Finite Group Databasebeta

← C73×#25402 #32934806

Subgroups — C73×#25402 #32934806

Order 18688.

1120 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C73C211yesmaximal, characteristic, complemented
2C2×#465×C73C211yesmaximal, characteristic, complemented
3C2×#460×C73C211yesmaximal, characteristic, complemented
4C2×#435×C73C211yesmaximal, characteristic, complemented
5C73×#2541C211yesmaximal, characteristic
6C73×#2536C211yesmaximal, characteristic, complemented
7C73×#2034C211yesmaximal, characteristic, complemented
8C73×#2033C211yesmaximal, characteristic, complemented
9C73×#2000C211yesmaximal, characteristic, complemented
10C73×#2000C211yesmaximal, characteristic, complemented
11C73×#1961C211yesmaximal, characteristic, complemented
12C73×#1949C211yesmaximal, characteristic, complemented
13C73×#1895C211yesmaximal, characteristic, complemented
14C73×#1893C211yesmaximal, characteristic, complemented
15C73×#1763C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×M16×C73C2211yescharacteristic
19C23×C8×C73C2211yescharacteristic
20C2×#127×C73—21no—
21C2×#127×C73C2211yescharacteristic
22C2×C22⋊Q8×C73C2211yescharacteristic
23C2×C22⋊Q8×C73C2211yescharacteristic
24C2×#121×C73C2211yescharacteristic
25C2×#121×C73C2211yescharacteristic
26C2×#121×C73C2211yescharacteristic
27C2×#121×C73C2211yescharacteristic
28C2×C4×Q8×C73C2211yescharacteristic
29C2×C4×D4×C73C2211yescharacteristic
30#468×C73—24no—
31#465×C73—24no—
32#460×C73—24no—
33#435×C73—24no—
34C2×#107×C73C2211yescharacteristic
35C2×#106×C73C2211yescharacteristic
36C2×C4⋊C8×C73C2211yescharacteristic
37C2×#103×C73C2211yescharacteristic
38C2×#103×C73C2211yescharacteristic
39C2×#102×C73C2211yescharacteristic
40C2×#102×C73C2211yescharacteristic
41C2×#102×C73C2211yescharacteristic
42C2×#102×C73C2211yescharacteristic
43C2×#102×C73C2211yescharacteristic
44C2×#102×C73C2211yescharacteristic
45C2×C22⋊C8×C73C2211yescharacteristic
46C2×C22⋊C8×C73C2211yescharacteristic
47C2×#97×C73C2211yescharacteristic
48#398×C73—21no—
49#394×C73—21no—
50#392×C73—21no—
51#392×C73—21no—
52#390×C73—21no—
53#388×C73—21no—
54#388×C73—21no—
55#382×C73C2211yescharacteristic
56#380×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58C4×C4⋊C4×C73C2211yescharacteristic
59#340×C73C2211yescharacteristic
60#340×C73C2211yescharacteristic
61#340×C73C2211yescharacteristic
62#340×C73C2211yescharacteristic
63C22×Q8×C73C2311yescharacteristic
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73—21no—
67C22×D4×C73—21no—
68C22×D4×C73—21no—
69C22×D4×C73—21no—
70C22×D4×C73D411yescharacteristic
71C22×D4×C73C2311yescharacteristic
72C22×D4×C73C2311yescharacteristic
73C23×C4×C73C2311yescharacteristic
74C23×C4×C73C2311yescharacteristic
75C2×SD16×C73—22no—
76C2×SD16×C73—22no—
77C2×SD16×C73—22no—
78C2×SD16×C73—22no—
79C2×SD16×C73—41no—
80C2×SD16×C73—41no—
81C2×M16×C73—22no—
82C2×M16×C73—22no—
83C2×M16×C73—41no—
84C22×C8×C73—22no—
85C22×C8×C73—22no—
86C22×C8×C73—41no—
87C22×C8×C73C2311yescharacteristic
88C22×C8×C73C2311yescharacteristic
89C22×C8×C73C2311yescharacteristic
90C22×C8×C73C2311yescharacteristic
91#127×C73—22no—
92#127×C73—22no—
93#127×C73—44no—
94C22⋊Q8×C73—22no—
95C22⋊Q8×C73—22no—
96C22⋊Q8×C73—41no—
97C22⋊Q8×C73—41no—
