Finite Group Databasebeta

← C73×#26002 #32935406

Subgroups — C73×#26002 #32935406

Order 18688.

730 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2442C211yesmaximal, characteristic
2C73×#2345C211yesmaximal, characteristic
3C73×#2101C211yesmaximal, characteristic, complemented
4C73×#2088C211yesmaximal, characteristic, complemented
5C73×#2086C211yesmaximal, characteristic, complemented
6C73×#2059C211yesmaximal, characteristic, complemented
7C73×#1989C211yesmaximal, characteristic, complemented
8C73×#1949C211yesmaximal, characteristic, complemented
9C73×#1920C211yesmaximal, characteristic, complemented
10C73×#1918C211yesmaximal, characteristic, complemented
11C73×#1853C211yesmaximal, characteristic
12C73×#1850C211yesmaximal, characteristic
13C73×#1824C211yesmaximal, characteristic
14C73×#1808C211yesmaximal, characteristic
15C2×#340×C73C211yesmaximal, characteristic
16C23×C8×C73C2211yescharacteristic
17C2×#125×C73C2211yescharacteristic
18C22×C4⋊C4×C73C2211yescharacteristic
19C22×C4⋊C4×C73C2211yescharacteristic
20C2×#107×C73C2211yescharacteristic
21C2×#107×C73C2211yescharacteristic
22C2×#106×C73C2211yescharacteristic
23C2×#106×C73C2211yescharacteristic
24C2×C4⋊C8×C73C2211yescharacteristic
25C2×C4⋊C8×C73C2211yescharacteristic
26C2×C22⋊C8×C73C2211yescharacteristic
27#400×C73—21no—
28#398×C73—21no—
29#389×C73C2211yescharacteristic
30#389×C73C2211yescharacteristic
31#389×C73C2211yescharacteristic
32#389×C73C2211yescharacteristic
33#387×C73—21no—
34#387×C73—21no—
35#385×C73—21no—
36#382×C73C2211yescharacteristic
37#380×C73—21no—
38#380×C73—21no—
39#380×C73C2211yescharacteristic
40#380×C73C2211yescharacteristic
41C4×C4⋊C4×C73C2211yescharacteristic
42C4×C4⋊C4×C73C2211yescharacteristic
43C4×C22⋊C4×C73—21no—
44C4×C22⋊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#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C23×C4×C73—21no—
60C23×C4×C73—21no—
61C23×C4×C73C2311yescharacteristic
62C22×C8×C73—22no—
63C22×C8×C73—22no—
64C22×C8×C73—41no—
65C22×C8×C73C2311yescharacteristic
66C22×C8×C73C2311yescharacteristic
67C22×C8×C73C2311yescharacteristic
68C22×C8×C73C2311yescharacteristic
69#125×C73—22no—
70#125×C73—41no—
71C2×C4⋊C4×C73—21no—
72C2×C4⋊C4×C73—22no—
73C2×C4⋊C4×C73—22no—
74C2×C4⋊C4×C73—21no—
75C2×C4⋊C4×C73—21no—
76C2×C4⋊C4×C73—21no—
77C2×C4⋊C4×C73—21no—
78C2×C4⋊C4×C73—21no—
79C2×C4⋊C4×C73—21no—
80C2×C4⋊C4×C73—21no—
81C2×C4⋊C4×C73—41no—
82C2×C4⋊C4×C73Q814yes—
83C2×C4⋊C4×C73C2311yescharacteristic
84C2×C4⋊C4×C73C2311yescharacteristic
85C2×C4⋊C4×C73C2311yescharacteristic
86C2×C4⋊C4×C73C2311yescharacteristic
87C2×C4⋊C4×C73C2311yescharacteristic
88C2×C4⋊C4×C73C2311yescharacteristic
89C2×C4⋊C4×C73C2311yescharacteristic
90C2×C4⋊C4×C73C2311yescharacteristic
91C2×C22⋊C4×C73—21no—
92C2×C22⋊C4×C73—21no—
93C2×C22⋊C4×C73D411yescharacteristic
94C2×C22⋊C4×C73D411yescharacteristic
95C2×C42×C73—21no—
96C2×C42×C73—21no—
97C2×C42×C73C2311yescharacteristic
98C2×C42×C73C2311yescharacteristic
99#107×C73—22no—
100#107×C73—41no—
101#106×C73—22no—
102#106×C73—41no—
103C4⋊C8×C73—22no—
104C4⋊C8×C73—41no—
105C22⋊C8×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—
