Finite Group Databasebeta

← C2×C3⋊#92285 #72254016

Subgroups — C2×C3⋊#92285 #72254016

Order 2916.

1052 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊#92285C212yesmaximal, direct product factor
2C2×C3×#6911C211yesmaximal, characteristic, complemented
3C2×C3×C3⋊#272C311yesmaximal, characteristic, complemented
4C2×C3⋊D3×3−1+2—31nomaximal
5C2×C3⋊#4178C311yesmaximal, characteristic, complemented
6C2×C3⋊#4178C311yesmaximal, characteristic, complemented
7C2×C3⋊#4178C311yesmaximal, characteristic, complemented
8C2×#92285—31nomaximal
9C2×#92285—31nomaximal
10C2×#92285—31nomaximal
11C3×#6911C2211yescharacteristic, complemented, Sylow
12C2×C32×3−1+2D311yescharacteristic, complemented
13C2×C32×H(3,𝔽3)—21no—
14C2×C32×H(3,𝔽3)C2×C311yescharacteristic
15C3×C3⋊#272C2×C312yescomplemented
16C3⋊D3×3−1+2—32no—
17C2×#6911—21no—
18C2×#6911—21no—
19C2×#6911—21no—
20C2×#6911—21no—
21C2×#6911—21no—
22C2×#6911—21no—
23C2×#6911—21no—
24C2×#6911—21no—
25C2×#6911—21no—
26C2×#6911—21no—
27C2×#6911—21no—
28C2×#6911—21no—
29C2×#6911D311yescharacteristic, complemented
30C2×#6911D311yescharacteristic, complemented
31C2×#6911D311yescharacteristic, complemented
32C2×C3×#732—21no—
33C2×C3×#732—21no—
34C2×C3×#732—21no—
35C2×C3×#732C2×C311yescharacteristic, complemented
36C2×C3×#732C2×C311yescharacteristic, complemented
37C2×C3×#732C2×C311yescharacteristic, complemented
38C3⋊#4178C2×C312yescomplemented
39C3⋊#4178C2×C312yescomplemented
40C3⋊#4178C2×C312yescomplemented
41#92285—32no—
42#92285—32no—
43#92285—32no—
44C2×C32×C3⋊D3—31no—
45C2×C32×C3⋊D3—91no—
46C2×C3⋊#272C3211yescharacteristic, complemented
47C2×C3×#272—31no—
48C2×C3×#272—31no—
49C2×C3×#272—31no—
50C2×C3×#272—91no—
51C2×C3×#272—91no—
52C2×C9×C3⋊D3—31no—
53C2×C9×C3⋊D3—31no—
54C2×C9×C3⋊D3—31no—
55C2×D3×3−1+2—91no—
56C2×D3×3−1+2—91no—
57C2×D3×3−1+2—91no—
58C2×D3×3−1+2—91no—
59C2×#4178—31no—
60C2×#4178—31no—
61C2×#4178—31no—
62C2×#4178—31no—
63C2×#4178—31no—
64C2×#4178—31no—
65C2×#4178—31no—
66C2×#4178—31no—
67C2×#4178—31no—
68C32×3−1+2C2×D311yescharacteristic, complemented
69C32×H(3,𝔽3)—21no—
70C32×H(3,𝔽3)C22×C311yescharacteristic
71#6911—21no—
72#6911—21no—
73#6911—21no—
74#6911—21no—
75#6911—21no—
76#6911—21no—
77#6911—21no—
78#6911—21no—
79#6911—21no—
80#6911—21no—
81#6911—21no—
82#6911—21no—
83#6911C2×D311yescharacteristic, complemented
84#6911C2×D311yescharacteristic, complemented
85#6911C2×D311yescharacteristic, complemented
86C3×#732—21no—
87C3×#732—21no—
88C3×#732—21no—
89C3×#732C22×C311yescharacteristic, complemented
