43#391×C73C2211yescharacteristic
44#391×C73C2211yescharacteristic
45#391×C73C2211yescharacteristic
46#389×C73C2211yescharacteristic
47#388×C73—21no—
48#388×C73—21no—
49#387×C73—21no—
50#380×C73—21no—
51#380×C73C2211yescharacteristic
52C4×C4⋊C4×C73—21no—
53C4×C4⋊C4×C73C2211yescharacteristic
54C4×C22⋊C4×C73—21no—
55C4×C22⋊C4×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62C22×Q8×C73—21no—
63C22×Q8×C73—22no—
64C22×Q8×C73—22no—
65C22×Q8×C73—22no—
66C22×Q8×C73—41no—
67C22×Q8×C73—41no—
68C22×Q8×C73C2×C414yes—
69C22×Q8×C73C2311yescharacteristic
70C22×Q8×C73C2311yescharacteristic
71C22×Q8×C73C2311yescharacteristic
72C23×C4×C73—21no—
73C23×C4×C73C2311yescharacteristic
74C2×Q16×C73—22no—
75C2×Q16×C73—22no—
76C2×Q16×C73—41no—
77C2×Q16×C73—41no—
78C2×Q16×C73C2×C414yes—
79C2×Q16×C73C2×C414yes—
80C2×M16×C73—22no—
81C2×M16×C73—22no—
82C2×M16×C73—41no—
83C22×C8×C73C2311yescharacteristic
84C22×C8×C73C2311yescharacteristic
85C22×C8×C73C2311yescharacteristic
86C22×C8×C73C2311yescharacteristic
87C22⋊Q8×C73—22no—
88C22⋊Q8×C73C2×C414yes—
89C4×Q8×C73—22no—
90C4×Q8×C73—22no—
91C4×Q8×C73—22no—
92C4×Q8×C73—41no—
93C4×Q8×C73—41no—
94C4×Q8×C73—41no—
95#117×C73—22no—
96#117×C73—41no—
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×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2311yescharacteristic
105C2×C4⋊C4×C73C2311yescharacteristic
106C2×C4⋊C4×C73C2311yescharacteristic
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73D411yescharacteristic
111C2×C22⋊C4×C73D411yescharacteristic
112C2×C42×C73—21no—
113C2×C42×C73—21no—
114C2×C42×C73—21no—
115C2×C42×C73—21no—
116C2×C42×C73—21no—
117C2×C42×C73C2311yescharacteristic
118C2×C42×C73C2311yescharacteristic
119#107×C73—22no—
120#106×C73—41no—
121#103×C73—22no—
122#103×C73—22no—
123#103×C73—22no—
124#103×C73—22no—
125#103×C73—41no—
126#103×C73C2×C414yes—
127#103×C73C2×C414yes—
128#103×C73D414yes—
129C22⋊C8×C73C2×C414yes—
130#97×C73—41no—
131C4×C8×C73—22no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73—21no—
138#95×C73—21no—
139#95×C73—21no—
140#95×C73—21no—
141#95×C73D411yescharacteristic
142#95×C73D411yescharacteristic
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—28no—
151C2×Q8×C73—21no—
152C2×Q8×C73—21no—
153C2×Q8×C73—21no—
154C2×Q8×C73—21no—
155C2×Q8×C73—21no—
156C2×Q8×C73—21no—
157C2×Q8×C73—21no—
158C2×Q8×C73—21no—
159C2×Q8×C73—42no—
160C2×Q8×C73—42no—
161C2×Q8×C73—44no—
162C2×Q8×C73—44no—
163C2×Q8×C73—44no—
164C2×Q8×C73C22×C412yes—
165C2×Q8×C73C22×C412yes—
166C2×Q8×C73C22×C412yes—
167C2×Q8×C73C2×D412yes—
168C2×Q8×C73#4112yes—
169C22×C4×C73—21no—
170C22×C4×C73—21no—
171C22×C4×C73—21no—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—24no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—21no—
181C22×C4×C73—21no—
182C22×C4×C73—42no—
183C22×C4×C73—42no—
184C22×C4×C73C22×C412yes—
185C22×C4×C73C2×D411yescharacteristic
186C22×C4×C73C2×D411yescharacteristic
187C22×C4×C73C2×D411yescharacteristic
188C22×C4×C73C2×D411yescharacteristic
189C22×C4×C73C2×D411yescharacteristic
190C22×C4×C73#4112yes—
191C22×C4×C73C2411yescharacteristic
192Q16×C73—28no—
193Q16×C73—44no—
194M16×C73—44no—
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—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73C22×C412yes—
205C2×C8×C73C22×C412yes—
206C2×C8×C73C2×D412yes—
207C4⋊C4×C73—24no—
208C4⋊C4×C73—21no—