98#121×C73—22no—
99#121×C73—22no—
100#121×C73—22no—
101#121×C73—22no—
102#121×C73—41no—
103#121×C73—41no—
104#121×C73—41no—
105#121×C73—41no—
106C4×Q8×C73—22no—
107C4×Q8×C73—22no—
108C4×D4×C73—22no—
109C4×D4×C73—22no—
110C2×C4⋊C4×C73—21no—
111C2×C4⋊C4×C73—21no—
112C2×C4⋊C4×C73—21no—
113C2×C4⋊C4×C73D411yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C4⋊C4×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C4⋊C4×C73C2311yescharacteristic
118C2×C4⋊C4×C73C2311yescharacteristic
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—21no—
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73D411yescharacteristic
128C2×C22⋊C4×C73D411yescharacteristic
129C2×C42×C73—21no—
130C2×C42×C73—21no—
131C2×C42×C73C2311yescharacteristic
132#107×C73—22no—
133#106×C73—22no—
134C4⋊C8×C73D414yescomplemented
135#103×C73—22no—
136#103×C73D414yescomplemented
137#102×C73—22no—
138#102×C73—22no—
139#102×C73—22no—
140#102×C73—22no—
141#102×C73—41no—
142#102×C73—41no—
143C22⋊C8×C73—22no—
144C22⋊C8×C73—22no—
145#97×C73—22no—
146#95×C73—21no—
147#95×C73—21no—
148#95×C73—21no—
149#95×C73—21no—
150#95×C73—21no—
151C24×C73—21no—
152C24×C73—21no—
153C24×C73C2×D411yescharacteristic
154C24×C73C2×D411yescharacteristic
155C2×Q8×C73—21no—
156C2×Q8×C73—21no—
157C2×Q8×C73—21no—
158C2×Q8×C73—21no—
159C2×Q8×C73—21no—
160C2×Q8×C73C2×D412yes—
161C2×D4×C73—22no—
162C2×D4×C73—22no—
163C2×D4×C73—21no—
164C2×D4×C73—21no—
165C2×D4×C73—21no—
166C2×D4×C73—21no—
167C2×D4×C73—21no—
168C2×D4×C73—21no—
169C2×D4×C73—21no—
170C2×D4×C73—21no—
171C2×D4×C73—21no—
172C2×D4×C73—21no—
173C2×D4×C73—21no—
174C2×D4×C73—21no—
175C2×D4×C73—41no—
176C2×D4×C73—42no—
177C2×D4×C73—42no—
178C2×D4×C73—42no—
179C2×D4×C73—42no—
180C2×D4×C73—42no—
181C2×D4×C73—42no—
182C2×D4×C73—42no—
183C2×D4×C73—42no—
184C2×D4×C73—42no—
185C2×D4×C73—42no—
186C2×D4×C73—42no—
187C2×D4×C73—42no—
188C2×D4×C73—81no—
189C2×D4×C73—81no—
190C2×D4×C73—81no—
191C2×D4×C73—81no—
192C2×D4×C73—81no—
193C2×D4×C73—81no—
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×C73C2×D411yescharacteristic
213C22×C4×C73C2×D411yescharacteristic
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2411yescharacteristic
217SD16×C73—44no—
218SD16×C73—44no—
219M16×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—44no—
230C2×C8×C73C2×D412yes—
231C2×C8×C73C2×D412yes—
232C2×C8×C73C2×D412yes—
233C4⋊C4×C73—22no—
234C4⋊C4×C73—21no—
235C4⋊C4×C73—21no—
236C4⋊C4×C73—21no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—42no—
243C4⋊C4×C73—42no—
244C4⋊C4×C73—42no—
245C4⋊C4×C73C2×D412yes—
246C4⋊C4×C73#4112yes—
247C22⋊C4×C73—22no—
248C22⋊C4×C73—22no—
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—42no—
256C22⋊C4×C73—42no—
257C42×C73—42no—
258C42×C73—42no—
259C42×C73C2×D412yes—
260C42×C73#4112yes—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—21no—
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—41no—
285C23×C73—41no—
286C23×C73—41no—
287C23×C73—41no—
288C23×C73AGL(1,ℤ/8)12yes—
289C23×C73C22×D411yescharacteristic
290Q8×C73—22no—
291Q8×C73—22no—
292Q8×C73—41no—
293Q8×C73—41no—
294D4×C73—44no—
295D4×C73—41no—
296D4×C73—41no—
297D4×C73—41no—
298D4×C73—41no—
299D4×C73—41no—
300D4×C73—41no—
301D4×C73—41no—
