Finite Group Databasebeta

← #13175852

Subgroups — #13175852

Order 1728.

2056 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6293C211yesmaximal, characteristic, complemented
2C2×#89019C211yesmaximal, characteristic, complemented
3#11723922C211yesmaximal, characteristic
4C3×#64087C211yesmaximal, characteristic, complemented
5C32×#878C211yesmaximal, characteristic, complemented
6#11723642C211yesmaximal, characteristic, complemented
7#11723622C211yesmaximal, characteristic
8#11723618C211yesmaximal, characteristic
9#11723536C211yesmaximal, characteristic, complemented
10#11723495C211yesmaximal, characteristic, complemented
11#11723485C211yesmaximal, characteristic, complemented
12#11723442C211yesmaximal, characteristic, complemented
13#11723394C211yesmaximal, characteristic, complemented
14#11723393C211yesmaximal, characteristic, complemented
15#11723391C211yesmaximal, characteristic, complemented
16#10596103—31nomaximal
17#10594072—34nomaximal
18C2×#6312C2211yescharacteristic
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C3×#634C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C2×C32×Dic6C2211yescharacteristic
25C2×#6293—24no—
26C2×#6293C2211yescharacteristic
27C2×#6293C2211yescharacteristic
28C2×#6293C2211yescharacteristic
29C2×#6293C2211yescharacteristic
30C2×#6293C2211yescharacteristic
31C2×#6289C2211yescharacteristic
32C2×#6289C2211yescharacteristic
33#89019—24no—
34C33×C22⋊C4C2211yescharacteristic
35#88859C2211yescharacteristic
36#88857C2211yescharacteristic
37C4×C3⋊(C3⋊Dic3)C2211yescharacteristic
38C3×#3757C2211yescharacteristic
39C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
40C3×#3750C2211yescharacteristic
41C3×#3750C2211yescharacteristic
42C32×#217C2211yescharacteristic
43C32×C4⋊Dic3C2211yescharacteristic
44C32×Dic3⋊C4C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46#88807C2211yescharacteristic
47#88806C2211yescharacteristic
48#88806C2211yescharacteristic
49#88806C2211yescharacteristic
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic
51#88804C2211yescharacteristic
52#88804C2211yescharacteristic
53Dic3×C3⋊Dic3C2211yescharacteristic
54Dic3×C3⋊Dic3C2211yescharacteristic
55C2×Q8×C3⋊D3—31no—
56C22×#634—31no—
57C22×#627—34no—
58C2×#3797—34no—
59C32×C22⋊Q8—31no—
60#64153—31no—
61C4×#638—31no—
62#64106—31no—
63#64105—31no—
64#64105—31no—
65#64097—31no—
66#64097—31no—
67#64096—31no—
68#64090—31no—
69#64090—31no—
70#64090—34no—
71#64090—64no—
72#64087—31no—
73#64087D311yescharacteristic, complemented
74C3×#878—34no—
75C3×#878D314yescomplemented
76#63982—34no—
77#63952—34no—
78#63952—34no—
79#63919—34no—
80#63895—34no—
81#63895—34no—
82#63865—34no—
83#63839—34no—
84#63839—34no—
