Finite Group Databasebeta

← C2×#10624904⋊C2 #72243947

Subgroups — C2×#10624904⋊C2 #72243947

Order 2916.

691 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#10624904⋊C2C212yesmaximal, direct product factor
2C2×#10624904C211yesmaximal, characteristic, complemented
3C2×C9⋊#272C311yesmaximal, characteristic
4C2×#92311—31nomaximal
5C2×#92311—31nomaximal
6C2×#92311—31nomaximal
7C2×#92308—31nomaximal
8C2×#92308—31nomaximal
9C2×#92308—31nomaximal
10C2×#6895⋊C2—31nomaximal
11C2×#92305—31nomaximal
12C2×#92295—31nomaximal
13C2×#92294—31nomaximal
14C2×#92294—31nomaximal
15C2×#92294—31nomaximal
16C2×C3⋊(D9⋊C9)—31nomaximal
17#10624904C2211yescharacteristic, complemented, Sylow
18C2×#6899—21no—
19C2×#6899—21no—
20C2×#6899—21no—
21C2×#6898D311yescharacteristic, complemented
22C2×#6898D311yescharacteristic, complemented
23C2×#6898D311yescharacteristic, complemented
24C2×#6897—21no—
25C2×#6897—21no—
26C2×#6897—21no—
27C2×#6896D311yescharacteristic, complemented
28C2×#6896D311yescharacteristic, complemented
29C2×#6896D311yescharacteristic, complemented
30C2×#6895D311yescharacteristic, complemented
31C2×#6894—21no—
32C2×#6894—21no—
33C2×#6894—21no—
34C2×#6894—21no—
35C2×#6894—21no—
36C2×#6893D311yescharacteristic
37C2×C9⋊H(3,𝔽3)—21no—
38C2×C9×3−1+2—21no—
39C2×C9×H(3,𝔽3)C2×C311yescharacteristic
40C2×#6887D311yescharacteristic, complemented
41C2×#6887D311yescharacteristic, complemented
42C2×#6887D311yescharacteristic, complemented
43C2×#6887D311yescharacteristic, complemented
44C2×C3×C9⋊C9D311yescharacteristic, complemented
45C9⋊#272C2×C312yes—
46#92311—32no—
47#92311—32no—
48#92311—32no—
49#92308—32no—
50#92308—32no—
51#92308—32no—
52#6895⋊C2—32no—
53#92305—32no—
54#92295—32no—
55#92294—32no—
56#92294—32no—
57#92294—32no—
58C3⋊(D9⋊C9)—32no—
59C2×C3⋊#272—31no—
60C2×C9×C3⋊D3—91no—
61C2×C3×C3⋊D9—31no—
62C2×C3×C3⋊D9—31no—
63C2×C3×C3⋊D9—31no—
64C2×C3×C3⋊D9—31no—
65C2×#4181—31no—
66C2×#4181—31no—
67C2×#4181—31no—
68C2×#4181—31no—
69C2×#4181—31no—
70C2×#4181—31no—
71C2×#4181—31no—
72C2×#4181—31no—
73C2×D9⋊C9—91no—
74C2×D9⋊C9—91no—
75C2×D9⋊C9—91no—
76C2×D9⋊C9—91no—
77C2×D9⋊C9—91no—
78C2×D9⋊C9—91no—
79C2×(C3⋊D3)⋊C9—91no—
80C2×(C3⋊D3)⋊C9—91no—
81C2×(C3⋊D3)⋊C9—91no—
82C2×C9×D9—91no—
83C2×C9×D9—91no—
84C2×C9×D9—91no—
85#6899—21no—
86#6899—21no—
87#6899—21no—
88#6898C2×D311yescharacteristic, complemented
89#6898C2×D311yescharacteristic, complemented
90#6898C2×D311yescharacteristic, complemented
91#6897—21no—
92#6897—21no—
93#6897—21no—
94#6896C2×D311yescharacteristic, complemented
95#6896C2×D311yescharacteristic, complemented
96#6896C2×D311yescharacteristic, complemented
97#6895C2×D311yescharacteristic, complemented
98#6894—21no—
