Finite Group Databasebeta

← C73×#32845 #32942249

Subgroups — C73×#32845 #32942249

Order 18688.

590 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2660C211yesmaximal, characteristic, complemented
2C73×#2644C211yesmaximal, characteristic
3C73×#2101C211yesmaximal, characteristic, complemented
4C73×#2100C211yesmaximal, characteristic, complemented
5C73×#2093C211yesmaximal, characteristic
6C73×#2092C211yesmaximal, characteristic
7C73×#2085C211yesmaximal, characteristic, complemented
8C73×#2083C211yesmaximal, characteristic, complemented
9C73×#2073C211yesmaximal, characteristic
10C73×#2071C211yesmaximal, characteristic
11C73×#2059C211yesmaximal, characteristic, complemented
12C73×#2057C211yesmaximal, characteristic, complemented
13C73×#2025C211yesmaximal, characteristic
14C73×#2023C211yesmaximal, characteristic
15C73×#1840C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C73C2211yescharacteristic
17C2×#125×C73C2211yescharacteristic
18C2×#107×C73C2211yescharacteristic
19C2×#107×C73C2211yescharacteristic
20C2×#107×C73C2211yescharacteristic
21C2×#106×C73C2211yescharacteristic
22C2×#102×C73C2211yescharacteristic
23C2×#102×C73C2211yescharacteristic
24C2×#102×C73C2211yescharacteristic
25C2×#102×C73C2211yescharacteristic
26#398×C73—21no—
27#398×C73—21no—
28#397×C73—21no—
29#397×C73—21no—
30#397×C73—21no—
31#396×C73—21no—
32#395×C73—21no—
33#395×C73—21no—
34#390×C73C2211yescharacteristic
35#390×C73C2211yescharacteristic
36#390×C73C2211yescharacteristic
37#389×C73C2211yescharacteristic
38#389×C73C2211yescharacteristic
39#389×C73C2211yescharacteristic
40#384×C73C2211yescharacteristic
41#384×C73C2211yescharacteristic
42#382×C73C2211yescharacteristic
43#382×C73C2211yescharacteristic
44#376×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#336×C73C2211yescharacteristic
54#336×C73C2211yescharacteristic
55#336×C73C2211yescharacteristic
56#336×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×Q8×C73—21no—
60C22×D4×C73C2311yescharacteristic
61C22×C8×C73C2311yescharacteristic
62C22×C8×C73C2311yescharacteristic
63C22×C8×C73C2311yescharacteristic
64C22×C8×C73C2311yescharacteristic
65C4⋊Q8×C73—41no—
66C4⋊Q8×C73—41no—
67#125×C73—41no—
68#125×C73—41no—
69C2×C4⋊C4×C73—21no—
70C2×C4⋊C4×C73—21no—
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×C73—21no—
78C2×C4⋊C4×C73—21no—
79C2×C4⋊C4×C73C2311yescharacteristic
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×C22⋊C4×C73—21no—
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×C73C2311yescharacteristic
93C2×C42×C73C2311yescharacteristic
94C2×C42×C73C2311yescharacteristic
95#107×C73—41no—
96#107×C73—41no—
97#107×C73—41no—
98#106×C73—41no—
99#102×C73—41no—
100#102×C73—41no—
101#102×C73—41no—
102#102×C73—41no—
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×C73D411yescharacteristic
111#95×C73D411yescharacteristic
112#95×C73D411yescharacteristic
113#95×C73D411yescharacteristic
114C24×C73—21no—
115C2×Q8×C73—42no—
116C2×Q8×C73—81no—
117C2×Q8×C73—81no—
118C2×D4×C73—21no—
119C2×D4×C73—21no—
120C2×D4×C73—21no—
121C2×D4×C73—21no—
122C2×D4×C73—21no—
123C2×D4×C73—21no—
124C22×C4×C73—21no—
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×C73C2×D411yescharacteristic
132C22×C4×C73C2×D411yescharacteristic
133C22×C4×C73C2×D411yescharacteristic
134C22×C4×C73C2×D411yescharacteristic
135C22×C4×C73C2×D411yescharacteristic
136C22×C4×C73C2×D411yescharacteristic
137C22×C4×C73C2411yescharacteristic
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—21no—
147C2×C8×C73—21no—
148C2×C8×C73—21no—
149C2×C8×C73—21no—
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—21no—
162C4⋊C4×C73—21no—
163C4⋊C4×C73—21no—
164C4⋊C4×C73—42no—
165C4⋊C4×C73—42no—
166C4⋊C4×C73—42no—
167C4⋊C4×C73—81no—
168C4⋊C4×C73—81no—
169C4⋊C4×C73—81no—
170C4⋊C4×C73—81no—
171C4⋊C4×C73—81no—
172C4⋊C4×C73—81no—
173C4⋊C4×C73—81no—
174C22⋊C4×C73—81no—
175C22⋊C4×C73—81no—
176C22⋊C4×C73—81no—
177C22⋊C4×C73—81no—
178C22⋊C4×C73—81no—
179C22⋊C4×C73—81no—
180C42×C73—21no—
181C42×C73—21no—
