Finite Group Databasebeta

← C73×#25006 #32934410

Subgroups — C73×#25006 #32934410

Order 18688.

700 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2538C211yesmaximal, characteristic
2C73×#2355C211yesmaximal, characteristic, complemented
3C73×#2101C211yesmaximal, characteristic, complemented
4C73×#2099C211yesmaximal, characteristic, complemented
5C73×#2073C211yesmaximal, characteristic
6C73×#2071C211yesmaximal, characteristic
7C73×#1985C211yesmaximal, characteristic, complemented
8C73×#1948C211yesmaximal, characteristic, complemented
9C73×#1926C211yesmaximal, characteristic
10C73×#1926C211yesmaximal, characteristic
11C73×#1920C211yesmaximal, characteristic, complemented
12C73×#1919C211yesmaximal, characteristic, complemented
13C73×#1836C211yesmaximal, characteristic, complemented
14C73×#1804C211yesmaximal, characteristic
15C73×#1762C211yesmaximal, characteristic
16C2×C22⋊Q8×C73—21no—
17C2×C4×Q8×C73C2211yescharacteristic
18C2×C4×D4×C73C2211yescharacteristic
19C2×#106×C73C2211yescharacteristic
20C2×#106×C73C2211yescharacteristic
21C2×C4⋊C8×C73C2211yescharacteristic
22C2×#102×C73C2211yescharacteristic
23C2×#102×C73C2211yescharacteristic
24C2×#102×C73C2211yescharacteristic
25C2×#102×C73C2211yescharacteristic
26C2×#97×C73C2211yescharacteristic
27#396×C73—21no—
28#396×C73—21no—
29#391×C73—21no—
30#390×C73C2211yescharacteristic
31#390×C73C2211yescharacteristic
32#389×C73C2211yescharacteristic
33#389×C73C2211yescharacteristic
34#387×C73—21no—
35#387×C73—21no—
36#384×C73C2211yescharacteristic
37#384×C73C2211yescharacteristic
38#382×C73C2211yescharacteristic
39#382×C73C2211yescharacteristic
40#380×C73—21no—
41C4×C4⋊C4×C73—21no—
42C4×C4⋊C4×C73C2211yescharacteristic
43C4×C4⋊C4×C73C2211yescharacteristic
44C4×C4⋊C4×C73C2211yescharacteristic
45#340×C73C2211yescharacteristic
46#340×C73C2211yescharacteristic
47#340×C73C2211yescharacteristic
48#340×C73C2211yescharacteristic
49#340×C73C2211yescharacteristic
50#340×C73C2211yescharacteristic
51#340×C73C2211yescharacteristic
52#340×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#336×C73C2211yescharacteristic
56#336×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×Q8×C73D411yescharacteristic
60C22×D4×C73C2311yescharacteristic
61C23×C4×C73—21no—
62C22×C8×C73C2311yescharacteristic
63C22×C8×C73C2311yescharacteristic
64C22×C8×C73C2311yescharacteristic
65C22×C8×C73C2311yescharacteristic
66C22⋊Q8×C73—44no—
67C4×Q8×C73—22no—
68C4×Q8×C73—22no—
69C4×D4×C73—22no—
70C4×D4×C73—22no—
71C2×C4⋊C4×C73—21no—
72C2×C4⋊C4×C73—21no—
73C2×C4⋊C4×C73—21no—
74C2×C4⋊C4×C73—21no—
75C2×C4⋊C4×C73—21no—
76C2×C4⋊C4×C73—21no—
77C2×C4⋊C4×C73D411yescharacteristic
78C2×C4⋊C4×C73D411yescharacteristic
79C2×C4⋊C4×C73D411yescharacteristic
80C2×C4⋊C4×C73C2311yescharacteristic
81C2×C4⋊C4×C73C2311yescharacteristic
82C2×C4⋊C4×C73C2311yescharacteristic
83C2×C4⋊C4×C73C2311yescharacteristic
84C2×C4⋊C4×C73C2311yescharacteristic
85C2×C4⋊C4×C73C2311yescharacteristic
86C2×C4⋊C4×C73C2311yescharacteristic
87C2×C22⋊C4×C73—21no—
88C2×C22⋊C4×C73—21no—
89C2×C22⋊C4×C73—21no—
90C2×C22⋊C4×C73—21no—
91C2×C22⋊C4×C73—21no—
92C2×C42×C73—21no—
93C2×C42×C73—21no—
94C2×C42×C73—21no—
95C2×C42×C73C2311yescharacteristic
96C2×C42×C73C2311yescharacteristic
97C2×C42×C73C2311yescharacteristic
98#106×C73—22no—
99#106×C73—22no—
100C4⋊C8×C73—22no—
101#102×C73—22no—