85#63838—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90#6312Q814yescomplemented
91C2×C3⋊(C3⋊Dic3)—22no—
92C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
93C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
94C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
95C4×C3⋊(C3⋊D3)—22no—
96C2×C3×C3⋊Dic3—22no—
97C2×C3×C3⋊Dic3C2311yescharacteristic
98C2×C3×C3⋊Dic3C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C3×#634—22no—
102C2×C32×Dic3—22no—
103C2×C32×Dic3C2311yescharacteristic
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C32×Dic6—22no—
108#6293—22no—
109#6293—22no—
110#6293—22no—
111#6293—22no—
112#6293D414yescomplemented
113#6289—22no—
114#6289—22no—
115#5632—94no—
116#5632—91no—
117C2×C32×Q8—31no—
118C22×C32×C4—31no—
119C2×#638—31no—
120C2×#638—34no—
121C2×#638—64no—
122C22×C3⋊Dic3—31no—
123C22×C3⋊Dic3—34no—
124C22×C3⋊Dic3—64no—
125C22×C3⋊Dic3C2×D311yescharacteristic
126Q8×C3⋊D3—64no—
127C2×C4×C3⋊D3—31no—
128C2×C4×C3⋊D3—34no—
129C2×C4×C3⋊D3—31no—
130C2×C4×C3⋊D3—31no—
131C2×C4×C3⋊D3—64no—
132C2×#634—31no—
133C2×#634—31no—
134C2×#634—31no—
135C2×#634—31no—
136C2×#634—31no—
137C2×#634—64no—
138C2×#634C2×D311yescharacteristic
139C22×C3×Dic3—34no—
140C22×C3×Dic3C2×D314yes—
141C2×C3×Dic6—34no—
142C2×C3×Dic6C2×D314yes—
143C2×#627—34no—
144C2×#627—34no—
145C2×#627—34no—
146C2×#627—34no—
147C2×#627—34no—
148C2×#627—616no—
149C2×#624—34no—
150C2×#624—34no—
151#3797—616no—
152C32×C4⋊C4—31no—
153C32×C4⋊C4—31no—
154C32×C4⋊C4—31no—
155C32×C22⋊C4—24no—
156C32×C22⋊C4—31no—
157C32×C22⋊C4C2×D314yes—
158C32×C22⋊C4C2×D311yescharacteristic
159#3757C2×D311yescharacteristic
160#3752—31no—
161#3752—34no—
162#3752—31no—
163#3752—31no—
164#3752—64no—
165C4⋊(C3⋊Dic3)—31no—
166C4⋊(C3⋊Dic3)C2×D311yescharacteristic
167#3750—31no—
168#3750—34no—
169#3750—31no—
170#3750—31no—
171#3750—31no—
172#3750—31no—
173#3750—64no—
174#3750C2×D311yescharacteristic
175#3750C2×D311yescharacteristic
176C4×C3⋊Dic3—31no—
177C4×C3⋊Dic3—34no—
178C4×C3⋊Dic3—31no—
179C4×C3⋊Dic3—31no—
180C4×C3⋊Dic3—64no—
181C3×#217—34no—
182C3×#217C2×D314yes—
183C3×C4⋊Dic3—34no—
184C3×C4⋊Dic3C2×D314yes—
185C3×Dic3⋊C4—34no—
186C3×Dic3⋊C4—34no—
187C3×Dic3⋊C4C2×D314yes—
188C3×Dic3⋊C4C2×D314yes—
189#3724—34no—
190#3724—34no—
191#3724—34no—
192Dic3⋊Dic3—34no—
193Dic3⋊Dic3—34no—
194#3722—34no—
195#3722—34no—
196Dic32—34no—
197Dic32—34no—
198C22×C33—21no—
199C22×C33—21no—
200C22×C33C2×Q812yescomplemented
201C22×C33C2411yescharacteristic
202C2×C3⋊(C3⋊D3)—21no—
203C2×C3⋊(C3⋊D3)—21no—
204C2×C3⋊(C3⋊D3)C2×Q812yescomplemented
205C33×C4—21no—
206C33×C4—21no—
207C3⋊(C3⋊Dic3)—21no—
208C3⋊(C3⋊Dic3)C2×D412yes—
209C3⋊(C3⋊Dic3)C2×Q812yescomplemented
210C3×C3⋊Dic3—21no—
211C3×C3⋊Dic3—21no—
212C3×C3⋊Dic3—21no—
