Finite Group Databasebeta

← C73×#25021 #32934425

Subgroups — C73×#25021 #32934425

Order 18688.

832 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C73C211yesmaximal, characteristic, complemented
2C2×#483×C73C211yesmaximal, characteristic, complemented
3C73×#2536C211yesmaximal, characteristic
4C73×#2352C211yesmaximal, characteristic
5C73×#2077C211yesmaximal, characteristic, complemented
6C73×#2077C211yesmaximal, characteristic, complemented
7C73×#2036C211yesmaximal, characteristic, complemented
8C73×#2036C211yesmaximal, characteristic, complemented
9C73×#1954C211yesmaximal, characteristic
10C73×#1949C211yesmaximal, characteristic, complemented
11C73×#1854C211yesmaximal, characteristic, complemented
12C73×#1852C211yesmaximal, characteristic, complemented
13C73×#1846C211yesmaximal, characteristic, complemented
14C73×#1805C211yesmaximal, characteristic, complemented
15C4×#103×C73C211yesmaximal, characteristic, complemented
16C2×C22⋊Q8×C73C2211yescharacteristic
17C2×C22⋊Q8×C73C2211yescharacteristic
18C2×C4×Q8×C73C2211yescharacteristic
19C2×C4×D4×C73C2211yescharacteristic
20C2×#117×C73C2211yescharacteristic
21C22×C4⋊C4×C73C2211yescharacteristic
22#485×C73—24no—
23#483×C73—24no—
24C2×#107×C73C2211yescharacteristic
25C2×#107×C73C2211yescharacteristic
26C2×#107×C73C2211yescharacteristic
27C2×#106×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29C2×#106×C73C2211yescharacteristic
30C2×C4⋊C8×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#103×C73C2211yescharacteristic
34C2×#103×C73C2211yescharacteristic
35C2×C22⋊C8×C73C2211yescharacteristic
36C2×C22⋊C8×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38C2×C22⋊C8×C73C2211yescharacteristic
39C2×C4×C8×C73C2211yescharacteristic
40#398×C73—21no—
41#394×C73—21no—
42#388×C73—21no—
43#388×C73—21no—
44#388×C73—21no—
45#387×C73—21no—
46#386×C73—21no—
47#382×C73C2211yescharacteristic
48#382×C73C2211yescharacteristic
49#380×C73C2211yescharacteristic
50#380×C73C2211yescharacteristic
51#380×C73C2211yescharacteristic
52#380×C73C2211yescharacteristic
53C4×C4⋊C4×C73C2211yescharacteristic
54C4×C22⋊C4×C73—21no—
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61C22×Q8×C73C2311yescharacteristic
62C22×D4×C73D411yescharacteristic
63C23×C4×C73—21no—
64C23×C4×C73C2311yescharacteristic
65C23×C4×C73C2311yescharacteristic
66C22×C8×C73C2311yescharacteristic
67C22×C8×C73C2311yescharacteristic
68C22×C8×C73C2311yescharacteristic
69C22×C8×C73C2311yescharacteristic
70C22⋊Q8×C73—22no—
71C22⋊Q8×C73—22no—
72C22⋊Q8×C73—41no—
73C22⋊Q8×C73—41no—
74C4×Q8×C73—22no—
75C4×Q8×C73—22no—
76C4×D4×C73—22no—
77C4×D4×C73—22no—
78#117×C73—22no—
79#117×C73—41no—
80C2×C4⋊C4×C73—22no—
81C2×C4⋊C4×C73—21no—
82C2×C4⋊C4×C73—21no—
83C2×C4⋊C4×C73—21no—
84C2×C4⋊C4×C73—21no—
85C2×C4⋊C4×C73—41no—
86C2×C4⋊C4×C73D411yescharacteristic
87C2×C4⋊C4×C73C2311yescharacteristic
88C2×C4⋊C4×C73C2311yescharacteristic
89C2×C4⋊C4×C73C2311yescharacteristic
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C4⋊C4×C73C2311yescharacteristic
92C2×C4⋊C4×C73C2311yescharacteristic
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C22⋊C4×C73—21no—
95C2×C22⋊C4×C73—21no—
96C2×C22⋊C4×C73—21no—
97C2×C22⋊C4×C73—21no—
98C2×C22⋊C4×C73—21no—
99C2×C22⋊C4×C73—21no—
100C2×C22⋊C4×C73—21no—
101C2×C22⋊C4×C73D411yescharacteristic
102C2×C22⋊C4×C73D411yescharacteristic
103C2×C42×C73—21no—
104C2×C42×C73—21no—
105C2×C42×C73—21no—
106C2×C42×C73C2311yescharacteristic
107#107×C73—22no—
108#107×C73—41no—
109#107×C73—41no—
110#106×C73—22no—
111#106×C73—22no—
112#106×C73—22no—
