Finite Group Databasebeta

← C109×#11157 #42129151

Subgroups — C109×#11157 #42129151

Order 27904.

922 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#418×C109C211yesmaximal, characteristic
2C2×#418×C109C211yesmaximal, characteristic
3C22×#100×C109C211yesmaximal, characteristic
4C2×#344×C109C211yesmaximal, characteristic, complemented
5C2×#344×C109C211yesmaximal, characteristic, complemented
6C109×#1738C211yesmaximal, characteristic, complemented
7C2×H(3,ℤ/4)×C109C211yesmaximal, characteristic, complemented
8C23×D4×C109C2211yescharacteristic
9C22×M16×C109C2211yescharacteristic
10C22×M16×C109C2211yescharacteristic
11C22×M16×C109C2211yescharacteristic
12C22×M16×C109C2211yescharacteristic
13C2×#117×C109C2211yescharacteristic
14C2×#117×C109C2211yescharacteristic
15#418×C109—22no—
16#418×C109—22no—
17#418×C109—22no—
18#418×C109—22no—
19C2×#102×C109—22no—
20C2×#102×C109—22no—
21C2×#100×C109—22no—
22C2×#100×C109—22no—
23C2×#100×C109C414yescomplemented
24#344×C109—22no—
25#344×C109—22no—
26#341×C109—22no—
27H(3,ℤ/4)×C109—22no—
28C25×C109—21no—
29C22×D4×C109—21no—
30C22×D4×C109—21no—
31C22×D4×C109—21no—
32C22×D4×C109—21no—
33C22×D4×C109—21no—
34C22×D4×C109—21no—
35C22×D4×C109—21no—
36C22×D4×C109—21no—
37C22×D4×C109—21no—
38C22×D4×C109—21no—
39C22×D4×C109—21no—
40C22×D4×C109C2×C412yes—
41C22×D4×C109D412yes—
42C22×D4×C109D412yes—
43C23×C4×C109C2311yescharacteristic
44C2×M16×C109—21no—
45C2×M16×C109—21no—
46C2×M16×C109—21no—
47C2×M16×C109—21no—
48C2×M16×C109—21no—
49C2×M16×C109—21no—
50C2×M16×C109—21no—
51C2×M16×C109—21no—
52C2×M16×C109—21no—
53C2×M16×C109—21no—
54C2×M16×C109—21no—
55C2×M16×C109—21no—
56C2×M16×C109—21no—
57C2×M16×C109—21no—
58C2×M16×C109—21no—
59C2×M16×C109—21no—
60C2×M16×C109—21no—
61C2×M16×C109—21no—
62C2×M16×C109—21no—
63C2×M16×C109—21no—
64C2×M16×C109—21no—
65C2×M16×C109C2×C412yes—
66C2×M16×C109C2×C412yes—
67C2×M16×C109D412yes—
68C22×C8×C109—21no—
69C22×C8×C109—21no—
70C22×C8×C109—21no—
71C22×C8×C109D412yes—
72#117×C109—21no—
73#117×C109—21no—
74#117×C109—21no—
75#117×C109—21no—
76#117×C109—21no—
77#117×C109—21no—
78#117×C109D412yes—
79#117×C109D412yes—
80C2×C4⋊C4×C109—21no—
81C2×C4⋊C4×C109—21no—
82C2×C22⋊C4×C109—21no—
83C2×C22⋊C4×C109—21no—
84C2×C42×C109—21no—
85C2×C42×C109—21no—
86#102×C109—28no—
87#102×C109—28no—
88#100×C109—28no—
89C24×C109—22no—
90C24×C109—22no—
91C24×C109—22no—
92C24×C109—41no—
93C24×C109—41no—
94C24×C109—41no—
95C24×C109—41no—
96C24×C109—84no—
97C24×C109#4111yescharacteristic
98C2×D4×C109—22no—
99C2×D4×C109—22no—
100C2×D4×C109—22no—
101C2×D4×C109—22no—
102C2×D4×C109—22no—
103C2×D4×C109—22no—
104C2×D4×C109—22no—
105C2×D4×C109—22no—
106C2×D4×C109—22no—
107C2×D4×C109—22no—
108C2×D4×C109—22no—
109C2×D4×C109—22no—
110C2×D4×C109—22no—
111C2×D4×C109—22no—
112C2×D4×C109—22no—
113C2×D4×C109—41no—
114C2×D4×C109—41no—
115C2×D4×C109—41no—
116C2×D4×C109—41no—
117C2×D4×C109—41no—
118C2×D4×C109—41no—
119C2×D4×C109—41no—
120C2×D4×C109—41no—
121C2×D4×C109—41no—
122C2×D4×C109—41no—
123C2×D4×C109—41no—
124C2×D4×C109—41no—
125C2×D4×C109C22⋊C414yes—
126C22×C4×C109—41no—
127C22×C4×C109—41no—
128C22×C4×C109C22×C411yescharacteristic
129C22×C4×C109C2×D411yescharacteristic
130C22×C4×C109C2×D411yescharacteristic
131C22×C4×C109C2×D411yescharacteristic
132C22×C4×C109C2×D411yescharacteristic
133C22×C4×C109C2×D411yescharacteristic
