Finite Group Databasebeta

← C73×#16327 #32925731

Subgroups — C73×#16327 #32925731

Order 18688.

1530 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C73C211yesmaximal, characteristic
2C2×#395×C73C211yesmaximal, characteristic, complemented
3C2×#395×C73C211yesmaximal, characteristic, complemented
4C2×#393×C73C211yesmaximal, characteristic
5C2×#389×C73C211yesmaximal, characteristic, complemented
6C2×#388×C73C211yesmaximal, characteristic
7C73×#1444C211yesmaximal, characteristic, complemented
8C73×#1443C211yesmaximal, characteristic, complemented
9C73×#1442C211yesmaximal, characteristic, complemented
10C73×#1442C211yesmaximal, characteristic, complemented
11C73×#1439C211yesmaximal, characteristic
12C73×#1439C211yesmaximal, characteristic
13C73×#1439C211yesmaximal, characteristic
14C73×#1439C211yesmaximal, characteristic
15C73×#1436C211yesmaximal, characteristic, complemented
16C23×Q8×C73C2211yescharacteristic
17C22×C4⋊C4×C73C2211yescharacteristic
18C22×C4⋊C4×C73C2211yescharacteristic
19C22×C4⋊C4×C73C2211yescharacteristic
20C22×C4⋊C4×C73C2211yescharacteristic
21C22×C4⋊C4×C73C2211yescharacteristic
22C22×C4⋊C4×C73C2211yescharacteristic
23C22×C4⋊C4×C73C2211yescharacteristic
24C22×C4⋊C4×C73C2211yescharacteristic
25C22×C22⋊C4×C73C2211yescharacteristic
26C22×C22⋊C4×C73C2211yescharacteristic
27C22×C22⋊C4×C73C2211yescharacteristic
28C22×C22⋊C4×C73C2211yescharacteristic
29C22×C22⋊C4×C73C2211yescharacteristic
30C22×C22⋊C4×C73C2211yescharacteristic
31C22×C22⋊C4×C73C2211yescharacteristic
32C22×C42×C73C2211yescharacteristic
33#399×C73—24no—
34#395×C73—24no—
35#395×C73—24no—
36#393×C73—24no—
37#389×C73—24no—
38#388×C73—24no—
39C2×#95×C73C2211yescharacteristic
40C2×#95×C73C2211yescharacteristic
41C2×#95×C73C2211yescharacteristic
42C2×#95×C73C2211yescharacteristic
43C2×#95×C73C2211yescharacteristic
44C2×#95×C73C2211yescharacteristic
45C2×#95×C73C2211yescharacteristic
46C2×#95×C73C2211yescharacteristic
47C2×#95×C73C2211yescharacteristic
48C2×#95×C73C2211yescharacteristic
49C2×#95×C73C2211yescharacteristic
50C2×#95×C73C2211yescharacteristic
51C2×#95×C73C2211yescharacteristic
52C2×#95×C73C2211yescharacteristic
53C2×#95×C73C2211yescharacteristic
54C2×#95×C73C2211yescharacteristic
55C2×#95×C73C2211yescharacteristic
56C2×#95×C73C2211yescharacteristic
57C25×C73C2311yescharacteristic
58C22×Q8×C73—22no—
59C22×Q8×C73—22no—
60C22×Q8×C73—22no—
61C22×Q8×C73—41no—
62C22×Q8×C73—41no—
63C22×Q8×C73—41no—
64C22×Q8×C73—41no—
65C23×C4×C73C2311yescharacteristic
66C23×C4×C73C2311yescharacteristic
67C23×C4×C73C2311yescharacteristic
68C23×C4×C73C2311yescharacteristic
69C23×C4×C73C2311yescharacteristic
70C23×C4×C73C2311yescharacteristic
