Finite Group Databasebeta

← C73×#25667 #32935071

Subgroups — C73×#25667 #32935071

Order 18688.

1020 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3511C211yesmaximal, characteristic
2C73×#3141C211yesmaximal, characteristic, complemented
3C73×#3079C211yesmaximal, characteristic, complemented
4C73×#2862C211yesmaximal, characteristic, complemented
5C73×#2040C214yesmaximal, complemented
6C73×#1997C211yesmaximal, characteristic, complemented
7C73×#1962C211yesmaximal, characteristic, complemented
8C73×#1860C214yesmaximal, complemented
9C4×#104×C73C211yesmaximal, characteristic, complemented
10#556×C73—21no—
11#555×C73—21no—
12#554×C73—21no—
13#553×C73—22no—
14#548×C73—22no—
15#547×C73—21no—
16#542×C73—22no—
17#537×C73C2212yes—
18#533×C73—21no—
19#532×C73—21no—
20#532×C73C2211yescharacteristic
21C2×C4⋊Q8×C73C2211yescharacteristic
22C2×C4⋊Q8×C73C2211yescharacteristic
23#520×C73C2212yes—
24C4×#41×C73C2211yescharacteristic
25#489×C73—22no—
26#487×C73—21no—
27#486×C73—21no—
28#477×C73—21no—
29#476×C73—21no—
30#475×C73—21no—
31#474×C73—21no—
32#428×C73C2212yes—
33#423×C73C2211yescharacteristic
34C2×#104×C73C2214yes—
35C2×#104×C73C2212yes—
36#417×C73C2212yes—
37#417×C73C2214yes—
38C4×M16×C73C2211yescharacteristic
39#391×C73—22no—
40#391×C73—22no—
41#382×C73C2214yes—
42C43×C73C2211yescharacteristic
43#343×C73C2214yes—
44#339×C73C2212yes—
45C2×#41×C73—22no—
46C2×#41×C73C2311yescharacteristic
47C2×#41×C73C2312yes—
48C22×Q8×C73—21no—
49C22×Q8×C73D412yes—
50C2×M16×C73C2312yes—
51C2×M16×C73C2312yes—
52C4⋊Q8×C73—21no—
53C4⋊Q8×C73—21no—
54C4⋊Q8×C73—21no—
55C4⋊Q8×C73—21no—
56C4⋊Q8×C73—21no—
57C4⋊Q8×C73—21no—
58C4⋊Q8×C73—21no—
59C4⋊Q8×C73—21no—
60C4⋊Q8×C73D411yescharacteristic
61#127×C73D411yescharacteristic
62#126×C73—24no—
63#125×C73—22no—
64#124×C73—22no—
65#124×C73—24no—
66#124×C73D412yes—
67#123×C73—24no—
68C22⋊Q8×C73—22no—
69C22⋊Q8×C73—24no—
70C22⋊Q8×C73—22no—
71C22⋊Q8×C73—22no—
72#121×C73—22no—
73#121×C73—22no—
74#121×C73—22no—
75#121×C73—21no—
76#121×C73—21no—
77#121×C73—24no—
78C4×Q8×C73—22no—
79C4×Q8×C73—22no—
80C4×Q8×C73D411yescharacteristic
81C4×Q8×C73D411yescharacteristic
82C4×D4×C73—22no—
83C4×D4×C73—22no—
84C4×D4×C73—21no—
85C4×D4×C73—21no—
86C4×D4×C73—24no—
87C4×D4×C73—21no—
88C4×D4×C73—21no—
89C4×D4×C73D411yescharacteristic
90C4×D4×C73D411yescharacteristic
91#117×C73—22no—
92#117×C73—22no—
93#117×C73—21no—
94#117×C73C2311yescharacteristic
95C2×C4⋊C4×C73—22no—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73D412yes—
98C2×C4⋊C4×C73C2312yes—
99C2×C4⋊C4×C73C2312yes—
100C2×C42×C73—21no—
101C2×C42×C73—21no—
102C2×C42×C73—21no—
103C2×C42×C73C2312yes—
104C2×C42×C73C2311yescharacteristic
105#107×C73—22no—
106#106×C73—22no—
107C4⋊C8×C73—21no—
108C4⋊C8×C73—21no—
109#104×C73—28no—
110#104×C73—24no—
111#103×C73—22no—
112#103×C73—24no—
113#102×C73—22no—
114#102×C73—24no—
115#97×C73—21no—
116C4×C8×C73—21no—
117#95×C73—28no—
118#41×C73—24no—
119#41×C73—22no—
120#41×C73—24no—
121#41×C73—22no—
122#41×C73—84no—
