Finite Group Databasebeta

← C3×#77281 #11808399

Subgroups — C3×#77281 #11808399

Order 1152.

1485 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic, complemented
2C2×C3×#892C211yesmaximal, characteristic, complemented
3C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
5C32×#396C211yesmaximal, characteristic, complemented
6C3×#4994C211yesmaximal, characteristic, complemented
7C3×#4991C211yesmaximal, characteristic, complemented
8C3×#4982C211yesmaximal, characteristic, complemented
9C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
10C3×#4961C211yesmaximal, characteristic, complemented
11C3×#4961C211yesmaximal, characteristic, complemented
12C3×#4960C211yesmaximal, characteristic
13C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
14C3×#4675C211yesmaximal, characteristic, complemented
15C3×#4666C211yesmaximal, characteristic, complemented
16C3×#2392—31nomaximal
17#77281C311yesmaximal, characteristic, direct product factor
18C22×C3×#67C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C4⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×C32×C22⋊C4C2211yescharacteristic
29C2×C32×C22⋊C4C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic
40C2×C3×C4⋊Dic3C2211yescharacteristic
41C2×C3×Dic3⋊C4C2211yescharacteristic
42C2×C3×Dic3⋊C4C2211yescharacteristic
43C2×C3×C4×Dic3C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45C2×C3×C4×Dic3C2211yescharacteristic
46C2×C3×C4×Dic3C2211yescharacteristic
47C3×#893—24no—
48C3×#892—24no—
49C3×#67⋊C4—24no—
50C3×#67⋊C4—24no—
51C32×#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56C3×C3⋊#95C2211yescharacteristic
57C2×C3×C4×D4—31no—
58C2×C3×C4×D4—31no—
59C2×C3×C4×D4—31no—
60C2×C3×#117—31no—
61C2×#893C2×C311yescharacteristic, complemented
62C2×#892C2×C311yescharacteristic, complemented
63C2×#67⋊C4C2×C311yescharacteristic, complemented
64C2×#67⋊C4C2×C311yescharacteristic, complemented
65C3×#398—31no—
66C3×#397—31no—
67C3×#396—21no—
68C3×#396—31no—
69C3×#396D311yescharacteristic, complemented
70C3×#396C2×C311yescharacteristic, complemented
71C3×#394—31no—
72C3×#394—31no—
73C3×#394—31no—
74C3×#392—31no—
75C3×C4×C4⋊C4—31no—
76C3×C4×C22⋊C4—31no—
77C3×C4×C22⋊C4—31no—
78#4994C2×C311yescharacteristic, complemented
79#4991C2×C311yescharacteristic, complemented
80#4982C2×C311yescharacteristic, complemented
81Dic3×C4⋊C4C2×C311yescharacteristic, complemented
82#4961C2×C311yescharacteristic, complemented
83#4961C2×C311yescharacteristic, complemented
84#4960C2×C311yescharacteristic
85Dic3×C22⋊C4C2×C311yescharacteristic, complemented
86#4675C2×C311yescharacteristic, complemented
87#4666C2×C311yescharacteristic, complemented
88C24×C32C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×C3×#67—22no—
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C2×C3×#67—22no—
101C2×C3×#67—22no—
102C2×C3×#67—22no—
103C22×C3×Dic3—22no—
104C22×C3×Dic3—22no—
105C22×C3×Dic3—22no—
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×C3×D12—22no—
113C2×C3×D12—22no—
114C2×C3×D12—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3—22no—
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3D414yescomplemented
