Finite Group Databasebeta

← C2×#11748198 #14429353

Subgroups — C2×#11748198 #14429353

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91796C211yesmaximal, characteristic, complemented
2C2×#91321C211yesmaximal, characteristic, complemented
3C2×#91312C211yesmaximal, characteristic
4C22×#6655C211yesmaximal, characteristic, complemented
5C2×C5×#824C211yesmaximal, characteristic, complemented
6C2×C3×#3955C211yesmaximal, characteristic, complemented
7C2×#90992C211yesmaximal, characteristic, complemented
8#11748198C218yesmaximal, direct product factor
9C2×#65043—31nomaximal, Hall
10C2×#6817C2211yescharacteristic
11C22×C5×Dic6C2211yescharacteristic
12C22×C3×D20C2211yescharacteristic
13C2×C3×C5×M16C2211yescharacteristic
14C22×C3⋊#168C2211yescharacteristic
15#91796—22no—
16#91796C2214yescomplemented
17C2×#6705—21no—
18C2×C8×D15—21no—
19C2×C5×#208C2211yescharacteristic
20C2×C3×#681C2211yescharacteristic
21#91321—22no—
22#91321C2214yescomplemented
23C2×#6663—21no—
24C2×#6660—21no—
25#91312—22no—
26#91312C2214yes—
27C2×#6657—21no—
28C2×#6655—21no—
29C2×#6655—21no—
30C2×#6655—22no—
31C2×#6655C2214yescomplemented
32C2×#6653—21no—
33C5×#824C2214yescomplemented
34C3×#3955C2214yescomplemented
35#90992C2214yescomplemented
36C2×#4748—51nomaximal, Hall
37C2×#4088—31no—
38C22×#688—31no—
39C2×#4054—31no—
40C2×#4053—31no—
41C2×C5×#101—31no—
42C2×#3955D311yescharacteristic, complemented
43C2×#3954—31no—
44#65043—38no—
45C23×C3×D5—21no—
46C22×C3×C4×C5C2311yescharacteristic
47C2×#1220—21no—
48#6817—21no—
49#6817—21no—
50#6817D412yes—
51#6817C2312yes—
52C2×D60D411yescharacteristic
53C2×C4×D15—21no—
54C2×Dic30D411yescharacteristic
55C22×C5×Dic3—21no—
56C2×C5×Dic6—21no—
57C2×C5×Dic6—21no—
58C2×C5×Dic6—21no—
59C2×C5×Dic6—21no—
60C2×C5×Dic6—21no—
61C2×C5×Dic6C2312yes—
62C2×C3×D20—21no—
63C2×C3×D20—21no—
64C2×C3×D20—21no—
65C2×C3×D20—21no—
66C2×C3×D20—21no—
67C2×C3×D20C2312yes—
68C3×C5×M16—21no—
69C3×C5×M16C2312yes—
70C2×C3×C5×C8—21no—
71C2×C3⋊#168D411yescharacteristic
72C2×C3⋊#168D411yescharacteristic
73C2×C3⋊#168D412yes—
74C2×C3⋊#168C2312yes—
75#6705—24no—
76C8×D15—24no—
77C5×#208—21no—
78C5×#208C2312yes—
79C2×C5×C3⋊C8—21no—
80C3×#681—21no—
81C3×#681C2312yes—
82C2×C3×#168—21no—
83#6663—24no—
84#6660—24no—
85#6657—24no—
86#6655—24no—
87#6655—24no—
88#6653—24no—
89C22×#214—51no—
90C2×#932—51no—
91C2×#909—51no—
92C2×#907—51no—
93C2×C3×#100—51no—
94C2×#824D511yescharacteristic, complemented
95C2×#822—51no—
96#4748—58no—
97C22×C5×Q8—31no—
98C2×#709—31no—
99C22×D20C2×D311yescharacteristic
100C2×C5×M16—31no—
101C2×C5×M16C2×D311yescharacteristic
102C2×#689—61no—
103#4088—34no—
104#4088—62no—
105C2×#688—34no—
106C2×#688—61no—
107C2×#688—61no—
108C2×#688—61no—
109C2×#688—62no—
110C2×#681C2×D311yescharacteristic
111C22×#168—31no—
112#4054—34no—
113#4054—62no—
114#4053—34no—
115#4053—62no—
116C2×D40—61no—
117C2×#677—61no—
118C2×#676—61no—
119C2×C8×D5—61no—
120C5×#101—34no—
121#3955C2×D314yescomplemented
122#3954—34no—
123C2×#471—151noSylow
124C23×C3×C5#4111yescharacteristic
125C22×D15—21no—
126C22×C3×D5—22no—
127C22×C3×D5—41no—
