Finite Group Databasebeta

← C73×#25176 #32934580

Subgroups — C73×#25176 #32934580

Order 18688.

1262 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C73C211yesmaximal, characteristic, complemented
2C2×#450×C73C211yesmaximal, characteristic
3C2×#450×C73C211yesmaximal, characteristic
4C2×#440×C73C211yesmaximal, characteristic, complemented
5C73×#2429C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C73C211yesmaximal, characteristic
7C73×#2067C211yesmaximal, characteristic, complemented
8C73×#2036C211yesmaximal, characteristic, complemented
9C73×#2036C211yesmaximal, characteristic, complemented
10C73×#2013C211yesmaximal, characteristic, complemented
11C73×#1973C211yesmaximal, characteristic, complemented
12C73×#1924C211yesmaximal, characteristic, complemented
13C73×#1880C211yesmaximal, characteristic, complemented
14C73×#1877C211yesmaximal, characteristic, complemented
15C73×#1862C211yesmaximal, characteristic, complemented
16C23×D4×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×SD16×C73C2211yescharacteristic
19C22×SD16×C73C2211yescharacteristic
20C22×SD16×C73C2211yescharacteristic
21C2×C4⋊Q8×C73C2211yescharacteristic, complemented
22C2×C22⋊Q8×C73C2211yescharacteristic
23C2×C22⋊Q8×C73C2211yescharacteristic
24C2×C4×Q8×C73C2211yescharacteristic, complemented
25C2×C4×D4×C73C2211yescharacteristic
26C2×C4×D4×C73C2211yescharacteristic
27C22×C22⋊C4×C73—21no—
28#461×C73—24no—
29#450×C73—24no—
30#450×C73—24no—
31#440×C73—24no—
32C2×#107×C73C2211yescharacteristic, complemented
33C2×#107×C73C2211yescharacteristic, complemented
34C2×C4⋊C8×C73C2211yescharacteristic, complemented
35C2×#103×C73C2211yescharacteristic, complemented
36C2×#103×C73C2211yescharacteristic, complemented
37C2×#103×C73C2211yescharacteristic, complemented
38C2×#103×C73C2211yescharacteristic, complemented
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×C22⋊C8×C73C2211yescharacteristic
44C2×C22⋊C8×C73C2211yescharacteristic
45C2×#97×C73C2211yescharacteristic, complemented
46#398×C73—21no—
47#396×C73—21no—
48#391×C73C2211yescharacteristic, complemented
49#390×C73C2211yescharacteristic
50#390×C73C2211yescharacteristic
51#389×C73—21no—
52#389×C73C2211yescharacteristic, complemented
53#388×C73—21no—
54#386×C73—21no—
55#386×C73—21no—
56#380×C73C2211yescharacteristic
57#379×C73—21no—
58C4×C22⋊C4×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic, complemented
60#340×C73C2211yescharacteristic, complemented
61#336×C73C2211yescharacteristic, complemented
62#336×C73C2211yescharacteristic, complemented
63C25×C73—21no—
64C22×Q8×C73C2311yescharacteristic
65C22×Q8×C73C2311yescharacteristic
66C22×D4×C73—22no—
67C22×D4×C73—22no—
68C22×D4×C73—22no—
69C22×D4×C73—22no—
70C22×D4×C73—21no—
71C22×D4×C73—41no—
72C22×D4×C73—41no—
73C22×D4×C73C2311yescharacteristic
74C22×D4×C73C2311yescharacteristic
75C23×C4×C73—21no—
76C23×C4×C73—21no—
77C23×C4×C73C2311yescharacteristic
78C2×SD16×C73—22no—
79C2×SD16×C73—22no—
80C2×SD16×C73—22no—
81C2×SD16×C73—22no—
82C2×SD16×C73—22no—
83C2×SD16×C73—22no—