71C23×C4×C73C2311yescharacteristic
72C23×C4×C73C2311yescharacteristic
73C23×C4×C73C2311yescharacteristic
74C23×C4×C73C2311yescharacteristic
75C23×C4×C73C2311yescharacteristic
76C23×C4×C73C2311yescharacteristic
77C23×C4×C73C2311yescharacteristic
78C23×C4×C73C2311yescharacteristic
79C2×C4⋊C4×C73—22no—
80C2×C4⋊C4×C73—22no—
81C2×C4⋊C4×C73—22no—
82C2×C4⋊C4×C73—22no—
83C2×C4⋊C4×C73—22no—
84C2×C4⋊C4×C73—22no—
85C2×C4⋊C4×C73—22no—
86C2×C4⋊C4×C73—22no—
87C2×C4⋊C4×C73—22no—
88C2×C4⋊C4×C73—22no—
89C2×C4⋊C4×C73—22no—
90C2×C4⋊C4×C73—22no—
91C2×C4⋊C4×C73—22no—
92C2×C4⋊C4×C73—22no—
93C2×C4⋊C4×C73—41no—
94C2×C4⋊C4×C73—41no—
95C2×C4⋊C4×C73—41no—
96C2×C4⋊C4×C73—41no—
97C2×C4⋊C4×C73—41no—
98C2×C4⋊C4×C73—41no—
99C2×C4⋊C4×C73—41no—
100C2×C4⋊C4×C73—41no—
101C2×C4⋊C4×C73—41no—
102C2×C4⋊C4×C73D414yes—
103C2×C22⋊C4×C73—22no—
104C2×C22⋊C4×C73—22no—
105C2×C22⋊C4×C73—22no—
106C2×C22⋊C4×C73—22no—
107C2×C22⋊C4×C73—22no—
108C2×C22⋊C4×C73—22no—
109C2×C22⋊C4×C73—22no—
110C2×C22⋊C4×C73—22no—
111C2×C22⋊C4×C73—22no—
112C2×C22⋊C4×C73—22no—
113C2×C22⋊C4×C73—22no—
114C2×C22⋊C4×C73—22no—
115C2×C22⋊C4×C73—41no—
116C2×C22⋊C4×C73—41no—
117C2×C22⋊C4×C73—41no—
118C2×C22⋊C4×C73—41no—
119C2×C22⋊C4×C73—41no—
120C2×C22⋊C4×C73—41no—
121C2×C22⋊C4×C73—41no—
122C2×C22⋊C4×C73—41no—
123C2×C22⋊C4×C73Q814yescomplemented
124C2×C42×C73—22no—
125C2×C42×C73—22no—
126C2×C42×C73—41no—
127#95×C73—22no—
128#95×C73—22no—
129#95×C73—22no—
130#95×C73—22no—
131#95×C73—22no—
132#95×C73—22no—
133#95×C73—22no—
134#95×C73—22no—
135#95×C73—22no—
136#95×C73—22no—
137#95×C73—22no—
138#95×C73—22no—
139#95×C73—22no—
140#95×C73—22no—
141#95×C73—41no—
142#95×C73—41no—
143#95×C73D414yes—
144#95×C73D414yes—
145C24×C73—21no—
146C24×C73—21no—
147C24×C73—21no—
148C24×C73—21no—
149C24×C73—21no—
150C24×C73—21no—
151C24×C73—21no—
152C24×C73—21no—
153C24×C73—21no—
154C24×C73—21no—
155C24×C73—21no—
156C24×C73—21no—
157C24×C73—21no—
158C24×C73—21no—
159C24×C73C2×Q812yes—
160C24×C73C2411yescharacteristic
161C2×Q8×C73—44no—
162C2×Q8×C73—44no—
163C2×Q8×C73—44no—
164C2×Q8×C73—44no—
165C2×Q8×C73—44no—
166C2×Q8×C73—44no—
167C2×Q8×C73—44no—
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—21no—
181C22×C4×C73—21no—
182C22×C4×C73—21no—
183C22×C4×C73—21no—
184C22×C4×C73—21no—
185C22×C4×C73—21no—
186C22×C4×C73—21no—
187C22×C4×C73—21no—
188C22×C4×C73—21no—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73—21no—
250C22×C4×C73—21no—
251C22×C4×C73—21no—
252C22×C4×C73C2×D412yes—
253C22×C4×C73C2×D412yes—
254C22×C4×C73C2×D412yes—
255C22×C4×C73C2×D412yes—
256C22×C4×C73C2×D412yes—
257C22×C4×C73C2×D412yes—
258C22×C4×C73C2×D412yes—
259C22×C4×C73C2×D412yes—
260C22×C4×C73C2×D412yes—
261C22×C4×C73C2×Q812yes—
262C22×C4×C73C2×Q812yes—
