Finite Group Databasebeta

← #25004221

Subgroups — #25004221

Order 11008.

922 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582903C211yesmaximal, characteristic
2C2×#14582903C211yesmaximal, characteristic
3C22×#13063241C211yesmaximal, characteristic
4C2×#14582669C211yesmaximal, characteristic, complemented
5C2×#14582669C211yesmaximal, characteristic, complemented
6#19134321C211yesmaximal, characteristic, complemented
7C2×C43×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C23×D172C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C22×#10621877C2211yescharacteristic
12#14582903—22no—
13#14582903—22no—
14#14582903—22no—
15#14582903—22no—
16C2×#13063245—22no—
17C2×#13063245—22no—
18C2×#13063241—22no—
19C2×#13063241—22no—
20C2×#13063241C414yescomplemented
21#14582669—22no—
22#14582669—22no—
23#14582663—22no—
24C22×M16×C43C2211yescharacteristic
25C2×#117×C43C2211yescharacteristic
26C2×#117×C43C2211yescharacteristic
27C43×H(3,ℤ/4)—22no—
28C24×D43—21no—
29C22×D172—21no—
30C22×D172—21no—
31C22×D172—21no—
32C22×D172—21no—
33C22×D172—21no—
34C22×D172—21no—
35C22×D172—21no—
36C22×D172—21no—
37C22×D172—21no—
38C22×D172—21no—
39C22×D172—21no—
40C22×D172C2×C412yes—
41C22×D172D412yes—
42C22×D172D412yes—
43C2×#10621877—21no—
44C2×#10621877—21no—
45C2×#10621877—21no—
46C2×#10621877—21no—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621877C2×C412yes—
60C2×#10621877D412yes—
61C22×C43⋊C8—21no—
62C22×C43⋊C8—21no—
63C22×C43⋊C8D412yes—
64#13063245—28no—
65#13063245—28no—
66#13063241—28no—
67C23×C4×C43C2311yescharacteristic
68C2×M16×C43—21no—
69C2×M16×C43—21no—
70C2×M16×C43—21no—
71C2×M16×C43—21no—
72C2×M16×C43—21no—
73C2×M16×C43C2×C412yes—
74C22×C8×C43—21no—
75#117×C43—21no—
76#117×C43—21no—
77#117×C43—21no—
78#117×C43—21no—
79#117×C43—21no—
80#117×C43—21no—
81#117×C43D412yes—
82#117×C43D412yes—
83C2×C4⋊C4×C43—21no—
84C2×C4⋊C4×C43—21no—
85C2×C22⋊C4×C43—21no—
86C2×C22⋊C4×C43—21no—
87C2×C42×C43—21no—
88C2×C42×C43—21no—
89C24×C43#4111yescharacteristic
90C23×D43—22no—
91C23×D43—22no—
92C23×D43—22no—
93C23×D43—41no—
94C23×D43—41no—
95C23×D43—41no—
96C23×D43—41no—
97C23×D43—84no—
98C22×C4×C43—41no—
99C22×C4×C43—41no—
100C22×C4×C43C22×C411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43#4111yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C22×C4×C43#4111yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C22×C4×C43#4111yescharacteristic
114C2×D172—22no—
115C2×D172—22no—
116C2×D172—22no—
117C2×D172—22no—
118C2×D172—22no—
119C2×D172—22no—
120C2×D172—22no—
121C2×D172—22no—
122C2×D172—22no—
123C2×D172—22no—
124C2×D172—22no—
125C2×D172—22no—
126C2×D172—22no—
127C2×D172—22no—
128C2×D172—22no—
129C2×D172—41no—
130C2×D172—41no—
131C2×D172—41no—
132C2×D172—41no—
133C2×D172—41no—
134C2×D172—41no—
135C2×D172—41no—
136C2×D172—41no—
137C2×D172—41no—
138C2×D172—41no—
139C2×D172—41no—
140C2×D172—41no—
141C2×D172C22⋊C414yes—
142M16×C43—22no—
143M16×C43—22no—
144M16×C43—41no—
145M16×C43—41no—
146C2×C8×C43—22no—
147C2×C8×C43—41no—
148C2×C8×C43—41no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—41no—
152C4⋊C4×C43—41no—
153C22⋊C4×C43—22no—
154C22⋊C4×C43—22no—
155C22⋊C4×C43—41no—
156C22⋊C4×C43—41no—
157C42×C43—22no—
