Finite Group Databasebeta

← C73×#59459 #32968863

Subgroups — C73×#59459 #32968863

Order 18688.

1684 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2792C214yesmaximal
2C73×#2586C214yesmaximal
3C73×#2584C212yesmaximal
4C73×#2567C212yesmaximal
5C73×#2567C212yesmaximal
6C73×#2552C211yesmaximal, characteristic
7C73×#2551C211yesmaximal, characteristic
8C73×#2550C212yesmaximal
9C73×#2451C212yesmaximal
10C73×#2451C212yesmaximal
11C73×#2370C212yesmaximal
12C73×#2365C211yesmaximal, characteristic
13C73×#2365C211yesmaximal, characteristic
14Q8×C4⋊C4×C73C212yesmaximal
15C4×C4⋊Q8×C73C211yesmaximal, characteristic
16C4×C4⋊Q8×C73C211yesmaximal, characteristic
17C4×#125×C73C211yesmaximal, characteristic
18C2×C4⋊Q8×C73C2211yescharacteristic
19C2×C4⋊Q8×C73C2212yes—
20C2×C4⋊Q8×C73C2212yes—
21C2×C4⋊Q8×C73C2211yescharacteristic
22C2×#125×C73C2212yes—
23C2×#125×C73C2211yescharacteristic
24C2×C4×Q8×C73C2212yes—
25C2×C4×Q8×C73C2212yes—
26C2×C4×Q8×C73C2212yes—
27C2×C4×Q8×C73C2212yes—
28#398×C73C2214yes—
29#398×C73C2214yes—
30#398×C73C2214yes—
31#395×C73C2214yes—
32#395×C73C2214yes—
33#395×C73C2214yes—
34#395×C73C2214yes—
35#395×C73C2214yes—
36#391×C73C2212yes—
37#391×C73C2214yes—
38#391×C73C2212yes—
39#391×C73C2214yes—
40#391×C73C2212yes—
41#391×C73C2212yes—
42#389×C73C2212yes—
43#389×C73C2211yescharacteristic
44#389×C73C2212yes—
45#389×C73C2212yes—
46#389×C73C2212yes—
47#389×C73C2214yes—
48#389×C73C2214yes—
49#389×C73C2212yes—
50#389×C73C2212yes—
51#389×C73C2214yes—
52#389×C73C2212yes—
53#389×C73C2212yes—
54#389×C73C2211yescharacteristic
55#389×C73C2211yescharacteristic
56#389×C73C2212yes—
57#389×C73C2211yescharacteristic
58#389×C73C2214yes—
59#387×C73C2214yes—
60#387×C73C2214yes—
61#387×C73C2212yes—
62#387×C73C2214yes—
63#387×C73C2214yes—
64#387×C73C2212yes—
65#384×C73C2214yes—
66#384×C73C2211yescharacteristic
67#384×C73C2212yes—
68#384×C73C2211yescharacteristic
69#382×C73C2211yescharacteristic
70C4×C4⋊C4×C73C2212yes—
71C4×C4⋊C4×C73C2212yes—
72C4×C4⋊C4×C73C2212yes—
73C4×C4⋊C4×C73C2212yes—
74C4×C4⋊C4×C73C2211yescharacteristic
75C4×C4⋊C4×C73C2211yescharacteristic
76C4×C4⋊C4×C73C2211yescharacteristic
77C4×C4⋊C4×C73C2211yescharacteristic
78C4×C4⋊C4×C73C2212yes—
79C4×C4⋊C4×C73C2212yes—
80C4×C4⋊C4×C73C2212yes—
81C4×C4⋊C4×C73C2214yes—
82C43×C73C2211yescharacteristic
83C22×Q8×C73C2312yes—
84C22×Q8×C73C2312yes—
85C22×Q8×C73C2314yes—
86C4⋊Q8×C73—24no—
87C4⋊Q8×C73—44no—
88C4⋊Q8×C73—44no—
89C4⋊Q8×C73Q818yescomplemented
90#125×C73—44no—
91#125×C73Q818yescomplemented
