Finite Group Databasebeta

← C2×#11736384 #14230605

Subgroups — C2×#11736384 #14230605

Order 1792.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90497C211yesmaximal, characteristic
2C2×#90220C211yesmaximal, characteristic, complemented
3C2×C7×#418C211yesmaximal, characteristic, complemented
4C2×#89990C211yesmaximal, characteristic, complemented
5C2×#89909C211yesmaximal, characteristic, complemented
6C2×#89900C211yesmaximal, characteristic, complemented
7C2×#89768C211yesmaximal, characteristic, complemented
8#11736384C2116yesmaximal, direct product factor
9C2×#89539C211yesmaximal, characteristic, complemented
10C2×#89549C211yesmaximal, characteristic, complemented
11C2×#89552C211yesmaximal, characteristic, complemented
12C2×#89555C211yesmaximal, characteristic, complemented
13C2×#89543C211yesmaximal, characteristic, complemented
14C2×#89540C211yesmaximal, characteristic, complemented
15C2×#89535C211yesmaximal, characteristic, complemented
16C2×#89530C211yesmaximal, characteristic, complemented
17C23×C7×D4C2211yescharacteristic
18C22×#1159C2211yescharacteristic
19C22×C7×M16C2211yescharacteristic
20C2×C7×#117C2211yescharacteristic
21C2×#6516—21no—
22C22×C22⋊Dic7—21no—
23#90497—24no—
24#90497C2218yes—
25C2×#6502—21no—
26C2×#6501C2211yescharacteristic
27C2×#6499C2211yescharacteristic
28C2×#6498—21no—
29C2×D4×Dic7C2211yescharacteristic
30C22×#1142C2211yescharacteristic
31C22×#1142C2211yescharacteristic
32C2×C4×C22⋊D7C2211yescharacteristic
33C2×#6487C2211yescharacteristic
34C2×#6487C2211yescharacteristic
35C22×Dic28C2211yescharacteristic, complemented
36C22×#1131C2211yescharacteristic, complemented
37#90220—24no—
38#90220C2218yescomplemented
39C2×#6460C2211yescharacteristic, complemented
40C2×D7×C4⋊C4C2211yescharacteristic, complemented
41C2×#6453C2211yescharacteristic, complemented
42C2×#6450C2211yescharacteristic, complemented
43C2×#6446—21no—
44C2×#6442—21no—
45C2×#6435—21no—
46C2×#6433—21no—
47C7×#418C2218yescomplemented
48C2×C7×#102C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C7×#102C2211yescharacteristic
51C2×C7×#102C2211yescharacteristic
52#89990C2218yescomplemented
53C2×#6406C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55C2×C22⋊(C7⋊C8)C2211yescharacteristic
56#89909C2218yescomplemented
57#89900C2218yescomplemented
58C2×(C2×D7)⋊C8C2211yescharacteristic, complemented
59C2×#6391C2211yescharacteristic, complemented
60C2×#6390C2211yescharacteristic, complemented
61C2×#6390C2211yescharacteristic, complemented
62C2×Dic7⋊C8C2211yescharacteristic, complemented
63C2×C8×Dic7C2211yescharacteristic, complemented
64#89768C2218yescomplemented
65C2×#6384C2211yescharacteristic, complemented