158C42×C43—22no—
159C42×C43—41no—
160C42×C43—41no—
161#10621877—22no—
162#10621877—22no—
163#10621877—22no—
164#10621877—22no—
165#10621877—41no—
166#10621877—41no—
167#10621877—41no—
168#10621877—41no—
169#10621877—41no—
170#10621877—41no—
171#10621877—41no—
172#10621877—41no—
173C2×C43⋊C8—22no—
174C2×C43⋊C8—22no—
175C2×C43⋊C8—22no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—41no—
179C2×C43⋊C8—41no—
180C2×C43⋊C8—41no—
181C2×C43⋊C8—41no—
182C23×C43—42no—
183C23×C43#11711yescharacteristic
184C23×C43#12111yescharacteristic
185C23×C43#12311yescharacteristic
186C23×C43#12311yescharacteristic
187C23×C43#12311yescharacteristic
188C23×C43#12411yescharacteristic
189C23×C43#12611yescharacteristic
190C22×D43—24no—
191C22×D43—42no—
192C22×D43—42no—
193C22×D43—42no—
194C22×D43—42no—
195C22×D43—42no—
196C22×D43—42no—
197C22×D43—84no—
198C22×D43—84no—
199C22×D43—84no—
200C22×D43—84no—
201C22×D43—84no—
202C22×D43—84no—
203C22×D43—84no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—82no—
207C2×C4×C43—82no—
208C2×C4×C43C2×C22⋊C411yescharacteristic
209C2×C4×C43#11711yescharacteristic
210C2×C4×C43C4×D411yescharacteristic
211C2×C4×C43C4×D411yescharacteristic
212C2×C4×C43C4×D411yescharacteristic
213C2×C4×C43C4×D411yescharacteristic
214C2×C4×C43#12011yescharacteristic
215C2×C4×C43#12011yescharacteristic
216C2×C4×C43#12111yescharacteristic
217C2×C4×C43#12111yescharacteristic
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43#12311yescharacteristic
224C2×C4×C43#12311yescharacteristic
225C2×C4×C43#12311yescharacteristic
226C2×C4×C43#12311yescharacteristic
227C2×C4×C43#12311yescharacteristic
228C2×C4×C43#12311yescharacteristic
229C2×C4×C43#12311yescharacteristic
230C2×C4×C43#12411yescharacteristic
231C2×C4×C43#12411yescharacteristic
232C2×C4×C43#12411yescharacteristic
233C2×C4×C43#12611yescharacteristic
234C2×C4×C43#12611yescharacteristic
235C2×C4×C43#12611yescharacteristic
236D172—24no—
237D172—24no—
238D172—42no—
239D172—42no—
240D172—42no—
241D172—42no—
242D172—42no—
243D172—42no—
244C8×C43—42no—
245C43⋊C8—42no—
246C43⋊C8—42no—
247C43⋊C8—42no—
248#11157—431nomaximal, Sylow
249C22×C43—22no—
250C22×C43—22no—
251C22×C43—22no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43#38111yescharacteristic
257C22×C43#38811yescharacteristic
258C22×C43#38811yescharacteristic
259C22×C43#39411yescharacteristic
260C22×C43#39411yescharacteristic
261C22×C43#39711yescharacteristic
262C22×C43#39711yescharacteristic
263C2×D43—44no—
264C2×D43—84no—
265C2×D43—84no—
266C2×D43—84no—
267C2×D43—84no—
268C2×D43—84no—
269C2×D43—84no—
270C2×D43—84no—
271C4×C43—82no—
272C4×C43—82no—
273C4×C43#38611yescharacteristic
274C4×C43#38611yescharacteristic
275C4×C43#38811yescharacteristic
276C4×C43#38811yescharacteristic
277C4×C43#39411yescharacteristic
278C4×C43#39411yescharacteristic
279C4×C43#39711yescharacteristic
280C4×C43#39711yescharacteristic
281C2×#418—431no—
282C2×#418—431no—
283C22×#100—431no—
284C2×#344—431no—
285C2×#344—431no—
286#1738—431no—
287C2×H(3,ℤ/4)D4311yescharacteristic, complemented
288C2×C43—21no—
289C2×C43—21no—
290C2×C43—21no—
291C2×C43—21no—
292C2×C43—21no—
293C2×C43—21no—
294C2×C43#144011yescharacteristic
295C2×C43#208112yes—