128C22×C3×D5—41no—
129C22×C3×D5—82no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5#4111yescharacteristic
135C2×C3×C4×C5C2411yescharacteristic
136#1220—22no—
137#1220—22no—
138C2×Dic15—21no—
139D60—21no—
140D60C2×D412yes—
141C4×D15—22no—
142C4×D15—22no—
143Dic30—21no—
144Dic30C2×D412yes—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—41no—
147C2×C5×Dic3—41no—
148C5×Dic6—22no—
149C5×Dic6—22no—
150C5×Dic6—41no—
151C5×Dic6—41no—
152C3×D20—22no—
153C3×D20—22no—
154C3×D20—41no—
155C3×D20—41no—
156C3×C5×C8—22no—
157C3⋊#168C2×D412yes—
158C3⋊#168C2×D412yes—
159C3×#168—22no—
160C5×C3⋊C8—22no—
161C22×C3×D4—51no—
162C2×#235—51no—
163C22×Dic6C2×D511yescharacteristic
164C2×C3×M16—51no—
165C2×C3×M16C2×D511yescharacteristic
166C2×#214—54no—
167C2×#214—101no—
168C2×#214—101no—
169C2×#214—101no—
170C2×#214—102no—
171#932—54no—
172#932—102no—
173C2×#213—101no—
174C2×#208C2×D511yescharacteristic
175C22×C3⋊C8—51no—
176#909—54no—
177#909—102no—
178#907—54no—
179#907—102no—
180C2×Dic12—101no—
181C2×#204—101no—
182C2×ΓL(1,𝔽25)—101no—
183C2×D3×C8—101no—
184C3×#100—54no—
185#824C2×D514yescomplemented
186#822—54no—
187C23×D5—21no—
188C2×C5×Q8—32no—
189C2×C5×Q8—61no—
190C2×C5×Q8—61no—
191C2×C5×Q8—61no—
192C2×C5×Q8—61no—
193C2×C5×Q8—61no—
194C22×C4×C5—61no—
195C22×C4×C5C22×D311yescharacteristic
196C2×C22⋊D5—61no—
197#709—32no—
198#709—32no—
199#709—61no—
200#709—61no—
201C2×D20—21no—
202C2×D20—21no—
203C2×D20—21no—
204C2×D20—21no—
205C2×D20—21no—
206C2×D20—31no—
207C2×D20C22×D312yes—
208C2×C4×D5—61no—
209C2×Dic10—31no—
210C5×M16—21no—
211C5×M16—32no—
212C5×M16—61no—
213C5×M16C22×D312yes—
214C2×C5×C8—21no—
215C2×C5×C8—61no—
216#689—64no—
217#688—64no—
218#688—64no—
219#688—64no—
220#681—21no—
221#681C22×D312yes—
222C2×#168—21no—
223C2×#168—31no—
224C2×#168—31no—
225C2×#168—32no—
226C2×#168—32no—
227D40—64no—
228#677—64no—
229#676—64no—
230C8×D5—64no—
231C2×#137—151no—
232C2×AGL(1,ℤ/8)—151no—
233C22×SD16—151no—
234C2×#131—151no—
235#471—158no—
236C2×#108—151no—
237C2×#101—31no—
238C2×#100—51no—
239C22×C3×C5—22no—
240C22×C3×C5#12111yescharacteristic
241C22×C3×C5#12111yescharacteristic
242C22×C3×C5C2×#4111yescharacteristic
243C2×D15—22no—
244C2×D15—42no—
245C2×C3×D5—42no—
246C2×C3×D5—82no—
247C2×C3×D5—82no—
248C2×C3×D5—82no—
249C3×C4×C5#12111yescharacteristic
250C3×C4×C5#12111yescharacteristic
251C3×C4×C5C22×D411yescharacteristic
252C3×C4×C5C22×D411yescharacteristic
253Dic15—22no—
254C5×Dic3—42no—
255C24×C3—101no—
256C2×C3×D4—52no—
257C2×C3×D4—101no—
258C2×C3×D4—101no—
259C2×C3×D4—101no—
260C2×C3×D4—101no—
261C2×C3×D4—101no—
262C22×C3×C4C22×D511yescharacteristic
263C2×#67—101no—
264C22×Dic3—21no—
265#235—52no—
266#235—52no—
267#235—101no—
268#235—101no—
269C2×D12—51no—
270C2×C4×D3—101no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—51no—
277C2×Dic6C22×D512yes—
278C3×M16—21no—
279C3×M16—52no—
280C3×M16—101no—
281C3×M16C22×D512yes—
282C2×C3×C8—21no—
283C2×C3×C8—101no—
284#214—104no—
285#214—104no—
286#214—104no—
287#213—104no—
288#208—21no—
289#208C22×D512yes—
290C2×C3⋊C8—21no—
291C2×C3⋊C8—51no—