90C3×#732C22×C311yescharacteristic, complemented
91C3×#732C22×C311yescharacteristic, complemented
92C2×C34—31no—
93C2×C34—61no—
94C2×C34C3×D311yescharacteristic
95C32×C3⋊D3—32no—
96C32×C3⋊D3—92no—
97C2×C3×3−1+2—21no—
98C2×C3×3−1+2—21no—
99C2×C3×3−1+2—21no—
100C2×C3×3−1+2—21no—
101C2×C3×3−1+2—61no—
102C2×C3×3−1+2—61no—
103C2×C3×3−1+2—61no—
104C2×C3×3−1+2—61no—
105C2×C3×3−1+2—61no—
106C2×C3×3−1+2—61no—
107C2×C3×3−1+2C3⋊D311yescharacteristic, complemented
108C2×C3×H(3,𝔽3)—21no—
109C2×C3×H(3,𝔽3)—21no—
110C2×C3×H(3,𝔽3)—21no—
111C2×C3×H(3,𝔽3)—21no—
112C2×C3×H(3,𝔽3)—21no—
113C2×C3×H(3,𝔽3)—21no—
114C2×C3×H(3,𝔽3)—21no—
115C2×C3×H(3,𝔽3)—21no—
116C2×C3×H(3,𝔽3)—21no—
117C2×C3×H(3,𝔽3)—21no—
118C2×C3×H(3,𝔽3)—21no—
119C2×C3×H(3,𝔽3)—21no—
120C2×C3×H(3,𝔽3)—21no—
121C2×C3×H(3,𝔽3)—21no—
122C2×C3×H(3,𝔽3)—21no—
123C2×C3×H(3,𝔽3)—21no—
124C2×C3×H(3,𝔽3)—31no—
125C2×C3×H(3,𝔽3)—31no—
126C2×C3×H(3,𝔽3)—61no—
127C2×C3×H(3,𝔽3)—61no—
128C2×C3×H(3,𝔽3)—61no—
129C2×C3×H(3,𝔽3)—61no—
130C2×C3×H(3,𝔽3)—61no—
131C2×C3×H(3,𝔽3)—61no—
132C2×C3×H(3,𝔽3)—61no—
133C2×C3×H(3,𝔽3)—61no—
134C2×C3×H(3,𝔽3)—61no—
135C2×C3×H(3,𝔽3)—61no—
136C2×C3×H(3,𝔽3)—61no—
137C2×C3×H(3,𝔽3)C3×D311yescharacteristic
138C2×C3×H(3,𝔽3)C3×D311yescharacteristic
139C2×C3×H(3,𝔽3)C3×D311yescharacteristic
140C2×C3×H(3,𝔽3)C2×C3211yescharacteristic
141C2×C32×C9C3×D311yescharacteristic, complemented
142C2×C32×C9C3×D311yescharacteristic, complemented
143C2×C32×C9C3×D311yescharacteristic, complemented
144C3⋊#272C2×C3212yescomplemented
145C3×#272—32no—
146C3×#272—32no—
147C3×#272—32no—
148C3×#272—92no—
149C3×#272—92no—
150C9×C3⋊D3—32no—
151C9×C3⋊D3—32no—
152C9×C3⋊D3—32no—
153D3×3−1+2—92no—
154D3×3−1+2—92no—
155D3×3−1+2—92no—
156D3×3−1+2—92no—
157C2×#732—21no—
158C2×#732—21no—
159C2×#732—21no—
160C2×#732—21no—
161C2×#732—21no—
162C2×#732—21no—
163C2×#732—21no—
164C2×#732—21no—
165C2×#732—21no—
166C2×#732—21no—
167C2×#732—21no—
168C2×#732—21no—
169C2×#732—21no—
170C2×#732—21no—
171C2×#732—21no—
172C2×#732—21no—
173C2×#732—21no—
174C2×#732—21no—
175C2×#732—21no—
176C2×#732—21no—
177C2×#732—21no—
178C2×#732—21no—
179C2×#732—21no—
180C2×#732—21no—
181C2×#732—21no—
182C2×#732—21no—
183C2×#732—21no—
184C2×#732—21no—
185C2×#732—21no—
186C2×#732—21no—
187C2×#732—21no—
188C2×#732—21no—
189C2×#732—21no—
190C2×#732—21no—
191C2×#732—21no—
192C2×#732—21no—
193C2×#732C3×D311yescharacteristic, complemented
194C2×#732C3×D311yescharacteristic, complemented
195C2×#732C3×D311yescharacteristic, complemented