296D43—84no—
297C23×D4—431no—
298C22×M16—431no—
299C22×M16—431no—
300C22×M16—431no—
301C22×M16C2×D4311yescharacteristic
302C2×#117C2×D4311yescharacteristic
303C2×#117C2×D4311yescharacteristic
304#418—862no—
305#418—862no—
306#418—862no—
307#418—862no—
308C2×#102—862no—
309C2×#102—862no—
310C2×#100—434no—
311C2×#100—862no—
312C2×#100—862no—
313#344—862no—
314#344—862no—
315#341—862no—
316H(3,ℤ/4)—22no—
317C43#1115711yescharacteristic, complemented, Sylow
318C25—861no—
319C22×D4—432no—
320C22×D4—432no—
321C22×D4—432no—
322C22×D4—861no—
323C22×D4—861no—
324C22×D4—861no—
325C22×D4—861no—
326C22×D4—861no—
327C22×D4—861no—
328C22×D4—861no—
329C22×D4—861no—
330C22×D4—861no—
331C22×D4—861no—
332C22×D4—861no—
333C23×C4C22×D4311yescharacteristic
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—432no—
340C2×M16—432no—
341C2×M16—861no—
342C2×M16—861no—
343C2×M16—861no—
344C2×M16—861no—
345C2×M16—861no—
346C2×M16—861no—
347C2×M16—861no—
348C2×M16—861no—
349C2×M16—861no—
350C2×M16—861no—
351C2×M16—861no—
352C2×M16—861no—
353C2×M16—861no—
354C2×M16—861no—
355C2×M16—861no—
356C2×M16—861no—
357C2×M16C4×D4312yes—
358C22×C8—21no—
359C22×C8—432no—
360C22×C8—861no—
361C22×C8—861no—
362#117—21no—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—21no—
367#117—21no—
368#117D17212yes—
369#117C22⋊D4312yes—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C42—21no—
375C2×C42—21no—
376#102—868no—
377#102—868no—
378#100—868no—
379C24—862no—
380C24—862no—
381C24—862no—
382C24—3444no—
383C24—1721no—
384C24—1721no—
385C24—1721no—
386C24—1721no—
387C24#1062190011yescharacteristic
388C2×D4—434no—
389C2×D4—862no—
390C2×D4—862no—
391C2×D4—862no—
392C2×D4—862no—
393C2×D4—862no—
394C2×D4—862no—
395C2×D4—862no—
396C2×D4—862no—
397C2×D4—862no—
398C2×D4—862no—
399C2×D4—862no—
400C2×D4—862no—
401C2×D4—862no—
402C2×D4—862no—
403C2×D4—862no—
404C2×D4—1721no—
405C2×D4—1721no—
406C2×D4—1721no—
407C2×D4—1721no—
408C2×D4—1721no—
409C2×D4—1721no—
410C2×D4—1721no—
411C2×D4—1721no—
412C2×D4—1721no—
413C2×D4—1721no—
414C2×D4—1721no—
415C2×D4—1721no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4C2×C4×D4311yescharacteristic
419C22×C4C2×D17211yescharacteristic
420C22×C4#1062189811yescharacteristic
421C22×C4#1062189811yescharacteristic
422C22×C4#1062189811yescharacteristic
423C22×C4#1062189811yescharacteristic
424C22×C4D4×D4311yescharacteristic
425C22×C4D4×D4311yescharacteristic
426C22×C4D4×D4311yescharacteristic
427C22×C4D4×D4311yescharacteristic
428C22×C4#1062190011yescharacteristic
429C22×C4#1062190211yescharacteristic
430C22×C4#1062190211yescharacteristic
431C22×C4C2×C22⋊D4311yescharacteristic
432M16—22no—
433M16—22no—
434M16—41no—
435M16—41no—
436M16—862no—
437M16—862no—
438M16—862no—
439M16—862no—
440M16—1721no—
441M16—1721no—
442M16—1721no—
443M16—1721no—
444M16—1721no—
445M16—1721no—
446M16—1721no—
447M16—1721no—
448C2×C8—22no—
449C2×C8—41no—
450C2×C8—41no—
451C2×C8—862no—
452C2×C8—862no—
453C2×C8—862no—
454C2×C8—862no—
455C2×C8—862no—
456C2×C8—1721no—
457C2×C8—1721no—
458C2×C8—1721no—
459C2×C8—1721no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C42—22no—
469C42—22no—
470C42—41no—
471C42—41no—
472C23—42no—
473C23—864no—
474C23—3444no—
