Finite Group Databasebeta

← C2×#13091386 #72244031

Subgroups — C2×#13091386 #72244031

Order 2916.

843 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13091386C212yesmaximal, direct product factor
2C2×#10624864C211yesmaximal, characteristic, complemented
3C2×C3×#4208C311yesmaximal, characteristic
4C2×C9×#272C311yesmaximal, characteristic
5C2×C9×#272C311yesmaximal, characteristic
6C2×C9×#272C311yesmaximal, characteristic
7C2×D3×C9⋊C9—31nomaximal
8C2×D3×C9⋊C9—31nomaximal
9C2×D3×C9⋊C9—31nomaximal
10C2×D3×C9⋊C9—31nomaximal
11#10624864C2211yescharacteristic, complemented, Sylow
12C2×C3×#737C2×C311yescharacteristic
13C3×#4208C2×C312yes—
14C2×C9×3−1+2—21no—
15C2×C9×3−1+2—21no—
16C2×C9×3−1+2—21no—
17C2×C9×3−1+2—21no—
18C2×C9×3−1+2—21no—
19C2×C9×3−1+2—21no—
20C2×C9×3−1+2—21no—
21C2×C9×3−1+2—21no—
22C2×C9×3−1+2—21no—
23C2×C9×3−1+2—21no—
24C2×C9×3−1+2—21no—
25C2×C9×3−1+2—21no—
26C2×C9×H(3,𝔽3)C2×C311yescharacteristic
27C2×C9×H(3,𝔽3)C2×C311yescharacteristic
28C2×C9×H(3,𝔽3)C2×C311yescharacteristic
29C2×#6887—21no—
30C2×#6887—21no—
31C2×#6887—21no—
32C2×#6887—21no—
33C2×C3×C9⋊C9D311yescharacteristic, complemented
34C2×C3×C9⋊C9D311yescharacteristic, complemented
35C2×C3×C9⋊C9D311yescharacteristic, complemented
36C2×C3×C9⋊C9D311yescharacteristic, complemented
37C9×#272C2×C312yes—
38C9×#272C2×C312yes—
39C9×#272C2×C312yes—
40D3×C9⋊C9—32no—
41D3×C9⋊C9—32no—
42D3×C9⋊C9—32no—
43D3×C9⋊C9—32no—
44C2×#4208C913yescomplemented
45C2×C3×#272C3211yescharacteristic
46C2×C3×D3×C9—31no—
47C2×C3×D3×C9—31no—
48C2×C3×D3×C9—31no—
49C2×C3×D3×C9—31no—
50C2×C3×D3×C9—31no—
51C2×C3×D3×C9—31no—
52C2×C3×D3×C9—31no—
53C2×C3×D3×C9—31no—
54C2×C3×D3×C9—31no—
55C2×C3×D3×C9—31no—
56C2×C3×D3×C9—31no—
57C2×C3×D3×C9—31no—
58C2×C3×D3×C9—31no—
59C2×C3×D3×C9—31no—
60C2×C3×D3×C9—31no—
61C2×C3×D3×C9—31no—
62C22×C9⋊C9—91no—
63C3×#737C22×C311yescharacteristic
64C9×3−1+2—21no—
65C9×3−1+2—21no—
66C9×3−1+2—21no—
67C9×3−1+2—21no—
68C9×3−1+2—21no—
69C9×3−1+2—21no—
70C9×3−1+2—21no—
71C9×3−1+2—21no—
72C9×3−1+2—21no—
73C9×3−1+2—21no—
74C9×3−1+2—21no—
75C9×3−1+2—21no—
76C9×H(3,𝔽3)C22×C311yescharacteristic
77C9×H(3,𝔽3)C22×C311yescharacteristic
78C9×H(3,𝔽3)C22×C311yescharacteristic
79#6887—21no—
80#6887—21no—
81#6887—21no—
82#6887—21no—
83C3×C9⋊C9C2×D311yescharacteristic, complemented
