Finite Group Databasebeta

← C73×#32793 #32942197

Subgroups — C73×#32793 #32942197

Order 18688.

592 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2629C211yesmaximal, characteristic
2C73×#2628C211yesmaximal, characteristic
3C73×#2101C211yesmaximal, characteristic, complemented
4C73×#2101C211yesmaximal, characteristic, complemented
5C73×#2100C211yesmaximal, characteristic, complemented
6C73×#2099C211yesmaximal, characteristic, complemented
7C73×#2077C211yesmaximal, characteristic
8C73×#2077C211yesmaximal, characteristic
9C73×#2076C211yesmaximal, characteristic
10C73×#2075C211yesmaximal, characteristic
11C73×#2059C211yesmaximal, characteristic, complemented
12C73×#2059C211yesmaximal, characteristic, complemented
13C73×#2058C211yesmaximal, characteristic, complemented
14C73×#2057C211yesmaximal, characteristic, complemented
15C73×#1818C211yesmaximal, characteristic
16C2×C4⋊Q8×C73C2211yescharacteristic
17C2×#125×C73C2211yescharacteristic
18C2×#117×C73C2211yescharacteristic
19C2×#107×C73C2211yescharacteristic
20C2×#107×C73C2211yescharacteristic
21C2×#106×C73C2211yescharacteristic
22C2×#106×C73C2211yescharacteristic
23C2×C22⋊C8×C73C2211yescharacteristic
24C2×C22⋊C8×C73C2211yescharacteristic
25#400×C73—21no—
26#399×C73—21no—
27#398×C73—21no—
28#398×C73—21no—
29#396×C73—21no—
30#396×C73—21no—
31#395×C73—21no—
32#393×C73—21no—
33#389×C73C2211yescharacteristic
34#389×C73C2211yescharacteristic
35#389×C73C2211yescharacteristic
36#389×C73C2211yescharacteristic
37#384×C73C2211yescharacteristic
38#382×C73C2211yescharacteristic
39#380×C73C2211yescharacteristic
40#380×C73C2211yescharacteristic
41#380×C73C2211yescharacteristic
42#380×C73C2211yescharacteristic
43#340×C73C2211yescharacteristic
44#340×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×C73—21no—
60C23×C4×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—
69#117×C73—41no—
70#117×C73—41no—
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×C73—21no—
80C2×C4⋊C4×C73D411yescharacteristic
81C2×C4⋊C4×C73D411yescharacteristic
82C2×C4⋊C4×C73C2311yescharacteristic
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×C22⋊C4×C73—21no—
91C2×C22⋊C4×C73—21no—
92C2×C22⋊C4×C73—21no—
93C2×C22⋊C4×C73—21no—
94C2×C22⋊C4×C73D411yescharacteristic
95C2×C22⋊C4×C73D411yescharacteristic
96C2×C42×C73C2311yescharacteristic
97C2×C42×C73C2311yescharacteristic
98#107×C73—41no—
99#107×C73—41no—
100#106×C73—41no—
101#106×C73—41no—
102C22⋊C8×C73—41no—
103C22⋊C8×C73—41no—
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×C73—21no—
113#95×C73—21no—
114C24×C73C2×D411yescharacteristic
115C2×Q8×C73—42no—
116C2×Q8×C73—81no—
117C2×Q8×C73—81no—
118C22×C4×C73—21no—
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—21no—
127C22×C4×C73—21no—
128C22×C4×C73—21no—
129C22×C4×C73—21no—
130C22×C4×C73—21no—
131C22×C4×C73—21no—
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—21no—
165C4⋊C4×C73—21no—
166C4⋊C4×C73—41no—
167C4⋊C4×C73—41no—
168C4⋊C4×C73—42no—
169C4⋊C4×C73—42no—
170C4⋊C4×C73—42no—
171C4⋊C4×C73—81no—
172C4⋊C4×C73—81no—
173C4⋊C4×C73—81no—
174C4⋊C4×C73—81no—
175C4⋊C4×C73—81no—
176C4⋊C4×C73—81no—
177C22⋊C4×C73—41no—
178C22⋊C4×C73—41no—
179C22⋊C4×C73—81no—
180C22⋊C4×C73—81no—
181C22⋊C4×C73—81no—
182C22⋊C4×C73—81no—
183C42×C73—21no—
184C42×C73—21no—
185C42×C73—21no—
186C42×C73—21no—
187C23×C73—21no—
188C23×C73—21no—
189C23×C73—21no—
190C23×C73—21no—
191C23×C73—21no—
192C23×C73—21no—
193C23×C73—21no—
194C23×C73C22×D411yescharacteristic
195Q8×C73—84no—
196C2×C4×C73—21no—
197C2×C4×C73—21no—
198C2×C4×C73—21no—