115#95×C73—21no—
116#95×C73D411yescharacteristic
117#95×C73D411yescharacteristic
118C24×C73C2×D411yescharacteristic
119C22×C4×C73—21no—
120C22×C4×C73—21no—
121C22×C4×C73—21no—
122C22×C4×C73—21no—
123C22×C4×C73—21no—
124C22×C4×C73—21no—
125C22×C4×C73—21no—
126C22×C4×C73—24no—
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—81no—
135C22×C4×C73—81no—
136C22×C4×C73—81no—
137C22×C4×C73C2×D411yescharacteristic
138C22×C4×C73C2×D411yescharacteristic
139C22×C4×C73C2×D411yescharacteristic
140C22×C4×C73C2×D411yescharacteristic
141C22×C4×C73C2×D411yescharacteristic
142C22×C4×C73C2×Q812yes—
143C22×C4×C73#4112yes—
144C22×C4×C73C2411yescharacteristic
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—
154C2×C8×C73—21no—
155C2×C8×C73—21no—
156C2×C8×C73—44no—
157C2×C8×C73#4112yes—
158C4⋊C4×C73—24no—
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—21no—
171C4⋊C4×C73—21no—
172C4⋊C4×C73—42no—
173C4⋊C4×C73—42no—
174C4⋊C4×C73—42no—
175C4⋊C4×C73—81no—
176C4⋊C4×C73—81no—
177C4⋊C4×C73—81no—
178C4⋊C4×C73—81no—
179C4⋊C4×C73C2×Q812yes—
180C4⋊C4×C73C2×Q812yes—
181C4⋊C4×C73#4112yes—
182C22⋊C4×C73—22no—
183C22⋊C4×C73—22no—
184C22⋊C4×C73—42no—
185C22⋊C4×C73—42no—
186C42×C73—21no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73—21no—
190C42×C73—81no—
191C42×C73—81no—
192C23×C73—21no—
193C23×C73—21no—
194C23×C73—21no—
195C23×C73—21no—
196C23×C73C22⋊Q812yes—
197C23×C73#13512yes—
198C23×C73#13712yes—
199C23×C73C22×D411yescharacteristic
200C2×C4×C73—21no—
201C2×C4×C73—21no—
202C2×C4×C73—22no—
203C2×C4×C73—22no—
204C2×C4×C73—22no—
205C2×C4×C73—22no—
206C2×C4×C73—22no—
207C2×C4×C73—22no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—22no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
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—21no—
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—41no—
241C2×C4×C73—41no—
242C2×C4×C73—84no—
243C2×C4×C73—84no—
244C2×C4×C73C22⋊Q812yes—
245C2×C4×C73C22×Q811yescharacteristic
246C2×C4×C73C2×#4111yescharacteristic
247C2×C4×C73C2×#4111yescharacteristic
248C2×C4×C73C2×#4111yescharacteristic
249C2×C4×C73H(5,𝔽2)11yescharacteristic
250C2×C4×C732−1+411yescharacteristic
251C8×C73—22no—
252C8×C73—41no—
253C8×C73—41no—
254C8×C73—41no—
255C22×C73—22no—
256C22×C73—22no—
257C22×C73—22no—
258C22×C73—22no—
259C22×C73—22no—
260C22×C73—22no—
261C22×C73#47914yes—
262C22×C73C2×C22⋊Q811yescharacteristic
263C22×C73#54611yescharacteristic
264C22×C73#54711yescharacteristic
265C22×C73C2×#13511yescharacteristic
266C22×C73C2×#13711yescharacteristic
267C22×C73#57611yescharacteristic
268C22×C73#57711yescharacteristic
269C4×C73—22no—
270C4×C73—42no—
271C4×C73—42no—
272C4×C73—41no—
273C4×C73—41no—
274C4×C73—41no—
275C4×C73—41no—
276C4×C73—42no—
277C4×C73—81no—
278C4×C73—81no—
279C4×C73—81no—
280C4×C73—81no—
281C4×C73—81no—
282C4×C73#53311yescharacteristic
283C4×C73#54411yescharacteristic
284C4×C73#55111yescharacteristic
285C4×C73#55211yescharacteristic
286#26002C7311yesmaximal, characteristic, direct product factor, Sylow
287C2×C73—24no—
288C2×C73#243811yescharacteristic
289C2×C73C2×#47911yescharacteristic
