Finite Group Databasebeta

← C107×#33552 #41059516

Subgroups — C107×#33552 #41059516

Order 27392.

1156 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#3533C211yesmaximal, characteristic, complemented
2C107×#3026C211yesmaximal, characteristic, complemented
3C2×#458×C107C211yesmaximal, characteristic, complemented
4C107×#3019C211yesmaximal, characteristic, complemented
5C107×#2201C212yesmaximal, complemented
6C107×#2200C212yesmaximal, complemented
7C107×#2198C212yesmaximal, complemented
8C107×#2197C212yesmaximal, complemented
9C107×#2127C211yesmaximal, characteristic, complemented
10C107×#2121C211yesmaximal, characteristic, complemented
11C2×#352×C107C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C107C2211yescharacteristic
13#575×C107—21no—
14#563×C107C2211yescharacteristic, complemented
15#562×C107—21no—
16#560×C107C2211yescharacteristic, complemented
17#559×C107C2211yescharacteristic, complemented
18#553×C107—21no—
19#552×C107—21no—
20#551×C107—21no—
21#551×C107C2211yescharacteristic, complemented
22#547×C107—21no—
23#546×C107—21no—
24#542×C107—21no—
25#540×C107—21no—
26#539×C107—21no—
27#538×C107—21no—
28#538×C107—21no—
29#535×C107C2211yescharacteristic
30#534×C107—21no—
31#534×C107C2211yescharacteristic
32#525×C107—21no—
33C2×#123×C107—21no—
34C2×#123×C107C2211yescharacteristic
35#458×C107—21no—
36#458×C107—21no—
37#458×C107—21no—
38#458×C107C2212yes—
39#458×C107C2212yes—
40#458×C107C2212yes—
41B(4,𝔽2)×C107—21no—
42B(4,𝔽2)×C107C2212yes—
43#455×C107—21no—
44#455×C107C2212yes—
45#453×C107—21no—
46#453×C107C2212yes—
47#421×C107—21no—
48C2×#100×C107C2211yescharacteristic
49C2×#99×C107—21no—
50C2×#99×C107—21no—
51C2×#99×C107C2211yescharacteristic
52C2×#99×C107C2211yescharacteristic
53#354×C107C2212yescomplemented
54#353×C107C2212yescomplemented
55#352×C107C2212yescomplemented
56#352×C107C2212yescomplemented
57#352×C107C2212yescomplemented
58AΣL(1,𝔽16)×C107C2212yescomplemented
59H(5,𝔽2)×C107—21no—
60H(5,𝔽2)×C107—21no—
61H(5,𝔽2)×C107—21no—
62H(5,𝔽2)×C107—42no—
63H(5,𝔽2)×C107C2312yes—
64C2×#41×C107—21no—
65C2×#41×C107—21no—
66C2×#41×C107—41no—
67C2×#41×C107D411yescharacteristic, complemented
68C22×D4×C107—21no—
69C22×D4×C107—21no—
70C22×D4×C107—41no—
71C22×D4×C107D411yescharacteristic
72C22×D4×C107C2311yescharacteristic
73C23×C4×C107D411yescharacteristic, complemented
74#137×C107—22no—
75#137×C107—41no—
76AGL(1,ℤ/8)×C107—22no—
77AGL(1,ℤ/8)×C107—41no—
78#135×C107—42no—
79C2×M16×C107—21no—
80C4⋊Q8×C107—21no—
81#127×C107D411yescharacteristic, complemented
82#127×C107C2311yescharacteristic
83#126×C107—21no—
84#126×C107—21no—
85#126×C107—21no—
86#126×C107—21no—
87#126×C107—21no—
88#126×C107—21no—
89#125×C107—21no—
90#125×C107—21no—
91#125×C107—21no—
92#124×C107—21no—
93#124×C107—21no—
94#124×C107—21no—
95#124×C107—21no—
96#124×C107D411yescharacteristic, complemented
