Finite Group Databasebeta

← #13178277

Subgroups — #13178277

Order 1728.

996 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64088C211yesmaximal, characteristic
2C3×#64088C211yesmaximal, characteristic
3C3×#64087C211yesmaximal, characteristic
4#11723721C211yesmaximal, characteristic
5#11723716C211yesmaximal, characteristic
6#11723716C211yesmaximal, characteristic
7#11723715C211yesmaximal, characteristic
8#11723680C211yesmaximal, characteristic, complemented
9#11723679C211yesmaximal, characteristic, complemented
10#11723669C211yesmaximal, characteristic, complemented
11#11723669C211yesmaximal, characteristic, complemented
12#11723669C211yesmaximal, characteristic, complemented
13#11723668C211yesmaximal, characteristic, complemented
14#11723666C211yesmaximal, characteristic, complemented
15#11723665C211yesmaximal, characteristic, complemented
16#10594031—31nomaximal
17#10594028—31nomaximal
18#10594027—31nomaximal
19C22×C3×C3⋊Dic3C2211yescharacteristic
20C2×C3×#634C2211yescharacteristic
21C2×#6296C2211yescharacteristic
22C33×C22⋊C4C2211yescharacteristic
23C3×#3757C2211yescharacteristic
24C3×#3757C2211yescharacteristic
25C3×#3757C2211yescharacteristic
26C3×#3757C2211yescharacteristic
27C3×#3757C2211yescharacteristic
28C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C3×#3750C2211yescharacteristic
32C3×#3750C2211yescharacteristic
33C3×#3750C2211yescharacteristic
34C3×#3750C2211yescharacteristic
35C3×#3750C2211yescharacteristic
36C3×#3750C2211yescharacteristic
37C3×C4×C3⋊Dic3C2211yescharacteristic
38C3×C4×C3⋊Dic3C2211yescharacteristic
39#88815C2211yescharacteristic
40#88815C2211yescharacteristic
41#88815C2211yescharacteristic
42#88815C2211yescharacteristic
43#88815C2211yescharacteristic
44#88815C2211yescharacteristic
45#88815C2211yescharacteristic
46#88815C2211yescharacteristic
47#88815C2211yescharacteristic
48#88815C2211yescharacteristic
49#88815C2211yescharacteristic
50#88813C2211yescharacteristic
51#88813C2211yescharacteristic
52#88813C2211yescharacteristic
53#88813C2211yescharacteristic
54#64088D311yescharacteristic
55#64088D311yescharacteristic
56#64087D311yescharacteristic
57C3×#879—31no—
58C3×#879—31no—
59C3×#879—31no—
60C3×#879—31no—
61C3×#879—61no—
62C3×#879—61no—
63C3×#878—31no—
64C3×#878—31no—
65C3×#878—61no—
66#63982—31no—
67#63964—31no—
68#63964—31no—
69#63957—31no—
70#63956—31no—
71#63956—31no—
72#63956—31no—
73#63956—31no—
74#63956—31no—
75#63956—31no—
76#63955—31no—
77#63955—31no—
78#63872—31no—
79#63870—31no—
80#63869—31no—
81#63869—31no—
82#63867—31no—
83#63867—31no—
84#63847—31no—
85#63847—31no—
86#63847—31no—
87#63846—31no—
88#63846—31no—
89#63846—31no—
90#63845—31no—
91#63845—31no—
92#63845—31no—
93#63844—31no—
94#63843—31no—