290C2×C73#308111yescharacteristic
291C2×C73#330111yescharacteristic
292C2×C73#331411yescharacteristic
293C2×C73#333911yescharacteristic
294C2×C73#334411yescharacteristic
295#2442C2×C7311yescharacteristic
296#2345C2×C7311yescharacteristic
297#2101C2×C7311yescharacteristic, complemented
298#2088C2×C7311yescharacteristic, complemented
299#2086C2×C7311yescharacteristic, complemented
300#2059C2×C7311yescharacteristic, complemented
301#1989C2×C7311yescharacteristic, complemented
302#1949C2×C7311yescharacteristic, complemented
303#1920C2×C7311yescharacteristic, complemented
304#1918C2×C7311yescharacteristic, complemented
305#1853C2×C7311yescharacteristic
306#1850C2×C7311yescharacteristic
307#1824C2×C7311yescharacteristic
308#1808C2×C7311yescharacteristic
309C2×#340C2×C7311yescharacteristic
310C73#2600211yescharacteristic, direct product factor, Sylow
311C23×C8C22×C7311yescharacteristic
312C2×#125C22×C7311yescharacteristic
313C22×C4⋊C4C22×C7311yescharacteristic
314C22×C4⋊C4C22×C7311yescharacteristic
315C2×#107C22×C7311yescharacteristic
316C2×#107C22×C7311yescharacteristic
317C2×#106C22×C7311yescharacteristic
318C2×#106C22×C7311yescharacteristic
319C2×C4⋊C8C22×C7311yescharacteristic
320C2×C4⋊C8C22×C7311yescharacteristic
321C2×C22⋊C8C22×C7311yescharacteristic
322#400—21no—
323#398—21no—
324#389C22×C7311yescharacteristic
325#389C22×C7311yescharacteristic
326#389C22×C7311yescharacteristic
327#389C22×C7311yescharacteristic
328#387—21no—
329#387—21no—
330#385—21no—
331#382C22×C7311yescharacteristic
332#380—21no—
333#380—21no—
334#380C22×C7311yescharacteristic
335#380C22×C7311yescharacteristic
336C4×C4⋊C4C22×C7311yescharacteristic
337C4×C4⋊C4C22×C7311yescharacteristic
338C4×C22⋊C4—21no—
339C4×C22⋊C4C22×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#340C22×C7311yescharacteristic
350#340C22×C7311yescharacteristic
351#340C22×C7311yescharacteristic
352#336C22×C7311yescharacteristic
353#336C22×C7311yescharacteristic
354C23×C4—21no—
355C23×C4—21no—
356C23×C4C23×C7311yescharacteristic
357C22×C8—22no—
358C22×C8—22no—
359C22×C8—41no—
360C22×C8C23×C7311yescharacteristic
361C22×C8C23×C7311yescharacteristic
362C22×C8C23×C7311yescharacteristic
363C22×C8C23×C7311yescharacteristic
364#125—22no—
365#125—41no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—41no—
377C2×C4⋊C4Q8×C7314yes—
378C2×C4⋊C4C23×C7311yescharacteristic
379C2×C4⋊C4C23×C7311yescharacteristic
380C2×C4⋊C4C23×C7311yescharacteristic
381C2×C4⋊C4C23×C7311yescharacteristic
382C2×C4⋊C4C23×C7311yescharacteristic
383C2×C4⋊C4C23×C7311yescharacteristic
384C2×C4⋊C4C23×C7311yescharacteristic
385C2×C4⋊C4C23×C7311yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4D4×C7311yescharacteristic
389C2×C22⋊C4D4×C7311yescharacteristic
390C2×C42—21no—
391C2×C42—21no—
392C2×C42C23×C7311yescharacteristic
393C2×C42C23×C7311yescharacteristic
394#107—22no—
395#107—41no—
396#106—22no—
397#106—41no—
398C4⋊C8—22no—
399C4⋊C8—41no—
400C22⋊C8—22no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95D4×C7311yescharacteristic
412#95D4×C7311yescharacteristic
413C24C2×D4×C7311yescharacteristic
