Finite Group Databasebeta

← C3×#79441 #11887359

Subgroups — C3×#79441 #11887359

Order 1152.

907 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5565C211yesmaximal, characteristic, complemented
2C3×#5550C211yesmaximal, characteristic, complemented
3C32×C8×D4C211yesmaximal, characteristic, complemented
4C3×#5115C211yesmaximal, characteristic, complemented
5C3×#5114C211yesmaximal, characteristic, complemented
6C3×#5113C211yesmaximal, characteristic, complemented
7C2×C3×#821C211yesmaximal, characteristic, complemented
8C3×#4847C211yesmaximal, characteristic, complemented
9C3×#4844C211yesmaximal, characteristic, complemented
10C3×#4737C211yesmaximal, characteristic, complemented
11C3×#4734C211yesmaximal, characteristic, complemented
12C3×#4732C211yesmaximal, characteristic, complemented
13C3×#4722C211yesmaximal, characteristic, complemented
14C3×#4697C211yesmaximal, characteristic, complemented
15C3×C4×D24C211yesmaximal, characteristic, complemented
16C3×#3297—31nomaximal
17#79441C311yesmaximal, characteristic, direct product factor
18C2×C3×#235C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic
23C3×#939—21no—
24C3×#937—21no—
25C3×#930C2211yescharacteristic
26C3×#930C2211yescharacteristic
27C3×#930C2211yescharacteristic, complemented
28C3×#926C2211yescharacteristic, complemented
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C3×#924C2211yescharacteristic
31C2×C3×D24C2211yescharacteristic
32C2×C3×D24C2211yescharacteristic
33C2×C3×#204C2211yescharacteristic, complemented
34C3×#898—21no—
35C3×#894—21no—
36C3×#884—21no—
37C3×#883—21no—
38C3×#67⋊C4—21no—
39C3×D3×C22⋊C4—21no—
40C3×#875C2211yescharacteristic
41C3×C4×D12C2211yescharacteristic
42C3×C4×D12C2211yescharacteristic, complemented
43C3×#870C2211yescharacteristic, complemented
44C32×C4⋊C8C2211yescharacteristic, complemented
45C32×C22⋊C8C2211yescharacteristic
46C32×C22⋊C8C2211yescharacteristic, complemented
47C32×C4×C8C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×#821C2211yescharacteristic
54C3×#821C2211yescharacteristic, complemented
55C3×#818C2211yescharacteristic, complemented
56C3×#818C2211yescharacteristic, complemented
57C3×#817C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59C3×#816C2211yescharacteristic, complemented
60C3×#816C2211yescharacteristic, complemented
61C3×#553—31no—
62C3×#546—31no—
63#5565C2×C311yescharacteristic, complemented
64#5550C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#484—31no—
67C3×#482—31no—
68C3×#478—31no—
69C3×#466—31no—
70C3×#465—31no—
71C3×#463—31no—
72C3×#449—31no—
73C3×#447—31no—
74C3×C4×D8—31no—
75C3×C8×D4—21no—
76C3×C8×D4D311yescharacteristic, complemented
77C3×C8×D4C2×C311yescharacteristic, complemented
78C3×#416—31no—
79C2×C3×#102—31no—
80#5115C2×C311yescharacteristic, complemented
81#5114C2×C311yescharacteristic, complemented
82#5113C2×C311yescharacteristic, complemented
83C2×#821C2×C311yescharacteristic, complemented
84#4847C2×C311yescharacteristic, complemented
85#4844C2×C311yescharacteristic, complemented
86#4737C2×C311yescharacteristic, complemented
87#4734C2×C311yescharacteristic, complemented
88#4732C2×C311yescharacteristic, complemented
89#4722C2×C311yescharacteristic, complemented
90#4697C2×C311yescharacteristic, complemented
91C4×D24C2×C311yescharacteristic, complemented
92C23×C3×D3—21no—
93C2×C32×D4D411yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C3×#235—22no—
102C3×#235—41no—
103C2×C3×D12—22no—
104C2×C3×D12—21no—
105C2×C3×D12—41no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×Dic6C2311yescharacteristic
113C2×C32×C8—41no—
114C2×C32×C8—41no—
115C2×C32×C8C2311yescharacteristic
116C2×C32×C8C2311yescharacteristic
117C2×C32×C8C2311yescharacteristic
