Finite Group Databasebeta

← C73×#25688 #32935092

Subgroups — C73×#25688 #32935092

Order 18688.

964 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3509C211yesmaximal, characteristic
2C73×#3165C211yesmaximal, characteristic, complemented
3C73×#3079C211yesmaximal, characteristic
4C73×#2862C211yesmaximal, characteristic, complemented
5C73×#2038C214yesmaximal
6C73×#1994C211yesmaximal, characteristic, complemented
7C73×#1966C211yesmaximal, characteristic, complemented
8C73×#1857C214yesmaximal, complemented
9C4×#104×C73C211yesmaximal, characteristic
10#557×C73—21no—
11#557×C73—21no—
12#556×C73—21no—
13#556×C73—21no—
14#552×C73—22no—
15#552×C73—22no—
16#541×C73—22no—
17#536×C73C2212yes—
18#533×C73—21no—
19#533×C73—21no—
20#533×C73C2211yescharacteristic
21C2×C4⋊Q8×C73C2211yescharacteristic
22C2×C4⋊Q8×C73C2211yescharacteristic
23#519×C73C2212yes—
24C4×#41×C73C2211yescharacteristic
25#501×C73—22no—
26#500×C73—21no—
27#498×C73—21no—
28#477×C73—21no—
29#476×C73—21no—
30#475×C73—21no—
31#474×C73—21no—
32#428×C73C2214yes—
33#428×C73C2212yes—
34#423×C73C2211yescharacteristic
35C2×#104×C73C2212yes—
36#417×C73C2212yes—
37C2×#101×C73C2214yes—
38C4×M16×C73C2211yescharacteristic
39#391×C73—22no—
40#391×C73C2214yes—
41#382×C73—22no—
42C43×C73C2211yescharacteristic
43#339×C73C2214yes—
44#339×C73C2212yes—
45C2×#41×C73C2311yescharacteristic
46C22×Q8×C73—21no—
47C22×Q8×C73C2312yes—
48C2×M16×C73C2312yes—
49C2×M16×C73C2312yes—
50C4⋊Q8×C73—22no—
51C4⋊Q8×C73—21no—
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×C73D411yescharacteristic
60C4⋊Q8×C73D411yescharacteristic
61#126×C73—24no—
62#126×C73—24no—
63#125×C73—22no—
64#125×C73—22no—
65#125×C73—24no—
66#125×C73—24no—
67#125×C73D412yes—
68#124×C73—22no—
69#123×C73—24no—
70C22⋊Q8×C73—22no—
71C22⋊Q8×C73—22no—
72C22⋊Q8×C73—21no—
73C22⋊Q8×C73—21no—
74C22⋊Q8×C73—22no—
75C22⋊Q8×C73—22no—
76C4×Q8×C73—22no—
77C4×Q8×C73—22no—
78C4×Q8×C73—22no—
79C4×Q8×C73—22no—
80C4×Q8×C73—22no—
81C4×Q8×C73—22no—
82C4×Q8×C73—21no—
83C4×Q8×C73—21no—
84C4×Q8×C73D411yescharacteristic
85C4×Q8×C73D411yescharacteristic
86C4×D4×C73—21no—
87C4×D4×C73—21no—
88C4×D4×C73D411yescharacteristic
89C4×D4×C73D411yescharacteristic
90#117×C73—22no—
91#117×C73—22no—
92#117×C73—24no—
93#117×C73—21no—
94#117×C73C2311yescharacteristic
95#117×C73C2312yes—
96C2×C4⋊C4×C73—21no—
97C2×C4⋊C4×C73D412yes—
98C2×C4⋊C4×C73D412yes—
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#107×C73—24no—
107#106×C73—22no—
108#106×C73—24no—
109C4⋊C8×C73—21no—
110C4⋊C8×C73—21no—
111#104×C73—24no—
112#103×C73—22no—
113#102×C73—22no—
114#101×C73—28no—
115#97×C73—21no—
116C4×C8×C73—21no—
117#95×C73—28no—
118#41×C73—22no—
119#41×C73—22no—
120C2×Q8×C73—21no—
121C2×Q8×C73—21no—