92C4×Q8×C73—28no—
93C4×Q8×C73—44no—
94C4×Q8×C73—44no—
95C4×Q8×C73—44no—
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2312yes—
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2312yes—
102C2×C4⋊C4×C73C2312yes—
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C4⋊C4×C73C2312yes—
105C2×C4⋊C4×C73C2314yes—
106C2×C4⋊C4×C73C2312yes—
107C2×C4⋊C4×C73C2314yes—
108C2×C4⋊C4×C73C2312yes—
109C2×C4⋊C4×C73C2312yes—
110C2×C4⋊C4×C73C2312yes—
111C2×C4⋊C4×C73C2314yes—
112C2×C4⋊C4×C73C2314yes—
113C2×C4⋊C4×C73C2314yes—
114C2×C4⋊C4×C73C2312yes—
115C2×C4⋊C4×C73C2314yes—
116C2×C4⋊C4×C73C2314yes—
117C2×C4⋊C4×C73C2312yes—
118C2×C4⋊C4×C73C2314yes—
119C2×C4⋊C4×C73C2312yes—
120C2×C4⋊C4×C73C2311yescharacteristic
121C2×C4⋊C4×C73C2311yescharacteristic
122C2×C4⋊C4×C73C2312yes—
123C2×C4⋊C4×C73C2312yes—
124C2×C4⋊C4×C73C2312yes—
125C2×C4⋊C4×C73C2311yescharacteristic
126C2×C42×C73C2312yes—
127C2×C42×C73C2312yes—
128C2×C42×C73C2312yes—
129C2×C42×C73C2312yes—
130C2×C42×C73C2314yes—
131C2×C42×C73C2311yescharacteristic
132C2×C42×C73C2311yescharacteristic
133C2×C42×C73C2311yescharacteristic
134C2×C42×C73C2311yescharacteristic
135C2×C42×C73C2314yes—
136C2×C42×C73C2314yes—
137C2×C42×C73C2311yescharacteristic
138C2×C42×C73C2311yescharacteristic
139C2×C42×C73C2311yescharacteristic
140#95×C73C2312yes—
141#95×C73C2312yes—
142#95×C73C2312yes—
143#95×C73C2312yes—
144#95×C73C2312yes—
145#95×C73C2314yes—
146#95×C73C2312yes—
147#95×C73C2312yes—
148#95×C73C2314yes—
149#95×C73C2312yes—
150#95×C73C2314yes—
151#95×C73C2312yes—
152#95×C73C2314yes—
153#95×C73C2312yes—
154#95×C73C2314yes—
155#95×C73C2314yes—
156#95×C73C2314yes—
157#95×C73C2314yes—
158C2×Q8×C73—24no—
159C2×Q8×C73—24no—
160C2×Q8×C73—24no—
161C2×Q8×C73—24no—
162C2×Q8×C73—42no—
163C2×Q8×C73—44no—
164C2×Q8×C73—44no—
165C2×Q8×C73—44no—
166C2×Q8×C73C2×Q818yes—
167C22×C4×C73C2412yes—
168C22×C4×C73C2412yes—
169C22×C4×C73C2412yes—
170C22×C4×C73C2412yes—
171C22×C4×C73C2414yes—
172C22×C4×C73C2411yescharacteristic
173C22×C4×C73C2412yes—
174C22×C4×C73C2411yescharacteristic
175C22×C4×C73C2411yescharacteristic
176C22×C4×C73C2412yes—
177C22×C4×C73C2411yescharacteristic
178C22×C4×C73C2412yes—
179C22×C4×C73C2414yes—
180C22×C4×C73C2412yes—
181C22×C4×C73C2411yescharacteristic
182C22×C4×C73C2411yescharacteristic
183C22×C4×C73C2411yescharacteristic
184C4⋊C4×C73—28no—
185C4⋊C4×C73—24no—
186C4⋊C4×C73—22no—
187C4⋊C4×C73—22no—
188C4⋊C4×C73—24no—
189C4⋊C4×C73—22no—
190C4⋊C4×C73—24no—
191C4⋊C4×C73—22no—
192C4⋊C4×C73—22no—
193C4⋊C4×C73—24no—
