Finite Group Databasebeta

← C109×#18434 #42136428

Subgroups — C109×#18434 #42136428

Order 27904.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3560C211yesmaximal, characteristic, complemented
2C109×#3213C211yesmaximal, characteristic, complemented
3C109×#3211C211yesmaximal, characteristic, complemented
4C109×#2662C211yesmaximal, characteristic, complemented
5C109×#1606C211yesmaximal, characteristic, complemented
6C109×#1604C211yesmaximal, characteristic, complemented
7C109×#1603C211yesmaximal, characteristic, complemented
8C109×#1601C211yesmaximal, characteristic, complemented
9C109×#1600C211yesmaximal, characteristic, complemented
10C109×#1598C211yesmaximal, characteristic, complemented
11C109×#1597C211yesmaximal, characteristic, complemented
12C109×#1595C211yesmaximal, characteristic, complemented
13C109×#1509C211yesmaximal, characteristic, complemented
14C109×#1502C211yesmaximal, characteristic, complemented
15C109×#1473C211yesmaximal, characteristic, complemented
16#563×C109—21no—
17#560×C109—21no—
18#553×C109—21no—
19#553×C109—21no—
20#551×C109—21no—
21#547×C109—21no—
22#546×C109—21no—
23#546×C109—21no—
24#542×C109—21no—
25#539×C109—21no—
26#539×C109C2211yescharacteristic
27#538×C109—21no—
28#538×C109—21no—
29#538×C109C2211yescharacteristic
30#537×C109C2211yescharacteristic
31#534×C109C2211yescharacteristic
32#532×C109C2211yescharacteristic
33#529×C109C2211yescharacteristic
34C2×#126×C109C2211yescharacteristic
35C2×#124×C109C2211yescharacteristic, complemented
36#496×C109—21no—
37#495×C109—21no—
38#489×C109—21no—
39#488×C109—21no—
40#464×C109—21no—
41#463×C109—21no—
42#463×C109—21no—
43#463×C109—21no—
44#451×C109C2211yescharacteristic, complemented
45#450×C109C2211yescharacteristic, complemented
46#448×C109C2211yescharacteristic
47#448×C109C2211yescharacteristic
48#448×C109C2211yescharacteristic, complemented
49#447×C109C2211yescharacteristic
50#447×C109C2211yescharacteristic
51#447×C109C2211yescharacteristic, complemented
52#432×C109C2211yescharacteristic, complemented
53#431×C109C2211yescharacteristic, complemented
54#396×C109—21no—
55#395×C109C2211yescharacteristic, complemented
56#394×C109—21no—
57#394×C109C2211yescharacteristic, complemented
58#393×C109C2211yescharacteristic
59#392×C109C2211yescharacteristic
60#390×C109—21no—
61#388×C109—21no—
62C4×C4⋊C4×C109C2211yescharacteristic, complemented
63#328×C109C2211yescharacteristic, complemented
64#328×C109C2211yescharacteristic, complemented
65#327×C109C2211yescharacteristic
66#327×C109C2211yescharacteristic
67#327×C109C2211yescharacteristic
68#327×C109C2211yescharacteristic
69#327×C109C2211yescharacteristic, complemented
70#327×C109C2211yescharacteristic, complemented
71#324×C109C2211yescharacteristic, complemented
72#324×C109C2211yescharacteristic, complemented
73#323×C109C2211yescharacteristic
74#323×C109C2211yescharacteristic
75C2×#41×C109—21no—
76C2×#41×C109—21no—
77C22×Q8×C109C2311yescharacteristic
78C22×D4×C109—21no—
79C22×D4×C109—21no—
80C22×D4×C109C2311yescharacteristic
81C2×Q16×C109—21no—
82C2×SD16×C109—21no—
83C2×SD16×C109—21no—
84C2×SD16×C109—21no—
85C2×SD16×C109—21no—
86C2×D8×C109—21no—
87C2×D8×C109—21no—
88C2×D8×C109—21no—
89C4⋊Q8×C109—21no—
90C4⋊Q8×C109D411yescharacteristic, complemented
91#127×C109D411yescharacteristic, complemented
92#126×C109—21no—
93#126×C109—21no—
94#126×C109—21no—
95#126×C109—21no—
96#126×C109—21no—