263C22×C4×C73#4112yes—
264C22×C4×C73#4112yes—
265C22×C4×C73#4112yes—
266C4⋊C4×C73—28no—
267C4⋊C4×C73—44no—
268C4⋊C4×C73—44no—
269C4⋊C4×C73—44no—
270C4⋊C4×C73—44no—
271C4⋊C4×C73—44no—
272C4⋊C4×C73—44no—
273C4⋊C4×C73—44no—
274C22⋊C4×C73—28no—
275C22⋊C4×C73—44no—
276C22⋊C4×C73—44no—
277C22⋊C4×C73—44no—
278C22⋊C4×C73—44no—
279C22⋊C4×C73—44no—
280C22⋊C4×C73—44no—
281C42×C73—44no—
282C23×C73—22no—
283C23×C73—22no—
284C23×C73—22no—
285C23×C73—22no—
286C23×C73—22no—
287C23×C73—22no—
288C23×C73—22no—
289C23×C73—41no—
290C23×C73—41no—
291C23×C73—41no—
292C23×C73—41no—
293C23×C73—41no—
294C23×C73—41no—
295C23×C73—41no—
296C23×C73—41no—
297C23×C73—41no—
298C23×C73—41no—
299C23×C73—41no—
300C23×C73—41no—
301C23×C73—41no—
302C23×C73—41no—
303C23×C73—41no—
304C23×C73—41no—
305C23×C73—41no—
306C23×C73—41no—
307C23×C73—41no—
308C23×C73—41no—
309C23×C73—41no—
310C23×C73—41no—
311C23×C73—41no—
312C23×C73—41no—
313C23×C73—41no—
314C23×C73—41no—
315C23×C73—41no—
316C23×C73—41no—
317C23×C73C22×D411yescharacteristic
318C23×C73C22×D411yescharacteristic
319C23×C73C22×D411yescharacteristic
320C23×C73C22×Q811yescharacteristic
321C23×C73C2×#4111yescharacteristic
322C23×C73C2×#4111yescharacteristic
323C23×C73C2×#4111yescharacteristic
324C23×C73H(5,𝔽2)11yescharacteristic
325C23×C73H(5,𝔽2)11yescharacteristic
326C23×C73H(5,𝔽2)11yescharacteristic
327C23×C73H(5,𝔽2)11yescharacteristic
328C23×C732−1+411yescharacteristic
329C23×C732−1+411yescharacteristic
330C23×C732−1+411yescharacteristic
331C23×C732−1+411yescharacteristic
332Q8×C73—416no—
333C2×C4×C73—22no—
334C2×C4×C73—22no—
335C2×C4×C73—22no—
336C2×C4×C73—22no—
337C2×C4×C73—22no—
338C2×C4×C73—22no—
339C2×C4×C73—22no—
340C2×C4×C73—22no—
341C2×C4×C73—22no—
342C2×C4×C73—22no—
343C2×C4×C73—22no—
344C2×C4×C73—22no—
345C2×C4×C73—22no—
346C2×C4×C73—22no—
347C2×C4×C73—22no—
348C2×C4×C73—22no—
349C2×C4×C73—22no—
350C2×C4×C73—22no—
351C2×C4×C73—22no—
352C2×C4×C73—22no—
353C2×C4×C73—22no—
354C2×C4×C73—22no—
355C2×C4×C73—22no—
356C2×C4×C73—22no—
357C2×C4×C73—22no—
358C2×C4×C73—22no—
359C2×C4×C73—22no—
360C2×C4×C73—22no—
361C2×C4×C73—22no—
362C2×C4×C73—22no—
363C2×C4×C73—22no—
364C2×C4×C73—22no—
365C2×C4×C73—22no—
366C2×C4×C73—22no—
367C2×C4×C73—22no—
368C2×C4×C73—22no—
369C2×C4×C73—22no—
370C2×C4×C73—22no—
371C2×C4×C73—22no—
372C2×C4×C73—41no—
373C2×C4×C73—41no—
374C2×C4×C73—41no—
375C2×C4×C73—41no—
376C2×C4×C73—41no—
377C2×C4×C73—41no—
378C2×C4×C73—41no—
379C2×C4×C73—41no—
380C2×C4×C73—41no—
381C2×C4×C73—41no—
382C2×C4×C73—41no—
383C2×C4×C73—41no—
384C2×C4×C73—41no—
385C2×C4×C73—41no—
386C2×C4×C73—41no—
387C2×C4×C73—41no—
388C2×C4×C73—41no—
389C2×C4×C73—41no—
390C2×C4×C73—41no—
391C2×C4×C73—41no—