194C4⋊C4×C73—42no—
195C4⋊C4×C73—42no—
196C4⋊C4×C73—42no—
197C4⋊C4×C73—44no—
198C4⋊C4×C73—42no—
199C4⋊C4×C73—42no—
200C4⋊C4×C73—44no—
201C4⋊C4×C73—44no—
202C4⋊C4×C73—42no—
203C4⋊C4×C73—44no—
204C4⋊C4×C73—44no—
205C4⋊C4×C73—44no—
206C4⋊C4×C73—44no—
207C4⋊C4×C73C2×Q818yes—
208C4⋊C4×C73C2×Q818yes—
209C4⋊C4×C73C2×Q814yes—
210C4⋊C4×C73C2×Q814yes—
211C4⋊C4×C73C2×Q818yes—
212C4⋊C4×C73C2×Q818yes—
213C4⋊C4×C73#4114yes—
214C42×C73—28no—
215C42×C73—24no—
216C42×C73—22no—
217C42×C73—22no—
218C42×C73—22no—
219C42×C73—24no—
220C42×C73—24no—
221C42×C73—24no—
222C42×C73—22no—
223C42×C73—41no—
224C42×C73—44no—
225C42×C73—44no—
226C42×C73C2×Q814yes—
227C42×C73C2×Q814yes—
228C23×C73C2511yescharacteristic
229Q8×C73—216no—
230Q8×C73—48no—
231Q8×C73—88no—
232C2×C4×C73—22no—
233C2×C4×C73—21no—
234C2×C4×C73—24no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—22no—
238C2×C4×C73—22no—
239C2×C4×C73—21no—
240C2×C4×C73—24no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—22no—
244C2×C4×C73—22no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—22no—
248C2×C4×C73—22no—
249C2×C4×C73—22no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—22no—
253C2×C4×C73—22no—
254C2×C4×C73—22no—
255C2×C4×C73—22no—
256C2×C4×C73—22no—
257C2×C4×C73—24no—
258C2×C4×C73—22no—
259C2×C4×C73—24no—
260C2×C4×C73—22no—
261C2×C4×C73—22no—
262C2×C4×C73—22no—
263C2×C4×C73—22no—
264C2×C4×C73—21no—
265C2×C4×C73—22no—
266C2×C4×C73—24no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73C22×Q812yes—
270C2×C4×C73C22×Q812yes—
271C2×C4×C73C22×Q812yes—
272C2×C4×C73C22×Q814yes—
273C2×C4×C73C22×Q814yes—
274C2×C4×C73C22×Q818yes—
275C2×C4×C73C22×Q812yes—
276C2×C4×C73C22×Q812yes—
277C2×C4×C73C22×Q812yes—
278C2×C4×C73C2×#4114yes—
279C2×C4×C73C2×#4112yes—
280C2×C4×C73H(5,𝔽2)12yes—
281C2×C4×C73H(5,𝔽2)12yes—
282C2×C4×C732−1+412yes—
283C22×C73C23×Q811yescharacteristic
284C22×C73C23×Q811yescharacteristic
285C22×C73C22×#4111yescharacteristic
286C22×C73C2×H(5,𝔽2)11yescharacteristic
287C22×C73C2×H(5,𝔽2)11yescharacteristic
288C22×C73C2×2−1+411yescharacteristic
289C22×C73#58511yescharacteristic
290C4×C73—28no—
291C4×C73—24no—
292C4×C73—22no—
293C4×C73—22no—
294C4×C73—22no—
295C4×C73—24no—
296C4×C73—24no—
297C4×C73—22no—
298C4×C73—42no—
299C4×C73—42no—
300C4×C73—41no—
301C4×C73—42no—
302C4×C73—44no—
303C4×C73—42no—
304C4×C73—42no—
305C4×C73#55414yes—
306C4×C73Q8214yes—
307#59459C7311yesmaximal, characteristic, direct product factor, Sylow
308C2×C73C2×#55411yescharacteristic
309C2×C73C2×Q8211yescharacteristic
