Finite Group Databasebeta

← C2×#11740922 #14225985

Subgroups — C2×#11740922 #14225985

Order 1792.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#544C211yesmaximal, characteristic, complemented
2C2×#90226C211yesmaximal, characteristic
3#11740922C2116yesmaximal, direct product factor
4C2×#89856C211yesmaximal, characteristic, complemented
5C2×#89859C211yesmaximal, characteristic, complemented
6C2×#89852C211yesmaximal, characteristic, complemented
7C2×#89860C211yesmaximal, characteristic, complemented
8C2×#89838C211yesmaximal, characteristic, complemented
9C2×#89838C211yesmaximal, characteristic, complemented
10C2×#89836C211yesmaximal, characteristic, complemented
11C2×#89839C211yesmaximal, characteristic, complemented
12C2×#89775C211yesmaximal, characteristic, complemented
13C2×#89775C211yesmaximal, characteristic, complemented
14C2×#89772C211yesmaximal, characteristic, complemented
15C2×#89740C211yesmaximal, characteristic, complemented
16C2×#89739C211yesmaximal, characteristic, complemented
17C7×#544—24no—
18C7×#544C2218yescomplemented
19C2×C7×C4⋊Q8—21no—
20C2×C7×C4⋊Q8C2211yescharacteristic
21C2×C7×C4⋊Q8C2211yescharacteristic
22C2×C7×#125—21no—
23C2×C7×#125C2211yescharacteristic
24C2×C7×#125C2211yescharacteristic
25C2×C7×C22⋊Q8—21no—
26C2×C7×C22⋊Q8—21no—
27C2×C7×#117C2211yescharacteristic
28C2×C7×#117C2211yescharacteristic
29C22×C7×C4⋊C4C2211yescharacteristic
30C2×#6493C2211yescharacteristic
31C2×#6493C2211yescharacteristic
32#90226—24no—
33#90226C2218yes—
34C2×#6457—21no—
35C2×#6457—21no—
36C2×#6447—21no—
37C2×#6447—21no—
38C2×#6437C2211yescharacteristic
39C2×C4×D28C2211yescharacteristic
40C2×C4×D28C2211yescharacteristic
41C2×#6433C2211yescharacteristic
42C2×C22⋊(C7⋊C8)C2211yescharacteristic
43C2×C22⋊(C7⋊C8)C2211yescharacteristic
44#89860C2218yescomplemented
45#89859C2218yescomplemented
46#89856C2218yescomplemented
47#89852C2218yescomplemented
48#89839C2218yescomplemented
49#89838C2218yescomplemented
50#89838C2218yescomplemented
51#89836C2218yescomplemented
52#89775C2218yescomplemented
53#89775C2218yescomplemented
54#89772C2218yescomplemented
55#89740C2218yescomplemented
56#89739C2218yescomplemented
57C2×#6383C2211yescharacteristic
58C2×#6383C2211yescharacteristic
59C2×#6383C2211yescharacteristic
60C2×#6383C2211yescharacteristic
61C2×#6383C2211yescharacteristic
62C2×#6383C2211yescharacteristic
63C2×#6383C2211yescharacteristic
64C2×#6383C2211yescharacteristic
65C2×#6382C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69C2×#6381C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71C2×#6381C2211yescharacteristic
72C2×#6381C2211yescharacteristic
73C2×C4⋊(C7⋊C8)C2211yescharacteristic