196C2×#732C3×D311yescharacteristic, complemented
197C2×#732C3×D311yescharacteristic, complemented
198C2×#732C3×D311yescharacteristic, complemented
199C2×#732C3×D311yescharacteristic, complemented
200C2×#732C3×D311yescharacteristic, complemented
201C2×#732C3×D311yescharacteristic, complemented
202#4178—32no—
203#4178—32no—
204#4178—32no—
205#4178—32no—
206#4178—32no—
207#4178—32no—
208#4178—32no—
209#4178—32no—
210#4178—32no—
211C2×C3×C3⋊D3—31no—
212C2×C3×C3⋊D3—91no—
213C2×C3×C3⋊D3—92no—
214C2×C3×C3⋊D3—91no—
215C2×C3×C3⋊D3—91no—
216C2×C32×D3—91no—
217C2×C32×D3—91no—
218C2×C32×D3—91no—
219C2×C32×D3—91no—
220C2×C32×D3—271no—
221C2×C32×D3—271no—
222C2×C32×D3—271no—
223C22×3−1+2—271no—
224C2×#272—31no—
225C2×#272—31no—
226C2×#272—31no—
227C2×#272—91no—
228C2×#272—91no—
229C2×D3×C9—91no—
230C2×D3×C9—91no—
231C2×D3×C9—91no—
232C2×D3×C9—91no—
233C2×D3×C9—91no—
234C2×D3×C9—91no—
235C2×D3×C9—91no—
236C2×D3×C9—91no—
237C2×D3×C9—91no—
238C2×D3×C9—91no—
239C2×D3×C9—91no—
240C2×D3×C9—91no—
241C34—31no—
242C34—61no—
243C34C2×C3×D311yescharacteristic
244C3×3−1+2—21no—
245C3×3−1+2—21no—
246C3×3−1+2—21no—
247C3×3−1+2—21no—
248C3×3−1+2—61no—
249C3×3−1+2—61no—
250C3×3−1+2—61no—
251C3×3−1+2—61no—
252C3×3−1+2—61no—
253C3×3−1+2—61no—
254C3×3−1+2C2×C3⋊D311yescharacteristic, complemented
255C3×H(3,𝔽3)—21no—
256C3×H(3,𝔽3)—21no—
257C3×H(3,𝔽3)—21no—
258C3×H(3,𝔽3)—21no—
259C3×H(3,𝔽3)—21no—
260C3×H(3,𝔽3)—21no—
261C3×H(3,𝔽3)—21no—
262C3×H(3,𝔽3)—21no—
263C3×H(3,𝔽3)—21no—
264C3×H(3,𝔽3)—21no—
265C3×H(3,𝔽3)—21no—
266C3×H(3,𝔽3)—21no—
267C3×H(3,𝔽3)—21no—
268C3×H(3,𝔽3)—21no—
269C3×H(3,𝔽3)—21no—
270C3×H(3,𝔽3)—21no—
271C3×H(3,𝔽3)—31no—
272C3×H(3,𝔽3)—31no—
273C3×H(3,𝔽3)—61no—
274C3×H(3,𝔽3)—61no—
275C3×H(3,𝔽3)—61no—
276C3×H(3,𝔽3)—61no—
277C3×H(3,𝔽3)—61no—
278C3×H(3,𝔽3)—61no—
279C3×H(3,𝔽3)—61no—
280C3×H(3,𝔽3)—61no—
281C3×H(3,𝔽3)—61no—
282C3×H(3,𝔽3)—61no—
283C3×H(3,𝔽3)—61no—
284C3×H(3,𝔽3)C2×C3×D311yescharacteristic
285C3×H(3,𝔽3)C2×C3×D311yescharacteristic
286C3×H(3,𝔽3)C2×C3×D311yescharacteristic
287C3×H(3,𝔽3)C22×C3211yescharacteristic
288C32×C9C2×C3×D311yescharacteristic, complemented
289C32×C9C2×C3×D311yescharacteristic, complemented
290C32×C9C2×C3×D311yescharacteristic, complemented
291#732—21no—
292#732—21no—
293#732—21no—
294#732—21no—
295#732—21no—
296#732—21no—
297#732—21no—
298#732—21no—
299#732—21no—
300#732—21no—
301#732—21no—
302#732—21no—
303#732—21no—
304#732—21no—
305#732—21no—
306#732—21no—
307#732—21no—
308#732—21no—
309#732—21no—
310#732—21no—
311#732—21no—
312#732—21no—
313#732—21no—
