Finite Group Databasebeta

← C2×#11737553 #14230427

Subgroups — C2×#11737553 #14230427

Order 1792.

2190 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#90515C211yesmaximal, characteristic, complemented
2C2×#90309C211yesmaximal, characteristic, complemented
3C2×C7×#449C211yesmaximal, characteristic, complemented
4C2×#90004C211yesmaximal, characteristic, complemented
5C2×#89943C211yesmaximal, characteristic, complemented
6C2×#89934C211yesmaximal, characteristic, complemented
7C2×#89930C211yesmaximal, characteristic, complemented
8C2×#89924C211yesmaximal, characteristic, complemented
9C2×#89814C211yesmaximal, characteristic, complemented
10#11737553C2116yesmaximal, direct product factor
11C2×#89587C211yesmaximal, characteristic, complemented
12C2×#89569C211yesmaximal, characteristic, complemented
13C2×#89544C211yesmaximal, characteristic, complemented
14C2×#89535C211yesmaximal, characteristic, complemented
15C2×#89500C211yesmaximal, characteristic, complemented
16C2×#89493C211yesmaximal, characteristic, complemented
17C22×C7×#41C2211yescharacteristic
18C22×#1159C2211yescharacteristic
19C22×C7×SD16C2211yescharacteristic
20C22×C7×D8C2211yescharacteristic
21C2×C7×#121C2211yescharacteristic
22#90515—24no—
23#90515C2218yescomplemented
24C2×#6509C2211yescharacteristic
25C2×#6507C2211yescharacteristic
26C2×#6502—21no—
27C2×#6502—21no—
28C2×#6501C2211yescharacteristic
29C2×#6498—21no—
30C2×D4×Dic7—21no—
31C2×D4×Dic7C2211yescharacteristic
32C2×D4×Dic7C2211yescharacteristic
33C22×#1142C2211yescharacteristic
34C2×#6492—21no—
35C2×C4×C22⋊D7C2211yescharacteristic
36C22×C4⋊Dic7C2211yescharacteristic
37C2×#6487C2211yescharacteristic
38C22×Dic7⋊C4—21no—
39C22×#1136C2211yescharacteristic
40C22×C8×D7C2211yescharacteristic
41#90309—24no—
42#90309C2218yescomplemented
43C2×#6455C2211yescharacteristic
44C2×#6453C2211yescharacteristic
45C2×#6449—21no—
46C2×#6442—21no—
47C7×#449C2218yescomplemented
48C2×C7×#103C2211yescharacteristic
49C2×C7×#102C2211yescharacteristic
50C2×C7×C22⋊C8C2211yescharacteristic
51#90004C2218yescomplemented
52C2×#6409C2211yescharacteristic
53C2×#6409C2211yescharacteristic
54C2×#6406C2211yescharacteristic
55C2×#6406C2211yescharacteristic
56C2×#6406C2211yescharacteristic
57#89943C2218yescomplemented
58#89934C2218yescomplemented
59#89930C2218yescomplemented
60#89924C2218yescomplemented
61C2×(C2×D7)⋊C8C2211yescharacteristic
62C2×#6391C2211yescharacteristic
63C2×#6391C2211yescharacteristic
64C2×#6390C2211yescharacteristic
65C2×#6390C2211yescharacteristic
66C2×#6389C2211yescharacteristic
67C2×Dic7⋊C8C2211yescharacteristic
68#89814C2218yescomplemented
69C2×#6384C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71#89587C2218yescomplemented
72#89569C2218yescomplemented
73#89544C2218yescomplemented
74#89535C2218yescomplemented
75#89500C2218yescomplemented
76#89493C2218yescomplemented