122C2×Q8×C73—22no—
123C2×Q8×C73—22no—
124C2×Q8×C73—24no—
125C2×Q8×C73—24no—
126C2×Q8×C73—44no—
127C2×Q8×C73—41no—
128C2×Q8×C73—41no—
129C2×Q8×C73C2×D411yescharacteristic
130C2×D4×C73—21no—
131C2×D4×C73C2×D411yescharacteristic
132C22×C4×C73—22no—
133C22×C4×C73—21no—
134C22×C4×C73—21no—
135C22×C4×C73—21no—
136C22×C4×C73—22no—
137C22×C4×C73C2×D414yes—
138C22×C4×C73C2×D411yescharacteristic
139C22×C4×C73C2×D411yescharacteristic
140C22×C4×C73C2411yescharacteristic
141M16×C73—22no—
142M16×C73—24no—
143M16×C73#4114yes—
144C2×C8×C73—22no—
145C2×C8×C73—22no—
146C4⋊C4×C73—24no—
147C4⋊C4×C73—24no—
148C4⋊C4×C73—24no—
149C4⋊C4×C73—24no—
150C4⋊C4×C73—22no—
151C4⋊C4×C73—22no—
152C4⋊C4×C73—22no—
153C4⋊C4×C73—22no—
154C4⋊C4×C73—21no—
155C4⋊C4×C73—21no—
156C4⋊C4×C73—21no—
157C4⋊C4×C73—21no—
158C4⋊C4×C73—22no—
159C4⋊C4×C73—22no—
160C4⋊C4×C73—22no—
161C4⋊C4×C73—22no—
162C4⋊C4×C73—41no—
163C4⋊C4×C73—41no—
164C4⋊C4×C73C2×D411yescharacteristic
165C4⋊C4×C73C2×D412yes—
166C4⋊C4×C73C2×D411yescharacteristic
167C4⋊C4×C73C2×D412yes—
168C22⋊C4×C73—24no—
169C22⋊C4×C73—24no—
170C22⋊C4×C73—21no—
171C22⋊C4×C73—22no—
172C22⋊C4×C73—21no—
173C22⋊C4×C73—21no—
174C42×C73—24no—
175C42×C73—24no—
176C42×C73—24no—
177C42×C73—21no—
178C42×C73—21no—
179C42×C73—21no—
180C42×C73—22no—
181C42×C73—22no—
182C42×C73—22no—
183C42×C73—42no—
184C42×C73C2×D411yescharacteristic
185C42×C73C2×D411yescharacteristic
186C42×C73C2×D411yescharacteristic
187C42×C73C2×D411yescharacteristic
188C23×C73—21no—
189C23×C73C22×D411yescharacteristic
190Q8×C73—21no—
191Q8×C73—21no—
192Q8×C73—42no—
193Q8×C73—42no—
194Q8×C73—44no—
195Q8×C73—42no—
196Q8×C73—42no—
197Q8×C73—82no—
198Q8×C73—82no—
199D4×C73—21no—
200D4×C73—21no—
201D4×C73—42no—
202C2×C4×C73—22no—
203C2×C4×C73—22no—
204C2×C4×C73—24no—
205C2×C4×C73—21no—
206C2×C4×C73—21no—
207C2×C4×C73—22no—
208C2×C4×C73—22no—
209C2×C4×C73—24no—
210C2×C4×C73—21no—
211C2×C4×C73—28no—
212C2×C4×C73—42no—
213C2×C4×C73—42no—
214C2×C4×C73—42no—
215C2×C4×C73—42no—
216C2×C4×C73—42no—
217C2×C4×C73—44no—
218C2×C4×C73—42no—
219C2×C4×C73#12011yescharacteristic
220C2×C4×C73#12011yescharacteristic
221C2×C4×C73#12011yescharacteristic
222C2×C4×C73#12011yescharacteristic
223C2×C4×C73C22×D411yescharacteristic
224C2×C4×C73C22×D411yescharacteristic
225C2×C4×C73C2×#4112yes—
226C2×C4×C732−1+412yes—
227C8×C73—24no—
228C8×C73—42no—
229C22×C73—21no—
230C22×C73—21no—
231C22×C73—41no—
232C22×C73—41no—
233C22×C73—41no—
234C22×C73C2×#12011yescharacteristic
235C22×C73#54712yes—
236C4×C73—21no—
237C4×C73—21no—
238C4×C73—44no—
239C4×C73—44no—
240C4×C73—41no—
241C4×C73—41no—
242C4×C73—42no—
243C4×C73—41no—
244C4×C73—42no—
245C4×C73—82no—
246C4×C73#45412yes—
247C4×C73#45612yes—
248C4×C73#53211yescharacteristic
