Finite Group Databasebeta

← C73×#24764 #32934168

Subgroups — C73×#24764 #32934168

Order 18688.

904 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#470×C73C211yesmaximal, characteristic
2C2×#467×C73C211yesmaximal, characteristic
3C2×#462×C73C211yesmaximal, characteristic, complemented
4C2×#424×C73C211yesmaximal, characteristic
5C73×#2621C211yesmaximal, characteristic
6C73×#2323C211yesmaximal, characteristic
7C73×#2068C211yesmaximal, characteristic, complemented
8C73×#2066C211yesmaximal, characteristic, complemented
9C73×#2056C211yesmaximal, characteristic, complemented
10C73×#2056C211yesmaximal, characteristic, complemented
11C73×#1981C211yesmaximal, characteristic, complemented
12C73×#1949C211yesmaximal, characteristic, complemented
13C73×#1894C211yesmaximal, characteristic
14C73×#1892C211yesmaximal, characteristic
15C73×#1805C211yesmaximal, characteristic, complemented
16C22×Q16×C73C2211yescharacteristic
17C22×Q16×C73C2211yescharacteristic
18C22×M16×C73C2211yescharacteristic
19C23×C8×C73C2211yescharacteristic
20C2×C4⋊Q8×C73C2211yescharacteristic
21C2×C22⋊Q8×C73C2211yescharacteristic
22C2×C22⋊Q8×C73C2211yescharacteristic
23C2×C22⋊Q8×C73C2211yescharacteristic
24C2×C4×Q8×C73C2211yescharacteristic
25C2×#117×C73C2211yescharacteristic
26#470×C73—24no—
27#467×C73—24no—
28#462×C73—24no—
29C2×#107×C73C2211yescharacteristic
30C2×#106×C73C2211yescharacteristic
31#424×C73—24no—
32C2×C4⋊C8×C73C2211yescharacteristic
33C2×C4⋊C8×C73C2211yescharacteristic
34C2×C4⋊C8×C73C2211yescharacteristic
35C2×C4⋊C8×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#103×C73C2211yescharacteristic
40C2×#103×C73C2211yescharacteristic
41C2×#103×C73C2211yescharacteristic
42C2×#103×C73C2211yescharacteristic
43C2×#103×C73C2211yescharacteristic
44#398×C73—21no—
45#398×C73—21no—
46#397×C73—21no—
47#397×C73—21no—
48#391×C73C2211yescharacteristic
49#391×C73C2211yescharacteristic
50#391×C73C2211yescharacteristic
51#389×C73—21no—
52#389×C73C2211yescharacteristic
53#388×C73—21no—
54#388×C73—21no—
55#387×C73—21no—
56#382×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63C22×Q8×C73C2311yescharacteristic
64C22×Q8×C73C2311yescharacteristic
65C22×Q8×C73C2311yescharacteristic
66C23×C4×C73C2311yescharacteristic
67C2×Q16×C73—22no—
68C2×Q16×C73—22no—
69C2×Q16×C73—22no—
70C2×Q16×C73—22no—
71C2×Q16×C73—41no—
72C2×Q16×C73—41no—
73C2×M16×C73—22no—
74C2×M16×C73—22no—
75C2×M16×C73—41no—
76C22×C8×C73—22no—
77C22×C8×C73—22no—
78C22×C8×C73—41no—
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C22×C8×C73C2311yescharacteristic
82C22×C8×C73C2311yescharacteristic
83C4⋊Q8×C73—22no—
84C4⋊Q8×C73—22no—
85C22⋊Q8×C73—22no—
86C22⋊Q8×C73—22no—
87C22⋊Q8×C73—22no—
88C22⋊Q8×C73—22no—
89C22⋊Q8×C73—22no—
90C22⋊Q8×C73D414yes—
91C4×Q8×C73—22no—
92C4×Q8×C73—22no—
93#117×C73—22no—
94#117×C73—22no—
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×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73—21no—
112C2×C22⋊C4×C73—21no—
113C2×C22⋊C4×C73D411yescharacteristic
114C2×C22⋊C4×C73D411yescharacteristic
115C2×C42×C73—21no—
116C2×C42×C73—21no—
117C2×C42×C73C2311yescharacteristic
118C2×C42×C73C2311yescharacteristic
119#107×C73—22no—
120#106×C73—22no—
121C4⋊C8×C73—22no—
122C4⋊C8×C73—22no—
123C4⋊C8×C73—22no—
124C4⋊C8×C73D414yes—
125#103×C73—22no—
126#103×C73—22no—
127#103×C73—22no—
128#103×C73—22no—
129#103×C73—22no—