74C2×C4⋊(C7⋊C8)C2211yescharacteristic
75C2×#6377C2211yescharacteristic
76C2×C4×C7⋊C8C2211yescharacteristic
77C2×#3241—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8—21no—
80C23×C4×C7—21no—
81C23×C4×C7C2311yescharacteristic
82C22×C22⋊D7—21no—
83C22×C22⋊D7—21no—
84C22×D28—21no—
85C22×D28—21no—
86C22×D28C2311yescharacteristic
87C22×D28C2311yescharacteristic
88C22×C4×D7—21no—
89C22×C4×D7—21no—
90C7×C4⋊Q8—28no—
91C7×C4⋊Q8—22no—
92C7×C4⋊Q8—22no—
93C7×C4⋊Q8C2314yes—
94C7×C4⋊Q8C2314yes—
95C7×#125—28no—
96C7×#125—22no—
97C7×#125—22no—
98C7×#125C2314yes—
99C7×#125C2314yes—
100C7×C22⋊Q8—28no—
101C7×C22⋊Q8—28no—
102C7×#117—22no—
103C7×#117D414yes—
104C7×#117C2314yes—
105C7×#117C2314yes—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4—22no—
108C2×C7×C4⋊C4—21no—
109C2×C7×C4⋊C4—21no—
110C2×C7×C4⋊C4—21no—
111C2×C7×C4⋊C4—21no—
112C2×C7×C4⋊C4—21no—
113C2×C7×C4⋊C4—21no—
114C2×C7×C4⋊C4D411yescharacteristic
115C2×C7×C4⋊C4D411yescharacteristic
116C2×C7×C4⋊C4C2311yescharacteristic
117C2×C7×C4⋊C4C2311yescharacteristic
118C2×C7×C4⋊C4C2311yescharacteristic
119C2×C7×C4⋊C4C2311yescharacteristic
120C2×C7×C4⋊C4C2314yes—
121C2×C7×C22⋊C4—21no—
122C2×C7×C22⋊C4D411yescharacteristic
123C2×C7×C22⋊C4D411yescharacteristic
124C2×C42×C7—21no—
125C2×C42×C7C2311yescharacteristic
126C2×C42×C7C2311yescharacteristic
127#6493—22no—
128#6493—22no—
129#6493C2314yes—
130#6493C2314yes—
131C2×(C2×D7)⋊C4—21no—
132C2×(C2×D7)⋊C4—21no—
133C2×(C2×D7)⋊C4—21no—
134C2×(C2×D7)⋊C4—21no—
135C2×C4⋊Dic7C2311yescharacteristic
136C2×C4⋊Dic7C2311yescharacteristic
137C2×Dic7⋊C4—21no—
138C2×Dic7⋊C4—21no—
139C22×C7⋊C8C2311yescharacteristic
140C22×C7⋊C8C2311yescharacteristic
141C22×C7⋊C8C2311yescharacteristic
142C22×C7⋊C8C2311yescharacteristic
143#6457—28no—
144#6457—28no—
145#6447—28no—
146#6447—28no—
147#6437—22no—
148#6437C2314yes—
149C4×D28—22no—
150C4×D28—22no—
151C4×D28C2314yes—
152C4×D28C2314yes—
153#6433—22no—
154#6433C2314yes—
155C22⋊(C7⋊C8)C2314yes—
156C22⋊(C7⋊C8)C2314yes—
157#6383C2314yes—
158#6383C2314yes—
159#6383C2314yes—
160#6383C2314yes—
161#6383C2314yes—
162#6383C2314yes—
163#6383C2314yes—
164#6383C2314yes—
165#6382C2314yes—
166#6382C2314yes—
167#6382C2314yes—
168#6382C2314yes—
169#6381C2314yes—
170#6381C2314yes—
171#6381C2314yes—
172#6381C2314yes—
173C4⋊(C7⋊C8)C2314yes—
174C4⋊(C7⋊C8)C2314yes—
175#6377C2314yes—
176C4×C7⋊C8C2314yes—
177C2×#544D711yescharacteristic, complemented
178C2×#540—71no—
179#3241—716no—
180C2×#501—71no—
181C2×#499—71no—
182C2×#490—71no—
183C2×#486—71no—
184C2×#481—71no—
185C2×#482—71no—
186C2×#482—71no—
187C2×#480—71no—
188C2×#478—71no—
189C2×#478—71no—
190C2×#476—71no—
191C2×#474—71no—
