Finite Group Databasebeta

← C73×#27136 #32936540

Subgroups — C73×#27136 #32936540

Order 18688.

642 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2513C211yesmaximal, characteristic
2C73×#2370C211yesmaximal, characteristic, complemented
3C73×#2101C211yesmaximal, characteristic, complemented
4C73×#2065C211yesmaximal, characteristic
5C73×#2059C211yesmaximal, characteristic, complemented
6C73×#2025C211yesmaximal, characteristic
7C73×#1949C211yesmaximal, characteristic, complemented
8C73×#1934C211yesmaximal, characteristic
9C73×#1926C211yesmaximal, characteristic
10C73×#1925C211yesmaximal, characteristic
11C73×#1925C211yesmaximal, characteristic
12C73×#1921C211yesmaximal, characteristic, complemented
13C73×#1918C211yesmaximal, characteristic, complemented
14C73×#1916C211yesmaximal, characteristic, complemented
15C4×#106×C73C211yesmaximal, characteristic, complemented
16C2×#125×C73C2211yescharacteristic
17C2×#107×C73C2211yescharacteristic
18C2×#107×C73C2211yescharacteristic
19C2×#106×C73C2211yescharacteristic
20C2×#106×C73C2211yescharacteristic
21C2×C4⋊C8×C73C2211yescharacteristic
22C2×#102×C73C2211yescharacteristic
23C2×#102×C73C2211yescharacteristic
24C2×#102×C73C2211yescharacteristic
25C2×#102×C73C2211yescharacteristic
26C2×C4×C8×C73C2211yescharacteristic
27#397×C73—21no—
28#397×C73—21no—
29#390×C73C2211yescharacteristic
30#390×C73C2211yescharacteristic
31#390×C73C2211yescharacteristic
32#389×C73—21no—
33#389×C73C2211yescharacteristic
34#389×C73C2211yescharacteristic
35#389×C73C2211yescharacteristic
36#388×C73—21no—
37#388×C73—21no—
38#387×C73—21no—
39#387×C73—21no—
40#382×C73C2211yescharacteristic
41C4×C4⋊C4×C73—21no—
42C4×C4⋊C4×C73C2211yescharacteristic
43C4×C4⋊C4×C73C2211yescharacteristic
44C4×C4⋊C4×C73C2211yescharacteristic
45C4×C4⋊C4×C73C2211yescharacteristic
46C4×C4⋊C4×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×D4×C73C2311yescharacteristic
60C22×C8×C73C2311yescharacteristic
61C22×C8×C73C2311yescharacteristic
62C22×C8×C73C2311yescharacteristic
63C22×C8×C73C2311yescharacteristic
64#125×C73—22no—
65#125×C73—22no—
66C2×C4⋊C4×C73—21no—
67C2×C4⋊C4×C73—21no—
68C2×C4⋊C4×C73—21no—
69C2×C4⋊C4×C73—21no—
70C2×C4⋊C4×C73—21no—
71C2×C4⋊C4×C73D411yescharacteristic
72C2×C4⋊C4×C73D411yescharacteristic
73C2×C4⋊C4×C73C2311yescharacteristic
74C2×C4⋊C4×C73C2311yescharacteristic
75C2×C4⋊C4×C73C2311yescharacteristic
76C2×C4⋊C4×C73C2311yescharacteristic
77C2×C4⋊C4×C73C2311yescharacteristic
78C2×C4⋊C4×C73C2311yescharacteristic
79C2×C4⋊C4×C73C2311yescharacteristic
80C2×C22⋊C4×C73—21no—
81C2×C22⋊C4×C73—21no—
82C2×C22⋊C4×C73—21no—
83C2×C22⋊C4×C73—21no—
84C2×C22⋊C4×C73—21no—
85C2×C22⋊C4×C73—21no—
86C2×C42×C73—21no—
87C2×C42×C73—21no—
88C2×C42×C73—21no—
89C2×C42×C73—21no—
90C2×C42×C73C2311yescharacteristic
91C2×C42×C73C2311yescharacteristic
92C2×C42×C73C2311yescharacteristic
93#107×C73—22no—
94#107×C73—22no—
95#106×C73—22no—
96#106×C73—22no—
97C4⋊C8×C73—22no—
98#102×C73—22no—
99#102×C73—22no—
100#102×C73—22no—
101#102×C73—22no—
102C4×C8×C73—22no—
103#95×C73—21no—
104#95×C73—21no—
105#95×C73—21no—
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×C73D411yescharacteristic