102#102×C73—22no—
103#102×C73—22no—
104#102×C73—22no—
105#97×C73—22no—
106#95×C73—21no—
107#95×C73—21no—
108#95×C73—21no—
109#95×C73—21no—
110#95×C73—21no—
111#95×C73—21no—
112#95×C73—21no—
113#95×C73—21no—
114#95×C73—21no—
115C24×C73—21no—
116C2×Q8×C73—22no—
117C2×Q8×C73—22no—
118C2×Q8×C73—41no—
119C2×D4×C73—21no—
120C2×D4×C73—21no—
121C2×D4×C73—21no—
122C2×D4×C73—21no—
123C2×D4×C73—21no—
124C2×D4×C73#4112yes—
125C22×C4×C73—21no—
126C22×C4×C73—21no—
127C22×C4×C73—21no—
128C22×C4×C73—21no—
129C22×C4×C73—21no—
130C22×C4×C73—21no—
131C22×C4×C73—21no—
132C22×C4×C73—42no—
133C22×C4×C73—42no—
134C22×C4×C73—42no—
135C22×C4×C73C2×D411yescharacteristic
136C22×C4×C73C2×D411yescharacteristic
137C22×C4×C73C2×D411yescharacteristic
138C22×C4×C73C2×D411yescharacteristic
139C22×C4×C73C2×D411yescharacteristic
140C22×C4×C73C2×D411yescharacteristic
141C22×C4×C73C2411yescharacteristic
142C2×C8×C73—21no—
143C2×C8×C73—21no—
144C2×C8×C73—21no—
145C2×C8×C73—21no—
146C2×C8×C73—21no—
147C2×C8×C73—21no—
148C2×C8×C73—21no—
149C2×C8×C73—21no—
150C2×C8×C73—21no—
151C2×C8×C73—21no—
152C2×C8×C73—21no—
153C2×C8×C73—21no—
154C4⋊C4×C73—22no—
155C4⋊C4×C73—22no—
156C4⋊C4×C73—22no—
157C4⋊C4×C73—21no—
158C4⋊C4×C73—21no—
159C4⋊C4×C73—21no—
160C4⋊C4×C73—21no—
161C4⋊C4×C73—21no—
162C4⋊C4×C73—21no—
163C4⋊C4×C73—21no—
164C4⋊C4×C73—21no—
165C4⋊C4×C73—21no—
166C4⋊C4×C73—21no—
167C4⋊C4×C73—21no—
168C4⋊C4×C73—21no—
169C4⋊C4×C73—21no—
170C4⋊C4×C73—42no—
171C4⋊C4×C73—42no—
172C4⋊C4×C73—42no—
173C4⋊C4×C73—42no—
174C4⋊C4×C73—81no—
175C4⋊C4×C73—81no—
176C4⋊C4×C73#4112yes—
177C22⋊C4×C73—42no—
178C22⋊C4×C73—42no—
179C22⋊C4×C73—42no—
180C22⋊C4×C73—81no—
181C22⋊C4×C73—81no—
182C42×C73—21no—
183C42×C73—21no—
184C42×C73—21no—
185C42×C73—21no—
186C42×C73—42no—
187C42×C73—81no—
188C42×C73—81no—
189C42×C73#4112yes—
190C42×C73#4112yes—
191C23×C73—22no—
192C23×C73—41no—
193C23×C73—41no—
194C23×C73—41no—
195C23×C73—41no—
196C23×C73—41no—
197C23×C73—41no—
198C23×C73C22×D411yescharacteristic
199Q8×C73—44no—
200D4×C73—22no—
201D4×C73—22no—
202D4×C73—41no—
203D4×C73—41no—
204C2×C4×C73—21no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—21no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—22no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
219C2×C4×C73—21no—
220C2×C4×C73—41no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73—41no—
224C2×C4×C73—41no—
225C2×C4×C73—41no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73—41no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—84no—
241C2×C4×C73#12312yes—
242C2×C4×C73#12312yes—
243C2×C4×C73AGL(1,ℤ/8)12yes—
244C2×C4×C73C2×#4111yescharacteristic
245C2×C4×C73C2×#4111yescharacteristic
246C2×C4×C73C2×#4111yescharacteristic
247C2×C4×C73C2×#4111yescharacteristic
248C2×C4×C732−1+411yescharacteristic
249C2×C4×C732−1+411yescharacteristic
250C8×C73—41no—
251C8×C73—41no—
252C8×C73—41no—
253C8×C73—41no—
254C22×C73—42no—
255C22×C73—42no—
256C22×C73—42no—
257C22×C73—81no—
258C22×C73—81no—
259C22×C73—81no—
260C22×C73—81no—
261C22×C73C2×#12311yescharacteristic
262C22×C73#54811yescharacteristic
263C22×C73#54811yescharacteristic
264C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
265C22×C73#57511yescharacteristic
266C22×C73#57711yescharacteristic
267C22×C73#57711yescharacteristic
268C4×C73—22no—
269C4×C73—22no—
270C4×C73—22no—
271C4×C73—41no—