95Dic3×Dic6—31no—
96#63840—31no—
97#63839—31no—
98#63839—31no—
99#63838—31no—
100#63837—31no—
101#63837—31no—
102C23×C33C2311yescharacteristic
103C2×C33×C4C2311yescharacteristic
104C2×C33×C4C2311yescharacteristic
105C2×C3×C3⋊Dic3—22no—
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C3×#634—22no—
119#6296—22no—
120#5701—91no—
121#5701—91no—
122#5625—91no—
123C22×C3⋊Dic3C2×D311yescharacteristic
124C2×#634C2×D311yescharacteristic
125C22×C3×Dic3—31no—
126C22×C3×Dic3—31no—
127C22×C3×Dic3—61no—
128C2×C3×Dic6—31no—
129C2×C3×Dic6—31no—
130C2×C3×Dic6—61no—
131C2×#627—31no—
132C2×#627—31no—
133C2×#627—31no—
134C32×C22⋊C4—21no—
135C32×C22⋊C4—21no—
136C32×C22⋊C4—21no—
137C32×C22⋊C4—41no—
138C32×C22⋊C4C2×D311yescharacteristic
139C32×C22⋊C4C2×D311yescharacteristic
140C32×C22⋊C4C2×D311yescharacteristic
141#3757C2×D311yescharacteristic
142#3757C2×D311yescharacteristic
143#3757C2×D311yescharacteristic
144#3757C2×D311yescharacteristic
145#3757C2×D311yescharacteristic
146C4⋊(C3⋊Dic3)C2×D311yescharacteristic
147C4⋊(C3⋊Dic3)C2×D311yescharacteristic
148C4⋊(C3⋊Dic3)C2×D311yescharacteristic
149#3750C2×D311yescharacteristic
150#3750C2×D311yescharacteristic
151#3750C2×D311yescharacteristic
152#3750C2×D311yescharacteristic
153#3750C2×D311yescharacteristic
154#3750C2×D311yescharacteristic
155C4×C3⋊Dic3C2×D311yescharacteristic
156C4×C3⋊Dic3C2×D311yescharacteristic
157C3×#217—31no—
158C3×#217—31no—
159C3×#217—31no—
160C3×#217—31no—
161C3×#217—31no—
162C3×#217—31no—
163C3×#217—31no—
164C3×#217—31no—
165C3×#217—31no—
166C3×#217—31no—
167C3×#217—61no—
168C3×#217—61no—
169C3×#217—61no—
170C3×#217—61no—
171C3×#217—61no—
172C3×C4⋊Dic3—31no—
173C3×C4⋊Dic3—31no—
174C3×C4⋊Dic3—31no—
175C3×C4⋊Dic3—31no—
176C3×C4⋊Dic3—31no—
177C3×C4⋊Dic3—31no—
178C3×C4⋊Dic3—61no—
179C3×C4⋊Dic3—61no—
180C3×C4⋊Dic3—61no—
181C3×Dic3⋊C4—31no—
182C3×Dic3⋊C4—31no—
183C3×Dic3⋊C4—31no—
184C3×Dic3⋊C4—31no—
185C3×Dic3⋊C4—31no—
186C3×Dic3⋊C4—31no—
187C3×Dic3⋊C4—31no—
188C3×Dic3⋊C4—31no—
189C3×Dic3⋊C4—31no—
190C3×Dic3⋊C4—31no—
191C3×Dic3⋊C4—31no—
192C3×Dic3⋊C4—31no—
193C3×Dic3⋊C4—61no—
194C3×Dic3⋊C4—61no—
195C3×Dic3⋊C4—61no—
196C3×Dic3⋊C4—61no—
197C3×Dic3⋊C4—61no—
198C3×Dic3⋊C4—61no—
199C3×C4×Dic3—31no—
200C3×C4×Dic3—31no—
201C3×C4×Dic3—31no—
202C3×C4×Dic3—31no—
203C3×C4×Dic3—61no—
204C3×C4×Dic3—61no—
205#3724—31no—
206#3724—31no—
207#3724—31no—
208#3724—31no—
209#3724—31no—
210#3724—31no—
211#3724—31no—
212#3724—31no—
213#3724—31no—
214#3724—31no—
215#3724—31no—
216Dic3⋊Dic3—31no—
217Dic3⋊Dic3—31no—
218Dic3⋊Dic3—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—31no—
224Dic3⋊Dic3—31no—
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—31no—
234Dic3⋊Dic3—31no—
235Dic3⋊Dic3—31no—
236Dic3⋊Dic3—31no—
237Dic3⋊Dic3—31no—