113C4⋊C8×C73—22no—
114#103×C73—22no—
115#103×C73—22no—
116#103×C73—22no—
117#103×C73D414yescomplemented
118C22⋊C8×C73—22no—
119C22⋊C8×C73—22no—
120C22⋊C8×C73—22no—
121C22⋊C8×C73—22no—
122C4×C8×C73—22no—
123#95×C73—21no—
124#95×C73—21no—
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73—21no—
131#95×C73—21no—
132C24×C73C2×D411yescharacteristic
133C24×C73C2×D411yescharacteristic
134C2×Q8×C73—21no—
135C2×Q8×C73—21no—
136C2×Q8×C73—21no—
137C2×Q8×C73—21no—
138C2×Q8×C73—21no—
139C2×Q8×C73C2×D412yes—
140C2×D4×C73—22no—
141C2×D4×C73—22no—
142C2×D4×C73—41no—
143C22×C4×C73—21no—
144C22×C4×C73—21no—
145C22×C4×C73—21no—
146C22×C4×C73—21no—
147C22×C4×C73—21no—
148C22×C4×C73—21no—
149C22×C4×C73—21no—
150C22×C4×C73—21no—
151C22×C4×C73—21no—
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—21no—
160C22×C4×C73—21no—
161C22×C4×C73—21no—
162C22×C4×C73—21no—
163C22×C4×C73—42no—
164C22×C4×C73—42no—
165C22×C4×C73—81no—
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73C2×D411yescharacteristic
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2411yescharacteristic
171C2×C8×C73—21no—
172C2×C8×C73—21no—
173C2×C8×C73—21no—
174C2×C8×C73—21no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73C2×D412yes—
182C2×C8×C73#4112yes—
183C4⋊C4×C73—22no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—42no—
198C4⋊C4×C73—42no—
199C4⋊C4×C73—42no—
200C4⋊C4×C73—42no—
201C4⋊C4×C73C2×D412yes—
202C22⋊C4×C73—22no—
203C22⋊C4×C73—22no—
204C22⋊C4×C73—42no—
205C22⋊C4×C73—42no—
206C22⋊C4×C73—42no—
207C22⋊C4×C73—42no—
208C22⋊C4×C73—42no—
209C22⋊C4×C73—42no—
210C22⋊C4×C73—81no—
211C42×C73—42no—
212C42×C73—42no—
213C42×C73—81no—
214C42×C73#4112yes—
215C42×C73#4112yes—
216C23×C73—21no—
217C23×C73—21no—
218C23×C73—21no—
219C23×C73—21no—
220C23×C73—21no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73—21no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73#13512yes—
230C23×C73C22×D411yescharacteristic
231Q8×C73—22no—
232Q8×C73—22no—
233Q8×C73—41no—
234Q8×C73—41no—
235D4×C73—44no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—21no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
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—21no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73—41no—
253C2×C4×C73—41no—
254C2×C4×C73—41no—
255C2×C4×C73—41no—
256C2×C4×C73—41no—
257C2×C4×C73—41no—
258C2×C4×C73—41no—
259C2×C4×C73—41no—
260C2×C4×C73—41no—
261C2×C4×C73—41no—
262C2×C4×C73—41no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
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—84no—
279C2×C4×C73#12312yes—
280C2×C4×C73#12312yes—
281C2×C4×C73C22×D411yescharacteristic
282C2×C4×C73C2×#4111yescharacteristic
283C2×C4×C73C2×#4111yescharacteristic
284C2×C4×C73C2×#4111yescharacteristic
285C2×C4×C73H(5,𝔽2)11yescharacteristic
286C2×C4×C732−1+411yescharacteristic
287C8×C73—22no—
288C8×C73—22no—
289C8×C73—41no—
290C8×C73—41no—
291C22×C73—22no—
292C22×C73—22no—
293C22×C73—22no—
294C22×C73—41no—
295C22×C73—41no—
296C22×C73—41no—
297C22×C73—41no—
298C22×C73—41no—
299C22×C73—41no—
300C22×C73—41no—
301C22×C73—41no—
302C22×C73—41no—
303C22×C73—41no—
304C22×C73—41no—
305C22×C73C2×#12311yescharacteristic
306C22×C73D4211yescharacteristic
307C22×C73#54711yescharacteristic
308C22×C73C2×#13511yescharacteristic
309C22×C73#57511yescharacteristic
310C22×C73#57711yescharacteristic
311C22×C73#57811yescharacteristic
312C4×C73—22no—
313C4×C73—22no—
314C4×C73—41no—
315C4×C73—41no—
316C4×C73—42no—
317C4×C73—42no—
318C4×C73—81no—
319C4×C73—81no—
320C4×C73—81no—
321C4×C73—81no—
322C4×C73—81no—
