Finite Group Databasebeta

← C73×#24892 #32934296

Subgroups — C73×#24892 #32934296

Order 18688.

958 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×#485×C73C211yesmaximal, characteristic, complemented
2C2×#419×C73C211yesmaximal, characteristic, complemented
3C73×#2409C211yesmaximal, characteristic
4C73×#2354C211yesmaximal, characteristic
5C73×#2096C211yesmaximal, characteristic, complemented
6C73×#2072C211yesmaximal, characteristic, complemented
7C73×#2036C211yesmaximal, characteristic, complemented
8C73×#2035C211yesmaximal, characteristic, complemented
9C73×#1928C211yesmaximal, characteristic, complemented
10C73×#1928C211yesmaximal, characteristic, complemented
11C73×#1873C211yesmaximal, characteristic, complemented
12C73×#1870C211yesmaximal, characteristic
13C73×#1854C211yesmaximal, characteristic, complemented
14C73×#1809C211yesmaximal, characteristic, complemented
15C73×#1787C211yesmaximal, characteristic, complemented
16C23×Q8×C73C2211yescharacteristic
17C22×M16×C73C2211yescharacteristic
18C2×C22⋊Q8×C73C2211yescharacteristic
19C2×C22⋊Q8×C73C2211yescharacteristic
20C2×C4×D4×C73C2211yescharacteristic
21C2×#117×C73C2211yescharacteristic
22C2×#117×C73C2211yescharacteristic
23#485×C73—24no—
24C2×#107×C73C2211yescharacteristic
25C2×#107×C73C2211yescharacteristic
26C2×#106×C73C2211yescharacteristic
27C2×#106×C73C2211yescharacteristic
28#419×C73—24no—
29C2×#103×C73C2211yescharacteristic
30C2×#103×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#103×C73C2211yescharacteristic
35C2×#103×C73C2211yescharacteristic
36C2×#103×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×C22⋊C8×C73C2211yescharacteristic
40#395×C73—21no—
41#393×C73—21no—
42#391×C73C2211yescharacteristic
43#391×C73C2211yescharacteristic
44#390×C73—21no—
45#388×C73—21no—
46#388×C73—21no—
47#386×C73—21no—
48#385×C73—21no—
49#384×C73C2211yescharacteristic
50#380×C73C2211yescharacteristic
51#380×C73C2211yescharacteristic
52#380×C73C2211yescharacteristic
53C4×C4⋊C4×C73—21no—
54C4×C4⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73—21no—
62C22×Q8×C73—22no—
63C22×Q8×C73—22no—
64C22×Q8×C73—22no—
65C22×Q8×C73—22no—
66C22×Q8×C73—41no—
67C22×Q8×C73—41no—
68C22×Q8×C73C2311yescharacteristic
69C22×Q8×C73C2311yescharacteristic
70C22×D4×C73D411yescharacteristic
71C23×C4×C73—21no—
72C23×C4×C73C2311yescharacteristic
73C23×C4×C73C2311yescharacteristic
74C2×M16×C73—22no—
75C2×M16×C73—22no—
76C2×M16×C73—41no—
77C22×C8×C73C2311yescharacteristic
78C22×C8×C73C2311yescharacteristic
79C22×C8×C73C2311yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C22⋊Q8×C73—22no—
82C22⋊Q8×C73—22no—
83C22⋊Q8×C73—41no—
84C22⋊Q8×C73—41no—
85C4×D4×C73—22no—
86C4×D4×C73—22no—
87#117×C73—22no—
88#117×C73—22no—
89#117×C73—41no—
90#117×C73—41no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—21no—
93C2×C4⋊C4×C73—21no—
94C2×C4⋊C4×C73—21no—
95C2×C4⋊C4×C73D411yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73D411yescharacteristic
110C2×C22⋊C4×C73D411yescharacteristic
111C2×C42×C73—21no—
112C2×C42×C73—21no—
113C2×C42×C73—21no—
114C2×C42×C73C2311yescharacteristic
115#107×C73—22no—
116#107×C73—41no—
117#106×C73—22no—
118#106×C73—41no—
119#103×C73—22no—
120#103×C73—22no—
121#103×C73—22no—
122#103×C73—22no—
123#103×C73—22no—
124#103×C73—41no—
125#103×C73—41no—
126#103×C73D414yescomplemented
127C22⋊C8×C73—22no—
128C22⋊C8×C73—22no—
129C22⋊C8×C73—41no—
130#95×C73—21no—
131#95×C73—21no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73—21no—
138C24×C73C2×D411yescharacteristic
139C24×C73C2×D411yescharacteristic
140C2×Q8×C73—21no—
141C2×Q8×C73—21no—
142C2×Q8×C73—28no—