238Dic32—31no—
239Dic32—31no—
240Dic32—31no—
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250C22×C33—21no—
251C22×C33—21no—
252C22×C33—21no—
253C22×C33C2411yescharacteristic
254C33×C4—21no—
255C33×C4—21no—
256C3×C3⋊Dic3—21no—
257C3×C3⋊Dic3—21no—
258C3×C3⋊Dic3—21no—
259C3×C3⋊Dic3—21no—
260C3×C3⋊Dic3—21no—
261C3×C3⋊Dic3—21no—
262C3×C3⋊Dic3—21no—
263C3×C3⋊Dic3—21no—
264C3×C3⋊Dic3—21no—
265C3×C3⋊Dic3—21no—
266C3×C3⋊Dic3—21no—
267C3×C3⋊Dic3#4112yes—
268C3×#126—91no—
269C3×#126—91no—
270C3×C22⋊Q8—91no—
271Q8×Dic3—91no—
272#944—91no—
273#926—91no—
274#924—91no—
275#890—91no—
276#890—91no—
277#890—91no—
278#890—91no—
279#890—91no—
280#889—91no—
281#889—91no—
282#889—91no—
283#889—91no—
284#889—91no—
285#889—91no—
286#889—91no—
287#889—91no—
288#888—91no—
289#888—91no—
290#887—91no—
291#887—91no—
292#887—91no—
293#879—31no—
294#879—31no—
295#879—31no—
296#879—31no—
297#879—61no—
298#879—61no—
299#879—91no—
300#879—91no—
301#879—91no—
302#879—91no—
303#879—91no—
304#879—91no—
305#878—31no—
306#878—31no—
307#878—61no—
308#878—91no—
309#878—91no—
310#877—91no—
311#877—91no—
312#870—91no—
313#870—91no—
314C4×Dic6—91no—
315C4×Dic6—91no—
316C23×C32—21no—
317C23×C32—21no—
318C23×C32—21no—
319C23×C32—41no—
320C23×C32C22×D311yescharacteristic
321C23×C32C22×D311yescharacteristic
322C23×C32C22×D311yescharacteristic
323C2×C32×C4—21no—
324C2×C32×C4—21no—
325C2×C32×C4—21no—
326C2×C32×C4—21no—
327C2×C32×C4—21no—
328C2×C32×C4—21no—
329C2×C32×C4—41no—
330C2×C32×C4—41no—
331C2×C32×C4C22×D311yescharacteristic
332C2×C32×C4C22×D311yescharacteristic
333C2×C32×C4C22×D311yescharacteristic
334C2×C32×C4C22×D311yescharacteristic
335C2×C32×C4C22×D311yescharacteristic
336C2×C32×C4C22×D311yescharacteristic
337C2×C3⋊Dic3—22no—
338C2×C3⋊Dic3C22×D311yescharacteristic
339C2×C3⋊Dic3C22×D311yescharacteristic
340C2×C3⋊Dic3C22×D311yescharacteristic
341C2×C3⋊Dic3C22×D311yescharacteristic
342C2×C3⋊Dic3C22×D311yescharacteristic
343C2×C3⋊Dic3C22×D311yescharacteristic
344C2×C3⋊Dic3C22×D311yescharacteristic
345C2×C3⋊Dic3C22×D311yescharacteristic
346C2×C3⋊Dic3C22×D311yescharacteristic
347C2×C3⋊Dic3C22×D311yescharacteristic
348C2×C3⋊Dic3C22×D311yescharacteristic
349C2×C3⋊Dic3C22×D311yescharacteristic
350#634—22no—
351C2×C3×Dic3—31no—
352C2×C3×Dic3—31no—
353C2×C3×Dic3—31no—
354C2×C3×Dic3—31no—
355C2×C3×Dic3—31no—
356C2×C3×Dic3—31no—
357C2×C3×Dic3—31no—
358C2×C3×Dic3—31no—
359C2×C3×Dic3—31no—
360C2×C3×Dic3—31no—
361C2×C3×Dic3—31no—
362C2×C3×Dic3—31no—
363C2×C3×Dic3—31no—
364C2×C3×Dic3—31no—
365C2×C3×Dic3—31no—
366C2×C3×Dic3—31no—
367C2×C3×Dic3—31no—
368C2×C3×Dic3—31no—
369C2×C3×Dic3—31no—
370C2×C3×Dic3—31no—
371C2×C3×Dic3—31no—
372C2×C3×Dic3—31no—
373C2×C3×Dic3—31no—
374C2×C3×Dic3—31no—
375C2×C3×Dic3—61no—