77C2×#3307—71nomaximal, Sylow
78C2×C7×#41—22no—
79C2×C7×#41—24no—
80C2×C7×#41—42no—
81C2×C7×#41C2314yes—
82C22×C7×Q8C2311yescharacteristic
83C22×C7×D4—21no—
84C22×C7×D4—21no—
85C22×C7×D4C2311yescharacteristic
86C22×C7×D4C2311yescharacteristic
87C23×C4×C7—21no—
88C23×C4×C7C2311yescharacteristic
89C22×C22⋊D7—21no—
90C22×C22⋊D7—21no—
91C22×C22⋊D7D411yescharacteristic
92C23×Dic7—21no—
93C23×Dic7—21no—
94C23×Dic7—21no—
95C23×Dic7—21no—
96C2×#1159—24no—
97C2×#1159—22no—
98C2×#1159—42no—
99C2×#1159C2314yes—
100C22×C4×D7C2311yescharacteristic
101C22×Dic14C2311yescharacteristic
102C2×C7×SD16—42no—
103C2×C7×SD16C2314yes—
104C2×C7×D8—24no—
105C2×C7×D8C2314yes—
106C22×C7×C8C2311yescharacteristic
107C22×C7×C8C2311yescharacteristic
108C7×#121—22no—
109C7×#121C2314yes—
110C2×C7×C4⋊C4C2311yescharacteristic
111C2×C7×C22⋊C4—21no—
112C2×C22⋊Dic7—21no—
113C2×C22⋊Dic7—21no—
114C2×C22⋊Dic7—21no—
115C2×C22⋊Dic7—21no—
116C2×C22⋊Dic7D411yescharacteristic
117#6509—22no—
118#6509C2314yes—
119#6507—22no—
120#6507C2314yes—
121#6502—28no—
122#6502—28no—
123#6501—22no—
124#6501C2314yes—
125#6498—28no—
126D4×Dic7—28no—
127D4×Dic7—22no—
128D4×Dic7—22no—
129D4×Dic7C2314yes—
130D4×Dic7C2314yes—
131C2×#1142—42no—
132C2×#1142C2314yes—
133#6492—28no—
134C4×C22⋊D7D414yes—
135C4×C22⋊D7C2314yes—
136C2×(C2×D7)⋊C4—21no—
137C2×(C2×D7)⋊C4—21no—
138C2×(C2×D7)⋊C4D411yescharacteristic
139C2×C4⋊Dic7—21no—
140C2×C4⋊Dic7—22no—
141C2×C4⋊Dic7—21no—
142C2×C4⋊Dic7C2311yescharacteristic
143C2×C4⋊Dic7C2311yescharacteristic
144C2×C4⋊Dic7C2311yescharacteristic
145C2×C4⋊Dic7C2314yes—
146#6487—22no—
147#6487C2314yes—
148C2×Dic7⋊C4—21no—
149C2×Dic7⋊C4—21no—
150C2×Dic7⋊C4—21no—
151C2×Dic7⋊C4—21no—
152C2×Dic7⋊C4—21no—
153C2×Dic7⋊C4—28no—
154C2×Dic7⋊C4D411yescharacteristic
155C2×C4×Dic7—21no—
156C2×C4×Dic7C2311yescharacteristic
157C2×#1136—42no—
158C2×#1136C2314yes—
159C22×C7⋊C8C2311yescharacteristic
160C22×C7⋊C8C2311yescharacteristic
161C2×C8×D7—42no—
162C2×C8×D7C2314yes—
163#6455—22no—
164#6455C2314yes—
165#6453—22no—
166#6453C2314yes—
167#6449—28no—
168#6442—28no—
169C7×#103C2314yes—
170C7×#102C2314yes—
171C7×C22⋊C8C2314yes—
172#6409C2314yes—
173#6409C2314yes—
174#6406C2314yes—
175#6406C2314yes—
176#6406C2314yes—
177(C2×D7)⋊C8C2314yes—
178#6391C2314yes—
179#6391C2314yes—
180#6390C2314yes—
181#6390C2314yes—
182#6389C2314yes—
183Dic7⋊C8C2314yes—
184#6384C2314yes—
185#6381C2314yes—
186C2×#553—71no—
187C2×#547—71no—
188#3307—716no—
189C2×#491—71no—
190C2×#485—71no—
191C2×#483—71no—
192C2×#478—71no—
193C2×#468—71no—
194C2×#465—71no—
195C2×#461—71no—
196C2×#449—71no—
197C2×#449D711yescharacteristic, complemented
198C2×#442—71no—
199C2×#435—71no—
200C2×#417—71no—
201C2×#416—71no—
202C24×C7—21no—
203C24×C7—21no—
204C24×C7C2×D411yescharacteristic
205C23×D7C2×D411yescharacteristic
206C7×#41—28no—
207C7×#41—44no—
208C7×#41—48no—
209C2×C7×Q8—21no—
210C2×C7×Q8—22no—