134C22×C4×C109C2×D411yescharacteristic
135C22×C4×C109#4111yescharacteristic
136C22×C4×C109#4111yescharacteristic
137C22×C4×C109#4111yescharacteristic
138C22×C4×C109#4111yescharacteristic
139C22×C4×C109#4111yescharacteristic
140C22×C4×C109#4111yescharacteristic
141C22×C4×C109#4111yescharacteristic
142M16×C109—22no—
143M16×C109—22no—
144M16×C109—22no—
145M16×C109—22no—
146M16×C109—22no—
147M16×C109—22no—
148M16×C109—41no—
149M16×C109—41no—
150M16×C109—41no—
151M16×C109—41no—
152M16×C109—41no—
153M16×C109—41no—
154M16×C109—41no—
155M16×C109—41no—
156M16×C109—41no—
157M16×C109—41no—
158C2×C8×C109—22no—
159C2×C8×C109—22no—
160C2×C8×C109—22no—
161C2×C8×C109—22no—
162C2×C8×C109—22no—
163C2×C8×C109—22no—
164C2×C8×C109—41no—
165C2×C8×C109—41no—
166C2×C8×C109—41no—
167C2×C8×C109—41no—
168C2×C8×C109—41no—
169C2×C8×C109—41no—
170C4⋊C4×C109—22no—
171C4⋊C4×C109—22no—
172C4⋊C4×C109—41no—
173C4⋊C4×C109—41no—
174C22⋊C4×C109—22no—
175C22⋊C4×C109—22no—
176C22⋊C4×C109—41no—
177C22⋊C4×C109—41no—
178C42×C109—22no—
179C42×C109—22no—
180C42×C109—41no—
181C42×C109—41no—
182C23×C109—24no—
183C23×C109—42no—
184C23×C109—42no—
185C23×C109—42no—
186C23×C109—42no—
187C23×C109—42no—
188C23×C109—42no—
189C23×C109—42no—
190C23×C109—84no—
191C23×C109—84no—
192C23×C109—84no—
193C23×C109—84no—
194C23×C109—84no—
195C23×C109—84no—
196C23×C109—84no—
197C23×C109#11711yescharacteristic
198C23×C109#12111yescharacteristic
199C23×C109#12311yescharacteristic
200C23×C109#12311yescharacteristic
201C23×C109#12311yescharacteristic
202C23×C109#12411yescharacteristic
203C23×C109#12611yescharacteristic
204D4×C109—24no—
205D4×C109—24no—
206D4×C109—42no—
207D4×C109—42no—
208D4×C109—42no—
209D4×C109—42no—
210D4×C109—42no—
211D4×C109—42no—
212C2×C4×C109—42no—
213C2×C4×C109—42no—
214C2×C4×C109—82no—
215C2×C4×C109—82no—
216C2×C4×C109C2×C22⋊C411yescharacteristic
217C2×C4×C109#11711yescharacteristic
218C2×C4×C109C4×D411yescharacteristic
219C2×C4×C109C4×D411yescharacteristic
220C2×C4×C109C4×D411yescharacteristic
221C2×C4×C109C4×D411yescharacteristic
222C2×C4×C109#12011yescharacteristic
223C2×C4×C109#12011yescharacteristic
224C2×C4×C109#12111yescharacteristic
225C2×C4×C109#12111yescharacteristic
226C2×C4×C109#12111yescharacteristic
227C2×C4×C109#12111yescharacteristic
228C2×C4×C109#12111yescharacteristic
229C2×C4×C109#12111yescharacteristic
230C2×C4×C109#12111yescharacteristic
231C2×C4×C109#12311yescharacteristic
232C2×C4×C109#12311yescharacteristic
233C2×C4×C109#12311yescharacteristic
234C2×C4×C109#12311yescharacteristic
235C2×C4×C109#12311yescharacteristic
236C2×C4×C109#12311yescharacteristic
237C2×C4×C109#12311yescharacteristic
238C2×C4×C109#12411yescharacteristic
239C2×C4×C109#12411yescharacteristic
240C2×C4×C109#12411yescharacteristic
241C2×C4×C109#12611yescharacteristic
242C2×C4×C109#12611yescharacteristic
243C2×C4×C109#12611yescharacteristic
244C8×C109—42no—
245C8×C109—42no—
246C8×C109—42no—
247C8×C109—42no—
248C22×C109—22no—
249C22×C109—22no—
250C22×C109—22no—
251C22×C109—41no—
252C22×C109—41no—
253C22×C109—41no—
254C22×C109—41no—
255C22×C109—44no—
256C22×C109—84no—
257C22×C109—84no—
258C22×C109—84no—
259C22×C109—84no—
260C22×C109—84no—
261C22×C109—84no—
262C22×C109—84no—
263C22×C109#38111yescharacteristic
264C22×C109#38811yescharacteristic
265C22×C109#38811yescharacteristic