123C2×Q8×C73—22no—
124C2×Q8×C73—22no—
125C2×Q8×C73—44no—
126C2×Q8×C73—44no—
127C2×Q8×C73—41no—
128C2×Q8×C73—41no—
129C2×Q8×C73C2×D412yes—
130C2×Q8×C73C2×D411yescharacteristic
131C2×D4×C73—21no—
132C2×D4×C73—22no—
133C2×D4×C73—24no—
134C2×D4×C73—21no—
135C2×D4×C73—21no—
136C2×D4×C73C2×D412yes—
137C2×D4×C73C2×D411yescharacteristic
138C22×C4×C73—22no—
139C22×C4×C73—24no—
140C22×C4×C73—21no—
141C22×C4×C73—21no—
142C22×C4×C73—21no—
143C22×C4×C73—22no—
144C22×C4×C73—22no—
145C22×C4×C73C2×D411yescharacteristic
146C22×C4×C73C2×D411yescharacteristic
147C22×C4×C73C2×D414yes—
148C22×C4×C73C2411yescharacteristic
149M16×C73—24no—
150M16×C73—22no—
151M16×C73—22no—
152C2×C8×C73—22no—
153C2×C8×C73—22no—
154C4⋊C4×C73—24no—
155C4⋊C4×C73—24no—
156C4⋊C4×C73—22no—
157C4⋊C4×C73—22no—
158C4⋊C4×C73—21no—
159C4⋊C4×C73—21no—
160C4⋊C4×C73—21no—
161C4⋊C4×C73—21no—
162C4⋊C4×C73—22no—
163C4⋊C4×C73—22no—
164C4⋊C4×C73—22no—
165C4⋊C4×C73—22no—
166C4⋊C4×C73—41no—
167C4⋊C4×C73—41no—
168C4⋊C4×C73C2×D411yescharacteristic
169C4⋊C4×C73C2×D411yescharacteristic
170C22⋊C4×C73—24no—
171C22⋊C4×C73—24no—
172C22⋊C4×C73—24no—
173C22⋊C4×C73—21no—
174C22⋊C4×C73—21no—
175C22⋊C4×C73—21no—
176C22⋊C4×C73—22no—
177C22⋊C4×C73—22no—
178C42×C73—24no—
179C42×C73—21no—
180C42×C73—21no—
181C42×C73—21no—
182C42×C73—22no—
183C42×C73—42no—
184C42×C73—42no—
185C42×C73C2×D411yescharacteristic
186C42×C73C2×D411yescharacteristic
187C42×C73C2×D411yescharacteristic
188C42×C73C2×D411yescharacteristic
189C42×C73#4114yescomplemented
190C23×C73—21no—
191C23×C73—22no—
192C23×C73C22×D411yescharacteristic
193Q8×C73—21no—
194Q8×C73—21no—
195Q8×C73—24no—
196Q8×C73—44no—
197Q8×C73—82no—
198Q8×C73—82no—
199Q8×C73—82no—
200D4×C73—21no—
201D4×C73—21no—
202D4×C73—24no—
203D4×C73—44no—
204D4×C73—42no—
205D4×C73—42no—
206D4×C73—42no—
207D4×C73—84no—
208C2×C4×C73—22no—
209C2×C4×C73—22no—
210C2×C4×C73—21no—
211C2×C4×C73—22no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—24no—
215C2×C4×C73—24no—
216C2×C4×C73—42no—
217C2×C4×C73—42no—
218C2×C4×C73—42no—
219C2×C4×C73—42no—
220C2×C4×C73—42no—
221C2×C4×C73—42no—
222C2×C4×C73—42no—
223C2×C4×C73—44no—
224C2×C4×C73—44no—
225C2×C4×C73—42no—
226C2×C4×C73—84no—
227C2×C4×C73#12011yescharacteristic
228C2×C4×C73#12011yescharacteristic
229C2×C4×C73#12011yescharacteristic
230C2×C4×C73#12011yescharacteristic
231C2×C4×C73C22×D411yescharacteristic
232C2×C4×C73C22×D411yescharacteristic
233C2×C4×C73C2×#4112yes—
234C2×C4×C732−1+412yes—
235C8×C73—42no—
236C8×C73—42no—
237C22×C73—21no—
238C22×C73—21no—
239C22×C73—42no—
240C22×C73—41no—
241C22×C73—41no—
242C22×C73—42no—
243C22×C73—41no—
244C22×C73—42no—
245C22×C73C2×#12011yescharacteristic
246C22×C73#54812yes—
247C4×C73—21no—
248C4×C73—21no—
249C4×C73—44no—
250C4×C73—42no—
251C4×C73—41no—
252C4×C73—41no—
253C4×C73—44no—
254C4×C73—41no—
255C4×C73—82no—
256C4×C73#45412yes—
257C4×C73#45512yes—
258C4×C73#53211yescharacteristic
259C4×C73#53611yescharacteristic
260C4×C73#54712yes—