323C4×C73—81no—
324C4×C73#53211yescharacteristic
325C4×C73#54211yescharacteristic
326C4×C73#54711yescharacteristic
327C4×C73#55311yescharacteristic
328#25021C7311yesmaximal, characteristic, direct product factor, Sylow
329C2×C73—42no—
330C2×C73—81no—
331C2×C73#242211yescharacteristic
332C2×C73#309111yescharacteristic
333C2×C73#309711yescharacteristic
334C2×C73#327711yescharacteristic
335C2×C73#328211yescharacteristic
336C2×C73#333611yescharacteristic
337C2×C73#335111yescharacteristic
338C2×#485C2×C7311yescharacteristic, complemented
339C2×#483C2×C7311yescharacteristic, complemented
340#2536C2×C7311yescharacteristic
341#2352C2×C7311yescharacteristic
342#2077C2×C7311yescharacteristic, complemented
343#2077C2×C7311yescharacteristic, complemented
344#2036C2×C7311yescharacteristic, complemented
345#2036C2×C7311yescharacteristic, complemented
346#1954C2×C7311yescharacteristic
347#1949C2×C7311yescharacteristic, complemented
348#1854C2×C7311yescharacteristic, complemented
349#1852C2×C7311yescharacteristic, complemented
350#1846C2×C7311yescharacteristic, complemented
351#1805C2×C7311yescharacteristic, complemented
352C4×#103C2×C7311yescharacteristic, complemented
353C73#2502111yescharacteristic, direct product factor, Sylow
354C2×C22⋊Q8C22×C7311yescharacteristic
355C2×C22⋊Q8C22×C7311yescharacteristic
356C2×C4×Q8C22×C7311yescharacteristic
357C2×C4×D4C22×C7311yescharacteristic
358C2×#117C22×C7311yescharacteristic
359C22×C4⋊C4C22×C7311yescharacteristic
360#485—24no—
361#483—24no—
362C2×#107C22×C7311yescharacteristic
363C2×#107C22×C7311yescharacteristic
364C2×#107C22×C7311yescharacteristic
365C2×#106C22×C7311yescharacteristic
366C2×#106C22×C7311yescharacteristic
367C2×#106C22×C7311yescharacteristic
368C2×C4⋊C8C22×C7311yescharacteristic
369C2×#103C22×C7311yescharacteristic
370C2×#103C22×C7311yescharacteristic
371C2×#103C22×C7311yescharacteristic
372C2×#103C22×C7311yescharacteristic
373C2×C22⋊C8C22×C7311yescharacteristic
374C2×C22⋊C8C22×C7311yescharacteristic
375C2×C22⋊C8C22×C7311yescharacteristic
376C2×C22⋊C8C22×C7311yescharacteristic
377C2×C4×C8C22×C7311yescharacteristic
378#398—21no—
379#394—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#387—21no—
384#386—21no—
385#382C22×C7311yescharacteristic
386#382C22×C7311yescharacteristic
387#380C22×C7311yescharacteristic
388#380C22×C7311yescharacteristic
389#380C22×C7311yescharacteristic
390#380C22×C7311yescharacteristic
391C4×C4⋊C4C22×C7311yescharacteristic
392C4×C22⋊C4—21no—
393#340C22×C7311yescharacteristic
394#340C22×C7311yescharacteristic
395#340C22×C7311yescharacteristic
396#340C22×C7311yescharacteristic
397#340C22×C7311yescharacteristic
398#340C22×C7311yescharacteristic
399C22×Q8C23×C7311yescharacteristic
400C22×D4D4×C7311yescharacteristic
401C23×C4—21no—
402C23×C4C23×C7311yescharacteristic
403C23×C4C23×C7311yescharacteristic
404C22×C8C23×C7311yescharacteristic
405C22×C8C23×C7311yescharacteristic
406C22×C8C23×C7311yescharacteristic
407C22×C8C23×C7311yescharacteristic
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—41no—
411C22⋊Q8—41no—
412C4×Q8—22no—
413C4×Q8—22no—
414C4×D4—22no—
415C4×D4—22no—
416#117—22no—
417#117—41no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—41no—
424C2×C4⋊C4D4×C7311yescharacteristic
425C2×C4⋊C4C23×C7311yescharacteristic
426C2×C4⋊C4C23×C7311yescharacteristic
427C2×C4⋊C4C23×C7311yescharacteristic
428C2×C4⋊C4C23×C7311yescharacteristic
429C2×C4⋊C4C23×C7311yescharacteristic
430C2×C4⋊C4C23×C7311yescharacteristic
431C2×C4⋊C4C23×C7311yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4D4×C7311yescharacteristic