192C2×#433—71no—
193C24×C7C2×D411yescharacteristic
194C23×D7—21no—
195C23×D7—21no—
196C2×C7×Q8—24no—
197C2×C7×Q8—24no—
198C2×C7×Q8—82no—
199C2×C7×Q8—82no—
200C22×C4×C7—22no—
201C22×C4×C7—22no—
202C22×C4×C7—21no—
203C22×C4×C7—21no—
204C22×C4×C7—21no—
205C22×C4×C7—21no—
206C22×C4×C7—24no—
207C22×C4×C7—82no—
208C22×C4×C7C2×D411yescharacteristic
209C22×C4×C7C2×D411yescharacteristic
210C22×C4×C7C2×D411yescharacteristic
211C22×C4×C7C2×D411yescharacteristic
212C22×C4×C7C2×D411yescharacteristic
213C22×C4×C7C2×D412yes—
214C22×C4×C7C2412yes—
215C22×C4×C7C2411yescharacteristic
216C2×C22⋊D7—24no—
217C2×C22⋊D7—24no—
218C2×C22⋊D7—82no—
219C2×C22⋊D7—82no—
220C22×Dic7—21no—
221C22×Dic7—21no—
222C2×D28—22no—
223C2×D28—22no—
224C2×D28—22no—
225C2×D28—22no—
226C2×D28—21no—
227C2×D28—21no—
228C2×D28—24no—
229C2×D28—24no—
230C2×D28—82no—
231C2×D28—82no—
232C2×D28C2412yes—
233C2×D28C2412yes—
234C2×C4×D7—24no—
235C2×C4×D7—24no—
236C2×C4×D7—82no—
237C2×C4×D7—82no—
238C7×C4⋊C4—24no—
239C7×C4⋊C4—21no—
240C7×C4⋊C4—21no—
241C7×C4⋊C4—24no—
242C7×C4⋊C4—24no—
243C7×C4⋊C4—24no—
244C7×C4⋊C4—24no—
245C7×C4⋊C4—24no—
246C7×C4⋊C4—24no—
247C7×C4⋊C4—21no—
248C7×C4⋊C4—21no—
249C7×C4⋊C4C2×D414yes—
250C7×C4⋊C4C2×D414yes—
251C7×C4⋊C4C2412yes—
252C7×C4⋊C4C2412yes—
253C7×C4⋊C4C2412yes—
254C7×C4⋊C4C2412yes—
255C7×C22⋊C4—24no—
256C7×C22⋊C4C2×D414yes—
257C7×C22⋊C4C2×D414yes—
258C42×C7—24no—
259C42×C7C2×D412yes—
260C42×C7C2×D412yes—
261C42×C7C2412yes—
262C42×C7C2412yes—
263(C2×D7)⋊C4—24no—
264(C2×D7)⋊C4—24no—
265(C2×D7)⋊C4—24no—
266(C2×D7)⋊C4—24no—
267C4⋊Dic7—21no—
268C4⋊Dic7—21no—
269C4⋊Dic7C2412yes—
270C4⋊Dic7C2412yes—
271Dic7⋊C4—24no—
272Dic7⋊C4—24no—
273C2×C7⋊C8—22no—
274C2×C7⋊C8—22no—
275C2×C7⋊C8—22no—
276C2×C7⋊C8—22no—
277C2×C7⋊C8C2412yes—
278C2×C7⋊C8C2412yes—
279C2×C7⋊C8C2412yes—
280C2×C7⋊C8C2412yes—
281#544—24no—
282#544C2×D718yescomplemented
283#540—78no—
284#540—144no—
285C2×C4⋊Q8—21no—
286C2×C4⋊Q8C2×D711yescharacteristic
287C2×C4⋊Q8C2×D711yescharacteristic
288C2×#127—71no—
289C2×#125—21no—
290C2×#125—71no—
291C2×#125C2×D711yescharacteristic
292C2×#125C2×D711yescharacteristic
293C2×#123—141no—
294C2×#123—141no—
295C2×C22⋊Q8—21no—
296C2×C22⋊Q8—21no—
297C2×#121—71no—
298C2×#121—71no—
299C2×#121—141no—
300C2×#121—141no—
301C2×C4×D4—71no—
302C2×C4×D4—71no—
303C2×#117C2×D711yescharacteristic
304C2×#117C2×D711yescharacteristic
305C22×C4⋊C4C2×D711yescharacteristic
306#501—78no—
307#499—78no—
308#490—78no—
309#486—78no—
310#482—78no—
311#482—78no—
312#481—78no—
313#480—78no—
314#478—78no—
315#478—78no—
316#476—78no—
317#474—78no—
318#433—78no—
319C2×#107—71no—
320C2×#107—71no—
321C2×#107—71no—
322C2×#107—71no—
323C2×#106—71no—