121C32×C4⋊C4—22no—
122C32×C4⋊C4—22no—
123C32×C4⋊C4—22no—
124C32×C22⋊C4—22no—
125C32×C22⋊C4—22no—
126C32×C22⋊C4—22no—
127C3×#217—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4—22no—
132C3×(C2×D3)⋊C4—22no—
133C3×(C2×D3)⋊C4—22no—
134C3×(C2×D3)⋊C4—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×C4⋊Dic3—22no—
137C3×C4⋊Dic3—22no—
138C3×Dic3⋊C4—22no—
139C3×Dic3⋊C4—22no—
140C3×C4×Dic3—22no—
141C3×C4×Dic3—22no—
142C3×C4×Dic3—22no—
143C3×C4×Dic3D414yescomplemented
144#2392—31noSylow
145C22×C3×D4—31no—
146C22×C3×D4—31no—
147C22×C3×D4—31no—
148C23×C3×C4—31no—
149C23×C3×C4—31no—
150C23×C3×C4—31no—
151C22×#67C22×C311yescharacteristic
152C22×#67C22×C311yescharacteristic
153C23×Dic3C22×C311yescharacteristic
154C22×D12C22×C311yescharacteristic
155C22×C4×D3C22×C311yescharacteristic
156C22×C4×D3C22×C311yescharacteristic
157C3×C4×D4—64no—
158C3×C4×D4—64no—
159C3×C4×D4—64no—
160C3×#117—64no—
161C2×C3×C4⋊C4—21no—
162C2×C3×C4⋊C4—21no—
163C2×C3×C4⋊C4—21no—
164C2×C3×C4⋊C4—31no—
165C2×C3×C4⋊C4—31no—
166C2×C3×C4⋊C4—31no—
167C2×C3×C4⋊C4—31no—
168C2×C3×C4⋊C4C2×D311yescharacteristic
169C2×C3×C4⋊C4C2×D311yescharacteristic
170C2×C3×C4⋊C4C2×D311yescharacteristic
171C2×C3×C4⋊C4C22×C311yescharacteristic
172C2×C3×C4⋊C4C22×C311yescharacteristic
173C2×C3×C4⋊C4C22×C311yescharacteristic
174C2×C3×C22⋊C4—21no—
175C2×C3×C22⋊C4—21no—
176C2×C3×C22⋊C4—21no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—31no—
182C2×C3×C22⋊C4—31no—
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C22⋊C4C2×D311yescharacteristic
187C2×C3×C22⋊C4C2×D311yescharacteristic
188C2×C3×C22⋊C4C2×D311yescharacteristic
189C2×C3×C22⋊C4C22×C311yescharacteristic
190C2×C3×C22⋊C4C22×C311yescharacteristic
191C2×C3×C22⋊C4C22×C311yescharacteristic
192C2×C3×C42—31no—
193C2×C3×C42—31no—
194C2×C3×C42—31no—
195C2×C3×C42—31no—
196C2×#217C22×C311yescharacteristic
197C2×(C2×D3)⋊C4C22×C311yescharacteristic
198C2×(C2×D3)⋊C4C22×C311yescharacteristic
199C2×(C2×D3)⋊C4C22×C311yescharacteristic
200C2×(C2×D3)⋊C4C22×C311yescharacteristic
201C2×(C2×D3)⋊C4C22×C311yescharacteristic
202C2×(C2×D3)⋊C4C22×C311yescharacteristic
203C2×(C2×D3)⋊C4C22×C311yescharacteristic
204C2×(C2×D3)⋊C4C22×C311yescharacteristic
205C2×C4⋊Dic3C22×C311yescharacteristic
206C2×C4⋊Dic3C22×C311yescharacteristic
207C2×Dic3⋊C4C22×C311yescharacteristic
208C2×Dic3⋊C4C22×C311yescharacteristic
209C2×C4×Dic3C22×C311yescharacteristic
210C2×C4×Dic3C22×C311yescharacteristic
211C2×C4×Dic3C22×C311yescharacteristic
212C2×C4×Dic3C22×C311yescharacteristic
213#893—24no—
214#892—24no—
215#67⋊C4—24no—
216#67⋊C4—24no—
217C3×#95—21no—
218C3×#95—31no—
219C3×#95—31no—
220C3×#95—31no—
221C3×#95—31no—
222C3×#95—31no—
223C3×#95C2×D311yescharacteristic
224C3×#95C22×C311yescharacteristic
225C3⋊#95C22×C311yescharacteristic
226C3⋊#95C22×C311yescharacteristic
227C3⋊#95C22×C311yescharacteristic
228C3⋊#95C22×C311yescharacteristic
229C3⋊#95C22×C311yescharacteristic
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32#4112yes—
237C23×C32C2411yescharacteristic
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3C2×D412yes—
251C22×C3×D3#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C2×D412yes—