84C2×SD16×C73—22no—
85C2×SD16×C73—22no—
86C2×SD16×C73—22no—
87C2×SD16×C73—41no—
88C2×SD16×C73—41no—
89C2×SD16×C73D414yes—
90C22×C8×C73C2311yescharacteristic
91C22×C8×C73C2311yescharacteristic
92C22×C8×C73C2311yescharacteristic
93C22×C8×C73C2311yescharacteristic
94C4⋊Q8×C73—22no—
95C4⋊Q8×C73—41no—
96C22⋊Q8×C73—22no—
97C22⋊Q8×C73—22no—
98C22⋊Q8×C73—41no—
99C22⋊Q8×C73—41no—
100C4×Q8×C73—22no—
101C4×Q8×C73—41no—
102C4×D4×C73—22no—
103C4×D4×C73—22no—
104C4×D4×C73—41no—
105C4×D4×C73—41no—
106C2×C4⋊C4×C73—21no—
107C2×C4⋊C4×C73—21no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—21no—
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73C2311yescharacteristic
113C2×C4⋊C4×C73C2311yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C22⋊C4×C73—21no—
117C2×C22⋊C4×C73—21no—
118C2×C22⋊C4×C73—21no—
119C2×C22⋊C4×C73—21no—
120C2×C22⋊C4×C73—21no—
121C2×C22⋊C4×C73—21no—
122C2×C22⋊C4×C73—21no—
123C2×C22⋊C4×C73—21no—
124C2×C22⋊C4×C73—21no—
125C2×C22⋊C4×C73—44no—
126C2×C22⋊C4×C73D411yescharacteristic
127C2×C22⋊C4×C73D411yescharacteristic
128C2×C42×C73—21no—
129C2×C42×C73C2311yescharacteristic
130C2×C42×C73C2311yescharacteristic
131#107×C73—22no—
132#107×C73—41no—
133C4⋊C8×C73—22no—
134#103×C73—22no—
135#103×C73—22no—
136#103×C73—22no—
137#103×C73—41no—
138#102×C73—22no—
139#102×C73—22no—
140#102×C73—22no—
141#102×C73D414yes—
142C22⋊C8×C73—22no—
143C22⋊C8×C73—22no—
144#97×C73—22no—
145#95×C73—21no—
146#95×C73—21no—
147#95×C73—21no—
148#95×C73—21no—
149#95×C73D411yescharacteristic
150#95×C73D411yescharacteristic
151C24×C73—21no—
152C24×C73—24no—
153C24×C73—21no—
154C24×C73—42no—
155C24×C73—42no—
156C24×C73—42no—
157C24×C73—42no—
158C24×C73—81no—
159C24×C73—81no—
160C24×C73C2×D411yescharacteristic
161C2×Q8×C73—21no—
162C2×Q8×C73—21no—
163C2×Q8×C73—21no—
164C2×Q8×C73—21no—
165C2×Q8×C73—21no—
166C2×Q8×C73—21no—
167C2×Q8×C73—21no—
168C2×Q8×C73—21no—
169C2×Q8×C73—21no—
170C2×Q8×C73—21no—
171C2×Q8×C73—21no—
172C2×Q8×C73C2×D412yes—
173C2×D4×C73—24no—
174C2×D4×C73—21no—
175C2×D4×C73—21no—
176C2×D4×C73—21no—
177C2×D4×C73—21no—
178C2×D4×C73—21no—
179C2×D4×C73—21no—
180C2×D4×C73—21no—
181C2×D4×C73—21no—
182C2×D4×C73—42no—
183C2×D4×C73—42no—
184C2×D4×C73—44no—
185C2×D4×C73—44no—
186C2×D4×C73—44no—
187C2×D4×C73—44no—
188C2×D4×C73C2×D412yes—
189C2×D4×C73C2×D412yes—
190C2×D4×C73#4112yes—
191C2×D4×C73#4112yes—
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—42no—
205C22×C4×C73—42no—
206C22×C4×C73—42no—
207C22×C4×C73—42no—
208C22×C4×C73—81no—
209C22×C4×C73—81no—
210C22×C4×C73C2×D411yescharacteristic
211C22×C4×C73C2×D411yescharacteristic
212C22×C4×C73C2×D411yescharacteristic
213C22×C4×C73C2×D411yescharacteristic
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73C2411yescharacteristic
216SD16×C73—28no—
217SD16×C73—44no—
218SD16×C73—44no—
219SD16×C73—44no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73C2×D412yes—
231C2×C8×C73C2×D412yes—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—21no—
235C4⋊C4×C73—21no—