392C2×C4×C73—41no—
393C2×C4×C73—41no—
394C2×C4×C73—41no—
395C2×C4×C73—41no—
396C2×C4×C73—41no—
397C2×C4×C73—41no—
398C2×C4×C73—41no—
399C2×C4×C73—41no—
400C2×C4×C73—41no—
401C2×C4×C73—41no—
402C2×C4×C73—41no—
403C2×C4×C73—41no—
404C2×C4×C73—41no—
405C2×C4×C73—41no—
406C2×C4×C73—41no—
407C2×C4×C73—41no—
408C2×C4×C73—41no—
409C2×C4×C73—41no—
410C2×C4×C73—41no—
411C2×C4×C73—41no—
412C2×C4×C73—41no—
413C2×C4×C73—41no—
414C2×C4×C73—41no—
415C2×C4×C73—41no—
416C2×C4×C73—41no—
417C2×C4×C73—41no—
418C2×C4×C73—41no—
419C2×C4×C73—41no—
420C2×C4×C73—41no—
421C2×C4×C73—41no—
422C2×C4×C73—41no—
423C2×C4×C73—41no—
424C2×C4×C73—41no—
425C2×C4×C73—41no—
426C2×C4×C73—41no—
427C2×C4×C73—41no—
428C2×C4×C73—41no—
429C2×C4×C73—41no—
430C2×C4×C73C22⋊Q814yes—
431C22×C73—42no—
432C22×C73—42no—
433C22×C73—42no—
434C22×C73—42no—
435C22×C73—42no—
436C22×C73—42no—
437C22×C73—42no—
438C22×C73—81no—
439C22×C73—81no—
440C22×C73—81no—
441C22×C73—81no—
442C22×C73—81no—
443C22×C73—81no—
444C22×C73—81no—
445C22×C73—81no—
446C22×C73C2×C22⋊Q811yescharacteristic
447C22×C73#52511yescharacteristic
448C22×C73#53211yescharacteristic
449C22×C73#53411yescharacteristic
450C22×C73#53511yescharacteristic
451C22×C73#53511yescharacteristic
452C22×C73#53611yescharacteristic
453C22×C73#53611yescharacteristic
454C22×C73#53611yescharacteristic
455C22×C73#53911yescharacteristic
456C22×C73#53911yescharacteristic
457C22×C73#54211yescharacteristic
458C22×C73#54211yescharacteristic
459C22×C73#54211yescharacteristic
460C22×C73#54211yescharacteristic
461C22×C73#54211yescharacteristic
462C22×C73#54211yescharacteristic
463C22×C73#54411yescharacteristic
464C22×C73#54411yescharacteristic
465C22×C73D4211yescharacteristic
466C22×C73D4211yescharacteristic
467C22×C73D4211yescharacteristic
468C22×C73#54711yescharacteristic
469C22×C73#54711yescharacteristic
470C22×C73#54811yescharacteristic
471C22×C73#54811yescharacteristic
472C22×C73D4×Q811yescharacteristic
473C22×C73D4×Q811yescharacteristic
474C22×C73#55111yescharacteristic
475C22×C73#55411yescharacteristic
476C22×C73#55411yescharacteristic
477C22×C73#56011yescharacteristic
478C22×C73#56311yescharacteristic
479C22×C73#56311yescharacteristic
480C22×C73#56311yescharacteristic
481C4×C73—24no—
482C4×C73—42no—
483C4×C73—42no—
484C4×C73—42no—
485C4×C73—42no—
486C4×C73—42no—
487C4×C73—42no—
488C4×C73—42no—
489C4×C73—42no—
490C4×C73—42no—
491C4×C73—42no—
492C4×C73—42no—
493C4×C73—81no—
494C4×C73—81no—
495#16327C7311yesmaximal, characteristic, direct product factor, Sylow
496C2×C73—82no—
497C2×C73#244911yescharacteristic
498C2×C73#245211yescharacteristic
499C2×C73#246111yescharacteristic
500C2×C73#262811yescharacteristic