213C3×C3⋊Dic3C2×D412yes—
214C32×Dic3—21no—
215C32×Dic3—21no—
216C32×Dic3—21no—
217C32×Dic3C2×D412yes—
218C2×D3×Q8—94no—
219C2×D3×Q8—91no—
220C22×Dic6—94no—
221C22×Dic6—91no—
222C3×C22⋊Q8—34no—
223C3×C22⋊Q8—91no—
224#944—94no—
225#944—91no—
226C4×#67—94no—
227C4×#67—91no—
228#897—94no—
229#897—91no—
230#896—94no—
231#896—94no—
232#896—91no—
233#896—91no—
234#888—94no—
235#888—94no—
236#888—91no—
237#888—91no—
238#887—94no—
239#887—91no—
240#67⋊C4—94no—
241#67⋊C4—91no—
242#67⋊C4—94no—
243#67⋊C4—91no—
244#67⋊C4—184no—
245#878—34no—
246#878—94no—
247#878—91no—
248#878C3⋊D311yescharacteristic, complemented
249C23×C32—24no—
250C23×C32C22×D314yes—
251C23×C32C22×D311yescharacteristic
252C22×C3⋊D3—31no—
253C22×C3⋊D3—34no—
254C22×C3⋊D3—64no—
255C32×Q8—62no—
256C2×C32×C4—24no—
257C2×C32×C4—24no—
258C2×C32×C4—31no—
259C2×C32×C4—31no—
260C2×C32×C4—31no—
261C2×C32×C4—31no—
262C2×C32×C4—62no—
263C2×C32×C4C22×D314yes—
264C2×C32×C4C22×D314yes—
265C2×C32×C4C22×D311yescharacteristic
266C2×C32×C4C22×D311yescharacteristic
267#638—34no—
268#638—316no—
269#638—616no—
270C2×C3⋊Dic3—22no—
271C2×C3⋊Dic3—31no—
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—34no—
275C2×C3⋊Dic3—34no—
276C2×C3⋊Dic3—34no—
277C2×C3⋊Dic3—64no—
278C2×C3⋊Dic3—64no—
279C2×C3⋊Dic3—64no—
280C2×C3⋊Dic3—62no—
281C2×C3⋊Dic3—68no—
282C2×C3⋊Dic3—128no—
283C2×C3⋊Dic3C22×D311yescharacteristic
284C2×C3⋊Dic3C22×D311yescharacteristic
285C2×C3⋊Dic3C22×D311yescharacteristic
286C2×C3⋊Dic3C22×D311yescharacteristic
287C4×C3⋊D3—62no—
288C4×C3⋊D3—62no—
289C4×C3⋊D3—62no—
290C4×C3⋊D3—68no—
291C4×C3⋊D3—128no—
292#634—22no—
293#634—34no—
294#634—62no—
295#634—62no—
296#634—62no—
297#634—62no—
298C2×C3×Dic3—28no—
299C2×C3×Dic3—34no—
300C2×C3×Dic3—34no—
301C2×C3×Dic3—34no—
302C2×C3×Dic3—34no—
303C2×C3×Dic3—68no—
304C2×C3×Dic3C22×D314yes—
305C2×C3×Dic3C22×D314yes—
306C2×C3×Dic3C22×D314yes—
307C2×C3×Dic3C22×D314yes—
308C3×Dic6—28no—
309C3×Dic6—68no—
310#627—316no—
311#627—68no—
312#627—68no—
313#627—68no—
314#627—68no—
315#624—68no—
316#624—68no—
317D4×Q8—271noSylow
318C2×C33—22no—
319C2×C33C22×D411yescharacteristic
320C2×C33C22×Q811yescharacteristic
321C2×C332−1+411yescharacteristic
322C3⋊(C3⋊D3)—22no—
323C2×C3×Q8—34no—
324C2×C3×Q8—91no—
325C22×C3×C4—34no—
326C22×C3×C4—91no—
327C2×#67—94no—
328C2×#67—91no—
329C2×#67—184no—
330C22×Dic3—34no—
331C22×Dic3—94no—
332C22×Dic3—91no—
333C22×Dic3—184no—
334C22×Dic3C2×C3⋊D311yescharacteristic
335D3×Q8—184no—
336D3×Q8—1816no—
337C2×C4×D3—94no—
338C2×C4×D3—94no—
339C2×C4×D3—94no—
340C2×C4×D3—91no—
341C2×C4×D3—91no—
342C2×C4×D3—91no—
343C2×C4×D3—184no—
344C2×Dic6—34no—
345C2×Dic6—94no—
346C2×Dic6—91no—
347C2×Dic6—94no—
348C2×Dic6—94no—
349C2×Dic6—94no—
