Finite Group Databasebeta

← C73×#26833 #32936237

Subgroups — C73×#26833 #32936237

Order 18688.

798 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#488×C73C211yesmaximal, characteristic
2C2×#440×C73C211yesmaximal, characteristic
3C73×#2453C211yesmaximal, characteristic, complemented
4C73×#2447C211yesmaximal, characteristic
5C73×#2068C211yesmaximal, characteristic, complemented
6C73×#2059C211yesmaximal, characteristic, complemented
7C73×#2055C211yesmaximal, characteristic
8C73×#2015C211yesmaximal, characteristic
9C73×#1971C211yesmaximal, characteristic, complemented
10C73×#1936C211yesmaximal, characteristic
11C73×#1935C211yesmaximal, characteristic, complemented
12C73×#1933C211yesmaximal, characteristic, complemented
13C73×#1878C211yesmaximal, characteristic, complemented
14C73×#1864C211yesmaximal, characteristic
15C73×#1771C211yesmaximal, characteristic, complemented
16C22×Q16×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C2×#125×C73C2211yescharacteristic
19C2×#124×C73C2211yescharacteristic
20C2×C4×Q8×C73C2211yescharacteristic
21C2×C4×D4×C73C2211yescharacteristic
22#488×C73—24no—
23#440×C73—24no—
24C2×#107×C73C2211yescharacteristic
25C2×#106×C73C2211yescharacteristic
26C2×C4⋊C8×C73C2211yescharacteristic
27C2×#103×C73C2211yescharacteristic
28C2×#103×C73C2211yescharacteristic
29C2×#103×C73C2211yescharacteristic
30C2×#103×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#97×C73C2211yescharacteristic
36C2×#97×C73C2211yescharacteristic
37C2×C4×C8×C73C2211yescharacteristic
38#400×C73—21no—
39#398×C73—21no—
40#397×C73—21no—
41#397×C73—21no—
42#391×C73C2211yescharacteristic
43#391×C73C2211yescharacteristic
44#391×C73C2211yescharacteristic
45#391×C73C2211yescharacteristic
46#390×C73C2211yescharacteristic
47#389×C73—21no—
48#389×C73C2211yescharacteristic
49#389×C73C2211yescharacteristic
50#389×C73C2211yescharacteristic
51#387×C73—21no—
52#385×C73—21no—
53#381×C73—21no—
54C4×C4⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73C2311yescharacteristic
62C22×Q8×C73C2311yescharacteristic
63C22×D4×C73C2311yescharacteristic
64C23×C4×C73—21no—
65C2×Q16×C73—22no—
66C2×Q16×C73—22no—
67C2×Q16×C73—41no—
68C2×SD16×C73—22no—
69C2×SD16×C73—22no—
70C2×SD16×C73—22no—
71C22×C8×C73C2311yescharacteristic
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C22×C8×C73C2311yescharacteristic
75#125×C73—22no—
76#125×C73—41no—
77#124×C73—22no—
78#124×C73—41no—
79C4×Q8×C73—22no—
80C4×Q8×C73—41no—
81C4×D4×C73—22no—
82C4×D4×C73—41no—
83C2×C4⋊C4×C73—21no—
84C2×C4⋊C4×C73—21no—
85C2×C4⋊C4×C73—21no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73D411yescharacteristic
90C2×C4⋊C4×C73D411yescharacteristic
91C2×C4⋊C4×C73C2311yescharacteristic
92C2×C4⋊C4×C73C2311yescharacteristic
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73C2311yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C22⋊C4×C73—21no—
97C2×C22⋊C4×C73—21no—
98C2×C22⋊C4×C73—21no—
99C2×C22⋊C4×C73—21no—
100C2×C22⋊C4×C73—21no—
101C2×C42×C73—21no—
102C2×C42×C73C2311yescharacteristic
103C2×C42×C73C2311yescharacteristic
104C2×C42×C73C2311yescharacteristic
105#107×C73—22no—
106#106×C73—41no—
107C4⋊C8×C73—22no—
108#103×C73—22no—
109#103×C73—22no—
110#103×C73—22no—
111#103×C73—22no—
112#103×C73—22no—
113#102×C73—22no—
114#102×C73—22no—
115#102×C73D414yes—
116#97×C73—22no—
117#97×C73—22no—
118C4×C8×C73—22no—
119#95×C73—21no—
120#95×C73—21no—
121#95×C73—21no—