249C4×C73#53611yescharacteristic
250C4×C73#54812yes—
251#25688C7311yesmaximal, characteristic, direct product factor, Sylow
252C2×C73—22no—
253C2×C73—81no—
254C2×C73#243211yescharacteristic
255C2×C73C2×#45411yescharacteristic
256C2×C73C2×#45611yescharacteristic
257#3509C2×C7311yescharacteristic
258#3165C2×C7311yescharacteristic, complemented
259#3079C2×C7311yescharacteristic
260#2862C2×C7311yescharacteristic, complemented
261#2038C2×C7314yes—
262#1994C2×C7311yescharacteristic, complemented
263#1966C2×C7311yescharacteristic, complemented
264#1857C2×C7314yescomplemented
265C4×#104C2×C7311yescharacteristic
266C73#2568811yescharacteristic, direct product factor, Sylow
267#557—21no—
268#557—21no—
269#556—21no—
270#556—21no—
271#552—22no—
272#552—22no—
273#541—22no—
274#536C22×C7312yes—
275#533—21no—
276#533—21no—
277#533C22×C7311yescharacteristic
278C2×C4⋊Q8C22×C7311yescharacteristic
279C2×C4⋊Q8C22×C7311yescharacteristic
280#519C22×C7312yes—
281C4×#41C22×C7311yescharacteristic
282#501—22no—
283#500—21no—
284#498—21no—
285#477—21no—
286#476—21no—
287#475—21no—
288#474—21no—
289#428C22×C7312yes—
290#428C22×C7314yes—
291#423C22×C7311yescharacteristic
292C2×#104C22×C7312yes—
293#417C22×C7312yes—
294C2×#101C22×C7314yes—
295C4×M16C22×C7311yescharacteristic
296#391—22no—
297#391C22×C7314yes—
298#382—22no—
299C43C22×C7311yescharacteristic
300#339C22×C7312yes—
301#339C22×C7314yes—
302C2×#41C23×C7311yescharacteristic
303C22×Q8—21no—
304C22×Q8C23×C7312yes—
305C2×M16C23×C7312yes—
306C2×M16C23×C7312yes—
307C4⋊Q8—22no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8D4×C7311yescharacteristic
317C4⋊Q8D4×C7311yescharacteristic
318#126—24no—
319#126—24no—
320#125—22no—
321#125—22no—
322#125—24no—
323#125—24no—
324#125D4×C7312yes—
325#124—22no—
326#123—24no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C4×Q8—22no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×Q8—21no—
340C4×Q8—21no—
341C4×Q8D4×C7311yescharacteristic
342C4×Q8D4×C7311yescharacteristic
343C4×D4—21no—
344C4×D4—21no—
345C4×D4D4×C7311yescharacteristic
346C4×D4D4×C7311yescharacteristic
347#117—22no—
348#117—22no—
349#117—24no—
350#117—21no—
351#117C23×C7311yescharacteristic
352#117C23×C7312yes—
353C2×C4⋊C4—21no—
354C2×C4⋊C4D4×C7312yes—
355C2×C4⋊C4D4×C7312yes—
356C2×C4⋊C4C23×C7312yes—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42C23×C7312yes—
361C2×C42C23×C7311yescharacteristic
362#107—22no—
363#107—24no—
364#106—22no—
365#106—24no—
366C4⋊C8—21no—
367C4⋊C8—21no—
368#104—24no—
369#103—22no—
370#102—22no—
371#101—28no—
372#97—21no—
373C4×C8—21no—
374#95—28no—
375#41—22no—
376#41—22no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—24no—
382C2×Q8—24no—