350C2×Dic6—94no—
351C2×Dic6—91no—
352C2×Dic6—91no—
353C2×Dic6—91no—
354C2×Dic6—91no—
355C2×Dic6—184no—
356C2×Dic6—1816no—
357C2×Dic6C2×C3⋊D311yescharacteristic
358C3×C4⋊C4—34no—
359C3×C4⋊C4—34no—
360C3×C4⋊C4—34no—
361C3×C4⋊C4—91no—
362C3×C4⋊C4—91no—
363C3×C4⋊C4—91no—
364C3×C22⋊C4—24no—
365C3×C22⋊C4—34no—
366C3×C22⋊C4—91no—
367C3×C22⋊C4D3214yes—
368C3×C22⋊C4C2×C3⋊D311yescharacteristic
369#217—34no—
370#217C2×C3⋊D311yescharacteristic
371(C2×D3)⋊C4—94no—
372(C2×D3)⋊C4—94no—
373(C2×D3)⋊C4—94no—
374(C2×D3)⋊C4—91no—
375(C2×D3)⋊C4—91no—
376(C2×D3)⋊C4—91no—
377(C2×D3)⋊C4—184no—
378C4⋊Dic3—34no—
379C4⋊Dic3—94no—
380C4⋊Dic3—91no—
381C4⋊Dic3C2×C3⋊D311yescharacteristic
382Dic3⋊C4—34no—
383Dic3⋊C4—34no—
384Dic3⋊C4—94no—
385Dic3⋊C4—94no—
386Dic3⋊C4—94no—
387Dic3⋊C4—94no—
388Dic3⋊C4—94no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—184no—
395Dic3⋊C4C2×C3⋊D311yescharacteristic
396Dic3⋊C4C2×C3⋊D311yescharacteristic
397C4×Dic3—94no—
398C4×Dic3—94no—
399C4×Dic3—94no—
400C4×Dic3—91no—
401C4×Dic3—91no—
402C4×Dic3—91no—
403C4×Dic3—184no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—24no—
407C22×C32—28no—
408C22×C32—24no—
409C22×C32—24no—
410C22×C32—44no—
411C22×C32—44no—
412C22×C32D3×Q818yescomplemented
413C22×C32D3×Q812yescomplemented
414C22×C32C23×D314yes—
415C22×C32C23×D311yescharacteristic
416C2×C3⋊D3—32no—
417C2×C3⋊D3—38no—
418C2×C3⋊D3—68no—
419C2×C3⋊D3—61no—
420C2×C3⋊D3—61no—
421C2×C3⋊D3—64no—
422C2×C3⋊D3—64no—
423C2×C3⋊D3—124no—
424C2×C3⋊D3—124no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—24no—
428C32×C4—24no—
429C32×C4—32no—
430C32×C4—44no—
431C32×C4—44no—
432C32×C4—61no—
433C32×C4—61no—
434C32×C4—61no—
435C3⋊Dic3—21no—
436C3⋊Dic3—21no—
437C3⋊Dic3—21no—
438C3⋊Dic3—32no—
439C3⋊Dic3—32no—
440C3⋊Dic3—38no—
441C3⋊Dic3—38no—
442C3⋊Dic3—68no—
443C3⋊Dic3—68no—
444C3⋊Dic3—61no—
445C3⋊Dic3—64no—
446C3⋊Dic3—124no—
447C3⋊Dic3D3×D412yes—
448C3×Dic3—24no—
449C3×Dic3—24no—
450C3×Dic3—24no—
451C3×Dic3—38no—
452C3×Dic3—64no—
453C3×Dic3—64no—
454C3×Dic3—64no—
455C3×Dic3D3×D418yes—
456C22×Q8—271no—
457C22×Q8—271no—
458C4⋊Q8—271no—
459C4⋊Q8—271no—
460C4⋊Q8—271no—
461C22⋊Q8—31no—
462C22⋊Q8—91no—
463C22⋊Q8—271no—
464C22⋊Q8—271no—
465C22⋊Q8—271no—
466C22⋊Q8—271no—
467C4×Q8—271no—
468C4×D4—271no—
469C4×D4—271no—
470C4×D4—271no—
471C33D4×Q811yescharacteristic, complemented, Sylow
472C23×C3—24no—
473C23×C3C2×D3214yes—
474C23×C3C22×C3⋊D311yescharacteristic
475C22×D3—94no—
476C22×D3—91no—
477C22×D3—184no—
478C3×Q8—68no—
479C3×Q8—182no—
480C2×C3×C4—24no—
481C2×C3×C4—24no—
482C2×C3×C4—34no—
483C2×C3×C4—34no—
484C2×C3×C4—34no—
485C2×C3×C4—34no—
486C2×C3×C4—68no—
487C2×C3×C4—91no—
488C2×C3×C4—91no—
489C2×C3×C4—91no—
490C2×C3×C4—91no—
491C2×C3×C4—182no—