66C2×#6384C2211yescharacteristic, complemented
67C2×#6382C2211yescharacteristic, complemented
68C2×#6381C2211yescharacteristic, complemented
69#89555C2218yescomplemented
70#89552C2218yescomplemented
71#89549C2218yescomplemented
72#89543C2218yescomplemented
73#89540C2218yescomplemented
74#89539C2218yescomplemented
75#89535C2218yescomplemented
76#89530C2218yescomplemented
77C2×#3323—71nomaximal, Sylow
78C25×C7—21no—
79C22×C7×D4—24no—
80C22×C7×D4—21no—
81C22×C7×D4—22no—
82C22×C7×D4—42no—
83C22×C7×D4C2311yescharacteristic
84C22×C7×D4C2314yes—
85C22×C7×D4C2311yescharacteristic
86C23×C4×C7C2311yescharacteristic
87C22×C22⋊D7—21no—
88C22×C22⋊D7—21no—
89C22×C22⋊D7D411yescharacteristic
90C23×Dic7—21no—
91C23×Dic7—21no—
92C2×#1159—24no—
93C2×#1159—22no—
94C2×#1159—42no—
95C2×#1159C2314yes—
96C22×C4×D7—21no—
97C22×C4×D7C2311yescharacteristic
98C22×Dic14C2311yescharacteristic
99C22×Dic14C2311yescharacteristic
100C2×C7×M16—42no—
101C2×C7×M16C2314yes—
102C22×C7×C8C2311yescharacteristic
103C22×C7×C8C2311yescharacteristic
104C7×#117—22no—
105C7×#117C2314yes—
106C2×C7×C4⋊C4C2311yescharacteristic
107C2×C7×C4⋊C4C2311yescharacteristic
108C2×C7×C22⋊C4—21no—
109C2×C42×C7—21no—
110#6516—28no—
111C2×C22⋊Dic7—21no—
112C2×C22⋊Dic7—21no—
113C2×C22⋊Dic7—21no—
114C2×C22⋊Dic7—21no—
115C2×C22⋊Dic7—21no—
116C2×C22⋊Dic7—21no—
117C2×C22⋊Dic7—28no—
118C2×C22⋊Dic7D411yescharacteristic
119#6502—28no—
120#6501—22no—
121#6501C2314yes—
122#6499—22no—
123#6499C2314yes—
124#6498—28no—
125D4×Dic7—22no—
126D4×Dic7C2314yes—
127C2×#1142—24no—
128C2×#1142—42no—
129C2×#1142C2314yes—
130C2×#1142C2314yes—
131C4×C22⋊D7D414yes—
132C4×C22⋊D7C2314yes—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4D411yescharacteristic
135C2×C4⋊Dic7—21no—
136C2×C4⋊Dic7—21no—
137C2×C4⋊Dic7C2311yescharacteristic
138C2×C4⋊Dic7C2311yescharacteristic
139#6487—22no—
140#6487—22no—
141#6487C2314yes—
142#6487C2314yes—
143C2×Dic7⋊C4—21no—
144C2×Dic7⋊C4—21no—
145C2×Dic7⋊C4—21no—
146C2×Dic7⋊C4—21no—
147C2×Dic7⋊C4—21no—
148C2×Dic7⋊C4D411yescharacteristic
149C2×C4×Dic7—21no—
150C2×C4×Dic7C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2311yescharacteristic
153C2×Dic28—42no—
154C2×Dic28C2314yescomplemented
155C2×#1131—42no—
156C2×#1131C2314yescomplemented
157#6460—22no—
158#6460C2314yescomplemented
159D7×C4⋊C4—22no—
160D7×C4⋊C4C2314yescomplemented
161#6453—22no—
162#6453C2314yescomplemented
163#6450—22no—
164#6450C2314yescomplemented
165#6446—28no—
166#6442—28no—
167#6435—28no—
168#6433—28no—
169C7×#102C2314yes—
170C7×#102C2314yes—
171C7×#102C2314yes—
172C7×#102C2314yes—
173#6406C2314yes—
174#6406C2314yes—
175C22⋊(C7⋊C8)C2314yes—
176(C2×D7)⋊C8C2314yescomplemented
177#6391C2314yescomplemented