268C2×C32×C4C2×D412yes—
269C2×C32×C4#4112yes—
270C3×#67—28no—
271C3×#67—28no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—44no—
286C2×C3×Dic3C2×D412yes—
287C2×C3×Dic3C2×D412yes—
288C2×C3×Dic3C2×D412yes—
289C2×C3×Dic3#4112yes—
290C2×C3×Dic3#4112yes—
291C3×D12—28no—
292C3×C4×D3—28no—
293C3×C4×D3—44no—
294C2×C4×D4—31no—
295C2×C4×D4—31no—
296C2×C4×D4—31no—
297C2×#117—31no—
298#398—31no—
299#397—31no—
300#396—31no—
301#396C3×D311yescharacteristic, complemented
302#394—31no—
303#394—31no—
304#394—31no—
305#392—31no—
306C4×C4⋊C4—31no—
307C4×C22⋊C4—31no—
308C4×C22⋊C4—31no—
309C24×C3—21no—
310C24×C3—31no—
311C24×C3—31no—
312C24×C3C22×D311yescharacteristic
313C24×C3C23×C311yescharacteristic
314C23×D3C23×C311yescharacteristic
315C23×D3C23×C311yescharacteristic
316C2×C3×D4—62no—
317C2×C3×D4—62no—
318C2×C3×D4—62no—
319C2×C3×D4—62no—
320C2×C3×D4—62no—
321C2×C3×D4—62no—
322C2×C3×D4—62no—
323C2×C3×D4—62no—
324C2×C3×D4—62no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—34no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—62no—
339C22×C3×C4—62no—
340C22×C3×C4—62no—
341C22×C3×C4—62no—
342C22×C3×C4—62no—
343C22×C3×C4—62no—
344C22×C3×C4—62no—
345C22×C3×C4—62no—
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C23×C311yescharacteristic
353C22×C3×C4C23×C311yescharacteristic
354C22×C3×C4C23×C311yescharacteristic
355C22×C3×C4C23×C311yescharacteristic
356C22×C3×C4C23×C311yescharacteristic
357C22×C3×C4C23×C311yescharacteristic
358C2×#67—22no—
359C2×#67—22no—
360C2×#67—22no—
361C2×#67—22no—
362C2×#67—22no—
363C2×#67—22no—
364C22×Dic3—22no—
365C22×Dic3—22no—
366C22×Dic3—22no—
367C22×Dic3C23×C311yescharacteristic
368C22×Dic3C23×C311yescharacteristic
369C22×Dic3C23×C311yescharacteristic
370C22×Dic3C23×C311yescharacteristic
371C22×Dic3C23×C311yescharacteristic
372C22×Dic3C23×C311yescharacteristic
373C2×D12—22no—
374C2×D12—22no—
375C2×D12—22no—
376C2×C4×D3—22no—
377C2×C4×D3—22no—
378C2×C4×D3—22no—
379C2×C4×D3—22no—
380C2×C4×D3—22no—
381C2×C4×D3C3×D414yescomplemented
382C3×C4⋊C4—22no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—22no—
385C3×C4⋊C4—22no—
386C3×C4⋊C4—22no—
387C3×C4⋊C4—22no—
388C3×C4⋊C4—42no—
389C3×C4⋊C4—42no—
390C3×C4⋊C4—42no—
391C3×C4⋊C4—62no—
392C3×C4⋊C4—62no—
393C3×C4⋊C4—62no—
394C3×C4⋊C4—62no—
395C3×C22⋊C4—22no—
396C3×C22⋊C4—22no—
397C3×C22⋊C4—22no—
398C3×C22⋊C4—22no—
399C3×C22⋊C4—22no—
400C3×C22⋊C4—22no—
401C3×C22⋊C4—42no—
402C3×C22⋊C4—42no—
403C3×C22⋊C4—42no—
404C3×C22⋊C4—62no—
405C3×C22⋊C4—62no—
406C3×C22⋊C4—62no—
407C3×C22⋊C4—62no—
408C3×C22⋊C4—62no—
409C3×C22⋊C4—62no—
410C3×C22⋊C4—62no—
411C3×C22⋊C4—62no—
412C3×C22⋊C4—62no—
413C3×C42—34no—
414C3×C42—62no—
415C3×C42—62no—
416C3×C42—62no—
417#217—22no—
418(C2×D3)⋊C4—22no—
419(C2×D3)⋊C4—22no—
420(C2×D3)⋊C4—22no—
421(C2×D3)⋊C4—22no—
422(C2×D3)⋊C4—22no—
423(C2×D3)⋊C4—22no—
424(C2×D3)⋊C4—22no—
425(C2×D3)⋊C4—22no—
426C4⋊Dic3—22no—
427C4⋊Dic3—22no—
428Dic3⋊C4—22no—
429Dic3⋊C4—22no—
430C4×Dic3—22no—
431C4×Dic3—22no—
432C4×Dic3—22no—
433C4×Dic3C3×D414yescomplemented
434C22×C32—22no—
435C22×C32—22no—
436C22×C32—22no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32—41no—