118C2×C32×C8C2311yescharacteristic
119C32×C4⋊C4D411yescharacteristic
120C32×C22⋊C4D411yescharacteristic
121C32×C22⋊C4D411yescharacteristic
122C32×C42C2311yescharacteristic
123C3×#217—21no—
124C3×#217—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×C4×Dic3—21no—
141C3×D24—22no—
142C3×D24—41no—
143C3×#204—41no—
144#3297—31noSylow
145C2×C3×#41—31no—
146C22×C3×D4—31no—
147C2×#235C22×C311yescharacteristic
148C22×D12C22×C311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×D8—31no—
151C2×C3×D8—31no—
152C22×C3×C8—21no—
153C22×C3×C8—21no—
154C22×C3×C8C2×D311yescharacteristic
155C22×C3×C8C2×D311yescharacteristic, complemented
156C22×C3×C8C22×C311yescharacteristic
157C22×C3×C8C22×C311yescharacteristic, complemented
158C3×#126—61no—
159C3×#125—31no—
160C3×#124—31no—
161C3×#123—61no—
162C3×#123—61no—
163C3×C22⋊Q8—31no—
164C3×#121—31no—
165C3×#121—31no—
166C3×#121—31no—
167C3×#121—61no—
168C3×#121—61no—
169C3×#120—61no—
170C3×C4×D4—21no—
171C3×C4×D4—31no—
172C3×C4×D4—31no—
173C3×C4×D4—61no—
174C3×C4×D4C2×D311yescharacteristic
175C3×C4×D4C22×C311yescharacteristic
176C3×#117—31no—
177C2×C3×C4⋊C4—31no—
178C2×C3×C22⋊C4—61no—
179#939—21no—
180#937—21no—
181#930C22×C311yescharacteristic
182#930C22×C311yescharacteristic
183#930C22×C311yescharacteristic, complemented
184#926C22×C311yescharacteristic, complemented
185C2×C4⋊Dic3C22×C311yescharacteristic
186#924C22×C311yescharacteristic
187C2×D24C22×C311yescharacteristic
188C2×D24C22×C311yescharacteristic
189C2×#204C22×C311yescharacteristic, complemented
190#898—21no—
191#894—21no—
192#884—21no—
193#883—21no—
194#67⋊C4—21no—
195D3×C22⋊C4—21no—
196#875C22×C311yescharacteristic
197C4×D12C22×C311yescharacteristic
198C4×D12C22×C311yescharacteristic, complemented
199#870C22×C311yescharacteristic, complemented
200C3×#107—31no—
201C3×#107—31no—
202C3×#106—31no—
203C3×C4⋊C8—21no—
204C3×C4⋊C8C2×D311yescharacteristic, complemented
205C3×C4⋊C8C22×C311yescharacteristic, complemented
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×C22⋊C8—21no—
217C3×C22⋊C8—21no—
218C3×C22⋊C8C2×D311yescharacteristic
219C3×C22⋊C8C2×D311yescharacteristic, complemented
220C3×C22⋊C8C22×C311yescharacteristic
221C3×C22⋊C8C22×C311yescharacteristic, complemented
222C3×C4×C8—21no—
223C3×C4×C8C2×D311yescharacteristic, complemented
224C3×C4×C8C22×C311yescharacteristic, complemented
225#821C22×C311yescharacteristic
226#821C22×C311yescharacteristic
227#821C22×C311yescharacteristic
228#821C22×C311yescharacteristic
229#821C22×C311yescharacteristic
230#821C22×C311yescharacteristic
231#821C22×C311yescharacteristic, complemented
232#818C22×C311yescharacteristic, complemented
233#818C22×C311yescharacteristic, complemented
234#817C22×C311yescharacteristic, complemented
235#816C22×C311yescharacteristic, complemented
236#816C22×C311yescharacteristic, complemented
237#816C22×C311yescharacteristic, complemented
238C23×C32C2×D411yescharacteristic
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—81no—
246C32×D4—22no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C3×#67—42no—
257C3×#67—42no—
258C3×#67—81no—
259C3×#67—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—81no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—42no—
272C3×D12#4112yes—
273C3×C4×D3—42no—
274C3×C4×D3—81no—
275C3×C4×D3—81no—
276C3×Dic6—21no—
277C3×Dic6—21no—
278C32×C8—21no—
279C32×C8—21no—
280C32×C8—21no—
281C32×C8—21no—
282#553—31no—
283#546—31no—
284#488—31no—
285#484—31no—
286#482—31no—
287#478—31no—
288#466—31no—
289#465—31no—
290#463—31no—
291#449—31no—
292#447—31no—
293C4×D8—31no—
294C8×D4C3×D311yescharacteristic, complemented
295#416—31no—
296C2×#102—31no—
297C24×C3—61no—
298C23×D3—21no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—31no—