324C2×#106—71no—
325C2×#106—71no—
326C2×#106—71no—
327C2×C4⋊C8—71no—
328C2×C4⋊C8—71no—
329C2×#102—71no—
330C2×#102—71no—
331C2×#102—71no—
332C2×#102—71no—
333C2×#102—71no—
334C2×#102—71no—
335C2×#102—71no—
336C2×#102—71no—
337C2×C22⋊C8—71no—
338C2×C22⋊C8—71no—
339C2×#97—71no—
340C2×C4×C8—71no—
341C23×C7—22no—
342C23×C7—22no—
343C23×C7—22no—
344C23×C7C22×D412yes—
345C23×C7C22×D411yescharacteristic
346C22×D7—22no—
347C22×D7—22no—
348C22×D7—42no—
349C22×D7—42no—
350C22×D7—42no—
351C22×D7—42no—
352C22×D7—42no—
353C22×D7—42no—
354C7×Q8—84no—
355C7×Q8—84no—
356C2×C4×C7—22no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—24no—
362C2×C4×C7—22no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—42no—
369C2×C4×C7—42no—
370C2×C4×C7—42no—
371C2×C4×C7—42no—
372C2×C4×C7—84no—
373C2×C4×C7C22×D412yes—
374C2×C4×C7C22×D412yes—
375C2×C4×C7C22×D412yes—
376C2×C4×C7C22×D412yes—
377C2×C4×C7C22×D412yes—
378C2×C4×C7C22×D411yescharacteristic
379C2×C4×C72−1+412yes—
380C2×C4×C72−1+412yes—
381C2×C4×C7C2511yescharacteristic
382C22⋊D7—84no—
383C22⋊D7—84no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—42no—
387C2×Dic7—42no—
388D28—22no—
389D28—22no—
390D28—22no—
391D28—22no—
392D28—42no—
393D28—42no—
394D28—84no—
395D28—84no—
396C4×D7—84no—
397C4×D7—84no—
398C7⋊C8—22no—
399C7⋊C8—22no—
400C7⋊C8—22no—
401C7⋊C8—22no—
402C22×Q8—21no—
403C22×Q8—21no—
404C22×D4—71no—
405C22×D4—71no—
406C22×D4—141no—
407C22×D4—141no—
408C22×D4—141no—
409C22×D4—141no—
410C23×C4—21no—
411C23×C4—141no—
412C23×C4—141no—
413C23×C4C22×D711yescharacteristic
414C22×C8—71no—
415C22×C8—71no—
416C22×C8—71no—
417C22×C8—71no—
418C4⋊Q8—28no—
419C4⋊Q8—22no—
420C4⋊Q8—22no—
421C4⋊Q8C22×D714yes—
422C4⋊Q8C22×D714yes—
423#127—74no—
424#127—142no—
425#125—28no—
426#125—22no—
427#125—22no—
428#125—74no—
429#125—142no—
430#125C22×D714yes—
431#125C22×D714yes—
432#123—148no—
433#123—148no—
434C22⋊Q8—28no—
435C22⋊Q8—28no—
436#121—74no—
437#121—74no—
438#121—142no—
439#121—142no—
440#121—148no—
441#121—148no—
442C4×D4—74no—
443C4×D4—74no—
444C4×D4—142no—
445C4×D4—142no—
446#117—22no—
447#117C22⋊D714yes—
448#117C22×D714yes—
449#117C22×D714yes—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—71no—
459C2×C4⋊C4—71no—
460C2×C4⋊C4—141no—
461C2×C4⋊C4—141no—
462C2×C4⋊C4C22⋊D711yescharacteristic
463C2×C4⋊C4C22⋊D711yescharacteristic
464C2×C4⋊C4C22×D711yescharacteristic
465C2×C4⋊C4C22×D711yescharacteristic
466C2×C4⋊C4C22×D714yes—
467C2×C4⋊C4C22×D711yescharacteristic
468C2×C4⋊C4C22×D711yescharacteristic
469C2×C22⋊C4—21no—
470C2×C22⋊C4—141no—
471C2×C22⋊C4—141no—
472C2×C22⋊C4—141no—
473C2×C22⋊C4—141no—
474C2×C22⋊C4C22⋊D711yescharacteristic