113#95×C73D411yescharacteristic
114C24×C73—21no—
115C2×D4×C73—21no—
116C2×D4×C73—21no—
117C2×D4×C73—21no—
118C2×D4×C73—21no—
119C2×D4×C73—21no—
120C2×D4×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—21no—
127C22×C4×C73—21no—
128C22×C4×C73C2×D411yescharacteristic
129C22×C4×C73C2×D411yescharacteristic
130C22×C4×C73C2×D411yescharacteristic
131C22×C4×C73C2×D411yescharacteristic
132C22×C4×C73C2×D411yescharacteristic
133C22×C4×C73C2×D411yescharacteristic
134C22×C4×C73C2411yescharacteristic
135C2×C8×C73—21no—
136C2×C8×C73—21no—
137C2×C8×C73—21no—
138C2×C8×C73—21no—
139C2×C8×C73—21no—
140C2×C8×C73—21no—
141C2×C8×C73—21no—
142C2×C8×C73—21no—
143C2×C8×C73—21no—
144C2×C8×C73—21no—
145C2×C8×C73—21no—
146C2×C8×C73#4112yes—
147C4⋊C4×C73—24no—
148C4⋊C4×C73—24no—
149C4⋊C4×C73—22no—
150C4⋊C4×C73—21no—
151C4⋊C4×C73—21no—
152C4⋊C4×C73—21no—
153C4⋊C4×C73—21no—
154C4⋊C4×C73—21no—
155C4⋊C4×C73—21no—
156C4⋊C4×C73—21no—
157C4⋊C4×C73—21no—
158C4⋊C4×C73—21no—
159C4⋊C4×C73—21no—
160C4⋊C4×C73—21no—
161C4⋊C4×C73—41no—
162C4⋊C4×C73—42no—
163C4⋊C4×C73—81no—
164C4⋊C4×C73—81no—
165C4⋊C4×C73#4112yes—
166C4⋊C4×C73#4112yes—
167C4⋊C4×C73#4112yes—
168C22⋊C4×C73—42no—
169C22⋊C4×C73—42no—
170C22⋊C4×C73—81no—
171C22⋊C4×C73—81no—
172C22⋊C4×C73—81no—
173C22⋊C4×C73—81no—
174C42×C73—21no—
175C42×C73—21no—
176C42×C73—21no—
177C42×C73—21no—
178C42×C73—21no—
179C42×C73—21no—
180C42×C73—42no—
181C42×C73—81no—
182C42×C73—81no—
183C42×C73—81no—
184C23×C73—41no—
185C23×C73—41no—
186C23×C73—41no—
187C23×C73—41no—
188C23×C73—41no—
189C23×C73—41no—
190C23×C73—41no—
191C23×C73C22×D411yescharacteristic
192D4×C73—41no—
193D4×C73—41no—
194D4×C73—41no—
195D4×C73—41no—
196C2×C4×C73—21no—
197C2×C4×C73—21no—
198C2×C4×C73—21no—
199C2×C4×C73—21no—
200C2×C4×C73—22no—
201C2×C4×C73—22no—
202C2×C4×C73—21no—
203C2×C4×C73—21no—
204C2×C4×C73—21no—
205C2×C4×C73—22no—
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—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—41no—
217C2×C4×C73—41no—
218C2×C4×C73—41no—
219C2×C4×C73—41no—
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#13512yes—
235C2×C4×C73C2×#4111yescharacteristic
236C2×C4×C73C2×#4111yescharacteristic
237C2×C4×C73C2×#4111yescharacteristic
238C2×C4×C73C2×#4111yescharacteristic
239C2×C4×C732−1+411yescharacteristic
240C2×C4×C732−1+411yescharacteristic
241C8×C73—22no—
242C8×C73—41no—
243C8×C73—41no—
244C8×C73—41no—
245C22×C73—81no—
246C22×C73—81no—
247C22×C73—81no—
248C22×C73—81no—
249C22×C73—81no—
250C22×C73—81no—
251C22×C73—81no—
252C22×C73#52511yescharacteristic
253C22×C73#54711yescharacteristic
254C22×C73#54811yescharacteristic
255C22×C73C2×#13511yescharacteristic
256C22×C73#57511yescharacteristic
257C22×C73#57611yescharacteristic
258C22×C73#57711yescharacteristic
259C4×C73—22no—
260C4×C73—41no—
261C4×C73—41no—
262C4×C73—41no—
263C4×C73—41no—
264C4×C73—42no—
265C4×C73—42no—
266C4×C73—41no—
267C4×C73—42no—
268C4×C73—81no—
269C4×C73—81no—
270C4×C73—81no—
271C4×C73—81no—
272C4×C73#52911yescharacteristic
273C4×C73#54111yescharacteristic
274C4×C73#55611yescharacteristic
275C4×C73#55611yescharacteristic
276#27136C7311yesmaximal, characteristic, direct product factor, Sylow
277C2×C73—161no—