182C42×C73—21no—
183C42×C73—21no—
184C42×C73—21no—
185C42×C73—21no—
186C23×C73—41no—
187C23×C73—41no—
188C23×C73—41no—
189C23×C73—41no—
190C23×C73—41no—
191C23×C73—41no—
192C23×C73—41no—
193C23×C73C22×D411yescharacteristic
194Q8×C73—84no—
195D4×C73—41no—
196D4×C73—41no—
197D4×C73—41no—
198D4×C73—41no—
199C2×C4×C73—21no—
200C2×C4×C73—21no—
201C2×C4×C73—21no—
202C2×C4×C73—21no—
203C2×C4×C73—21no—
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—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
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—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73H(5,𝔽2)11yescharacteristic
239C2×C4×C73H(5,𝔽2)11yescharacteristic
240C2×C4×C732−1+411yescharacteristic
241C2×C4×C732−1+411yescharacteristic
242C2×C4×C732−1+411yescharacteristic
243C2×C4×C732−1+411yescharacteristic
244C8×C73—41no—
245C8×C73—41no—
246C8×C73—41no—
247C8×C73—41no—
248C22×C73—81no—
249C22×C73—81no—
250C22×C73—81no—
251C22×C73—81no—
252C22×C73—81no—
253C22×C73—81no—
254C22×C73—81no—
255C22×C73#53511yescharacteristic
256C22×C73#53611yescharacteristic
257C22×C73#53611yescharacteristic
258C22×C73#57611yescharacteristic
259C22×C73#57611yescharacteristic
260C22×C73#57711yescharacteristic
261C22×C73#57811yescharacteristic
262C4×C73—41no—
263C4×C73—41no—
264C4×C73—41no—
265C4×C73—41no—
266C4×C73—41no—
267C4×C73—41no—
268C4×C73—81no—
269C4×C73—81no—
270C4×C73—81no—
271C4×C73—81no—
272C4×C73—81no—
273C4×C73—81no—
274C4×C73—81no—
275C4×C73#56311yescharacteristic
276C4×C73#56311yescharacteristic
277C4×C73#56311yescharacteristic
278C4×C73#56311yescharacteristic
279#32845C7311yesmaximal, characteristic, direct product factor, Sylow
280C2×C73—161no—
281C2×C73#282111yescharacteristic
282C2×C73#322011yescharacteristic
283C2×C73#322511yescharacteristic
284C2×C73#324111yescharacteristic
285C2×C73#324111yescharacteristic
286C2×C73#324311yescharacteristic
287C2×C73#324311yescharacteristic
288#2660C2×C7311yescharacteristic, complemented
289#2644C2×C7311yescharacteristic
290#2101C2×C7311yescharacteristic, complemented
291#2100C2×C7311yescharacteristic, complemented
292#2093C2×C7311yescharacteristic
293#2092C2×C7311yescharacteristic
294#2085C2×C7311yescharacteristic, complemented
295#2083C2×C7311yescharacteristic, complemented
296#2073C2×C7311yescharacteristic
297#2071C2×C7311yescharacteristic
298#2059C2×C7311yescharacteristic, complemented
299#2057C2×C7311yescharacteristic, complemented
300#2025C2×C7311yescharacteristic
301#2023C2×C7311yescharacteristic
302#1840C2×C7311yescharacteristic, complemented
303C73#3284511yescharacteristic, direct product factor, Sylow
304C2×C4⋊Q8C22×C7311yescharacteristic
305C2×#125C22×C7311yescharacteristic
306C2×#107C22×C7311yescharacteristic
307C2×#107C22×C7311yescharacteristic
308C2×#107C22×C7311yescharacteristic
309C2×#106C22×C7311yescharacteristic
310C2×#102C22×C7311yescharacteristic
311C2×#102C22×C7311yescharacteristic
312C2×#102C22×C7311yescharacteristic
313C2×#102C22×C7311yescharacteristic
314#398—21no—
315#398—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#396—21no—
320#395—21no—
321#395—21no—
322#390C22×C7311yescharacteristic
323#390C22×C7311yescharacteristic
324#390C22×C7311yescharacteristic
325#389C22×C7311yescharacteristic
326#389C22×C7311yescharacteristic
327#389C22×C7311yescharacteristic
328#384C22×C7311yescharacteristic
329#384C22×C7311yescharacteristic
330#382C22×C7311yescharacteristic
331#382C22×C7311yescharacteristic
332#376C22×C7311yescharacteristic
333#340C22×C7311yescharacteristic
334#340C22×C7311yescharacteristic
335#340C22×C7311yescharacteristic
336#340C22×C7311yescharacteristic
337#340C22×C7311yescharacteristic
338#340C22×C7311yescharacteristic
339#340C22×C7311yescharacteristic
340#340C22×C7311yescharacteristic
341#336C22×C7311yescharacteristic
342#336C22×C7311yescharacteristic
343#336C22×C7311yescharacteristic
344#336C22×C7311yescharacteristic
345#336C22×C7311yescharacteristic
346#336C22×C7311yescharacteristic
347C22×Q8—21no—