209C4⋊C4×C73—21no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73—42no—
217C4⋊C4×C73—42no—
218C4⋊C4×C73—42no—
219C4⋊C4×C73—42no—
220C4⋊C4×C73C22×C412yes—
221C4⋊C4×C73C2×D412yes—
222C22⋊C4×C73—24no—
223C22⋊C4×C73—22no—
224C22⋊C4×C73—41no—
225C22⋊C4×C73—42no—
226C22⋊C4×C73—42no—
227C42×C73—21no—
228C42×C73—21no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—42no—
232C42×C73—42no—
233C42×C73—42no—
234C42×C73—42no—
235C42×C73—42no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73C4×D412yes—
243C23×C73C22×D411yescharacteristic
244Q8×C73—22no—
245Q8×C73—22no—
246Q8×C73—22no—
247Q8×C73—22no—
248Q8×C73—22no—
249Q8×C73—22no—
250Q8×C73—22no—
251Q8×C73—48no—
252Q8×C73—41no—
253Q8×C73—41no—
254Q8×C73—41no—
255Q8×C73—41no—
256Q8×C73C4×D414yes—
257C2×C4×C73—22no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—22no—
261C2×C4×C73—22no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—21no—
272C2×C4×C73—22no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—21no—
277C2×C4×C73—21no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—48no—
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—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73C4×D412yes—
300C2×C4×C73#13712yes—
301C2×C4×C73C23×C411yescharacteristic
302C2×C4×C73C22×D411yescharacteristic
303C2×C4×C73C2×#4111yescharacteristic
304C2×C4×C73C2×#4111yescharacteristic
305C2×C4×C73H(5,𝔽2)11yescharacteristic
306C2×C4×C73H(5,𝔽2)11yescharacteristic
307C8×C73—22no—
308C8×C73—22no—
309C8×C73—22no—
310C8×C73—41no—
311C22×C73—22no—
312C22×C73—22no—
313C22×C73—22no—
314C22×C73—41no—
315C22×C73—41no—
316C22×C73—41no—
317C22×C73—41no—
318C22×C73C2×C4×D411yescharacteristic
319C22×C73D4211yescharacteristic
320C22×C73#54611yescharacteristic
321C22×C73C2×#13711yescharacteristic
322C22×C73#57511yescharacteristic
323C22×C73#57811yescharacteristic
324C22×C73#57811yescharacteristic
325C4×C73—22no—
326C4×C73—24no—
327C4×C73—22no—
328C4×C73—41no—
329C4×C73—42no—
330C4×C73—42no—
331C4×C73—42no—
332C4×C73—41no—
333C4×C73—42no—
334C4×C73—41no—
335C4×C73—81no—
336C4×C73—81no—
337C4×C73—81no—
338C4×C73C2×C4×D411yescharacteristic
339C4×C73#51811yescharacteristic
340C4×C73#54611yescharacteristic
341C4×C73#55111yescharacteristic
342#22881C7311yesmaximal, characteristic, direct product factor, Sylow
343C2×C73—42no—
344C2×C73#235811yescharacteristic
345C2×C73C4×#13711yescharacteristic
346C2×C73#295011yescharacteristic
347C2×C73#326911yescharacteristic
348C2×C73#327011yescharacteristic
349C2×C73#332711yescharacteristic
350C2×C73#332811yescharacteristic
351C2×#451C2×C7311yescharacteristic
352C2×C4×Q16C2×C7311yescharacteristic, complemented
353C2×#419C2×C7311yescharacteristic
354#2362C2×C7311yescharacteristic
355Q8×C22⋊C4C2×C7311yescharacteristic
356#1971C2×C7311yescharacteristic, complemented
357#1933C2×C7311yescharacteristic, complemented
358#1928C2×C7311yescharacteristic, complemented
359#1894C2×C7311yescharacteristic
360#1878C2×C7311yescharacteristic, complemented
361#1878C2×C7311yescharacteristic, complemented
362#1865C2×C7311yescharacteristic, complemented
363#1854C2×C7311yescharacteristic
364#1763C2×C7311yescharacteristic, complemented
365#1753C2×C7311yescharacteristic
366C73#2288111yescharacteristic, direct product factor, Sylow
367C23×Q8C22×C7311yescharacteristic