97#124×C107C2311yescharacteristic
98#123×C107—21no—
99#123×C107—21no—
100#123×C107—21no—
101#123×C107—21no—
102#123×C107—21no—
103#123×C107—21no—
104#123×C107—21no—
105#123×C107—21no—
106#123×C107—21no—
107#123×C107—21no—
108#123×C107—21no—
109#123×C107—21no—
110#123×C107—22no—
111#123×C107—22no—
112#123×C107—22no—
113#123×C107—41no—
114#123×C107—42no—
115#123×C107D411yescharacteristic
116#123×C107D411yescharacteristic, complemented
117#123×C107D411yescharacteristic, complemented
118#123×C107C2311yescharacteristic
119#123×C107C2311yescharacteristic
120#123×C107C2311yescharacteristic
121C22⋊Q8×C107—21no—
122C22⋊Q8×C107—21no—
123C22⋊Q8×C107—21no—
124C22⋊Q8×C107—21no—
125C22⋊Q8×C107—21no—
126C22⋊Q8×C107—21no—
127C22⋊Q8×C107—21no—
128C22⋊Q8×C107—21no—
129#121×C107—21no—
130#121×C107—21no—
131#121×C107—21no—
132#121×C107—21no—
133#121×C107—21no—
134#121×C107—21no—
135#121×C107—21no—
136#121×C107—21no—
137#121×C107—21no—
138#121×C107—21no—
139#121×C107—21no—
140#121×C107—21no—
141#121×C107—42no—
142#120×C107—21no—
143#120×C107—21no—
144#120×C107—21no—
145#120×C107—21no—
146#120×C107—22no—
147#120×C107—41no—
148#120×C107D411yescharacteristic
149#120×C107C2311yescharacteristic
150C4×Q8×C107—21no—
151C4×D4×C107—21no—
152C4×D4×C107—21no—
153C4×D4×C107—21no—
154C4×D4×C107—21no—
155C4×D4×C107—21no—
156C4×D4×C107—21no—
157C4×D4×C107—21no—
158C4×D4×C107—21no—
159C4×D4×C107—21no—
160#117×C107—21no—
161#117×C107—21no—
162#117×C107—21no—
163#117×C107D411yescharacteristic, complemented
164C2×C4⋊C4×C107—21no—
165C2×C4⋊C4×C107—21no—
166C2×C4⋊C4×C107—41no—
167C2×C22⋊C4×C107—21no—
168C2×C22⋊C4×C107—21no—
169C2×C22⋊C4×C107—21no—
170C2×C22⋊C4×C107—21no—
171C2×C22⋊C4×C107—41no—
172C2×C22⋊C4×C107D411yescharacteristic
173C2×C22⋊C4×C107D411yescharacteristic, complemented
174#104×C107—22no—
175#104×C107—22no—
176#100×C107—21no—
177#100×C107C2312yes—
178#99×C107—21no—
179#99×C107—21no—
180#99×C107—22no—
181#99×C107—22no—
182#99×C107—22no—
183#99×C107—22no—
184#99×C107C2312yes—
185#99×C107C2312yes—
186C24×C107—21no—
187C24×C107—21no—
188C24×C107C2×D411yescharacteristic
189C24×C107C2×D411yescharacteristic
190C24×C107C2×D411yescharacteristic
191#41×C107—22no—
192#41×C107—22no—
193#41×C107—42no—
194#41×C107—41no—
195#41×C107—42no—
196#41×C107—42no—
197#41×C107—41no—
198#41×C107—41no—
199#41×C107—42no—
200#41×C107—41no—
201#41×C107—81no—
202#41×C107—81no—
203C2×Q8×C107—21no—
204C2×Q8×C107—21no—
205C2×Q8×C107—21no—
206C2×Q8×C107C2×D411yescharacteristic
207C2×D4×C107—21no—
208C2×D4×C107—22no—
209C2×D4×C107—22no—
210C2×D4×C107—21no—
211C2×D4×C107—21no—
212C2×D4×C107—22no—
213C2×D4×C107—22no—
214C2×D4×C107—21no—
215C2×D4×C107—21no—
216C2×D4×C107—21no—
217C2×D4×C107—21no—
218C2×D4×C107—21no—
219C2×D4×C107—21no—
220C2×D4×C107—21no—
221C2×D4×C107—21no—
222C2×D4×C107—21no—
223C2×D4×C107—41no—
224C2×D4×C107—41no—