84C3×C9⋊C9C2×D311yescharacteristic, complemented
85C3×C9⋊C9C2×D311yescharacteristic, complemented
86C3×C9⋊C9C2×D311yescharacteristic, complemented
87C2×#737—23no—
88C2×#737—23no—
89C2×#737—23no—
90C2×#737—23no—
91C2×#737C2×C913yescomplemented
92C2×C3×3−1+2—21no—
93C2×C3×3−1+2—21no—
94C2×C3×3−1+2—21no—
95C2×C3×3−1+2—21no—
96C2×C3×H(3,𝔽3)C2×C3211yescharacteristic
97C2×C32×C9C3×D311yescharacteristic
98C2×C32×C9C3×D311yescharacteristic
99C2×C32×C9C3×D311yescharacteristic
100C2×C32×C9C3×D311yescharacteristic
101C2×C32×C9C3×D311yescharacteristic
102C2×C32×C9C3×D311yescharacteristic
103C2×C32×C9C3×D311yescharacteristic
104C2×C32×C9C3×D311yescharacteristic
105C2×C32×C9C3×D311yescharacteristic
106C2×C32×C9C3×D311yescharacteristic
107C2×C32×C9C3×D311yescharacteristic
108C2×C32×C9C3×D311yescharacteristic
109C2×C32×C9C3×D311yescharacteristic
110C2×C32×C9C3×D311yescharacteristic
111C2×C32×C9C3×D311yescharacteristic
112C2×C32×C9C3×D311yescharacteristic
113#4208C2×C916yescomplemented
114C3×#272C2×C3212yes—
115C3×D3×C9—32no—
116C3×D3×C9—32no—
117C3×D3×C9—32no—
118C3×D3×C9—32no—
119C3×D3×C9—32no—
120C3×D3×C9—32no—
121C3×D3×C9—32no—
122C3×D3×C9—32no—
123C3×D3×C9—32no—
124C3×D3×C9—32no—
125C3×D3×C9—32no—
126C3×D3×C9—32no—
127C3×D3×C9—32no—
128C3×D3×C9—32no—
129C3×D3×C9—32no—
130C3×D3×C9—32no—
131C2×C9⋊C9—21no—
132C2×C9⋊C9—21no—
133C2×C9⋊C9—21no—
134C2×C9⋊C9—21no—
135C2×C9⋊C9—21no—
136C2×C9⋊C9—21no—
137C2×C9⋊C9—21no—
138C2×C9⋊C9—21no—
139C2×C9⋊C9—21no—
140C2×C9⋊C9—21no—
141C2×C9⋊C9—21no—
142C2×C9⋊C9—21no—
143C2×C9⋊C9—21no—
144C2×C9⋊C9—21no—
145C2×C9⋊C9—21no—
146C2×C9⋊C9—21no—
147C2×C9⋊C9—21no—
148C2×C9⋊C9—21no—
149C2×C9⋊C9—21no—
150C2×C9⋊C9—21no—
151C2×C9⋊C9—21no—
152C2×C9⋊C9—21no—
153C2×C9⋊C9—21no—
154C2×C9⋊C9—21no—
155C2×C9⋊C9—21no—
156C2×C9⋊C9—21no—
157C2×C9⋊C9—21no—
158C2×C9⋊C9—21no—
159C2×C9⋊C9—92no—
160C2×C9⋊C9C3⋊D311yescharacteristic
161C2×C32⋊C9—21no—
162C2×C32⋊C9—21no—
163C2×C32⋊C9—21no—
164C2×C32⋊C9—21no—
165C2×C32⋊C9—21no—
166C2×C32⋊C9—21no—
167C2×C32⋊C9—21no—
168C2×C32⋊C9—21no—
169C2×C32⋊C9—21no—
170C2×C32⋊C9—21no—
171C2×C32⋊C9—21no—
172C2×C32⋊C9—21no—
173C2×C92—21no—
174C2×C92—21no—
175C2×C92—21no—
176C2×C92—21no—
177C2×C92—21no—
178C2×C92—21no—
179C2×C92—21no—
180C2×C92—21no—
181C2×C92—21no—