368C22×Q16C22×C7311yescharacteristic
369C22×Q16C22×C7311yescharacteristic
370C22×M16C22×C7311yescharacteristic
371C2×C22⋊Q8C22×C7311yescharacteristic
372C2×C4×Q8C22×C7311yescharacteristic
373C2×C4×Q8C22×C7311yescharacteristic
374C2×C4×Q8C22×C7311yescharacteristic
375C2×#117C22×C7311yescharacteristic
376#451C4×C7318yescomplemented
377C4×Q16—24no—
378C2×#107C22×C7311yescharacteristic
379C2×#106C22×C7311yescharacteristic
380#419—24no—
381C2×#103C22×C7311yescharacteristic
382C2×#103C22×C7311yescharacteristic
383C2×#103C22×C7311yescharacteristic
384C2×#103C22×C7311yescharacteristic
385C2×#103C22×C7311yescharacteristic
386C2×#103C22×C7311yescharacteristic
387C2×#103C22×C7311yescharacteristic
388C2×#103C22×C7311yescharacteristic
389C2×C22⋊C8C22×C7311yescharacteristic
390C2×#97C22×C7311yescharacteristic
391C2×C4×C8C22×C7311yescharacteristic
392#391—21no—
393#391—21no—
394#391C22×C7311yescharacteristic
395#391C22×C7311yescharacteristic
396#391C22×C7311yescharacteristic
397#389C22×C7311yescharacteristic
398#388—21no—
399#388—21no—
400#387—21no—
401#380—21no—
402#380C22×C7311yescharacteristic
403C4×C4⋊C4—21no—
404C4×C4⋊C4C22×C7311yescharacteristic
405C4×C22⋊C4—21no—
406C4×C22⋊C4C22×C7311yescharacteristic
407#340C22×C7311yescharacteristic
408#340C22×C7311yescharacteristic
409#340C22×C7311yescharacteristic
410#340C22×C7311yescharacteristic
411#336C22×C7311yescharacteristic
412#336C22×C7311yescharacteristic
413C22×Q8—21no—
414C22×Q8—22no—
415C22×Q8—22no—
416C22×Q8—22no—
417C22×Q8—41no—
418C22×Q8—41no—
419C22×Q8C2×C4×C7314yes—
420C22×Q8C23×C7311yescharacteristic
421C22×Q8C23×C7311yescharacteristic
422C22×Q8C23×C7311yescharacteristic
423C23×C4—21no—
424C23×C4C23×C7311yescharacteristic
425C2×Q16—22no—
426C2×Q16—22no—
427C2×Q16—41no—
428C2×Q16—41no—
429C2×Q16C2×C4×C7314yes—
430C2×Q16C2×C4×C7314yes—
431C2×M16—22no—
432C2×M16—22no—
433C2×M16—41no—
434C22×C8C23×C7311yescharacteristic
435C22×C8C23×C7311yescharacteristic
436C22×C8C23×C7311yescharacteristic
437C22×C8C23×C7311yescharacteristic
438C22⋊Q8—22no—
439C22⋊Q8C2×C4×C7314yes—
440C4×Q8—22no—
441C4×Q8—22no—
442C4×Q8—22no—
443C4×Q8—41no—
444C4×Q8—41no—
445C4×Q8—41no—
446#117—22no—
447#117—41no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4C23×C7311yescharacteristic
454C2×C4⋊C4C23×C7311yescharacteristic
455C2×C4⋊C4C23×C7311yescharacteristic
456C2×C4⋊C4C23×C7311yescharacteristic
457C2×C4⋊C4C23×C7311yescharacteristic
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4D4×C7311yescharacteristic
462C2×C22⋊C4D4×C7311yescharacteristic
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42C23×C7311yescharacteristic
469C2×C42C23×C7311yescharacteristic
470#107—22no—
471#106—41no—
472#103—22no—
473#103—22no—
474#103—22no—
475#103—22no—
476#103—41no—
477#103C2×C4×C7314yes—
478#103C2×C4×C7314yes—
479#103D4×C7314yes—
480C22⋊C8C2×C4×C7314yes—
481#97—41no—
482C4×C8—22no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95D4×C7311yescharacteristic
493#95D4×C7311yescharacteristic
494C24C2×D4×C7311yescharacteristic
495C2×Q8—24no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—28no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8C22×C4×C7312yes—
516C2×Q8C22×C4×C7312yes—
517C2×Q8C22×C4×C7312yes—
518C2×Q8C2×D4×C7312yes—
519C2×Q8#41×C7312yes—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—24no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4C22×C4×C7312yes—