225C2×D4×C107—42no—
226C2×D4×C107—42no—
227C2×D4×C107—41no—
228C2×D4×C107—41no—
229C2×D4×C107—41no—
230C2×D4×C107—41no—
231C2×D4×C107—42no—
232C2×D4×C107—42no—
233C2×D4×C107—41no—
234C2×D4×C107—41no—
235C2×D4×C107—41no—
236C2×D4×C107—41no—
237C2×D4×C107—41no—
238C2×D4×C107—42no—
239C2×D4×C107C2×D411yescharacteristic
240C2×D4×C107C2×D411yescharacteristic
241C2×D4×C107C2×D411yescharacteristic
242C2×D4×C107C2×D411yescharacteristic
243C2×D4×C107C2411yescharacteristic
244C22×C4×C107—21no—
245C22×C4×C107—21no—
246C22×C4×C107—21no—
247C22×C4×C107—21no—
248C22×C4×C107—21no—
249C22×C4×C107—21no—
250C22×C4×C107—21no—
251C22×C4×C107—21no—
252C22×C4×C107—21no—
253C22×C4×C107—21no—
254C22×C4×C107—21no—
255C22×C4×C107—41no—
256C22×C4×C107—41no—
257C22×C4×C107—41no—
258C22×C4×C107—41no—
259C22×C4×C107—41no—
260C22×C4×C107C2×D411yescharacteristic
261C22×C4×C107C2×D411yescharacteristic
262C22×C4×C107C2×D411yescharacteristic
263C22×C4×C107C2×D411yescharacteristic
264Q16×C107—42no—
265SD16×C107—42no—
266SD16×C107—42no—
267D8×C107—42no—
268M16×C107—22no—
269M16×C107—41no—
270C2×C8×C107—41no—
271C4⋊C4×C107—21no—
272C4⋊C4×C107—21no—
273C4⋊C4×C107—21no—
274C4⋊C4×C107—21no—
275C4⋊C4×C107—21no—
276C4⋊C4×C107—21no—
277C4⋊C4×C107—21no—
278C4⋊C4×C107—21no—
279C4⋊C4×C107—21no—
280C4⋊C4×C107—21no—
281C4⋊C4×C107—21no—
282C4⋊C4×C107—21no—
283C4⋊C4×C107—21no—
284C4⋊C4×C107—21no—
285C4⋊C4×C107—21no—
286C4⋊C4×C107—21no—
287C4⋊C4×C107—21no—
288C4⋊C4×C107—21no—
289C4⋊C4×C107—21no—
290C4⋊C4×C107—42no—
291C4⋊C4×C107—42no—
292C4⋊C4×C107—42no—
293C22⋊C4×C107—21no—
294C22⋊C4×C107—21no—
295C22⋊C4×C107—21no—
296C22⋊C4×C107—21no—
297C22⋊C4×C107—21no—
298C22⋊C4×C107—21no—
299C22⋊C4×C107—21no—
300C22⋊C4×C107—21no—
301C22⋊C4×C107—21no—
302C22⋊C4×C107—21no—
303C22⋊C4×C107—21no—
304C22⋊C4×C107—21no—
305C22⋊C4×C107—21no—
306C22⋊C4×C107—21no—
307C22⋊C4×C107—21no—
308C22⋊C4×C107—21no—
309C22⋊C4×C107—21no—
310C22⋊C4×C107—21no—
311C22⋊C4×C107—21no—
312C22⋊C4×C107—21no—
313C22⋊C4×C107—21no—
314C22⋊C4×C107—21no—
315C22⋊C4×C107—21no—
316C22⋊C4×C107—22no—
317C22⋊C4×C107—22no—
318C22⋊C4×C107—42no—
319C22⋊C4×C107—41no—
320C22⋊C4×C107—41no—
321C22⋊C4×C107—42no—
322C22⋊C4×C107—42no—
323C22⋊C4×C107—42no—
324C22⋊C4×C107C2×D411yescharacteristic
325C22⋊C4×C107C2×D411yescharacteristic
326C22⋊C4×C107C2×D411yescharacteristic
327C22⋊C4×C107C2×D411yescharacteristic
328C42×C107—21no—
329C42×C107—21no—
330C42×C107—21no—
331C42×C107—21no—
332C42×C107C2×D411yescharacteristic
333C42×C107C2×D411yescharacteristic
334C23×C107—21no—
335C23×C107—21no—
336C23×C107—21no—
337C23×C107—21no—
338C23×C107—22no—
339C23×C107—22no—
340C23×C107—21no—
341C23×C107—21no—
342C23×C107—41no—
343C23×C107—41no—
344C23×C107—41no—
345C23×C107—41no—
346C23×C107—81no—
347C23×C107—81no—
348C23×C107—81no—
349C23×C107—82no—
350C23×C107—161no—
351C23×C107#12011yescharacteristic