501C2×C73#263211yescharacteristic
502C2×C73#266311yescharacteristic
503C2×C73#266911yescharacteristic
504C2×C73#267411yescharacteristic
505C2×C73#267411yescharacteristic
506C2×C73#267711yescharacteristic
507C2×C73#272011yescharacteristic
508C2×C73#272311yescharacteristic
509C2×C73#272911yescharacteristic
510C2×C73#274211yescharacteristic
511C2×C73#283811yescharacteristic
512C2×#399C2×C7311yescharacteristic
513C2×#395C2×C7311yescharacteristic, complemented
514C2×#395C2×C7311yescharacteristic, complemented
515C2×#393C2×C7311yescharacteristic
516C2×#389C2×C7311yescharacteristic, complemented
517C2×#388C2×C7311yescharacteristic
518#1444C2×C7311yescharacteristic, complemented
519#1443C2×C7311yescharacteristic, complemented
520#1442C2×C7311yescharacteristic, complemented
521#1442C2×C7311yescharacteristic, complemented
522#1439C2×C7311yescharacteristic
523#1439C2×C7311yescharacteristic
524#1439C2×C7311yescharacteristic
525#1439C2×C7311yescharacteristic
526#1436C2×C7311yescharacteristic, complemented
527C73#1632711yescharacteristic, direct product factor, Sylow
528C23×Q8C22×C7311yescharacteristic
529C22×C4⋊C4C22×C7311yescharacteristic
530C22×C4⋊C4C22×C7311yescharacteristic
531C22×C4⋊C4C22×C7311yescharacteristic
532C22×C4⋊C4C22×C7311yescharacteristic
533C22×C4⋊C4C22×C7311yescharacteristic
534C22×C4⋊C4C22×C7311yescharacteristic
535C22×C4⋊C4C22×C7311yescharacteristic
536C22×C4⋊C4C22×C7311yescharacteristic
537C22×C22⋊C4C22×C7311yescharacteristic
538C22×C22⋊C4C22×C7311yescharacteristic
539C22×C22⋊C4C22×C7311yescharacteristic
540C22×C22⋊C4C22×C7311yescharacteristic
541C22×C22⋊C4C22×C7311yescharacteristic
542C22×C22⋊C4C22×C7311yescharacteristic
543C22×C22⋊C4C22×C7311yescharacteristic
544C22×C42C22×C7311yescharacteristic
545#399—24no—
546#395—24no—
547#395—24no—
548#393—24no—
549#389—24no—
550#388—24no—
551C2×#95C22×C7311yescharacteristic
552C2×#95C22×C7311yescharacteristic
553C2×#95C22×C7311yescharacteristic
554C2×#95C22×C7311yescharacteristic
555C2×#95C22×C7311yescharacteristic
556C2×#95C22×C7311yescharacteristic
557C2×#95C22×C7311yescharacteristic
558C2×#95C22×C7311yescharacteristic
559C2×#95C22×C7311yescharacteristic
560C2×#95C22×C7311yescharacteristic
561C2×#95C22×C7311yescharacteristic
562C2×#95C22×C7311yescharacteristic
563C2×#95C22×C7311yescharacteristic
564C2×#95C22×C7311yescharacteristic
565C2×#95C22×C7311yescharacteristic
566C2×#95C22×C7311yescharacteristic
567C2×#95C22×C7311yescharacteristic
568C2×#95C22×C7311yescharacteristic
569C25C23×C7311yescharacteristic
570C22×Q8—22no—
571C22×Q8—22no—
572C22×Q8—22no—
573C22×Q8—41no—
574C22×Q8—41no—
575C22×Q8—41no—
576C22×Q8—41no—
577C23×C4C23×C7311yescharacteristic
578C23×C4C23×C7311yescharacteristic