97#126×C109—21no—
98#126×C109—21no—
99#126×C109—21no—
100#126×C109—21no—
101#125×C109—21no—
102#125×C109—21no—
103#125×C109D411yescharacteristic, complemented
104#124×C109—21no—
105#124×C109—21no—
106#124×C109—21no—
107#124×C109—21no—
108#124×C109—21no—
109#124×C109—21no—
110#124×C109—21no—
111#124×C109—21no—
112#124×C109D411yescharacteristic, complemented
113#123×C109—21no—
114#123×C109—21no—
115#123×C109—21no—
116#123×C109—21no—
117#123×C109—21no—
118#123×C109—21no—
119#123×C109—21no—
120#123×C109—21no—
121#123×C109—21no—
122#123×C109—21no—
123#123×C109—21no—
124#123×C109—21no—
125C22⋊Q8×C109—21no—
126C22⋊Q8×C109—21no—
127C22⋊Q8×C109—21no—
128C22⋊Q8×C109—21no—
129C22⋊Q8×C109—21no—
130C22⋊Q8×C109—21no—
131C22⋊Q8×C109—21no—
132C22⋊Q8×C109C2311yescharacteristic
133#121×C109—21no—
134#121×C109—21no—
135#121×C109—21no—
136#121×C109—21no—
137#121×C109—21no—
138#121×C109—21no—
139#121×C109—21no—
140#121×C109—21no—
141#121×C109—21no—
142#121×C109—21no—
143#121×C109—21no—
144#121×C109—21no—
145#121×C109C2311yescharacteristic
146#121×C109C2311yescharacteristic
147#121×C109C2311yescharacteristic
148#120×C109—21no—
149#120×C109—21no—
150#120×C109—21no—
151#120×C109—21no—
152#120×C109—21no—
153C4×Q8×C109D411yescharacteristic, complemented
154C4×D4×C109—21no—
155C4×D4×C109—21no—
156C4×D4×C109—21no—
157C4×D4×C109—21no—
158C4×D4×C109—21no—
159C4×D4×C109—21no—
160C4×D4×C109—21no—
161C4×D4×C109—21no—
162C4×D4×C109D411yescharacteristic, complemented
163C4×D4×C109D411yescharacteristic, complemented
164C4×D4×C109D411yescharacteristic, complemented
165#117×C109—21no—
166#117×C109—21no—
167C2×C4⋊C4×C109—21no—
168C2×C4⋊C4×C109—21no—
169C2×C4⋊C4×C109—21no—
170C2×C4⋊C4×C109D411yescharacteristic
171C2×C4⋊C4×C109D411yescharacteristic
172C2×C4⋊C4×C109C2311yescharacteristic
173C2×C22⋊C4×C109—21no—
174C2×C22⋊C4×C109—21no—
175C2×C22⋊C4×C109—21no—
176C2×C22⋊C4×C109—21no—
177C2×C22⋊C4×C109—21no—
178C2×C22⋊C4×C109—21no—
179C2×C22⋊C4×C109—21no—
180C2×C22⋊C4×C109—21no—
181C2×C22⋊C4×C109D411yescharacteristic
182C2×C22⋊C4×C109D411yescharacteristic
183C2×C22⋊C4×C109C2311yescharacteristic
184C2×C42×C109—21no—
185C2×C42×C109C2311yescharacteristic
186C4⋊C8×C109—21no—
187C4⋊C8×C109—21no—
188#103×C109—21no—
189#103×C109—21no—
190#103×C109—21no—
191#103×C109—21no—
192#102×C109—21no—
193#102×C109—21no—
194#102×C109—21no—
195#102×C109—21no—
196C22⋊C8×C109C2311yescharacteristic
197C22⋊C8×C109C2311yescharacteristic
198C22⋊C8×C109C2311yescharacteristic
199C22⋊C8×C109C2311yescharacteristic
200#97×C109—21no—
201C4×C8×C109—21no—
202#95×C109—21no—
203#95×C109—21no—
204#95×C109C2311yescharacteristic
205#95×C109C2311yescharacteristic
206C24×C109—21no—
207C24×C109—21no—
208C24×C109C2×D411yescharacteristic
209#41×C109—81no—
210#41×C109—81no—
211#41×C109—81no—
212#41×C109—81no—
213C2×Q8×C109—21no—
214C2×Q8×C109—21no—
215C2×Q8×C109—21no—
216C2×Q8×C109—21no—
217C2×Q8×C109—81no—
218C2×Q8×C109C2×D411yescharacteristic
219C2×D4×C109—21no—
220C2×D4×C109—21no—
221C2×D4×C109—21no—
222C2×D4×C109—21no—
223C2×D4×C109—21no—
224C2×D4×C109—21no—
225C2×D4×C109—21no—
226C2×D4×C109—21no—
227C2×D4×C109—21no—
228C2×D4×C109—21no—
229C2×D4×C109—21no—
230C2×D4×C109—21no—
231C2×D4×C109—21no—
232C2×D4×C109—21no—
233C2×D4×C109—42no—
234C2×D4×C109—81no—
235C2×D4×C109—81no—
236C2×D4×C109—81no—
237C2×D4×C109—81no—
238C2×D4×C109—81no—
239C2×D4×C109C2×D411yescharacteristic