122#95×C73—21no—
123#95×C73—21no—
124#95×C73—21no—
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73—21no—
130#95×C73D411yescharacteristic
131#95×C73D411yescharacteristic
132C24×C73—21no—
133C2×Q8×C73—21no—
134C2×Q8×C73—21no—
135C2×Q8×C73—21no—
136C2×Q8×C73—21no—
137C2×Q8×C73—21no—
138C2×Q8×C73—21no—
139C2×Q8×C73—21no—
140C2×Q8×C73—21no—
141C2×Q8×C73—21no—
142C2×Q8×C73—21no—
143C2×Q8×C73—21no—
144C2×Q8×C73#4112yes—
145C2×D4×C73—21no—
146C2×D4×C73—21no—
147C2×D4×C73—21no—
148C2×D4×C73—21no—
149C2×D4×C73—21no—
150C2×D4×C73C2×D412yes—
151C22×C4×C73—21no—
152C22×C4×C73—21no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—42no—
159C22×C4×C73—42no—
160C22×C4×C73—81no—
161C22×C4×C73C2×D411yescharacteristic
162C22×C4×C73C2×D411yescharacteristic
163C22×C4×C73C2×D411yescharacteristic
164C22×C4×C73C2×D411yescharacteristic
165C22×C4×C73C2×D411yescharacteristic
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73C2411yescharacteristic
168Q16×C73—44no—
169SD16×C73—28no—
170C2×C8×C73—21no—
171C2×C8×C73—21no—
172C2×C8×C73—21no—
173C2×C8×C73—21no—
174C2×C8×C73—21no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73C2×D412yes—
180C2×C8×C73#4112yes—
181C2×C8×C73#4112yes—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—41no—
192C4⋊C4×C73—41no—
193C4⋊C4×C73—42no—
194C4⋊C4×C73—42no—
195C4⋊C4×C73—42no—
196C4⋊C4×C73—42no—
197C4⋊C4×C73—42no—
198C4⋊C4×C73—81no—
199C4⋊C4×C73C2×D412yes—
200C22⋊C4×C73—42no—
201C22⋊C4×C73—42no—
202C22⋊C4×C73—42no—
203C22⋊C4×C73—42no—
204C22⋊C4×C73—81no—
205C42×C73—21no—
206C42×C73—21no—
207C42×C73—21no—
208C42×C73—21no—
209C42×C73—21no—
210C42×C73—21no—
211C42×C73—42no—
212C23×C73—22no—
213C23×C73—41no—
214C23×C73—41no—
215C23×C73—41no—
216C23×C73—41no—
217C23×C73—41no—
218C23×C73—41no—
219C23×C73C22×D411yescharacteristic
220Q8×C73—22no—
221Q8×C73—22no—
222Q8×C73—41no—
223Q8×C73—41no—
224Q8×C73—41no—
225Q8×C73—41no—
226Q8×C73—41no—
227Q8×C73—41no—
228D4×C73—22no—
229D4×C73—22no—
230D4×C73—41no—
231D4×C73—41no—
232C2×C4×C73—21no—
233C2×C4×C73—21no—
234C2×C4×C73—21no—
235C2×C4×C73—21no—
236C2×C4×C73—21no—
237C2×C4×C73—21no—
238C2×C4×C73—22no—
239C2×C4×C73—22no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—41no—
253C2×C4×C73—41no—
254C2×C4×C73—41no—
255C2×C4×C73—41no—
256C2×C4×C73—41no—
257C2×C4×C73—41no—
258C2×C4×C73—41no—
259C2×C4×C73—41no—
260C2×C4×C73—41no—
261C2×C4×C73—41no—
262C2×C4×C73—41no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—84no—
272C2×C4×C73C22×D411yescharacteristic
273C2×C4×C73C2×#4111yescharacteristic
274C2×C4×C73C2×#4111yescharacteristic
275C2×C4×C73C2×#4111yescharacteristic
276C2×C4×C73H(5,𝔽2)11yescharacteristic
277C2×C4×C732−1+411yescharacteristic
278C8×C73—22no—
279C8×C73—22no—
280C8×C73—22no—
281C8×C73—41no—
282C22×C73—42no—
283C22×C73—42no—
284C22×C73—42no—
285C22×C73—81no—
286C22×C73—81no—
287C22×C73—81no—
288C22×C73—81no—
289C22×C73#53211yescharacteristic
290C22×C73D4211yescharacteristic
291C22×C73#54811yescharacteristic
292C22×C73#57511yescharacteristic
293C22×C73#57511yescharacteristic
294C22×C73#57711yescharacteristic
295C22×C73#57811yescharacteristic
296C4×C73—41no—
297C4×C73—41no—
298C4×C73—42no—
299C4×C73—41no—
300C4×C73—41no—
301C4×C73—42no—
302C4×C73—41no—
303C4×C73—41no—
304C4×C73—81no—
305C4×C73—81no—
306C4×C73—81no—
307C4×C73—81no—
308C4×C73—81no—
309C4×C73#52511yescharacteristic
310C4×C73#54211yescharacteristic
311C4×C73#54711yescharacteristic