261#25667C7311yesmaximal, characteristic, direct product factor, Sylow
262C2×C73—22no—
263C2×C73—81no—
264C2×C73—82no—
265C2×C73#243211yescharacteristic
266C2×C73C2×#45511yescharacteristic
267C2×C73C2×#45411yescharacteristic
268#3511C2×C7311yescharacteristic
269#3141C2×C7311yescharacteristic, complemented
270#3079C2×C7311yescharacteristic, complemented
271#2862C2×C7311yescharacteristic, complemented
272#2040C2×C7314yescomplemented
273#1997C2×C7311yescharacteristic, complemented
274#1962C2×C7311yescharacteristic, complemented
275#1860C2×C7314yescomplemented
276C4×#104C2×C7311yescharacteristic, complemented
277C73#2566711yescharacteristic, direct product factor, Sylow
278#556—21no—
279#555—21no—
280#554—21no—
281#553—22no—
282#548—22no—
283#547—21no—
284#542—22no—
285#537C22×C7312yes—
286#533—21no—
287#532—21no—
288#532C22×C7311yescharacteristic
289C2×C4⋊Q8C22×C7311yescharacteristic
290C2×C4⋊Q8C22×C7311yescharacteristic
291#520C22×C7312yes—
292C4×#41C22×C7311yescharacteristic
293#489—22no—
294#487—21no—
295#486—21no—
296#477—21no—
297#476—21no—
298#475—21no—
299#474—21no—
300#428C22×C7312yes—
301#423C22×C7311yescharacteristic
302C2×#104C22×C7314yes—
303C2×#104C22×C7312yes—
304#417C22×C7312yes—
305#417C22×C7314yes—
306C4×M16C22×C7311yescharacteristic
307#391—22no—
308#391—22no—
309#382C22×C7314yes—
310C43C22×C7311yescharacteristic
311#343C22×C7314yes—
312#339C22×C7312yes—
313C2×#41—22no—
314C2×#41C23×C7311yescharacteristic
315C2×#41C23×C7312yes—
316C22×Q8—21no—
317C22×Q8D4×C7312yes—
318C2×M16C23×C7312yes—
319C2×M16C23×C7312yes—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8—21no—
323C4⋊Q8—21no—
324C4⋊Q8—21no—
325C4⋊Q8—21no—
326C4⋊Q8—21no—
327C4⋊Q8—21no—
328C4⋊Q8D4×C7311yescharacteristic
329#127D4×C7311yescharacteristic
330#126—24no—
331#125—22no—
332#124—22no—
333#124—24no—
334#124D4×C7312yes—
335#123—24no—
336C22⋊Q8—22no—
337C22⋊Q8—24no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340#121—22no—
341#121—22no—
342#121—22no—
343#121—21no—
344#121—21no—
345#121—24no—
346C4×Q8—22no—
347C4×Q8—22no—
348C4×Q8D4×C7311yescharacteristic
349C4×Q8D4×C7311yescharacteristic
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—24no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4D4×C7311yescharacteristic
358C4×D4D4×C7311yescharacteristic
359#117—22no—
360#117—22no—
361#117—21no—
362#117C23×C7311yescharacteristic
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4D4×C7312yes—
366C2×C4⋊C4C23×C7312yes—
367C2×C4⋊C4C23×C7312yes—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—21no—
371C2×C42C23×C7312yes—
372C2×C42C23×C7311yescharacteristic
373#107—22no—
374#106—22no—
375C4⋊C8—21no—
376C4⋊C8—21no—
377#104—28no—
378#104—24no—
379#103—22no—
380#103—24no—
381#102—22no—
382#102—24no—
383#97—21no—
384C4×C8—21no—
385#95—28no—
386#41—24no—
387#41—22no—
388#41—24no—
389#41—22no—
390#41—84no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—44no—
394C2×Q8—44no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8C2×D4×C7312yes—
