Finite Group Databasebeta

← C73×#25997 #32935401

Subgroups — C73×#25997 #32935401

Order 18688.

694 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2441C211yesmaximal, characteristic
2C73×#2347C211yesmaximal, characteristic
3C73×#2100C211yesmaximal, characteristic, complemented
4C73×#2087C211yesmaximal, characteristic, complemented
5C73×#2086C211yesmaximal, characteristic, complemented
6C73×#2059C211yesmaximal, characteristic, complemented
7C73×#1989C211yesmaximal, characteristic, complemented
8C73×#1947C211yesmaximal, characteristic, complemented
9C73×#1919C211yesmaximal, characteristic, complemented
10C73×#1918C211yesmaximal, characteristic, complemented
11C73×#1854C211yesmaximal, characteristic
12C73×#1850C211yesmaximal, characteristic
13C73×#1825C211yesmaximal, characteristic
14C73×#1808C211yesmaximal, characteristic
15C73×#1735C211yesmaximal, characteristic
16C23×C8×C73C2211yescharacteristic
17C2×#125×C73C2211yescharacteristic
18C2×#117×C73C2211yescharacteristic
19C2×#117×C73C2211yescharacteristic
20C2×#107×C73C2211yescharacteristic
21C2×#107×C73C2211yescharacteristic
22C2×#107×C73C2211yescharacteristic
23C2×#106×C73C2211yescharacteristic
24C2×C4⋊C8×C73C2211yescharacteristic
25C2×C4⋊C8×C73C2211yescharacteristic
26C2×C22⋊C8×C73C2211yescharacteristic
27#399×C73—21no—
28#396×C73—21no—
29#389×C73—21no—
30#389×C73C2211yescharacteristic
31#389×C73C2211yescharacteristic
32#389×C73C2211yescharacteristic
33#389×C73C2211yescharacteristic
34#388×C73—21no—
35#388×C73—21no—
36#387×C73—21no—
37#384×C73C2211yescharacteristic
38#383×C73—21no—
39#380×C73C2211yescharacteristic
40#380×C73C2211yescharacteristic
41C4×C4⋊C4×C73—21no—
42C4×C4⋊C4×C73C2211yescharacteristic
43C4×C4⋊C4×C73C2211yescharacteristic
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×C73C2311yescharacteristic
60C22×C8×C73—22no—
61C22×C8×C73—22no—
62C22×C8×C73—41no—
63C22×C8×C73C2311yescharacteristic
64C22×C8×C73C2311yescharacteristic
65C22×C8×C73C2311yescharacteristic
66C22×C8×C73C2311yescharacteristic
67#125×C73—22no—
68#125×C73—41no—
69#117×C73—22no—
70#117×C73—22no—
71#117×C73—41no—
72#117×C73Q814yes—
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×C73—21no—
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×C4⋊C4×C73C2311yescharacteristic
88C2×C4⋊C4×C73C2311yescharacteristic
89C2×C22⋊C4×C73—21no—
90C2×C22⋊C4×C73—21no—
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×C73—21no—
98C2×C42×C73—21no—
99C2×C42×C73C2311yescharacteristic
100C2×C42×C73C2311yescharacteristic
101#107×C73—22no—
102#107×C73—41no—
103#107×C73—41no—
104#106×C73—22no—
105C4⋊C8×C73—22no—
106C4⋊C8×C73—41no—
107C22⋊C8×C73—22no—
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—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×Q812yes—
137C22×C4×C73#4112yes—
138C22×C4×C73C2411yescharacteristic
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—
150C2×C8×C73—44no—
151C2×C8×C73#4112yes—
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—42no—
166C4⋊C4×C73—42no—
167C4⋊C4×C73—42no—
168C4⋊C4×C73—42no—
169C4⋊C4×C73—42no—
170C4⋊C4×C73—42no—
171C4⋊C4×C73—81no—
172C4⋊C4×C73—81no—
173C4⋊C4×C73C2×Q812yes—
174C4⋊C4×C73C2×Q812yes—
175C4⋊C4×C73#4112yes—
176C22⋊C4×C73—24no—
177C22⋊C4×C73—22no—
178C22⋊C4×C73—41no—
179C22⋊C4×C73—42no—
180C22⋊C4×C73—81no—
181C22⋊C4×C73—81no—
182C42×C73—24no—
183C42×C73—21no—
184C42×C73—21no—
185C42×C73—21no—
186C42×C73—21no—
187C42×C73—42no—
188C42×C73—81no—
189C42×C73—81no—
190C23×C73—21no—
191C23×C73—21no—
192C23×C73—21no—
193C23×C73—21no—
194C23×C73—21no—
195C23×C73—21no—
196C23×C73C22⋊Q812yes—
197C23×C73C22×D411yescharacteristic
198C2×C4×C73—21no—
199C2×C4×C73—21no—