352C23×C107#12011yescharacteristic
353C23×C107#12011yescharacteristic
354C23×C107C22×D411yescharacteristic
355C23×C107C22×D411yescharacteristic
356Q8×C107—22no—
357Q8×C107—41no—
358Q8×C107—41no—
359Q8×C107—81no—
360Q8×C107—81no—
361D4×C107—22no—
362D4×C107—41no—
363D4×C107—41no—
364D4×C107—41no—
365D4×C107—41no—
366D4×C107—41no—
367D4×C107—41no—
368D4×C107—42no—
369D4×C107—42no—
370D4×C107—42no—
371D4×C107—42no—
372D4×C107—42no—
373D4×C107—42no—
374D4×C107—41no—
375D4×C107—41no—
376D4×C107—41no—
377D4×C107—41no—
378D4×C107—81no—
379D4×C107—81no—
380D4×C107—81no—
381D4×C107—81no—
382D4×C107—81no—
383D4×C107—81no—
384D4×C107—81no—
385D4×C107—81no—
386D4×C107—81no—
387D4×C107—162no—
388C2×C4×C107—21no—
389C2×C4×C107—21no—
390C2×C4×C107—22no—
391C2×C4×C107—22no—
392C2×C4×C107—21no—
393C2×C4×C107—21no—
394C2×C4×C107—21no—
395C2×C4×C107—21no—
396C2×C4×C107—21no—
397C2×C4×C107—21no—
398C2×C4×C107—21no—
399C2×C4×C107—21no—
400C2×C4×C107—21no—
401C2×C4×C107—21no—
402C2×C4×C107—42no—
403C2×C4×C107—42no—
404C2×C4×C107—41no—
405C2×C4×C107—41no—
406C2×C4×C107—41no—
407C2×C4×C107—41no—
408C2×C4×C107—41no—
409C2×C4×C107—41no—
410C2×C4×C107—41no—
411C2×C4×C107—41no—
412C2×C4×C107—42no—
413C2×C4×C107—42no—
414C2×C4×C107—81no—
415C2×C4×C107—81no—
416C2×C4×C107—81no—
417C2×C4×C107—81no—
418C2×C4×C107—81no—
419C2×C4×C107—81no—
420C2×C4×C107—81no—
421C2×C4×C107—81no—
422C2×C4×C107—82no—
423C2×C4×C107—161no—
424C2×C4×C107#12011yescharacteristic
425C2×C4×C107C22×D411yescharacteristic
426C8×C107—42no—
427C22×C107—21no—
428C22×C107—21no—
429C22×C107—21no—
430C22×C107—21no—
431C22×C107—41no—
432C22×C107—41no—
433C22×C107—41no—
434C22×C107—41no—
435C22×C107—41no—
436C22×C107—42no—
437C22×C107—41no—
438C22×C107—41no—
439C22×C107—41no—
440C22×C107—41no—
441C22×C107—42no—
442C22×C107—41no—
443C22×C107—41no—
444C22×C107—81no—
445C22×C107—81no—
446C22×C107—81no—
447C22×C107—82no—
448C22×C107—82no—
449C22×C107—82no—
450C22×C107—82no—
451C22×C107—161no—
452C22×C107—161no—
453C22×C107B(4,𝔽2)11yescharacteristic
454C22×C107B(4,𝔽2)11yescharacteristic
455C22×C107C2×#12011yescharacteristic
456C4×C107—21no—
457C4×C107—21no—
458C4×C107—41no—
459C4×C107—41no—
460C4×C107—41no—
461C4×C107—41no—
462C4×C107—41no—
463C4×C107—41no—
464C4×C107—42no—
465C4×C107—41no—
466C4×C107—41no—
467C4×C107—41no—
468C4×C107—41no—
469C4×C107—82no—
470C4×C107—82no—
471#33552C10711yesmaximal, characteristic, direct product factor, Sylow
472C2×C107—21no—
473C2×C107—21no—
474C2×C107—21no—
475C2×C107—41no—
476C2×C107—41no—
477C2×C107—41no—
478C2×C107—41no—
479C2×C107—81no—
480C2×C107—81no—
481C2×C107—82no—
482C2×C107C2×B(4,𝔽2)11yescharacteristic
483#3533C2×C10711yescharacteristic, complemented
484#3026C2×C10711yescharacteristic, complemented
485C2×#458C2×C10711yescharacteristic, complemented
486#3019C2×C10711yescharacteristic, complemented