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—41no—
212C2×C4×C73—41no—
213C2×C4×C73—41no—
214C2×C4×C73—41no—
215C2×C4×C73—41no—
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—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73H(5,𝔽2)11yescharacteristic
240C2×C4×C73H(5,𝔽2)11yescharacteristic
241C2×C4×C732−1+411yescharacteristic
242C2×C4×C732−1+411yescharacteristic
243C2×C4×C732−1+411yescharacteristic
244C2×C4×C732−1+411yescharacteristic
245C8×C73—41no—
246C8×C73—41no—
247C8×C73—41no—
248C8×C73—41no—
249C22×C73—41no—
250C22×C73—41no—
251C22×C73—41no—
252C22×C73—41no—
253C22×C73—41no—
254C22×C73—41no—
255C22×C73—41no—
256C22×C73#53411yescharacteristic
257C22×C73#53611yescharacteristic
258C22×C73#53611yescharacteristic
259C22×C73#57611yescharacteristic
260C22×C73#57711yescharacteristic
261C22×C73#57711yescharacteristic
262C22×C73#57811yescharacteristic
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—81no—
276C4×C73#56311yescharacteristic
277C4×C73#56311yescharacteristic
278C4×C73#56311yescharacteristic
279C4×C73#56311yescharacteristic
280#32793C7311yesmaximal, characteristic, direct product factor, Sylow
281C2×C73—81no—
282C2×C73#281711yescharacteristic
283C2×C73#319811yescharacteristic
284C2×C73#320111yescharacteristic
285C2×C73#324111yescharacteristic
286C2×C73#324211yescharacteristic
287C2×C73#324311yescharacteristic
288C2×C73#324411yescharacteristic
289#2629C2×C7311yescharacteristic
290#2628C2×C7311yescharacteristic
291#2101C2×C7311yescharacteristic, complemented
292#2101C2×C7311yescharacteristic, complemented
293#2100C2×C7311yescharacteristic, complemented
294#2099C2×C7311yescharacteristic, complemented
295#2077C2×C7311yescharacteristic
296#2077C2×C7311yescharacteristic
297#2076C2×C7311yescharacteristic
298#2075C2×C7311yescharacteristic
299#2059C2×C7311yescharacteristic, complemented
300#2059C2×C7311yescharacteristic, complemented
301#2058C2×C7311yescharacteristic, complemented
302#2057C2×C7311yescharacteristic, complemented
303#1818C2×C7311yescharacteristic
304C73#3279311yescharacteristic, direct product factor, Sylow
305C2×C4⋊Q8C22×C7311yescharacteristic
306C2×#125C22×C7311yescharacteristic
307C2×#117C22×C7311yescharacteristic
308C2×#107C22×C7311yescharacteristic
309C2×#107C22×C7311yescharacteristic
310C2×#106C22×C7311yescharacteristic
311C2×#106C22×C7311yescharacteristic
312C2×C22⋊C8C22×C7311yescharacteristic
313C2×C22⋊C8C22×C7311yescharacteristic
314#400—21no—
315#399—21no—
316#398—21no—
317#398—21no—
318#396—21no—
319#396—21no—
320#395—21no—
321#393—21no—
322#389C22×C7311yescharacteristic
323#389C22×C7311yescharacteristic
324#389C22×C7311yescharacteristic
325#389C22×C7311yescharacteristic
326#384C22×C7311yescharacteristic
327#382C22×C7311yescharacteristic
328#380C22×C7311yescharacteristic
329#380C22×C7311yescharacteristic
330#380C22×C7311yescharacteristic
331#380C22×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#340C22×C7311yescharacteristic
341#340C22×C7311yescharacteristic
342#340C22×C7311yescharacteristic
343#340C22×C7311yescharacteristic
344#336C22×C7311yescharacteristic
345#336C22×C7311yescharacteristic
346#336C22×C7311yescharacteristic
347#336C22×C7311yescharacteristic
348C22×Q8—21no—
349C23×C4C23×C7311yescharacteristic
350C22×C8C23×C7311yescharacteristic
351C22×C8C23×C7311yescharacteristic
352C22×C8C23×C7311yescharacteristic
353C22×C8C23×C7311yescharacteristic
354C4⋊Q8—41no—
355C4⋊Q8—41no—
356#125—41no—
357#125—41no—
358#117—41no—
359#117—41no—