278C2×C73#246911yescharacteristic
279C2×C73#310211yescharacteristic
280C2×C73#311911yescharacteristic
281C2×C73#333711yescharacteristic
282C2×C73#334711yescharacteristic
283C2×C73#336111yescharacteristic
284C2×C73#337111yescharacteristic
285#2513C2×C7311yescharacteristic
286#2370C2×C7311yescharacteristic, complemented
287#2101C2×C7311yescharacteristic, complemented
288#2065C2×C7311yescharacteristic
289#2059C2×C7311yescharacteristic, complemented
290#2025C2×C7311yescharacteristic
291#1949C2×C7311yescharacteristic, complemented
292#1934C2×C7311yescharacteristic
293#1926C2×C7311yescharacteristic
294#1925C2×C7311yescharacteristic
295#1925C2×C7311yescharacteristic
296#1921C2×C7311yescharacteristic, complemented
297#1918C2×C7311yescharacteristic, complemented
298#1916C2×C7311yescharacteristic, complemented
299C4×#106C2×C7311yescharacteristic, complemented
300C73#2713611yescharacteristic, direct product factor, Sylow
301C2×#125C22×C7311yescharacteristic
302C2×#107C22×C7311yescharacteristic
303C2×#107C22×C7311yescharacteristic
304C2×#106C22×C7311yescharacteristic
305C2×#106C22×C7311yescharacteristic
306C2×C4⋊C8C22×C7311yescharacteristic
307C2×#102C22×C7311yescharacteristic
308C2×#102C22×C7311yescharacteristic
309C2×#102C22×C7311yescharacteristic
310C2×#102C22×C7311yescharacteristic
311C2×C4×C8C22×C7311yescharacteristic
312#397—21no—
313#397—21no—
314#390C22×C7311yescharacteristic
315#390C22×C7311yescharacteristic
316#390C22×C7311yescharacteristic
317#389—21no—
318#389C22×C7311yescharacteristic
319#389C22×C7311yescharacteristic
320#389C22×C7311yescharacteristic
321#388—21no—
322#388—21no—
323#387—21no—
324#387—21no—
325#382C22×C7311yescharacteristic
326C4×C4⋊C4—21no—
327C4×C4⋊C4C22×C7311yescharacteristic
328C4×C4⋊C4C22×C7311yescharacteristic
329C4×C4⋊C4C22×C7311yescharacteristic
330C4×C4⋊C4C22×C7311yescharacteristic
331C4×C4⋊C4C22×C7311yescharacteristic
332#340C22×C7311yescharacteristic
333#340C22×C7311yescharacteristic
334#340C22×C7311yescharacteristic
335#340C22×C7311yescharacteristic
336#340C22×C7311yescharacteristic
337#340C22×C7311yescharacteristic
338#340C22×C7311yescharacteristic
339#340C22×C7311yescharacteristic
340#336C22×C7311yescharacteristic
341#336C22×C7311yescharacteristic
342#336C22×C7311yescharacteristic
343#336C22×C7311yescharacteristic
344C22×D4C23×C7311yescharacteristic
345C22×C8C23×C7311yescharacteristic
346C22×C8C23×C7311yescharacteristic
347C22×C8C23×C7311yescharacteristic
348C22×C8C23×C7311yescharacteristic
349#125—22no—
350#125—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4D4×C7311yescharacteristic
357C2×C4⋊C4D4×C7311yescharacteristic
358C2×C4⋊C4C23×C7311yescharacteristic
359C2×C4⋊C4C23×C7311yescharacteristic
360C2×C4⋊C4C23×C7311yescharacteristic
361C2×C4⋊C4C23×C7311yescharacteristic
362C2×C4⋊C4C23×C7311yescharacteristic
363C2×C4⋊C4C23×C7311yescharacteristic
364C2×C4⋊C4C23×C7311yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C42—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42C23×C7311yescharacteristic
376C2×C42C23×C7311yescharacteristic
377C2×C42C23×C7311yescharacteristic
378#107—22no—
379#107—22no—
380#106—22no—
381#106—22no—