302C2×C3×D4—21no—
303C2×C3×D4—31no—
304C2×C3×D4—31no—
305C2×C3×D4—31no—
306C2×C3×D4—62no—
307C2×C3×D4—61no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4—61no—
312C2×C3×D4—121no—
313C2×C3×D4D1211yescharacteristic
314C2×C3×D4C3×D411yescharacteristic
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4—61no—
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C23×C311yescharacteristic
324C22×C3×C4C23×C311yescharacteristic
325C2×#67—21no—
326C2×#67—21no—
327C2×#67—21no—
328C2×#67—21no—
329C22×Dic3—21no—
330#235—22no—
331#235—41no—
332C2×D12—22no—
333C2×D12—21no—
334C2×D12—41no—
335C2×D12C23×C311yescharacteristic
336C2×D12C23×C311yescharacteristic
337C2×D12C23×C311yescharacteristic
338C2×C4×D3—21no—
339C2×C4×D3—21no—
340C2×C4×D3—21no—
341C2×Dic6C23×C311yescharacteristic
342C3×SD16—121no—
343C3×D8—62no—
344C3×D8—121no—
345C2×C3×C8—21no—
346C2×C3×C8—21no—
347C2×C3×C8—21no—
348C2×C3×C8—21no—
349C2×C3×C8—41no—
350C2×C3×C8—41no—
351C2×C3×C8—41no—
352C2×C3×C8—41no—
353C2×C3×C8—42no—
354C2×C3×C8—42no—
355C2×C3×C8C22×D311yescharacteristic
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C23×C311yescharacteristic
360C2×C3×C8C23×C311yescharacteristic
361C2×C3×C8C23×C311yescharacteristic
362C2×C3×C8C23×C311yescharacteristic
363C3×C4⋊C4—21no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4D1211yescharacteristic
373C3×C4⋊C4C3×D411yescharacteristic
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—61no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C22⋊C4—61no—
385C3×C22⋊C4D1211yescharacteristic
386C3×C22⋊C4D1211yescharacteristic
387C3×C22⋊C4C3×D411yescharacteristic
388C3×C22⋊C4C3×D411yescharacteristic
389C3×C42—21no—
390C3×C42—61no—
391C3×C42C22×D311yescharacteristic
392C3×C42C23×C311yescharacteristic
393#217—21no—
394#217—21no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—21no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—21no—
401(C2×D3)⋊C4—21no—
402C4⋊Dic3—21no—
403C4⋊Dic3C23×C311yescharacteristic
404C4⋊Dic3C23×C311yescharacteristic
405C4⋊Dic3C23×C311yescharacteristic
406C4⋊Dic3C23×C311yescharacteristic
407Dic3⋊C4—21no—
408Dic3⋊C4—21no—
409Dic3⋊C4—21no—
410C4×Dic3—21no—
411D24—22no—
412D24—41no—
413#204—41no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32#13512yes—
420C22×C32C22×D411yescharacteristic
421C2×C3×D3—22no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—84no—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4C2×#4111yescharacteristic
436C32×C4H(5,𝔽2)11yescharacteristic
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—31no—
443C22×D4—31no—
444C2×SD16—31no—
445C2×D8—31no—
446C2×D8—31no—
447C22×C8C2×C3×D311yescharacteristic
448C22×C8C2×C3×D311yescharacteristic, complemented
449#126—61no—
450#125—31no—
451#124—31no—
452#123—61no—
453#123—61no—
454C22⋊Q8—31no—
455#121—31no—
456#121—31no—
457#121—31no—
458#121—61no—
459#121—61no—
460#120—61no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—61no—
464C4×D4C2×C3×D311yescharacteristic
465#117—31no—
466C2×C4⋊C4—31no—
467C2×C22⋊C4—61no—
468#107—31no—
469#107—31no—
470#106—31no—
471C4⋊C8C2×C3×D311yescharacteristic, complemented
472#103—31no—
473#103—31no—
474#103—31no—
475#102—31no—
476#102—31no—
477#102—31no—
478#102—31no—
479#102—31no—
480#102—31no—
481#102—31no—
482C22⋊C8C2×C3×D311yescharacteristic
483C22⋊C8C2×C3×D311yescharacteristic, complemented
484C4×C8C2×C3×D311yescharacteristic, complemented
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—122no—
491C23×C3—122no—
492C23×C3—241no—
493C23×C3C2×D1211yescharacteristic
494C23×C3C2×D1211yescharacteristic
495C23×C3C2×C3×D411yescharacteristic
496C23×C3C2×C3×D411yescharacteristic
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—42no—