240C2×D4×C109C2×D411yescharacteristic
241C2×D4×C109C2×D411yescharacteristic
242C22×C4×C109—21no—
243C22×C4×C109—21no—
244C22×C4×C109—21no—
245C22×C4×C109—21no—
246C22×C4×C109—21no—
247C22×C4×C109—21no—
248C22×C4×C109—21no—
249C22×C4×C109—21no—
250C22×C4×C109—21no—
251C22×C4×C109—21no—
252C22×C4×C109—21no—
253C22×C4×C109C2×D411yescharacteristic
254C22×C4×C109C2×D411yescharacteristic
255C22×C4×C109C2×D411yescharacteristic
256C22×C4×C109C2×D411yescharacteristic
257C22×C4×C109C2×D411yescharacteristic
258C22×C4×C109C2411yescharacteristic
259Q16×C109—81no—
260SD16×C109—81no—
261SD16×C109—81no—
262SD16×C109—81no—
263SD16×C109—81no—
264D8×C109—81no—
265D8×C109—81no—
266D8×C109—81no—
267C2×C8×C109—21no—
268C2×C8×C109—21no—
269C2×C8×C109—21no—
270C2×C8×C109—21no—
271C4⋊C4×C109—21no—
272C4⋊C4×C109—21no—
273C4⋊C4×C109—21no—
274C4⋊C4×C109—21no—
275C4⋊C4×C109—21no—
276C4⋊C4×C109—21no—
277C4⋊C4×C109—21no—
278C4⋊C4×C109—21no—
279C4⋊C4×C109—21no—
280C4⋊C4×C109—21no—
281C4⋊C4×C109—21no—
282C4⋊C4×C109—21no—
283C4⋊C4×C109—21no—
284C4⋊C4×C109—21no—
285C4⋊C4×C109—21no—
286C4⋊C4×C109—21no—
287C4⋊C4×C109—21no—
288C4⋊C4×C109—42no—
289C4⋊C4×C109—81no—
290C4⋊C4×C109C2×D411yescharacteristic
291C4⋊C4×C109C2×D411yescharacteristic
292C4⋊C4×C109C2×D411yescharacteristic
293C4⋊C4×C109C2×D411yescharacteristic
294C22⋊C4×C109—21no—
295C22⋊C4×C109—21no—
296C22⋊C4×C109—21no—
297C22⋊C4×C109—21no—
298C22⋊C4×C109—21no—
299C22⋊C4×C109—21no—
300C22⋊C4×C109—21no—
301C22⋊C4×C109—21no—
302C22⋊C4×C109—21no—
303C22⋊C4×C109—21no—
304C22⋊C4×C109—21no—
305C22⋊C4×C109—21no—
306C22⋊C4×C109—21no—
307C22⋊C4×C109—21no—
308C22⋊C4×C109—21no—
309C22⋊C4×C109—21no—
310C22⋊C4×C109—21no—
311C22⋊C4×C109—21no—
312C22⋊C4×C109—21no—
313C22⋊C4×C109—21no—
314C22⋊C4×C109—21no—
315C22⋊C4×C109—21no—
316C22⋊C4×C109—21no—
317C22⋊C4×C109—21no—
318C22⋊C4×C109—21no—
319C22⋊C4×C109—42no—
320C22⋊C4×C109—41no—
321C22⋊C4×C109—41no—
322C22⋊C4×C109—41no—
323C22⋊C4×C109—41no—
324C22⋊C4×C109—81no—
325C22⋊C4×C109—81no—
326C22⋊C4×C109—81no—
327C42×C109—21no—
328C42×C109—21no—
329C42×C109—21no—
330C42×C109—81no—
331C42×C109C2×D411yescharacteristic
332C42×C109C2×D411yescharacteristic
333C42×C109C2×D411yescharacteristic
334C42×C109C2×D411yescharacteristic
335C23×C109—21no—
336C23×C109—21no—
337C23×C109—21no—
338C23×C109—21no—
339C23×C109—21no—
340C23×C109—21no—
341C23×C109—41no—
342C23×C109—41no—
343C23×C109—41no—
344C23×C109—41no—
345C23×C109—41no—
346C23×C109—41no—
347C23×C109—41no—
348C23×C109—41no—
349C23×C109—41no—
350C23×C109—81no—
351C23×C109—81no—
352C23×C109—81no—
353C23×C109C22×D411yescharacteristic
354Q8×C109—41no—
355Q8×C109—41no—
356Q8×C109—41no—
357Q8×C109—41no—
358Q8×C109—41no—
359Q8×C109—81no—
360Q8×C109—81no—
361D4×C109—41no—
362D4×C109—41no—
363D4×C109—41no—
364D4×C109—41no—
365D4×C109—41no—
366D4×C109—41no—
367D4×C109—41no—
368D4×C109—41no—
369D4×C109—41no—
370D4×C109—41no—
371D4×C109—41no—
372D4×C109—41no—
373D4×C109—41no—
374D4×C109—81no—
375D4×C109—81no—
376D4×C109—81no—
377D4×C109—81no—
378D4×C109—81no—
379D4×C109—81no—
380D4×C109—81no—
381D4×C109—81no—
382D4×C109—81no—
383D4×C109—84no—
384C2×C4×C109—21no—
385C2×C4×C109—21no—
386C2×C4×C109—22no—
387C2×C4×C109—21no—
388C2×C4×C109—21no—
389C2×C4×C109—21no—
390C2×C4×C109—21no—
391C2×C4×C109—21no—
392C2×C4×C109—21no—
393C2×C4×C109—21no—
394C2×C4×C109—21no—
395C2×C4×C109—21no—
396C2×C4×C109—21no—
397C2×C4×C109—41no—
398C2×C4×C109—41no—