310C2×C73Q8×#4111yescharacteristic
311C2×C73#350211yescharacteristic
312C2×C73#350311yescharacteristic
313C2×C73#352011yescharacteristic
314C2×C73#354611yescharacteristic
315#2792C2×C7314yes—
316#2586C2×C7314yes—
317#2584C2×C7312yes—
318#2567C2×C7312yes—
319#2567C2×C7312yes—
320#2552C2×C7311yescharacteristic
321#2551C2×C7311yescharacteristic
322#2550C2×C7312yes—
323#2451C2×C7312yes—
324#2451C2×C7312yes—
325#2370C2×C7312yes—
326#2365C2×C7311yescharacteristic
327#2365C2×C7311yescharacteristic
328Q8×C4⋊C4C2×C7312yes—
329C4×C4⋊Q8C2×C7311yescharacteristic
330C4×C4⋊Q8C2×C7311yescharacteristic
331C4×#125C2×C7311yescharacteristic
332C73#5945911yescharacteristic, direct product factor, Sylow
333C2×C4⋊Q8C22×C7311yescharacteristic
334C2×C4⋊Q8C22×C7312yes—
335C2×C4⋊Q8C22×C7312yes—
336C2×C4⋊Q8C22×C7311yescharacteristic
337C2×#125C22×C7312yes—
338C2×#125C22×C7311yescharacteristic
339C2×C4×Q8C22×C7312yes—
340C2×C4×Q8C22×C7312yes—
341C2×C4×Q8C22×C7312yes—
342C2×C4×Q8C22×C7312yes—
343#398C22×C7314yes—
344#398C22×C7314yes—
345#398C22×C7314yes—
346#395C22×C7314yes—
347#395C22×C7314yes—
348#395C22×C7314yes—
349#395C22×C7314yes—
350#395C22×C7314yes—
351#391C22×C7312yes—
352#391C22×C7312yes—
353#391C22×C7314yes—
354#391C22×C7312yes—
355#391C22×C7314yes—
356#391C22×C7312yes—
357#389C22×C7311yescharacteristic
358#389C22×C7311yescharacteristic
359#389C22×C7312yes—
360#389C22×C7311yescharacteristic
361#389C22×C7311yescharacteristic
362#389C22×C7312yes—
363#389C22×C7312yes—
364#389C22×C7314yes—
365#389C22×C7312yes—
366#389C22×C7314yes—
367#389C22×C7312yes—
368#389C22×C7314yes—
369#389C22×C7312yes—
370#389C22×C7312yes—
371#389C22×C7314yes—
372#389C22×C7312yes—
373#389C22×C7312yes—
374#387C22×C7312yes—
375#387C22×C7312yes—
376#387C22×C7314yes—
377#387C22×C7314yes—
378#387C22×C7314yes—
379#387C22×C7314yes—
380#384C22×C7311yescharacteristic
381#384C22×C7311yescharacteristic
382#384C22×C7314yes—
383#384C22×C7312yes—
384#382C22×C7311yescharacteristic
385C4×C4⋊C4C22×C7312yes—
386C4×C4⋊C4C22×C7312yes—
387C4×C4⋊C4C22×C7311yescharacteristic
388C4×C4⋊C4C22×C7311yescharacteristic
389C4×C4⋊C4C22×C7312yes—
390C4×C4⋊C4C22×C7311yescharacteristic
391C4×C4⋊C4C22×C7311yescharacteristic
392C4×C4⋊C4C22×C7312yes—
393C4×C4⋊C4C22×C7312yes—
394C4×C4⋊C4C22×C7312yes—
395C4×C4⋊C4C22×C7312yes—
396C4×C4⋊C4C22×C7314yes—
397C43C22×C7311yescharacteristic
398C22×Q8C23×C7312yes—
399C22×Q8C23×C7312yes—
400C22×Q8C23×C7314yes—
401C4⋊Q8—24no—
402C4⋊Q8—44no—
403C4⋊Q8—44no—
404C4⋊Q8Q8×C7318yescomplemented