579C23×C4C23×C7311yescharacteristic
580C23×C4C23×C7311yescharacteristic
581C23×C4C23×C7311yescharacteristic
582C23×C4C23×C7311yescharacteristic
583C23×C4C23×C7311yescharacteristic
584C23×C4C23×C7311yescharacteristic
585C23×C4C23×C7311yescharacteristic
586C23×C4C23×C7311yescharacteristic
587C23×C4C23×C7311yescharacteristic
588C23×C4C23×C7311yescharacteristic
589C23×C4C23×C7311yescharacteristic
590C23×C4C23×C7311yescharacteristic
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4D4×C7314yes—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—22no—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—41no—
628C2×C22⋊C4—41no—
629C2×C22⋊C4—41no—
630C2×C22⋊C4—41no—
631C2×C22⋊C4—41no—
632C2×C22⋊C4—41no—
633C2×C22⋊C4—41no—
634C2×C22⋊C4—41no—
635C2×C22⋊C4Q8×C7314yescomplemented
636C2×C42—22no—
637C2×C42—22no—
638C2×C42—41no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—22no—
652#95—22no—
653#95—41no—
654#95—41no—
655#95D4×C7314yes—
656#95D4×C7314yes—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24C2×Q8×C7312yes—
672C24C24×C7311yescharacteristic
673C2×Q8—44no—
674C2×Q8—44no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×Q8—44no—
678C2×Q8—44no—
679C2×Q8—44no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4C2×D4×C7312yes—
765C22×C4C2×D4×C7312yes—
766C22×C4C2×D4×C7312yes—
767C22×C4C2×D4×C7312yes—
768C22×C4C2×D4×C7312yes—
769C22×C4C2×D4×C7312yes—
770C22×C4C2×D4×C7312yes—
771C22×C4C2×D4×C7312yes—
772C22×C4C2×D4×C7312yes—
773C22×C4C2×Q8×C7312yes—
774C22×C4C2×Q8×C7312yes—
775C22×C4#41×C7312yes—
776C22×C4#41×C7312yes—
777C22×C4#41×C7312yes—
778C4⋊C4—28no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C4⋊C4—44no—
785C4⋊C4—44no—
786C22⋊C4—28no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C22⋊C4—44no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C22⋊C4—44no—
793C42—44no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23C22×D4×C7311yescharacteristic
830C23C22×D4×C7311yescharacteristic
831C23C22×D4×C7311yescharacteristic
832C23C22×Q8×C7311yescharacteristic
833C23C2×#41×C7311yescharacteristic
834C23C2×#41×C7311yescharacteristic
835C23C2×#41×C7311yescharacteristic
836C23H(5,𝔽2)×C7311yescharacteristic
837C23H(5,𝔽2)×C7311yescharacteristic
838C23H(5,𝔽2)×C7311yescharacteristic
839C23H(5,𝔽2)×C7311yescharacteristic
840C232−1+4×C7311yescharacteristic
841C232−1+4×C7311yescharacteristic
842C232−1+4×C7311yescharacteristic
843C232−1+4×C7311yescharacteristic
844Q8—416no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4C22⋊Q8×C7314yes—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—81no—
951C22—81no—
952C22—81no—
953C22—81no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22C2×C22⋊Q8×C7311yescharacteristic