314#732—21no—
315#732—21no—
316#732—21no—
317#732—21no—
318#732—21no—
319#732—21no—
320#732—21no—
321#732—21no—
322#732—21no—
323#732—21no—
324#732—21no—
325#732—21no—
326#732—21no—
327#732C2×C3×D311yescharacteristic, complemented
328#732C2×C3×D311yescharacteristic, complemented
329#732C2×C3×D311yescharacteristic, complemented
330#732C2×C3×D311yescharacteristic, complemented
331#732C2×C3×D311yescharacteristic, complemented
332#732C2×C3×D311yescharacteristic, complemented
333#732C2×C3×D311yescharacteristic, complemented
334#732C2×C3×D311yescharacteristic, complemented
335#732C2×C3×D311yescharacteristic, complemented
336C2×C33—21no—
337C2×C33—21no—
338C2×C33—21no—
339C2×C33—21no—
340C2×C33—31no—
341C2×C33—31no—
342C2×C33—31no—
343C2×C33—31no—
344C2×C33—61no—
345C2×C33—61no—
346C2×C33—61no—
347C2×C33—61no—
348C2×C33—61no—
349C2×C33—61no—
350C2×C33—61no—
351C2×C33—61no—
352C2×C33—61no—
353C2×C33—61no—
354C2×C33—61no—
355C2×C33—61no—
356C2×C33—61no—
357C2×C33—61no—
358C2×C33—61no—
359C2×C33—61no—
360C2×C33—92no—
361C2×C33—181no—
362C2×C33—181no—
363C2×C33—181no—
364C2×C33—182no—
365C2×C33—181no—
366C2×C33—186no—
367C2×C33—183no—
368C2×C33(C3⋊D3)⋊C311yescharacteristic
369C2×C33(C3⋊D3)⋊C311yescharacteristic
370C2×C33(C3⋊D3)⋊C311yescharacteristic
371C2×C33C32×D311yescharacteristic
372C2×C33C3×C3⋊D311yescharacteristic
373C3×C3⋊D3—32no—
374C3×C3⋊D3—92no—
375C3×C3⋊D3—92no—
376C3×C3⋊D3—94no—
377C3×C3⋊D3—92no—
378C32×D3—92no—
379C32×D3—92no—
380C32×D3—92no—
381C32×D3—92no—
382C32×D3—272no—
383C32×D3—272no—
384C32×D3—272no—
385C2×3−1+2—61no—
386C2×3−1+2—61no—
387C2×3−1+2—61no—
388C2×3−1+2—61no—
389C2×3−1+2—61no—
390C2×3−1+2—62no—
391C2×3−1+2—61no—
392C2×3−1+2—61no—
393C2×3−1+2—61no—
394C2×3−1+2—61no—
395C2×3−1+2—61no—
396C2×3−1+2—61no—
397C2×3−1+2—61no—
398C2×3−1+2—272no—
399C2×H(3,𝔽3)—21no—
400C2×H(3,𝔽3)—21no—
401C2×H(3,𝔽3)—21no—
402C2×H(3,𝔽3)—21no—
403C2×H(3,𝔽3)—21no—
404C2×H(3,𝔽3)—21no—
405C2×H(3,𝔽3)—21no—
406C2×H(3,𝔽3)—21no—
407C2×H(3,𝔽3)—21no—
408C2×H(3,𝔽3)—21no—
409C2×H(3,𝔽3)—21no—
410C2×H(3,𝔽3)—21no—
411C2×H(3,𝔽3)—31no—
412C2×H(3,𝔽3)—31no—
413C2×H(3,𝔽3)—61no—
414C2×H(3,𝔽3)—61no—
415C2×H(3,𝔽3)—61no—
416C2×H(3,𝔽3)—61no—
417C2×H(3,𝔽3)—61no—
418C2×H(3,𝔽3)—61no—
419C2×H(3,𝔽3)—61no—
420C2×H(3,𝔽3)—61no—
421C2×H(3,𝔽3)—61no—
422C2×H(3,𝔽3)—61no—
423C2×H(3,𝔽3)—61no—
424C2×H(3,𝔽3)—61no—
425C2×H(3,𝔽3)—61no—
426C2×H(3,𝔽3)—61no—
427C2×H(3,𝔽3)—61no—
428C2×H(3,𝔽3)—61no—
429C2×H(3,𝔽3)—61no—
430C2×H(3,𝔽3)—61no—
431C2×H(3,𝔽3)—61no—
432C2×H(3,𝔽3)—61no—
433C2×H(3,𝔽3)—61no—