292C2×C3⋊C8—51no—
293C2×C3⋊C8—52no—
294C2×C3⋊C8—52no—
295Dic12—104no—
296#204—104no—
297ΓL(1,𝔽25)—104no—
298D3×C8—104no—
299C23×C5#23511yescharacteristic
300C22×D5—22no—
301C22×D5—41no—
302C22×D5—41no—
303C22×D5—61no—
304C22×D5—82no—
305C5×Q8—62no—
306C5×Q8—62no—
307C5×Q8—121no—
308C5×Q8—121no—
309C2×C4×C5—62no—
310C2×C4×C5—121no—
311C2×C4×C5—121no—
312C2×C4×C5#23511yescharacteristic
313C2×C4×C5D3×D411yescharacteristic
314C2×C4×C5D3×D411yescharacteristic
315C2×C4×C5D3×D411yescharacteristic
316C2×C4×C5D3×D411yescharacteristic
317C2×C4×C5C23×D311yescharacteristic
318C22⋊D5—62no—
319C22⋊D5—62no—
320C2×Dic5—61no—
321D20—22no—
322D20—22no—
323D20—32no—
324D20—41no—
325D20—41no—
326D20—61no—
327C4×D5—62no—
328C4×D5—62no—
329Dic10—32no—
330Dic10—61no—
331C5×C8—22no—
332C5×C8—62no—
333#168—22no—
334#168—32no—
335#168—32no—
336C2×#41—151no—
337C22×Q8—31no—
338C22×D4—51no—
339#137—154no—
340#137—302no—
341AGL(1,ℤ/8)—154no—
342AGL(1,ℤ/8)—302no—
343C2×Q16—301no—
344C2×SD16—154no—
345C2×SD16—301no—
346C2×SD16—301no—
347C2×SD16—301no—
348C2×SD16—301no—
349C2×SD16—302no—
350C2×D8—301no—
351#131—154no—
352#131—302no—
353C2×M16—31no—
354C2×M16—51no—
355C2×M16—301no—
356C2×M16D3×D511yescharacteristic
357C22×C8—151no—
358C22×C8—301no—
359#108—154no—
360#101—34no—
361#100—54no—
362C2×C3×C5—21no—
363C2×C3×C5—21no—
364C2×C3×C5#47112yescomplemented
365C2×C3×C5C2×#12111yescharacteristic
366D15—42no—
367C3×D5—82no—
368C23×C3—102no—
369C23×C3—201no—
370C23×C3—201no—
371C23×C3—402no—
372C23×C3#70911yescharacteristic
373C22×D3—101no—
374C3×D4—102no—
375C3×D4—102no—
376C3×D4—201no—
377C3×D4—201no—
378C2×C3×C4#70911yescharacteristic
379C2×C3×C4D4×D511yescharacteristic
380C2×C3×C4D4×D511yescharacteristic
381C2×C3×C4D4×D511yescharacteristic
382C2×C3×C4D4×D511yescharacteristic
383C2×C3×C4C23×D511yescharacteristic
384#67—102no—
385#67—102no—
386C2×Dic3—22no—
387C2×Dic3—41no—
388C2×Dic3—41no—
389C2×Dic3—101no—
390D12—52no—
391D12—101no—
392C4×D3—102no—
393C4×D3—102no—
394Dic6—22no—
395Dic6—22no—
396Dic6—41no—
397Dic6—41no—
398Dic6—52no—
399Dic6—101no—
400C3×C8—22no—
401C3×C8—102no—
402C3⋊C8—22no—
403C3⋊C8—52no—
404C3⋊C8—52no—
405C22×C5—22no—
406C22×C5#88411yescharacteristic
407C22×C5#88411yescharacteristic
408C22×C5C2×#23511yescharacteristic
409C2×D5—42no—
410C2×D5—62no—
411C2×D5—82no—
412C2×D5—82no—
413C2×D5—82no—
414C2×D5—122no—
415C4×C5—122no—
416C4×C5#88411yescharacteristic
417C4×C5#88411yescharacteristic
418C4×C5C2×D3×D411yescharacteristic
419C4×C5C2×D3×D411yescharacteristic
420Dic5—62no—
421C24—101no—
422#41—152no—
423#41—152no—
424#41—301no—
425#41—301no—
426C2×Q8—32no—
427C2×Q8—61no—
428C2×Q8—61no—
429C2×Q8—61no—
430C2×Q8—61no—
431C2×Q8—61no—
432C2×Q8—151no—
433C2×D4—52no—
434C2×D4—101no—
435C2×D4—101no—
436C2×D4—101no—
437C2×D4—101no—
438C2×D4—101no—
439C2×D4—151no—
440C2×D4—301no—
441C22×C4—61no—
442C22×C4—301no—
443C22×C4C2×D3×D511yescharacteristic
444Q16—304no—
445SD16—304no—
446SD16—304no—
447SD16—304no—
448SD16—304no—
449D8—304no—
450M16—21no—
451M16—32no—
452M16—52no—
453M16—61no—
454M16—101no—
455M16—304no—