143C2×Q8×C73—21no—
144C2×Q8×C73—21no—
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—42no—
152C2×Q8×C73—42no—
153C2×Q8×C73—44no—
154C2×Q8×C73—44no—
155C2×Q8×C73—44no—
156C2×Q8×C73—42no—
157C2×Q8×C73C2×D412yes—
158C2×Q8×C73#4112yes—
159C2×D4×C73—22no—
160C2×D4×C73—22no—
161C2×D4×C73—41no—
162C22×C4×C73—21no—
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×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—21no—
178C22×C4×C73—21no—
179C22×C4×C73—21no—
180C22×C4×C73—42no—
181C22×C4×C73—42no—
182C22×C4×C73—42no—
183C22×C4×C73C2×D411yescharacteristic
184C22×C4×C73C2×D411yescharacteristic
185C22×C4×C73C2×D411yescharacteristic
186C22×C4×C73C2×D411yescharacteristic
187C22×C4×C73#4112yes—
188C22×C4×C73#4112yes—
189C22×C4×C73C2411yescharacteristic
190M16×C73—44no—
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—
202C2×C8×C73C2×D412yes—
203C4⋊C4×C73—22no—
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—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—42no—
216C4⋊C4×C73—42no—
217C4⋊C4×C73—42no—
218C4⋊C4×C73—81no—
219C4⋊C4×C73C2×D412yes—
220C22⋊C4×C73—22no—
221C22⋊C4×C73—22no—
222C22⋊C4×C73—42no—
223C22⋊C4×C73—42no—
224C22⋊C4×C73—42no—
225C22⋊C4×C73—42no—
226C22⋊C4×C73—42no—
227C22⋊C4×C73—81no—
228C22⋊C4×C73—81no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—42no—
232C42×C73—42no—
233C42×C73—42no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73#12312yes—
248C23×C73C22×D411yescharacteristic
249Q8×C73—22no—
250Q8×C73—22no—
251Q8×C73—22no—
252Q8×C73—22no—
253Q8×C73—48no—
254Q8×C73—41no—
255Q8×C73—41no—
256Q8×C73—41no—
257Q8×C73—41no—
258D4×C73—44no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—22no—
264C2×C4×C73—22no—
265C2×C4×C73—22no—
266C2×C4×C73—22no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—22no—
270C2×C4×C73—21no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—21no—
274C2×C4×C73—21no—
275C2×C4×C73—21no—
276C2×C4×C73—48no—
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—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73#12312yes—
303C2×C4×C73#13712yes—
304C2×C4×C73C22×D411yescharacteristic
305C2×C4×C73C2×#4111yescharacteristic
306C2×C4×C73C2×#4111yescharacteristic
307C2×C4×C73C2×#4111yescharacteristic
308C2×C4×C73H(5,𝔽2)11yescharacteristic
309C2×C4×C73H(5,𝔽2)11yescharacteristic
310C8×C73—22no—
311C8×C73—41no—
312C8×C73—41no—
313C8×C73—41no—
314C22×C73—22no—
315C22×C73—22no—
316C22×C73—22no—
317C22×C73—41no—
318C22×C73—41no—
319C22×C73—41no—
320C22×C73—41no—
321C22×C73—41no—
322C22×C73—41no—
323C22×C73—41no—
324C22×C73—41no—
325C22×C73—41no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73C2×#12311yescharacteristic
329C22×C73D4211yescharacteristic
330C22×C73#54611yescharacteristic
331C22×C73C2×#13711yescharacteristic
332C22×C73#57511yescharacteristic
333C22×C73#57711yescharacteristic
334C22×C73#57811yescharacteristic
335C4×C73—22no—
336C4×C73—22no—
337C4×C73—41no—
338C4×C73—41no—
339C4×C73—42no—
340C4×C73—42no—
341C4×C73—42no—
342C4×C73—81no—
343C4×C73—81no—
344C4×C73—81no—
345C4×C73—81no—
346C4×C73—81no—
347C4×C73#52511yescharacteristic
348C4×C73#53811yescharacteristic
349C4×C73#54611yescharacteristic
350C4×C73#55111yescharacteristic
351#24892C7311yesmaximal, characteristic, direct product factor, Sylow
352C2×C73—42no—
353C2×C73—81no—
354C2×C73#241811yescharacteristic
355C2×C73#309511yescharacteristic
356C2×C73#309711yescharacteristic
357C2×C73#326911yescharacteristic
358C2×C73#327811yescharacteristic
359C2×C73#332111yescharacteristic
360C2×C73#332811yescharacteristic
361C2×#485C2×C7311yescharacteristic, complemented