434C2×H(3,𝔽3)—61no—
435C2×H(3,𝔽3)—61no—
436C2×H(3,𝔽3)—61no—
437C2×H(3,𝔽3)—61no—
438C2×H(3,𝔽3)—61no—
439C2×H(3,𝔽3)—61no—
440C2×H(3,𝔽3)—61no—
441C2×H(3,𝔽3)—61no—
442C2×H(3,𝔽3)—61no—
443C2×H(3,𝔽3)—61no—
444C2×H(3,𝔽3)—61no—
445C2×H(3,𝔽3)—61no—
446C2×H(3,𝔽3)—61no—
447C2×H(3,𝔽3)—61no—
448C2×H(3,𝔽3)C32×D311yescharacteristic
449C2×H(3,𝔽3)C32×D311yescharacteristic
450C2×H(3,𝔽3)C32×D311yescharacteristic
451C2×C3×C9—21no—
452C2×C3×C9—21no—
453C2×C3×C9—21no—
454C2×C3×C9—31no—
455C2×C3×C9—31no—
456C2×C3×C9—31no—
457C2×C3×C9—31no—
458C2×C3×C9—61no—
459C2×C3×C9—61no—
460C2×C3×C9—61no—
461C2×C3×C9—61no—
462C2×C3×C9—61no—
463C2×C3×C9C3×C3⋊D311yescharacteristic, complemented
464C2×C3×C9C3×C3⋊D311yescharacteristic, complemented
465C2×C3×C9C3×C3⋊D311yescharacteristic, complemented
466#272—32no—
467#272—32no—
468#272—32no—
469#272—92no—
470#272—92no—
471D3×C9—92no—
472D3×C9—92no—
473D3×C9—92no—
474D3×C9—92no—
475D3×C9—92no—
476D3×C9—92no—
477D3×C9—92no—
478D3×C9—92no—
479D3×C9—92no—
480D3×C9—92no—
481D3×C9—92no—
482D3×C9—92no—
483C22×C32—271no—
484C2×C3⋊D3—31no—
485C2×C3⋊D3—91no—
486C2×C3×D3—91no—
487C2×C3×D3—91no—
488C2×C3×D3—91no—
489C2×C3×D3—91no—
490C2×C3×D3—271no—
491C2×C3×D3—271no—
492C2×C3×D3—271no—
493C2×C3×D3—271no—
494C2×C3×D3—271no—
495C2×C3×D3—271no—
496C2×C3×D3—271no—
497C2×C3×D3—272no—
498C2×C3×D3—271no—
499C2×C3×D3—272no—
500C2×C3×D3—272no—
501C2×C3×D3—271no—
502C2×C3×D3—271no—
503C22×C9—271no—
504C22×C9—271no—
505C22×C9—271no—
506C33—21no—
507C33—21no—
508C33—21no—
509C33—21no—
510C33—31no—
511C33—31no—
512C33—31no—
513C33—31no—
514C33—61no—
515C33—61no—
516C33—61no—
517C33—61no—
518C33—61no—
519C33—61no—
520C33—61no—
521C33—61no—
522C33—61no—
523C33—61no—
524C33—61no—
525C33—61no—
526C33—61no—
527C33—61no—
528C33—61no—
529C33—61no—
530C33—92no—
531C33—181no—
532C33—181no—
533C33—181no—
534C33—182no—
535C33—181no—
536C33—186no—
537C33—183no—
538C33C2×(C3⋊D3)⋊C311yescharacteristic
539C33C2×(C3⋊D3)⋊C311yescharacteristic
540C33C2×(C3⋊D3)⋊C311yescharacteristic
541C33C2×C32×D311yescharacteristic
542C33C2×C3×C3⋊D311yescharacteristic
5433−1+2—61no—
5443−1+2—61no—
5453−1+2—61no—
5463−1+2—61no—
5473−1+2—61no—
5483−1+2—61no—
5493−1+2—61no—
5503−1+2—61no—
5513−1+2—61no—
5523−1+2—61no—
5533−1+2—61no—
5543−1+2—62no—
5553−1+2—61no—
556H(3,𝔽3)—21no—
557H(3,𝔽3)—21no—
558H(3,𝔽3)—21no—
559H(3,𝔽3)—21no—
560H(3,𝔽3)—21no—
561H(3,𝔽3)—21no—
562H(3,𝔽3)—21no—
563H(3,𝔽3)—21no—
564H(3,𝔽3)—21no—
565H(3,𝔽3)—21no—
566H(3,𝔽3)—21no—
567H(3,𝔽3)—21no—
568H(3,𝔽3)—31no—