441C22×C32C22×D411yescharacteristic
442C22×C32C22×D411yescharacteristic
443C22×C32C2×#4111yescharacteristic
444C22×C32C2×#4111yescharacteristic
445C22×C32C2×#4111yescharacteristic
446C22×C32C2×#4111yescharacteristic
447C22×C32C2×#4111yescharacteristic
448C2×C3×D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—22no—
452C2×C3×D3—22no—
453C2×C3×D3—22no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C32×C4—22no—
463C32×C4—22no—
464C32×C4—22no—
465C32×C4—41no—
466C32×C4—41no—
467C32×C4—41no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—41no—
471C3×Dic3—41no—
472C3×Dic3—41no—
473C3×Dic3#12114yes—
474C22×D4—31no—
475C22×D4—31no—
476C22×D4—31no—
477C23×C4—31no—
478C23×C4—31no—
479C23×C4—31no—
480C4×D4—64no—
481C4×D4—64no—
482C4×D4—64no—
483#117—64no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—31no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4C2×C3×D311yescharacteristic
489C2×C4⋊C4C2×C3×D311yescharacteristic
490C2×C4⋊C4C2×C3×D311yescharacteristic
491C2×C22⋊C4—31no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—31no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4C2×C3×D311yescharacteristic
501C2×C22⋊C4C2×C3×D311yescharacteristic
502C2×C22⋊C4C2×C3×D311yescharacteristic
503C2×C42—31no—
504C2×C42—31no—
505C2×C42—31no—
506C2×C42—31no—
507#95—31no—
508#95—31no—
509#95—31no—
510#95—31no—
511#95—31no—
512#95C2×C3×D311yescharacteristic
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—22no—
527C23×C3—32no—
528C23×C3—32no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3#23912yes—
548C23×C3C3×#4112yes—
549C23×C3C23×D311yescharacteristic
550C23×C3C24×C311yescharacteristic
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—21no—
563C22×D3C2×C3×D412yes—
564C22×D3C3×#4112yes—
565C3×D4—68no—
566C3×D4—68no—
567C3×D4—68no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—32no—
602C2×C3×C4—32no—
603C2×C3×C4—32no—
604C2×C3×C4—32no—
605C2×C3×C4—32no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—68no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—61no—
625C2×C3×C4—61no—
626C2×C3×C4—61no—
627C2×C3×C4—61no—
628C2×C3×C4—61no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—124no—
636C2×C3×C4—124no—
637C2×C3×C4D3×D412yes—
638C2×C3×C4D3×D412yes—
639C2×C3×C4#23712yes—
640C2×C3×C4C2×C3×D412yes—
641C2×C3×C4C2×C3×D412yes—
642C2×C3×C4C3×#4112yes—
643#67—28no—
644#67—28no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—21no—
648C2×Dic3—21no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—44no—
659C2×Dic3C2×C3×D412yes—
660C2×Dic3C2×C3×D412yes—
661C2×Dic3C2×C3×D412yes—
662C2×Dic3C3×#4112yes—
663C2×Dic3C3×#4112yes—
664D12—28no—
665C4×D3—28no—
666C4×D3—44no—
667C2×C32—42no—
668C2×C32C2×#12111yescharacteristic
669C2×C32#52511yescharacteristic
670C2×C32#52511yescharacteristic
671C2×C32#52511yescharacteristic
672C2×C32#52911yescharacteristic
673C2×C32#52911yescharacteristic
674C2×C32#53211yescharacteristic
675C3×D3—42no—
676C3×D3—42no—
677C24—31no—
678C24—31no—
679C24C22×C3×D311yescharacteristic
680C2×D4—62no—
681C2×D4—62no—
682C2×D4—62no—
683C2×D4—62no—
684C2×D4—62no—
685C2×D4—62no—