382C4⋊C8—22no—
383#102—22no—
384#102—22no—
385#102—22no—
386#102—22no—
387C4×C8—22no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95D4×C7311yescharacteristic
398#95D4×C7311yescharacteristic
399C24—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4C2×D4×C7311yescharacteristic
414C22×C4C2×D4×C7311yescharacteristic
415C22×C4C2×D4×C7311yescharacteristic
416C22×C4C2×D4×C7311yescharacteristic
417C22×C4C2×D4×C7311yescharacteristic
418C22×C4C2×D4×C7311yescharacteristic
419C22×C4C24×C7311yescharacteristic
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8#41×C7312yes—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—41no—
447C4⋊C4—42no—
448C4⋊C4—81no—
449C4⋊C4—81no—
450C4⋊C4#41×C7312yes—
451C4⋊C4#41×C7312yes—
452C4⋊C4#41×C7312yes—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—81no—
456C22⋊C4—81no—
457C22⋊C4—81no—
458C22⋊C4—81no—
459C42—21no—
460C42—21no—
461C42—21no—
462C42—21no—
463C42—21no—
464C42—21no—
465C42—42no—
466C42—81no—
467C42—81no—
468C42—81no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23C22×D4×C7311yescharacteristic
477D4—41no—
478D4—41no—
479D4—41no—
480D4—41no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4#135×C7312yes—
520C2×C4C2×#41×C7311yescharacteristic
521C2×C4C2×#41×C7311yescharacteristic
522C2×C4C2×#41×C7311yescharacteristic
523C2×C4C2×#41×C7311yescharacteristic
524C2×C42−1+4×C7311yescharacteristic
525C2×C42−1+4×C7311yescharacteristic
526C8—22no—
527C8—41no—
528C8—41no—
529C8—41no—
530C22—81no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22#525×C7311yescharacteristic
538C22#547×C7311yescharacteristic
539C22#548×C7311yescharacteristic
540C22C2×#135×C7311yescharacteristic
541C22#575×C7311yescharacteristic
542C22#576×C7311yescharacteristic
543C22#577×C7311yescharacteristic
544C4—22no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—42no—
550C4—42no—
551C4—41no—
552C4—42no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—81no—
557C4#529×C7311yescharacteristic
558C4#541×C7311yescharacteristic
559C4#556×C7311yescharacteristic
560C4#556×C7311yescharacteristic
561C2—161no—
562C2C73×#246911yescharacteristic
563C2C73×#310211yescharacteristic
564C2C73×#311911yescharacteristic
565C2C73×#333711yescharacteristic
566C2C73×#334711yescharacteristic
567C2C73×#336111yescharacteristic
568C2C73×#337111yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D4×C73C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C4⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#2370C2semidirect
3. C73×#2101C2semidirect
5. C73×#2059C2semidirect
7. C73×#1949C2semidirect
12. C73×#1921C2semidirect
13. C73×#1918C2semidirect
14. C73×#1916C2semidirect
15. C4×#106×C73C2semidirect
276. #27136C73direct (N × H)
286. #2370C2×C73semidirect
287. #2101C2×C73semidirect
289. #2059C2×C73semidirect
291. #1949C2×C73semidirect
296. #1921C2×C73semidirect
297. #1918C2×C73semidirect
298. #1916C2×C73semidirect
299. C4×#106C2×C73semidirect
300. C73#27136direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#25132
C73×#23702
C73×#21012
C73×#20652
C73×#20592
C73×#20252
C73×#19492
C73×#19342
C73×#19262
C73×#19252
C73×#19212
C73×#19182
C73×#19162
C4×#106×C732
#2713673