266C22×C109#39411yescharacteristic
267C22×C109#39411yescharacteristic
268C22×C109#39711yescharacteristic
269C22×C109#39711yescharacteristic
270C4×C109—82no—
271C4×C109—82no—
272C4×C109#38611yescharacteristic
273C4×C109#38611yescharacteristic
274C4×C109#38811yescharacteristic
275C4×C109#38811yescharacteristic
276C4×C109#39411yescharacteristic
277C4×C109#39411yescharacteristic
278C4×C109#39711yescharacteristic
279C4×C109#39711yescharacteristic
280#11157C10911yesmaximal, characteristic, direct product factor, Sylow
281C2×C109—21no—
282C2×C109—21no—
283C2×C109—21no—
284C2×C109—21no—
285C2×C109—21no—
286C2×C109—21no—
287C2×C109—84no—
288C2×C109#144011yescharacteristic
289C2×C109#208112yes—
290C2×#418C2×C10911yescharacteristic
291C2×#418C2×C10911yescharacteristic
292C22×#100C2×C10911yescharacteristic
293C2×#344C2×C10911yescharacteristic, complemented
294C2×#344C2×C10911yescharacteristic, complemented
295#1738C2×C10911yescharacteristic, complemented
296C2×H(3,ℤ/4)C2×C10911yescharacteristic, complemented
297C109#1115711yescharacteristic, direct product factor, Sylow
298C23×D4C22×C10911yescharacteristic
299C22×M16C22×C10911yescharacteristic
300C22×M16C22×C10911yescharacteristic
301C22×M16C22×C10911yescharacteristic
302C22×M16C22×C10911yescharacteristic
303C2×#117C22×C10911yescharacteristic
304C2×#117C22×C10911yescharacteristic
305#418—22no—
306#418—22no—
307#418—22no—
308#418—22no—
309C2×#102—22no—
310C2×#102—22no—
311C2×#100—22no—
312C2×#100—22no—
313C2×#100C4×C10914yescomplemented
314#344—22no—
315#344—22no—
316#341—22no—
317H(3,ℤ/4)—22no—
318C25—21no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4C2×C4×C10912yes—
331C22×D4D4×C10912yes—
332C22×D4D4×C10912yes—
333C23×C4C23×C10911yescharacteristic
334C2×M16—21no—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16C2×C4×C10912yes—
356C2×M16C2×C4×C10912yes—
357C2×M16D4×C10912yes—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8D4×C10912yes—
362#117—21no—
363#117—21no—
364#117—21no—
365#117—21no—
366#117—21no—
367#117—21no—
368#117D4×C10912yes—
369#117D4×C10912yes—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C42—21no—
375C2×C42—21no—
376#102—28no—
377#102—28no—
378#100—28no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—41no—
383C24—41no—
384C24—41no—
385C24—41no—
386C24—84no—
387C24#41×C10911yescharacteristic
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4C22⋊C4×C10914yes—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4C22×C4×C10911yescharacteristic
419C22×C4C2×D4×C10911yescharacteristic
420C22×C4C2×D4×C10911yescharacteristic
421C22×C4C2×D4×C10911yescharacteristic
422C22×C4C2×D4×C10911yescharacteristic
423C22×C4C2×D4×C10911yescharacteristic
424C22×C4C2×D4×C10911yescharacteristic
425C22×C4#41×C10911yescharacteristic
426C22×C4#41×C10911yescharacteristic
427C22×C4#41×C10911yescharacteristic
428C22×C4#41×C10911yescharacteristic
429C22×C4#41×C10911yescharacteristic
430C22×C4#41×C10911yescharacteristic
431C22×C4#41×C10911yescharacteristic
432M16—22no—
433M16—22no—
434M16—22no—
435M16—22no—
436M16—22no—
437M16—22no—
438M16—41no—
439M16—41no—
440M16—41no—
441M16—41no—
442M16—41no—
443M16—41no—
444M16—41no—
445M16—41no—
446M16—41no—
447M16—41no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—41no—
455C2×C8—41no—
456C2×C8—41no—
457C2×C8—41no—
458C2×C8—41no—