536C22×C4C2×D4×C7311yescharacteristic
537C22×C4C2×D4×C7311yescharacteristic
538C22×C4C2×D4×C7311yescharacteristic
539C22×C4C2×D4×C7311yescharacteristic
540C22×C4C2×D4×C7311yescharacteristic
541C22×C4#41×C7312yes—
542C22×C4C24×C7311yescharacteristic
543Q16—28no—
544Q16—44no—
545M16—44no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8C22×C4×C7312yes—
556C2×C8C22×C4×C7312yes—
557C2×C8C2×D4×C7312yes—
558C4⋊C4—24no—
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—42no—
570C4⋊C4—42no—
571C4⋊C4C22×C4×C7312yes—
572C4⋊C4C2×D4×C7312yes—
573C22⋊C4—24no—
574C22⋊C4—22no—
575C22⋊C4—41no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—42no—
583C42—42no—
584C42—42no—
585C42—42no—
586C42—42no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23C4×D4×C7312yes—
594C23C22×D4×C7311yescharacteristic
595Q8—22no—
596Q8—22no—
597Q8—22no—
598Q8—22no—
599Q8—22no—
600Q8—22no—
601Q8—22no—
602Q8—48no—
603Q8—41no—
604Q8—41no—
605Q8—41no—
606Q8—41no—
607Q8C4×D4×C7314yes—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
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—21no—
631C2×C4—21no—
632C2×C4—48no—
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×C4C4×D4×C7312yes—
651C2×C4#137×C7312yes—
652C2×C4C23×C4×C7311yescharacteristic
653C2×C4C22×D4×C7311yescharacteristic
654C2×C4C2×#41×C7311yescharacteristic
655C2×C4C2×#41×C7311yescharacteristic
656C2×C4H(5,𝔽2)×C7311yescharacteristic
657C2×C4H(5,𝔽2)×C7311yescharacteristic
658C8—22no—
659C8—22no—
660C8—22no—
661C8—41no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22C2×C4×D4×C7311yescharacteristic
670C22D42×C7311yescharacteristic
671C22#546×C7311yescharacteristic
672C22C2×#137×C7311yescharacteristic
673C22#575×C7311yescharacteristic
674C22#578×C7311yescharacteristic
675C22#578×C7311yescharacteristic
676C4—22no—
677C4—22no—
678C4—24no—
679C4—41no—
680C4—42no—
681C4—41no—
682C4—41no—
683C4—42no—
684C4—42no—
685C4—42no—
686C4—81no—
687C4—81no—
688C4—81no—
689C4C2×C4×D4×C7311yescharacteristic
690C4#518×C7311yescharacteristic
691C4#546×C7311yescharacteristic
692C4#551×C7311yescharacteristic
693C2—42no—
694C2C73×#235811yescharacteristic
695C2C4×#137×C7311yescharacteristic
696C2C73×#295011yescharacteristic
697C2C73×#326911yescharacteristic
698C2C73×#327011yescharacteristic
699C2C73×#332711yescharacteristic
700C2C73×#332811yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutatorC2×C4C23×C4×C73
Frattini, cosocleC22×C4C24×C73
prime radicalC24×C73C2×D4
LCSG ▷ C2×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
2. C2×C4×Q16×C73C2semidirect
6. C73×#1971C2semidirect
7. C73×#1933C2semidirect
8. C73×#1928C2semidirect
10. C73×#1878C2semidirect
11. C73×#1878C2semidirect
12. C73×#1865C2semidirect
14. C73×#1763C2semidirect
25. #451×C73C4semidirect
342. #22881C73direct (N × H)
352. C2×C4×Q16C2×C73semidirect
356. #1971C2×C73semidirect
357. #1933C2×C73semidirect
358. #1928C2×C73semidirect
360. #1878C2×C73semidirect
361. #1878C2×C73semidirect
362. #1865C2×C73semidirect
364. #1763C2×C73semidirect
366. C73#22881direct (N × H)
376. #451C4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#451×C732
C2×C4×Q16×C732
C2×#419×C732
C73×#23622
Q8×C22⋊C4×C732
C73×#19712
C73×#19332
C73×#19282
C73×#18942
C73×#18782
C73×#18652
C73×#18542
C73×#17632
C73×#17532
#2288173