492C2×C3×C4C2×D3214yes—
493C2×C3×C4C2×D3214yes—
494C2×C3×C4C22×C3⋊D311yescharacteristic
495C2×C3×C4C22×C3⋊D311yescharacteristic
496#67—916no—
497#67—94no—
498#67—1816no—
499C2×Dic3—22no—
500C2×Dic3—34no—
501C2×Dic3—34no—
502C2×Dic3—34no—
503C2×Dic3—34no—
504C2×Dic3—68no—
505C2×Dic3—94no—
506C2×Dic3—94no—
507C2×Dic3—91no—
508C2×Dic3—91no—
509C2×Dic3—94no—
510C2×Dic3—91no—
511C2×Dic3—184no—
512C2×Dic3—184no—
513C2×Dic3—184no—
514C2×Dic3—182no—
515C2×Dic3—188no—
516C2×Dic3—368no—
517C2×Dic3C22×C3⋊D311yescharacteristic
518C2×Dic3C22×C3⋊D311yescharacteristic
519C2×Dic3C22×C3⋊D311yescharacteristic
520C2×Dic3C22×C3⋊D311yescharacteristic
521C4×D3—182no—
522C4×D3—188no—
523C4×D3—188no—
524C4×D3—182no—
525C4×D3—188no—
526C4×D3—182no—
527C4×D3—368no—
528Dic6—22no—
529Dic6—68no—
530Dic6—916no—
531Dic6—94no—
532Dic6—182no—
533Dic6—182no—
534Dic6—182no—
535Dic6—188no—
536Dic6—188no—
537Dic6—188no—
538Dic6—188no—
539Dic6—182no—
540C2×C32—22no—
541C2×C32—24no—
542C2×C32—24no—
543C2×C32—24no—
544C2×C32—28no—
545C2×C32—48no—
546C2×C32C2×D3×D414yes—
547C2×C32C2×D3×D411yescharacteristic
548C2×C32C2×D3×Q814yes—
549C2×C32C2×D3×Q811yescharacteristic
550C2×C32#101014yes—
551C2×C32#101011yescharacteristic
552C3⋊D3—62no—
553C3⋊D3—68no—
554C3⋊D3—128no—
555C2×Q8—31no—
556C2×Q8—91no—
557C2×Q8—271no—
558C2×Q8—271no—
559C2×Q8—271no—
560C2×Q8—271no—
561C2×Q8—271no—
562C2×Q8—544no—
563C2×Q8—544no—
564C2×D4—271no—
565C22×C4—31no—
566C22×C4—91no—
567C22×C4—271no—
568C22×C4—271no—
569C22×C4—271no—
570C22×C4—271no—
571C4⋊C4—31no—
572C4⋊C4—31no—
573C4⋊C4—31no—
574C4⋊C4—91no—
575C4⋊C4—91no—
576C4⋊C4—91no—
577C4⋊C4—271no—
578C4⋊C4—271no—
579C4⋊C4—271no—
580C4⋊C4—271no—
581C4⋊C4—271no—
582C4⋊C4—271no—
583C22⋊C4—31no—
584C22⋊C4—91no—
585C22⋊C4—271no—
586C22⋊C4—271no—
587C22⋊C4—271no—
588C22⋊C4D3×C3⋊D311yescharacteristic
589C42—271no—
590C42—271no—
591C42—271no—
592C22×C3—24no—
593C22×C3—24no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—24no—
597C22×C3—28no—
598C22×C3—44no—
599C22×C3—44no—
600C22×C3#379718yescomplemented
601C22×C3Q8×C3⋊D312yescomplemented
602C22×C3C22×D3214yes—
603C22×C3C23×C3⋊D311yescharacteristic
604C2×D3—98no—
605C2×D3—92no—
606C2×D3—188no—
607C2×D3—184no—
608C2×D3—184no—
609C2×D3—181no—
610C2×D3—181no—
611C2×D3—364no—
612C2×D3—364no—
613C3×C4—24no—
614C3×C4—24no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—38no—
618C3×C4—44no—
619C3×C4—44no—
620C3×C4—64no—
621C3×C4—64no—
622C3×C4—64no—
623C3×C4—92no—
624C3×C4—181no—
625C3×C4—181no—
626C3×C4—181no—
627Dic3—21no—
628Dic3—21no—
629Dic3—21no—
630Dic3—38no—
631Dic3—64no—
632Dic3—64no—
633Dic3—64no—
634Dic3—98no—
635Dic3—98no—
636Dic3—92no—
637Dic3—92no—
638Dic3—188no—
639Dic3—188no—
640Dic3—184no—
