Finite Group Databasebeta

← C2×#11741105 #14232417

Subgroups — C2×#11741105 #14232417

Order 1792.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#556C211yesmaximal, characteristic
2C2×#90232C211yesmaximal, characteristic
3#11741105C2116yesmaximal, direct product factor
4C2×#89863C211yesmaximal, characteristic, complemented
5C2×#89852C211yesmaximal, characteristic, complemented
6C2×#89824C211yesmaximal, characteristic, complemented
7C2×#89823C211yesmaximal, characteristic, complemented
8C2×#89816C211yesmaximal, characteristic, complemented
9C2×#89817C211yesmaximal, characteristic, complemented
10C2×#89794C211yesmaximal, characteristic, complemented
11C2×#89802C211yesmaximal, characteristic, complemented
12C2×#89783C211yesmaximal, characteristic
13C2×#89768C211yesmaximal, characteristic, complemented
14C2×#89768C211yesmaximal, characteristic, complemented
15C2×#89767C211yesmaximal, characteristic, complemented
16C2×#89770C211yesmaximal, characteristic, complemented
17C7×#556—24no—
18C7×#556C2218yes—
19C2×C7×C4⋊Q8C2211yescharacteristic
20C2×C7×#126—21no—
21C2×C7×#126—21no—
22C2×C7×#124—21no—
23C2×C7×C22⋊Q8C2211yescharacteristic
24C2×C7×C22⋊Q8C2211yescharacteristic
25C2×C4×C7×Q8—21no—
26C2×C4×C7×Q8C2211yescharacteristic
27C2×C4×C7×D4C2211yescharacteristic
28C2×C7×#117C2211yescharacteristic
29C2×C7×#117C2211yescharacteristic
30C22×#1144C2211yescharacteristic
31C2×#6498—21no—
32C2×#6489C2211yescharacteristic
33C22×C4⋊Dic7C2211yescharacteristic
34C2×#6487C2211yescharacteristic
35C2×#6487C2211yescharacteristic
36C22×#1136C2211yescharacteristic
37C23×C7⋊C8C2211yescharacteristic
38#90232—24no—
39#90232C2218yes—
40C2×#6452—21no—
41C2×#6442—21no—
42C2×#6440—21no—
43C2×#6433C2211yescharacteristic
44C2×C4×Dic14C2211yescharacteristic
45C2×#6409C2211yescharacteristic
46C2×#6409C2211yescharacteristic
47C2×#6409C2211yescharacteristic
48C2×C22⋊(C7⋊C8)C2211yescharacteristic
49C2×C22⋊(C7⋊C8)C2211yescharacteristic
50#89863C2218yescomplemented
51#89852C2218yescomplemented
52#89824C2218yescomplemented
53#89823C2218yescomplemented
54#89817C2218yescomplemented
55#89816C2218yescomplemented
56#89802C2218yescomplemented
57#89794C2218yescomplemented
58#89783C2218yes—
59#89770C2218yescomplemented
60#89768C2218yescomplemented
61#89768C2218yescomplemented
62#89767C2218yescomplemented
63C2×#6384C2211yescharacteristic
64C2×#6384C2211yescharacteristic
65C2×#6384C2211yescharacteristic
66C2×#6382C2211yescharacteristic
67C2×#6382C2211yescharacteristic
68C2×#6382C2211yescharacteristic
69C2×#6382C2211yescharacteristic
70C2×#6381C2211yescharacteristic
71C2×#6381C2211yescharacteristic
