Finite Group Databasebeta

← C107×#10972 #41036936

Subgroups — C107×#10972 #41036936

Order 27392.

1634 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#534×C107C211yesmaximal, characteristic
2C22×#99×C107C212yesmaximal, complemented
3C22×#99×C107C211yesmaximal, characteristic, complemented
4C107×#2308C211yesmaximal, characteristic, complemented
5C2×#342×C107C212yesmaximal, complemented
6C23×D4×C107C2211yescharacteristic
7C23×D4×C107C2211yescharacteristic
8#534×C107—24no—
9#534×C107—24no—
10C2×#123×C107—21no—
11C2×#123×C107C412yescomplemented
12C2×#121×C107—22no—
13C2×#120×C107—21no—
14C2×#120×C107C412yescomplemented
15C22×C22⋊C4×C107C2212yes—
16C22×C22⋊C4×C107C2212yes—
17C22×C22⋊C4×C107C2211yescharacteristic
18C2×#99×C107—22no—
19C2×#99×C107—24no—
20C2×#99×C107—24no—
21C2×#99×C107—24no—
22C2×#99×C107—24no—
23#386×C107—24no—
24#381×C107—21no—
25#379×C107—21no—
26#342×C107—24no—
27C25×C107C2×C411yescharacteristic
28C25×C107D411yescharacteristic
29C25×C107C2311yescharacteristic
30C22×D4×C107—22no—
31C22×D4×C107—22no—
32C22×D4×C107—22no—
33C22×D4×C107—22no—
34C22×D4×C107—21no—
35C22×D4×C107—21no—
36C22×D4×C107—22no—
37C22×D4×C107—22no—
38C22×D4×C107—22no—
39C22×D4×C107—22no—
40C22×D4×C107—22no—
41C22×D4×C107—22no—
42C22×D4×C107—22no—
43C22×D4×C107—22no—
44C22×D4×C107C2×C412yes—
45C22×D4×C107D412yes—
46C22×D4×C107D414yes—
47C23×C4×C107—21no—
48C23×C4×C107—22no—
49C23×C4×C107—22no—
50C23×C4×C107C2×C411yescharacteristic
51C23×C4×C107D411yescharacteristic
52#123×C107—28no—
53#123×C107—24no—
54#123×C107—24no—
55#121×C107—216no—
56#120×C107—28no—
57#120×C107—24no—
58#120×C107—24no—
59C2×C4⋊C4×C107—22no—
60C2×C22⋊C4×C107—22no—
61C2×C22⋊C4×C107—21no—
62C2×C22⋊C4×C107—22no—
63C2×C22⋊C4×C107—22no—
64C2×C22⋊C4×C107—22no—
65C2×C22⋊C4×C107—22no—
66C2×C22⋊C4×C107—22no—
67C2×C22⋊C4×C107—22no—
68C2×C22⋊C4×C107—22no—
69C2×C22⋊C4×C107—22no—
70C2×C22⋊C4×C107—22no—
71C2×C22⋊C4×C107—22no—
72C2×C22⋊C4×C107—22no—
73C2×C22⋊C4×C107—22no—
74C2×C22⋊C4×C107—24no—
75C2×C22⋊C4×C107C2×C412yes—
76C2×C22⋊C4×C107D414yes—
77C2×C22⋊C4×C107D414yescomplemented
78C2×C22⋊C4×C107D414yescomplemented
79#99×C107—216no—
80#99×C107—28no—
81#95×C107—24no—
82C24×C107—21no—
83C24×C107—21no—
84C24×C107—21no—
85C24×C107—22no—
86C24×C107—22no—
87C24×C107—22no—
88C24×C107—22no—
89C24×C107—21no—
90C24×C107—82no—
91C24×C107—82no—
92C24×C107—82no—
93C24×C107C22⋊C412yes—
94C24×C107C22⋊C412yescomplemented
95C24×C107C22×C411yescharacteristic
96C24×C107C2×D411yescharacteristic
97C24×C107C2×D411yescharacteristic
98C24×C107C2×D412yes—
99C24×C107C2×D412yes—
100C24×C107C2×D412yes—
101C24×C107C2×D412yes—
102C24×C107#4112yes—
103C24×C107#4112yes—
104C2×D4×C107—22no—
105C2×D4×C107—22no—
106C2×D4×C107—24no—
107C2×D4×C107—24no—
108C2×D4×C107—22no—
109C2×D4×C107—24no—
110C2×D4×C107—24no—
111C2×D4×C107—24no—
112C2×D4×C107—24no—
113C2×D4×C107—24no—
114C2×D4×C107—24no—
115C2×D4×C107—24no—
116C2×D4×C107—22no—
117C2×D4×C107—24no—
118C2×D4×C107—28no—
119C2×D4×C107—41no—
120C2×D4×C107—41no—
121C2×D4×C107—42no—
122C2×D4×C107—42no—
123C2×D4×C107—42no—
124C2×D4×C107—42no—
125C2×D4×C107—42no—
126C2×D4×C107—42no—
127C2×D4×C107—42no—
128C2×D4×C107—42no—
129C2×D4×C107—42no—
130C2×D4×C107—41no—