376C2×C3×Dic3—61no—
377C2×C3×Dic3—61no—
378C2×C3×Dic3—61no—
379C2×C3×Dic3—61no—
380C2×C3×Dic3—61no—
381C2×C3×Dic3—61no—
382C2×C3×Dic3—61no—
383C2×C3×Dic3—61no—
384C2×C3×Dic3—61no—
385C2×C3×Dic3—61no—
386C2×C3×Dic3—61no—
387C2×C3×Dic3—62no—
388C2×C3×Dic3—62no—
389C2×C3×Dic3—122no—
390C3×Dic6—62no—
391C3×Dic6—62no—
392C3×Dic6—122no—
393#627—62no—
394#627—62no—
395#627—62no—
396#541—271noSylow
397C2×C33—41no—
398C2×C33C2×#4111yescharacteristic
399C2×C332−1+411yescharacteristic
400C2×C332−1+411yescharacteristic
401C2×C3×Q8—91no—
402C22×C3×C4—91no—
403C22×Dic3—31no—
404C22×Dic3—31no—
405C22×Dic3—61no—
406C2×Dic6—31no—
407C2×Dic6—31no—
408C2×Dic6—61no—
409C2×Dic6—91no—
410C2×Dic6—91no—
411C2×Dic6—91no—
412C3×C4⋊C4—91no—
413C3×C4⋊C4—91no—
414C3×C4⋊C4—91no—
415C3×C4⋊C4—91no—
416C3×C4⋊C4—91no—
417C3×C4⋊C4—91no—
418C3×C4⋊C4—91no—
419C3×C4⋊C4—91no—
420C3×C4⋊C4—91no—
421C3×C22⋊C4—21no—
422C3×C22⋊C4—21no—
423C3×C22⋊C4—21no—
424C3×C22⋊C4—41no—
425C3×C22⋊C4—91no—
426C3×C22⋊C4—91no—
427C3×C22⋊C4—91no—
428C3×C22⋊C4—91no—
429C3×C22⋊C4—91no—
430C3×C22⋊C4D3211yescharacteristic
431C3×C22⋊C4D3211yescharacteristic
432C3×C22⋊C4D3211yescharacteristic
433C3×C42—91no—
434C3×C42—91no—
435#217—31no—
436#217—31no—
437#217—31no—
438#217—31no—
439#217—31no—
440#217—31no—
441#217—31no—
442#217—31no—
443#217—31no—
444#217—31no—
445#217—61no—
446#217—61no—
447#217—61no—
448#217—61no—
449#217—61no—
450C4⋊Dic3—31no—
451C4⋊Dic3—31no—
452C4⋊Dic3—31no—
453C4⋊Dic3—31no—
454C4⋊Dic3—31no—
455C4⋊Dic3—31no—
456C4⋊Dic3—61no—
457C4⋊Dic3—61no—
458C4⋊Dic3—61no—
459C4⋊Dic3—91no—
460C4⋊Dic3—91no—
461C4⋊Dic3—91no—
462C4⋊Dic3—91no—
463C4⋊Dic3—91no—
464C4⋊Dic3—91no—
465C4⋊Dic3—91no—
466C4⋊Dic3—91no—
467C4⋊Dic3—91no—
468C4⋊Dic3—91no—
469C4⋊Dic3—91no—
470Dic3⋊C4—31no—
471Dic3⋊C4—31no—
472Dic3⋊C4—31no—
473Dic3⋊C4—31no—
474Dic3⋊C4—31no—
475Dic3⋊C4—31no—
476Dic3⋊C4—31no—
477Dic3⋊C4—31no—
478Dic3⋊C4—31no—
479Dic3⋊C4—31no—
480Dic3⋊C4—31no—
481Dic3⋊C4—31no—
482Dic3⋊C4—61no—
483Dic3⋊C4—61no—
484Dic3⋊C4—61no—
485Dic3⋊C4—61no—
486Dic3⋊C4—61no—
487Dic3⋊C4—61no—
488Dic3⋊C4—91no—
489Dic3⋊C4—91no—
490Dic3⋊C4—91no—
491Dic3⋊C4—91no—
492Dic3⋊C4—91no—
493Dic3⋊C4—91no—
494Dic3⋊C4—91no—
495Dic3⋊C4—91no—
496Dic3⋊C4—91no—
497Dic3⋊C4—91no—
498Dic3⋊C4—91no—
499Dic3⋊C4—91no—
500Dic3⋊C4—91no—
501Dic3⋊C4—91no—
502Dic3⋊C4—91no—
503Dic3⋊C4—91no—
504Dic3⋊C4—91no—
505Dic3⋊C4—91no—
506Dic3⋊C4—91no—
507Dic3⋊C4—91no—
508Dic3⋊C4—91no—
509Dic3⋊C4—91no—
510C4×Dic3—31no—
511C4×Dic3—31no—
512C4×Dic3—31no—
513C4×Dic3—31no—
514C4×Dic3—61no—
515C4×Dic3—61no—
516C4×Dic3—91no—
517C4×Dic3—91no—
518C4×Dic3—91no—
519C4×Dic3—91no—
520C4×Dic3—91no—
521C4×Dic3—91no—
522C4×Dic3—91no—
523C4×Dic3—91no—
524C4×Dic3—91no—
525C4×Dic3—91no—
526C4×Dic3—91no—
527C4×Dic3—91no—