487#2201C2×C10712yescomplemented
488#2200C2×C10712yescomplemented
489#2198C2×C10712yescomplemented
490#2197C2×C10712yescomplemented
491#2127C2×C10711yescharacteristic, complemented
492#2121C2×C10711yescharacteristic, complemented
493C2×#352C2×C10711yescharacteristic, complemented
494C107#3355211yescharacteristic, direct product factor, Sylow
495C2×H(5,𝔽2)C22×C10711yescharacteristic
496#575—21no—
497#563C22×C10711yescharacteristic, complemented
498#562—21no—
499#560C22×C10711yescharacteristic, complemented
500#559C22×C10711yescharacteristic, complemented
501#553—21no—
502#552—21no—
503#551—21no—
504#551C22×C10711yescharacteristic, complemented
505#547—21no—
506#546—21no—
507#542—21no—
508#540—21no—
509#539—21no—
510#538—21no—
511#538—21no—
512#535C22×C10711yescharacteristic
513#534—21no—
514#534C22×C10711yescharacteristic
515#525—21no—
516C2×#123—21no—
517C2×#123C22×C10711yescharacteristic
518#458—21no—
519#458—21no—
520#458—21no—
521#458C22×C10712yes—
522#458C22×C10712yes—
523#458C22×C10712yes—
524B(4,𝔽2)—21no—
525B(4,𝔽2)C22×C10712yes—
526#455—21no—
527#455C22×C10712yes—
528#453—21no—
529#453C22×C10712yes—
530#421—21no—
531C2×#100C22×C10711yescharacteristic
532C2×#99—21no—
533C2×#99—21no—
534C2×#99C22×C10711yescharacteristic
535C2×#99C22×C10711yescharacteristic
536#354C22×C10712yescomplemented
537#353C22×C10712yescomplemented
538#352C22×C10712yescomplemented
539#352C22×C10712yescomplemented
540#352C22×C10712yescomplemented
541AΣL(1,𝔽16)C22×C10712yescomplemented
542H(5,𝔽2)—21no—
543H(5,𝔽2)—21no—
544H(5,𝔽2)—21no—
545H(5,𝔽2)—42no—
546H(5,𝔽2)C23×C10712yes—
547C2×#41—21no—
548C2×#41—21no—
549C2×#41—41no—
550C2×#41D4×C10711yescharacteristic, complemented
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—41no—
554C22×D4D4×C10711yescharacteristic
555C22×D4C23×C10711yescharacteristic
556C23×C4D4×C10711yescharacteristic, complemented
557#137—22no—
558#137—41no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—41no—
561#135—42no—
562C2×M16—21no—
563C4⋊Q8—21no—
564#127D4×C10711yescharacteristic, complemented
565#127C23×C10711yescharacteristic
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#124—21no—
576#124—21no—
577#124—21no—
578#124—21no—
579#124D4×C10711yescharacteristic, complemented
580#124C23×C10711yescharacteristic
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—22no—
594#123—22no—
595#123—22no—
596#123—41no—
597#123—42no—
598#123D4×C10711yescharacteristic
599#123D4×C10711yescharacteristic, complemented
600#123D4×C10711yescharacteristic, complemented
601#123C23×C10711yescharacteristic
602#123C23×C10711yescharacteristic
603#123C23×C10711yescharacteristic
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—42no—
625#120—21no—
626#120—21no—
627#120—21no—
628#120—21no—
629#120—22no—
630#120—41no—
631#120D4×C10711yescharacteristic
632#120C23×C10711yescharacteristic
633C4×Q8—21no—