99#6894—21no—
100#6894—21no—
101#6894—21no—
102#6894—21no—
103#6893C2×D311yescharacteristic
104C9⋊H(3,𝔽3)—21no—
105C9×3−1+2—21no—
106C9×H(3,𝔽3)C22×C311yescharacteristic
107#6887C2×D311yescharacteristic, complemented
108#6887C2×D311yescharacteristic, complemented
109#6887C2×D311yescharacteristic, complemented
110#6887C2×D311yescharacteristic, complemented
111C3×C9⋊C9C2×D311yescharacteristic, complemented
112C2×C3×3−1+2—21no—
113C2×C3×3−1+2—21no—
114C2×C3×3−1+2—21no—
115C2×C3×3−1+2—21no—
116C2×C3×H(3,𝔽3)C3×D311yescharacteristic
117C2×C32×C9—21no—
118C2×C32×C9C3×D311yescharacteristic
119C2×C32×C9C3×D311yescharacteristic
120C2×C32×C9C3×D311yescharacteristic
121C2×C32×C9C3×D311yescharacteristic
122C2×C32×C9C3⋊D311yescharacteristic
123C3⋊#272—32no—
124C9×C3⋊D3—92no—
125C3×C3⋊D9—32no—
126C3×C3⋊D9—32no—
127C3×C3⋊D9—32no—
128C3×C3⋊D9—32no—
129C2×C9⋊C9—21no—
130C2×C9⋊C9—21no—
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—21no—
160C2×C9⋊C9—21no—
161C2×C9⋊C9—21no—
162C2×C9⋊C9C3⋊D311yescharacteristic
163C2×C9⋊C9C3⋊D311yescharacteristic
164C2×C9⋊C9C3⋊D311yescharacteristic
165C2×C9⋊C9C3⋊D311yescharacteristic
166C2×C9⋊C9C3⋊D311yescharacteristic
167C2×C9⋊C9C3⋊D311yescharacteristic
168C2×C32⋊C9—21no—
169C2×C32⋊C9—21no—
170C2×C32⋊C9—21no—
171C2×C32⋊C9—21no—
172C2×C32⋊C9—21no—
173C2×C32⋊C9—21no—
174C2×C32⋊C9—21no—
175C2×C32⋊C9—21no—
176C2×C32⋊C9—21no—
177C2×C32⋊C9—21no—
178C2×C32⋊C9—21no—
179C2×C32⋊C9C3×D311yescharacteristic
180C2×C32⋊C9C3×D311yescharacteristic
181C2×C32⋊C9C3×D311yescharacteristic
182C2×C32⋊C9C3×D311yescharacteristic
183C2×C32⋊C9C3×D311yescharacteristic
184C2×C32⋊C9C3×D311yescharacteristic
185C2×C32⋊C9C3×D311yescharacteristic
186C2×C32⋊C9C3×D311yescharacteristic
187C2×C32⋊C9C3⋊D311yescharacteristic
188C2×C32⋊C9C3⋊D311yescharacteristic
189C2×C32⋊C9C3⋊D311yescharacteristic
190C2×C92—21no—
191C2×C92—21no—
192C2×C92—21no—
193C2×C92C3⋊D311yescharacteristic
194C2×C92C3⋊D311yescharacteristic
195C2×C92C3⋊D311yescharacteristic
196#4181—32no—
197#4181—32no—
198#4181—32no—
199#4181—32no—
200#4181—32no—
201#4181—32no—
202#4181—32no—
203#4181—32no—
204D9⋊C9—92no—
205D9⋊C9—92no—
206D9⋊C9—92no—
207D9⋊C9—92no—
208D9⋊C9—92no—
209D9⋊C9—92no—
210(C3⋊D3)⋊C9—92no—
211(C3⋊D3)⋊C9—92no—
212(C3⋊D3)⋊C9—92no—
213C9×D9—92no—
214C9×D9—92no—
215C9×D9—92no—
216C2×C3×C3⋊D3—91no—
217C2×C3×C3⋊D3—91no—
218C2×C3×C3⋊D3—91no—
219C2×C3×C3⋊D3—91no—
220C2×#272—271no—
221C2×#272—271no—
222C2×#272—271no—
223C2×C3⋊D9—31no—
224C2×C3⋊D9—31no—
225C2×C3⋊D9—31no—
226C2×C3⋊D9—31no—
227C2×D3×C9—271no—
228C2×D3×C9—271no—
229C2×D3×C9—271no—
230C2×D3×C9—271no—
231C2×C3×D9—91no—
232C2×C3×D9—91no—
233C2×C3×D9—91no—
234C2×C3×D9—91no—
235C2×C3×D9—91no—