236C4⋊C4×C73—21no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—42no—
240C4⋊C4×C73—42no—
241C4⋊C4×C73—42no—
242C4⋊C4×C73—42no—
243C4⋊C4×C73—42no—
244C4⋊C4×C73—42no—
245C4⋊C4×C73C2×D412yes—
246C22⋊C4×C73—22no—
247C22⋊C4×C73—22no—
248C22⋊C4×C73—42no—
249C22⋊C4×C73—42no—
250C22⋊C4×C73—42no—
251C22⋊C4×C73—42no—
252C22⋊C4×C73—42no—
253C22⋊C4×C73—42no—
254C22⋊C4×C73—42no—
255C22⋊C4×C73—81no—
256C22⋊C4×C73—81no—
257C42×C73—21no—
258C42×C73—21no—
259C42×C73—21no—
260C42×C73—21no—
261C42×C73—42no—
262C23×C73—21no—
263C23×C73—22no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—22no—
267C23×C73—22no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—22no—
272C23×C73—48no—
273C23×C73—48no—
274C23×C73—41no—
275C23×C73—41no—
276C23×C73—41no—
277C23×C73—41no—
278C23×C73—41no—
279C23×C73—41no—
280C23×C73—41no—
281C23×C73—41no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73—84no—
285C23×C73—84no—
286C23×C73—84no—
287C23×C73—84no—
288C23×C73—84no—
289C23×C73#13712yes—
290C23×C73C22×D411yescharacteristic
291Q8×C73—22no—
292Q8×C73—22no—
293Q8×C73—41no—
294Q8×C73—41no—
295Q8×C73—41no—
296Q8×C73—41no—
297Q8×C73—41no—
298Q8×C73—41no—
299D4×C73—22no—
300D4×C73—22no—
301D4×C73—22no—
302D4×C73—22no—
303D4×C73—22no—
304D4×C73—48no—
305D4×C73—41no—
306D4×C73—41no—
307D4×C73#12114yes—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—21no—
312C2×C4×C73—21no—
313C2×C4×C73—21no—
314C2×C4×C73—22no—
315C2×C4×C73—22no—
316C2×C4×C73—21no—
317C2×C4×C73—21no—
318C2×C4×C73—21no—
319C2×C4×C73—21no—
320C2×C4×C73—21no—
321C2×C4×C73—21no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
324C2×C4×C73—41no—
325C2×C4×C73—41no—
326C2×C4×C73—41no—
327C2×C4×C73—41no—
328C2×C4×C73—41no—
329C2×C4×C73—41no—
330C2×C4×C73—41no—
331C2×C4×C73—41no—
332C2×C4×C73—41no—
333C2×C4×C73—41no—
334C2×C4×C73—41no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
337C2×C4×C73—41no—
338C2×C4×C73—41no—
339C2×C4×C73—41no—
340C2×C4×C73—41no—
341C2×C4×C73—41no—
342C2×C4×C73—41no—
343C2×C4×C73—41no—
344C2×C4×C73—84no—
345C2×C4×C73—84no—
346C2×C4×C73AGL(1,ℤ/8)12yes—
347C2×C4×C73C22×D411yescharacteristic
348C2×C4×C73C22×D411yescharacteristic
349C2×C4×C73C2×#4111yescharacteristic
350C2×C4×C73C2×#4111yescharacteristic
351C2×C4×C73H(5,𝔽2)11yescharacteristic
352C2×C4×C73H(5,𝔽2)11yescharacteristic
353C8×C73—22no—
354C8×C73—22no—
355C8×C73—41no—
356C8×C73—41no—
357C22×C73—22no—
358C22×C73—24no—
359C22×C73—22no—
360C22×C73—22no—
361C22×C73—42no—
362C22×C73—41no—
363C22×C73—42no—
364C22×C73—41no—
365C22×C73—42no—
366C22×C73—41no—
367C22×C73—42no—
368C22×C73—42no—
369C22×C73—42no—
370C22×C73—41no—
371C22×C73—42no—
372C22×C73—42no—
373C22×C73—42no—
374C22×C73—816no—
375C22×C73—81no—
376C22×C73—81no—
377C22×C73—81no—
378C22×C73—81no—
379C22×C73#52511yescharacteristic
380C22×C73D4211yescharacteristic
381C22×C73D4211yescharacteristic
382C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C73C2×#13711yescharacteristic
384C22×C73#57711yescharacteristic
385C22×C73#57711yescharacteristic
386C4×C73—22no—
387C4×C73—41no—