399C2×C4×C109—41no—
400C2×C4×C109—41no—
401C2×C4×C109—41no—
402C2×C4×C109—41no—
403C2×C4×C109—41no—
404C2×C4×C109—41no—
405C2×C4×C109—41no—
406C2×C4×C109—41no—
407C2×C4×C109—41no—
408C2×C4×C109—41no—
409C2×C4×C109—81no—
410C2×C4×C109—81no—
411C2×C4×C109—81no—
412C2×C4×C109—81no—
413C2×C4×C109—81no—
414C2×C4×C109—81no—
415C2×C4×C109—81no—
416C2×C4×C109—81no—
417C2×C4×C109#12011yescharacteristic
418C2×C4×C109#12011yescharacteristic
419C2×C4×C109#12011yescharacteristic
420C2×C4×C109#12011yescharacteristic
421C2×C4×C109C22×D411yescharacteristic
422C2×C4×C109C22×D411yescharacteristic
423C8×C109—41no—
424C8×C109—41no—
425C8×C109—41no—
426C8×C109—41no—
427C22×C109—21no—
428C22×C109—21no—
429C22×C109—41no—
430C22×C109—41no—
431C22×C109—41no—
432C22×C109—41no—
433C22×C109—41no—
434C22×C109—41no—
435C22×C109—41no—
436C22×C109—41no—
437C22×C109—41no—
438C22×C109—41no—
439C22×C109—41no—
440C22×C109—41no—
441C22×C109—81no—
442C22×C109—81no—
443C22×C109—81no—
444C22×C109—81no—
445C22×C109—81no—
446C22×C109—81no—
447C22×C109—81no—
448C22×C109—81no—
449C22×C109—81no—
450C22×C109—162no—
451C22×C109C2×#12011yescharacteristic
452C22×C109#57611yescharacteristic
453C22×C109#57711yescharacteristic
454C4×C109—21no—
455C4×C109—21no—
456C4×C109—21no—
457C4×C109—21no—
458C4×C109—21no—
459C4×C109—21no—
460C4×C109—42no—
461C4×C109—41no—
462C4×C109—41no—
463C4×C109—41no—
464C4×C109—41no—
465C4×C109—41no—
466C4×C109—41no—
467C4×C109—41no—
468C4×C109—41no—
469C4×C109—81no—
470C4×C109—81no—
471#18434C10911yesmaximal, characteristic, direct product factor, Sylow
472C2×C109—21no—
473C2×C109—21no—
474C2×C109—81no—
475C2×C109—81no—
476C2×C109—81no—
477C2×C109—81no—
478C2×C109—161no—
479C2×C109#301211yescharacteristic
480C2×C109#301811yescharacteristic
481C2×C109#302711yescharacteristic
482#3560C2×C10911yescharacteristic, complemented
483#3213C2×C10911yescharacteristic, complemented
484#3211C2×C10911yescharacteristic, complemented
485#2662C2×C10911yescharacteristic, complemented
486#1606C2×C10911yescharacteristic, complemented
487#1604C2×C10911yescharacteristic, complemented
488#1603C2×C10911yescharacteristic, complemented
489#1601C2×C10911yescharacteristic, complemented
490#1600C2×C10911yescharacteristic, complemented
491#1598C2×C10911yescharacteristic, complemented
492#1597C2×C10911yescharacteristic, complemented
493#1595C2×C10911yescharacteristic, complemented
494#1509C2×C10911yescharacteristic, complemented
495#1502C2×C10911yescharacteristic, complemented
496#1473C2×C10911yescharacteristic, complemented
497C109#1843411yescharacteristic, direct product factor, Sylow
498#563—21no—
499#560—21no—
500#553—21no—
501#553—21no—
502#551—21no—
503#547—21no—
504#546—21no—
505#546—21no—
506#542—21no—
507#539—21no—
508#539C22×C10911yescharacteristic
509#538—21no—
510#538—21no—
511#538C22×C10911yescharacteristic
512#537C22×C10911yescharacteristic
513#534C22×C10911yescharacteristic
514#532C22×C10911yescharacteristic
515#529C22×C10911yescharacteristic
516C2×#126C22×C10911yescharacteristic
517C2×#124C22×C10911yescharacteristic, complemented
518#496—21no—
519#495—21no—
520#489—21no—
521#488—21no—
522#464—21no—
523#463—21no—
524#463—21no—
525#463—21no—
526#451C22×C10911yescharacteristic, complemented
527#450C22×C10911yescharacteristic, complemented
528#448C22×C10911yescharacteristic
529#448C22×C10911yescharacteristic
530#448C22×C10911yescharacteristic, complemented