178#6390C2314yescomplemented
179#6390C2314yescomplemented
180Dic7⋊C8C2314yescomplemented
181C8×Dic7C2314yescomplemented
182#6384C2314yescomplemented
183#6384C2314yescomplemented
184#6382C2314yescomplemented
185#6381C2314yescomplemented
186C2×#552—71no—
187C2×#546—71no—
188#3323—716no—
189C2×#488—71no—
190C2×#481—71no—
191C2×#485—71no—
192C2×#478—71no—
193C2×#470—71no—
194C2×#468—71no—
195C2×#464—71no—
196C2×#452—71no—
197C2×#450—71no—
198C2×C4×SD16—71no—
199C2×#436—71no—
200C2×#417—71no—
201C2×#418D711yescharacteristic, complemented
202C24×C7—21no—
203C24×C7—21no—
204C24×C7—24no—
205C24×C7—44no—
206C24×C7—44no—
207C24×C7—82no—
208C24×C7C2×D411yescharacteristic
209C23×D7C2×D411yescharacteristic
210C2×C7×D4—28no—
211C2×C7×D4—21no—
212C2×C7×D4—24no—
213C2×C7×D4—21no—
214C2×C7×D4—22no—
215C2×C7×D4—22no—
216C2×C7×D4—22no—
217C2×C7×D4—44no—
218C2×C7×D4—48no—
219C2×C7×D4—44no—
220C2×C7×D4#4114yes—
221C2×C7×D4C2412yes—
222C2×C7×D4C2412yes—
223C22×C4×C7—22no—
224C22×C4×C7—22no—
225C22×C4×C7—21no—
226C22×C4×C7—21no—
227C22×C4×C7C2×D411yescharacteristic
228C22×C4×C7C2×D412yes—
229C22×C4×C7C2412yes—
230C22×C4×C7C2411yescharacteristic
231C2×C22⋊D7—24no—
232C2×C22⋊D7—24no—
233C2×C22⋊D7—42no—
234C2×C22⋊D7—44no—
235C2×C22⋊D7—82no—
236C2×C22⋊D7C2×D414yes—
237C22×Dic7—21no—
238C22×Dic7—21no—
239C22×Dic7—21no—
240C22×Dic7—21no—
241C22×Dic7—24no—
242C22×Dic7—24no—
243C22×Dic7—44no—
244C22×Dic7—82no—
245C22×Dic7C2×D411yescharacteristic
246C22×Dic7C2×D411yescharacteristic
247C22×Dic7C2×D411yescharacteristic
248#1159—28no—
249#1159—44no—
250#1159—48no—
251C2×C4×D7—22no—
252C2×C4×D7—22no—
253C2×C4×D7—24no—
254C2×C4×D7—44no—
255C2×C4×D7C2×D412yes—
256C2×C4×D7C2412yes—
257C2×Dic14—22no—
258C2×Dic14—22no—
259C2×Dic14—22no—
260C2×Dic14—22no—
261C2×Dic14—21no—
262C2×Dic14—21no—
263C2×Dic14C2412yes—
264C2×Dic14C2412yes—
265C7×M16—44no—
266C2×C7×C8—22no—
267C2×C7×C8—22no—
268C2×C7×C8C2412yes—
269C2×C7×C8C2412yes—
270C7×C4⋊C4—21no—
271C7×C4⋊C4—21no—
272C7×C4⋊C4C2412yes—
273C7×C4⋊C4C2412yes—
274C7×C22⋊C4—24no—
275C42×C7—24no—
276C22⋊Dic7—24no—
277C22⋊Dic7—24no—
278C22⋊Dic7—24no—
279C22⋊Dic7—24no—
280C22⋊Dic7—24no—
281C22⋊Dic7—24no—
282C22⋊Dic7C2×D414yes—
283#1142—28no—
284#1142—44no—
285(C2×D7)⋊C4—24no—
286(C2×D7)⋊C4C2×D414yes—
287C4⋊Dic7—21no—
288C4⋊Dic7—21no—
289C4⋊Dic7—24no—
290C4⋊Dic7—24no—
291C4⋊Dic7C2412yes—
292C4⋊Dic7C2412yes—
293Dic7⋊C4—24no—
294Dic7⋊C4—24no—
295Dic7⋊C4—24no—
296Dic7⋊C4—24no—
297Dic7⋊C4—24no—
298Dic7⋊C4C2×D414yes—
299C4×Dic7—24no—
300C4×Dic7C2×D412yes—
301C4×Dic7C2412yes—
302C2×C7⋊C8—22no—
303C2×C7⋊C8—22no—
304C2×C7⋊C8C2412yes—
305C2×C7⋊C8C2412yes—
306Dic28—44no—
307#1131—44no—
308C22×#41—71no—
309C23×D4C2×D711yescharacteristic