211C2×C7×Q8—22no—
212C2×C7×Q8C2412yes—
213C2×C7×D4—24no—
214C2×C7×D4—24no—
215C2×C7×D4—21no—
216C2×C7×D4—21no—
217C2×C7×D4—22no—
218C2×C7×D4—22no—
219C2×C7×D4—22no—
220C2×C7×D4—44no—
221C2×C7×D4—44no—
222C2×C7×D4#4114yes—
223C2×C7×D4C2412yes—
224C2×C7×D4C2412yes—
225C22×C4×C7—22no—
226C22×C4×C7—22no—
227C22×C4×C7—21no—
228C22×C4×C7—21no—
229C22×C4×C7—24no—
230C22×C4×C7—44no—
231C22×C4×C7C2×D411yescharacteristic
232C22×C4×C7C2×D412yes—
233C22×C4×C7C2412yes—
234C22×C4×C7C2411yescharacteristic
235C2×C22⋊D7—24no—
236C2×C22⋊D7—24no—
237C2×C22⋊D7—42no—
238C2×C22⋊D7—44no—
239C2×C22⋊D7—82no—
240C2×C22⋊D7C2×D414yes—
241C22×Dic7—21no—
242C22×Dic7—21no—
243C22×Dic7—21no—
244C22×Dic7—21no—
245C22×Dic7—24no—
246C22×Dic7—24no—
247C22×Dic7—24no—
248C22×Dic7—24no—
249C22×Dic7—44no—
250C22×Dic7—44no—
251C22×Dic7—82no—
252C22×Dic7—82no—
253C22×Dic7C2×D411yescharacteristic
254C22×Dic7C2×D411yescharacteristic
255C22×Dic7C2×D411yescharacteristic
256#1159—28no—
257#1159—44no—
258#1159—48no—
259C2×C4×D7—22no—
260C2×C4×D7—22no—
261C2×C4×D7C2×D412yes—
262C2×C4×D7C2412yes—
263C2×Dic14—22no—
264C2×Dic14—22no—
265C2×Dic14—21no—
266C2×Dic14C2412yes—
267C7×SD16—44no—
268C7×D8—28no—
269C2×C7×C8—22no—
270C2×C7×C8—22no—
271C2×C7×C8C2412yes—
272C2×C7×C8C2412yes—
273C7×C4⋊C4—21no—
274C7×C4⋊C4C2412yes—
275C7×C22⋊C4—24no—
276C22⋊Dic7—24no—
277C22⋊Dic7—24no—
278C22⋊Dic7—24no—
279C22⋊Dic7—24no—
280C22⋊Dic7C2×D414yes—
281#1142—44no—
282(C2×D7)⋊C4—24no—
283(C2×D7)⋊C4—24no—
284(C2×D7)⋊C4C2×D414yes—
285C4⋊Dic7—24no—
286C4⋊Dic7—21no—
287C4⋊Dic7—21no—
288C4⋊Dic7—21no—
289C4⋊Dic7—24no—
290C4⋊Dic7C2412yes—
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—
302#1136—44no—
303C2×C7⋊C8—22no—
304C2×C7⋊C8—22no—
305C2×C7⋊C8C2412yes—
306C2×C7⋊C8C2412yes—
307C8×D7—44no—
308C22×#41—71no—
309C22×#41C2×D711yescharacteristic
310C22×SD16—71no—
311C22×SD16C2×D711yescharacteristic
312C22×D8C2×D711yescharacteristic
313C22×M16—71no—
314C23×C8—71no—
315#553—78no—
316#553—144no—
317#547—78no—
318#547—144no—
319C2×C4⋊Q8—71no—
320C2×#126—141no—
321C2×#125—71no—
322C2×#123—141no—
323C2×#123—141no—
324C2×#123—141no—
325C2×C22⋊Q8—71no—
326C2×C22⋊Q8—71no—
327C2×#121—71no—
328C2×#121—141no—
329C2×#121—141no—
330C2×#121C2×D711yescharacteristic
331C2×C4×D4—71no—
332C2×C4×D4—71no—
333C2×C4×D4—71no—
334C2×C4×D4—141no—
335C2×#117—71no—
336C22×C4⋊C4—71no—
337C22×C4⋊C4—141no—
338#491—78no—
339#485—78no—
340#483—78no—
341#478—78no—
342#468—78no—
343#465—78no—
344#461—78no—
345#449—78no—
346#449C2×D718yescomplemented
347#442—78no—
348#435—78no—
349C2×#107—71no—
350C2×#106—71no—
351C2×#106—71no—
352C2×C4⋊C8—71no—
353#417—78no—
354#416—78no—
355C2×#103—71no—
356C2×#103—71no—
357C2×#103—71no—
358C2×#103—71no—
359C2×#103—71no—
360C2×#103C2×D711yescharacteristic
361C2×#102—71no—
362C2×#102—71no—
363C2×#102—71no—
364C2×#102C2×D711yescharacteristic
365C2×C22⋊C8—71no—