531#447C22×C10911yescharacteristic
532#447C22×C10911yescharacteristic
533#447C22×C10911yescharacteristic, complemented
534#432C22×C10911yescharacteristic, complemented
535#431C22×C10911yescharacteristic, complemented
536#396—21no—
537#395C22×C10911yescharacteristic, complemented
538#394—21no—
539#394C22×C10911yescharacteristic, complemented
540#393C22×C10911yescharacteristic
541#392C22×C10911yescharacteristic
542#390—21no—
543#388—21no—
544C4×C4⋊C4C22×C10911yescharacteristic, complemented
545#328C22×C10911yescharacteristic, complemented
546#328C22×C10911yescharacteristic, complemented
547#327C22×C10911yescharacteristic
548#327C22×C10911yescharacteristic
549#327C22×C10911yescharacteristic
550#327C22×C10911yescharacteristic
551#327C22×C10911yescharacteristic, complemented
552#327C22×C10911yescharacteristic, complemented
553#324C22×C10911yescharacteristic, complemented
554#324C22×C10911yescharacteristic, complemented
555#323C22×C10911yescharacteristic
556#323C22×C10911yescharacteristic
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C10911yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C10911yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C10911yescharacteristic, complemented
573#127D4×C10911yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C10911yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C10911yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C10911yescharacteristic
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—21no—
625#121—21no—
626#121—21no—
627#121C23×C10911yescharacteristic
628#121C23×C10911yescharacteristic
629#121C23×C10911yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C10911yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C10911yescharacteristic, complemented
645C4×D4D4×C10911yescharacteristic, complemented
646C4×D4D4×C10911yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C10911yescharacteristic
653C2×C4⋊C4D4×C10911yescharacteristic
654C2×C4⋊C4C23×C10911yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C10911yescharacteristic
664C2×C22⋊C4D4×C10911yescharacteristic
665C2×C22⋊C4C23×C10911yescharacteristic
666C2×C42—21no—
667C2×C42C23×C10911yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C10911yescharacteristic
679C22⋊C8C23×C10911yescharacteristic
680C22⋊C8C23×C10911yescharacteristic
681C22⋊C8C23×C10911yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C10911yescharacteristic
687#95C23×C10911yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C10911yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C10911yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C10911yescharacteristic
722C2×D4C2×D4×C10911yescharacteristic
723C2×D4C2×D4×C10911yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
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×C4C2×D4×C10911yescharacteristic
736C22×C4C2×D4×C10911yescharacteristic
737C22×C4C2×D4×C10911yescharacteristic
738C22×C4C2×D4×C10911yescharacteristic
739C22×C4C2×D4×C10911yescharacteristic
740C22×C4C24×C10911yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C4⋊C4—21no—
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—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C10911yescharacteristic
773C4⋊C4C2×D4×C10911yescharacteristic
774C4⋊C4C2×D4×C10911yescharacteristic
775C4⋊C4C2×D4×C10911yescharacteristic