310C22×Q16—71no—
311C22×SD16—71no—
312C22×SD16—71no—
313C22×M16—71no—
314C22×M16C2×D711yescharacteristic
315#552—78no—
316#552—144no—
317#546—78no—
318#546—144no—
319C2×#126—141no—
320C2×#125—71no—
321C2×#125—141no—
322C2×#124—71no—
323C2×#123—141no—
324C2×#123—141no—
325C2×C22⋊Q8—71no—
326C2×C22⋊Q8—71no—
327C2×C22⋊Q8—71no—
328C2×#121—71no—
329C2×#121—141no—
330C2×#120—141no—
331C2×C4×Q8—71no—
332C2×C4×D4—71no—
333C2×C4×D4—71no—
334C2×#117—141no—
335C2×#117C2×D711yescharacteristic
336C22×C4⋊C4—71no—
337C22×C22⋊C4—141no—
338#488—78no—
339#485—78no—
340#481—78no—
341#478—78no—
342#470—78no—
343#468—78no—
344#464—78no—
345#452—78no—
346#450—78no—
347C4×SD16—78no—
348#436—78no—
349C2×#107—71no—
350C2×#106—71no—
351C2×#106—71no—
352C2×C4⋊C8—71no—
353#418C2×D718yescomplemented
354#417—78no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#102—71no—
360C2×#102—71no—
361C2×#102C2×D711yescharacteristic
362C2×#102C2×D711yescharacteristic
363C2×#102C2×D711yescharacteristic
364C2×#102C2×D711yescharacteristic
365C2×C22⋊C8—71no—
366C2×C22⋊C8—71no—
367C2×C4×C8—71no—
368C23×C7—24no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—48no—
375C23×C7—48no—
376C23×C7—42no—
377C23×C7—42no—
378C23×C7—42no—
379C23×C7—42no—
380C23×C7—42no—
381C23×C7—84no—
382C23×C7—816no—
383C23×C7C22×D412yes—
384C23×C7C22×D411yescharacteristic
385C22×D7—22no—
386C22×D7—22no—
387C22×D7—22no—
388C22×D7C22×D412yes—
389C7×D4—24no—
390C7×D4—22no—
391C7×D4—22no—
392C7×D4—22no—
393C7×D4—48no—
394C7×D4—42no—
395C7×D4C2×#4114yes—
396C2×C4×C7—22no—
397C2×C4×C7—24no—
398C2×C4×C7—22no—
399C2×C4×C7—22no—
400C2×C4×C7—22no—
401C2×C4×C7—22no—
402C2×C4×C7—42no—
403C2×C4×C7—42no—
404C2×C4×C7C22×D412yes—
405C2×C4×C7C22×D411yescharacteristic
406C2×C4×C7C2×#4112yes—
407C2×C4×C7H(5,𝔽2)12yes—
408C2×C4×C7C2511yescharacteristic
409C22⋊D7—44no—
410C22⋊D7—48no—
411C22⋊D7—84no—
412C2×Dic7—22no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—48no—
420C2×Dic7—42no—
421C2×Dic7—42no—
422C2×Dic7—42no—
423C2×Dic7—42no—
424C2×Dic7—84no—
425C2×Dic7C22×D412yes—
426C2×Dic7C22×D412yes—
427C2×Dic7C22×D412yes—
428C4×D7—24no—
429C4×D7—22no—
430C4×D7—22no—
431C4×D7—48no—
432Dic14—22no—
433Dic14—22no—
434Dic14—22no—
435Dic14—22no—
436Dic14—42no—
437Dic14—42no—
438C7×C8—22no—
439C7×C8—22no—
440C7⋊C8—22no—
441C7⋊C8—22no—
442C25—21no—
443C2×#41—74no—
444C2×#41—142no—
445C2×#41—144no—
446C2×#41—282no—
447C22×Q8—71no—
448C22×Q8—71no—
449C22×D4—24no—
450C22×D4—21no—
451C22×D4—22no—
452C22×D4—42no—
453C22×D4—71no—
454C22×D4—141no—
455C22×D4—141no—
456C22×D4C22×D711yescharacteristic
457C22×D4C22×D714yes—
458C22×D4C22×D711yescharacteristic
459C23×C4—71no—
460C23×C4—141no—
461C23×C4—141no—
462C23×C4—141no—