686C2×D4—62no—
687C2×D4—62no—
688C2×D4—62no—
689C22×C4—31no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—34no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—62no—
697C22×C4—62no—
698C22×C4—62no—
699C22×C4—62no—
700C22×C4—62no—
701C22×C4—62no—
702C22×C4—62no—
703C22×C4—62no—
704C22×C4C22×C3×D311yescharacteristic
705C22×C4C22×C3×D311yescharacteristic
706C22×C4C22×C3×D311yescharacteristic
707C22×C4C22×C3×D311yescharacteristic
708C22×C4C22×C3×D311yescharacteristic
709C22×C4C22×C3×D311yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—62no—
714C4⋊C4—62no—
715C4⋊C4—62no—
716C4⋊C4—62no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—62no—
721C22⋊C4—62no—
722C22⋊C4—62no—
723C22⋊C4—62no—
724C22⋊C4—62no—
725C22⋊C4—62no—
726C22⋊C4—62no—
727C22⋊C4—62no—
728C22⋊C4—62no—
729C42—34no—
730C42—62no—
731C42—62no—
732C42—62no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—42no—
747C22×C3—42no—
748C22×C3—42no—
749C22×C3—41no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—62no—
758C22×C3—62no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—81no—
764C22×C3—81no—
765C22×C3—81no—
766C22×C3—81no—
767C22×C3—121no—
768C22×C3—121no—
769C22×C3—121no—
770C22×C3—121no—
771C22×C3—121no—
772C22×C3—121no—
773C22×C3—121no—
774C22×C3—121no—
775C22×C3C2×D3×D411yescharacteristic
776C22×C3C2×D3×D411yescharacteristic
777C22×C3C2×#23711yescharacteristic
778C22×C3C2×#23911yescharacteristic
779C22×C3D3×#4111yescharacteristic
780C22×C3D3×#4111yescharacteristic
781C22×C3D3×#4111yescharacteristic
782C22×C3C22×C3×D411yescharacteristic
783C22×C3C22×C3×D411yescharacteristic
784C22×C3C2×C3×#4111yescharacteristic
785C22×C3C2×C3×#4111yescharacteristic
786C22×C3C2×C3×#4111yescharacteristic
787C22×C3C2×C3×#4111yescharacteristic
788C22×C3C2×C3×#4111yescharacteristic
789C2×D3—22no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—41no—
796C2×D3—41no—
797C2×D3—41no—
798C2×D3—41no—
799C2×D3—41no—
800C2×D3—41no—
801C2×D3—41no—
802C2×D3—41no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—22no—
809C3×C4—34no—
810C3×C4—42no—
811C3×C4—42no—
812C3×C4—42no—
813C3×C4—41no—
814C3×C4—41no—
815C3×C4—41no—
816C3×C4—41no—
817C3×C4—41no—
818C3×C4—41no—
819C3×C4—62no—
820C3×C4—62no—
821C3×C4—81no—
822C3×C4—81no—
823C3×C4—81no—
824C3×C4—121no—
825C3×C4—121no—
826C3×C4—121no—
827Dic3—22no—
828Dic3—22no—
829Dic3—41no—
830Dic3—41no—
831Dic3—41no—
832Dic3C3×#12114yes—
833C32#239211yescharacteristic, complemented, Sylow
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—32no—
841C23—32no—
842C23—61no—
843C23—61no—
844C23—61no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23—61no—
849C23—61no—
850C23—61no—
851C23—61no—
852C23—61no—
853C23—61no—
854C23C3×#23912yes—
855C23C23×C3×D311yescharacteristic
856D4—68no—
857D4—68no—
858D4—68no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—32no—
875C2×C4—32no—
876C2×C4—32no—
877C2×C4—32no—
878C2×C4—32no—
879C2×C4—68no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—61no—
892C2×C4—61no—
893C2×C4—124no—
894C2×C4—124no—
895C2×C4C3×D3×D412yes—
896C2×C4C3×D3×D412yes—
897C2×C4C3×#23712yes—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—21no—