388C4×C73—42no—
389C4×C73—41no—
390C4×C73—41no—
391C4×C73—41no—
392C4×C73—42no—
393C4×C73—81no—
394C4×C73—81no—
395C4×C73—81no—
396C4×C73—81no—
397C4×C73C2×#12111yescharacteristic
398C4×C73#53811yescharacteristic
399C4×C73#54611yescharacteristic
400C4×C73#54611yescharacteristic
401#25176C7311yesmaximal, characteristic, direct product factor, Sylow
402C2×C73—42no—
403C2×C73—44no—
404C2×C73—82no—
405C2×C73#242411yescharacteristic
406C2×C73#311011yescharacteristic
407C2×C73#312311yescharacteristic
408C2×C73#326511yescharacteristic
409C2×C73#326611yescharacteristic
410C2×C73#326611yescharacteristic
411C2×C73#327211yescharacteristic
412C2×#461C2×C7311yescharacteristic, complemented
413C2×#450C2×C7311yescharacteristic
414C2×#450C2×C7311yescharacteristic
415C2×#440C2×C7311yescharacteristic, complemented
416#2429C2×C7311yescharacteristic, complemented
417D4×C22⋊C4C2×C7311yescharacteristic
418#2067C2×C7311yescharacteristic, complemented
419#2036C2×C7311yescharacteristic, complemented
420#2036C2×C7311yescharacteristic, complemented
421#2013C2×C7311yescharacteristic, complemented
422#1973C2×C7311yescharacteristic, complemented
423#1924C2×C7311yescharacteristic, complemented
424#1880C2×C7311yescharacteristic, complemented
425#1877C2×C7311yescharacteristic, complemented
426#1862C2×C7311yescharacteristic, complemented
427C73#2517611yescharacteristic, direct product factor, Sylow
428C23×D4C22×C7311yescharacteristic
429C22×SD16C22×C7311yescharacteristic
430C22×SD16C22×C7311yescharacteristic
431C22×SD16C22×C7311yescharacteristic
432C22×SD16C22×C7311yescharacteristic
433C2×C4⋊Q8C22×C7311yescharacteristic, complemented
434C2×C22⋊Q8C22×C7311yescharacteristic
435C2×C22⋊Q8C22×C7311yescharacteristic
436C2×C4×Q8C22×C7311yescharacteristic, complemented
437C2×C4×D4C22×C7311yescharacteristic
438C2×C4×D4C22×C7311yescharacteristic
439C22×C22⋊C4—21no—
440#461—24no—
441#450—24no—
442#450—24no—
443#440—24no—
444C2×#107C22×C7311yescharacteristic, complemented
445C2×#107C22×C7311yescharacteristic, complemented
446C2×C4⋊C8C22×C7311yescharacteristic, complemented
447C2×#103C22×C7311yescharacteristic, complemented
448C2×#103C22×C7311yescharacteristic, complemented
449C2×#103C22×C7311yescharacteristic, complemented
450C2×#103C22×C7311yescharacteristic, complemented
451C2×#102C22×C7311yescharacteristic
452C2×#102C22×C7311yescharacteristic
453C2×#102C22×C7311yescharacteristic
454C2×#102C22×C7311yescharacteristic
455C2×C22⋊C8C22×C7311yescharacteristic
456C2×C22⋊C8C22×C7311yescharacteristic
457C2×#97C22×C7311yescharacteristic, complemented
458#398—21no—
459#396—21no—
460#391C22×C7311yescharacteristic, complemented
461#390C22×C7311yescharacteristic
462#390C22×C7311yescharacteristic
463#389—21no—
464#389C22×C7311yescharacteristic, complemented
465#388—21no—
466#386—21no—
467#386—21no—
468#380C22×C7311yescharacteristic
469#379—21no—
470C4×C22⋊C4C22×C7311yescharacteristic
471#340C22×C7311yescharacteristic, complemented
472#340C22×C7311yescharacteristic, complemented