366C2×C22⋊C8C2×D711yescharacteristic
367C2×#97—71no—
368C23×C7—24no—
369C23×C7—22no—
370C23×C7—22no—
371C23×C7—22no—
372C23×C7—22no—
373C23×C7—22no—
374C23×C7—42no—
375C23×C7—42no—
376C23×C7—42no—
377C23×C7—42no—
378C23×C7—42no—
379C23×C7C22×D412yes—
380C23×C7C22×D411yescharacteristic
381C22×D7—22no—
382C22×D7—22no—
383C22×D7—22no—
384C22×D7C22×D412yes—
385C7×Q8—22no—
386C7×Q8—22no—
387C7×Q8—42no—
388C7×D4—24no—
389C7×D4—22no—
390C7×D4—22no—
391C7×D4—22no—
392C7×D4—48no—
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—48no—
403C2×C4×C7—42no—
404C2×C4×C7—42no—
405C2×C4×C7C22×D412yes—
406C2×C4×C7C22×D411yescharacteristic
407C2×C4×C7C2×#4112yes—
408C2×C4×C7H(5,𝔽2)12yes—
409C2×C4×C7C2511yescharacteristic
410C22⋊D7—44no—
411C22⋊D7—48no—
412C22⋊D7—84no—
413C2×Dic7—22no—
414C2×Dic7—22no—
415C2×Dic7—22no—
416C2×Dic7—22no—
417C2×Dic7—22no—
418C2×Dic7—22no—
419C2×Dic7—22no—
420C2×Dic7—48no—
421C2×Dic7—48no—
422C2×Dic7—42no—
423C2×Dic7—42no—
424C2×Dic7—42no—
425C2×Dic7—42no—
426C2×Dic7—84no—
427C2×Dic7—84no—
428C2×Dic7C22×D412yes—
429C2×Dic7C22×D412yes—
430C2×Dic7C22×D412yes—
431C4×D7—24no—
432C4×D7—22no—
433C4×D7—22no—
434Dic14—22no—
435Dic14—22no—
436Dic14—42no—
437C7×C8—22no—
438C7×C8—22no—
439C7⋊C8—22no—
440C7⋊C8—22no—
441C2×#41—22no—
442C2×#41—24no—
443C2×#41—42no—
444C2×#41—74no—
445C2×#41—142no—
446C2×#41—144no—
447C2×#41—282no—
448C2×#41C22×D714yes—
449C22×Q8—71no—
450C22×Q8C22×D711yescharacteristic
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—71no—
454C22×D4—141no—
455C22×D4—141no—
456C22×D4C22×D711yescharacteristic
457C22×D4C22×D711yescharacteristic
458C23×C4—21no—
459C23×C4—71no—
460C23×C4—141no—
461C23×C4—141no—
462C23×C4—141no—
463C23×C4—141no—
464C23×C4C22×D711yescharacteristic
465C2×SD16—42no—
466C2×SD16—74no—
467C2×SD16—282no—
468C2×SD16C22×D714yes—
469C2×D8—24no—
470C2×D8C22×D714yes—
471C2×M16—74no—
472C2×M16—282no—
473C22×C8—71no—
474C22×C8—71no—
475C22×C8—74no—
476C22×C8—282no—
477C22×C8C22×D711yescharacteristic
478C22×C8C22×D711yescharacteristic
479C4⋊Q8—74no—
480C4⋊Q8—142no—
481#126—148no—
482#125—74no—
483#125—142no—
484#123—148no—
485#123—148no—
486#123—148no—
487C22⋊Q8—74no—
488C22⋊Q8—74no—
489C22⋊Q8—142no—
490C22⋊Q8—142no—
491#121—22no—
492#121—74no—
493#121—142no—
494#121—148no—
495#121—148no—
496#121C22×D714yes—
497C4×D4—74no—
498C4×D4—74no—
499C4×D4—74no—
500C4×D4—74no—
501C4×D4—142no—
502C4×D4—142no—
503C4×D4—148no—
504#117—74no—
505#117—142no—
506C2×C4⋊C4—71no—
507C2×C4⋊C4—71no—
508C2×C4⋊C4—71no—
509C2×C4⋊C4—74no—
510C2×C4⋊C4—71no—
511C2×C4⋊C4—148no—
512C2×C4⋊C4—141no—
513C2×C4⋊C4—141no—
514C2×C4⋊C4—141no—
515C2×C4⋊C4—141no—
516C2×C4⋊C4—141no—
517C2×C4⋊C4—141no—
518C2×C4⋊C4—142no—
519C2×C4⋊C4—141no—
520C2×C4⋊C4C22×D711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—71no—
523C2×C22⋊C4—71no—
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—71no—