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⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4D4×C7311yescharacteristic
370C2×C4⋊C4D4×C7311yescharacteristic
371C2×C4⋊C4C23×C7311yescharacteristic
372C2×C4⋊C4C23×C7311yescharacteristic
373C2×C4⋊C4C23×C7311yescharacteristic
374C2×C4⋊C4C23×C7311yescharacteristic
375C2×C4⋊C4C23×C7311yescharacteristic
376C2×C4⋊C4C23×C7311yescharacteristic
377C2×C4⋊C4C23×C7311yescharacteristic
378C2×C4⋊C4C23×C7311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4D4×C7311yescharacteristic
384C2×C22⋊C4D4×C7311yescharacteristic
385C2×C42C23×C7311yescharacteristic
386C2×C42C23×C7311yescharacteristic
387#107—41no—
388#107—41no—
389#106—41no—
390#106—41no—
391C22⋊C8—41no—
392C22⋊C8—41no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403C24C2×D4×C7311yescharacteristic
404C2×Q8—42no—
405C2×Q8—81no—
406C2×Q8—81no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4C2×D4×C7311yescharacteristic
422C22×C4C2×D4×C7311yescharacteristic
423C22×C4C2×D4×C7311yescharacteristic
424C22×C4C2×D4×C7311yescharacteristic
425C22×C4C2×D4×C7311yescharacteristic
426C22×C4C24×C7311yescharacteristic
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—
438C2×C8—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—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—81no—
461C4⋊C4—81no—
462C4⋊C4—81no—
463C4⋊C4—81no—
464C4⋊C4—81no—
465C4⋊C4—81no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—81no—
469C22⋊C4—81no—
470C22⋊C4—81no—
471C22⋊C4—81no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23C22×D4×C7311yescharacteristic
484Q8—84no—
485C2×C4—21no—
486C2×C4—21no—
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—41no—
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—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×C4H(5,𝔽2)×C7311yescharacteristic
529C2×C4H(5,𝔽2)×C7311yescharacteristic
530C2×C42−1+4×C7311yescharacteristic
531C2×C42−1+4×C7311yescharacteristic
532C2×C42−1+4×C7311yescharacteristic
533C2×C42−1+4×C7311yescharacteristic
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22#534×C7311yescharacteristic
546C22#536×C7311yescharacteristic
547C22#536×C7311yescharacteristic
548C22#576×C7311yescharacteristic
549C22#577×C7311yescharacteristic
550C22#577×C7311yescharacteristic
551C22#578×C7311yescharacteristic
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4#563×C7311yescharacteristic
566C4#563×C7311yescharacteristic
567C4#563×C7311yescharacteristic
568C4#563×C7311yescharacteristic
569C2—81no—
570C2C73×#281711yescharacteristic
571C2C73×#319811yescharacteristic
572C2C73×#320111yescharacteristic
573C2C73×#324111yescharacteristic
574C2C73×#324211yescharacteristic
575C2C73×#324311yescharacteristic
576C2C73×#324411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC24×C73C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C2×#117×C73 ◁ G

Complements

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

NH ≅ G/Ntype
3. C73×#2101C2semidirect
4. C73×#2101C2semidirect
5. C73×#2100C2semidirect
6. C73×#2099C2semidirect
11. C73×#2059C2semidirect
12. C73×#2059C2semidirect
13. C73×#2058C2semidirect
14. C73×#2057C2semidirect
280. #32793C73direct (N × H)
291. #2101C2×C73semidirect
292. #2101C2×C73semidirect
293. #2100C2×C73semidirect
294. #2099C2×C73semidirect
299. #2059C2×C73semidirect
300. #2059C2×C73semidirect
301. #2058C2×C73semidirect
302. #2057C2×C73semidirect
304. C73#32793direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#26292
C73×#26282
C73×#21012
C73×#21002
C73×#20992
C73×#20772
C73×#20762
C73×#20752
C73×#20592
C73×#20582
C73×#20572
C73×#18182
#3279373