130#103×C73—22no—
131#103×C73—41no—
132#103×C73—41no—
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×C73—21no—
142#95×C73—21no—
143#95×C73—21no—
144C24×C73C2×D411yescharacteristic
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×Q8×C73—21no—
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—21no—
160C2×Q8×C73—21no—
161C2×Q8×C73—21no—
162C2×Q8×C73C2×D412yes—
163C22×C4×C73—21no—
164C22×C4×C73—21no—
165C22×C4×C73—21no—
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×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C22×C4×C73C2×D411yescharacteristic
178C22×C4×C73C2×D411yescharacteristic
179C22×C4×C73C2×D411yescharacteristic
180C22×C4×C73C2×D412yes—
181C22×C4×C73#4112yes—
182C22×C4×C73C2411yescharacteristic
183Q16×C73—44no—
184Q16×C73—44no—
185M16×C73—44no—
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—21no—
195C2×C8×C73—21no—
196C2×C8×C73—44no—
197C2×C8×C73C2×D412yes—
198C2×C8×C73C2×D412yes—
199C4⋊C4×C73—24no—
200C4⋊C4×C73—22no—
201C4⋊C4×C73—22no—
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—42no—
214C4⋊C4×C73—42no—
215C4⋊C4×C73—42no—
216C4⋊C4×C73—81no—
217C4⋊C4×C73C2×D412yes—
218C22⋊C4×C73—24no—
219C22⋊C4×C73—22no—
220C22⋊C4×C73—22no—
221C22⋊C4×C73—42no—
222C22⋊C4×C73—42no—
223C22⋊C4×C73—81no—
224C42×C73—21no—
225C42×C73—21no—
226C42×C73—42no—
227C42×C73—81no—
228C42×C73C2×D412yes—
229C42×C73#4112yes—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73#12112yes—
237C23×C73C22×D411yescharacteristic
238Q8×C73—22no—
239Q8×C73—22no—
240Q8×C73—41no—
241Q8×C73—41no—
242Q8×C73—41no—
243Q8×C73—41no—
244Q8×C73—41no—
245Q8×C73—41no—
246Q8×C73—41no—
247Q8×C73—41no—
248Q8×C73—41no—
249Q8×C73—41no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—22no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—22no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
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—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73#12112yes—
291C2×C4×C73#12112yes—
292C2×C4×C73#12112yes—
293C2×C4×C73C22×D411yescharacteristic
294C2×C4×C73C22×D411yescharacteristic
295C2×C4×C73C2×#4111yescharacteristic
296C2×C4×C73C2×#4111yescharacteristic
297C2×C4×C73H(5,𝔽2)11yescharacteristic
298C2×C4×C732−1+411yescharacteristic
299C8×C73—22no—
300C8×C73—22no—
301C8×C73—41no—
302C8×C73—41no—
303C22×C73—22no—
304C22×C73—22no—
305C22×C73—22no—
306C22×C73—41no—
307C22×C73—41no—
308C22×C73—41no—
309C22×C73—41no—
310C22×C73C2×#12111yescharacteristic
311C22×C73C2×#12111yescharacteristic
312C22×C73#53711yescharacteristic
313C22×C73#57711yescharacteristic
314C22×C73#57811yescharacteristic
315C22×C73#57811yescharacteristic
316C22×C73#57811yescharacteristic
317C4×C73—22no—
318C4×C73—22no—
319C4×C73—22no—
320C4×C73—42no—
321C4×C73—42no—
322C4×C73—41no—
323C4×C73—41no—
324C4×C73—81no—
325C4×C73—81no—
326C4×C73—81no—
327C4×C73—81no—
328C4×C73—81no—
329C4×C73—81no—
330C4×C73D4211yescharacteristic
331C4×C73#54711yescharacteristic
332C4×C73#54811yescharacteristic
333C4×C73#55311yescharacteristic
334#24764C7311yesmaximal, characteristic, direct product factor, Sylow
335C2×C73—42no—
336C2×C73#241611yescharacteristic
337C2×C73#304411yescharacteristic
338C2×C73#304611yescharacteristic
339C2×C73#305911yescharacteristic
340C2×C73#306311yescharacteristic
341C2×C73#325811yescharacteristic
342C2×C73#326111yescharacteristic