405#125—44no—
406#125Q8×C7318yescomplemented
407C4×Q8—28no—
408C4×Q8—44no—
409C4×Q8—44no—
410C4×Q8—44no—
411C2×C4⋊C4C23×C7311yescharacteristic
412C2×C4⋊C4C23×C7312yes—
413C2×C4⋊C4C23×C7314yes—
414C2×C4⋊C4C23×C7311yescharacteristic
415C2×C4⋊C4C23×C7312yes—
416C2×C4⋊C4C23×C7311yescharacteristic
417C2×C4⋊C4C23×C7311yescharacteristic
418C2×C4⋊C4C23×C7312yes—
419C2×C4⋊C4C23×C7311yescharacteristic
420C2×C4⋊C4C23×C7312yes—
421C2×C4⋊C4C23×C7312yes—
422C2×C4⋊C4C23×C7314yes—
423C2×C4⋊C4C23×C7314yes—
424C2×C4⋊C4C23×C7312yes—
425C2×C4⋊C4C23×C7312yes—
426C2×C4⋊C4C23×C7314yes—
427C2×C4⋊C4C23×C7314yes—
428C2×C4⋊C4C23×C7314yes—
429C2×C4⋊C4C23×C7314yes—
430C2×C4⋊C4C23×C7312yes—
431C2×C4⋊C4C23×C7314yes—
432C2×C4⋊C4C23×C7312yes—
433C2×C4⋊C4C23×C7312yes—
434C2×C4⋊C4C23×C7312yes—
435C2×C4⋊C4C23×C7311yescharacteristic
436C2×C4⋊C4C23×C7311yescharacteristic
437C2×C4⋊C4C23×C7312yes—
438C2×C4⋊C4C23×C7312yes—
439C2×C4⋊C4C23×C7312yes—
440C2×C4⋊C4C23×C7311yescharacteristic
441C2×C42C23×C7311yescharacteristic
442C2×C42C23×C7311yescharacteristic
443C2×C42C23×C7312yes—
444C2×C42C23×C7312yes—
445C2×C42C23×C7312yes—
446C2×C42C23×C7312yes—
447C2×C42C23×C7314yes—
448C2×C42C23×C7311yescharacteristic
449C2×C42C23×C7311yescharacteristic
450C2×C42C23×C7314yes—
451C2×C42C23×C7314yes—
452C2×C42C23×C7311yescharacteristic
453C2×C42C23×C7311yescharacteristic
454C2×C42C23×C7311yescharacteristic
455#95C23×C7312yes—
456#95C23×C7312yes—
457#95C23×C7312yes—
458#95C23×C7312yes—
459#95C23×C7312yes—
460#95C23×C7314yes—
461#95C23×C7312yes—
462#95C23×C7312yes—
463#95C23×C7314yes—
464#95C23×C7312yes—
465#95C23×C7314yes—
466#95C23×C7312yes—
467#95C23×C7314yes—
468#95C23×C7312yes—
469#95C23×C7314yes—
470#95C23×C7314yes—
471#95C23×C7314yes—
472#95C23×C7314yes—
473C2×Q8—24no—
474C2×Q8—24no—
475C2×Q8—24no—
476C2×Q8—24no—
477C2×Q8—42no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8C2×Q8×C7318yes—
482C22×C4C24×C7312yes—
483C22×C4C24×C7312yes—
484C22×C4C24×C7312yes—
485C22×C4C24×C7312yes—
486C22×C4C24×C7314yes—
487C22×C4C24×C7311yescharacteristic
488C22×C4C24×C7312yes—
489C22×C4C24×C7311yescharacteristic
490C22×C4C24×C7311yescharacteristic
491C22×C4C24×C7312yes—
492C22×C4C24×C7311yescharacteristic
493C22×C4C24×C7312yes—
494C22×C4C24×C7314yes—
495C22×C4C24×C7312yes—
496C22×C4C24×C7311yescharacteristic
497C22×C4C24×C7311yescharacteristic
498C22×C4C24×C7311yescharacteristic
499C4⋊C4—28no—
500C4⋊C4—24no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—24no—
504C4⋊C4—22no—