302D4×C73—41no—
303D4×C73—84no—
304D4×C73—84no—
305D4×C73—84no—
306D4×C73—84no—
307D4×C73—84no—
308D4×C73—84no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—21no—
312C2×C4×C73—21no—
313C2×C4×C73—21no—
314C2×C4×C73—21no—
315C2×C4×C73—22no—
316C2×C4×C73—21no—
317C2×C4×C73—21no—
318C2×C4×C73—22no—
319C2×C4×C73—22no—
320C2×C4×C73—21no—
321C2×C4×C73—21no—
322C2×C4×C73—41no—
323C2×C4×C73—41no—
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—41no—
345C2×C4×C73#12112yes—
346C2×C4×C73#12112yes—
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—22no—
356C8×C73—41no—
357C22×C73—22no—
358C22×C73—22no—
359C22×C73—22no—
360C22×C73—41no—
361C22×C73—41no—
362C22×C73—41no—
363C22×C73—41no—
364C22×C73—41no—
365C22×C73—41no—
366C22×C73—41no—
367C22×C73—41no—
368C22×C73—41no—
369C22×C73—41no—
370C22×C73—41no—
371C22×C73—81no—
372C22×C73—81no—
373C22×C73—81no—
374C22×C73—81no—
375C22×C73—81no—
376C22×C73—81no—
377C22×C73—81no—
378C22×C73—81no—
379C22×C73—81no—
380C22×C73—81no—
381C22×C73—81no—
382C22×C73—81no—
383C22×C73—81no—
384C22×C73—81no—
385C22×C73C2×#12111yescharacteristic
386C22×C73D4211yescharacteristic
387C22×C73#54611yescharacteristic
388C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C73#57511yescharacteristic
390C22×C73#57711yescharacteristic
391C22×C73#57711yescharacteristic
392C4×C73—22no—
393C4×C73—22no—
394C4×C73—41no—
395C4×C73—41no—
396C4×C73—42no—
397C4×C73—42no—
398C4×C73—42no—
399C4×C73—81no—
400C4×C73—81no—
401C4×C73—81no—
402C4×C73#53211yescharacteristic
403C4×C73#54011yescharacteristic
404C4×C73D4211yescharacteristic
405C4×C73#55011yescharacteristic
406#25402C7311yesmaximal, characteristic, direct product factor, Sylow
407C2×C73—42no—
408C2×C73—81no—
409C2×C73—161no—
410C2×C73—161no—
411C2×C73#242811yescharacteristic
412C2×C73#305511yescharacteristic
413C2×C73#305711yescharacteristic
414C2×C73#326511yescharacteristic
415C2×C73#327111yescharacteristic
416C2×C73#331011yescharacteristic
417C2×C73#331711yescharacteristic
418C2×#468C2×C7311yescharacteristic, complemented
419C2×#465C2×C7311yescharacteristic, complemented
420C2×#460C2×C7311yescharacteristic, complemented
421C2×#435C2×C7311yescharacteristic, complemented
422#2541C2×C7311yescharacteristic
423#2536C2×C7311yescharacteristic, complemented
424#2034C2×C7311yescharacteristic, complemented
425#2033C2×C7311yescharacteristic, complemented
426#2000C2×C7311yescharacteristic, complemented
427#2000C2×C7311yescharacteristic, complemented
428#1961C2×C7311yescharacteristic, complemented
429#1949C2×C7311yescharacteristic, complemented
430#1895C2×C7311yescharacteristic, complemented
431#1893C2×C7311yescharacteristic, complemented
432#1763C2×C7311yescharacteristic, complemented
433C73#2540211yescharacteristic, direct product factor, Sylow
434C22×SD16C22×C7311yescharacteristic
435C22×SD16C22×C7311yescharacteristic
436C22×M16C22×C7311yescharacteristic
437C23×C8C22×C7311yescharacteristic
438C2×#127—21no—
439C2×#127C22×C7311yescharacteristic
440C2×C22⋊Q8C22×C7311yescharacteristic
441C2×C22⋊Q8C22×C7311yescharacteristic
442C2×#121C22×C7311yescharacteristic
443C2×#121C22×C7311yescharacteristic
444C2×#121C22×C7311yescharacteristic
445C2×#121C22×C7311yescharacteristic