72C2×#6381C2211yescharacteristic
73C2×#6381C2211yescharacteristic
74C2×#6381C2211yescharacteristic
75C2×C4⋊(C7⋊C8)C2211yescharacteristic
76C2×#6377C2211yescharacteristic
77C2×#3349—71nomaximal, Sylow
78C22×C7×Q8—21no—
79C22×C7×Q8C2311yescharacteristic
80C22×C7×D4D411yescharacteristic
81C23×C4×C7C2311yescharacteristic
82C23×C4×C7C2311yescharacteristic
83C23×Dic7—21no—
84C22×Dic14C2311yescharacteristic
85C7×C4⋊Q8—22no—
86C7×C4⋊Q8C2314yes—
87C7×#126—28no—
88C7×#126—28no—
89C7×#124—28no—
90C7×C22⋊Q8—22no—
91C7×C22⋊Q8—22no—
92C7×C22⋊Q8C2314yes—
93C7×C22⋊Q8C2314yes—
94C4×C7×Q8—28no—
95C4×C7×Q8—22no—
96C4×C7×Q8C2314yes—
97C4×C7×D4D414yes—
98C4×C7×D4C2314yes—
99C7×#117—22no—
100C7×#117—22no—
101C7×#117C2314yes—
102C7×#117C2314yes—
103C2×C7×C4⋊C4—21no—
104C2×C7×C4⋊C4—21no—
105C2×C7×C4⋊C4—21no—
106C2×C7×C4⋊C4—21no—
107C2×C7×C4⋊C4D411yescharacteristic
108C2×C7×C4⋊C4C2311yescharacteristic
109C2×C7×C4⋊C4C2311yescharacteristic
110C2×C7×C4⋊C4C2311yescharacteristic
111C2×C7×C22⋊C4—21no—
112C2×C7×C22⋊C4—21no—
113C2×C7×C22⋊C4—21no—
114C2×C7×C22⋊C4—21no—
115C2×C7×C22⋊C4D411yescharacteristic
116C2×C7×C22⋊C4D411yescharacteristic
117C2×C42×C7—21no—
118C2×C42×C7—21no—
119C2×C42×C7—21no—
120C2×C42×C7C2311yescharacteristic
121C2×C22⋊Dic7—21no—
122C2×C22⋊Dic7—21no—
123C2×C22⋊Dic7—21no—
124C2×#1144—24no—
125C2×#1144C2314yes—
126#6498—28no—
127#6489—22no—
128#6489C2314yes—
129C2×C4⋊Dic7—21no—
130C2×C4⋊Dic7—22no—
131C2×C4⋊Dic7C2311yescharacteristic
132C2×C4⋊Dic7C2311yescharacteristic
133C2×C4⋊Dic7C2311yescharacteristic
134C2×C4⋊Dic7C2314yes—
135#6487—22no—
136#6487—22no—
137#6487C2314yes—
138#6487C2314yes—
139C2×Dic7⋊C4—21no—
140C2×Dic7⋊C4—21no—
141C2×Dic7⋊C4—21no—
142C2×Dic7⋊C4—21no—
143C2×Dic7⋊C4—21no—
144C2×C4×Dic7—21no—
145C2×C4×Dic7—21no—
146C2×#1136—24no—
147C2×#1136C2314yes—
148C22×C7⋊C8—24no—
149C22×C7⋊C8C2311yescharacteristic
150C22×C7⋊C8C2311yescharacteristic
151C22×C7⋊C8C2311yescharacteristic
152C22×C7⋊C8C2314yes—
153C22×C7⋊C8C2311yescharacteristic
154#6452—28no—
155#6442—28no—
156#6440—28no—
157#6433—22no—
158#6433C2314yes—
159C4×Dic14—22no—
160C4×Dic14C2314yes—
161#6409C2314yes—
162#6409C2314yes—
163#6409C2314yes—
164C22⋊(C7⋊C8)C2314yes—
165C22⋊(C7⋊C8)C2314yes—
166#6384C2314yes—
167#6384C2314yes—
168#6384C2314yes—
169#6382C2314yes—
170#6382C2314yes—
171#6382C2314yes—
172#6382C2314yes—
173#6381C2314yes—
174#6381C2314yes—
175#6381C2314yes—
176#6381C2314yes—
177#6381C2314yes—
178C4⋊(C7⋊C8)C2314yes—
179#6377C2314yes—
180C2×#556D711yescharacteristic
181C2×#552—71no—
182#3349—716no—
183C2×#501—71no—
184C2×#484—71no—
185C2×#485—71no—
186C2×#485—71no—
187C2×#485—71no—
188C2×#479—71no—