272C4×C73—41no—
273C4×C73—41no—
274C4×C73—42no—
275C4×C73—81no—
276C4×C73—81no—
277C4×C73—81no—
278C4×C73—81no—
279C4×C73—81no—
280C4×C73—81no—
281C4×C73#52911yescharacteristic
282C4×C73#54111yescharacteristic
283C4×C73#55211yescharacteristic
284C4×C73#55611yescharacteristic
285#25006C7311yesmaximal, characteristic, direct product factor, Sylow
286C2×C73—82no—
287C2×C73#242111yescharacteristic
288C2×C73#309411yescharacteristic
289C2×C73#309911yescharacteristic
290C2×C73#336811yescharacteristic
291C2×C73#337311yescharacteristic
292C2×C73#337611yescharacteristic
293C2×C73#337611yescharacteristic
294#2538C2×C7311yescharacteristic
295#2355C2×C7311yescharacteristic, complemented
296#2101C2×C7311yescharacteristic, complemented
297#2099C2×C7311yescharacteristic, complemented
298#2073C2×C7311yescharacteristic
299#2071C2×C7311yescharacteristic
300#1985C2×C7311yescharacteristic, complemented
301#1948C2×C7311yescharacteristic, complemented
302#1926C2×C7311yescharacteristic
303#1926C2×C7311yescharacteristic
304#1920C2×C7311yescharacteristic, complemented
305#1919C2×C7311yescharacteristic, complemented
306#1836C2×C7311yescharacteristic, complemented
307#1804C2×C7311yescharacteristic
308#1762C2×C7311yescharacteristic
309C73#2500611yescharacteristic, direct product factor, Sylow
310C2×C22⋊Q8—21no—
311C2×C4×Q8C22×C7311yescharacteristic
312C2×C4×D4C22×C7311yescharacteristic
313C2×#106C22×C7311yescharacteristic
314C2×#106C22×C7311yescharacteristic
315C2×C4⋊C8C22×C7311yescharacteristic
316C2×#102C22×C7311yescharacteristic
317C2×#102C22×C7311yescharacteristic
318C2×#102C22×C7311yescharacteristic
319C2×#102C22×C7311yescharacteristic
320C2×#97C22×C7311yescharacteristic
321#396—21no—
322#396—21no—
323#391—21no—
324#390C22×C7311yescharacteristic
325#390C22×C7311yescharacteristic
326#389C22×C7311yescharacteristic
327#389C22×C7311yescharacteristic
328#387—21no—
329#387—21no—
330#384C22×C7311yescharacteristic
331#384C22×C7311yescharacteristic
332#382C22×C7311yescharacteristic
333#382C22×C7311yescharacteristic
334#380—21no—
335C4×C4⋊C4—21no—
336C4×C4⋊C4C22×C7311yescharacteristic
337C4×C4⋊C4C22×C7311yescharacteristic
338C4×C4⋊C4C22×C7311yescharacteristic
339#340C22×C7311yescharacteristic
340#340C22×C7311yescharacteristic
341#340C22×C7311yescharacteristic
342#340C22×C7311yescharacteristic
343#340C22×C7311yescharacteristic
344#340C22×C7311yescharacteristic
345#340C22×C7311yescharacteristic
346#340C22×C7311yescharacteristic
347#340C22×C7311yescharacteristic
348#340C22×C7311yescharacteristic
349#336C22×C7311yescharacteristic
350#336C22×C7311yescharacteristic
351#336C22×C7311yescharacteristic
352#336C22×C7311yescharacteristic
353C22×Q8D4×C7311yescharacteristic
354C22×D4C23×C7311yescharacteristic
355C23×C4—21no—
356C22×C8C23×C7311yescharacteristic
357C22×C8C23×C7311yescharacteristic
358C22×C8C23×C7311yescharacteristic
359C22×C8C23×C7311yescharacteristic
360C22⋊Q8—44no—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×D4—22no—
364C4×D4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4D4×C7311yescharacteristic
372C2×C4⋊C4D4×C7311yescharacteristic
373C2×C4⋊C4D4×C7311yescharacteristic
374C2×C4⋊C4C23×C7311yescharacteristic
375C2×C4⋊C4C23×C7311yescharacteristic
376C2×C4⋊C4C23×C7311yescharacteristic
377C2×C4⋊C4C23×C7311yescharacteristic
378C2×C4⋊C4C23×C7311yescharacteristic