463C23×C4C22×D711yescharacteristic
464C2×Q16—74no—
465C2×Q16—282no—
466C2×SD16—74no—
467C2×SD16—74no—
468C2×SD16—144no—
469C2×SD16—282no—
470C2×M16—42no—
471C2×M16—74no—
472C2×M16—282no—
473C2×M16C22×D714yes—
474C22×C8—71no—
475C22×C8—71no—
476C22×C8C22×D711yescharacteristic
477C22×C8C22×D711yescharacteristic
478#126—148no—
479#125—74no—
480#125—148no—
481#125—142no—
482#124—74no—
483#124—142no—
484#123—148no—
485#123—148no—
486C22⋊Q8—74no—
487C22⋊Q8—74no—
488C22⋊Q8—74no—
489C22⋊Q8—142no—
490C22⋊Q8—142no—
491C22⋊Q8—142no—
492#121—74no—
493#121—148no—
494#121—142no—
495#120—148no—
496C4×Q8—74no—
497C4×Q8—142no—
498C4×D4—74no—
499C4×D4—74no—
500C4×D4—74no—
501C4×D4—142no—
502#117—22no—
503#117—148no—
504#117C22×D714yes—
505C2×C4⋊C4—71no—
506C2×C4⋊C4—71no—
507C2×C4⋊C4—71no—
508C2×C4⋊C4—74no—
509C2×C4⋊C4—142no—
510C2×C4⋊C4—141no—
511C2×C4⋊C4—141no—
512C2×C4⋊C4—141no—
513C2×C4⋊C4—141no—
514C2×C4⋊C4—141no—
515C2×C4⋊C4—141no—
516C2×C4⋊C4—141no—
517C2×C4⋊C4C22×D711yescharacteristic
518C2×C4⋊C4C22×D711yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—71no—
521C2×C22⋊C4—71no—
522C2×C22⋊C4—148no—
523C2×C22⋊C4—141no—
524C2×C22⋊C4—141no—
525C2×C22⋊C4—141no—
526C2×C22⋊C4—141no—
527C2×C22⋊C4—141no—
528C2×C22⋊C4—141no—
529C2×C22⋊C4—141no—
530C2×C42—21no—
531C2×C42—71no—
532C2×C42—141no—
533#107—74no—
534#106—74no—
535#106—74no—
536C4⋊C8—74no—
537#103—74no—
538#103—74no—
539#103—74no—
540#103—74no—
541#102—74no—
542#102—74no—
543#102C22×D714yes—
544#102C22×D714yes—
545#102C22×D714yes—
546#102C22×D714yes—
547C22⋊C8—74no—
548C22⋊C8—74no—
549C4×C8—74no—
550C22×C7—24no—
551C22×C7—22no—
552C22×C7—22no—
553C22×C7—22no—
554C22×C7—44no—
555C22×C7—48no—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7—42no—
561C22×C7—816no—
562C22×C7—84no—
563C22×C7#54612yes—
564C22×C7#57512yes—
565C22×C7#57712yes—
566C22×C7C23×D411yescharacteristic
567C2×D7—22no—
568C2×D7—22no—
569C2×D7—22no—
570C2×D7—44no—
571C4×C7—22no—
572C4×C7—42no—
573C4×C7—42no—
574C4×C7#54612yes—
575C4×C7C22×#4111yescharacteristic
576C4×C7C2×H(5,𝔽2)11yescharacteristic
577Dic7—22no—
578Dic7—22no—
579Dic7—22no—
580Dic7—42no—
581Dic7—42no—
582Dic7—42no—
583Dic7—42no—
584C24—21no—
585C24—21no—
586C24—24no—
587C24—44no—
588C24—44no—
589C24—71no—
590C24—82no—
591C24D4×D711yescharacteristic
592#41—148no—
593#41—284no—
594#41—288no—
595C2×Q8—72no—
596C2×Q8—72no—
597C2×Q8—141no—
598C2×Q8—141no—
599C2×Q8—142no—
600C2×Q8—142no—
601C2×Q8—142no—
602C2×Q8—142no—
603C2×D4—28no—
604C2×D4—22no—
605C2×D4—21no—
606C2×D4—24no—
607C2×D4—21no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—44no—
611C2×D4—48no—
612C2×D4—44no—
613C2×D4—74no—
614C2×D4—144no—
615C2×D4—144no—
616C2×D4—282no—