131C2×D4×C107—41no—
132C2×D4×C107—42no—
133C2×D4×C107—42no—
134C2×D4×C107—42no—
135C2×D4×C107—42no—
136C2×D4×C107—42no—
137C2×D4×C107—84no—
138C22×C4×C107—22no—
139C22×C4×C107—21no—
140C22×C4×C107—21no—
141C22×C4×C107—22no—
142C22×C4×C107—22no—
143C22×C4×C107—21no—
144C22×C4×C107—22no—
145C22×C4×C107—22no—
146C22×C4×C107—21no—
147C22×C4×C107—24no—
148C22×C4×C107—24no—
149C22×C4×C107—24no—
150C22×C4×C107—42no—
151C22×C4×C107—42no—
152C22×C4×C107—42no—
153C22×C4×C107—42no—
154C22×C4×C107—82no—
155C22×C4×C107—84no—
156C22×C4×C107—84no—
157C22×C4×C107C22⋊C412yes—
158C22×C4×C107C22⋊C412yescomplemented
159C4⋊C4×C107—28no—
160C22⋊C4×C107—28no—
161C22⋊C4×C107—28no—
162C22⋊C4×C107—22no—
163C22⋊C4×C107—24no—
164C22⋊C4×C107—24no—
165C22⋊C4×C107—24no—
166C22⋊C4×C107—24no—
167C22⋊C4×C107—24no—
168C22⋊C4×C107—42no—
169C22⋊C4×C107—42no—
170C22⋊C4×C107—42no—
171C22⋊C4×C107—42no—
172C22⋊C4×C107—84no—
173C22⋊C4×C107C22⋊C414yescomplemented
174C23×C107—22no—
175C23×C107—22no—
176C23×C107—22no—
177C23×C107—22no—
178C23×C107—24no—
179C23×C107—44no—
180C23×C107—42no—
181C23×C107—44no—
182C23×C107—42no—
183C23×C107—42no—
184C23×C107—44no—
185C23×C107—44no—
186C23×C107—44no—
187C23×C107—41no—
188C23×C107—41no—
189C23×C107—42no—
190C23×C107—42no—
191C23×C107—42no—
192C23×C107—82no—
193C23×C107—84no—
194C23×C107—82no—
195C23×C107—82no—
196C23×C107—82no—
197C23×C107—82no—
198C23×C107—82no—
199C23×C107—82no—
200C23×C107—84no—
201C23×C107—84no—
202C23×C107—84no—
203C23×C107C2×C22⋊C411yescharacteristic
204C23×C107C2×C22⋊C411yescharacteristic
205C23×C107C2×C22⋊C411yescharacteristic
206C23×C107C4×D412yes—
207C23×C107C4×D412yes—
208C23×C107#12011yescharacteristic
209C23×C107#12012yes—
210C23×C107#12012yes—
211C23×C107#12011yescharacteristic
212C23×C107#12012yes—
213C23×C107#12112yes—
214C23×C107#12112yes—
215C23×C107#12112yes—
216C23×C107#12112yes—
217C23×C107#12112yes—
218C23×C107#12112yes—
219C23×C107#12311yescharacteristic
220C23×C107#12311yescharacteristic
221C23×C107#12312yes—
222C23×C107#12412yes—
223C23×C107#12712yes—
224D4×C107—44no—
225D4×C107—44no—
226D4×C107—44no—
227D4×C107—44no—
228D4×C107—44no—
229D4×C107—44no—
230D4×C107—44no—
231D4×C107—44no—
232D4×C107—88no—
233C2×C4×C107—24no—
234C2×C4×C107—22no—
235C2×C4×C107—22no—
236C2×C4×C107—22no—
237C2×C4×C107—24no—
238C2×C4×C107—22no—
239C2×C4×C107—44no—
240C2×C4×C107—41no—
241C2×C4×C107—41no—
242C2×C4×C107—42no—
243C2×C4×C107—42no—
244C2×C4×C107—42no—
245C2×C4×C107—48no—
246C2×C4×C107—44no—
247C2×C4×C107—44no—
248C2×C4×C107—84no—
249C2×C4×C107—84no—
250C2×C4×C107—84no—
251C2×C4×C107—84no—
252C2×C4×C107—84no—
253C2×C4×C107—84no—
254C22×C107—22no—
255C22×C107—22no—
256C22×C107—24no—
257C22×C107—24no—
258C22×C107—22no—
259C22×C107—42no—
260C22×C107—42no—
261C22×C107—42no—
262C22×C107—42no—
263C22×C107—42no—
264C22×C107—41no—
265C22×C107—41no—
266C22×C107—42no—
267C22×C107—42no—
268C22×C107—42no—
269C22×C107—42no—
270C22×C107—41no—
271C22×C107—42no—
272C22×C107—41no—
273C22×C107—42no—
274C22×C107—42no—
275C22×C107—44no—
276C22×C107—44no—
277C22×C107—44no—
278C22×C107—42no—
279C22×C107—42no—
280C22×C107—82no—
281C22×C107—84no—
282C22×C107—84no—
283C22×C107—82no—
284C22×C107—84no—
285C22×C107—84no—