634C4×D4—21no—
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643#117—21no—
644#117—21no—
645#117—21no—
646#117D4×C10711yescharacteristic, complemented
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—41no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—41no—
655C2×C22⋊C4D4×C10711yescharacteristic
656C2×C22⋊C4D4×C10711yescharacteristic, complemented
657#104—22no—
658#104—22no—
659#100—21no—
660#100C23×C10712yes—
661#99—21no—
662#99—21no—
663#99—22no—
664#99—22no—
665#99—22no—
666#99—22no—
667#99C23×C10712yes—
668#99C23×C10712yes—
669C24—21no—
670C24—21no—
671C24C2×D4×C10711yescharacteristic
672C24C2×D4×C10711yescharacteristic
673C24C2×D4×C10711yescharacteristic
674#41—22no—
675#41—22no—
676#41—42no—
677#41—41no—
678#41—42no—
679#41—42no—
680#41—41no—
681#41—41no—
682#41—42no—
683#41—41no—
684#41—81no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8C2×D4×C10711yescharacteristic
690C2×D4—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—22no—
696C2×D4—22no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—41no—
707C2×D4—41no—
708C2×D4—42no—
709C2×D4—42no—
710C2×D4—41no—
711C2×D4—41no—
712C2×D4—41no—
713C2×D4—41no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—42no—
722C2×D4C2×D4×C10711yescharacteristic
723C2×D4C2×D4×C10711yescharacteristic
724C2×D4C2×D4×C10711yescharacteristic
725C2×D4C2×D4×C10711yescharacteristic
726C2×D4C24×C10711yescharacteristic
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4C2×D4×C10711yescharacteristic
744C22×C4C2×D4×C10711yescharacteristic
745C22×C4C2×D4×C10711yescharacteristic
746C22×C4C2×D4×C10711yescharacteristic
747Q16—42no—
748SD16—42no—
749SD16—42no—
750D8—42no—
751M16—22no—
752M16—41no—
753C2×C8—41no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—42no—
774C4⋊C4—42no—
775C4⋊C4—42no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—22no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—42no—
805C22⋊C4—42no—
806C22⋊C4—42no—
807C22⋊C4C2×D4×C10711yescharacteristic
808C22⋊C4C2×D4×C10711yescharacteristic
809C22⋊C4C2×D4×C10711yescharacteristic
810C22⋊C4C2×D4×C10711yescharacteristic
811C42—21no—
812C42—21no—
813C42—21no—
814C42—21no—
815C42C2×D4×C10711yescharacteristic
816C42C2×D4×C10711yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—22no—
822C23—22no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—81no—
830C23—81no—
831C23—81no—
832C23—82no—
833C23—161no—
834C23#120×C10711yescharacteristic
835C23#120×C10711yescharacteristic
836C23#120×C10711yescharacteristic
837C23C22×D4×C10711yescharacteristic
838C23C22×D4×C10711yescharacteristic
839Q8—22no—
840Q8—41no—
841Q8—41no—
842Q8—81no—
843Q8—81no—
844D4—22no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—42no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—41no—
860D4—42no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868D4—81no—