182C2×C92—21no—
183C2×C92—21no—
184C2×C92—21no—
185C2×C32×D3—31no—
186C2×C32×D3—31no—
187C2×C32×D3—31no—
188C2×C32×D3—31no—
189C22×C3×C9—91no—
190C22×C3×C9—91no—
191C22×C3×C9—91no—
192C22×C3×C9—91no—
193C2×#272C3×C911yescharacteristic
194C2×D3×C9—33no—
195C2×D3×C9—33no—
196C2×D3×C9—33no—
197C2×D3×C9—33no—
198C2×D3×C9—91no—
199C2×D3×C9—91no—
200C2×D3×C9—91no—
201C2×D3×C9—91no—
202C2×D3×C9—91no—
203C2×D3×C9—91no—
204C2×D3×C9—91no—
205C2×D3×C9—91no—
206C2×D3×C9—91no—
207C2×D3×C9—91no—
208C2×D3×C9—91no—
209C2×D3×C9—91no—
210#737—23no—
211#737—23no—
212#737—23no—
213#737—23no—
214#737C22×C913yescomplemented
215C3×3−1+2—21no—
216C3×3−1+2—21no—
217C3×3−1+2—21no—
218C3×3−1+2—21no—
219C3×H(3,𝔽3)C22×C3211yescharacteristic
220C32×C9C2×C3×D311yescharacteristic
221C32×C9C2×C3×D311yescharacteristic
222C32×C9C2×C3×D311yescharacteristic
223C32×C9C2×C3×D311yescharacteristic
224C32×C9C2×C3×D311yescharacteristic
225C32×C9C2×C3×D311yescharacteristic
226C32×C9C2×C3×D311yescharacteristic
227C32×C9C2×C3×D311yescharacteristic
228C32×C9C2×C3×D311yescharacteristic
229C32×C9C2×C3×D311yescharacteristic
230C32×C9C2×C3×D311yescharacteristic
231C32×C9C2×C3×D311yescharacteristic
232C32×C9C2×C3×D311yescharacteristic
233C32×C9C2×C3×D311yescharacteristic
234C32×C9C2×C3×D311yescharacteristic
235C32×C9C2×C3×D311yescharacteristic
236C9⋊C9—21no—
237C9⋊C9—21no—
238C9⋊C9—21no—
239C9⋊C9—21no—
240C9⋊C9—21no—
241C9⋊C9—21no—
242C9⋊C9—21no—
243C9⋊C9—21no—
244C9⋊C9—21no—
245C9⋊C9—21no—
246C9⋊C9—21no—
247C9⋊C9—21no—
248C9⋊C9—21no—
249C9⋊C9—21no—
250C9⋊C9—21no—
251C9⋊C9—21no—
252C9⋊C9—21no—
253C9⋊C9—21no—
254C9⋊C9—21no—
255C9⋊C9—21no—
256C9⋊C9—21no—
257C9⋊C9—21no—
258C9⋊C9—21no—
259C9⋊C9—21no—
260C9⋊C9—21no—
261C9⋊C9—21no—
262C9⋊C9—21no—
263C9⋊C9—21no—
264C9⋊C9C2×C3⋊D311yescharacteristic
265C32⋊C9—21no—
266C32⋊C9—21no—
267C32⋊C9—21no—
268C32⋊C9—21no—
269C32⋊C9—21no—
270C32⋊C9—21no—
271C32⋊C9—21no—
272C32⋊C9—21no—
273C32⋊C9—21no—
274C32⋊C9—21no—
275C32⋊C9—21no—
276C32⋊C9—21no—
277C92—21no—
278C92—21no—
279C92—21no—
280C92—21no—
281C92—21no—
282C92—21no—
283C92—21no—
284C92—21no—
285C92—21no—
286C92—21no—
287C92—21no—
288C92—21no—
289C2×C33C32×D311yescharacteristic
290C2×C33C32×D311yescharacteristic
291C2×C33C32×D311yescharacteristic
292C2×C33C32×D311yescharacteristic