459C2×C8—41no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C42—22no—
469C42—22no—
470C42—41no—
471C42—41no—
472C23—24no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—84no—
481C23—84no—
482C23—84no—
483C23—84no—
484C23—84no—
485C23—84no—
486C23—84no—
487C23#117×C10911yescharacteristic
488C23#121×C10911yescharacteristic
489C23#123×C10911yescharacteristic
490C23#123×C10911yescharacteristic
491C23#123×C10911yescharacteristic
492C23#124×C10911yescharacteristic
493C23#126×C10911yescharacteristic
494D4—24no—
495D4—24no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—42no—
500D4—42no—
501D4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—82no—
505C2×C4—82no—
506C2×C4C2×C22⋊C4×C10911yescharacteristic
507C2×C4#117×C10911yescharacteristic
508C2×C4C4×D4×C10911yescharacteristic
509C2×C4C4×D4×C10911yescharacteristic
510C2×C4C4×D4×C10911yescharacteristic
511C2×C4C4×D4×C10911yescharacteristic
512C2×C4#120×C10911yescharacteristic
513C2×C4#120×C10911yescharacteristic
514C2×C4#121×C10911yescharacteristic
515C2×C4#121×C10911yescharacteristic
516C2×C4#121×C10911yescharacteristic
517C2×C4#121×C10911yescharacteristic
518C2×C4#121×C10911yescharacteristic
519C2×C4#121×C10911yescharacteristic
520C2×C4#121×C10911yescharacteristic
521C2×C4#123×C10911yescharacteristic
522C2×C4#123×C10911yescharacteristic
523C2×C4#123×C10911yescharacteristic
524C2×C4#123×C10911yescharacteristic
525C2×C4#123×C10911yescharacteristic
526C2×C4#123×C10911yescharacteristic
527C2×C4#123×C10911yescharacteristic
528C2×C4#124×C10911yescharacteristic
529C2×C4#124×C10911yescharacteristic
530C2×C4#124×C10911yescharacteristic
531C2×C4#126×C10911yescharacteristic
532C2×C4#126×C10911yescharacteristic
533C2×C4#126×C10911yescharacteristic
534C8—42no—
535C8—42no—
536C8—42no—
537C8—42no—
538C22—22no—
539C22—22no—
540C22—22no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—44no—
546C22—84no—
547C22—84no—
548C22—84no—
549C22—84no—
550C22—84no—
551C22—84no—
552C22—84no—
553C22#381×C10911yescharacteristic
554C22#388×C10911yescharacteristic
555C22#388×C10911yescharacteristic
556C22#394×C10911yescharacteristic
557C22#394×C10911yescharacteristic
558C22#397×C10911yescharacteristic
559C22#397×C10911yescharacteristic
560C4—82no—
561C4—82no—
562C4#386×C10911yescharacteristic
563C4#386×C10911yescharacteristic
564C4#388×C10911yescharacteristic
565C4#388×C10911yescharacteristic
566C4#394×C10911yescharacteristic
567C4#394×C10911yescharacteristic
568C4#397×C10911yescharacteristic
569C4#397×C10911yescharacteristic
570C2—21no—
571C2—21no—
572C2—21no—
573C2—21no—
574C2—21no—
575C2—21no—
576C2—84no—
577C2C109×#144011yescharacteristic
578C2C109×#208112yes—
subgroupG/H
center, socleC22×C109#397
commutatorC22×C4C22×C4×C109
Frattini, cosocleC23×C4C23×C109
prime radicalC23×D4×C109C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#344×C109C2semidirect
5. C2×#344×C109C2semidirect
6. C109×#1738C2semidirect
7. C2×H(3,ℤ/4)×C109C2semidirect
23. C2×#100×C109C4semidirect
280. #11157C109direct (N × H)
293. C2×#344C2×C109semidirect
294. C2×#344C2×C109semidirect
295. #1738C2×C109semidirect
296. C2×H(3,ℤ/4)C2×C109semidirect
297. C109#11157direct (N × H)
313. C2×#100C4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#418×C1092
C22×#100×C1092
C2×#344×C1092
C109×#17382
C2×H(3,ℤ/4)×C1092
#11157109