531C2×C42—141no—
532#107—74no—
533#106—74no—
534#106—74no—
535C4⋊C8—74no—
536#103—74no—
537#103—74no—
538#103—74no—
539#103—74no—
540#103—74no—
541#103C22×D714yes—
542#102—74no—
543#102—74no—
544#102—74no—
545#102C22×D714yes—
546C22⋊C8—74no—
547C22⋊C8C22×D714yes—
548#97—74no—
549C22×C7—24no—
550C22×C7—22no—
551C22×C7—22no—
552C22×C7—22no—
553C22×C7—44no—
554C22×C7—48no—
555C22×C7—42no—
556C22×C7—42no—
557C22×C7—42no—
558C22×C7—42no—
559C22×C7—42no—
560C22×C7—84no—
561C22×C7#54612yes—
562C22×C7#57512yes—
563C22×C7#57712yes—
564C22×C7C23×D411yescharacteristic
565C2×D7—22no—
566C2×D7—22no—
567C2×D7—22no—
568C2×D7—44no—
569C4×C7—22no—
570C4×C7—42no—
571C4×C7—42no—
572C4×C7#54612yes—
573C4×C7C22×#4111yescharacteristic
574C4×C7C2×H(5,𝔽2)11yescharacteristic
575Dic7—22no—
576Dic7—22no—
577Dic7—22no—
578Dic7—42no—
579Dic7—42no—
580Dic7—42no—
581Dic7—42no—
582C24—21no—
583C24—21no—
584C24—71no—
585C24D4×D711yescharacteristic
586#41—28no—
587#41—44no—
588#41—48no—
589#41—148no—
590#41—284no—
591#41—288no—
592C2×Q8—21no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—72no—
596C2×Q8—141no—
597C2×Q8—142no—
598C2×Q8—142no—
599C2×Q8C23×D712yes—
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—44no—
608C2×D4—44no—
609C2×D4—74no—
610C2×D4—144no—
611C2×D4—144no—
612C2×D4—282no—
613C2×D4—284no—
614C2×D4—562no—
615C2×D4#115914yes—
616C2×D4C23×D712yes—
617C2×D4C23×D712yes—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—44no—
624C22×C4—71no—
625C22×C4—71no—
626C22×C4—71no—
627C22×C4—72no—
628C22×C4—72no—
629C22×C4—144no—
630C22×C4—144no—
631C22×C4—144no—
632C22×C4—142no—
633C22×C4—142no—
634C22×C4—141no—
635C22×C4—141no—
636C22×C4—141no—
637C22×C4—141no—
638C22×C4—144no—
639C22×C4—284no—
640C22×C4—284no—
641C22×C4—562no—
642C22×C4—562no—
643C22×C4D4×D712yes—
644C22×C4D4×D711yescharacteristic
645C22×C4C23×D712yes—
646C22×C4C23×D711yescharacteristic
647SD16—44no—
648SD16—284no—
649D8—28no—
650M16—284no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—72no—
654C2×C8—72no—
655C2×C8—142no—
656C2×C8—142no—
657C2×C8—284no—
658C2×C8C23×D712yes—
659C2×C8C23×D712yes—
660C4⋊C4—21no—
661C4⋊C4—74no—
662C4⋊C4—72no—
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—141no—
672C4⋊C4—141no—
673C4⋊C4—144no—
674C4⋊C4—141no—
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—
685C42—72no—
686C42—72no—
687C42—144no—
688C2×C7—42no—
689C2×C7—44no—
690C2×C7—82no—
691C2×C7#330714yescomplemented
692C2×C7C2×#54611yescharacteristic
693C2×C7C2×#57511yescharacteristic
694C2×C7C2×#57711yescharacteristic
695D7—42no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—24no—
700C23—22no—
701C23—22no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—72no—
708C23—142no—
709C23—142no—
710C23—142no—
711C23C2×D4×D712yes—
712C23C2×D4×D711yescharacteristic
713Q8—22no—
714Q8—22no—
715Q8—42no—
716Q8—142no—
717Q8—142no—