189C2×#477—71no—
190C2×#470—71no—
191C2×#467—71no—
192C2×#441—71no—
193C2×#435—71no—
194C2×#428—71no—
195C2×#427—71no—
196C24×C7C2×D411yescharacteristic
197C24×C7C2×D411yescharacteristic
198C2×C7×Q8—21no—
199C2×C7×Q8—24no—
200C2×C7×Q8—22no—
201C2×C7×Q8—22no—
202C2×C7×Q8—44no—
203C2×C7×Q8C2412yes—
204C2×C7×D4—42no—
205C2×C7×D4C2×D414yes—
206C22×C4×C7—22no—
207C22×C4×C7—22no—
208C22×C4×C7—22no—
209C22×C4×C7—22no—
210C22×C4×C7—21no—
211C22×C4×C7—21no—
212C22×C4×C7—21no—
213C22×C4×C7—21no—
214C22×C4×C7C2×D411yescharacteristic
215C22×C4×C7C2×D411yescharacteristic
216C22×C4×C7C2×D411yescharacteristic
217C22×C4×C7C2×D411yescharacteristic
218C22×C4×C7C2×D412yes—
219C22×C4×C7C2×D412yes—
220C22×C4×C7C2412yes—
221C22×C4×C7C2412yes—
222C22×C4×C7C2411yescharacteristic
223C22×Dic7—24no—
224C22×Dic7—21no—
225C22×Dic7—21no—
226C22×Dic7—21no—
227C22×Dic7—21no—
228C22×Dic7—44no—
229C2×Dic14—22no—
230C2×Dic14—22no—
231C2×Dic14—21no—
232C2×Dic14C2412yes—
233C7×C4⋊C4—24no—
234C7×C4⋊C4—24no—
235C7×C4⋊C4—24no—
236C7×C4⋊C4—24no—
237C7×C4⋊C4—21no—
238C7×C4⋊C4—21no—
239C7×C4⋊C4—21no—
240C7×C4⋊C4C2×D414yes—
241C7×C4⋊C4C2412yes—
242C7×C4⋊C4C2412yes—
243C7×C4⋊C4C2412yes—
244C7×C22⋊C4—24no—
245C7×C22⋊C4—24no—
246C7×C22⋊C4—24no—
247C7×C22⋊C4—24no—
248C7×C22⋊C4C2×D414yes—
249C7×C22⋊C4C2×D414yes—
250C42×C7—24no—
251C42×C7—24no—
252C42×C7—24no—
253C42×C7C2×D412yes—
254C42×C7C2412yes—
255C22⋊Dic7—24no—
256C22⋊Dic7—24no—
257C22⋊Dic7—24no—
258#1144—28no—
259C4⋊Dic7—21no—
260C4⋊Dic7—21no—
261C4⋊Dic7—21no—
262C4⋊Dic7—24no—
263C4⋊Dic7C2412yes—
264C4⋊Dic7C2412yes—
265C4⋊Dic7C2412yes—
266Dic7⋊C4—24no—
267Dic7⋊C4—24no—
268Dic7⋊C4—24no—
269Dic7⋊C4—24no—
270Dic7⋊C4—24no—
271C4×Dic7—24no—
272C4×Dic7—24no—
273#1136—28no—
274C2×C7⋊C8—22no—
275C2×C7⋊C8—22no—
276C2×C7⋊C8—22no—
277C2×C7⋊C8—28no—
278C2×C7⋊C8#4114yes—
279C2×C7⋊C8C2412yes—
280C2×C7⋊C8C2412yes—
281C2×C7⋊C8C2412yes—
282C2×C7⋊C8C2412yes—
283C22×Q16—71no—
284C22×M16—71no—
285C23×C8—71no—
286#556—24no—
287#556C2×D718yes—
288#552—78no—
289#552—144no—
290C2×C4⋊Q8C2×D711yescharacteristic
291C2×#126—21no—
292C2×#126—21no—
293C2×#126—141no—
294C2×#125—71no—
295C2×#125—141no—
296C2×#124—21no—
297C2×#123—141no—
298C2×C22⋊Q8—71no—
299C2×C22⋊Q8—71no—
300C2×C22⋊Q8C2×D711yescharacteristic
301C2×C22⋊Q8C2×D711yescharacteristic
302C2×C4×Q8—21no—
303C2×C4×Q8—71no—
304C2×C4×Q8C2×D711yescharacteristic
305C2×C4×D4C2×D711yescharacteristic
306C2×#117—71no—
307C2×#117—141no—
308C2×#117C2×D711yescharacteristic
309C2×#117C2×D711yescharacteristic
310C22×C4⋊C4—71no—
311#501—78no—
312#485—78no—
313#485—78no—
314#485—78no—
315#484—78no—
316#479—78no—
317#477—78no—