343C2×#470C2×C7311yescharacteristic
344C2×#467C2×C7311yescharacteristic
345C2×#462C2×C7311yescharacteristic, complemented
346C2×#424C2×C7311yescharacteristic
347#2621C2×C7311yescharacteristic
348#2323C2×C7311yescharacteristic
349#2068C2×C7311yescharacteristic, complemented
350#2066C2×C7311yescharacteristic, complemented
351#2056C2×C7311yescharacteristic, complemented
352#2056C2×C7311yescharacteristic, complemented
353#1981C2×C7311yescharacteristic, complemented
354#1949C2×C7311yescharacteristic, complemented
355#1894C2×C7311yescharacteristic
356#1892C2×C7311yescharacteristic
357#1805C2×C7311yescharacteristic, complemented
358C73#2476411yescharacteristic, direct product factor, Sylow
359C22×Q16C22×C7311yescharacteristic
360C22×Q16C22×C7311yescharacteristic
361C22×M16C22×C7311yescharacteristic
362C23×C8C22×C7311yescharacteristic
363C2×C4⋊Q8C22×C7311yescharacteristic
364C2×C22⋊Q8C22×C7311yescharacteristic
365C2×C22⋊Q8C22×C7311yescharacteristic
366C2×C22⋊Q8C22×C7311yescharacteristic
367C2×C4×Q8C22×C7311yescharacteristic
368C2×#117C22×C7311yescharacteristic
369#470—24no—
370#467—24no—
371#462—24no—
372C2×#107C22×C7311yescharacteristic
373C2×#106C22×C7311yescharacteristic
374#424—24no—
375C2×C4⋊C8C22×C7311yescharacteristic
376C2×C4⋊C8C22×C7311yescharacteristic
377C2×C4⋊C8C22×C7311yescharacteristic
378C2×C4⋊C8C22×C7311yescharacteristic
379C2×#103C22×C7311yescharacteristic
380C2×#103C22×C7311yescharacteristic
381C2×#103C22×C7311yescharacteristic
382C2×#103C22×C7311yescharacteristic
383C2×#103C22×C7311yescharacteristic
384C2×#103C22×C7311yescharacteristic
385C2×#103C22×C7311yescharacteristic
386C2×#103C22×C7311yescharacteristic
387#398—21no—
388#398—21no—
389#397—21no—
390#397—21no—
391#391C22×C7311yescharacteristic
392#391C22×C7311yescharacteristic
393#391C22×C7311yescharacteristic
394#389—21no—
395#389C22×C7311yescharacteristic
396#388—21no—
397#388—21no—
398#387—21no—
399#382C22×C7311yescharacteristic
400#380C22×C7311yescharacteristic
401C4×C4⋊C4C22×C7311yescharacteristic
402#340C22×C7311yescharacteristic
403#340C22×C7311yescharacteristic
404#340C22×C7311yescharacteristic
405#340C22×C7311yescharacteristic
406C22×Q8C23×C7311yescharacteristic
407C22×Q8C23×C7311yescharacteristic
408C22×Q8C23×C7311yescharacteristic
409C23×C4C23×C7311yescharacteristic
410C2×Q16—22no—
411C2×Q16—22no—
412C2×Q16—22no—
413C2×Q16—22no—
414C2×Q16—41no—
415C2×Q16—41no—
416C2×M16—22no—
417C2×M16—22no—
418C2×M16—41no—
419C22×C8—22no—
420C22×C8—22no—
421C22×C8—41no—
422C22×C8C23×C7311yescharacteristic
423C22×C8C23×C7311yescharacteristic
424C22×C8C23×C7311yescharacteristic
425C22×C8C23×C7311yescharacteristic
426C4⋊Q8—22no—
427C4⋊Q8—22no—
428C22⋊Q8—22no—
429C22⋊Q8—22no—
430C22⋊Q8—22no—
431C22⋊Q8—22no—
432C22⋊Q8—22no—
433C22⋊Q8D4×C7314yes—
434C4×Q8—22no—
435C4×Q8—22no—
436#117—22no—
437#117—22no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4D4×C7311yescharacteristic
446C2×C4⋊C4D4×C7311yescharacteristic
447C2×C4⋊C4C23×C7311yescharacteristic
448C2×C4⋊C4C23×C7311yescharacteristic
449C2×C4⋊C4C23×C7311yescharacteristic
450C2×C4⋊C4C23×C7311yescharacteristic
451C2×C4⋊C4C23×C7311yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4D4×C7311yescharacteristic
457C2×C22⋊C4D4×C7311yescharacteristic
458C2×C42—21no—
459C2×C42—21no—
460C2×C42C23×C7311yescharacteristic
461C2×C42C23×C7311yescharacteristic
462#107—22no—
463#106—22no—