456M16C2×D3×D512yes—
457C2×C8—21no—
458C2×C8—61no—
459C2×C8—101no—
460C2×C8—151no—
461C2×C8—151no—
462C2×C8—152no—
463C2×C8—152no—
464C2×C8—304no—
465C3×C5C2×#47111yescharacteristic, complemented, Hall
466C22×C3—22no—
467C22×C3—202no—
468C22×C3—402no—
469C22×C3—402no—
470C22×C3—402no—
471C22×C3#403011yescharacteristic
472C22×C3#403011yescharacteristic
473C22×C3C2×#70911yescharacteristic
474C2×D3—102no—
475C2×D3—202no—
476C3×C4#403011yescharacteristic
477C3×C4#403011yescharacteristic
478C3×C4C2×D4×D511yescharacteristic
479C3×C4C2×D4×D511yescharacteristic
480Dic3—42no—
481Dic3—102no—
482C2×C5—21no—
483C2×C5—21no—
484C2×C5#474812yescomplemented
485C2×C5C2×#88411yescharacteristic
486D5—82no—
487D5—122no—
488C23—102no—
489C23—201no—
490C23—201no—
491C23—301no—
492C23—402no—
493C23#677111yescharacteristic
494Q8—62no—
495Q8—62no—
496Q8—121no—
497Q8—121no—
498Q8—152no—
499Q8—301no—
500D4—102no—
501D4—102no—
502D4—152no—
503D4—201no—
504D4—201no—
505D4—302no—
506D4—302no—
507D4—301no—
508C2×C4—62no—
509C2×C4—121no—
510C2×C4—121no—
511C2×C4—301no—
512C2×C4—302no—
513C2×C4—302no—
514C2×C4#677111yescharacteristic
515C2×C4#677711yescharacteristic
516C2×C4#677711yescharacteristic
517C2×C4#679011yescharacteristic
518C2×C4#679011yescharacteristic
519C2×C4C22×D3×D511yescharacteristic
520C8—22no—
521C8—62no—
522C8—102no—
523C8—152no—
524C8—152no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—402no—
528C2×C3#6504312yescomplemented
529C2×C3C2×#403011yescharacteristic
530D3—202no—
531C5C2×#474811yescharacteristic, complemented, Sylow
532C22—22no—
533C22—202no—
534C22—302no—
535C22—402no—
536C22—402no—
537C22—402no—
538C22—602no—
539C22#9146111yescharacteristic
540C22#9146111yescharacteristic
541C22C2×#677111yescharacteristic
542C4—122no—
543C4—302no—
544C4#9146111yescharacteristic
545C4#9146111yescharacteristic
546C4C2×#677711yescharacteristic
547C4C2×#679011yescharacteristic
548C3C2×#6504311yescharacteristic, complemented, Sylow
549C2—21no—
550C2—21no—
551C2—402no—
552C2—602no—
553C2#1174819812yesdirect product factor
554C2C2×#9146111yescharacteristic
subgroupG/H
centerC22#91461
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5#121
prime radicalC2×#91312C2
hypercenterC2×M16D3×D5
hypocenterC3×C5C2×#471
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#91796C2semidirect
2. C2×#91321C2semidirect
4. C22×#6655C2semidirect
5. C2×C5×#824C2semidirect
6. C2×C3×#3955C2semidirect
7. C2×#90992C2semidirect
8. #11748198C2direct (N × H)
16. #91796C22semidirect
22. #91321C22semidirect
31. C2×#6655C22semidirect
33. C5×#824C22semidirect
34. C3×#3955C22semidirect
35. #90992C22semidirect
42. C2×#3955D3semidirect
94. C2×#824D5semidirect
121. #3955C2×D3semidirect
185. #824C2×D5semidirect
364. C2×C3×C5#471semidirect
465. C3×C5C2×#471semidirect
484. C2×C5#4748semidirect
528. C2×C3#65043semidirect
531. C5C2×#4748semidirect
548. C3C2×#65043semidirect
553. C2#11748198direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917962
C2×#913212
C2×#913122
C22×#66552
C2×C5×#8242
C2×C3×#39552
C2×#909922
#117481982
C2×#650433
C2×#47485