312C4×C73#55111yescharacteristic
313#26833C7311yesmaximal, characteristic, direct product factor, Sylow
314C2×C73—82no—
315C2×C73#246111yescharacteristic
316C2×C73#317811yescharacteristic
317C2×C73#318311yescharacteristic
318C2×C73#326711yescharacteristic
319C2×C73#326911yescharacteristic
320C2×C73#337111yescharacteristic
321C2×C73#337711yescharacteristic
322C2×#488C2×C7311yescharacteristic
323C2×#440C2×C7311yescharacteristic
324#2453C2×C7311yescharacteristic, complemented
325#2447C2×C7311yescharacteristic
326#2068C2×C7311yescharacteristic, complemented
327#2059C2×C7311yescharacteristic, complemented
328#2055C2×C7311yescharacteristic
329#2015C2×C7311yescharacteristic
330#1971C2×C7311yescharacteristic, complemented
331#1936C2×C7311yescharacteristic
332#1935C2×C7311yescharacteristic, complemented
333#1933C2×C7311yescharacteristic, complemented
334#1878C2×C7311yescharacteristic, complemented
335#1864C2×C7311yescharacteristic
336#1771C2×C7311yescharacteristic, complemented
337C73#2683311yescharacteristic, direct product factor, Sylow
338C22×Q16C22×C7311yescharacteristic
339C22×SD16C22×C7311yescharacteristic
340C2×#125C22×C7311yescharacteristic
341C2×#124C22×C7311yescharacteristic
342C2×C4×Q8C22×C7311yescharacteristic
343C2×C4×D4C22×C7311yescharacteristic
344#488—24no—
345#440—24no—
346C2×#107C22×C7311yescharacteristic
347C2×#106C22×C7311yescharacteristic
348C2×C4⋊C8C22×C7311yescharacteristic
349C2×#103C22×C7311yescharacteristic
350C2×#103C22×C7311yescharacteristic
351C2×#103C22×C7311yescharacteristic
352C2×#103C22×C7311yescharacteristic
353C2×#103C22×C7311yescharacteristic
354C2×#102C22×C7311yescharacteristic
355C2×#102C22×C7311yescharacteristic
356C2×#102C22×C7311yescharacteristic
357C2×#97C22×C7311yescharacteristic
358C2×#97C22×C7311yescharacteristic
359C2×C4×C8C22×C7311yescharacteristic
360#400—21no—
361#398—21no—
362#397—21no—
363#397—21no—
364#391C22×C7311yescharacteristic
365#391C22×C7311yescharacteristic
366#391C22×C7311yescharacteristic
367#391C22×C7311yescharacteristic
368#390C22×C7311yescharacteristic
369#389—21no—
370#389C22×C7311yescharacteristic
371#389C22×C7311yescharacteristic
372#389C22×C7311yescharacteristic
373#387—21no—
374#385—21no—
375#381—21no—
376C4×C4⋊C4C22×C7311yescharacteristic
377#340C22×C7311yescharacteristic
378#340C22×C7311yescharacteristic
379#340C22×C7311yescharacteristic
380#340C22×C7311yescharacteristic
381#336C22×C7311yescharacteristic
382#336C22×C7311yescharacteristic
383C22×Q8C23×C7311yescharacteristic
384C22×Q8C23×C7311yescharacteristic
385C22×D4C23×C7311yescharacteristic
386C23×C4—21no—
387C2×Q16—22no—
388C2×Q16—22no—
389C2×Q16—41no—
390C2×SD16—22no—
391C2×SD16—22no—
392C2×SD16—22no—
393C22×C8C23×C7311yescharacteristic
394C22×C8C23×C7311yescharacteristic
395C22×C8C23×C7311yescharacteristic
396C22×C8C23×C7311yescharacteristic
397#125—22no—
398#125—41no—
399#124—22no—
400#124—41no—
401C4×Q8—22no—
402C4×Q8—41no—
403C4×D4—22no—
404C4×D4—41no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4D4×C7311yescharacteristic
412C2×C4⋊C4D4×C7311yescharacteristic
413C2×C4⋊C4C23×C7311yescharacteristic
414C2×C4⋊C4C23×C7311yescharacteristic
415C2×C4⋊C4C23×C7311yescharacteristic
416C2×C4⋊C4C23×C7311yescharacteristic
417C2×C4⋊C4C23×C7311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C42—21no—
424C2×C42C23×C7311yescharacteristic
425C2×C42C23×C7311yescharacteristic
426C2×C42C23×C7311yescharacteristic