475C2×C22⋊C4C22⋊D711yescharacteristic
476C2×C42—21no—
477C2×C42C22×D711yescharacteristic
478C2×C42C22×D711yescharacteristic
479#107—74no—
480#107—74no—
481#107—74no—
482#107—74no—
483#106—74no—
484#106—74no—
485#106—74no—
486#106—74no—
487C4⋊C8—74no—
488C4⋊C8—74no—
489#102—74no—
490#102—74no—
491#102—74no—
492#102—74no—
493#102—74no—
494#102—74no—
495#102—74no—
496#102—74no—
497C22⋊C8—74no—
498C22⋊C8—74no—
499#97—74no—
500C4×C8—74no—
501C22×C7—22no—
502C22×C7—22no—
503C22×C7—22no—
504C22×C7—44no—
505C22×C7#53612yes—
506C22×C7#57612yes—
507C22×C7#57712yes—
508C22×C7C23×D411yescharacteristic
509C2×D7—42no—
510C2×D7—42no—
511C2×D7—42no—
512C2×D7—42no—
513C2×D7—42no—
514C2×D7—42no—
515C2×D7—84no—
516C2×D7—84no—
517C4×C7—22no—
518C4×C7—22no—
519C4×C7—22no—
520C4×C7—22no—
521C4×C7—22no—
522C4×C7—42no—
523C4×C7—42no—
524C4×C7—42no—
525C4×C7—42no—
526C4×C7#53612yes—
527C4×C7C2×2−1+411yescharacteristic
528C4×C7C2×2−1+411yescharacteristic
529Dic7—42no—
530Dic7—42no—
531C24—141no—
532C24—141no—
533C24C2×C22⋊D711yescharacteristic
534C2×Q8—24no—
535C2×Q8—24no—
536C2×Q8—82no—
537C2×Q8—82no—
538C2×D4—72no—
539C2×D4—72no—
540C2×D4—144no—
541C2×D4—144no—
542C2×D4—142no—
543C2×D4—142no—
544C2×D4—142no—
545C2×D4—142no—
546C2×D4—141no—
547C2×D4—141no—
548C2×D4—144no—
549C2×D4—144no—
550C2×D4—562no—
551C2×D4—562no—
552C2×D4—562no—
553C2×D4—562no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—82no—
562C22×C4—141no—
563C22×C4—141no—
564C22×C4—144no—
565C22×C4—144no—
566C22×C4—562no—
567C22×C4—562no—
568C22×C4C2×C22⋊D712yes—
569C22×C4C2×C22⋊D711yescharacteristic
570C22×C4C2×C22⋊D711yescharacteristic
571C22×C4C2×C22⋊D711yescharacteristic
572C22×C4C2×C22⋊D711yescharacteristic
573C22×C4C2×C22⋊D711yescharacteristic
574C22×C4C23×D712yes—
575C22×C4C23×D711yescharacteristic
576C2×C8—72no—
577C2×C8—72no—
578C2×C8—72no—
579C2×C8—72no—
580C2×C8—142no—
581C2×C8—142no—
582C2×C8—142no—
583C2×C8—142no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—72no—
596C4⋊C4—72no—
597C4⋊C4—144no—
598C4⋊C4—144no—
599C4⋊C4—141no—
600C4⋊C4—141no—
601C4⋊C4C2×C22⋊D714yes—
602C4⋊C4C2×C22⋊D714yes—
603C4⋊C4C23×D712yes—
604C4⋊C4C23×D712yes—
605C4⋊C4C23×D712yes—
606C4⋊C4C23×D712yes—
607C22⋊C4—24no—
608C22⋊C4—144no—
609C22⋊C4—144no—
610C22⋊C4—144no—
611C22⋊C4—144no—
612C22⋊C4C2×C22⋊D714yes—
613C22⋊C4C2×C22⋊D714yes—
614C42—24no—
615C42C2×C22⋊D712yes—
616C42C2×C22⋊D712yes—
617C42C23×D712yes—
618C42C23×D712yes—
619C2×C7—42no—
620C2×C7#324114yescomplemented
621C2×C7C2×#53611yescharacteristic
622C2×C7C2×#57611yescharacteristic
623C2×C7C2×#57711yescharacteristic
624D7—82no—
625D7—82no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—142no—