293C32×D3—32no—
294C32×D3—32no—
295C32×D3—32no—
296C32×D3—32no—
297C2×3−1+2—26no—
298C2×3−1+2—26no—
299C2×3−1+2—26no—
300C2×3−1+2—26no—
301C2×3−1+2—23no—
302C2×3−1+2—23no—
303C2×3−1+2—23no—
304C2×3−1+2—23no—
305C2×H(3,𝔽3)—21no—
306C2×H(3,𝔽3)—21no—
307C2×H(3,𝔽3)—21no—
308C2×H(3,𝔽3)—21no—
309C2×H(3,𝔽3)C2×C3×C911yescharacteristic
310C2×C3×C9—21no—
311C2×C3×C9—21no—
312C2×C3×C9—21no—
313C2×C3×C9—21no—
314C2×C3×C9—23no—
315C2×C3×C9—23no—
316C2×C3×C9—23no—
317C2×C3×C9—23no—
318C2×C3×C9—21no—
319C2×C3×C9—21no—
320C2×C3×C9—21no—
321C2×C3×C9—21no—
322C2×C3×C9—21no—
323C2×C3×C9—21no—
324C2×C3×C9—21no—
325C2×C3×C9—21no—
326C2×C3×C9—21no—
327C2×C3×C9—21no—
328C2×C3×C9—21no—
329C2×C3×C9—21no—
330C2×C3×C9—91no—
331C2×C3×C9—91no—
332C2×C3×C9—91no—
333C2×C3×C9—91no—
334C2×C3×C9—91no—
335C2×C3×C9—92no—
336C2×C3×C9—92no—
337C2×C3×C9—92no—
338C2×C3×C9—92no—
339C2×C3×C9—181no—
340C2×C3×C9—181no—
341C2×C3×C9—181no—
342C2×C3×C9—181no—
343C2×C3×C9—181no—
344C2×C3×C9—181no—
345C2×C3×C9—181no—
346C2×C3×C9D3×C913yescomplemented
347C2×C3×C9D3×C913yescomplemented
348C2×C3×C9D3×C913yescomplemented
349C2×C3×C9D3×C913yescomplemented
350C2×C3×C9C3×C3⋊D311yescharacteristic
351C2×C3×C9C3×C3⋊D311yescharacteristic
352C2×C3×C9C3×C3⋊D311yescharacteristic
353C2×C3×C9C3×C3⋊D311yescharacteristic
354#272C2×C3×C912yes—
355D3×C9—36no—
356D3×C9—36no—
357D3×C9—36no—
358D3×C9—36no—
359D3×C9—92no—
360D3×C9—92no—
361D3×C9—92no—
362D3×C9—92no—
363D3×C9—92no—
364D3×C9—92no—
365D3×C9—92no—
366D3×C9—92no—
367D3×C9—92no—
368D3×C9—92no—
369D3×C9—92no—
370D3×C9—92no—
371C22×C32—91no—
372C2×C3×D3—31no—
373C2×C3×D3—31no—
374C2×C3×D3—31no—
375C2×C3×D3—31no—
376C2×C3×D3—31no—
377C2×C3×D3—31no—
378C2×C3×D3—31no—
379C2×C3×D3—31no—
380C2×C3×D3—31no—
381C2×C3×D3—31no—
382C2×C3×D3—31no—
383C2×C3×D3—31no—
384C2×C3×D3—31no—
385C2×C3×D3—31no—
386C2×C3×D3—31no—
387C2×C3×D3—31no—
388C22×C9—93no—
389C22×C9—271no—
390C22×C9—271no—
391C22×C9—271no—
392C33C2×C32×D311yescharacteristic
393C33C2×C32×D311yescharacteristic
394C33C2×C32×D311yescharacteristic
395C33C2×C32×D311yescharacteristic
3963−1+2—26no—
3973−1+2—26no—
3983−1+2—26no—
3993−1+2—26no—
4003−1+2—23no—
4013−1+2—23no—
4023−1+2—23no—
4033−1+2—23no—
404H(3,𝔽3)—21no—
405H(3,𝔽3)—21no—
406H(3,𝔽3)—21no—
407H(3,𝔽3)—21no—