505C4⋊C4—24no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—24no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—44no—
513C4⋊C4—42no—
514C4⋊C4—42no—
515C4⋊C4—44no—
516C4⋊C4—44no—
517C4⋊C4—42no—
518C4⋊C4—44no—
519C4⋊C4—44no—
520C4⋊C4—44no—
521C4⋊C4—44no—
522C4⋊C4C2×Q8×C7318yes—
523C4⋊C4C2×Q8×C7318yes—
524C4⋊C4C2×Q8×C7314yes—
525C4⋊C4C2×Q8×C7314yes—
526C4⋊C4C2×Q8×C7318yes—
527C4⋊C4C2×Q8×C7318yes—
528C4⋊C4#41×C7314yes—
529C42—28no—
530C42—24no—
531C42—22no—
532C42—22no—
533C42—22no—
534C42—24no—
535C42—24no—
536C42—24no—
537C42—22no—
538C42—41no—
539C42—44no—
540C42—44no—
541C42C2×Q8×C7314yes—
542C42C2×Q8×C7314yes—
543C23C25×C7311yescharacteristic
544Q8—216no—
545Q8—48no—
546Q8—88no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—24no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—24no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4C22×Q8×C7312yes—
585C2×C4C22×Q8×C7312yes—
586C2×C4C22×Q8×C7312yes—
587C2×C4C22×Q8×C7314yes—
588C2×C4C22×Q8×C7314yes—
589C2×C4C22×Q8×C7318yes—
590C2×C4C22×Q8×C7312yes—
591C2×C4C22×Q8×C7312yes—
592C2×C4C22×Q8×C7312yes—
593C2×C4C2×#41×C7314yes—
594C2×C4C2×#41×C7312yes—
595C2×C4H(5,𝔽2)×C7312yes—
596C2×C4H(5,𝔽2)×C7312yes—
597C2×C42−1+4×C7312yes—
598C22C23×Q8×C7311yescharacteristic
599C22C23×Q8×C7311yescharacteristic
600C22C22×#41×C7311yescharacteristic
601C22C2×H(5,𝔽2)×C7311yescharacteristic
602C22C2×H(5,𝔽2)×C7311yescharacteristic
603C22C2×2−1+4×C7311yescharacteristic
604C22#585×C7311yescharacteristic
605C4—28no—
606C4—24no—
607C4—22no—
608C4—22no—
609C4—22no—
610C4—24no—
611C4—24no—
612C4—22no—
613C4—42no—
614C4—42no—
615C4—42no—
616C4—42no—
617C4—44no—
618C4—41no—
619C4—42no—
620C4#554×C7314yes—
621C4Q82×C7314yes—
622C2C2×#554×C7311yescharacteristic
623C2C2×Q82×C7311yescharacteristic
624C2Q8×#41×C7311yescharacteristic
625C2C73×#350211yescharacteristic
626C2C73×#350311yescharacteristic
627C2C73×#352011yescharacteristic
628C2C73×#354611yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C73C25
commutator, Frattini, cosocleC23C25×C73
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

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

NH ≅ G/Ntype
89. C4⋊Q8×C73Q8semidirect
91. #125×C73Q8semidirect
307. #59459C73direct (N × H)
332. C73#59459direct (N × H)
404. C4⋊Q8Q8×C73semidirect
406. #125Q8×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#27922
C73×#25862
C73×#25842
C73×#25672
C73×#25522
C73×#25512
C73×#25502
C73×#24512
C73×#23702
C73×#23652
Q8×C4⋊C4×C732
C4×C4⋊Q8×C732
C4×#125×C732
#5945973