501C22×D3—42no—
502C22×D3—81no—
503C3×Q8—61no—
504C3×Q8—61no—
505C3×D4—24no—
506C3×D4—22no—
507C3×D4—22no—
508C3×D4—32no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—61no—
513C3×D4—61no—
514C3×D4—122no—
515C3×D4—122no—
516C3×D4—122no—
517C3×D4—241no—
518C3×D4—241no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—122no—
542C2×C3×C4—241no—
543C2×C3×C4—241no—
544C2×C3×C4—241no—
545C2×C3×C4C2×D1211yescharacteristic
546C2×C3×C4C2×D1211yescharacteristic
547C2×C3×C4C2×D1211yescharacteristic
548C2×C3×C4C2×D1211yescharacteristic
549C2×C3×C4C2×C3×D411yescharacteristic
550C2×C3×C4C2×C3×D411yescharacteristic
551C2×C3×C4C2×C3×D411yescharacteristic
552C2×C3×C4C2×C3×D411yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C24×C311yescharacteristic
555#67—42no—
556#67—42no—
557#67—81no—
558#67—81no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—81no—
565D12—21no—
566D12—21no—
567D12—21no—
568D12—21no—
569D12—21no—
570D12—42no—
571D12C3×#4112yes—
572C4×D3—42no—
573C4×D3—81no—
574C4×D3—81no—
575Dic6—21no—
576Dic6—21no—
577C3×C8—22no—
578C3×C8—21no—
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—21no—
582C3×C8—21no—
583C3×C8—21no—
584C3×C8—21no—
585C3×C8—21no—
586C3×C8—41no—
587C3×C8—41no—
588C3×C8—41no—
589C2×C32—22no—
590C2×C32—41no—
591C2×C32#54611yescharacteristic
592C2×C32C2×#13511yescharacteristic
593C2×C32#57611yescharacteristic
594C3×D3—42no—
595C3×D3—81no—
596C3×D3—81no—
597C24—61no—
598#41—62no—
599#41—121no—
600C2×Q8—31no—
601C2×D4—31no—
602C2×D4—31no—
603C2×D4—31no—
604C2×D4—62no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—61no—
610C2×D4—121no—
611C2×D4C3×D1211yescharacteristic
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4C22×C3×D311yescharacteristic
617C22×C4C22×C3×D311yescharacteristic
618SD16—121no—
619D8—62no—
620D8—121no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8C22×C3×D311yescharacteristic
624C2×C8C22×C3×D311yescharacteristic
625C2×C8C22×C3×D311yescharacteristic
626C2×C8C22×C3×D311yescharacteristic
627C4⋊C4—31no—
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—61no—
635C4⋊C4C3×D1211yescharacteristic
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4C3×D1211yescharacteristic
646C22⋊C4C3×D1211yescharacteristic
647C42—61no—
648C42C22×C3×D311yescharacteristic
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—22no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—22no—
661C22×C3—21no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—62no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—244no—
676C22×C3#90412yes—
677C22×C3C3×#13512yes—
678C22×C3C22×D1211yescharacteristic
679C22×C3C22×C3×D411yescharacteristic
680C2×D3—22no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—84no—
690C3×C4—22no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—121no—
705C3×C4—121no—
706C3×C4—121no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4#100411yescharacteristic
710C3×C4D3×#4111yescharacteristic
711C3×C4C2×C3×#4111yescharacteristic
712C3×C4C3×H(5,𝔽2)11yescharacteristic
713Dic3—41no—
714Dic3—41no—
715Dic3—41no—
716Dic3—41no—
717Dic3—41no—
718C32#329711yescharacteristic, complemented, Sylow
719C23—61no—
720C23—61no—
721C23—61no—
722C23—122no—
723C23—122no—
724C23—241no—
725C23C2×C3×D1211yescharacteristic
726C23C2×C3×D1211yescharacteristic
727Q8—61no—
728Q8—61no—
729D4—22no—
730D4—32no—
731D4—61no—
732D4—61no—
733D4—61no—
734D4—61no—
735D4—61no—
736D4—122no—
737D4—122no—
738D4—122no—
739D4—241no—
740D4—241no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—122no—
751C2×C4—241no—
752C2×C4—241no—
753C2×C4—241no—
754C2×C4C2×C3×D1211yescharacteristic
755C2×C4C2×C3×D1211yescharacteristic