408H(3,𝔽3)C22×C3×C911yescharacteristic
409C3×C9—21no—
410C3×C9—21no—
411C3×C9—21no—
412C3×C9—21no—
413C3×C9—23no—
414C3×C9—23no—
415C3×C9—23no—
416C3×C9—23no—
417C3×C9—21no—
418C3×C9—21no—
419C3×C9—21no—
420C3×C9—21no—
421C3×C9—21no—
422C3×C9—21no—
423C3×C9—21no—
424C3×C9—21no—
425C3×C9—21no—
426C3×C9—21no—
427C3×C9—21no—
428C3×C9—21no—
429C3×C9—91no—
430C3×C9—91no—
431C3×C9—91no—
432C3×C9—91no—
433C3×C9—91no—
434C3×C9—181no—
435C3×C9—181no—
436C3×C9—181no—
437C3×C9—181no—
438C3×C9—181no—
439C3×C9—181no—
440C3×C9—181no—
441C3×C9C2×D3×C913yescomplemented
442C3×C9C2×D3×C913yescomplemented
443C3×C9C2×D3×C913yescomplemented
444C3×C9C2×D3×C913yescomplemented
445C3×C9C2×C3×C3⋊D311yescharacteristic
446C3×C9C2×C3×C3⋊D311yescharacteristic
447C3×C9C2×C3×C3⋊D311yescharacteristic
448C3×C9C2×C3×C3⋊D311yescharacteristic
449C2×C32—21no—
450C2×C32—21no—
451C2×C32—21no—
452C2×C32—21no—
453C2×C32—31no—
454C2×C32—31no—
455C2×C32—31no—
456C2×C32—61no—
457C2×C32—61no—
458C2×C32—61no—
459C2×C32—61no—
460C2×C32—61no—
461C2×C32—61no—
462C2×C32—61no—
463C2×C32—61no—
464C2×C32—61no—
465C2×C32—92no—
466C2×C32C3×D3×C911yescharacteristic
467C2×C32C3×D3×C911yescharacteristic
468C2×C32C3×D3×C911yescharacteristic
469C2×C32C3×D3×C911yescharacteristic
470C2×C32C32×C3⋊D311yescharacteristic
471C3×D3—32no—
472C3×D3—32no—
473C3×D3—32no—
474C3×D3—32no—
475C3×D3—32no—
476C3×D3—32no—
477C3×D3—32no—
478C3×D3—32no—
479C3×D3—32no—
480C3×D3—32no—
481C3×D3—32no—
482C3×D3—32no—
483C3×D3—32no—
484C3×D3—32no—
485C3×D3—32no—
486C3×D3—32no—
487C2×C9—23no—
488C2×C9—23no—
489C2×C9—23no—
490C2×C9—23no—
491C2×C9—31no—
492C2×C9—31no—
493C2×C9—31no—
494C2×C9—61no—
495C2×C9—61no—
496C2×C9—61no—
497C2×C9—61no—
498C2×C9—61no—
499C2×C9—61no—
500C2×C9—61no—
501C2×C9—61no—
502C2×C9—61no—
503C2×C9—61no—
504C2×C9—61no—
505C2×C9—61no—
506C2×C9—96no—
507C2×C9—272no—
508C2×C9—272no—
509C2×C9—272no—
510C2×C9C9×C3⋊D313yes—
511C22×C3—91no—
512C22×C3—91no—
513C22×C3—91no—
514C22×C3—91no—
515C2×D3—31no—
516C2×D3—31no—
517C2×D3—31no—
518C2×D3—31no—
519C32—21no—
520C32—21no—
521C32—21no—
522C32—21no—
523C32—31no—
524C32—31no—
525C32—31no—
526C32—61no—
527C32—61no—
528C32—61no—
529C32—61no—
530C32—61no—
531C32—61no—
532C32—61no—
533C32—61no—
534C32—61no—
535C32C2×C3×D3×C911yescharacteristic