383C2×Q8—44no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8C2×D4×C7311yescharacteristic
387C2×D4—21no—
388C2×D4C2×D4×C7311yescharacteristic
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4C2×D4×C7314yes—
395C22×C4C2×D4×C7311yescharacteristic
396C22×C4C2×D4×C7311yescharacteristic
397C22×C4C24×C7311yescharacteristic
398M16—22no—
399M16—24no—
400M16#41×C7314yes—
401C2×C8—22no—
402C2×C8—22no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—24no—
406C4⋊C4—24no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4C2×D4×C7311yescharacteristic
422C4⋊C4C2×D4×C7312yes—
423C4⋊C4C2×D4×C7311yescharacteristic
424C4⋊C4C2×D4×C7312yes—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—21no—
428C22⋊C4—22no—
429C22⋊C4—21no—
430C22⋊C4—21no—
431C42—24no—
432C42—24no—
433C42—24no—
434C42—21no—
435C42—21no—
436C42—21no—
437C42—22no—
438C42—22no—
439C42—22no—
440C42—42no—
441C42C2×D4×C7311yescharacteristic
442C42C2×D4×C7311yescharacteristic
443C42C2×D4×C7311yescharacteristic
444C42C2×D4×C7311yescharacteristic
445C23—21no—
446C23C22×D4×C7311yescharacteristic
447Q8—21no—
448Q8—21no—
449Q8—42no—
450Q8—42no—
451Q8—42no—
452Q8—42no—
453Q8—44no—
454Q8—82no—
455Q8—82no—
456D4—21no—
457D4—21no—
458D4—42no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—21no—
468C2×C4—28no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—42no—
476C2×C4#120×C7311yescharacteristic
477C2×C4#120×C7311yescharacteristic
478C2×C4#120×C7311yescharacteristic
479C2×C4#120×C7311yescharacteristic
480C2×C4C22×D4×C7311yescharacteristic
481C2×C4C22×D4×C7311yescharacteristic
482C2×C4C2×#41×C7312yes—
483C2×C42−1+4×C7312yes—
484C8—24no—
485C8—42no—
486C22—21no—
487C22—21no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22C2×#120×C7311yescharacteristic
492C22#547×C7312yes—
493C4—21no—
494C4—21no—
495C4—44no—
496C4—41no—
497C4—42no—
498C4—41no—
499C4—42no—
500C4—44no—
501C4—41no—
502C4—82no—
503C4#454×C7312yes—
504C4#456×C7312yes—
505C4#532×C7311yescharacteristic
506C4#536×C7311yescharacteristic
507C4#548×C7312yes—
508C2—22no—
509C2—81no—
510C2C73×#243211yescharacteristic
511C2C2×#454×C7311yescharacteristic
512C2C2×#456×C7311yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#41×C73C23
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×#3165C2semidirect
4. C73×#2862C2semidirect
6. C73×#1994C2semidirect
7. C73×#1966C2semidirect
8. C73×#1857C2semidirect
251. #25688C73direct (N × H)
258. #3165C2×C73semidirect
260. #2862C2×C73semidirect
262. #1994C2×C73semidirect
263. #1966C2×C73semidirect
264. #1857C2×C73semidirect
266. C73#25688direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#35092
C73×#31652
C73×#30792
C73×#28622
C73×#20382
C73×#19942
C73×#19662
C73×#18572
C4×#104×C732
#2568873