398C2×Q8C2×D4×C7311yescharacteristic
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—24no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4C2×D4×C7312yes—
405C2×D4C2×D4×C7311yescharacteristic
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4C2×D4×C7311yescharacteristic
414C22×C4C2×D4×C7311yescharacteristic
415C22×C4C2×D4×C7314yes—
416C22×C4C24×C7311yescharacteristic
417M16—24no—
418M16—22no—
419M16—22no—
420C2×C8—22no—
421C2×C8—22no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—41no—
435C4⋊C4—41no—
436C4⋊C4C2×D4×C7311yescharacteristic
437C4⋊C4C2×D4×C7311yescharacteristic
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—21no—
442C22⋊C4—21no—
443C22⋊C4—21no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C42—24no—
447C42—21no—
448C42—21no—
449C42—21no—
450C42—22no—
451C42—42no—
452C42—42no—
453C42C2×D4×C7311yescharacteristic
454C42C2×D4×C7311yescharacteristic
455C42C2×D4×C7311yescharacteristic
456C42C2×D4×C7311yescharacteristic
457C42#41×C7314yescomplemented
458C23—21no—
459C23—22no—
460C23C22×D4×C7311yescharacteristic
461Q8—21no—
462Q8—21no—
463Q8—24no—
464Q8—44no—
465Q8—82no—
466Q8—82no—
467Q8—82no—
468D4—21no—
469D4—21no—
470D4—24no—
471D4—44no—
472D4—42no—
473D4—42no—
474D4—42no—
475D4—84no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—44no—
492C2×C4—44no—
493C2×C4—42no—
494C2×C4—84no—
495C2×C4#120×C7311yescharacteristic
496C2×C4#120×C7311yescharacteristic
497C2×C4#120×C7311yescharacteristic
498C2×C4#120×C7311yescharacteristic
499C2×C4C22×D4×C7311yescharacteristic
500C2×C4C22×D4×C7311yescharacteristic
501C2×C4C2×#41×C7312yes—
502C2×C42−1+4×C7312yes—
503C8—42no—
504C8—42no—
505C22—21no—
506C22—21no—
507C22—41no—
508C22—42no—
509C22—41no—
510C22—42no—
511C22—42no—
512C22—41no—
513C22C2×#120×C7311yescharacteristic
514C22#548×C7312yes—
515C4—21no—
516C4—21no—
517C4—44no—
518C4—41no—
519C4—44no—
520C4—41no—
521C4—42no—
522C4—41no—
523C4—82no—
524C4#454×C7312yes—
525C4#455×C7312yes—
526C4#532×C7311yescharacteristic
527C4#536×C7311yescharacteristic
528C4#547×C7312yes—
529C2—22no—
530C2—81no—
531C2—82no—
532C2C73×#243211yescharacteristic
533C2C2×#455×C7311yescharacteristic
534C2C2×#454×C7311yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#3511C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#3141C2semidirect
3. C73×#3079C2semidirect
4. C73×#2862C2semidirect
5. C73×#2040C2semidirect
6. C73×#1997C2semidirect
7. C73×#1962C2semidirect
8. C73×#1860C2semidirect
9. C4×#104×C73C2semidirect
189. C42×C73#41semidirect
261. #25667C73direct (N × H)
269. #3141C2×C73semidirect
270. #3079C2×C73semidirect
271. #2862C2×C73semidirect
272. #2040C2×C73semidirect
273. #1997C2×C73semidirect
274. #1962C2×C73semidirect
275. #1860C2×C73semidirect
276. C4×#104C2×C73semidirect
277. C73#25667direct (N × H)
457. C42#41×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35112
C73×#31412
C73×#30792
C73×#28622
C73×#20402
C73×#19972
C73×#19622
C73×#18602
C4×#104×C732
#2566773