464C4⋊C8—22no—
465C4⋊C8—22no—
466C4⋊C8—22no—
467C4⋊C8D4×C7314yes—
468#103—22no—
469#103—22no—
470#103—22no—
471#103—22no—
472#103—22no—
473#103—22no—
474#103—41no—
475#103—41no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487C24C2×D4×C7311yescharacteristic
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8C2×D4×C7312yes—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4C2×D4×C7311yescharacteristic
519C22×C4C2×D4×C7311yescharacteristic
520C22×C4C2×D4×C7311yescharacteristic
521C22×C4C2×D4×C7311yescharacteristic
522C22×C4C2×D4×C7311yescharacteristic
523C22×C4C2×D4×C7312yes—
524C22×C4#41×C7312yes—
525C22×C4C24×C7311yescharacteristic
526Q16—44no—
527Q16—44no—
528M16—44no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—44no—
540C2×C8C2×D4×C7312yes—
541C2×C8C2×D4×C7312yes—
542C4⋊C4—24no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—81no—
560C4⋊C4C2×D4×C7312yes—
561C22⋊C4—24no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—81no—
567C42—21no—
568C42—21no—
569C42—42no—
570C42—81no—
571C42C2×D4×C7312yes—
572C42#41×C7312yes—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23#121×C7312yes—
580C23C22×D4×C7311yescharacteristic
581Q8—22no—
582Q8—22no—
583Q8—41no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—41no—
591Q8—41no—
592Q8—41no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
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#121×C7312yes—
634C2×C4#121×C7312yes—
635C2×C4#121×C7312yes—
636C2×C4C22×D4×C7311yescharacteristic
637C2×C4C22×D4×C7311yescharacteristic
638C2×C4C2×#41×C7311yescharacteristic
639C2×C4C2×#41×C7311yescharacteristic
640C2×C4H(5,𝔽2)×C7311yescharacteristic
641C2×C42−1+4×C7311yescharacteristic
642C8—22no—
643C8—22no—
644C8—41no—
645C8—41no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22C2×#121×C7311yescharacteristic
654C22C2×#121×C7311yescharacteristic
655C22#537×C7311yescharacteristic
656C22#577×C7311yescharacteristic
657C22#578×C7311yescharacteristic
658C22#578×C7311yescharacteristic
659C22#578×C7311yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—42no—
664C4—41no—
665C4—41no—
666C4—42no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4D42×C7311yescharacteristic
674C4#547×C7311yescharacteristic
675C4#548×C7311yescharacteristic
676C4#553×C7311yescharacteristic
677C2—42no—
678C2C73×#241611yescharacteristic
679C2C73×#304411yescharacteristic
680C2C73×#304611yescharacteristic
681C2C73×#305911yescharacteristic
682C2C73×#306311yescharacteristic
683C2C73×#325811yescharacteristic
684C2C73×#326111yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC24×C73C2×D4
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
3. C2×#462×C73C2semidirect
7. C73×#2068C2semidirect
8. C73×#2066C2semidirect
9. C73×#2056C2semidirect
10. C73×#2056C2semidirect
11. C73×#1981C2semidirect
12. C73×#1949C2semidirect
15. C73×#1805C2semidirect
334. #24764C73direct (N × H)
345. C2×#462C2×C73semidirect
349. #2068C2×C73semidirect
350. #2066C2×C73semidirect
351. #2056C2×C73semidirect
352. #2056C2×C73semidirect
353. #1981C2×C73semidirect
354. #1949C2×C73semidirect
357. #1805C2×C73semidirect
358. C73#24764direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#470×C732
C2×#467×C732
C2×#462×C732
C2×#424×C732
C73×#26212
C73×#23232
C73×#20682
C73×#20662
C73×#20562
C73×#19812
C73×#19492
C73×#18942
C73×#18922
C73×#18052
#2476473