869D4—81no—
870D4—162no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4—82no—
906C2×C4—161no—
907C2×C4#120×C10711yescharacteristic
908C2×C4C22×D4×C10711yescharacteristic
909C8—42no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—41no—
926C22—41no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—161no—
935C22—161no—
936C22B(4,𝔽2)×C10711yescharacteristic
937C22B(4,𝔽2)×C10711yescharacteristic
938C22C2×#120×C10711yescharacteristic
939C4—21no—
940C4—21no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—42no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—82no—
953C4—82no—
954C2—21no—
955C2—21no—
956C2—21no—
957C2—41no—
958C2—41no—
959C2—41no—
960C2—41no—
961C2—81no—
962C2—81no—
963C2—82no—
964C2C2×B(4,𝔽2)×C10711yescharacteristic
subgroupG/H
center, socleC2×C107C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C107
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C107 ◁ C23×C107 ◁ C22×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C107×#3533C2semidirect
2. C107×#3026C2semidirect
3. C2×#458×C107C2semidirect
4. C107×#3019C2semidirect
5. C107×#2201C2semidirect
6. C107×#2200C2semidirect
7. C107×#2198C2semidirect
8. C107×#2197C2semidirect
9. C107×#2127C2semidirect
10. C107×#2121C2semidirect
11. C2×#352×C107C2semidirect
14. #563×C107C22semidirect
16. #560×C107C22semidirect
17. #559×C107C22semidirect
21. #551×C107C22semidirect
53. #354×C107C22semidirect
54. #353×C107C22semidirect
55. #352×C107C22semidirect
56. #352×C107C22semidirect
57. #352×C107C22semidirect
58. AΣL(1,𝔽16)×C107C22semidirect
67. C2×#41×C107D4semidirect
73. C23×C4×C107D4semidirect
81. #127×C107D4semidirect
96. #124×C107D4semidirect
116. #123×C107D4semidirect
117. #123×C107D4semidirect
163. #117×C107D4semidirect
173. C2×C22⋊C4×C107D4semidirect
471. #33552C107direct (N × H)
483. #3533C2×C107semidirect
484. #3026C2×C107semidirect
485. C2×#458C2×C107semidirect
486. #3019C2×C107semidirect
487. #2201C2×C107semidirect
488. #2200C2×C107semidirect
489. #2198C2×C107semidirect
490. #2197C2×C107semidirect
491. #2127C2×C107semidirect
492. #2121C2×C107semidirect
493. C2×#352C2×C107semidirect
494. C107#33552direct (N × H)
497. #563C22×C107semidirect
499. #560C22×C107semidirect
500. #559C22×C107semidirect
504. #551C22×C107semidirect
536. #354C22×C107semidirect
537. #353C22×C107semidirect
538. #352C22×C107semidirect
539. #352C22×C107semidirect
540. #352C22×C107semidirect
541. AΣL(1,𝔽16)C22×C107semidirect
550. C2×#41D4×C107semidirect
556. C23×C4D4×C107semidirect
564. #127D4×C107semidirect
579. #124D4×C107semidirect
599. #123D4×C107semidirect
600. #123D4×C107semidirect
646. #117D4×C107semidirect
656. C2×C22⋊C4D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#35332
C107×#30262
C2×#458×C1072
C107×#30192
C107×#22012
C107×#22002
C107×#21982
C107×#21972
C107×#21272
C107×#21212
C2×#352×C1072
#33552107