617C2×D4—284no—
618C2×D4—562no—
619C2×D4#115714yes—
620C2×D4C23×D712yes—
621C2×D4C23×D712yes—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—71no—
627C22×C4—71no—
628C22×C4—71no—
629C22×C4—72no—
630C22×C4—72no—
631C22×C4—144no—
632C22×C4—144no—
633C22×C4—144no—
634C22×C4—142no—
635C22×C4—142no—
636C22×C4—141no—
637C22×C4—141no—
638C22×C4—141no—
639C22×C4—141no—
640C22×C4—284no—
641C22×C4—284no—
642C22×C4—562no—
643C22×C4D4×D712yes—
644C22×C4D4×D711yescharacteristic
645C22×C4C23×D712yes—
646C22×C4C23×D711yescharacteristic
647Q16—284no—
648SD16—148no—
649SD16—284no—
650M16—44no—
651M16—284no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—72no—
655C2×C8—72no—
656C2×C8—142no—
657C2×C8—142no—
658C2×C8C23×D712yes—
659C2×C8C23×D712yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—74no—
663C4⋊C4—72no—
664C4⋊C4—72no—
665C4⋊C4—144no—
666C4⋊C4—144no—
667C4⋊C4—144no—
668C4⋊C4—144no—
669C4⋊C4—144no—
670C4⋊C4—144no—
671C4⋊C4—144no—
672C4⋊C4—141no—
673C4⋊C4—141no—
674C4⋊C4C23×D712yes—
675C4⋊C4C23×D712yes—
676C22⋊C4—24no—
677C22⋊C4—74no—
678C22⋊C4—74no—
679C22⋊C4—144no—
680C22⋊C4—144no—
681C22⋊C4—144no—
682C22⋊C4—144no—
683C22⋊C4—144no—
684C22⋊C4—144no—
685C22⋊C4—144no—
686C42—24no—
687C42—72no—
688C42—72no—
689C42—144no—
690C2×C7—42no—
691C2×C7—44no—
692C2×C7—82no—
693C2×C7#332314yescomplemented
694C2×C7C2×#54611yescharacteristic
695C2×C7C2×#57511yescharacteristic
696C2×C7C2×#57711yescharacteristic
697D7—42no—
698C23—22no—
699C23—24no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—48no—
705C23—48no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—72no—
712C23—84no—
713C23—816no—
714C23—142no—
715C23—142no—
716C23—142no—
717C23C2×D4×D712yes—
718C23C2×D4×D711yescharacteristic
719Q8—142no—
720Q8—142no—
721Q8—142no—
722Q8—142no—
723Q8—282no—
724Q8—282no—
725D4—24no—
726D4—22no—
727D4—22no—
728D4—22no—
729D4—48no—
730D4—42no—
731D4—284no—
732D4—288no—
733D4—564no—
734D4C2×#115714yes—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—72no—
744C2×C4—72no—
745C2×C4—72no—
746C2×C4—142no—
747C2×C4—142no—
748C2×C4—142no—
749C2×C4—144no—
750C2×C4—142no—
751C2×C4—142no—
752C2×C4—142no—
753C2×C4—142no—
754C2×C4—142no—
755C2×C4—142no—
756C2×C4—288no—
757C2×C4—288no—
758C2×C4—282no—
759C2×C4—282no—
760C2×C4—282no—
761C2×C4—282no—
762C2×C4—564no—
763C2×C4C2×#115712yes—
764C2×C4C2×D4×D712yes—
765C2×C4C2×D4×D711yescharacteristic
766C2×C4#654812yes—
767C2×C4C24×D711yescharacteristic
768C8—22no—
769C8—22no—
770C8—142no—
771C8—142no—
772C7C2×#332311yescharacteristic, complemented, Sylow
773C22—22no—
774C22—22no—
775C22—22no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—48no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—816no—