236C2×C3×D9—91no—
237C2×C3×D9—91no—
238C2×C3×D9—91no—
239C2×C3×D9—91no—
240C3×3−1+2—21no—
241C3×3−1+2—21no—
242C3×3−1+2—21no—
243C3×3−1+2—21no—
244C3×H(3,𝔽3)C2×C3×D311yescharacteristic
245C32×C9—21no—
246C32×C9C2×C3×D311yescharacteristic
247C32×C9C2×C3×D311yescharacteristic
248C32×C9C2×C3×D311yescharacteristic
249C32×C9C2×C3×D311yescharacteristic
250C32×C9C2×C3⋊D311yescharacteristic
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⋊C9—21no—
265C9⋊C9—21no—
266C9⋊C9—21no—
267C9⋊C9—21no—
268C9⋊C9—21no—
269C9⋊C9—21no—
270C9⋊C9—21no—
271C9⋊C9—21no—
272C9⋊C9—21no—
273C9⋊C9—21no—
274C9⋊C9—21no—
275C9⋊C9—21no—
276C9⋊C9—21no—
277C9⋊C9—21no—
278C9⋊C9—21no—
279C9⋊C9—21no—
280C9⋊C9—21no—
281C9⋊C9—21no—
282C9⋊C9—21no—
283C9⋊C9—21no—
284C9⋊C9C2×C3⋊D311yescharacteristic
285C9⋊C9C2×C3⋊D311yescharacteristic
286C9⋊C9C2×C3⋊D311yescharacteristic
287C9⋊C9C2×C3⋊D311yescharacteristic
288C9⋊C9C2×C3⋊D311yescharacteristic
289C9⋊C9C2×C3⋊D311yescharacteristic
290C32⋊C9—21no—
291C32⋊C9—21no—
292C32⋊C9—21no—
293C32⋊C9—21no—
294C32⋊C9—21no—
295C32⋊C9—21no—
296C32⋊C9—21no—
297C32⋊C9—21no—
298C32⋊C9—21no—
299C32⋊C9—21no—
300C32⋊C9—21no—
301C32⋊C9C2×C3×D311yescharacteristic
302C32⋊C9C2×C3×D311yescharacteristic
303C32⋊C9C2×C3×D311yescharacteristic
304C32⋊C9C2×C3×D311yescharacteristic
305C32⋊C9C2×C3×D311yescharacteristic
306C32⋊C9C2×C3×D311yescharacteristic
307C32⋊C9C2×C3×D311yescharacteristic
308C32⋊C9C2×C3×D311yescharacteristic
309C32⋊C9C2×C3⋊D311yescharacteristic
310C32⋊C9C2×C3⋊D311yescharacteristic
311C32⋊C9C2×C3⋊D311yescharacteristic
312C92—21no—
313C92—21no—
314C92—21no—
315C92C2×C3⋊D311yescharacteristic
316C92C2×C3⋊D311yescharacteristic
317C92C2×C3⋊D311yescharacteristic
318C2×C33C3×C3⋊D311yescharacteristic
319C2×C33C3×C3⋊D311yescharacteristic
320C2×C33C3×C3⋊D311yescharacteristic
321C2×C33C3×C3⋊D311yescharacteristic
322C3×C3⋊D3—92no—
323C3×C3⋊D3—92no—
324C3×C3⋊D3—92no—
325C3×C3⋊D3—92no—
326C2×3−1+2—61no—
327C2×3−1+2—61no—
328C2×3−1+2—61no—
329C2×3−1+2—181no—
330C2×3−1+2—181no—
331C2×3−1+2—181no—
332C2×H(3,𝔽3)—31no—
333C2×H(3,𝔽3)—31no—
334C2×H(3,𝔽3)—31no—
335C2×C3×C9—21no—
336C2×C3×C9—21no—
337C2×C3×C9—21no—
338C2×C3×C9—21no—
339C2×C3×C9—21no—
340C2×C3×C9—21no—
341C2×C3×C9—21no—
342C2×C3×C9—21no—
343C2×C3×C9—21no—
344C2×C3×C9—21no—
345C2×C3×C9—21no—
346C2×C3×C9—21no—
347C2×C3×C9—21no—
348C2×C3×C9—31no—
349C2×C3×C9—31no—
350C2×C3×C9—61no—
351C2×C3×C9—61no—
352C2×C3×C9—61no—
353C2×C3×C9—61no—
354C2×C3×C9—61no—
355C2×C3×C9—61no—
356C2×C3×C9—61no—
357C2×C3×C9—61no—
358C2×C3×C9—61no—
359C2×C3×C9—181no—
360C2×C3×C9C3×C3⋊D311yescharacteristic
361C2×C3×C9C3×C3⋊D311yescharacteristic
362C2×C3×C9C3×C3⋊D311yescharacteristic