473#336C22×C7311yescharacteristic, complemented
474#336C22×C7311yescharacteristic, complemented
475C25—21no—
476C22×Q8C23×C7311yescharacteristic
477C22×Q8C23×C7311yescharacteristic
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—22no—
482C22×D4—21no—
483C22×D4—41no—
484C22×D4—41no—
485C22×D4C23×C7311yescharacteristic
486C22×D4C23×C7311yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4C23×C7311yescharacteristic
490C2×SD16—22no—
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—22no—
499C2×SD16—41no—
500C2×SD16—41no—
501C2×SD16D4×C7314yes—
502C22×C8C23×C7311yescharacteristic
503C22×C8C23×C7311yescharacteristic
504C22×C8C23×C7311yescharacteristic
505C22×C8C23×C7311yescharacteristic
506C4⋊Q8—22no—
507C4⋊Q8—41no—
508C22⋊Q8—22no—
509C22⋊Q8—22no—
510C22⋊Q8—41no—
511C22⋊Q8—41no—
512C4×Q8—22no—
513C4×Q8—41no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—41no—
517C4×D4—41no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4C23×C7311yescharacteristic
525C2×C4⋊C4C23×C7311yescharacteristic
526C2×C4⋊C4C23×C7311yescharacteristic
527C2×C4⋊C4C23×C7311yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—44no—
538C2×C22⋊C4D4×C7311yescharacteristic
539C2×C22⋊C4D4×C7311yescharacteristic
540C2×C42—21no—
541C2×C42C23×C7311yescharacteristic
542C2×C42C23×C7311yescharacteristic
543#107—22no—
544#107—41no—
545C4⋊C8—22no—
546#103—22no—
547#103—22no—
548#103—22no—
549#103—41no—
550#102—22no—
551#102—22no—
552#102—22no—
553#102D4×C7314yes—
554C22⋊C8—22no—
555C22⋊C8—22no—
556#97—22no—
557#95—21no—
558#95—21no—
559#95—21no—
560#95—21no—
561#95D4×C7311yescharacteristic
562#95D4×C7311yescharacteristic
563C24—21no—
564C24—24no—
565C24—21no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—81no—
571C24—81no—
572C24C2×D4×C7311yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8C2×D4×C7312yes—
585C2×D4—24no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4C2×D4×C7312yes—
601C2×D4C2×D4×C7312yes—
602C2×D4#41×C7312yes—
603C2×D4#41×C7312yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4C2×D4×C7311yescharacteristic
623C22×C4C2×D4×C7311yescharacteristic
624C22×C4C2×D4×C7311yescharacteristic
625C22×C4C2×D4×C7311yescharacteristic
626C22×C4C2×D4×C7311yescharacteristic
627C22×C4C24×C7311yescharacteristic
628SD16—28no—
629SD16—44no—
630SD16—44no—
631SD16—44no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8C2×D4×C7312yes—
643C2×C8C2×D4×C7312yes—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4C2×D4×C7312yes—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—42no—
674C23—21no—
675C23—22no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—22no—
684C23—48no—
685C23—48no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23#137×C7312yes—
702C23C22×D4×C7311yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4#121×C7314yes—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—84no—
757C2×C4—84no—
758C2×C4AGL(1,ℤ/8)×C7312yes—
759C2×C4C22×D4×C7311yescharacteristic
760C2×C4C22×D4×C7311yescharacteristic
761C2×C4C2×#41×C7311yescharacteristic