446C2×C4×Q8C22×C7311yescharacteristic
447C2×C4×D4C22×C7311yescharacteristic
448#468—24no—
449#465—24no—
450#460—24no—
451#435—24no—
452C2×#107C22×C7311yescharacteristic
453C2×#106C22×C7311yescharacteristic
454C2×C4⋊C8C22×C7311yescharacteristic
455C2×#103C22×C7311yescharacteristic
456C2×#103C22×C7311yescharacteristic
457C2×#102C22×C7311yescharacteristic
458C2×#102C22×C7311yescharacteristic
459C2×#102C22×C7311yescharacteristic
460C2×#102C22×C7311yescharacteristic
461C2×#102C22×C7311yescharacteristic
462C2×#102C22×C7311yescharacteristic
463C2×C22⋊C8C22×C7311yescharacteristic
464C2×C22⋊C8C22×C7311yescharacteristic
465C2×#97C22×C7311yescharacteristic
466#398—21no—
467#394—21no—
468#392—21no—
469#392—21no—
470#390—21no—
471#388—21no—
472#388—21no—
473#382C22×C7311yescharacteristic
474#380C22×C7311yescharacteristic
475#380C22×C7311yescharacteristic
476C4×C4⋊C4C22×C7311yescharacteristic
477#340C22×C7311yescharacteristic
478#340C22×C7311yescharacteristic
479#340C22×C7311yescharacteristic
480#340C22×C7311yescharacteristic
481C22×Q8C23×C7311yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4D4×C7311yescharacteristic
489C22×D4C23×C7311yescharacteristic
490C22×D4C23×C7311yescharacteristic
491C23×C4C23×C7311yescharacteristic
492C23×C4C23×C7311yescharacteristic
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—41no—
498C2×SD16—41no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16—41no—
502C22×C8—22no—
503C22×C8—22no—
504C22×C8—41no—
505C22×C8C23×C7311yescharacteristic
506C22×C8C23×C7311yescharacteristic
507C22×C8C23×C7311yescharacteristic
508C22×C8C23×C7311yescharacteristic
509#127—22no—
510#127—22no—
511#127—44no—
512C22⋊Q8—22no—
513C22⋊Q8—22no—
514C22⋊Q8—41no—
515C22⋊Q8—41no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—41no—
521#121—41no—
522#121—41no—
523#121—41no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×D4—22no—
527C4×D4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4D4×C7311yescharacteristic
532C2×C4⋊C4C23×C7311yescharacteristic
533C2×C4⋊C4C23×C7311yescharacteristic
534C2×C4⋊C4C23×C7311yescharacteristic
535C2×C4⋊C4C23×C7311yescharacteristic
536C2×C4⋊C4C23×C7311yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4D4×C7311yescharacteristic
546C2×C22⋊C4D4×C7311yescharacteristic
547C2×C42—21no—
548C2×C42—21no—
549C2×C42C23×C7311yescharacteristic
550#107—22no—
551#106—22no—
552C4⋊C8D4×C7314yescomplemented
553#103—22no—
554#103D4×C7314yescomplemented
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—41no—
560#102—41no—
561C22⋊C8—22no—
562C22⋊C8—22no—
563#97—22no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95—21no—
569C24—21no—
570C24—21no—
571C24C2×D4×C7311yescharacteristic
572C24C2×D4×C7311yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8C2×D4×C7312yes—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—41no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—42no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—81no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4C2×D4×C7311yescharacteristic
631C22×C4C2×D4×C7311yescharacteristic
632C22×C4C2×D4×C7311yescharacteristic
633C22×C4C2×D4×C7311yescharacteristic
634C22×C4C24×C7311yescharacteristic
635SD16—44no—
636SD16—44no—