756C2×C4C2×C3×D1211yescharacteristic
757C2×C4C2×C3×D1211yescharacteristic
758C2×C4C23×C3×D311yescharacteristic
759C8—21no—
760C8—21no—
761C8—21no—
762C8—21no—
763C2×C3—22no—
764C2×C3—22no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—42no—
769C2×C3—42no—
770C2×C3—41no—
771C2×C3—41no—
772C2×C3—122no—
773C2×C3—241no—
774C2×C3—241no—
775C2×C3#555411yescharacteristic
776C2×C3C2×#90411yescharacteristic
777C2×C3#575211yescharacteristic
778C2×C3C3×#54611yescharacteristic
779C2×C3C2×C3×#13511yescharacteristic
780C2×C3C3×#57611yescharacteristic
781D3—42no—
782D3—81no—
783D3—81no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—62no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—244no—
799C22C3×#90412yes—
800C22C22×C3×D1211yescharacteristic
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—121no—
806C4—121no—
807C4—121no—
808C4—121no—
809C4—121no—
810C4C3×#100411yescharacteristic
811C4C3×D3×#4111yescharacteristic
812C3—21no—
813C3#7944111yescharacteristic, direct product factor
814C3C3×#329711yescharacteristic, complemented
815C2—22no—
816C2—41no—
817C2—122no—
818C2—241no—
819C2—241no—
820C2C3×#555411yescharacteristic
821C2C2×C3×#90411yescharacteristic
822C2C3×#575211yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C8×D4C2
socleC22×C32C22×D4
hypercenterC3×C8×D4D3
hypocenterC3C3×#3297
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×C8×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5565C2semidirect
2. C3×#5550C2semidirect
3. C32×C8×D4C2semidirect
4. C3×#5115C2semidirect
5. C3×#5114C2semidirect
6. C3×#5113C2semidirect
7. C2×C3×#821C2semidirect
8. C3×#4847C2semidirect
9. C3×#4844C2semidirect
10. C3×#4737C2semidirect
11. C3×#4734C2semidirect
12. C3×#4732C2semidirect
13. C3×#4722C2semidirect
14. C3×#4697C2semidirect
15. C3×C4×D24C2semidirect
17. #79441C3direct (N × H)
21. C22×C32×C8C22semidirect
27. C3×#930C22semidirect
28. C3×#926C22semidirect
33. C2×C3×#204C22semidirect
42. C3×C4×D12C22semidirect
43. C3×#870C22semidirect
44. C32×C4⋊C8C22semidirect
46. C32×C22⋊C8C22semidirect
47. C32×C4×C8C22semidirect
54. C3×#821C22semidirect
55. C3×#818C22semidirect
56. C3×#818C22semidirect
57. C3×#817C22semidirect
58. C3×#816C22semidirect
59. C3×#816C22semidirect
60. C3×#816C22semidirect
63. #5565C2×C3semidirect
64. #5550C2×C3semidirect
76. C3×C8×D4D3semidirect
77. C3×C8×D4C2×C3semidirect
80. #5115C2×C3semidirect
81. #5114C2×C3semidirect
82. #5113C2×C3semidirect
83. C2×#821C2×C3semidirect
84. #4847C2×C3semidirect
85. #4844C2×C3semidirect
86. #4737C2×C3semidirect
87. #4734C2×C3semidirect
88. #4732C2×C3semidirect
89. #4722C2×C3semidirect
90. #4697C2×C3semidirect
91. C4×D24C2×C3semidirect
155. C22×C3×C8C2×D3semidirect
157. C22×C3×C8C22×C3semidirect
183. #930C22×C3semidirect
184. #926C22×C3semidirect
189. C2×#204C22×C3semidirect
198. C4×D12C22×C3semidirect
199. #870C22×C3semidirect
204. C3×C4⋊C8C2×D3semidirect
205. C3×C4⋊C8C22×C3semidirect
219. C3×C22⋊C8C2×D3semidirect
221. C3×C22⋊C8C22×C3semidirect
223. C3×C4×C8C2×D3semidirect
224. C3×C4×C8C22×C3semidirect
231. #821C22×C3semidirect
232. #818C22×C3semidirect
233. #818C22×C3semidirect
234. #817C22×C3semidirect
235. #816C22×C3semidirect
236. #816C22×C3semidirect
237. #816C22×C3semidirect
294. C8×D4C3×D3semidirect
448. C22×C8C2×C3×D3semidirect
471. C4⋊C8C2×C3×D3semidirect
483. C22⋊C8C2×C3×D3semidirect
484. C4×C8C2×C3×D3semidirect
718. C32#3297semidirect
813. C3#79441direct (N × H)
814. C3C3×#3297semidirect

Maximal subgroups

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

subgroupindex
C3×#55652
C3×#55502
C32×C8×D42
C3×#51152
C3×#51142
C3×#51132
C2×C3×#8212
C3×#48472
C3×#48442
C3×#47372
C3×#47342
C3×#47322
C3×#47222
C3×#46972
C3×C4×D242
C3×#32973
#794413