762C2×C4C2×#41×C7311yescharacteristic
763C2×C4H(5,𝔽2)×C7311yescharacteristic
764C2×C4H(5,𝔽2)×C7311yescharacteristic
765C8—22no—
766C8—22no—
767C8—41no—
768C8—41no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—24no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—41no—
779C22—42no—
780C22—41no—
781C22—42no—
782C22—41no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22#525×C7311yescharacteristic
792C22D42×C7311yescharacteristic
793C22D42×C7311yescharacteristic
794C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
795C22C2×#137×C7311yescharacteristic
796C22#577×C7311yescharacteristic
797C22#577×C7311yescharacteristic
798C4—22no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4C2×#121×C7311yescharacteristic
810C4#538×C7311yescharacteristic
811C4#546×C7311yescharacteristic
812C4#546×C7311yescharacteristic
813C2—42no—
814C2—44no—
815C2—82no—
816C2C73×#242411yescharacteristic
817C2C73×#311011yescharacteristic
818C2C73×#312311yescharacteristic
819C2C73×#326511yescharacteristic
820C2C73×#326611yescharacteristic
821C2C73×#326611yescharacteristic
822C2C73×#327211yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC23×D4×C73C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#461×C73C2semidirect
4. C2×#440×C73C2semidirect
5. C73×#2429C2semidirect
7. C73×#2067C2semidirect
8. C73×#2036C2semidirect
9. C73×#2036C2semidirect
10. C73×#2013C2semidirect
11. C73×#1973C2semidirect
12. C73×#1924C2semidirect
13. C73×#1880C2semidirect
14. C73×#1877C2semidirect
15. C73×#1862C2semidirect
21. C2×C4⋊Q8×C73C22semidirect
24. C2×C4×Q8×C73C22semidirect
32. C2×#107×C73C22semidirect
33. C2×#107×C73C22semidirect
34. C2×C4⋊C8×C73C22semidirect
35. C2×#103×C73C22semidirect
36. C2×#103×C73C22semidirect
37. C2×#103×C73C22semidirect
38. C2×#103×C73C22semidirect
45. C2×#97×C73C22semidirect
48. #391×C73C22semidirect
52. #389×C73C22semidirect
59. #340×C73C22semidirect
60. #340×C73C22semidirect
61. #336×C73C22semidirect
62. #336×C73C22semidirect
401. #25176C73direct (N × H)
412. C2×#461C2×C73semidirect
415. C2×#440C2×C73semidirect
416. #2429C2×C73semidirect
418. #2067C2×C73semidirect
419. #2036C2×C73semidirect
420. #2036C2×C73semidirect
421. #2013C2×C73semidirect
422. #1973C2×C73semidirect
423. #1924C2×C73semidirect
424. #1880C2×C73semidirect
425. #1877C2×C73semidirect
426. #1862C2×C73semidirect
427. C73#25176direct (N × H)
433. C2×C4⋊Q8C22×C73semidirect
436. C2×C4×Q8C22×C73semidirect
444. C2×#107C22×C73semidirect
445. C2×#107C22×C73semidirect
446. C2×C4⋊C8C22×C73semidirect
447. C2×#103C22×C73semidirect
448. C2×#103C22×C73semidirect
449. C2×#103C22×C73semidirect
450. C2×#103C22×C73semidirect
457. C2×#97C22×C73semidirect
460. #391C22×C73semidirect
464. #389C22×C73semidirect
471. #340C22×C73semidirect
472. #340C22×C73semidirect
473. #336C22×C73semidirect
474. #336C22×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C732
C2×#450×C732
C2×#440×C732
C73×#24292
D4×C22⋊C4×C732
C73×#20672
C73×#20362
C73×#20132
C73×#19732
C73×#19242
C73×#18802
C73×#18772
C73×#18622
#2517673