630C23—142no—
631C23—282no—
632C23—282no—
633C23—282no—
634C23—282no—
635C23—282no—
636C23—282no—
637C23C22×C22⋊D712yes—
638C23C22×C22⋊D711yescharacteristic
639Q8—84no—
640Q8—84no—
641D4—142no—
642D4—142no—
643D4—142no—
644D4—142no—
645D4—282no—
646D4—282no—
647D4—564no—
648D4—564no—
649D4—564no—
650D4—564no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—84no—
668C2×C4—142no—
669C2×C4—142no—
670C2×C4—282no—
671C2×C4—282no—
672C2×C4—564no—
673C2×C4—564no—
674C2×C4#655112yes—
675C2×C4#655112yes—
676C2×C4C22×C22⋊D712yes—
677C2×C4C22×C22⋊D712yes—
678C2×C4C22×C22⋊D712yes—
679C2×C4C22×C22⋊D712yes—
680C2×C4C22×C22⋊D712yes—
681C2×C4C22×C22⋊D711yescharacteristic
682C2×C4C24×D711yescharacteristic
683C8—142no—
684C8—142no—
685C8—142no—
686C8—142no—
687C7C2×#324111yescharacteristic, complemented, Sylow
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—282no—
693C22—282no—
694C22—282no—
695C22—282no—
696C22—282no—
697C22—282no—
698C22—564no—
699C22—564no—
700C22#9050712yes—
701C22#9052612yes—
702C22#9052812yes—
703C22C23×C22⋊D711yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—42no—
713C4—282no—
714C4—282no—
715C4#9050712yes—
716C4C2×#655111yescharacteristic
717C4C2×#655111yescharacteristic
718C2—42no—
719C2—562no—
720C2—562no—
721C2#1174092214yesdirect product factor
722C2C2×#9050711yescharacteristic
723C2C2×#9052611yescharacteristic
724C2C2×#9052811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#544C2
socleC23×C7C22×D4
prime radicalC2×#90226C2
hypercenterC2×#544D7
hypocenterC7C2×#3241
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. C2×C7×#544C2semidirect
3. #11740922C2direct (N × H)
4. C2×#89856C2semidirect
5. C2×#89859C2semidirect
6. C2×#89852C2semidirect
7. C2×#89860C2semidirect
8. C2×#89838C2semidirect
9. C2×#89838C2semidirect
10. C2×#89836C2semidirect
11. C2×#89839C2semidirect
12. C2×#89775C2semidirect
13. C2×#89775C2semidirect
14. C2×#89772C2semidirect
15. C2×#89740C2semidirect
16. C2×#89739C2semidirect
18. C7×#544C22semidirect
44. #89860C22semidirect
45. #89859C22semidirect
46. #89856C22semidirect
47. #89852C22semidirect
48. #89839C22semidirect
49. #89838C22semidirect
50. #89838C22semidirect
51. #89836C22semidirect
52. #89775C22semidirect
53. #89775C22semidirect
54. #89772C22semidirect
55. #89740C22semidirect
56. #89739C22semidirect
177. C2×#544D7semidirect
282. #544C2×D7semidirect
620. C2×C7#3241semidirect
687. C7C2×#3241semidirect
721. C2#11740922direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5442
C2×#902262
#117409222
C2×#898562
C2×#898592
C2×#898522
C2×#898602
C2×#898382
C2×#898362
C2×#898392
C2×#897752
C2×#897722
C2×#897402
C2×#897392
C2×#32417