718Q8—282no—
719D4—24no—
720D4—22no—
721D4—22no—
722D4—22no—
723D4—48no—
724D4—48no—
725D4—42no—
726D4—284no—
727D4—288no—
728D4—564no—
729D4C2×#115914yes—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—48no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—72no—
740C2×C4—72no—
741C2×C4—72no—
742C2×C4—142no—
743C2×C4—142no—
744C2×C4—142no—
745C2×C4—144no—
746C2×C4—142no—
747C2×C4—142no—
748C2×C4—142no—
749C2×C4—142no—
750C2×C4—142no—
751C2×C4—142no—
752C2×C4—288no—
753C2×C4—288no—
754C2×C4—282no—
755C2×C4—282no—
756C2×C4—282no—
757C2×C4—282no—
758C2×C4—564no—
759C2×C4—564no—
760C2×C4C2×D4×D712yes—
761C2×C4C2×D4×D711yescharacteristic
762C2×C4C2×#115912yes—
763C2×C4#654812yes—
764C2×C4C24×D711yescharacteristic
765C8—22no—
766C8—22no—
767C8—142no—
768C8—142no—
769C7C2×#330711yescharacteristic, complemented, Sylow
770C22—22no—
771C22—22no—
772C22—24no—
773C22—22no—
774C22—42no—
775C22—44no—
776C22—48no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—142no—
783C22—142no—
784C22—142no—
785C22—284no—
786C22#9028212yes—
787C22#9046112yes—
788C22#9046412yes—
789C22C22×D4×D711yescharacteristic
790C4—22no—
791C4—42no—
792C4—42no—
793C4—142no—
794C4—142no—
795C4—142no—
796C4—282no—
797C4—282no—
798C4—282no—
799C4—282no—
800C4#9028212yes—
801C4C22×#115911yescharacteristic
802C4C2×#654811yescharacteristic
803C2—42no—
804C2—44no—
805C2—82no—
806C2—282no—
807C2#1173755314yesdirect product factor
808C2C2×#9028211yescharacteristic
809C2C2×#9046111yescharacteristic
810C2C2×#9046411yescharacteristic
subgroupG/H
centerC23C2×D4×D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#449C2
socleC23×C7C22×D4
hypercenterC2×#449D7
hypocenterC7C2×#3307
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#90515C2semidirect
2. C2×#90309C2semidirect
3. C2×C7×#449C2semidirect
4. C2×#90004C2semidirect
5. C2×#89943C2semidirect
6. C2×#89934C2semidirect
7. C2×#89930C2semidirect
8. C2×#89924C2semidirect
9. C2×#89814C2semidirect
10. #11737553C2direct (N × H)
11. C2×#89587C2semidirect
12. C2×#89569C2semidirect
13. C2×#89544C2semidirect
14. C2×#89535C2semidirect
15. C2×#89500C2semidirect
16. C2×#89493C2semidirect
23. #90515C22semidirect
42. #90309C22semidirect
47. C7×#449C22semidirect
51. #90004C22semidirect
57. #89943C22semidirect
58. #89934C22semidirect
59. #89930C22semidirect
60. #89924C22semidirect
68. #89814C22semidirect
71. #89587C22semidirect
72. #89569C22semidirect
73. #89544C22semidirect
74. #89535C22semidirect
75. #89500C22semidirect
76. #89493C22semidirect
197. C2×#449D7semidirect
346. #449C2×D7semidirect
691. C2×C7#3307semidirect
769. C7C2×#3307semidirect
807. C2#11737553direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#905152
C2×#903092
C2×C7×#4492
C2×#900042
C2×#899432
C2×#899342
C2×#899302
C2×#899242
C2×#898142
#117375532
C2×#895872
C2×#895692
C2×#895442
C2×#895352
C2×#895002
C2×#894932
C2×#33077