785C22—84no—
786C22—142no—
787C22—142no—
788C22—142no—
789C22—284no—
790C22#9018112yes—
791C22#9046412yes—
792C22#9046612yes—
793C22C22×D4×D711yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—142no—
798C4—142no—
799C4—142no—
800C4—282no—
801C4—282no—
802C4—282no—
803C4—282no—
804C4#9018112yes—
805C4C22×#115711yescharacteristic
806C4C2×#654811yescharacteristic
807C2—42no—
808C2—44no—
809C2—82no—
810C2—282no—
811C2#1173638414yesdirect product factor
812C2C2×#9018111yescharacteristic
813C2C2×#9046411yescharacteristic
814C2C2×#9046611yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#418C2
socleC23×C7C22×D4
prime radicalC2×#90497C2
hypercenterC2×#418D7
hypocenterC7C2×#3323
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#90220C2semidirect
3. C2×C7×#418C2semidirect
4. C2×#89990C2semidirect
5. C2×#89909C2semidirect
6. C2×#89900C2semidirect
7. C2×#89768C2semidirect
8. #11736384C2direct (N × H)
9. C2×#89539C2semidirect
10. C2×#89549C2semidirect
11. C2×#89552C2semidirect
12. C2×#89555C2semidirect
13. C2×#89543C2semidirect
14. C2×#89540C2semidirect
15. C2×#89535C2semidirect
16. C2×#89530C2semidirect
35. C22×Dic28C22semidirect
36. C22×#1131C22semidirect
38. #90220C22semidirect
39. C2×#6460C22semidirect
40. C2×D7×C4⋊C4C22semidirect
41. C2×#6453C22semidirect
42. C2×#6450C22semidirect
47. C7×#418C22semidirect
52. #89990C22semidirect
56. #89909C22semidirect
57. #89900C22semidirect
58. C2×(C2×D7)⋊C8C22semidirect
59. C2×#6391C22semidirect
60. C2×#6390C22semidirect
61. C2×#6390C22semidirect
62. C2×Dic7⋊C8C22semidirect
63. C2×C8×Dic7C22semidirect
64. #89768C22semidirect
65. C2×#6384C22semidirect
66. C2×#6384C22semidirect
67. C2×#6382C22semidirect
68. C2×#6381C22semidirect
69. #89555C22semidirect
70. #89552C22semidirect
71. #89549C22semidirect
72. #89543C22semidirect
73. #89540C22semidirect
74. #89539C22semidirect
75. #89535C22semidirect
76. #89530C22semidirect
154. C2×Dic28C23semidirect
156. C2×#1131C23semidirect
158. #6460C23semidirect
160. D7×C4⋊C4C23semidirect
162. #6453C23semidirect
164. #6450C23semidirect
176. (C2×D7)⋊C8C23semidirect
177. #6391C23semidirect
178. #6390C23semidirect
179. #6390C23semidirect
180. Dic7⋊C8C23semidirect
181. C8×Dic7C23semidirect
182. #6384C23semidirect
183. #6384C23semidirect
184. #6382C23semidirect
185. #6381C23semidirect
201. C2×#418D7semidirect
353. #418C2×D7semidirect
693. C2×C7#3323semidirect
772. C7C2×#3323semidirect
811. C2#11736384direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#904972
C2×#902202
C2×C7×#4182
C2×#899902
C2×#899092
C2×#899002
C2×#897682
#117363842
C2×#895392
C2×#895492
C2×#895522
C2×#895552
C2×#895432
C2×#895402
C2×#895352
C2×#895302
C2×#33237