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—24no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—81no—
430C22×C4—81no—
431C22×C4—81no—
432C22×C4C2×D4×C7311yescharacteristic
433C22×C4C2×D4×C7311yescharacteristic
434C22×C4C2×D4×C7311yescharacteristic
435C22×C4C2×D4×C7311yescharacteristic
436C22×C4C2×D4×C7311yescharacteristic
437C22×C4C2×Q8×C7312yes—
438C22×C4#41×C7312yes—
439C22×C4C24×C7311yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—44no—
452C2×C8#41×C7312yes—
453C4⋊C4—24no—
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—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—81no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4—81no—
474C4⋊C4C2×Q8×C7312yes—
475C4⋊C4C2×Q8×C7312yes—
476C4⋊C4#41×C7312yes—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—42no—
480C22⋊C4—42no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—81no—
486C42—81no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23C22⋊Q8×C7312yes—
492C23#135×C7312yes—
493C23#137×C7312yes—
494C23C22×D4×C7311yescharacteristic
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
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—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—84no—
538C2×C4—84no—
539C2×C4C22⋊Q8×C7312yes—
540C2×C4C22×Q8×C7311yescharacteristic
541C2×C4C2×#41×C7311yescharacteristic
542C2×C4C2×#41×C7311yescharacteristic
543C2×C4C2×#41×C7311yescharacteristic
544C2×C4H(5,𝔽2)×C7311yescharacteristic
545C2×C42−1+4×C7311yescharacteristic
546C8—22no—
547C8—41no—
548C8—41no—
549C8—41no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22#479×C7314yes—
557C22C2×C22⋊Q8×C7311yescharacteristic
558C22#546×C7311yescharacteristic
559C22#547×C7311yescharacteristic
560C22C2×#135×C7311yescharacteristic
561C22C2×#137×C7311yescharacteristic
562C22#576×C7311yescharacteristic
563C22#577×C7311yescharacteristic
564C4—22no—
565C4—41no—
566C4—41no—
567C4—42no—
568C4—42no—
569C4—42no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4#533×C7311yescharacteristic
578C4#544×C7311yescharacteristic
579C4#551×C7311yescharacteristic
580C4#552×C7311yescharacteristic
581C2—24no—
582C2C73×#243811yescharacteristic
583C2C2×#479×C7311yescharacteristic
584C2C73×#308111yescharacteristic
585C2C73×#330111yescharacteristic
586C2C73×#331411yescharacteristic
587C2C73×#333911yescharacteristic
588C2C73×#334411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC24×C73C2×D4
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
3. C73×#2101C2semidirect
4. C73×#2088C2semidirect
5. C73×#2086C2semidirect
6. C73×#2059C2semidirect
7. C73×#1989C2semidirect
8. C73×#1949C2semidirect
9. C73×#1920C2semidirect
10. C73×#1918C2semidirect
286. #26002C73direct (N × H)
297. #2101C2×C73semidirect
298. #2088C2×C73semidirect
299. #2086C2×C73semidirect
300. #2059C2×C73semidirect
301. #1989C2×C73semidirect
302. #1949C2×C73semidirect
303. #1920C2×C73semidirect
304. #1918C2×C73semidirect
310. C73#26002direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#24422
C73×#23452
C73×#21012
C73×#20882
C73×#20862
C73×#20592
C73×#19892
C73×#19492
C73×#19202
C73×#19182
C73×#18532
C73×#18502
C73×#18242
C73×#18082
C2×#340×C732
#2600273