905C2×C3—42no—
906C2×C3—42no—
907C2×C3—82no—
908C2×C3—122no—
909C2×C3—122no—
910C2×C3#559611yescharacteristic
911C2×C3D3×#12111yescharacteristic
912C2×C3#560611yescharacteristic
913C2×C3#562411yescharacteristic
914C2×C3#562711yescharacteristic
915C2×C3#562711yescharacteristic
916C2×C3#570611yescharacteristic
917C2×C3C2×C3×#12111yescharacteristic
918C2×C3C3×#52511yescharacteristic
919C2×C3C3×#52511yescharacteristic
920C2×C3C3×#52511yescharacteristic
921C2×C3C3×#52911yescharacteristic
922C2×C3C3×#52911yescharacteristic
923C2×C3C3×#53211yescharacteristic
924D3—42no—
925D3—42no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—62no—
934C22—62no—
935C22—62no—
936C22—62no—
937C22—62no—
938C22—62no—
939C22—121no—
940C22—121no—
941C22—121no—
942C22—121no—
943C22—121no—
944C22—121no—
945C22—121no—
946C22—121no—
947C22C2×C3×D3×D411yescharacteristic
948C22C2×C3×D3×D411yescharacteristic
949C22C2×C3×#23711yescharacteristic
950C22C2×C3×#23911yescharacteristic
951C22C3×D3×#4111yescharacteristic
952C22C3×D3×#4111yescharacteristic
953C22C3×D3×#4111yescharacteristic
954C4—22no—
955C4—22no—
956C4—22no—
957C4—34no—
958C4—41no—
959C4—41no—
960C4—41no—
961C4—62no—
962C4—62no—
963C4—121no—
964C4—121no—
965C4—121no—
966C3—21no—
967C3#7728111yescharacteristic, direct product factor
968C3C3×#239211yescharacteristic, complemented
969C2—42no—
970C2—122no—
971C2—122no—
972C2C3×#559611yescharacteristic
973C2C3×D3×#12111yescharacteristic
974C2C3×#560611yescharacteristic
975C2C3×#562411yescharacteristic
976C2C3×#562711yescharacteristic
977C2C3×#562711yescharacteristic
978C2C3×#570611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#396C2
socleC23×C32C24
prime radicalC3×#4960C2
hypercenterC3×#396D3
hypocenterC3C3×#2392
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#396

Complements

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

NH ≅ G/Ntype
1. C2×C3×#893C2semidirect
2. C2×C3×#892C2semidirect
3. C2×C3×#67⋊C4C2semidirect
4. C2×C3×#67⋊C4C2semidirect
5. C32×#396C2semidirect
6. C3×#4994C2semidirect
7. C3×#4991C2semidirect
8. C3×#4982C2semidirect
9. C3×Dic3×C4⋊C4C2semidirect
10. C3×#4961C2semidirect
11. C3×#4961C2semidirect
13. C3×Dic3×C22⋊C4C2semidirect
14. C3×#4675C2semidirect
15. C3×#4666C2semidirect
17. #77281C3direct (N × H)
61. C2×#893C2×C3semidirect
62. C2×#892C2×C3semidirect
63. C2×#67⋊C4C2×C3semidirect
64. C2×#67⋊C4C2×C3semidirect
69. C3×#396D3semidirect
70. C3×#396C2×C3semidirect
78. #4994C2×C3semidirect
79. #4991C2×C3semidirect
80. #4982C2×C3semidirect
81. Dic3×C4⋊C4C2×C3semidirect
82. #4961C2×C3semidirect
83. #4961C2×C3semidirect
85. Dic3×C22⋊C4C2×C3semidirect
86. #4675C2×C3semidirect
87. #4666C2×C3semidirect
120. C2×C3×C4×D3D4semidirect
143. C3×C4×Dic3D4semidirect
301. #396C3×D3semidirect
381. C2×C4×D3C3×D4semidirect
433. C4×Dic3C3×D4semidirect
833. C32#2392semidirect
967. C3#77281direct (N × H)
968. C3C3×#2392semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×C3×#8922
C2×C3×#67⋊C42
C32×#3962
C3×#49942
C3×#49912
C3×#49822
C3×Dic3×C4⋊C42
C3×#49612
C3×#49602
C3×Dic3×C22⋊C42
C3×#46752
C3×#46662
C3×#23923
#772813