536C32C2×C3×D3×C911yescharacteristic
537C32C2×C3×D3×C911yescharacteristic
538C32C2×C3×D3×C911yescharacteristic
539C32C2×C32×C3⋊D311yescharacteristic
540C9—23no—
541C9—23no—
542C9—23no—
543C9—23no—
544C9—31no—
545C9—31no—
546C9—31no—
547C9—61no—
548C9—61no—
549C9—61no—
550C9—61no—
551C9—61no—
552C9—61no—
553C9—61no—
554C9—61no—
555C9—61no—
556C9—61no—
557C9—61no—
558C9—61no—
559C9C2×C9×C3⋊D313yes—
560C2×C3—31no—
561C2×C3—61no—
562C2×C3—61no—
563C2×C3—61no—
564C2×C3—61no—
565C2×C3—61no—
566C2×C3—61no—
567C2×C3—61no—
568C2×C3—92no—
569C2×C3—92no—
570C2×C3—92no—
571C2×C3—92no—
572C2×C3C3×C9×C3⋊D311yescharacteristic
573C2×C3#9239411yescharacteristic
574C2×C3#9239411yescharacteristic
575C2×C3#9239411yescharacteristic
576D3—32no—
577D3—32no—
578D3—32no—
579D3—32no—
580C22—91noSylow
581C3—31no—
582C3—61no—
583C3—61no—
584C3—61no—
585C3—61no—
586C3—61no—
587C3—61no—
588C3—61no—
589C3C2×C3×C9×C3⋊D311yescharacteristic
590C3C2×#9239411yescharacteristic
591C3C2×#9239411yescharacteristic
592C3C2×#9239411yescharacteristic
593C2—92no—
594C2#1309138611yescharacteristic, direct product factor
subgroupG/H
center, socleC2×C32C32×C3⋊D3
commutator, hypocenterH(3,𝔽3)C22×C3×C9
FrattiniC32C2×C32×C3⋊D3
FittingC2×#10624864C2
prime radicalC2×C3×#272C32
cosocleC3×H(3,𝔽3)C22×C32
hypercenterC2×C9⋊C9C3⋊D3
LCSG ▷ H(3,𝔽3)
UCSC1 ◁ C2×C32 ◁ C2×C9⋊C9

Complements

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

NH ≅ G/Ntype
1. #13091386C2direct (N × H)
2. C2×#10624864C2semidirect
11. #10624864C22semidirect
33. C2×C3×C9⋊C9D3semidirect
34. C2×C3×C9⋊C9D3semidirect
35. C2×C3×C9⋊C9D3semidirect
36. C2×C3×C9⋊C9D3semidirect
44. C2×#4208C9semidirect
83. C3×C9⋊C9C2×D3semidirect
84. C3×C9⋊C9C2×D3semidirect
85. C3×C9⋊C9C2×D3semidirect
86. C3×C9⋊C9C2×D3semidirect
91. C2×#737C2×C9semidirect
113. #4208C2×C9semidirect
214. #737C22×C9semidirect
346. C2×C3×C9D3×C9semidirect
347. C2×C3×C9D3×C9semidirect
348. C2×C3×C9D3×C9semidirect
349. C2×C3×C9D3×C9semidirect
441. C3×C9C2×D3×C9semidirect
442. C3×C9C2×D3×C9semidirect
443. C3×C9C2×D3×C9semidirect
444. C3×C9C2×D3×C9semidirect
594. C2#13091386direct (N × H)

Maximal subgroups

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

subgroupindex
#130913862
C2×#106248642
C2×C3×#42083
C2×C9×#2723
C2×D3×C9⋊C93