318#470—78no—
319#467—78no—
320#441—78no—
321#435—78no—
322#428—78no—
323#427—78no—
324C2×#107—71no—
325C2×#107—71no—
326C2×#107—71no—
327C2×#107—71no—
328C2×#107—71no—
329C2×#106—71no—
330C2×#106—71no—
331C2×#106—71no—
332C2×#106—71no—
333C2×C4⋊C8—71no—
334C2×#103—71no—
335C2×#103—71no—
336C2×#103—71no—
337C2×#103—71no—
338C2×#103—71no—
339C2×#103—71no—
340C2×C22⋊C8—71no—
341C2×C22⋊C8—71no—
342C2×#97—71no—
343C23×C7—22no—
344C23×C7—22no—
345C23×C7—22no—
346C23×C7—22no—
347C23×C7—22no—
348C23×C7—22no—
349C23×C7C22×D412yes—
350C23×C7C22×D412yes—
351C23×C7C22×D411yescharacteristic
352C7×Q8—22no—
353C7×Q8—22no—
354C7×Q8—48no—
355C7×Q8—42no—
356C7×D4—44no—
357C2×C4×C7—22no—
358C2×C4×C7—22no—
359C2×C4×C7—22no—
360C2×C4×C7—22no—
361C2×C4×C7—24no—
362C2×C4×C7—24no—
363C2×C4×C7—22no—
364C2×C4×C7—22no—
365C2×C4×C7—22no—
366C2×C4×C7—22no—
367C2×C4×C7—22no—
368C2×C4×C7—22no—
369C2×C4×C7—22no—
370C2×C4×C7—22no—
371C2×C4×C7—42no—
372C2×C4×C7—42no—
373C2×C4×C7—42no—
374C2×C4×C7—42no—
375C2×C4×C7C22×D412yes—
376C2×C4×C7C22×D412yes—
377C2×C4×C7C22×D412yes—
378C2×C4×C7C22×D412yes—
379C2×C4×C7C22×D411yescharacteristic
380C2×C4×C7C2×#4112yes—
381C2×C4×C72−1+412yes—
382C2×C4×C7C2511yescharacteristic
383C2×Dic7—22no—
384C2×Dic7—22no—
385C2×Dic7—22no—
386C2×Dic7—22no—
387C2×Dic7—48no—
388C2×Dic7—42no—
389C2×Dic7—42no—
390C2×Dic7—42no—
391C2×Dic7—42no—
392Dic14—22no—
393Dic14—22no—
394Dic14—42no—
395C7⋊C8—22no—
396C7⋊C8—22no—
397C7⋊C8—22no—
398C7⋊C8C2×#4114yes—
399C22×Q8—21no—
400C22×Q8—71no—
401C22×Q8C22×D711yescharacteristic
402C22×D4C22⋊D711yescharacteristic
403C23×C4—141no—
404C23×C4C22×D711yescharacteristic
405C23×C4C22×D711yescharacteristic
406C2×Q16—74no—
407C2×Q16—144no—
408C2×M16—74no—
409C2×M16—144no—
410C22×C8—71no—
411C22×C8—71no—
412C22×C8—74no—
413C22×C8—71no—
414C22×C8—71no—
415C22×C8—144no—
416C4⋊Q8—22no—
417C4⋊Q8C22×D714yes—
418#126—28no—
419#126—28no—
420#126—148no—
421#125—74no—
422#125—148no—
423#125—142no—
424#124—28no—
425#123—148no—
426C22⋊Q8—22no—
427C22⋊Q8—22no—
428C22⋊Q8—74no—
429C22⋊Q8—74no—
430C22⋊Q8—142no—
431C22⋊Q8—142no—
432C22⋊Q8C22×D714yes—
433C22⋊Q8C22×D714yes—
434C4×Q8—28no—
435C4×Q8—22no—
436C4×Q8—74no—
437C4×Q8—142no—
438C4×Q8C22×D714yes—
439C4×D4C22⋊D714yes—
440C4×D4C22×D714yes—
441#117—22no—
442#117—22no—
443#117—74no—
444#117—142no—
445#117—148no—
446#117C22×D714yes—
447#117C22×D714yes—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—71no—
453C2×C4⋊C4—71no—
454C2×C4⋊C4—74no—
455C2×C4⋊C4—71no—
456C2×C4⋊C4—141no—
457C2×C4⋊C4—142no—
458C2×C4⋊C4—141no—
459C2×C4⋊C4—141no—
460C2×C4⋊C4—141no—
461C2×C4⋊C4—141no—
462C2×C4⋊C4—141no—