641Dic3—181no—
642Dic3—364no—
643Dic3D4×C3⋊D312yes—
644C32—24no—
645C32#563214yescomplemented
646C32#563211yescharacteristic, complemented
647C23—271no—
648C23C2×D3×C3⋊D311yescharacteristic
649Q8—62no—
650Q8—182no—
651Q8—274no—
652Q8—542no—
653Q8—542no—
654Q8—542no—
655Q8—542no—
656D4—274no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—62no—
662C2×C4—91no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—91no—
666C2×C4—182no—
667C2×C4—271no—
668C2×C4—271no—
669C2×C4—271no—
670C2×C4—542no—
671C2×C4—542no—
672C2×C4—542no—
673C2×C4—542no—
674C2×C4C2×D3×C3⋊D311yescharacteristic
675C2×C4C2×D3×C3⋊D311yescharacteristic
676C2×C3—22no—
677C2×C3—28no—
678C2×C3—24no—
679C2×C3—24no—
680C2×C3—24no—
681C2×C3—48no—
682C2×C3C2×#379714yes—
683C2×C3#6430914yes—
684C2×C3D32×D414yes—
685C2×C3C2×D4×C3⋊D311yescharacteristic
686C2×C3C2×Q8×C3⋊D311yescharacteristic
687C2×C3#6436711yescharacteristic
688D3—182no—
689D3—188no—
690D3—368no—
691C22—21no—
692C22—21no—
693C22—272no—
694C22—541no—
695C22—541no—
696C22#8901912yescomplemented
697C22C22×D3×C3⋊D311yescharacteristic
698C4—21no—
699C4—21no—
700C4—32no—
701C4—61no—
702C4—61no—
703C4—61no—
704C4—92no—
705C4—181no—
706C4—181no—
707C4—181no—
708C4—272no—
709C4—272no—
710C4—541no—
711C3—24no—
712C3#1059407214yescomplemented
713C3#1059610311yescharacteristic, complemented
714C2—22no—
715C2—542no—
716C2C2×#8901911yescharacteristic
717C2#1172458211yescharacteristic
718C2D3×D4×C3⋊D311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radicalC2×#6312C22
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33D4×Q8
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#6293C2semidirect
2. C2×#89019C2semidirect
4. C3×#64087C2semidirect
5. C32×#878C2semidirect
6. #11723642C2semidirect
9. #11723536C2semidirect
10. #11723495C2semidirect
11. #11723485C2semidirect
12. #11723442C2semidirect
13. #11723394C2semidirect
14. #11723393C2semidirect
15. #11723391C2semidirect
73. #64087D3semidirect
75. C3×#878D3semidirect
90. #6312Q8semidirect
112. #6293D4semidirect
200. C22×C33C2×Q8semidirect
204. C2×C3⋊(C3⋊D3)C2×Q8semidirect
209. C3⋊(C3⋊Dic3)C2×Q8semidirect
248. #878C3⋊D3semidirect
412. C22×C32D3×Q8semidirect
413. C22×C32D3×Q8semidirect
471. C33D4×Q8semidirect
600. C22×C3#3797semidirect
601. C22×C3Q8×C3⋊D3semidirect
645. C32#5632semidirect
646. C32#5632semidirect
696. C22#89019semidirect
712. C3#10594072semidirect
713. C3#10596103semidirect

Maximal subgroups

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

subgroupindex
C22×#62932
C2×#890192
#117239222
C3×#640872
C32×#8782
#117236422
#117236222
#117236182
#117235362
#117234952
#117234852
#117234422
#117233942
#117233932
#117233912
#105961033
#105940723