528C22×C32—21no—
529C22×C32—22no—
530C22×C32—21no—
531C22×C32—21no—
532C22×C32—21no—
533C22×C32—21no—
534C22×C32—21no—
535C22×C32—21no—
536C22×C32—21no—
537C22×C32—21no—
538C22×C32—21no—
539C22×C32—21no—
540C22×C32—21no—
541C22×C32—41no—
542C22×C32—41no—
543C22×C32—41no—
544C22×C32—42no—
545C22×C32—41no—
546C22×C32—41no—
547C22×C32—41no—
548C22×C32—41no—
549C22×C32—41no—
550C22×C32—41no—
551C22×C32—81no—
552C22×C32—81no—
553C22×C32C23×D311yescharacteristic
554C22×C32C23×D311yescharacteristic
555C22×C32C23×D311yescharacteristic
556C32×C4—21no—
557C32×C4—21no—
558C32×C4—21no—
559C32×C4—21no—
560C32×C4—21no—
561C32×C4—21no—
562C32×C4—41no—
563C32×C4—41no—
564C32×C4—41no—
565C32×C4—41no—
566C32×C4—41no—
567C32×C4—41no—
568C32×C4—81no—
569C32×C4—81no—
570C3⋊Dic3—21no—
571C3⋊Dic3—21no—
572C3⋊Dic3—21no—
573C3⋊Dic3—21no—
574C3⋊Dic3—21no—
575C3⋊Dic3—21no—
576C3⋊Dic3—21no—
577C3⋊Dic3—21no—
578C3⋊Dic3—21no—
579C3⋊Dic3—21no—
580C3⋊Dic3—21no—
581C3⋊Dic3#23712yes—
582C3×Dic3—32no—
583C3×Dic3—32no—
584C3×Dic3—62no—
585C3×Dic3—61no—
586C3×Dic3—61no—
587C3×Dic3—61no—
588C3×Dic3—61no—
589C3×Dic3—61no—
590C3×Dic3—61no—
591C3×Dic3—61no—
592C3×Dic3—61no—
593C3×Dic3—61no—
594C3×Dic3—61no—
595C3×Dic3—61no—
596C3×Dic3—61no—
597C3×Dic3—61no—
598C3×Dic3—61no—
599C3×Dic3—61no—
600C3×Dic3—61no—
601C3×Dic3—61no—
602C3×Dic3—61no—
603C3×Dic3—61no—
604C3×Dic3—61no—
605C3×Dic3—61no—
606C3×Dic3—61no—
607C3×Dic3—121no—
608C3×Dic3—121no—
609C3×Dic3—121no—
610C3×Dic3—121no—
611C3×Dic3—121no—
612C3×Dic3—121no—
613C3×Dic3—121no—
614C3×Dic3—121no—
615C3×Dic3—121no—
616C3×Dic3—121no—
617C3×Dic3—121no—
618C4⋊Q8—271no—
619#126—91no—
620#126—91no—
621#126—271no—
622#126—271no—
623#125—271no—
624#125—271no—
625#125—271no—
626#125—271no—
627#125—271no—
628C22⋊Q8—91no—
629C22⋊Q8—271no—
630C4×Q8—271no—
631C4×Q8—271no—
632#117—271no—
633C33#54111yescharacteristic, complemented, Sylow
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—41no—
638C23×C3C2×D3211yescharacteristic
639C23×C3C2×D3211yescharacteristic
640C23×C3C2×D3211yescharacteristic
641C3×Q8—182no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—41no—
649C2×C3×C4—41no—
650C2×C3×C4—91no—
651C2×C3×C4—91no—
652C2×C3×C4—91no—
653C2×C3×C4—91no—
654C2×C3×C4—91no—
655C2×C3×C4—91no—
656C2×C3×C4—91no—
657C2×C3×C4—91no—
658C2×C3×C4—91no—
659C2×C3×C4—91no—
660C2×C3×C4—91no—
661C2×C3×C4—91no—
662C2×C3×C4—182no—
663C2×C3×C4C2×D3211yescharacteristic
664C2×C3×C4C2×D3211yescharacteristic
665C2×C3×C4C2×D3211yescharacteristic
666C2×C3×C4C2×D3211yescharacteristic
667C2×C3×C4C2×D3211yescharacteristic
668C2×C3×C4C2×D3211yescharacteristic
669C2×Dic3—31no—
670C2×Dic3—31no—
671C2×Dic3—31no—
672C2×Dic3—31no—
673C2×Dic3—31no—
674C2×Dic3—31no—
675C2×Dic3—31no—