637M16—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—44no—
648C2×C8C2×D4×C7312yes—
649C2×C8C2×D4×C7312yes—
650C2×C8C2×D4×C7312yes—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4C2×D4×C7312yes—
664C4⋊C4#41×C7312yes—
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C42—42no—
676C42—42no—
677C42C2×D4×C7312yes—
678C42#41×C7312yes—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23AGL(1,ℤ/8)×C7312yes—
707C23C22×D4×C7311yescharacteristic
708Q8—22no—
709Q8—22no—
710Q8—41no—
711Q8—41no—
712D4—44no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—84no—
722D4—84no—
723D4—84no—
724D4—84no—
725D4—84no—
726D4—84no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
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—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4#121×C7312yes—
764C2×C4#121×C7312yes—
765C2×C4C22×D4×C7311yescharacteristic
766C2×C4C22×D4×C7311yescharacteristic
767C2×C4C2×#41×C7311yescharacteristic
768C2×C4C2×#41×C7311yescharacteristic
769C2×C4H(5,𝔽2)×C7311yescharacteristic
770C2×C4H(5,𝔽2)×C7311yescharacteristic
771C8—22no—
772C8—22no—
773C8—22no—
774C8—41no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×#121×C7311yescharacteristic
804C22D42×C7311yescharacteristic
805C22#546×C7311yescharacteristic
806C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
807C22#575×C7311yescharacteristic
808C22#577×C7311yescharacteristic
809C22#577×C7311yescharacteristic
810C4—22no—
811C4—22no—
812C4—42no—
813C4—42no—
814C4—41no—
815C4—41no—
816C4—42no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4#532×C7311yescharacteristic
821C4#540×C7311yescharacteristic
822C4D42×C7311yescharacteristic
823C4#550×C7311yescharacteristic
824C2—42no—
825C2—81no—
826C2—161no—
827C2—161no—
828C2C73×#242811yescharacteristic
829C2C73×#305511yescharacteristic
830C2C73×#305711yescharacteristic
831C2C73×#326511yescharacteristic
832C2C73×#327111yescharacteristic
833C2C73×#331011yescharacteristic
834C2C73×#331711yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2541C2
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×#468×C73C2semidirect
2. C2×#465×C73C2semidirect
3. C2×#460×C73C2semidirect
4. C2×#435×C73C2semidirect
6. C73×#2536C2semidirect
7. C73×#2034C2semidirect
8. C73×#2033C2semidirect
9. C73×#2000C2semidirect
10. C73×#2000C2semidirect
11. C73×#1961C2semidirect
12. C73×#1949C2semidirect
13. C73×#1895C2semidirect
14. C73×#1893C2semidirect
15. C73×#1763C2semidirect
134. C4⋊C8×C73D4semidirect
136. #103×C73D4semidirect
406. #25402C73direct (N × H)
418. C2×#468C2×C73semidirect
419. C2×#465C2×C73semidirect
420. C2×#460C2×C73semidirect
421. C2×#435C2×C73semidirect
423. #2536C2×C73semidirect
424. #2034C2×C73semidirect
425. #2033C2×C73semidirect
426. #2000C2×C73semidirect
427. #2000C2×C73semidirect
428. #1961C2×C73semidirect
429. #1949C2×C73semidirect
430. #1895C2×C73semidirect
431. #1893C2×C73semidirect
432. #1763C2×C73semidirect
433. C73#25402direct (N × H)
552. C4⋊C8D4×C73semidirect
554. #103D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C732
C2×#465×C732
C2×#460×C732
C2×#435×C732
C73×#25412
C73×#25362
C73×#20342
C73×#20332
C73×#20002
C73×#19612
C73×#19492
C73×#18952
C73×#18932
C73×#17632
#2540273