286C22×C107—82no—
287C22×C107#37911yescharacteristic
288C22×C107#38611yescharacteristic
289C22×C107#38612yes—
290C22×C107#38611yescharacteristic
291C22×C107#39012yes—
292C22×C107#39212yes—
293C22×C107#39212yes—
294C22×C107#39412yes—
295C22×C107#39412yes—
296C4×C107—44no—
297C4×C107—42no—
298C4×C107—42no—
299C4×C107—84no—
300C4×C107—84no—
301#10972C10711yesmaximal, characteristic, direct product factor, Sylow
302C2×C107—21no—
303C2×C107—22no—
304C2×C107—22no—
305C2×C107—21no—
306C2×C107—22no—
307C2×C107—22no—
308C2×C107—22no—
309C2×C107—22no—
310C2×C107—82no—
311C2×C107—82no—
312C2×C107#143811yescharacteristic
313C2×C107#191312yes—
314C2×#534C2×C10711yescharacteristic
315C22×#99C2×C10712yescomplemented
316C22×#99C2×C10711yescharacteristic, complemented
317#2308C2×C10711yescharacteristic, complemented
318C2×#342C2×C10712yescomplemented
319C107#1097211yescharacteristic, direct product factor, Sylow
320C23×D4C22×C10711yescharacteristic
321C23×D4C22×C10711yescharacteristic
322#534—24no—
323#534—24no—
324C2×#123—21no—
325C2×#123C4×C10712yescomplemented
326C2×#121—22no—
327C2×#120—21no—
328C2×#120C4×C10712yescomplemented
329C22×C22⋊C4C22×C10712yes—
330C22×C22⋊C4C22×C10712yes—
331C22×C22⋊C4C22×C10711yescharacteristic
332C2×#99—22no—
333C2×#99—24no—
334C2×#99—24no—
335C2×#99—24no—
336C2×#99—24no—
337#386—24no—
338#381—21no—
339#379—21no—
340#342—24no—
341C25C2×C4×C10711yescharacteristic
342C25D4×C10711yescharacteristic
343C25C23×C10711yescharacteristic
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4C2×C4×C10712yes—
359C22×D4D4×C10712yes—
360C22×D4D4×C10714yes—
361C23×C4—21no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4C2×C4×C10711yescharacteristic
365C23×C4D4×C10711yescharacteristic
366#123—28no—
367#123—24no—
368#123—24no—
369#121—216no—
370#120—28no—
371#120—24no—
372#120—24no—
373C2×C4⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4C2×C4×C10712yes—
390C2×C22⋊C4D4×C10714yes—
391C2×C22⋊C4D4×C10714yescomplemented
392C2×C22⋊C4D4×C10714yescomplemented
393#99—216no—
394#99—28no—
395#95—24no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—21no—
404C24—82no—
405C24—82no—
406C24—82no—
407C24C22⋊C4×C10712yes—
408C24C22⋊C4×C10712yescomplemented
409C24C22×C4×C10711yescharacteristic
410C24C2×D4×C10711yescharacteristic
411C24C2×D4×C10711yescharacteristic
412C24C2×D4×C10712yes—
413C24C2×D4×C10712yes—
414C24C2×D4×C10712yes—
415C24C2×D4×C10712yes—
416C24#41×C10712yes—
417C24#41×C10712yes—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—22no—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—24no—
428C2×D4—24no—
429C2×D4—24no—
430C2×D4—22no—
431C2×D4—24no—
432C2×D4—28no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4—42no—
440C2×D4—42no—
441C2×D4—42no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—42no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—84no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—82no—
469C22×C4—84no—
470C22×C4—84no—
471C22×C4C22⋊C4×C10712yes—
472C22×C4C22⋊C4×C10712yescomplemented
473C4⋊C4—28no—
474C22⋊C4—28no—
475C22⋊C4—28no—
476C22⋊C4—22no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—84no—
487C22⋊C4C22⋊C4×C10714yescomplemented