676C2×Dic3—31no—
677C2×Dic3—31no—
678C2×Dic3—31no—
679C2×Dic3—31no—
680C2×Dic3—31no—
681C2×Dic3—31no—
682C2×Dic3—31no—
683C2×Dic3—31no—
684C2×Dic3—31no—
685C2×Dic3—31no—
686C2×Dic3—31no—
687C2×Dic3—31no—
688C2×Dic3—31no—
689C2×Dic3—31no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—61no—
694C2×Dic3—61no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—61no—
705C2×Dic3—62no—
706C2×Dic3—62no—
707C2×Dic3—122no—
708Dic6—62no—
709Dic6—62no—
710Dic6—122no—
711Dic6—182no—
712Dic6—182no—
713Dic6—182no—
714C2×C32—21no—
715C2×C32—21no—
716C2×C32—21no—
717C2×C32—21no—
718C2×C32—21no—
719C2×C32—21no—
720C2×C32—21no—
721C2×C32—21no—
722C2×C32—21no—
723C2×C32—41no—
724C2×C32—41no—
725C2×C32—41no—
726C2×C32—41no—
727C2×C32—42no—
728C2×C32—41no—
729C2×C32—41no—
730C2×C32—81no—
731C2×C32—81no—
732C2×C32—82no—
733C2×C32C2×#23711yescharacteristic
734C2×C32#100711yescharacteristic
735C2×C32D3×#4111yescharacteristic
736C2×C32D3×#4111yescharacteristic
737C2×C32#101011yescharacteristic
738C2×C32#101011yescharacteristic
739C2×C32#101011yescharacteristic
740C2×C32#101011yescharacteristic
741C2×C32#101011yescharacteristic
742C2×Q8—91no—
743C2×Q8—271no—
744C22×C4—91no—
745C4⋊C4—91no—
746C4⋊C4—91no—
747C4⋊C4—91no—
748C4⋊C4—91no—
749C4⋊C4—91no—
750C4⋊C4—91no—
751C4⋊C4—91no—
752C4⋊C4—91no—
753C4⋊C4—91no—
754C4⋊C4—271no—
755C4⋊C4—271no—
756C4⋊C4—271no—
757C4⋊C4—271no—
758C4⋊C4—271no—
759C4⋊C4—271no—
760C4⋊C4—271no—
761C4⋊C4—271no—
762C4⋊C4—271no—
763C4⋊C4—271no—
764C4⋊C4—271no—
765C22⋊C4—91no—
766C22⋊C4—91no—
767C22⋊C4—91no—
768C22⋊C4—91no—
769C22⋊C4—91no—
770C22⋊C4#111311yescharacteristic
771C42—91no—
772C42—91no—
773C42—271no—
774C42—271no—
775C42—271no—
776C42—271no—
777C22×C3—22no—
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—21no—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—41no—
791C22×C3—41no—
792C22×C3—41no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—41no—
798C22×C3—42no—
799C22×C3—41no—
800C22×C3—81no—
801C22×C3—81no—
802C22×C3C22×D3211yescharacteristic
803C22×C3C22×D3211yescharacteristic
804C22×C3C22×D3211yescharacteristic
805C3×C4—21no—
806C3×C4—21no—
807C3×C4—21no—
808C3×C4—21no—
809C3×C4—21no—
810C3×C4—21no—
811C3×C4—41no—
812C3×C4—41no—
813C3×C4—41no—
814C3×C4—41no—
815C3×C4—41no—
816C3×C4—41no—
817C3×C4—81no—
818C3×C4—81no—
819C3×C4—92no—
820C3×C4—181no—
821C3×C4—181no—
822C3×C4—181no—
823C3×C4—181no—
824C3×C4—181no—
825C3×C4—181no—
826C3×C4—181no—
827C3×C4—181no—
828C3×C4—181no—
829C3×C4—181no—
830C3×C4—181no—
831Dic3—32no—
832Dic3—32no—
833Dic3—62no—
834Dic3—61no—
835Dic3—61no—
836Dic3—61no—
837Dic3—61no—
838Dic3—61no—
839Dic3—61no—
840Dic3—61no—
841Dic3—61no—
842Dic3—61no—
843Dic3—61no—
844Dic3—61no—
845Dic3—61no—
846Dic3—61no—