463C2×C4⋊C4C22⋊D711yescharacteristic
464C2×C4⋊C4C22×D711yescharacteristic
465C2×C4⋊C4C22×D711yescharacteristic
466C2×C4⋊C4C22×D711yescharacteristic
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—141no—
472C2×C22⋊C4—141no—
473C2×C22⋊C4—141no—
474C2×C22⋊C4C22⋊D711yescharacteristic
475C2×C22⋊C4C22⋊D711yescharacteristic
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42—141no—
480C2×C42—141no—
481C2×C42C22×D711yescharacteristic
482#107—74no—
483#107—74no—
484#107—74no—
485#107—74no—
486#107—74no—
487#106—74no—
488#106—74no—
489#106—74no—
490#106—74no—
491C4⋊C8—74no—
492#103—74no—
493#103—74no—
494#103—74no—
495#103—74no—
496#103—74no—
497#103—74no—
498C22⋊C8—74no—
499C22⋊C8—74no—
500#97—74no—
501C22×C7—22no—
502C22×C7—22no—
503C22×C7—22no—
504C22×C7—22no—
505C22×C7—22no—
506C22×C7—22no—
507C22×C7—44no—
508C22×C7—44no—
509C22×C7#54712yes—
510C22×C7#57512yes—
511C22×C7#57812yes—
512C22×C7C23×D411yescharacteristic
513C4×C7—22no—
514C4×C7—22no—
515C4×C7—22no—
516C4×C7—22no—
517C4×C7—42no—
518C4×C7—42no—
519C4×C7—42no—
520C4×C7—42no—
521C4×C7#54712yes—
522C4×C7C22×#4111yescharacteristic
523C4×C7C2×2−1+411yescharacteristic
524Dic7—42no—
525Dic7—42no—
526Dic7—42no—
527Dic7—42no—
528C24C2×C22⋊D711yescharacteristic
529C24C2×C22⋊D711yescharacteristic
530C2×Q8—21no—
531C2×Q8—24no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—44no—
535C2×Q8—72no—
536C2×Q8—141no—
537C2×Q8—142no—
538C2×Q8—142no—
539C2×Q8C23×D712yes—
540C2×D4—42no—
541C2×D4C2×C22⋊D714yes—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—144no—
551C22×C4—141no—
552C22×C4—141no—
553C22×C4—141no—
554C22×C4—141no—
555C22×C4—284no—
556C22×C4C2×C22⋊D712yes—
557C22×C4C2×C22⋊D712yes—
558C22×C4C2×C22⋊D711yescharacteristic
559C22×C4C2×C22⋊D711yescharacteristic
560C22×C4C2×C22⋊D711yescharacteristic
561C22×C4C2×C22⋊D711yescharacteristic
562C22×C4C23×D712yes—
563C22×C4C23×D712yes—
564C22×C4C23×D711yescharacteristic
565Q16—148no—
566M16—148no—
567C2×C8—74no—
568C2×C8—72no—
569C2×C8—72no—
570C2×C8—72no—
571C2×C8—72no—
572C2×C8—148no—
573C2×C8—142no—
574C2×C8—142no—
575C2×C8—142no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—72no—
584C4⋊C4—72no—
585C4⋊C4—72no—
586C4⋊C4—144no—
587C4⋊C4—144no—
588C4⋊C4—144no—
589C4⋊C4—144no—
590C4⋊C4—144no—
591C4⋊C4—141no—
592C4⋊C4—141no—
593C4⋊C4—144no—
594C4⋊C4—141no—
595C4⋊C4C2×C22⋊D714yes—
596C4⋊C4C23×D712yes—
597C4⋊C4C23×D712yes—
598C4⋊C4C23×D712yes—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—144no—
604C22⋊C4—144no—
605C22⋊C4—144no—
606C22⋊C4C2×C22⋊D714yes—
607C22⋊C4C2×C22⋊D714yes—
608C42—24no—
609C42—24no—
610C42—24no—
611C42—144no—
612C42—144no—