363C2×C3×C9C3×C3⋊D311yescharacteristic
364C2×C3×C9C3×C3⋊D311yescharacteristic
365C2×C3×C9C3×C3⋊D311yescharacteristic
366C2×C3×C9C3×C3⋊D311yescharacteristic
367C2×C3×C9C3×C3⋊D311yescharacteristic
368C2×C3×C9C3×C3⋊D311yescharacteristic
369C2×C3×C9C3⋊(C3⋊D3)11yescharacteristic
370#272—272no—
371#272—272no—
372#272—272no—
373C3⋊D9—32no—
374C3⋊D9—32no—
375C3⋊D9—32no—
376C3⋊D9—32no—
377D3×C9—272no—
378D3×C9—272no—
379D3×C9—272no—
380D3×C9—272no—
381C3×D9—92no—
382C3×D9—92no—
383C3×D9—92no—
384C3×D9—92no—
385C3×D9—92no—
386C3×D9—92no—
387C3×D9—92no—
388C3×D9—92no—
389C3×D9—92no—
390C2×C3⋊D3—91no—
391C2×C3⋊D3—91no—
392C2×C3⋊D3—91no—
393C2×C3⋊D3—91no—
394C2×C3×D3—271no—
395C2×C3×D3—271no—
396C2×C3×D3—271no—
397C2×C3×D3—271no—
398C2×C3×D3—811no—
399C2×C3×D3—811no—
400C2×C3×D3—811no—
401C22×C9—811no—
402C2×D9—91no—
403C2×D9—91no—
404C2×D9—91no—
405C2×D9—91no—
406C2×D9—91no—
407C2×D9—91no—
408C2×D9—91no—
409C2×D9—91no—
410C2×D9—91no—
411C33C2×C3×C3⋊D311yescharacteristic
412C33C2×C3×C3⋊D311yescharacteristic
413C33C2×C3×C3⋊D311yescharacteristic
414C33C2×C3×C3⋊D311yescharacteristic
4153−1+2—61no—
4163−1+2—61no—
4173−1+2—61no—
4183−1+2—181no—
4193−1+2—181no—
4203−1+2—181no—
421H(3,𝔽3)—31no—
422H(3,𝔽3)—31no—
423H(3,𝔽3)—31no—
424C3×C9—21no—
425C3×C9—21no—
426C3×C9—21no—
427C3×C9—21no—
428C3×C9—21no—
429C3×C9—21no—
430C3×C9—21no—
431C3×C9—21no—
432C3×C9—21no—
433C3×C9—21no—
434C3×C9—21no—
435C3×C9—21no—
436C3×C9—21no—
437C3×C9—31no—
438C3×C9—31no—
439C3×C9—61no—
440C3×C9—61no—
441C3×C9—61no—
442C3×C9—61no—
443C3×C9—61no—
444C3×C9—61no—
445C3×C9—61no—
446C3×C9—61no—
447C3×C9—61no—
448C3×C9—181no—
449C3×C9C2×C3×C3⋊D311yescharacteristic
450C3×C9C2×C3×C3⋊D311yescharacteristic
451C3×C9C2×C3×C3⋊D311yescharacteristic
452C3×C9C2×C3×C3⋊D311yescharacteristic
453C3×C9C2×C3×C3⋊D311yescharacteristic
454C3×C9C2×C3×C3⋊D311yescharacteristic
455C3×C9C2×C3×C3⋊D311yescharacteristic
456C3×C9C2×C3×C3⋊D311yescharacteristic
457C3×C9C2×C3×C3⋊D311yescharacteristic
458C3×C9C2×C3⋊(C3⋊D3)11yescharacteristic
459C2×C32—31no—
460C2×C32—31no—
461C2×C32—31no—
462C2×C32—31no—
463C2×C32—31no—
464C2×C32—61no—
465C2×C32—61no—
466C2×C32—61no—
467C2×C32—61no—
468C2×C32—61no—
469C2×C32—61no—
470C2×C32#420711yescharacteristic
471C2×C32#420711yescharacteristic
472C2×C32#420711yescharacteristic
473C2×C32C3×C3⋊(C3⋊D3)11yescharacteristic
474C3⋊D3—92no—
475C3⋊D3—92no—
476C3⋊D3—92no—
477C3⋊D3—92no—
478C3×D3—272no—
479C3×D3—272no—
480C3×D3—272no—
481C3×D3—272no—
482C3×D3—812no—
483C3×D3—812no—
484C3×D3—812no—
485C2×C9—21no—
486C2×C9—31no—
487C2×C9—31no—
488C2×C9—31no—
489C2×C9—61no—
490C2×C9—61no—
491C2×C9—61no—
492C2×C9—61no—
493C2×C9—61no—
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—61no—