569H(3,𝔽3)—31no—
570H(3,𝔽3)—61no—
571H(3,𝔽3)—61no—
572H(3,𝔽3)—61no—
573H(3,𝔽3)—61no—
574H(3,𝔽3)—61no—
575H(3,𝔽3)—61no—
576H(3,𝔽3)—61no—
577H(3,𝔽3)—61no—
578H(3,𝔽3)—61no—
579H(3,𝔽3)—61no—
580H(3,𝔽3)—61no—
581H(3,𝔽3)—61no—
582H(3,𝔽3)—61no—
583H(3,𝔽3)—61no—
584H(3,𝔽3)—61no—
585H(3,𝔽3)—61no—
586H(3,𝔽3)—61no—
587H(3,𝔽3)—61no—
588H(3,𝔽3)—61no—
589H(3,𝔽3)—61no—
590H(3,𝔽3)—61no—
591H(3,𝔽3)—61no—
592H(3,𝔽3)—61no—
593H(3,𝔽3)—61no—
594H(3,𝔽3)—61no—
595H(3,𝔽3)—61no—
596H(3,𝔽3)—61no—
597H(3,𝔽3)—61no—
598H(3,𝔽3)—61no—
599H(3,𝔽3)—61no—
600H(3,𝔽3)—61no—
601H(3,𝔽3)—61no—
602H(3,𝔽3)—61no—
603H(3,𝔽3)—61no—
604H(3,𝔽3)—61no—
605H(3,𝔽3)C2×C32×D311yescharacteristic
606H(3,𝔽3)C2×C32×D311yescharacteristic
607H(3,𝔽3)C2×C32×D311yescharacteristic
608C3×C9—21no—
609C3×C9—21no—
610C3×C9—21no—
611C3×C9—31no—
612C3×C9—31no—
613C3×C9—31no—
614C3×C9—31no—
615C3×C9—61no—
616C3×C9—61no—
617C3×C9—61no—
618C3×C9—61no—
619C3×C9—61no—
620C3×C9C2×C3×C3⋊D311yescharacteristic, complemented
621C3×C9C2×C3×C3⋊D311yescharacteristic, complemented
622C3×C9C2×C3×C3⋊D311yescharacteristic, complemented
623C2×C32—21no—
624C2×C32—21no—
625C2×C32—21no—
626C2×C32—21no—
627C2×C32—31no—
628C2×C32—31no—
629C2×C32—31no—
630C2×C32—31no—
631C2×C32—61no—
632C2×C32—61no—
633C2×C32—62no—
634C2×C32—61no—
635C2×C32—61no—
636C2×C32—61no—
637C2×C32—61no—
638C2×C32—61no—
639C2×C32—61no—
640C2×C32—61no—
641C2×C32—61no—
642C2×C32—61no—
643C2×C32—61no—
644C2×C32—61no—
645C2×C32—61no—
646C2×C32—61no—
647C2×C32—61no—
648C2×C32—91no—
649C2×C32—181no—
650C2×C32—182no—
651C2×C32—182no—
652C2×C32—182no—
653C2×C32—182no—
654C2×C32—181no—
655C2×C32—181no—
656C2×C32—181no—
657C2×C32—182no—
658C2×C32—181no—
659C2×C32—182no—
660C2×C32—182no—
661C2×C32—181no—
662C2×C32—181no—
663C2×C32—181no—
664C2×C32—181no—
665C2×C32—182no—
666C2×C32—181no—
667C2×C32—182no—
668C2×C32—182no—
669C2×C32—181no—
670C2×C32—181no—
671C2×C32—183no—
672C2×C32—183no—
673C2×C32—183no—
674C2×C32—183no—
675C2×C32—183no—
676C2×C32—183no—
677C2×C32—183no—
678C2×C32—183no—
679C2×C32—183no—
680C2×C32—181no—
681C2×C32—181no—
682C2×C32—181no—
683C2×C32—181no—
684C2×C32—181no—
685C2×C32—272no—
686C2×C32C3×(C3⋊D3)⋊C311yescharacteristic
687C2×C32C3×(C3⋊D3)⋊C311yescharacteristic
688C2×C32C3×(C3⋊D3)⋊C311yescharacteristic
689C2×C32C3⋊((C3⋊D3)⋊C3)11yescharacteristic
690C2×C32C32×C3⋊D311yescharacteristic
691C3⋊D3—32no—
692C3⋊D3—92no—
693C3×D3—92no—
694C3×D3—92no—
695C3×D3—92no—
696C3×D3—92no—
697C3×D3—272no—
698C3×D3—272no—
699C3×D3—272no—
700C3×D3—272no—