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—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C10911yescharacteristic
814C42C2×D4×C10911yescharacteristic
815C42C2×D4×C10911yescharacteristic
816C42C2×D4×C10911yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C10911yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C10911yescharacteristic
900C2×C4#120×C10911yescharacteristic
901C2×C4#120×C10911yescharacteristic
902C2×C4#120×C10911yescharacteristic
903C2×C4C22×D4×C10911yescharacteristic
904C2×C4C22×D4×C10911yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C10911yescharacteristic
934C22#576×C10911yescharacteristic
935C22#577×C10911yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C109×#301211yescharacteristic
961C2C109×#301811yescharacteristic
962C2C109×#302711yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC22×C4C24×C109
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C109 ◁ C2×C42×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#3560C2semidirect
2. C109×#3213C2semidirect
3. C109×#3211C2semidirect
4. C109×#2662C2semidirect
5. C109×#1606C2semidirect
6. C109×#1604C2semidirect
7. C109×#1603C2semidirect
8. C109×#1601C2semidirect
9. C109×#1600C2semidirect
10. C109×#1598C2semidirect
11. C109×#1597C2semidirect
12. C109×#1595C2semidirect
13. C109×#1509C2semidirect
14. C109×#1502C2semidirect
15. C109×#1473C2semidirect
35. C2×#124×C109C22semidirect
44. #451×C109C22semidirect
45. #450×C109C22semidirect
48. #448×C109C22semidirect
51. #447×C109C22semidirect
52. #432×C109C22semidirect
53. #431×C109C22semidirect
55. #395×C109C22semidirect
57. #394×C109C22semidirect
62. C4×C4⋊C4×C109C22semidirect
63. #328×C109C22semidirect
64. #328×C109C22semidirect
69. #327×C109C22semidirect
70. #327×C109C22semidirect
71. #324×C109C22semidirect
72. #324×C109C22semidirect
90. C4⋊Q8×C109D4semidirect
91. #127×C109D4semidirect
103. #125×C109D4semidirect
112. #124×C109D4semidirect
153. C4×Q8×C109D4semidirect
162. C4×D4×C109D4semidirect
163. C4×D4×C109D4semidirect
164. C4×D4×C109D4semidirect
471. #18434C109direct (N × H)
482. #3560C2×C109semidirect
483. #3213C2×C109semidirect
484. #3211C2×C109semidirect
485. #2662C2×C109semidirect
486. #1606C2×C109semidirect
487. #1604C2×C109semidirect
488. #1603C2×C109semidirect
489. #1601C2×C109semidirect
490. #1600C2×C109semidirect
491. #1598C2×C109semidirect
492. #1597C2×C109semidirect
493. #1595C2×C109semidirect
494. #1509C2×C109semidirect
495. #1502C2×C109semidirect
496. #1473C2×C109semidirect
497. C109#18434direct (N × H)
517. C2×#124C22×C109semidirect
526. #451C22×C109semidirect
527. #450C22×C109semidirect
530. #448C22×C109semidirect
533. #447C22×C109semidirect
534. #432C22×C109semidirect
535. #431C22×C109semidirect
537. #395C22×C109semidirect
539. #394C22×C109semidirect
544. C4×C4⋊C4C22×C109semidirect
545. #328C22×C109semidirect
546. #328C22×C109semidirect
551. #327C22×C109semidirect
552. #327C22×C109semidirect
553. #324C22×C109semidirect
554. #324C22×C109semidirect
572. C4⋊Q8D4×C109semidirect
573. #127D4×C109semidirect
585. #125D4×C109semidirect
594. #124D4×C109semidirect
635. C4×Q8D4×C109semidirect
644. C4×D4D4×C109semidirect
645. C4×D4D4×C109semidirect
646. C4×D4D4×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#35602
C109×#32132
C109×#32112
C109×#26622
C109×#16062
C109×#16042
C109×#16032
C109×#16012
C109×#16002
C109×#15982
C109×#15972
C109×#15952
C109×#15092
C109×#15022
C109×#14732
#18434109