362C2×#419C2×C7311yescharacteristic, complemented
363#2409C2×C7311yescharacteristic
364#2354C2×C7311yescharacteristic
365#2096C2×C7311yescharacteristic, complemented
366#2072C2×C7311yescharacteristic, complemented
367#2036C2×C7311yescharacteristic, complemented
368#2035C2×C7311yescharacteristic, complemented
369#1928C2×C7311yescharacteristic, complemented
370#1928C2×C7311yescharacteristic, complemented
371#1873C2×C7311yescharacteristic, complemented
372#1870C2×C7311yescharacteristic
373#1854C2×C7311yescharacteristic, complemented
374#1809C2×C7311yescharacteristic, complemented
375#1787C2×C7311yescharacteristic, complemented
376C73#2489211yescharacteristic, direct product factor, Sylow
377C23×Q8C22×C7311yescharacteristic
378C22×M16C22×C7311yescharacteristic
379C2×C22⋊Q8C22×C7311yescharacteristic
380C2×C22⋊Q8C22×C7311yescharacteristic
381C2×C4×D4C22×C7311yescharacteristic
382C2×#117C22×C7311yescharacteristic
383C2×#117C22×C7311yescharacteristic
384#485—24no—
385C2×#107C22×C7311yescharacteristic
386C2×#107C22×C7311yescharacteristic
387C2×#106C22×C7311yescharacteristic
388C2×#106C22×C7311yescharacteristic
389#419—24no—
390C2×#103C22×C7311yescharacteristic
391C2×#103C22×C7311yescharacteristic
392C2×#103C22×C7311yescharacteristic
393C2×#103C22×C7311yescharacteristic
394C2×#103C22×C7311yescharacteristic
395C2×#103C22×C7311yescharacteristic
396C2×#103C22×C7311yescharacteristic
397C2×#103C22×C7311yescharacteristic
398C2×C22⋊C8C22×C7311yescharacteristic
399C2×C22⋊C8C22×C7311yescharacteristic
400C2×C22⋊C8C22×C7311yescharacteristic
401#395—21no—
402#393—21no—
403#391C22×C7311yescharacteristic
404#391C22×C7311yescharacteristic
405#390—21no—
406#388—21no—
407#388—21no—
408#386—21no—
409#385—21no—
410#384C22×C7311yescharacteristic
411#380C22×C7311yescharacteristic
412#380C22×C7311yescharacteristic
413#380C22×C7311yescharacteristic
414C4×C4⋊C4—21no—
415C4×C4⋊C4C22×C7311yescharacteristic
416#340C22×C7311yescharacteristic
417#340C22×C7311yescharacteristic
418#340C22×C7311yescharacteristic
419#340C22×C7311yescharacteristic
420#336C22×C7311yescharacteristic
421#336C22×C7311yescharacteristic
422C22×Q8—21no—
423C22×Q8—22no—
424C22×Q8—22no—
425C22×Q8—22no—
426C22×Q8—22no—
427C22×Q8—41no—
428C22×Q8—41no—
429C22×Q8C23×C7311yescharacteristic
430C22×Q8C23×C7311yescharacteristic
431C22×D4D4×C7311yescharacteristic
432C23×C4—21no—
433C23×C4C23×C7311yescharacteristic
434C23×C4C23×C7311yescharacteristic
435C2×M16—22no—
436C2×M16—22no—
437C2×M16—41no—
438C22×C8C23×C7311yescharacteristic
439C22×C8C23×C7311yescharacteristic
440C22×C8C23×C7311yescharacteristic
441C22×C8C23×C7311yescharacteristic
442C22⋊Q8—22no—
443C22⋊Q8—22no—
444C22⋊Q8—41no—
445C22⋊Q8—41no—
446C4×D4—22no—
447C4×D4—22no—
448#117—22no—
449#117—22no—
450#117—41no—
451#117—41no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4D4×C7311yescharacteristic
457C2×C4⋊C4C23×C7311yescharacteristic
458C2×C4⋊C4C23×C7311yescharacteristic
459C2×C4⋊C4C23×C7311yescharacteristic
460C2×C4⋊C4C23×C7311yescharacteristic
461C2×C4⋊C4C23×C7311yescharacteristic
462C2×C4⋊C4C23×C7311yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4D4×C7311yescharacteristic
471C2×C22⋊C4D4×C7311yescharacteristic
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42C23×C7311yescharacteristic
476#107—22no—
477#107—41no—
478#106—22no—
479#106—41no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103—22no—
484#103—22no—
485#103—41no—
486#103—41no—
487#103D4×C7314yescomplemented
488C22⋊C8—22no—
489C22⋊C8—22no—
490C22⋊C8—41no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499C24C2×D4×C7311yescharacteristic