847Dic3—61no—
848Dic3—61no—
849Dic3—61no—
850Dic3—61no—
851Dic3—61no—
852Dic3—61no—
853Dic3—61no—
854Dic3—61no—
855Dic3—61no—
856Dic3—121no—
857Dic3—121no—
858Dic3—121no—
859Dic3—121no—
860Dic3—121no—
861Dic3—121no—
862Dic3—121no—
863Dic3—121no—
864Dic3—121no—
865Dic3—121no—
866Dic3—121no—
867C32—21no—
868C32—21no—
869C32—21no—
870C32—41no—
871C32#562511yescharacteristic, complemented
872C32#570111yescharacteristic, complemented
873C32#570111yescharacteristic, complemented
874C23C2×#111311yescharacteristic
875Q8—182no—
876Q8—542no—
877C2×C4—91no—
878C2×C4—91no—
879C2×C4—91no—
880C2×C4—91no—
881C2×C4—91no—
882C2×C4—91no—
883C2×C4—91no—
884C2×C4—91no—
885C2×C4—91no—
886C2×C4—91no—
887C2×C4—91no—
888C2×C4—91no—
889C2×C4—182no—
890C2×C4C2×#111311yescharacteristic
891C2×C4C2×#111311yescharacteristic
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—21no—
898C2×C3—21no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—42no—
902C2×C3—41no—
903C2×C3—41no—
904C2×C3—41no—
905C2×C3—41no—
906C2×C3—41no—
907C2×C3—41no—
908C2×C3—81no—
909C2×C3—81no—
910C2×C3—82no—
911C2×C3#6429711yescharacteristic
912C2×C3#6429711yescharacteristic
913C2×C3#6429811yescharacteristic
914C2×C3#6430911yescharacteristic
915C2×C3#6430911yescharacteristic
916C2×C3#6430911yescharacteristic
917C2×C3D3×#23711yescharacteristic
918C2×C3D3×#23711yescharacteristic
919C2×C3#6431211yescharacteristic
920C22—21no—
921C22—21no—
922C22—21no—
923C22C22×#111311yescharacteristic
924C4—21no—
925C4—21no—
926C4—92no—
927C4—181no—
928C4—181no—
929C4—181no—
930C4—181no—
931C4—181no—
932C4—181no—
933C4—181no—
934C4—181no—
935C4—181no—
936C4—181no—
937C4—181no—
938C3—21no—
939C3—21no—
940C3—21no—
941C3—41no—
942C3#1059402711yescharacteristic, complemented
943C3#1059402811yescharacteristic, complemented
944C3#1059403111yescharacteristic, complemented
945C2—41no—
946C2#1172461411yescharacteristic
947C2#1172462011yescharacteristic
948C2#1172462211yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radicalC23×C33C23
hypercenterC22⋊C4#1113
hypocenterC33#541
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #11723680C2semidirect
9. #11723679C2semidirect
10. #11723669C2semidirect
11. #11723669C2semidirect
12. #11723669C2semidirect
13. #11723668C2semidirect
14. #11723666C2semidirect
15. #11723665C2semidirect
633. C33#541semidirect
871. C32#5625semidirect
872. C32#5701semidirect
873. C32#5701semidirect
942. C3#10594027semidirect
943. C3#10594028semidirect
944. C3#10594031semidirect

Maximal subgroups

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

subgroupindex
C3×#640882
C3×#640872
#117237212
#117237162
#117237152
#117236802
#117236792
#117236692
#117236682
#117236662
#117236652
#105940313
#105940283
#105940273