379C2×C4⋊C4C23×C7311yescharacteristic
380C2×C4⋊C4C23×C7311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42C23×C7311yescharacteristic
390C2×C42C23×C7311yescharacteristic
391C2×C42C23×C7311yescharacteristic
392#106—22no—
393#106—22no—
394C4⋊C8—22no—
395#102—22no—
396#102—22no—
397#102—22no—
398#102—22no—
399#97—22no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409C24—21no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—41no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4#41×C7312yes—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4C2×D4×C7311yescharacteristic
430C22×C4C2×D4×C7311yescharacteristic
431C22×C4C2×D4×C7311yescharacteristic
432C22×C4C2×D4×C7311yescharacteristic
433C22×C4C2×D4×C7311yescharacteristic
434C22×C4C2×D4×C7311yescharacteristic
435C22×C4C24×C7311yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—81no—
469C4⋊C4—81no—
470C4⋊C4#41×C7312yes—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—81no—
475C22⋊C4—81no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—42no—
481C42—81no—
482C42—81no—
483C42#41×C7312yes—
484C42#41×C7312yes—
485C23—22no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23C22×D4×C7311yescharacteristic
493Q8—44no—
494D4—22no—
495D4—22no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—84no—
535C2×C4#123×C7312yes—
536C2×C4#123×C7312yes—
537C2×C4AGL(1,ℤ/8)×C7312yes—
538C2×C4C2×#41×C7311yescharacteristic
539C2×C4C2×#41×C7311yescharacteristic
540C2×C4C2×#41×C7311yescharacteristic
541C2×C4C2×#41×C7311yescharacteristic
542C2×C42−1+4×C7311yescharacteristic
543C2×C42−1+4×C7311yescharacteristic
544C8—41no—
545C8—41no—
546C8—41no—
547C8—41no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22C2×#123×C7311yescharacteristic
556C22#548×C7311yescharacteristic
557C22#548×C7311yescharacteristic
558C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
559C22#575×C7311yescharacteristic
560C22#577×C7311yescharacteristic
561C22#577×C7311yescharacteristic
562C4—22no—
563C4—22no—
564C4—22no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—42no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4#529×C7311yescharacteristic
576C4#541×C7311yescharacteristic
577C4#552×C7311yescharacteristic
578C4#556×C7311yescharacteristic
579C2—82no—
580C2C73×#242111yescharacteristic
581C2C73×#309411yescharacteristic
582C2C73×#309911yescharacteristic
583C2C73×#336811yescharacteristic
584C2C73×#337311yescharacteristic
585C2C73×#337611yescharacteristic
586C2C73×#337611yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D4×C73C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×C4×Q8×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#2355C2semidirect
3. C73×#2101C2semidirect
4. C73×#2099C2semidirect
7. C73×#1985C2semidirect
8. C73×#1948C2semidirect
11. C73×#1920C2semidirect
12. C73×#1919C2semidirect
13. C73×#1836C2semidirect
285. #25006C73direct (N × H)
295. #2355C2×C73semidirect
296. #2101C2×C73semidirect
297. #2099C2×C73semidirect
300. #1985C2×C73semidirect
301. #1948C2×C73semidirect
304. #1920C2×C73semidirect
305. #1919C2×C73semidirect
306. #1836C2×C73semidirect
309. C73#25006direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#25382
C73×#23552
C73×#21012
C73×#20992
C73×#20732
C73×#20712
C73×#19852
C73×#19482
C73×#19262
C73×#19202
C73×#19192
C73×#18362
C73×#18042
C73×#17622
#2500673