475C23—3444no—
476C23—3444no—
477C23—3444no—
478C23—3444no—
479C23—3444no—
480C23—3444no—
481C23—1722no—
482C23—1722no—
483C23—1722no—
484C23—1722no—
485C23—1722no—
486C23—1722no—
487C23#1306328311yescharacteristic
488C23#1306329711yescharacteristic
489C23#1306330711yescharacteristic
490C23#1306330711yescharacteristic
491C23#1306330911yescharacteristic
492C23#1306331111yescharacteristic
493C23#1306332011yescharacteristic
494D4—864no—
495D4—864no—
496D4—1722no—
497D4—1722no—
498D4—1722no—
499D4—1722no—
500D4—1722no—
501D4—1722no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—82no—
505C2×C4—82no—
506C2×C4C22⋊C4×D4311yescharacteristic
507C2×C4#1306328211yescharacteristic
508C2×C4(C22⋊D43)⋊C411yescharacteristic
509C2×C4C4×C22⋊D4311yescharacteristic
510C2×C4#1306328711yescharacteristic
511C2×C4C4×D17211yescharacteristic
512C2×C4#1306329311yescharacteristic
513C2×C4#1306329511yescharacteristic
514C2×C4#1306329611yescharacteristic
515C2×C4#1306329811yescharacteristic
516C2×C4#1306329811yescharacteristic
517C2×C4#1306329811yescharacteristic
518C2×C4#1306329911yescharacteristic
519C2×C4#1306330011yescharacteristic
520C2×C4#1306330011yescharacteristic
521C2×C4#1306330711yescharacteristic
522C2×C4#1306330811yescharacteristic
523C2×C4#1306331011yescharacteristic
524C2×C4#1306331011yescharacteristic
525C2×C4#1306331011yescharacteristic
526C2×C4#1306331011yescharacteristic
527C2×C4#1306331011yescharacteristic
528C2×C4#1306331111yescharacteristic
529C2×C4#1306331311yescharacteristic
530C2×C4#1306331411yescharacteristic
531C2×C4#1306331911yescharacteristic
532C2×C4#1306332011yescharacteristic
533C2×C4#1306332011yescharacteristic
534C8—42no—
535C8—1722no—
536C8—1722no—
537C8—1722no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—3444no—
546C22—3444no—
547C22—3444no—
548C22—3444no—
549C22—3444no—
550C22—3444no—
551C22—3444no—
552C22—1724no—
553C22#1458276111yescharacteristic
554C22#1458278911yescharacteristic
555C22#1458279111yescharacteristic
556C22#1458281411yescharacteristic
557C22#1458281511yescharacteristic
558C22#1458282611yescharacteristic
559C22#1458282811yescharacteristic
560C4—82no—
561C4—82no—
562C4#1458277511yescharacteristic
563C4#1458277711yescharacteristic
564C4#1458278811yescharacteristic
565C4#1458279011yescharacteristic
566C4#1458281611yescharacteristic
567C4#1458281711yescharacteristic
568C4#1458282511yescharacteristic
569C4#1458282811yescharacteristic
570C2—21no—
571C2—21no—
572C2—21no—
573C2—21no—
574C2—21no—
575C2—21no—
576C2—3444no—
577C2#1913284311yescharacteristic
578C2#1913605712yes—
subgroupG/H
centerC22#14582828
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×H(3,ℤ/4)C2
socleC22×C43#397
prime radicalC23×D172C22
cosocleC23×C4×C43C23
hypercenterC2×H(3,ℤ/4)D43
hypocenterC43#11157
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. C2×#14582669C2semidirect
5. C2×#14582669C2semidirect
6. #19134321C2semidirect
7. C2×C43×H(3,ℤ/4)C2semidirect
20. C2×#13063241C4semidirect
287. C2×H(3,ℤ/4)D43semidirect
317. C43#11157semidirect

Maximal subgroups

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

subgroupindex
C2×#145829032
C22×#130632412
C2×#145826692
#191343212
C2×C43×H(3,ℤ/4)2
#1115743