701C3×D3—272no—
702C3×D3—272no—
703C3×D3—272no—
704C3×D3—274no—
705C3×D3—272no—
706C3×D3—274no—
707C3×D3—274no—
708C3×D3—272no—
709C3×D3—272no—
710C2×C9—31no—
711C2×C9—61no—
712C2×C9—61no—
713C2×C9—61no—
714C2×C9—61no—
715C2×C9—61no—
716C2×C9—272no—
717C2×C9—272no—
718C2×C9—272no—
719C22×C3—271no—
720C22×C3—811no—
721C2×D3—91no—
722C2×D3—91no—
723C2×D3—91no—
724C2×D3—91no—
725C2×D3—271no—
726C2×D3—271no—
727C2×D3—271no—
728C32—21no—
729C32—21no—
730C32—21no—
731C32—21no—
732C32—31no—
733C32—31no—
734C32—31no—
735C32—31no—
736C32—61no—
737C32—61no—
738C32—62no—
739C32—61no—
740C32—61no—
741C32—61no—
742C32—61no—
743C32—61no—
744C32—61no—
745C32—61no—
746C32—61no—
747C32—61no—
748C32—61no—
749C32—61no—
750C32—61no—
751C32—61no—
752C32—61no—
753C32—91no—
754C32—181no—
755C32—182no—
756C32—182no—
757C32—182no—
758C32—182no—
759C32—181no—
760C32—181no—
761C32—181no—
762C32—182no—
763C32—181no—
764C32—182no—
765C32—182no—
766C32—181no—
767C32—181no—
768C32—181no—
769C32—181no—
770C32—182no—
771C32—181no—
772C32—182no—
773C32—182no—
774C32—181no—
775C32—181no—
776C32—183no—
777C32—183no—
778C32—183no—
779C32—183no—
780C32—183no—
781C32—183no—
782C32—183no—
783C32—183no—
784C32—183no—
785C32—181no—
786C32—181no—
787C32—181no—
788C32—181no—
789C32—181no—
790C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
791C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
792C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
793C32C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
794C32C2×C32×C3⋊D311yescharacteristic
795C9—31no—
796C9—61no—
797C9—61no—
798C9—61no—
799C9—61no—
800C9—61no—
801C2×C3—21no—
802C2×C3—31no—
803C2×C3—31no—
804C2×C3—61no—
805C2×C3—61no—
806C2×C3—61no—
807C2×C3—61no—
808C2×C3—61no—
809C2×C3—61no—
810C2×C3—91no—
811C2×C3—181no—
812C2×C3—181no—
813C2×C3—181no—
814C2×C3—181no—
815C2×C3—181no—
816C2×C3—181no—
817C2×C3—181no—
818C2×C3—181no—
819C2×C3—181no—
820C2×C3—181no—
821C2×C3—181no—
822C2×C3—181no—
823C2×C3—181no—
824C2×C3—181no—
825C2×C3—272no—
826C2×C3—812no—
827C2×C3#9228511yescharacteristic, complemented
828C2×C3C3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
829D3—92no—
830D3—92no—
831D3—92no—
832D3—92no—
833D3—272no—
834D3—272no—
835D3—272no—
836C22—271noSylow
837C3—21no—
838C3—31no—
839C3—31no—
840C3—61no—
841C3—61no—
842C3—61no—
843C3—61no—
844C3—61no—
845C3—61no—
846C3—91no—
847C3—181no—
848C3—181no—
849C3—181no—
850C3—181no—
851C3—181no—
852C3—181no—
853C3—181no—
854C3—181no—
855C3—181no—
856C3—181no—