507C2×C9—61no—
508C2×C9—812no—
509C2×C9#420811yescharacteristic
510D9—92no—
511D9—92no—
512D9—92no—
513D9—92no—
514D9—92no—
515D9—92no—
516D9—92no—
517D9—92no—
518D9—92no—
519C22×C3—811no—
520C2×D3—271no—
521C2×D3—271no—
522C2×D3—271no—
523C2×D3—271no—
524C2×D3—811no—
525C2×D3—811no—
526C2×D3—811no—
527C32—31no—
528C32—31no—
529C32—31no—
530C32—31no—
531C32—31no—
532C32—61no—
533C32—61no—
534C32—61no—
535C32—61no—
536C32—61no—
537C32—61no—
538C32C2×#420711yescharacteristic
539C32C2×#420711yescharacteristic
540C32C2×#420711yescharacteristic
541C32C2×C3×C3⋊(C3⋊D3)11yescharacteristic
542C9—21no—
543C9—31no—
544C9—31no—
545C9—31no—
546C9—61no—
547C9—61no—
548C9—61no—
549C9—61no—
550C9—61no—
551C9—61no—
552C9—61no—
553C9—61no—
554C9—61no—
555C9—61no—
556C9—61no—
557C9—61no—
558C9—61no—
559C9—61no—
560C9—61no—
561C9—61no—
562C9—61no—
563C9—61no—
564C9—61no—
565C9C2×#420811yescharacteristic
566C2×C3—21no—
567C2×C3—31no—
568C2×C3—61no—
569C2×C3—61no—
570C2×C3—181no—
571C2×C3—181no—
572C2×C3—181no—
573C2×C3—812no—
574C2×C3C3⋊#420711yescharacteristic
575C2×C3C3⋊#420811yescharacteristic
576D3—272no—
577D3—272no—
578D3—272no—
579D3—272no—
580D3—812no—
581D3—812no—
582D3—812no—
583C22—811noSylow
584C3—21no—
585C3—31no—
586C3—61no—
587C3—61no—
588C3—181no—
589C3—181no—
590C3—181no—
591C3C2×C3⋊#420711yescharacteristic
592C3C2×C3⋊#420811yescharacteristic
593C2—812no—
594C2#10624904⋊C211yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3C3⋊#4207
commutator, cosocle, hypocenterC9×H(3,𝔽3)C22×C3
FrattiniC32C2×C3×C3⋊(C3⋊D3)
FittingC2×#10624904C2
socleC2×C32C3×C3⋊(C3⋊D3)
prime radicalC2×C9⋊#272C3
LCSG ▷ C9×H(3,𝔽3)
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. #10624904⋊C2C2direct (N × H)
2. C2×#10624904C2semidirect
17. #10624904C22semidirect
21. C2×#6898D3semidirect
22. C2×#6898D3semidirect
23. C2×#6898D3semidirect
27. C2×#6896D3semidirect
28. C2×#6896D3semidirect
29. C2×#6896D3semidirect
30. C2×#6895D3semidirect
40. C2×#6887D3semidirect
41. C2×#6887D3semidirect
42. C2×#6887D3semidirect
43. C2×#6887D3semidirect
44. C2×C3×C9⋊C9D3semidirect
88. #6898C2×D3semidirect
89. #6898C2×D3semidirect
90. #6898C2×D3semidirect
94. #6896C2×D3semidirect
95. #6896C2×D3semidirect
96. #6896C2×D3semidirect
97. #6895C2×D3semidirect
107. #6887C2×D3semidirect
108. #6887C2×D3semidirect
109. #6887C2×D3semidirect
110. #6887C2×D3semidirect
111. C3×C9⋊C9C2×D3semidirect
594. C2#10624904⋊C2direct (N × H)

Maximal subgroups

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

subgroupindex
#10624904⋊C22
C2×#106249042
C2×C9⋊#2723
C2×#923113
C2×#923083
C2×#6895⋊C23
C2×#923053
C2×#922953
C2×#922943
C2×C3⋊(D9⋊C9)3