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—44no—
494C23—42no—
495C23—44no—
496C23—42no—
497C23—42no—
498C23—44no—
499C23—44no—
500C23—44no—
501C23—41no—
502C23—41no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—82no—
507C23—84no—
508C23—82no—
509C23—82no—
510C23—82no—
511C23—82no—
512C23—82no—
513C23—82no—
514C23—84no—
515C23—84no—
516C23—84no—
517C23C2×C22⋊C4×C10711yescharacteristic
518C23C2×C22⋊C4×C10711yescharacteristic
519C23C2×C22⋊C4×C10711yescharacteristic
520C23C4×D4×C10712yes—
521C23C4×D4×C10712yes—
522C23#120×C10711yescharacteristic
523C23#120×C10712yes—
524C23#120×C10712yes—
525C23#120×C10711yescharacteristic
526C23#120×C10712yes—
527C23#121×C10712yes—
528C23#121×C10712yes—
529C23#121×C10712yes—
530C23#121×C10712yes—
531C23#121×C10712yes—
532C23#121×C10712yes—
533C23#123×C10711yescharacteristic
534C23#123×C10711yescharacteristic
535C23#123×C10712yes—
536C23#124×C10712yes—
537C23#127×C10712yes—
538D4—44no—
539D4—44no—
540D4—44no—
541D4—44no—
542D4—44no—
543D4—44no—
544D4—44no—
545D4—44no—
546D4—88no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—44no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—48no—
560C2×C4—44no—
561C2×C4—44no—
562C2×C4—84no—
563C2×C4—84no—
564C2×C4—84no—
565C2×C4—84no—
566C2×C4—84no—
567C2×C4—84no—
568C22—22no—
569C22—22no—
570C22—24no—
571C22—24no—
572C22—22no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—41no—
579C22—41no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—41no—
585C22—42no—
586C22—41no—
587C22—42no—
588C22—42no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—42no—
593C22—42no—
594C22—82no—
595C22—84no—
596C22—84no—
597C22—82no—
598C22—84no—
599C22—84no—
600C22—82no—
601C22#379×C10711yescharacteristic
602C22#386×C10711yescharacteristic
603C22#386×C10712yes—
604C22#386×C10711yescharacteristic
605C22#390×C10712yes—
606C22#392×C10712yes—
607C22#392×C10712yes—
608C22#394×C10712yes—
609C22#394×C10712yes—
610C4—44no—
611C4—42no—
612C4—42no—
613C4—84no—
614C4—84no—
615C2—21no—
616C2—22no—
617C2—22no—
618C2—21no—
619C2—22no—
620C2—22no—
621C2—22no—
622C2—22no—
623C2—82no—
624C2—82no—
625C2C107×#143811yescharacteristic
626C2C107×#191312yes—
subgroupG/H
center, socleC22×C107#386
commutatorC24C22×C4×C107
Frattini, cosocleC25C23×C107
prime radicalC2×#534×C107C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C25×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#99×C107C2semidirect
3. C22×#99×C107C2semidirect
4. C107×#2308C2semidirect
5. C2×#342×C107C2semidirect
11. C2×#123×C107C4semidirect
14. C2×#120×C107C4semidirect
77. C2×C22⋊C4×C107D4semidirect
78. C2×C22⋊C4×C107D4semidirect
94. C24×C107C22⋊C4semidirect
158. C22×C4×C107C22⋊C4semidirect
173. C22⋊C4×C107C22⋊C4semidirect
301. #10972C107direct (N × H)
315. C22×#99C2×C107semidirect
316. C22×#99C2×C107semidirect
317. #2308C2×C107semidirect
318. C2×#342C2×C107semidirect
319. C107#10972direct (N × H)
325. C2×#123C4×C107semidirect
328. C2×#120C4×C107semidirect
391. C2×C22⋊C4D4×C107semidirect
392. C2×C22⋊C4D4×C107semidirect
408. C24C22⋊C4×C107semidirect
472. C22×C4C22⋊C4×C107semidirect
487. C22⋊C4C22⋊C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#534×C1072
C22×#99×C1072
C107×#23082
C2×#342×C1072
#10972107