500C24C2×D4×C7311yescharacteristic
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—28no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8—42no—
518C2×Q8C2×D4×C7312yes—
519C2×Q8#41×C7312yes—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—41no—
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—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4C2×D4×C7311yescharacteristic
545C22×C4C2×D4×C7311yescharacteristic
546C22×C4C2×D4×C7311yescharacteristic
547C22×C4C2×D4×C7311yescharacteristic
548C22×C4#41×C7312yes—
549C22×C4#41×C7312yes—
550C22×C4C24×C7311yescharacteristic
551M16—44no—
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—
563C2×C8C2×D4×C7312yes—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—81no—
580C4⋊C4C2×D4×C7312yes—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—81no—
589C22⋊C4—81no—
590C42—21no—
591C42—21no—
592C42—42no—
593C42—42no—
594C42—42no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23#123×C7312yes—
609C23C22×D4×C7311yescharacteristic
610Q8—22no—
611Q8—22no—
612Q8—22no—
613Q8—22no—
614Q8—48no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619D4—44no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—48no—
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—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4#123×C7312yes—
664C2×C4#137×C7312yes—
665C2×C4C22×D4×C7311yescharacteristic
666C2×C4C2×#41×C7311yescharacteristic
667C2×C4C2×#41×C7311yescharacteristic
668C2×C4C2×#41×C7311yescharacteristic
669C2×C4H(5,𝔽2)×C7311yescharacteristic
670C2×C4H(5,𝔽2)×C7311yescharacteristic
671C8—22no—
672C8—41no—
673C8—41no—
674C8—41no—
675C22—22no—
676C22—22no—
677C22—22no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22C2×#123×C7311yescharacteristic
690C22D42×C7311yescharacteristic
691C22#546×C7311yescharacteristic
692C22C2×#137×C7311yescharacteristic
693C22#575×C7311yescharacteristic
694C22#577×C7311yescharacteristic
695C22#578×C7311yescharacteristic
696C4—22no—
697C4—22no—
698C4—42no—
699C4—41no—
700C4—41no—
701C4—42no—
702C4—42no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4#525×C7311yescharacteristic
709C4#538×C7311yescharacteristic
710C4#546×C7311yescharacteristic
711C4#551×C7311yescharacteristic
712C2—42no—
713C2—81no—
714C2C73×#241811yescharacteristic
715C2C73×#309511yescharacteristic
716C2C73×#309711yescharacteristic
717C2C73×#326911yescharacteristic
718C2C73×#327811yescharacteristic
719C2C73×#332111yescharacteristic
720C2C73×#332811yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D4×C73D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C4×D4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#485×C73C2semidirect
2. C2×#419×C73C2semidirect
5. C73×#2096C2semidirect
6. C73×#2072C2semidirect
7. C73×#2036C2semidirect
8. C73×#2035C2semidirect
9. C73×#1928C2semidirect
10. C73×#1928C2semidirect
11. C73×#1873C2semidirect
13. C73×#1854C2semidirect
14. C73×#1809C2semidirect
15. C73×#1787C2semidirect
126. #103×C73D4semidirect
351. #24892C73direct (N × H)
361. C2×#485C2×C73semidirect
362. C2×#419C2×C73semidirect
365. #2096C2×C73semidirect
366. #2072C2×C73semidirect
367. #2036C2×C73semidirect
368. #2035C2×C73semidirect
369. #1928C2×C73semidirect
370. #1928C2×C73semidirect
371. #1873C2×C73semidirect
373. #1854C2×C73semidirect
374. #1809C2×C73semidirect
375. #1787C2×C73semidirect
376. C73#24892direct (N × H)
487. #103D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C732
C2×#419×C732
C73×#24092
C73×#23542
C73×#20962
C73×#20722
C73×#20362
C73×#20352
C73×#19282
C73×#18732
C73×#18702
C73×#18542
C73×#18092
C73×#17872
#2489273