427#107—22no—
428#106—41no—
429C4⋊C8—22no—
430#103—22no—
431#103—22no—
432#103—22no—
433#103—22no—
434#103—22no—
435#102—22no—
436#102—22no—
437#102D4×C7314yes—
438#97—22no—
439#97—22no—
440C4×C8—22no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95D4×C7311yescharacteristic
453#95D4×C7311yescharacteristic
454C24—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8#41×C7312yes—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4C2×D4×C7312yes—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—81no—
483C22×C4C2×D4×C7311yescharacteristic
484C22×C4C2×D4×C7311yescharacteristic
485C22×C4C2×D4×C7311yescharacteristic
486C22×C4C2×D4×C7311yescharacteristic
487C22×C4C2×D4×C7311yescharacteristic
488C22×C4C2×D4×C7311yescharacteristic
489C22×C4C24×C7311yescharacteristic
490Q16—44no—
491SD16—28no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8C2×D4×C7312yes—
502C2×C8#41×C7312yes—
503C2×C8#41×C7312yes—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—42no—
516C4⋊C4—42no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—81no—
521C4⋊C4C2×D4×C7312yes—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—42no—
525C22⋊C4—42no—
526C22⋊C4—81no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—42no—
534C23—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23C22×D4×C7311yescharacteristic
542Q8—22no—
543Q8—22no—
544Q8—41no—
545Q8—41no—
546Q8—41no—
547Q8—41no—
548Q8—41no—
549Q8—41no—
550D4—22no—
551D4—22no—
552D4—41no—
553D4—41no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—84no—
594C2×C4C22×D4×C7311yescharacteristic
595C2×C4C2×#41×C7311yescharacteristic
596C2×C4C2×#41×C7311yescharacteristic
597C2×C4C2×#41×C7311yescharacteristic
598C2×C4H(5,𝔽2)×C7311yescharacteristic
599C2×C42−1+4×C7311yescharacteristic
600C8—22no—
601C8—22no—
602C8—22no—
603C8—41no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22#532×C7311yescharacteristic
612C22D42×C7311yescharacteristic
613C22#548×C7311yescharacteristic
614C22#575×C7311yescharacteristic
615C22#575×C7311yescharacteristic
616C22#577×C7311yescharacteristic
617C22#578×C7311yescharacteristic
618C4—42no—
619C4—41no—
620C4—41no—
621C4—42no—
622C4—41no—
623C4—41no—
624C4—41no—
625C4—41no—
626C4—81no—
627C4—81no—
628C4—81no—
629C4—81no—
630C4—81no—
631C4#525×C7311yescharacteristic
632C4#542×C7311yescharacteristic
633C4#547×C7311yescharacteristic
634C4#551×C7311yescharacteristic
635C2—82no—
636C2C73×#246111yescharacteristic
637C2C73×#317811yescharacteristic
638C2C73×#318311yescharacteristic
639C2C73×#326711yescharacteristic
640C2C73×#326911yescharacteristic
641C2C73×#337111yescharacteristic
642C2C73×#337711yescharacteristic
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
3. C73×#2453C2semidirect
5. C73×#2068C2semidirect
6. C73×#2059C2semidirect
9. C73×#1971C2semidirect
11. C73×#1935C2semidirect
12. C73×#1933C2semidirect
13. C73×#1878C2semidirect
15. C73×#1771C2semidirect
313. #26833C73direct (N × H)
324. #2453C2×C73semidirect
326. #2068C2×C73semidirect
327. #2059C2×C73semidirect
330. #1971C2×C73semidirect
332. #1935C2×C73semidirect
333. #1933C2×C73semidirect
334. #1878C2×C73semidirect
336. #1771C2×C73semidirect
337. C73#26833direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#488×C732
C2×#440×C732
C73×#24532
C73×#24472
C73×#20682
C73×#20592
C73×#20552
C73×#20152
C73×#19712
C73×#19362
C73×#19352
C73×#19332
C73×#18782
C73×#18642
C73×#17712
#2683373