613C42C2×C22⋊D712yes—
614C42C23×D712yes—
615C2×C7—42no—
616C2×C7—42no—
617C2×C7#334914yescomplemented
618C2×C7C2×#54711yescharacteristic
619C2×C7C2×#57511yescharacteristic
620C2×C7C2×#57811yescharacteristic
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23C22×C22⋊D712yes—
628C23C22×C22⋊D712yes—
629C23C22×C22⋊D711yescharacteristic
630Q8—22no—
631Q8—22no—
632Q8—48no—
633Q8—42no—
634Q8—142no—
635Q8—142no—
636Q8—282no—
637D4—44no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—142no—
657C2×C4—142no—
658C2×C4—142no—
659C2×C4—142no—
660C2×C4—288no—
661C2×C4—282no—
662C2×C4—282no—
663C2×C4—282no—
664C2×C4—282no—
665C2×C4D7×#4112yes—
666C2×C4#655412yes—
667C2×C4C22×C22⋊D712yes—
668C2×C4C22×C22⋊D712yes—
669C2×C4C22×C22⋊D712yes—
670C2×C4C22×C22⋊D712yes—
671C2×C4C22×C22⋊D711yescharacteristic
672C2×C4C24×D711yescharacteristic
673C8—74no—
674C8—142no—
675C8—142no—
676C8—142no—
677C7C2×#334911yescharacteristic, complemented, Sylow
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—44no—
685C22—44no—
686C22#9051312yes—
687C22#9051512yes—
688C22#9052912yes—
689C22C23×C22⋊D711yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—282no—
699C4—282no—
700C4—282no—
701C4—282no—
702C4#9051512yes—
703C4C2×D7×#4111yescharacteristic
704C4C2×#655411yescharacteristic
705C2—42no—
706C2—42no—
707C2#1174110514yesdirect product factor
708C2C2×#9051311yescharacteristic
709C2C2×#9051511yescharacteristic
710C2C2×#9052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D7
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC2×C7×#556C2
socleC23×C7C22×D4
prime radicalC22×C7×D4D4
hypercenterC2×#556D7
hypocenterC7C2×#3349
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
3. #11741105C2direct (N × H)
4. C2×#89863C2semidirect
5. C2×#89852C2semidirect
6. C2×#89824C2semidirect
7. C2×#89823C2semidirect
8. C2×#89816C2semidirect
9. C2×#89817C2semidirect
10. C2×#89794C2semidirect
11. C2×#89802C2semidirect
13. C2×#89768C2semidirect
14. C2×#89768C2semidirect
15. C2×#89767C2semidirect
16. C2×#89770C2semidirect
50. #89863C22semidirect
51. #89852C22semidirect
52. #89824C22semidirect
53. #89823C22semidirect
54. #89817C22semidirect
55. #89816C22semidirect
56. #89802C22semidirect
57. #89794C22semidirect
59. #89770C22semidirect
60. #89768C22semidirect
61. #89768C22semidirect
62. #89767C22semidirect
617. C2×C7#3349semidirect
677. C7C2×#3349semidirect
707. C2#11741105direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5562
C2×#902322
#117411052
C2×#898632
C2×#898522
C2×#898242
C2×#898232
C2×#898162
C2×#898172
C2×#897942
C2×#898022
C2×#897832
C2×#897682
C2×#897672
C2×#897702
C2×#33497