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—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×C73C22⋊Q812yes—
240C2×C4×C73#13512yes—
241C2×C4×C73C22×Q811yescharacteristic
242C2×C4×C73C2×#4111yescharacteristic
243C2×C4×C73C2×#4111yescharacteristic
244C2×C4×C73C2×#4111yescharacteristic
245C2×C4×C73H(5,𝔽2)11yescharacteristic
246C2×C4×C732−1+411yescharacteristic
247C8×C73—22no—
248C8×C73—41no—
249C8×C73—41no—
250C8×C73—41no—
251C22×C73—22no—
252C22×C73—22no—
253C22×C73—22no—
254C22×C73—41no—
255C22×C73—41no—
256C22×C73—41no—
257C22×C73—41no—
258C22×C73C2×C22⋊Q811yescharacteristic
259C22×C73#54611yescharacteristic
260C22×C73#54711yescharacteristic
261C22×C73C2×#13511yescharacteristic
262C22×C73#57511yescharacteristic
263C22×C73#57611yescharacteristic
264C22×C73#57811yescharacteristic
265C4×C73—22no—
266C4×C73—22no—
267C4×C73—42no—
268C4×C73—42no—
269C4×C73—41no—
270C4×C73—41no—
271C4×C73—42no—
272C4×C73—41no—
273C4×C73—81no—
274C4×C73—81no—
275C4×C73—81no—
276C4×C73—81no—
277C4×C73—81no—
278C4×C73#53311yescharacteristic
279C4×C73#54411yescharacteristic
280C4×C73#55111yescharacteristic
281C4×C73#55211yescharacteristic
282#25997C7311yesmaximal, characteristic, direct product factor, Sylow
283C2×C73—42no—
284C2×C73#243811yescharacteristic
285C2×C73#307611yescharacteristic
286C2×C73#308311yescharacteristic
287C2×C73#330211yescharacteristic
288C2×C73#330911yescharacteristic
289C2×C73#333911yescharacteristic
290C2×C73#334911yescharacteristic
291#2441C2×C7311yescharacteristic
292#2347C2×C7311yescharacteristic
293#2100C2×C7311yescharacteristic, complemented
294#2087C2×C7311yescharacteristic, complemented
295#2086C2×C7311yescharacteristic, complemented
296#2059C2×C7311yescharacteristic, complemented
297#1989C2×C7311yescharacteristic, complemented
298#1947C2×C7311yescharacteristic, complemented
299#1919C2×C7311yescharacteristic, complemented
300#1918C2×C7311yescharacteristic, complemented
301#1854C2×C7311yescharacteristic
302#1850C2×C7311yescharacteristic
303#1825C2×C7311yescharacteristic
304#1808C2×C7311yescharacteristic
305#1735C2×C7311yescharacteristic
306C73#2599711yescharacteristic, direct product factor, Sylow
307C23×C8C22×C7311yescharacteristic
308C2×#125C22×C7311yescharacteristic
309C2×#117C22×C7311yescharacteristic
310C2×#117C22×C7311yescharacteristic
311C2×#107C22×C7311yescharacteristic
312C2×#107C22×C7311yescharacteristic
313C2×#107C22×C7311yescharacteristic
314C2×#106C22×C7311yescharacteristic
315C2×C4⋊C8C22×C7311yescharacteristic
316C2×C4⋊C8C22×C7311yescharacteristic
317C2×C22⋊C8C22×C7311yescharacteristic
318#399—21no—
319#396—21no—
320#389—21no—
321#389C22×C7311yescharacteristic
322#389C22×C7311yescharacteristic
323#389C22×C7311yescharacteristic
324#389C22×C7311yescharacteristic
325#388—21no—
326#388—21no—
327#387—21no—
328#384C22×C7311yescharacteristic
329#383—21no—
330#380C22×C7311yescharacteristic
331#380C22×C7311yescharacteristic
332C4×C4⋊C4—21no—
333C4×C4⋊C4C22×C7311yescharacteristic
334C4×C4⋊C4C22×C7311yescharacteristic
335C4×C22⋊C4C22×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#340C22×C7311yescharacteristic
345#340C22×C7311yescharacteristic
346#340C22×C7311yescharacteristic
347#340C22×C7311yescharacteristic
348#336C22×C7311yescharacteristic
349#336C22×C7311yescharacteristic
350C23×C4C23×C7311yescharacteristic
351C22×C8—22no—
352C22×C8—22no—
353C22×C8—41no—
354C22×C8C23×C7311yescharacteristic
355C22×C8C23×C7311yescharacteristic
356C22×C8C23×C7311yescharacteristic
357C22×C8C23×C7311yescharacteristic
358#125—22no—
359#125—41no—
360#117—22no—
361#117—22no—
362#117—41no—
363#117Q8×C7314yes—
364C2×C4⋊C4—21no—