959C22#525×C7311yescharacteristic
960C22#532×C7311yescharacteristic
961C22#534×C7311yescharacteristic
962C22#535×C7311yescharacteristic
963C22#535×C7311yescharacteristic
964C22#536×C7311yescharacteristic
965C22#536×C7311yescharacteristic
966C22#536×C7311yescharacteristic
967C22#539×C7311yescharacteristic
968C22#539×C7311yescharacteristic
969C22#542×C7311yescharacteristic
970C22#542×C7311yescharacteristic
971C22#542×C7311yescharacteristic
972C22#542×C7311yescharacteristic
973C22#542×C7311yescharacteristic
974C22#542×C7311yescharacteristic
975C22#544×C7311yescharacteristic
976C22#544×C7311yescharacteristic
977C22D42×C7311yescharacteristic
978C22D42×C7311yescharacteristic
979C22D42×C7311yescharacteristic
980C22#547×C7311yescharacteristic
981C22#547×C7311yescharacteristic
982C22#548×C7311yescharacteristic
983C22#548×C7311yescharacteristic
984C22D4×Q8×C7311yescharacteristic
985C22D4×Q8×C7311yescharacteristic
986C22#551×C7311yescharacteristic
987C22#554×C7311yescharacteristic
988C22#554×C7311yescharacteristic
989C22#560×C7311yescharacteristic
990C22#563×C7311yescharacteristic
991C22#563×C7311yescharacteristic
992C22#563×C7311yescharacteristic
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—81no—
1006C4—81no—
1007C2—82no—
1008C2C73×#244911yescharacteristic
1009C2C73×#245211yescharacteristic
1010C2C73×#246111yescharacteristic
1011C2C73×#262811yescharacteristic
1012C2C73×#263211yescharacteristic
1013C2C73×#266311yescharacteristic
1014C2C73×#266911yescharacteristic
1015C2C73×#267411yescharacteristic
1016C2C73×#267411yescharacteristic
1017C2C73×#267711yescharacteristic
1018C2C73×#272011yescharacteristic
1019C2C73×#272311yescharacteristic
1020C2C73×#272911yescharacteristic
1021C2C73×#274211yescharacteristic
1022C2C73×#283811yescharacteristic
subgroupG/H
center, socleC24×C73C24
commutator, Frattini, cosocleC24C24×C73
prime radicalC25×C73C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#395×C73C2semidirect
3. C2×#395×C73C2semidirect
5. C2×#389×C73C2semidirect
7. C73×#1444C2semidirect
8. C73×#1443C2semidirect
9. C73×#1442C2semidirect
10. C73×#1442C2semidirect
15. C73×#1436C2semidirect
123. C2×C22⋊C4×C73Q8semidirect
495. #16327C73direct (N × H)
513. C2×#395C2×C73semidirect
514. C2×#395C2×C73semidirect
516. C2×#389C2×C73semidirect
518. #1444C2×C73semidirect
519. #1443C2×C73semidirect
520. #1442C2×C73semidirect
521. #1442C2×C73semidirect
526. #1436C2×C73semidirect
527. C73#16327direct (N × H)
635. C2×C22⋊C4Q8×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#399×C732
C2×#395×C732
C2×#393×C732
C2×#389×C732
C2×#388×C732
C73×#14442
C73×#14432
C73×#14422
C73×#14392
C73×#14362
#1632773