857C3—181no—
858C3—181no—
859C3—181no—
860C3—181no—
861C3C2×#9228511yescharacteristic, complemented
862C3C2×C3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
863C2—272no—
864C2C3⋊#9228511yescharacteristic, direct product factor
subgroupG/H
centerC2×C3C3×C3⋊((C3⋊D3)⋊C3)
commutator, cosocle, hypocenterC3×H(3,𝔽3)C22×C32
FrattiniC32C2×C32×C3⋊D3
FittingC2×C3×#6911C2
socleC2×C32C3×(C3⋊D3)⋊C3
hypercenterC2×C32C3⋊((C3⋊D3)⋊C3)
LCSG ▷ C3×H(3,𝔽3)
UCSC1 ◁ C2×C3 ◁ C2×C32

Complements

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

NH ≅ G/Ntype
1. C3⋊#92285C2direct (N × H)
2. C2×C3×#6911C2semidirect
3. C2×C3×C3⋊#272C3semidirect
5. C2×C3⋊#4178C3semidirect
6. C2×C3⋊#4178C3semidirect
7. C2×C3⋊#4178C3semidirect
11. C3×#6911C22semidirect
12. C2×C32×3−1+2D3semidirect
15. C3×C3⋊#272C2×C3semidirect
29. C2×#6911D3semidirect
30. C2×#6911D3semidirect
31. C2×#6911D3semidirect
35. C2×C3×#732C2×C3semidirect
36. C2×C3×#732C2×C3semidirect
37. C2×C3×#732C2×C3semidirect
38. C3⋊#4178C2×C3semidirect
39. C3⋊#4178C2×C3semidirect
40. C3⋊#4178C2×C3semidirect
46. C2×C3⋊#272C32semidirect
68. C32×3−1+2C2×D3semidirect
83. #6911C2×D3semidirect
84. #6911C2×D3semidirect
85. #6911C2×D3semidirect
89. C3×#732C22×C3semidirect
90. C3×#732C22×C3semidirect
91. C3×#732C22×C3semidirect
107. C2×C3×3−1+2C3⋊D3semidirect
141. C2×C32×C9C3×D3semidirect
142. C2×C32×C9C3×D3semidirect
143. C2×C32×C9C3×D3semidirect
144. C3⋊#272C2×C32semidirect
193. C2×#732C3×D3semidirect
194. C2×#732C3×D3semidirect
195. C2×#732C3×D3semidirect
196. C2×#732C3×D3semidirect
197. C2×#732C3×D3semidirect
198. C2×#732C3×D3semidirect
199. C2×#732C3×D3semidirect
200. C2×#732C3×D3semidirect
201. C2×#732C3×D3semidirect
254. C3×3−1+2C2×C3⋊D3semidirect
288. C32×C9C2×C3×D3semidirect
289. C32×C9C2×C3×D3semidirect
290. C32×C9C2×C3×D3semidirect
327. #732C2×C3×D3semidirect
328. #732C2×C3×D3semidirect
329. #732C2×C3×D3semidirect
330. #732C2×C3×D3semidirect
331. #732C2×C3×D3semidirect
332. #732C2×C3×D3semidirect
333. #732C2×C3×D3semidirect
334. #732C2×C3×D3semidirect
335. #732C2×C3×D3semidirect
463. C2×C3×C9C3×C3⋊D3semidirect
464. C2×C3×C9C3×C3⋊D3semidirect
465. C2×C3×C9C3×C3⋊D3semidirect
620. C3×C9C2×C3×C3⋊D3semidirect
621. C3×C9C2×C3×C3⋊D3semidirect
622. C3×C9C2×C3×C3⋊D3semidirect
827. C2×C3#92285semidirect
861. C3C2×#92285semidirect
864. C2C3⋊#92285direct (N × H)

Maximal subgroups

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

subgroupindex
C3⋊#922852
C2×C3×#69112
C2×C3×C3⋊#2723
C2×C3⋊D3×3−1+23
C2×C3⋊#41783
C2×#922853