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⋊C4—21no—
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×C4⋊C4C23×C7311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4D4×C7311yescharacteristic
385C2×C22⋊C4D4×C7311yescharacteristic
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42C23×C7311yescharacteristic
391C2×C42C23×C7311yescharacteristic
392#107—22no—
393#107—41no—
394#107—41no—
395#106—22no—
396C4⋊C8—22no—
397C4⋊C8—41no—
398C22⋊C8—22no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95D4×C7311yescharacteristic
408#95D4×C7311yescharacteristic
409C24C2×D4×C7311yescharacteristic
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×C4—21no—
422C22×C4C2×D4×C7311yescharacteristic
423C22×C4C2×D4×C7311yescharacteristic
424C22×C4C2×D4×C7311yescharacteristic
425C22×C4C2×D4×C7311yescharacteristic
426C22×C4C2×D4×C7311yescharacteristic
427C22×C4C2×Q8×C7312yes—
428C22×C4#41×C7312yes—
429C22×C4C24×C7311yescharacteristic
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—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—44no—
442C2×C8#41×C7312yes—
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—21no—
456C4⋊C4—42no—
457C4⋊C4—42no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C4⋊C4—81no—
463C4⋊C4—81no—
464C4⋊C4C2×Q8×C7312yes—
465C4⋊C4C2×Q8×C7312yes—
466C4⋊C4#41×C7312yes—
467C22⋊C4—24no—
468C22⋊C4—22no—
469C22⋊C4—41no—
470C22⋊C4—42no—
471C22⋊C4—81no—
472C22⋊C4—81no—
473C42—24no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—42no—
479C42—81no—
480C42—81no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23C22⋊Q8×C7312yes—
488C23C22×D4×C7311yescharacteristic
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
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×C4—41no—
529C2×C4—41no—
530C2×C4C22⋊Q8×C7312yes—
531C2×C4#135×C7312yes—
532C2×C4C22×Q8×C7311yescharacteristic
533C2×C4C2×#41×C7311yescharacteristic
534C2×C4C2×#41×C7311yescharacteristic
535C2×C4C2×#41×C7311yescharacteristic
536C2×C4H(5,𝔽2)×C7311yescharacteristic
537C2×C42−1+4×C7311yescharacteristic
538C8—22no—
539C8—41no—
540C8—41no—
541C8—41no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22C2×C22⋊Q8×C7311yescharacteristic
550C22#546×C7311yescharacteristic
551C22#547×C7311yescharacteristic
552C22C2×#135×C7311yescharacteristic
553C22#575×C7311yescharacteristic
554C22#576×C7311yescharacteristic
555C22#578×C7311yescharacteristic
556C4—22no—
557C4—22no—
558C4—41no—
559C4—42no—
560C4—41no—
561C4—42no—
562C4—42no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4—81no—
569C4#533×C7311yescharacteristic
570C4#544×C7311yescharacteristic
571C4#551×C7311yescharacteristic
572C4#552×C7311yescharacteristic
573C2—42no—
574C2C73×#243811yescharacteristic
575C2C73×#307611yescharacteristic
576C2C73×#308311yescharacteristic
577C2C73×#330211yescharacteristic
578C2C73×#330911yescharacteristic
579C2C73×#333911yescharacteristic
580C2C73×#334911yescharacteristic
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×#2100C2semidirect
4. C73×#2087C2semidirect
5. C73×#2086C2semidirect
6. C73×#2059C2semidirect
7. C73×#1989C2semidirect
8. C73×#1947C2semidirect
9. C73×#1919C2semidirect
10. C73×#1918C2semidirect
282. #25997C73direct (N × H)
293. #2100C2×C73semidirect
294. #2087C2×C73semidirect
295. #2086C2×C73semidirect
296. #2059C2×C73semidirect
297. #1989C2×C73semidirect
298. #1947C2×C73semidirect
299. #1919C2×C73semidirect
300. #1918C2×C73semidirect
306. C73#25997direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#24412
C73×#23472
C73×#21002
C73×#20872
C73×#20862
C73×#20592
C73×#19892
C73×#19472
C73×#19192
C73×#19182
C73×#18542
C73×#18502
C73×#18252
C73×#18082
C73×#17352
#2599773