348C22×D4C23×C7311yescharacteristic
349C22×C8C23×C7311yescharacteristic
350C22×C8C23×C7311yescharacteristic
351C22×C8C23×C7311yescharacteristic
352C22×C8C23×C7311yescharacteristic
353C4⋊Q8—41no—
354C4⋊Q8—41no—
355#125—41no—
356#125—41no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4C23×C7311yescharacteristic
368C2×C4⋊C4C23×C7311yescharacteristic
369C2×C4⋊C4C23×C7311yescharacteristic
370C2×C4⋊C4C23×C7311yescharacteristic
371C2×C4⋊C4C23×C7311yescharacteristic
372C2×C4⋊C4C23×C7311yescharacteristic
373C2×C4⋊C4C23×C7311yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C42C23×C7311yescharacteristic
381C2×C42C23×C7311yescharacteristic
382C2×C42C23×C7311yescharacteristic
383#107—41no—
384#107—41no—
385#107—41no—
386#106—41no—
387#102—41no—
388#102—41no—
389#102—41no—
390#102—41no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95D4×C7311yescharacteristic
399#95D4×C7311yescharacteristic
400#95D4×C7311yescharacteristic
401#95D4×C7311yescharacteristic
402C24—21no—
403C2×Q8—42no—
404C2×Q8—81no—
405C2×Q8—81no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4C2×D4×C7311yescharacteristic
420C22×C4C2×D4×C7311yescharacteristic
421C22×C4C2×D4×C7311yescharacteristic
422C22×C4C2×D4×C7311yescharacteristic
423C22×C4C2×D4×C7311yescharacteristic
424C22×C4C2×D4×C7311yescharacteristic
425C22×C4C24×C7311yescharacteristic
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—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—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—42no—
453C4⋊C4—42no—
454C4⋊C4—42no—
455C4⋊C4—81no—
456C4⋊C4—81no—
457C4⋊C4—81no—
458C4⋊C4—81no—
459C4⋊C4—81no—
460C4⋊C4—81no—
461C4⋊C4—81no—
462C22⋊C4—81no—
463C22⋊C4—81no—
464C22⋊C4—81no—
465C22⋊C4—81no—
466C22⋊C4—81no—
467C22⋊C4—81no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—21no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23C22×D4×C7311yescharacteristic
482Q8—84no—
483D4—41no—
484D4—41no—
485D4—41no—
486D4—41no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
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—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
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—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4H(5,𝔽2)×C7311yescharacteristic
527C2×C4H(5,𝔽2)×C7311yescharacteristic
528C2×C42−1+4×C7311yescharacteristic
529C2×C42−1+4×C7311yescharacteristic
530C2×C42−1+4×C7311yescharacteristic
531C2×C42−1+4×C7311yescharacteristic
532C8—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22#535×C7311yescharacteristic
544C22#536×C7311yescharacteristic
545C22#536×C7311yescharacteristic
546C22#576×C7311yescharacteristic
547C22#576×C7311yescharacteristic
548C22#577×C7311yescharacteristic
549C22#578×C7311yescharacteristic
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4#563×C7311yescharacteristic
564C4#563×C7311yescharacteristic
565C4#563×C7311yescharacteristic
566C4#563×C7311yescharacteristic
567C2—161no—
568C2C73×#282111yescharacteristic
569C2C73×#322011yescharacteristic
570C2C73×#322511yescharacteristic
571C2C73×#324111yescharacteristic
572C2C73×#324111yescharacteristic
573C2C73×#324311yescharacteristic
574C2C73×#324311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D4×C73C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ #376×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#2660C2semidirect
3. C73×#2101C2semidirect
4. C73×#2100C2semidirect
7. C73×#2085C2semidirect
8. C73×#2083C2semidirect
11. C73×#2059C2semidirect
12. C73×#2057C2semidirect
15. C73×#1840C2semidirect
279. #32845C73direct (N × H)
288. #2660C2×C73semidirect
290. #2101C2×C73semidirect
291. #2100C2×C73semidirect
294. #2085C2×C73semidirect
295. #2083C2×C73semidirect
298. #2059C2×C73semidirect
299. #2057C2×C73semidirect
302. #1840C2×C73semidirect
303. C73#32845direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#26602
C73×#26442
C73×#21012
C73×#21002
C73×#20932
C73×#20922
C73×#20852
C73×#20832
C73×#20732
C73×#20712
C73×#20592
C73×#20572
C73×#20252
C73×#20232
C73×#18402
#3284573