440C2×C22⋊C4D4×C7311yescharacteristic
441C2×C42—21no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42C23×C7311yescharacteristic
445#107—22no—
446#107—41no—
447#107—41no—
448#106—22no—
449#106—22no—
450#106—22no—
451C4⋊C8—22no—
452#103—22no—
453#103—22no—
454#103—22no—
455#103D4×C7314yescomplemented
456C22⋊C8—22no—
457C22⋊C8—22no—
458C22⋊C8—22no—
459C22⋊C8—22no—
460C4×C8—22no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470C24C2×D4×C7311yescharacteristic
471C24C2×D4×C7311yescharacteristic
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8C2×D4×C7312yes—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—41no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—81no—
504C22×C4C2×D4×C7311yescharacteristic
505C22×C4C2×D4×C7311yescharacteristic
506C22×C4C2×D4×C7311yescharacteristic
507C22×C4C2×D4×C7311yescharacteristic
508C22×C4C24×C7311yescharacteristic
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8C2×D4×C7312yes—
520C2×C8#41×C7312yes—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4C2×D4×C7312yes—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—81no—
549C42—42no—
550C42—42no—
551C42—81no—
552C42#41×C7312yes—
553C42#41×C7312yes—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23#135×C7312yes—
568C23C22×D4×C7311yescharacteristic
569Q8—22no—
570Q8—22no—
571Q8—41no—
572Q8—41no—
573D4—44no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—84no—
617C2×C4#123×C7312yes—
618C2×C4#123×C7312yes—
619C2×C4C22×D4×C7311yescharacteristic
620C2×C4C2×#41×C7311yescharacteristic
621C2×C4C2×#41×C7311yescharacteristic
622C2×C4C2×#41×C7311yescharacteristic
623C2×C4H(5,𝔽2)×C7311yescharacteristic
624C2×C42−1+4×C7311yescharacteristic
625C8—22no—
626C8—22no—
627C8—41no—
628C8—41no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22C2×#123×C7311yescharacteristic
644C22D42×C7311yescharacteristic
645C22#547×C7311yescharacteristic
646C22C2×#135×C7311yescharacteristic
647C22#575×C7311yescharacteristic
648C22#577×C7311yescharacteristic
649C22#578×C7311yescharacteristic
650C4—22no—
651C4—22no—
652C4—42no—
653C4—41no—
654C4—41no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4#532×C7311yescharacteristic
663C4#542×C7311yescharacteristic
664C4#547×C7311yescharacteristic
665C4#553×C7311yescharacteristic
666C2—42no—
667C2—81no—
668C2C73×#242211yescharacteristic
669C2C73×#309111yescharacteristic
670C2C73×#309711yescharacteristic
671C2C73×#327711yescharacteristic
672C2C73×#328211yescharacteristic
673C2C73×#333611yescharacteristic
674C2C73×#335111yescharacteristic
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×#483×C73C2semidirect
5. C73×#2077C2semidirect
6. C73×#2077C2semidirect
7. C73×#2036C2semidirect
8. C73×#2036C2semidirect
10. C73×#1949C2semidirect
11. C73×#1854C2semidirect
12. C73×#1852C2semidirect
13. C73×#1846C2semidirect
14. C73×#1805C2semidirect
15. C4×#103×C73C2semidirect
117. #103×C73D4semidirect
328. #25021C73direct (N × H)
338. C2×#485C2×C73semidirect
339. C2×#483C2×C73semidirect
342. #2077C2×C73semidirect
343. #2077C2×C73semidirect
344. #2036C2×C73semidirect
345. #2036C2×C73semidirect
347. #1949C2×C73semidirect
348. #1854C2×C73semidirect
349. #1852C2×C73semidirect
350. #1846C2×C73semidirect
351. #1805C2×C73semidirect
352. C4×#103C2×C73semidirect
353. C73#25021direct (N × H)
455. #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×#483×C732
C73×#25362
C73×#23522
C73×#20772
C73×#20362
C73×#19542
C73×#19492
C73×#18542
C73×#18522
C73×#18462
C73×#18052
C4×#103×C732
#2502173